WO2018093906A1

WO2018093906A1 - Verifying structural integrity of materials using multiple current injection points and one or more current extraction points

Info

Publication number: WO2018093906A1
Application number: PCT/US2017/061809
Authority: WO
Inventors: Christopher R. Yungers; David H. Redinger; Jennifer F. Schumacher
Original assignee: 3M Innovative Properties Co
Current assignee: 3M Innovative Properties Co
Priority date: 2016-11-16
Filing date: 2017-11-15
Publication date: 2018-05-24
Anticipated expiration: 2019-05-16

Abstract

A system may include a computing device and an electrical signal source. The computing device may cause the electrical signal source to apply an electrical signal to a plurality of current injection electrodes electrically coupled to a material. The electrical signal may be extracted from the material through at least one current extraction electrode. The plurality of current injection electrodes may be arranged symmetrically with reference to a symmetry of the material. While the electrical signal is being applied to the material, the computing device may measure a first voltage using a first measurement electrode and a second voltage using a second measurement electrode. The first measurement electrode and the second measurement electrode may be positioned symmetrically with reference to the symmetry of the material. By comparing the first measured voltage and the second measured voltage, the computing device may determine whether the material includes a crack or other defect.

Description

VERIFYING STRUCTURAL INTEGRITY OF MATERIALS USING MULTIPLE CURRENT INJECTION POINTS AND ONE OR MORE CURRENT EXTRACTION POINTS

This application is related to U.S. Provisional Application number 62/423, 137 filed November 16, 2016, and U.S. Provisional Application number 62/502,054 filed on May 5, 2017, which are incorporated herein by reference in their entirety. TECHNICAL FIELD

The disclosure relates to techniques for verifying structural integrity of conductive or semiconductive materials.

BACKGROUND

Many materials are useful when their mechanical properties remain intact, but less useful when damaged, such as when cracked. Thus, detection whether these materials are damaged is important. As one example, ceramic body plating is used to protect soldiers, police officers, and other security personnel from projectiles. Ceramic body plating may be useful when undamaged, but may be replaced after being damaged, e.g., after cracking.

X-ray scanning, including X-ray radiography and X-ray computed tomography (CT scanning) may be used to detect cracks or other defects in materials. However, such techniques may utilize large and heavy scanners, which may not be easily portable. Further, X-ray scanning and X-ray CT scanning may be relatively expensive, relatively slow, or both. SUMMARY

In some examples, the disclosure describes a method for detecting a crack or defect in a material. The method may include applying an electrical signal to a plurality of current injection electrodes electrically coupled to the material. The plurality of current injection electrodes may be positioned substantially symmetrically with reference to a symmetry of the material. The method also may include extracting the electrical signal through a single current extraction electrode. The current extraction electrode may be positioned on the symmetry of the material. The method may further include, while applying the electrical signal to the plurality of current injection electrodes, determining a voltage difference between a first voltage measured using a first measurement electrode and a second voltage measured using a second measurement electrode. The first and second measurement electrodes are positioned substantially symmetrically with reference to the symmetry of the material. The method additionally may include determining whether the material includes a crack or other defect based on the voltage difference.

In some examples, the disclosure describes a method for detecting a crack or defect in a material. The method may include applying a first electrical signal to a plurality of current injection electrodes electrically coupled to the material. The plurality of current injection electrodes may be positioned substantially symmetrically with reference to a symmetry of the material. The method also may include extracting the first electrical signal through a first current extraction electrode. The first current extraction electrode is positioned at a first location of the material. The method further may include, while applying the first electrical signal to the plurality of current injection electrodes, determining a first voltage difference between a first voltage measured using a first measurement electrode and a second voltage measured using a second measurement electrode. The first and second measurement electrodes may be positioned substantially symmetrically with reference to the symmetry of the material. The method additionally may include applying a second electrical signal to the plurality of current injection electrodes and extracting the second electrical signal through a second current extraction electrode. The second current extraction electrode may be positioned at a second location of the material, and the first and second locations may be substantially symmetric with reference to the symmetry of the material. The method also may include, while applying the second electrical signal to the plurality of current injection electrodes, determining a second voltage difference between a third voltage measured using the first measurement electrode and a fourth voltage measured using the second measurement electrode, and determining whether the material includes a crack or other defect based on the first voltage difference and the second voltage difference.

In some examples, the disclosure describes a system including a set of N electrodes electrically coupled to a material; an electrical signal source; and a computing device. The computing device may be configured to cause the electrical signal source to apply an electrical signal to a plurality of current injection electrodes. The plurality of current injection electrodes are positioned substantially

symmetrically with reference to a symmetry of the material and are from the set of N electrodes. The computing device also may be configured to cause the electrical signal to be extracted through a single current extraction electrode. The single current extraction electrode may be positioned on the symmetry of the material and is from the set of N electrodes. The computing device further may be configured to, while the electrical signal source is applying the electrical signal to the plurality of current injection electrodes, determine a voltage difference between a first voltage measured using a first measurement electrode and a second voltage measured using a second measurement electrode. The first and second measurement electrodes may be positioned substantially symmetrically with reference to the symmetry of the material. The computing device additionally may be configured to determine whether the material includes a crack or other defect based on the voltage difference.

In some examples, the disclosure describes a system including a set of N electrodes electrically coupled to a material; an electrical signal source; and a computing device. The computing device may be configured to cause the electrical signal source to apply a first electrical signal to a plurality of current injection electrodes electrically coupled to the material. The plurality of current injection electrodes may be positioned substantially symmetrically with reference to a symmetry of the material and are from the set of N electrodes. The computing device also may be configured to cause the first electrical signal to be extracted through a first current extraction electrode. The current extraction electrode may be positioned at a first location of the material and is from the set of N electrodes. The computing device further may be configured to, while the electrical signal source is applying the first electrical signal to the plurality of current injection electrodes, determine a first voltage difference between a first voltage measured using a first measurement electrode and a second voltage measured using a second measurement electrode. The first and second measurement electrodes may be positioned substantially symmetrically with reference to the symmetry of the material. The computing device additionally may be configured to cause the electrical signal source to apply a second electrical signal to the plurality of current injection electrodes electrically coupled to the material and cause the second electrical signal to be extracted through a second current extraction electrode. The second current extraction electrode may be positioned at a second location of the material and is from the set of N electrodes, and the first and second locations may be substantially symmetric with reference to the symmetry of the material. The computing device also may be configured to, while the electrical signal source is applying the second electrical signal to the plurality of current injection electrodes, determine a second voltage difference between a third voltage measured using the first measurement electrode and a fourth voltage measured using the second measurement electrode. The computing device additionally may be configured to determine whether the material includes a crack or other defect based on the first voltage difference and the second voltage difference.

The details of one or more examples are set forth in the accompanying drawings and the description below. Other features, objects, and advantages will be apparent from the description and drawings, and from the claims.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a conceptual block diagram illustrating an example system for determining whether a material includes a crack or other defect using a plurality of current injection electrodes and at least one current extraction electrode.

FIG. 2 is a flow diagram illustrating an example technique for determining whether a material includes a crack or other defect using a plurality of current injection electrodes and a single current extraction electrode.

FIG. 3 is a conceptual block diagram illustrating an example system for determining whether a material includes a crack or other defect using a plurality of current injection electrodes and a single current extraction electrode in a configuration including at least two current injection electrodes, a single current extraction electrode, and two measurement electrodes.

FIG. 4 is an equivalent circuit diagram of the system configuration shown in FIG. 3 in the absence of a crack or other defect.

FIG. 5 is a flow diagram illustrating an example technique for determining whether a material includes a crack or other defect using a plurality of current injection electrodes and at least two current extraction electrodes.

FIG. 6 is a conceptual block diagram illustrating an example system for determining whether a material includes a crack or other defect using a plurality of current injection electrodes and at least two current extraction electrodes in a first configuration including a plurality of current injection electrodes, a first current extraction electrodes, and two measurement electrodes.

FIG. 7 is an equivalent circuit diagram of the system configuration shown in FIG. 6 in the absence of a crack or other defect.

FIG. 8 is a conceptual block diagram illustrating an example system for determining whether a material includes a crack or other defect using a plurality of current injection electrodes and at least two current extraction electrodes in a second configuration including a plurality of current injection electrodes, a second current extraction electrode, and two measurement electrodes.

FIG. 9 is an equivalent circuit diagram of the system configuration shown in FIG. 10 in the absence of a crack or other defect.

FIG. 10 is an equivalent circuit diagram of a system configuration in which measurement voltages are measured with respect to a voltage reference derived from the electrical signal applied to the current injection electrodes, in the absence of a crack or other defect.

FIGS. 11-14 are circuit diagrams of example system configurations including various locations of current sources for determining whether a material includes a crack or other defect using at least one current injection electrode and a plurality of current extraction electrodes.

DETAILED DESCRIPTION

The disclosure describes systems and techniques for verifying structural integrity of a material. In some examples, a system may include a computing device and an electrical signal source. The techniques may include applying an electrical signal from the electrical signal source to a plurality of current injection electrodes electrically coupled to a material and extracting the electrical signal through at least one current extraction electrode. The material may include a symmetry. A symmetry is a point, a line, a plane, a curve, or a manifold, for which a single mathematical operation made with reference to the symmetry maps each respective volume of the material to another respective volume of the material. The plurality of current injection electrodes may be arranged symmetrically with reference to the symmetry of the material. While the electrical signal is being applied to the material, the computing device may measure a first voltage using a first measurement electrode and a second voltage using a second measurement electrode. In some examples, the first measurement electrode and the second measurement electrode may be positioned symmetrically with reference to the symmetry of the material. By comparing the first measured voltage and the second measured voltage, the computing device may determine whether the material includes a crack or other defect.

In some examples, the current extraction electrode may include a single current extraction electrode, which may be positioned on the symmetry of the material, e.g., near an opposite side or end of the material as the plurality of current injection electrodes. As the current extraction electrode is positioned on the symmetry of the material and the plurality of current injection electrodes are positioned symmetrically with reference to the symmetry of the material, the respective currents flowing from each respective current injection electrode to the single current extraction electrode may be substantially the same (e.g., the same or nearly the same) in the absence or a crack or defect in the material. However, if material includes a crack or other defect, the respective currents flowing from the respective current injection electrodes to the single current extraction electrode may not be substantially the same, as the crack or other defect affects the resistance of the material to current flowing across the crack or other defect. Hence, if the first measured voltage and the second measured voltage are different, the computing device may determine that the material includes a crack or other defect.

In some examples, rather than using a single current extraction electrode, at least two current extraction electrodes may be used, one current extraction electrode for each set of voltage measurements. A first current extraction electrode may be positioned at a first position of the material, and a second current extraction electrode may be positioned at a second position of the material. The first and second positions may be symmetric with reference to the symmetry of the material. In a first measurement set, the electrical signal source may apply a first electrical signal to the plurality of current injection electrodes, and the first electrical signal may be extracted through the first current extraction electrode. The computing device may measure a first measured voltage using the first measurement electrode and a second measured voltage using the second measurement electrode. The computing device may determine a first voltage difference between the first measured voltage and the second measured voltage.

In a second measurement set, the electrical signal source may apply a second electrical signal to the plurality of current injection electrodes, and the second electrical signal may be extracted through the second current extraction electrode. The computing device may measure a third measured voltage using the first measurement electrode and a fourth measured voltage using the second measurement electrode. The computing device may determine a second voltage difference between the third measured voltage and the fourth measured voltage. As the first and second current extraction electrodes are positioned symmetrically with reference to the symmetry of the material and the plurality of current injection electrodes are positioned symmetrically with reference to the symmetry of the material, the first voltage difference and the second voltage difference are substantially the same (e.g., the same or nearly the same) in magnitude in the absence of a crack or other defect. However, if the material includes a crack or other defect, the respective currents flowing from the respective current injection electrode to the respective current extraction electrodes may not be substantially the same, as the crack or other defect affects the resistance of the material to current flowing across the crack or other defect. This may result in the first voltage difference and the second voltage difference being different in magnitude. Hence, if the first voltage difference and the second voltage difference are different in magnitude, the computing device may determine that the material includes a crack or other defect.

In some examples, regardless of whether a single current extraction electrode or at least two current extraction electrodes is used, the computing device may measure respective voltages using more than two electrodes. For example, the computing device may measure respective voltages using a plurality of respective measurement electrode sets. For each of the plurality of respective measurement electrode sets, the computing device may determine a respective voltage difference between a first respective voltage measured using a respective first measurement electrode from the respective measurement electrode set and a second respective voltage measured using a respective second measurement electrode from the respective measurement electrode set. For each of the plurality of respective measurement electrode sets, the respective first measurement electrode and the respective second measurement electrode may be positioned symmetrically with reference to the symmetry of the material. The computing device may utilize voltage differences for each of the plurality of respective measurement electrode sets to determine whether the material includes a crack or other defect.

Utilizing comparisons between multiple voltage measurements from a material may allow determination of whether a material includes a crack or other defect without previous measurement of control voltages, which may simplify determination of whether the material includes the crack or other defect. Further, as the multiple voltage measurements are performed at substantially the same time (e.g., as part of a single set of measurements), the material may be expected to be at substantially the same temperature (e.g., the same temperature or nearly the same temperature). Thus, temperature may be less of a factor in the comparisons. This may be important for some materials, such as semiconductors, whose conductivity changes significantly as a function of temperature.

Other techniques also may be used to detect cracks in a material. For example, X-ray radiography or X-ray computed tomography (CT) may be used to detect cracks in a material. However, X-ray radiography and X-ray CT utilize relatively large, relatively expensive equipment to perform the crack detection. This may prevent X-ray radiography and X-ray CT from being portable, such as being used to test materials in the environments in which they are used. Moreover, X-ray radiography and X- ray CT may be relatively time consuming. In contrast, the techniques and systems described herein may be smaller, less expensive, and quicker to operate than X-ray radiography and X-ray CT systems. In some examples, the techniques described herein may allow determination of whether a material includes a crack or other defect in the field, where the material is being used, rather than requiring the material to be transported to the X-ray radiography or X-ray CT system.

FIG. 1 is a conceptual block diagram illustrating an example system for determining whether a material includes a crack or other defect using a plurality of current injection electrodes and at least one current extraction electrode. System 10 of FIG. 1 includes a computing device 12, an electrical signal source 14, a plurality of electrodes 18A-18V (collectively, "electrodes 18"), a switch network 20, and an optional reference electrode 22. Electrodes 18 are electrically coupled to material 16.

Material 16 may be any material for which detection of a potential crack or other defect is desired. In some examples, material 16 may be an electrically conductive or an electrically

semiconductive material. For example, material 16 may include a metal, an alloy, a metalloid, a semiconductor, an electrically conductive or semiconductive ceramic, or the like. In some examples, material 16 may include a ceramic such as boron carbide (B₄C), silicon carbide (SiC), alumina (AI₂O3), composites thereof, or the like.

Material 16 may be used in any one of a wide variety of applications. For example, material 16 may be a ceramic that has relatively high hardness, a relatively high Young's modulus, a relatively high tensile strength, and may be used in ceramic armor plating. Ceramic armor plating may be used in body armor for military and police personnel, vehicle armor, or the like. Example materials for ceramic armor plating include boron carbide (B4C), silicon carbide (SiC), alumina (AI2O3), composites thereof, or the like.

Material 16 may define any geometry, and the geometry of material 16 may be based at least in part on the intended use for material 16. For example, ceramic armor plating may have a geometry defined by the surface that the armor plating will be applied to. Example geometries for material 16 include, but are not limited to, polygonal solids, such as rectangular solids or solids with more sides.

In some examples, material 16 may define a geometry that has a symmetry, i.e., is symmetric. As used herein, a symmetry is a point, line, plane, curve, or manifold, with reference to which a single mathematical operation maps each volume of material 16 to another volume of material 16. In the example of FIG. 1, material 16 includes a plane of symmetry 24, across which there is mirror symmetry. As described in further detail below, in some examples in which material 16 includes a symmetry, computing device 12 may compare voltages measured using electrodes or electrode pairs that are symmetrical with reference to the symmetry, e.g., plane of symmetry 24, to determine whether material 16 includes a crack or other defect.

Electrical signal source 14 may include any device configured to output an electrical signal to electrodes 18. The electrical signal may include an alternating current (AC) signal or a direct current (DC) signal. In some examples, electrical signal source 14 may output a current signal; in other examples, electrical signal source 14 may output a voltage signal. In some examples, electrical signal source 14 may include a power source, such as a battery, a capacitor, a supercapacitor, a transformer electrically connected to a mains voltage, or the like. In some examples, in addition to the power source, electrical signal source 14 may include analog or digital circuitry configured to receive the electrical signal from the power source and modify the electrical signal into a format suitable for output to electrodes 18.

Switch network 20 includes a plurality of inputs and a plurality of outputs, with respective inputs electrically coupled to each respective output by the network of switches. For example, switch network 20 may include a pair of inputs electrically coupled to electrical signal source 14, and at least a pair of inputs electrically coupled to computing device 12. Switch network 20 may include at least as many outputs as there are electrodes 18 and 22. For example, in the example shown in FIG. 1, system 10 includes twenty-three electrodes, and switch network 20 thus includes at least twenty-three outputs. Each electrode of electrodes 18 and reference electrode 22 is electrically coupled to a respective output of switch network 20.

Computing device 12 is configured to control operation of system 10, including electrical signal source 14 and switch network 20. Computing device 12 may include any of a wide range of devices, including computer servers, desktop computers, notebook (i.e., laptop) computers, tablet computers, and the like. In some examples, computing device 12 may include a processor. The processor may include one or more microprocessors, digital signal processors (DSP), application specific integrated circuits (ASIC), field programmable gate arrays (FPGA), or other digital logic circuitry. In some examples, computing device 12 may include an analog -to-digital converter (ADC), or system 10 may include an ADC separate from computing device 12. In examples in which the ADC is separate from computing device 12, the ADC may be electrically coupled between a selected measurement electrode and computing device 12. The ADC may measure the voltage using the selected measurement electrode, e.g., under control of computing device 12.

Computing device 12 is communicatively coupled to electrical signal source 14 and electrically coupled to switch network 20, e.g., either directly or indirectly via an external device, such as an ADC. Computing device 12 may be configured to control electrical signal source 14 to output an electrical signal, and may be configured to control switch network 20 to connect a selected plurality of electrodes of electrodes 18 to electrical signal source 14 to serve as current injection electrodes, such that the electrical signal output by electrical signal source 14 is output to the plurality of current injection electrodes.

Computing device 12 is also configured to cause switch network 20 to connect a selected electrode of electrodes 18 to computing device 12 to serve as a current extraction electrode through which the electrical signal is extracted, e.g., to ground. Further, computing device 12 is configured to cause switch network 20 to connect selected electrodes either individuals or in pairs to computing device 12 to serve as a measurement electrode or pair of measurement electrodes. In this way, computing device 12 may determine a voltage using a measurement electrode or a pair of measurement electrodes in response to the electrical signal output by electrical signal source 14.

Electrodes 18 include a plurality of electrodes electrically coupled to material 16. In some examples, as shown in FIG. 1, each electrode of electrodes 18 is also electrically coupled to switch network 20. Each of electrodes 18 may be electrically connected to material 16 using any suitable type of electrical coupling, including, for example, an electrically conductive adhesive, an electrically conductive solder, embedding electrodes 18 in material 16, a dielectric coupling via capacitive coupling, or the like.

Electrodes 18 may be attached to any surface of material 16. The surface to which electrodes 18 are attached may affect the direction in which the electrical field extends and current flows within material 16. Cracks or other defects may affect the magnitude of the voltage more significantly when the electrical field and current flow extends across a plane of the crack (e.g., normal to a surface of the crack). As such, in some examples, the likely locations of cracks or other defects and the likely orientation of cracks or other defects within material 16 may be predicted based on the use for material 16. In some of these examples, electrodes 18 may then be attached to material 16 so that the electrical field and current flow within material 16 extends substantially normal to a predicted orientation of the crack or other defect.

In some examples, rather than predicting a location of the crack or other defect within material 16 and placing electrodes 18 based on the prediction, electrodes 18 may be attached to more than one surface of material 16. For example, if material 16 is in the shape of a cube, electrodes 18 may be attached to three orthogonal surfaces of the cube. By attaching a respective electrode of electrodes 18 to three orthogonal surfaces, the electrical field and current flow may be caused to extend in one of three orthogonal directions depending on the electrodes 18 through which the electrical signal is applied. This may increase the likelihood that the induced electrical field and current flow will extend within material 16 normal to the plane of any crack in material 16. Other examples are possible for other shapes. In some examples, electrodes 18 are distributed across a surface area of material 16, as shown in FIG. 1. In other examples, electrodes 18 are distributed around a perimeter of material 16. In some examples, plurality of electrodes 18 may be referred to as a set of N electrodes 18.

In some examples, electrodes 18 may be positioned on material 16 according to a selected geometric relationship. For example, electrodes 18 may be positioned on material 16 so that each electrode of electrodes 18 is substantially symmetric to another one of electrodes 18 with reference to the symmetry of material 16. In the example of FIG. 1, first electrode 18A is substantially symmetric to seventh electrode 18G with reference to plane of symmetry 24, second electrode 18B is substantially symmetric to sixth electrode 18F with reference to plane of symmetry 24, third electrode 18C is substantially symmetric to fifth electrode 18E with reference to plane of symmetry 24, and so on.

As another example, electrodes 18 may be positioned on material 16 so that a respective pair of electrodes is substantially symmetric to another respective pair of electrodes 18 with reference to the symmetry of material 16. For example, a first pair of electrodes may include first electrode 18A and twenty-second electrode 18V and a second pair of electrodes may include seventh electrode 18G and eighth electrode 18H. The first pair of electrodes is symmetric to the second pair of electrodes with reference to plane of symmetry 24.

In some examples, electrodes 18 may be positioned on material 16 so that each respective pair of electrodes is substantially symmetric to another respective pair of electrodes 18 with reference to the symmetry of material 16. This may be accomplished in examples in which each electrode of electrodes 18 is substantially symmetric to another one of electrodes 18 with reference to the symmetry of material 16, and a respective electrode of two symmetric electrodes is used in each respective pair of electrodes in a symmetric pair of electrodes.

Further, in some examples, two electrodes may be positioned on the symmetry of material 16, e.g., on plane of symmetry 24 shown in FIG. 1. For example, fourth electrode 18D and fifteenth electrode 180 are positioned on plane of symmetry 24. In other examples, electrodes are not positioned on the symmetry of material 16.

In some examples, positioning electrodes 18 to be exactly symmetrical may be difficult to achieve in practice. Hence, electrodes 18 may be positioned to be substantially symmetrical. As used here, substantially symmetrical means that the electrodes are placed approximately symmetrical with reference to a symmetry of material 16, e.g., within about 0.5 mm of being symmetric, within about 0.2 mm of being symmetric or within about 0.1 mm of being symmetric.

In some examples, system 10 may optionally include reference electrode 22, which may not be electrically coupled to material 16 and may be used for single-ended voltage measurements between one electrode of plurality of electrodes 18 and reference electrode 22. Reference electrode 22 may be at a selected voltage, such a ground or an offset voltage. In some examples, computing device 12 may use the single-ended voltages in the techniques described herein to determine whether material 16 includes a crack or other defect. In other examples, computing device 12 may determine differential voltages between two electrodes electrically coupled to material 16 by comparing (e.g., subtracting) single ended voltages associated with the two electrodes, and computing device 12 may use these differential voltages in the techniques described herein to determine whether material 16 includes a crack or other defect. In still other examples, computing device 12 may determine a voltage between two of electrodes 18 directly, e.g., without first determining two single-ended voltages.

Computing device 12 may be configured to cause electrical signal source 14 to apply an electrical signal to a plurality of current injection electrodes electrically coupled to material 16 and cause the electrical signal to be extracted through at least one current extraction electrode by causing switch network 20 to electrically couple to the at least one current extraction electrode. The plurality of current injection electrodes may include a plurality of electrodes 18. Similarly, the at least one current extraction electrode may include at least one of electrodes 18. Each current injection electrode of the plurality of current injection electrodes may be different from each current extraction electrode of the at least one current extraction electrode.

The plurality of current injection electrodes may be arranged symmetrically with reference to the symmetry of material 16, e.g., with reference to plane of symmetry 24. The plurality of current injection electrodes may include at least two current injection electrodes, and may include any number of current injection electrodes greater than two. For example, the plurality of current injection electrodes may include an even number of current injection electrodes. For each respective pair of the even number of current injection electrodes, a first electrode of the pair may be positioned symmetrically to the second electrode of the pair with reference to the symmetry of material 16, e.g., plane of symmetry 24. For example, the plurality of current injection electrodes may include seventh electrode 18G, sixth electrode 18F, second electrode 18B, and first electrode 18A. First electrode 18A is positioned symmetrically to seventh electrode 18G with reference to plane of symmetry 24 and second electrode 18B is positioned symmetrically to sixth electrode 18F with reference to plane of symmetry 24.

Computing device 12 may cause switch network 20 to connect the plurality of current injection electrodes and the current extraction electrode so that a current source (e.g., included in electrical signal source 14) injects the injection current through a high side or a low side with reference to a voltage source. Examples of different high side current source and low side current source configurations are shown and described with reference to FIGS. 4, 7, and 9-15.

While electrical signal source 14 is applying the electrical signal to material 16 using the plurality of current injection electrodes and the at least one current extraction electrode, computing device 12 may determine a first measured voltage using a first measurement electrode and a second measured voltage using a second measurement electrode. In some examples, the first measurement electrode and the second measurement electrode may be positioned symmetrically with reference to the symmetry of material 16, e.g., plane of symmetry 24. For example, the first electrode may be any one of electrodes 18A, 18B, 18C, 18V, 18U, 18T, 18S, 18R, 18Q, or 18P, and the second electrode may be a corresponding one of electrodes 18G, 18F, 18E, 18H, 181, 18J, 18K, 18L, 18M, or 18N. By comparing the first measured voltage and the second measured voltage, computing device 12 may determine whether material 16 includes a crack or other defect.

In some examples, computing device 12 may measure respective voltages using more than two measurement electrodes. For example, computing device 12 may measure respective voltages using a plurality of respective measurement electrode sets. For each of the plurality of respective measurement electrode sets, computing device 12 may determine a respective voltage difference between a first respective voltage measured using a respective first measurement electrode from the respective measurement electrode set and a second respective voltage measured using a respective second measurement electrode from the respective measurement electrode set. For each of the plurality of respective measurement electrode sets, the respective first measurement electrode and the respective second measurement electrode may be positioned symmetrically with reference to the symmetry of the material. For example, a first measurement electrode set may include first electrode 18A and seventh electrode 18G, a second measurement electrode set may include twenty-second electrode 18V and eighth electrode 18H, and so on. Computing device 12 may utilize voltage differences for each of the plurality of respective measurement electrode sets to determine whether material 16 includes a crack or other defect.

Utilizing comparisons between multiple voltage measurements from material 16 may allow determination of whether material 16 includes a crack or other defect without previous measurement of control voltages, which may simplify determination of whether material 16 includes the crack or other defect. Further, as the multiple voltage measurements are performed at substantially the same time (e.g., as part of a single set of measurements), material 16 may be expected to be at substantially the same temperature (e.g., the same temperature or nearly the same temperature). Thus, temperature may be less of a factor in the comparisons. This may be important for some materials, such as semiconductors, whose conductivity changes significantly as a function of temperature.

In some examples, the at least one current extraction electrode utilized for the voltage measurements may include a single current extraction electrode, which may be positioned on the symmetry of material 16, e.g., on plane of symmetry 24. FIG. 2 is a flow diagram illustrating an example technique for determining whether a material includes a crack or other defect using a plurality of current injection electrodes and a single current extraction electrode. The technique of FIG. 2 will be described with concurrent reference to system 10 of FIG. 3, but it will be understood that other systems that include more or fewer components than system 10 may perform the technique of FIG. 2 (e.g., a system that includes only computing device 12), and that system 10 may be used to perform other techniques (e.g., the techniques of FIG. 5, among other techniques). FIG. 3 is a conceptual block diagram illustrating an example system 10 for determining whether a material 16 includes a crack or other defect using a plurality of current injection electrodes and a single current extraction electrode in a configuration including two current injection electrodes 18B and 18F, a single current extraction electrode 180, and two measurement electrodes 18V and 18H. Aside from the configuration of electrodes 18, system 10 in FIG. 3 is similar to or substantially the same as system 10 illustrated in FIG. 1. The technique of FIG. 2 may include applying an electrical signal to a plurality of current injection electrodes positioned symmetrically with reference to a symmetry of material 16, e.g., on plane of symmetry 24 (32). For example, computing device 12 may cause switch network 20 to electrically couple a plurality of electrodes of electrodes 18 to electrical signal source 14 as the plurality of current injection electrodes. As shown in FIG. 3, the plurality of current injection electrodes may include second electrode 18B and sixth electrode 18F (referred to as current injection electrodes 18B and 18F with reference to FIGS. 2 and 3), which are positioned symmetrically with reference to plane of symmetry 24. In general, any number of electrodes 18 may be coupled to switch network 20 as current injection electrodes, as long as the arrangement of the current injection electrodes is symmetrical with reference to a symmetry of material 16, e.g., plane of symmetry 24. For example, any of electrodes 18A-18V other than the electrode being used as the current extraction electrode may be used as a current injection electrode. Computing device 12 then may cause electrical signal source 14 to apply the electrical signal to the plurality of current injection electrodes 18B and 18F.

The technique of FIG. 2 also includes extracting the electrical signal through a single current extraction electrode (34). For example, computing device 12 may cause switch network 20 to electrically couple an electrode from electrodes 18 to electrical signal source 14 or to ground as the single current extraction electrode. In the example shown in FIG. 3, the single current extraction electrode is fifteenth electrode 180 (referred to as single current extraction electrode 180 with reference to FIGS. 2 and 3).

In some examples, as shown in FIG. 3, single current extraction electrode 180 may be positioned near an opposite side or end of material 16 as the plurality of current injection electrodes 18B and 18F. This may result in more even current flow through the volume of material 16, e.g., compared to current injection electrodes positioned nearer to the single current extraction electrode 180, such as electrodes 18N and 18P. This may improve a likelihood that a crack or other defect present in material 16 is detected by the technique of FIG. 2.

The technique of FIG. 2 also includes determining a voltage difference between a first voltage measured using a first measurement electrode and a second voltage measured using a second measurement electrode (36). For example, computing device 12 may cause switch network 20 to electrically couple a first electrode to computing device 12 to be the first measurement electrode and to electrically couple a second electrode to computing device 12 to be the second measurement electrode.

In some examples, computing device 12 may be configured to select the first and second measurement electrodes from electrodes 18. For example, as shown in FIG. 3, eighth electrode 18H may be the first measurement electrode and twenty-second electrode 18V may be the second measurement electrode. Regardless of which electrodes computing device 12 selects as the first and second measurement electrodes, the first and second measurement electrodes may be positioned symmetric to each other with reference to a symmetry of material 16, e.g., plane of symmetry 24.

Computing device 12 may be configured to measure the first measured voltage between the first measurement electrode and a third measurement electrode. In some examples, the third measurement electrode may be another electrode from electrodes 18, such that the first measured voltage is a differential voltage between the first measurement electrode and the third measurement electrode. In other examples, the third measurement electrode may be reference electrode 22, and the first measured voltage may be a single-ended voltage.

Similarly, computing device 12 may be configured to measure the second measured voltage between the second measurement electrode and a fourth measurement electrode. In some examples, the fourth measurement electrode may be another electrode from electrodes 18, such that the second measured voltage is a differential voltage between the second electrode and the fourth measurement electrode. In other examples, the fourth electrode may be reference electrode 22, and the second measured voltage may be a single-ended voltage. In examples in which the third and fourth measurement electrodes are not reference electrode 22, the third and fourth measurement electrodes may be positioned symmetric to each other with reference to a symmetry of material 16, e.g., plane of symmetry 24.

Once computing device 12 measures the first measured voltage using the first measurement electrode and measures the second measured voltage using the second measurement electrode, computing device 12 may determine a voltage difference between the first measured voltage and the second measured voltage (36). For example, computing device 12 may be configured to subtract the first measured voltage from the second measured voltage or subtract the second measured voltage from the first measured voltage.

In some examples, the technique of FIG. 2 optionally includes determining whether additional voltage differences are to be determined using additional measurement electrodes (38). For example, computing device 12 may be configured to determine respective voltage differences for each respective measurement electrode set of a plurality of respective measurement electrode sets. Each respective measurement electrode set may include a respective first measurement electrode and a respective second measurement electrode. Each respective first and second measurement electrodes may be positioned symmetric to each other with reference to a symmetry of material 16, e.g., plane of symmetry 24.

Further, computing device 12 may be configured to measure the respective first voltage using the respective first measurement electrode and a respective third measurement electrode, which may be reference electrode 22 or another electrode of electrodes 18. Similarly, computing device 12 may be configured to measure the respective second voltage using the respective second measurement electrode and a respective fourth measurement electrode, which may be reference electrode 22 or another electrode of electrodes 18. If the respective third and fourth measurement electrodes are not the reference electrode 22, then each respective third and fourth measurement electrodes may be positioned symmetric to each other with reference to a symmetry of material 16, e.g., plane of symmetry 24.

For each of the plurality of respective measurement electrode sets, computing device 12 may determine a respective voltage difference between a first respective voltage measured using the respective first measurement electrode and a second respective voltage measured using the respective second measurement electrode.

Hence, computing device 12 may be configured to determine whether additional voltage differences are to be determined using additional measurement electrodes (38). In response to determining that additional voltage differences are to be determined using additional measurement electrodes (the "YES" branch of decision block 38), computing device 12 may determine a respective voltage difference between a respective first voltage measured using a respective first measurement electrode and a respective second voltage measured using a respective second measurement electrode (36). For example, computing device 12 may cause switch network 20 to electrically couple selected electrodes from electrodes 18, reference electrode 22, or the like to computing device 12, may measure the respective first voltage using the respective first electrode, may measure the respective second voltage using the respective second electrode, and may determine a respective voltage difference between the respective first voltage and the respective second voltage (36). Computing device 12 may iterate this process until computing device 12 determines that no additional voltage differences are to be determined using additional measurement electrodes (the "NO" branch of decision block 38).

In response to determining that no additional voltage differences are to be determined using additional measurement electrodes (the "NO" branch of decision block 38), computing device 12 may determine whether material 16 includes a crack or other defect based on the respective voltage differences (40). In order to make this determination, computing device 12 may be configured to determine that a non-zero voltage difference (or a voltage difference that is greater than a threshold value) indicates a presence of a crack or other defect, and a voltage difference of zero (or a voltage difference that is less than a threshold value) indicates that material 16 does not include a crack or other defect.

To understand why this is the case, FIG. 4 is an equivalent circuit diagram of a system configuration similar to that shown in FIG. 3 in the absence of a crack or other defect. As shown in FIG. 4, a first current source 41 outputs a test current II = 1*1 to a first current injection electrode 42 and a second current source 43 outputs a test current IR = 1*1 to a second current injection electrode 44. The first and second injection electrodes 42 and 44 are positioned symmetrically with reference to a symmetry of material 46. Once the test currents II and IR enter material 46, the test currents conduct through material 46 to single current extraction electrode 48. A first current I_r flows to single current extraction electrode 48 through equivalent resistance R. A second current Ik flows to single current extraction electrode 48 through an equivalent resistance K*R. Equivalent resistances R and K*R represent the resistances of the portions of material 46 through which the first current I_r and the second current Ik flow. M*R represents the resistance of the material between the two injection electrodes 42 and 44. In the absence of cracks or defects in material 46, the magnitudes of currents Ik and I_r will be approximately proportional to the relative distances between first current injection electrode 42 and single current extraction electrode 48 and between second current injection electrode 44 and single current extraction electrode 48. K represents this proportionality. In the example of FIG. 4, as single current extraction electrode 48 is on the symmetry of material 46 and first and second current injection electrodes 42 and 44 are positioned symmetrically with reference to the symmetry, K = 1. The respective currents Ik and I_r are combined at single current extraction electrode 48 and pass through a resistance Ri, at which a reference voltage VRI may be measured.

By examination of FIG. 4 and with K=l :

M*R*Ip + Vr = M*R*In + Vl (4)

Rearranging equation ( 1) yields:

From equation (5), it is clear that the magnitude of the difference between Vi and V_r is proportional to the mismatch between the internal currents I_r and Ik. As single current extraction electrode 48 is positioned on the symmetry of material 46 and the first and second current injection electrodes 42 and 44 are positioned symmetrically with reference to the symmetry of material 46, the respective internal currents will be substantially the same (e.g., the same or nearly the same) in the absence or a crack or defect in material 46. As used here, substantially the same means voltages are within a threshold amount of each other. The threshold amount may be a predetermined percentage of the measured voltage, such as, for example, 20%, 10%, 5%, or 1%.

However, a crack or other defect may increase the equivalent resistance of the portion of material

46 in which the crack or defect is located. This may cause an imbalance in the equivalent resistances K*R and R, causing the internal currents to no longer be equal. As the magnitude of the difference between Vi and V_r is proportional to the mismatch between the internal currents, unequal internal currents, and thus unequal equivalent resistances, may be detected by measuring Vi and V_r. Hence, if the first measured voltage (e.g., Vi) and the second measured voltage (V_r) are different or are different by more than a threshold amount, computing device 12 may determine that material 16 or 46 includes a crack or other defect.

Returning now to FIG. 2, computing device 12 may determine whether material 16 includes a crack or other defect based on the respective voltage differences (40). For example, computing device 12 may determine that a voltage difference that is non-zero or whose magnitude or absolute value is greater than a threshold value indicates that material 16 includes a crack or other defect. On the other hand, computing device 12 may determine that a voltage difference that is zero or whose magnitude or absolute value is less than a threshold value indicates that material 16 does not include a crack or other defect.

In some examples in which computing device 12 determines a plurality of respective voltage differences, computing device 12 may compare each respective voltage difference to a threshold value and determine the number of voltage differences that are greater than the threshold value. Computing device 12 then may compare this number to a threshold number and determine whether material 16 includes a crack or other defect based on if the number of voltage differences that indicate a crack or other defect is greater than the threshold number.

In other examples in which computing device 12 determines a plurality of respective voltage differences, computing device 12 may mathematically manipulate the respective voltage differences to arrive at a single score for material 16. For example, computing device 12 may sum the respective voltage differences, square each respective voltage differences and sum the squares of the respective voltage differences, average the respective voltage differences, determine a weighted average of the respective voltage differences, or the like to determine a single score for material 16. Computing device 16 then may compare the single score to a threshold score value and determine that material 16 includes a crack or other defect if the single score is greater than the threshold score value.

In some examples, in addition to using the voltage differences to determine whether material 16 includes a crack or other defect, computing device 12 may utilize a control voltage difference or respective control voltage differences. The control voltage difference may represent the voltage difference determined for a give combination of measurement electrodes when material 16 does not include a crack or other defect. The control voltage difference may be based on material 16, a model, or an average of a plurality of materials that are similar to or substantially the same as material 16. For example, computing device 12 or another similar computing device may determine the control voltage difference at a time at which material 16 is manufactured, or a time at which an independent measurement (e.g., X-ray radiology or X-ray CT scan) may be used to verify that material 16 is intact, undamaged, or does not include a crack. Computing device 12 or another similar computing device may determine the control voltage by applying the electrical signal to the plurality of current injection electrodes 18B and 18F, extracting the electrical signal through the single current extraction electrode 180, and determining the control voltage difference using first and second measurement electrodes, e.g., electrodes 18H and 18V. In some examples, the control voltage difference(s) may be determined using similar or substantially the same combinations of current injection electrodes, current extraction electrode, and measurement electrodes as are used to determine the voltage difference(s) described above.

In other examples, the control voltage difference(s) may be determined using a model of the material in an intact (undamaged) state. For example, computing device 12 may execute the model of material 16 and determine the control voltage difference(s) based on the model. In some examples, the model may include a physics-based model of the electrical properties of material 16. In some other examples, the control voltage difference(s) may be determined as an average (e.g., mean) of a plurality of similar materials (e.g., in geometry and composition) that are known to be intact (undamaged). This control voltage difference(s) may be stored (e.g., in a memory device associated with computing device 12) for later use.

In examples in which computing device 12 utilizes control voltage differences, computing device 12 may compare a respective voltage difference to a respective control voltage difference. The respective control voltage difference may be associated with the same combination of current injection electrodes, current extraction electrode, and measurement electrodes as the respective voltage difference. The comparison between the respective voltage difference and the respective control voltage difference may include subtracting the respective control voltage difference from the respective voltage difference or dividing the respective voltage difference by the respective control voltage difference. By utilizing control voltage differences in this manner, the technique may account for variations between the respective measured voltages that exist even in the absence of cracks or other defects. For example, material 16 may include inhomogeneities, different grain structures, or the like, which may cause the first and second measured voltages to not be exactly the same. Hence, there may still be variations between the first and second measured voltages even if the absence of cracks or other defects. As the control voltage differences represent electrical behavior of material 16 in the absence of cracks or other defects, the control voltage differences may help account for the variations in the first and second measured voltages.

After the respective voltage differences have been compared to the respective control voltage differences, computing device 12 may utilize the results of the respective comparisons (e.g., the differences or ratios) to determine whether material 16 includes a crack or other defect according to the techniques described above.

In some examples, rather than utilizing a single current extraction electrode, a technique for determining whether a material includes a crack or other defect may utilize at least two current extraction electrodes, each current extraction electrode being utilized for a separate set of measurements. FIG. 5 is a flow diagram illustrating an example technique for determining whether a material includes a crack or other defect using a plurality of current injection electrodes and at least two current extraction electrodes. The technique of FIG. 5 will be described with concurrent reference to system 10 of FIGS. 6 and 8, but it will be understood that other systems that include more or fewer components than system 10 may perform the technique of FIG. 5 (e.g., a system that includes only computing device 12), and that system 10 may be used to perform other techniques (e.g., the techniques of FIG. 2, among other techniques). FIG. 6 is a conceptual block diagram illustrating an example system 10 for determining whether material 16 includes a crack or other defect using a plurality of current injection electrodes and at least two current extraction electrodes. FIG. 6 illustrates system 10 in a first configuration including a plurality of current injection electrodes 18B and 18F, a first current extraction electrode 18P, and two measurement electrodes 18H and 18V. FIG. 8 illustrates system 10 in a second configuration including the plurality of current injection electrodes 18B and 18F, a second current extraction electrode 18N, and two measurement electrodes 18H and 18V. Aside from the configuration of electrodes 18, system 10 in FIGS. 6 and 8 is similar to or substantially the same as system 10 illustrated in FIG. 1.

The technique of FIG. 5 includes applying a first electrical signal to a plurality of current injection electrodes electrically coupled to material 16 (52). Step (52) may be similar to or substantially the same as steps (32) described above with reference to FIG. 2.

The technique of FIG. 5 also includes extracting the first electrical signal through a first current extraction electrode (54). For example, computing device 12 may cause switch network 20 to electrically couple an electrode of electrodes 18 to electrical signal source 14 or ground as the first current extraction electrode. As shown in FIG. 6, the first current extraction electrode may be sixteenth electrode 18P (referred to as first current extraction electrode 18P with reference to FIGS. 5, 6, and 8).

The technique of FIG. 5 also includes determining a voltage difference between a first voltage measured using a first measurement electrode and a second voltage measured using a second

measurement electrode (56). In some examples, the technique of FIG. 5 optionally includes determining whether additional voltage differences are to be determined using additional measurement electrodes (58). Steps (56) and (58) may be similar to or substantially the same as steps (36) and (38), respectively described above with reference to FIG. 2.

In response to determining that no additional voltage differences are to be determined using additional measurement electrodes (the "NO" branch of decision block 58), computing device 12 may be configured to apply a second electrical signal to the plurality of current injection electrodes 18B and 18F (60). Steps (60) may be similar to or substantially the same as steps (32) described above with reference to FIG. 2.

The technique of FIG. 5 also includes extracting the second electrical signal through a second current extraction electrode (62). For example, computing device 12 may cause switch network 20 to electrically couple an electrode of electrodes 18 to electrical signal source 14 or ground as the second current extraction electrode. As shown in FIG. 8, the second current extraction electrode may be fourteenth electrode 18N (referred to as second current extraction electrode 18N with reference to FIGS.

5, 6, and 8). Second current extraction electrode 18N is positioned symmetrically to first current extraction electrode 18P with reference to plane of symmetry 24 of material 16. In other words, the location of second current extraction electrode 18N is symmetric to the location of first current extraction electrode 18P with reference to a symmetry of material 16, e.g., plane of symmetry 24.

The technique of FIG. 5 also includes determining a voltage difference between a third voltage measured using the first measurement electrode and a fourth voltage measured using the second measurement electrode (64). In some examples, the technique of FIG. 5 optionally includes determining whether additional voltage differences are to be determined using additional measurement electrodes (66).

Steps (64) and (66) may be similar to or substantially the same as steps (36) and (38), respectively, described above with reference to FIG. 2.

Although FIGS. 5, 6, and 8 illustrate a technique that utilizes two current extraction electrodes

18P and 18N for two measurement sets, in other examples, a technique may utilize any number of current extraction electrodes for a corresponding number of measurement sets, as long as the arbitrary number of current extraction electrodes are symmetrically positioned with respect to a symmetry of material 16, e.g., plane of symmetry 24.

In response to determining that no additional voltage differences are to be determined using additional measurement electrodes (the "NO" branch of decision block 66), computing device 12 may be configured to determine whether material 16 includes a crack or other defect based on the respective voltage differences (68). In order to make this determination, computing device 12 may be configured to determine that a non-zero difference (or a difference that is greater than a threshold value) between two voltage differences associated with the same measurement electrodes and different current extraction electrodes indicates a presence of a crack or other defect, and a difference of zero (or a difference that is less than a threshold value) between two voltage differences associated with the same measurement electrodes and different current extraction electrodes indicates that material 16 does not include a crack or other defect. To understand why this is the case, FIG. 7 is an equivalent circuit diagram of a system configuration similar to that shown in FIG. 6 in the absence of a crack or other defect. As shown in FIG. 7, a first current source 71 outputs a first test current II = 1*1 to a first current injection electrode 72 and a second current source 73 outputs a second test current IR = 1*1 to a second current injection electrode 74. First and second current injection electrodes 72 and 74 are positioned symmetrically with reference to a symmetry of material 76. Once the test currents II and IR enter material 46, the test currents conduct through material 76 to first current extraction electrode 78. A first current Ik flows to first current extraction electrode 78 through equivalent resistances R. A second current I_r flows to first current extraction electrode 78 through an equivalent resistance K*R. Equivalent resistances R and K*R represent the resistances of the portions of material 76 through which the first current Ik and the second current I_r flow. A portion of current I_c also may flow through equivalent resistance P*R within material 76. In the absence of cracks or defects in material 76, the magnitudes of currents Ik and I_r will be approximately proportional to the relative distances between first current injection electrode 72 and first current extraction electrode 78 and between second current injection electrode 74 and first current extraction electrode 78. K represents this proportionality. The respective currents are combined through the first current extraction electrode 78 and pass through a resistance Ri, at which a voltage VRI may be measured.

FIG. 9 is an equivalent circuit diagram of a system configuration similar to that shown in FIG. 8 in the absence of a crack or other defect. As shown in FIG. 9, a first current source 71 outputs a first test current II = 1*1 to first current injection electrode 72 and a second current source 73outputs a second test current IR = 1*1 to second current injection electrode 74. Once the test currents II and IR enter material 76, the test currents conduct through material 76 to second current extraction electrode 80. Second current extraction electrode 80 is positioned symmetrically to first current extraction electrode 78 with reference to a symmetry of material 76. A first current Ik flows to second current extraction electrode 80 through equivalent resistances K*R. A second current I_r flows to second current extraction electrode 80 through an equivalent resistance R. Equivalent resistances K*R and R represent the resistances of the portions of material 76 through which the first current Ik and the second current I_r flow. In the absence of cracks or defects in material 76, the magnitudes of currents Ik and I_r will be approximately proportional to the relative distances between first current injection electrode 72 and second current extraction electrode 80 and between second current injection electrode 74 and second current extraction electrode 80. K represents this proportionality. The respective currents are combined through the second current extraction electrode 80 and pass through a resistance Ri, at which a voltage VRI may be measured.

By examination of FIG. 9:

Vr - R*I_r + = Vi - K*R*I_k (7)

I_r + I_k = 2*I = I_p + I„ (8)

M*R*I_P + V_r = M*R*I„ + Vi (10)

Rearranging equation (7) yields: AV = (V! - V_r) = (K*I_k - I_r)*R (1 1)

From equation (1 1), it is clear that the magnitude of the difference between Vi and V_r is proportional to the mismatch between the internal currents Ik and I_r.

If the current extraction electrode is connected to first current extraction electrode 78, as in FIG. 7, by examination:

Vr - K*R*Ir = Vl - R*I_k (12)

Rearranging equation ( 12) yields:

AV = (V! - V_r) = (I_k - K*I_r)*R (13)

By symmetry, Ik in FIG. 7 is equivalent to I_r in FIG 9, so swapping Ik and I_r in equation (13) and then comparing to equation (1 1) yields :

AV(FIG 7) = R*(I_r - K*I_k) = -(K*I_k - I_r)*R = -AV(FIG 9) (14) From equation (14), it is apparent that the difference between Vi and V_r for extraction electrodes 78 and 80 will have the same magnitude and opposite sign (in the absence of crack or other defect). As such, in the absence of a crack or other defect in material 76, a sum of the voltage difference (Vi - Vr) determined using first current extraction electrode 78 and the voltage difference (Vi - Vr) determined using second current extraction electrode 80 will be approximately zero (e.g., zero or nearly zero). In other words, in the absence of a crack or other defect in material 76, a magnitude or absolute value of the voltage difference (Vi - Vr) determined using first current extraction electrode 78 will be substantially the same (e.g., the same or nearly the same) as the voltage difference (Vi - Vr) determined using second current extraction electrode 80. As used here, substantially the same means voltages are within a threshold amount of each other. The threshold amount may be a predetermined percentage of the measured voltage, such as, for example, 20%, 10%, 5%, or 1%.

However, a crack or other defect will change the equivalent resistance of the portion of material 76 in which the crack or defect is located. This will cause an imbalance in the equivalent resistances K*R and R, changing the proportionality of the internal currents. Further, this imbalance will not be symmetrical, so a magnitude or absolute value of the voltage difference (Vi - Vr) determined using first current extraction electrode 78 (a first voltage difference) will no longer be substantially the same (e.g., the same or nearly the same) as the voltage difference (Vi - Vr) determined using second current extraction electrode 80 (a second voltage difference). Hence, if a magnitude or absolute value of the first voltage difference and a magnitude or absolute value of the second voltage difference are different or are different by more than a threshold amount, computing device 12 may determine that material 16 or 76 includes a crack or other defect.

Returning now to FIG. 5, computing device 12 may determine whether material 16 includes a crack or other defect based on the respective voltage differences (68). For example, in response to a difference between a first voltage difference associated with the first current extraction electrode 18P and a measurement electrode set and a second voltage difference associated with the second current extraction electrode 18N and the measurement electrode set being a non-zero value or greater than a threshold value, computing device 12 may determine that material 16 includes the crack or other defect. As another example, in response to a difference between an absolute value of the first voltage difference associated with the first current extraction electrode 18P and a measurement electrode set and an absolute value of the second voltage difference associated with the second current extraction electrode 18N and the measurement electrode set being a non-zero value or greater than a threshold value, computing device 12 may determine that material 16 includes the crack or other defect. On the other hand, in response to a difference between a first voltage difference associated with the first current extraction electrode 18P and a measurement electrode set and a second voltage difference associated with the second current extraction electrode 18N and a measurement electrode set being zero or less than a threshold value, computing device 12 may determine that material 16 does not include a crack or other defect.

In some examples in which computing device 12 determines a plurality of differences between respective voltage differences associated with the same measurement electrode set, computing device 12 may compare each respective difference between the voltage differences associated with the same measurement electrode set to a threshold value and determine a number of differences that is greater than the threshold value. Computing device 12 then may compare this number to a threshold number and determine whether material 16 includes a crack or other defect based on if the number of differences that indicate a crack or other defect is greater than the threshold number.

In other examples in which computing device 12 determines a plurality of differences between respective voltage differences associated with the same measurement electrode set, computing device 12 may mathematically manipulate the respective differences to arrive at a single score for material 16. For example, computing device 12 may sum the respective differences, square each respective difference and sum the squares of the respective differences, average the respective differences, determine a weighted average of the respective differences, or the like to determine a single score for material 16. Computing device 16 then may compare the single score to a threshold score value and determine that material 16 includes a crack or other defect if the single score is greater than the threshold score value.

In some examples, in addition to using the respective differences between voltage differences to determine whether material 16 includes a crack or other defect, computing device 12 may utilize a control voltage difference or respective control voltage differences, as described above with reference to FIG. 2.

In examples in which computing device 12 utilizes control voltage differences, computing device 12 may compare a respective voltage difference to a respective control voltage difference. The respective control voltage difference may be associated with the same combination of current injection electrode, current extraction electrodes, and measurement electrodes as the respective voltage difference. The comparison between the respective voltage difference and the respective control voltage difference may include subtracting the respective control voltage difference from the respective voltage difference or dividing the respective voltage difference by the respective control voltage difference. By utilizing control voltage differences in this manner, the technique may account for variations between the respective measured voltages that exist even in the absence of cracks or other defects. For example, material 16 may include inhomogeneities, different grain structures, or the like, which may cause the first and second measured voltages to not be exactly the same. Hence, there may still be variations between the first and second measured voltages even in the absence of cracks or other defects. As the control voltage differences represent electrical behavior of material 16 in the absence of cracks or other defects, the control voltage differences may help account for the variations in the first and second measured voltages.

In some examples, for any of the techniques described herein, voltages may be measured with respect to a voltage reference derived from the measurement current. FIG. 10 is an equivalent circuit diagram of a system configuration in which measurement voltages are measured with respect to a voltage reference derived from the electrical signal applied to the current injection electrode, in the absence of a crack or other defect. In the circuit shown in FIG. 10, a first current source 81 injects a current II = 1*1 to first current injection electrode 82 and a second current source 83 injects a current IR = 1*1 into second current injection electrode 84. The currents propagate through two equivalent resistances, Re_qi and Re_qr, with values (1-K)*I through Re_qi and K*I through Re_qr. A bridge resistor, R_m, shunts current between the two equivalent resistances, Re_qi and Re_qr. The two currents are summed at the top of Ri, which returns to ground. As before in FIGS. 4, 7, and 9, VRI = 2*I*Ri. If VRI is measured using a reference electrode coupled to the non-grounded node of Ri and is used as the reference for an ADC, then the digitized value for any differential voltage pair is given by the following:

AV[M] = (l-K)*I*Re_qi-K*I*Re_qr (13)

= I*((l-K)*Re_ql-K*Re_qr) (14)

ADC(AV[M]) = AV[M]*([2^aA]-1)/VRI = I*((l-K)*Re_qi-K*Re_qr)*([2^AA]-l)/2*I*Ri

= ((l-K)*Re_ql-K*Re_qr)*([2^AA]-l)/2*Ri

Where Re_qi = The equivalent resistance between the voltage nodes Vi and VRI

Re_qr = The equivalent resistance between the voltage nodes V_r and VRI

A = The ADC resolution in bits

K = Splitting factor and K < 1

Note that the digitized value for the measured differential voltage is not dependent on the source current II +IR = 2*1, so current source noise is effectively cancelled from the measurement (assuming matched current sources II and IR).

FIGS. 11-14 are circuit diagrams of example system configurations including various locations of current sources for determining whether a material includes a crack or other defect using at least one current injection electrode and a plurality of current extraction electrodes. FIG. 11 illustrates an example system 100 that includes two high side current sources 102A and 102B connected between a supply voltage, VS, and a material 104. Each of high side current sources 102A and 102B is configured to output a respective test current, II and IR, to a respective current injection electrode 106A and 106B electrically coupled to material 104. Current injection electrodes 106A and 106B are positioned symmetrically on material 104 with reference to a plane of symmetry of material 104. System 100 also includes a plurality of measurement electrodes 1L-5L and 1R-5R electrically coupled to material 104, which may be used to measure single-ended or differential voltages associated with material 104. In other examples, system 100 may include more or fewer measurement electrodes.

The test currents Land IR enter material 104 through current injection electrodes 106A and 106B, respectively, and travel through material 104 to current extraction electrode 108. Current extraction electrode is positioned on the plane of symmetry of material 104. Assuming that material 104 does not include a crack or other defect, a first voltage (e.g., VL or a voltage measured using one of measurement electrodes 1L-5L) will be substantially the same as a voltage measured using a symmetrical measurement electrode (e.g., VR or a voltage measured using a corresponding one of measurement electrodes 1R-5R). In some examples, respective voltages, VL and VR, may be measured at first current injection electrode 106A and second current injection electrode 106B. VL and VR may be used to determine whether material 104 includes a crack or other defect.

The extracted current includes a combination of the injected currents and conducts through a resistor Ri to Ground. A reference voltage VRI may be measured between the extraction point and Ground.

FIG. 12 illustrates an example system 110 that includes two low side current sources 112A and 112B connected between current injection electrodes 116A and 116B electrically coupled to material 114 and resistor Ri. In this example, the injection currents flow out of material 114 through current injection electrodes 116A and 116B. Current injection electrodes 116A and 116B are positioned symmetrically on material 114 with reference to a plane of symmetry of material 114. System 110 also includes a plurality of measurement electrodes 1L-5L and 1R-5R electrically coupled to material 114, which may be used to measure single-ended or differential voltages associated with material 114. In other examples, system 110 may include more or fewer measurement electrodes.

The test currents Land IR exit material 114 through current injection electrodes 116A and 116B, respectively, and are summed at the common node of Ri. The summed current passes through resistor Ri, through the supply voltage source VS, and into material 114 at the VS connection, which is the single extraction electrode 118, which is positioned on the plane of symmetry of material 114. Assuming that material 114 does not include a crack or other defect, a first voltage (e.g., VL or a voltage measured using one of measurement electrodes 1L-5L) will be substantially the same as a voltage measured using a symmetrical measurement electrode (e.g., VR or a voltage measured using a corresponding one of measurement electrodes 1R-5R). In some examples, respective voltages, VL and VR, may be measured at first current injection electrode 116A and second current injection electrode 116B. VL and VR may be used to determine whether material 104 includes a crack or other defect. A reference voltage VRI may be measured between the resistor Ri summing point and Ground.

FIG. 13 illustrates an example system 120 that includes two high side current sources 122A and 122B connected between a supply voltage, VS, and a material 124. Each of high side current sources 122A and 122B is configured to output a respective test current, II and IR, to a respective current injection electrode 126A and 126B electrically coupled to material 124. Current injection electrodes 126A and 126B are positioned symmetrically on material 124 with reference to a plane of symmetry of material 124. System 120 also includes a plurality of measurement electrodes 1L-5L and 1R-5R electrically coupled to material 124, which may be used to measure single-ended or differential voltages associated with material 124. In other examples, system 120 may include more or fewer measurement electrodes.

The test currents Land IR enter material 124 through current injection electrodes 126A and 126B, respectively, and travel through material 124 to current extraction electrode 128A or 128B. Depending on the position of switch 129, the injection current passes through either the first current extraction electrode 128A or the second current extraction electrode 128B. First current extraction electrode 128A and second current extraction electrode 128B are positioned on material 124 symmetrically with reference to the plane of symmetry of material 124. Assuming that material 124 does not include a crack or other defect, a difference between a first voltage (e.g., VL or a voltage measured using one of measurement electrodes 1L-5L) and a second voltage measured using a symmetrical measurement electrode (e.g., VR or a voltage measured using a corresponding one of measurement electrodes 1R-5R) when first current extraction electrode 128A is used will be substantially the same as a difference between a third voltage (e.g., VL or a voltage measured using one of measurement electrodes 1L-5L) and a fourth voltage measured using a symmetrical measurement electrode (e.g., VR or a voltage measured using a corresponding one of measurement electrodes 1R-5R) when second current extraction electrode 128B is used. In some examples, respective voltages, VL and VR, may be measured at first current injection electrode 126A and second current injection electrode 126B. VL and VR may be used to determine whether material 104 includes a crack or other defect.

FIG. 14 illustrates an example system 130 that includes two low side current sources 132A and

132B connected between current injection electrodes 136A and 136B electrically coupled to material 134 and resistor Ri. In this example, the injection currents flow out of material 134 through current injection electrodes 136A and 136B. Current injection electrodes 136A and 136B are positioned symmetrically on material 134 with reference to a plane of symmetry of material 134. System 130 also includes a plurality of measurement electrodes 1L-5L and 1R-5R electrically coupled to material 134, which may be used to measure single-ended or differential voltages associated with material 134. In other examples, system 130 may include more or fewer measurement electrodes.

The test currents Land IR exit material 134 through current injection electrodes 136A and 136B, respectively, and are summed at the common node of Ri. The summed current passes through resistor R_1; through the supply voltage source VS, and into material 134 at the VS connection, which, depending on the position of switch 139, is one of first current extraction electrode 138A or second current extraction electrode 138B. First current extraction electrode 138A and second current extraction electrode 138B are positioned on material 134 symmetrically with reference to the plane of symmetry of material 134. Assuming that material 134 does not include a crack or other defect, a difference between a first voltage (e.g., VL or a voltage measured using one of measurement electrodes 1L-5L) and a second voltage measured using a symmetrical measurement electrode (e.g., VR or a voltage measured using a corresponding one of measurement electrodes 1R-5R) when first current extraction electrode 138A is used will be substantially the same as a difference between a third voltage (e.g., VL or a voltage measured using one of measurement electrodes 1L-5L) and a fourth voltage measured using a symmetrical measurement electrode (e.g., VR or a voltage measured using a corresponding one of measurement electrodes 1R-5R) when second current extraction electrode 138B is used. VL and VR may be used to determine whether material 134 includes a crack or other defect. A reference voltage VRI may be measured between the resistor Ri summing point and Ground or the supply voltage VS.

Clause 1 : A method for detecting a crack or defect in a material, the method comprising:

applying an electrical signal to a plurality of current injection electrodes electrically coupled to the material, wherein the plurality of current injection electrodes are positioned substantially symmetrically with reference to a symmetry of the material; extracting the electrical signal through a single current extraction electrode, wherein the single current extraction electrode is positioned on the symmetry of the material; while applying the electrical signal to the plurality of current injection electrodes, determining a voltage difference between a first voltage measured using a first measurement electrode and a second voltage measured using a second measurement electrode, wherein the first and second measurement electrodes are positioned substantially symmetrically with reference to the symmetry of the material; and determining whether the material includes a crack or other defect based on the voltage difference.

Clause 2: The method of clause 1, wherein: determining the voltage difference between the first voltage measured using the first measurement electrode and the second voltage measured using the second measurement electrode comprises, while applying the electrical signal to the plurality of current injection electrodes, determining a voltage difference between a first differential voltage determined using the first measurement electrode and a third measurement electrode and a second differential voltage determined using the second measurement electrode and a fourth measurement electrode, wherein the third measurement electrode and the fourth measurement electrode are positioned substantially symmetrically with reference to the symmetry of the material.

Clause 3 : The method of clause 1 or 2, wherein the symmetry of the material is a point, a line, a plane, a curve, or a manifold, and wherein a single mathematical operation made with reference to the symmetry maps the first electrode to the second electrode.

Clause 4: The method of any one of clauses 1 to 3, wherein the plurality of current injection electrodes is a first current injection electrode and a second current injection electrode.

Clause 5: The method of any one of clauses 1 to 4, wherein the first voltage is a first single- ended voltage measured using the first measurement electrode and a reference electrode, and wherein the second voltage is a second single-ended voltage measured using the second measurement electrode and the reference electrode. Clause 6: The method of clause 5, wherein the reference electrode is electrically connected to a non-grounded node of a resistor electrically connected between the single current extraction electrode and electrical ground.

Clause 7: The method of any one of clauses 1 to 6, wherein determining whether the material includes the crack or other defect based on the voltage difference comprises determining that the material includes the crack or other defect in response to the voltage difference being a non-zero value.

Clause 8: The method of clause 7, wherein determining that the material includes the crack or other defect in response to the voltage difference being a non-zero value comprises determining that the material includes the crack or other defect in response to an absolute value of the voltage difference being greater than a threshold voltage value .

Clause 9: The method of any one of clause 1 to 8, wherein: determining the voltage difference between the first voltage measured using the first measurement electrode and the second voltage measured using the second measurement electrode comprises, while applying the electrical signal to the plurality of current injection electrodes, determining, for each respective measurement electrode set of a plurality of respective measurement electrode sets, a respective voltage difference between a respective first voltage measured using a respective first measurement electrode from the respective measurement electrode set and a respective second voltage measured using a respective second measurement electrode from the respective measurement electrode set; for each respective measurement electrode set, the respective first measurement electrode and the respective second measurement electrode are positioned substantially symmetrically with reference to the symmetry of the material; and determining whether the material includes a crack or other defect based on the respective voltage differences.

Clause 10: The method of clause 9, wherein a plurality of electrodes are distributed around a perimeter of the material, and wherein the plurality of electrodes include the plurality of current injection electrodes, the single current extraction electrode, and the plurality of respective measurement electrode sets.

Clause 1 1 : The method of any one of clauses 1 to 10, wherein determining whether the material includes the crack or other defect based on the voltage difference comprises: determining an adjusted voltage difference based on the voltage difference and a control voltage difference associated with the first and second measurement electrodes; and determining whether the material includes the crack or other defect based on the adjusted voltage difference.

Clause 12: A method for detecting a crack or defect in a material, the method comprising:

applying a first electrical signal to a plurality of current injection electrodes electrically coupled to the material, wherein the plurality of current injection electrodes are positioned substantially symmetrically with reference to a symmetry of the material; extracting the first electrical signal through a first current extraction electrode, wherein the first current extraction electrode is positioned at a first location of the material; while applying the first electrical signal to the plurality of current injection electrodes, determining a first voltage difference between a first voltage measured using a first measurement electrode and a second voltage measured using a second measurement electrode, wherein the first and second measurement electrodes are positioned substantially symmetrically with reference to the symmetry of the material; applying a second electrical signal to the plurality of current injection electrodes; extracting the second electrical signal through a second current extraction electrode, wherein the second current extraction electrode is positioned at a second location of the material, wherein the first and second locations are substantially symmetric with reference to the symmetry of the material; while applying the second electrical signal to the plurality of current injection electrodes, determining a second voltage difference between a third voltage measured using the first measurement electrode and a fourth voltage measured using the second measurement electrode; and determining whether the material includes a crack or other defect based on the first voltage difference and the second voltage difference.

Clause 13 : The method of clause 12, wherein: determining the first voltage difference between the first voltage measured using the first measurement electrode and the second voltage measured using the second measurement electrode comprises, while applying the first electrical signal to the plurality of current injection electrodes, determining the first voltage difference between a first differential voltage determined using the first measurement electrode and a third measurement electrode and a second differential voltage determined using the second measurement electrode and a fourth measurement electrode, wherein the third measurement electrode and the fourth measurement electrode are positioned substantially symmetrically with reference to the symmetry of the material; and determining the second voltage difference between the third voltage measured using the first measurement electrode and the secondvoltage measured using the fourth measurement electrode comprises, while applying the second electrical signal to plurality of current injection electrodes, determining a second voltage difference between a third differential voltage determined using the first measurement electrode and the third measurement electrode and a fourth differential voltage determined using the second measurement electrode and the fourth measurement electrode.

Clause 14: The method of clause 12 or 13, wherein the symmetry of the material is a point, a line, a plane, a curve, or a manifold, and wherein a single mathematical operation made with reference to the symmetry maps the first electrode to the second electrode.

Clause 15 : The method of any one of clauses 12 to 14, wherein the plurality of current injection electrodes is a first current injection electrode and a second current injection electrode.

Clause 16: The method of any one of clauses 12 to 15, wherein the first voltage is a first single- ended voltage measured using the first measurement electrode and a reference electrode, wherein the second voltage is a second single-ended voltage measured using the second measurement electrode and the reference electrode, wherein the third voltage is a third single-ended voltage measured using the first measurement electrode and the reference electrode, and wherein the fourth voltage is a fourth single- ended voltage measured using the second measurement electrode and the reference electrode.

Clause 17: The method of clause 16, wherein the reference electrode is electrically connected to a non-grounded node of a resistor electrically connected between the first and second current extraction electrodes and electrical ground. Clause 18: The method of any one of clauses 12 to 17, wherein determining whether the material includes the crack or other defect based on the first voltage difference and the second voltage difference comprises determining that the material includes the crack or other defect in response to a difference between the first voltage difference and the second voltage difference being a non-zero value.

Clause 19: The method of clause 18, wherein determining that the material includes the crack or other defect in response to the voltage difference being a non-zero value comprises determining that the material includes the crack or other defect in response to an absolute value of the difference between the first voltage difference and the second voltage difference being greater than a threshold voltage value.

Clause 20: The method of any one of clauses 12 to 19, wherein: determining the first voltage difference between the first voltage measured using the first measurement electrode and the second voltage measured using the second measurement electrode comprises, while applying the first electrical signal to the plurality of current injection electrodes, determining, for each respective measurement electrode set of a plurality of respective measurement electrode sets, a respective first voltage difference between a respective first voltage measured using a respective first measurement electrode from the respective measurement electrode set and a respective second voltage measured using a respective second measurement electrode from the respective measurement electrode set; for each respective measurement electrode set, the respective first measurement electrode and the respective second measurement electrodes are positioned substantially symmetrically with reference to the symmetry of the material; determining the second voltage difference between the third voltage measured using the first

measurement electrode and the fourth voltage measured using the second measurement electrode comprises, while applying the second electrical signal to the plurality of current injection electrodes, determining, for each respective measurement electrode set of the plurality of respective measurement electrode sets, a respective third voltage difference between a respective third voltage measured using the respective first measurement electrode from the respective measurement electrode set and a respective fourth voltage measured using the respective second measurement electrode from the respective measurement electrode set; and determining whether the material includes a crack or other defect based on the respective voltage differences.

Clause 21 : The method of claim 20, wherein a plurality of electrodes are distributed around a perimeter of the material, and wherein the plurality of electrodes include the plurality of current injection electrodes, the first and second current extraction electrodes, and the plurality of respective measurement electrode sets.

Clause 22: The method of any one of clauses 12 to 21, wherein determining whether the material includes the crack or other defect based on the first voltage difference and the second voltage difference comprises: determining a first adjusted voltage difference based on the first voltage difference and a control voltage difference associated with the first and second measurement electrodes and the first current extraction electrode; determining a second adjusted voltage difference based on the second voltage difference and a control voltage difference associated with the first and second measurement electrodes and second current extraction electrode; and determining whether the material includes the crack or other defect based on the first adjusted voltage difference and the second adjusted voltage difference.

Clause 23 : A system comprising: a set of N electrodes electrically coupled to a material; an electrical signal source; and a computing device configured to: cause the electrical signal source to apply an electrical signal to a plurality of current injection electrodes, wherein the plurality of current injection electrodes are positioned substantially symmetrically with reference to a symmetry of the material and are from the set of N electrodes; cause the electrical signal to be extracted through a single current extraction electrode, wherein the single current extraction electrode is positioned on the symmetry of the material and is from the set of N electrodes; while the electrical signal source is applying the electrical signal to the plurality of current injection electrodes, determine a voltage difference between a first voltage measured using a first measurement electrode and a second voltage measured using a second

measurement electrode, wherein the first and second measurement electrodes are positioned substantially symmetrically with reference to the symmetry of the material; and determine whether the material includes a crack or other defect based on the voltage difference.

Clause 24: The system of clause 23, wherein: the computing device is configured to determine the voltage difference between the first voltage measured using the first measurement electrode and the second voltage measured using the second measurement electrode by at least, while the electrical signal source is applying the electrical signal to the plurality of current injection electrodes, determining a voltage difference between a first differential voltage determined using the first measurement electrode and a third measurement electrode and a second differential voltage determined using the second measurement electrode and a fourth measurement electrode, wherein the third measurement electrode and the fourth measurement electrode are positioned substantially symmetrically with reference to the symmetry of the material.

Clause 25 : The system of clause 23 or 24, wherein the symmetry of the material is a point, a line, a plane, a curve, or a manifold, and wherein a single mathematical operation made with reference to the symmetry maps each electrode of the set of N electrodes to another of the electrodes of the set of N electrodes.

Clause 26: The system of any one of clauses 23 to 25, wherein the plurality of current injection electrodes is a first current injection electrode and a second current injection electrode.

Clause 27: The system of any one of clauses 23 to 26, wherein the first voltage is a first single- ended voltage measured using the first measurement electrode and a reference electrode, and wherein the second voltage is a second single-ended voltage measured using the second measurement electrode and the reference electrode.

Clause 28: The system of clause 27, wherein the reference electrode is electrically connected to a non-grounded node of a resistor electrically connected between the single current extraction electrode and electrical ground.

Clause 29: The system of any one of clauses 23 to 28, wherein the computing device is configured to determine whether the material includes the crack or other defect based on the voltage difference by at least determining that the material includes the crack or other defect in response to the voltage difference being a non-zero value.

Clause 30: The system of clause 29, wherein the computing device is configured to determine that the material includes the crack or other defect in response to the voltage difference being a non-zero value by at least determining that the material includes the crack or other defect in response to an absolute value of the voltage difference being greater than a threshold voltage value.

Clause 31 : The system of any one of clauses 23 to 30, wherein: the computing device is configured to determine the voltage difference between the first voltage measured using the first measurement electrode and the second voltage measured using the second measurement electrode by at least, while the electrical signal source is applying the electrical signal to the plurality of current injection electrodes, determining, for each respective measurement electrode set of a plurality of respective measurement electrode sets, a respective voltage difference between a respective first voltage measured using a respective first measurement electrode from the respective measurement electrode set and a respective second voltage measured using a respective second measurement electrode from the respective measurement electrode set; for each respective measurement electrode set, the respective first measurement electrode and the respective second measurement electrodes are positioned substantially symmetrically with reference to the symmetry of the material; and the computing device is configured to determine whether the material includes a crack or other defect based on the respective voltage differences.

Clause 32: The system of clause 31, wherein the set of N electrodes are distributed around a perimeter of the material, and wherein the set of N electrodes includes the plurality of current injection electrodes, the single current extraction electrode, and the plurality of respective measurement electrode sets.

Clause 33 : The system of any one of clauses 23 to 32, wherein the computing device is configured to determine whether the material includes the crack or other defect based on the voltage difference by at least: determining an adjusted voltage difference based on the voltage difference and a control voltage difference associated with the first and second measurement electrodes; and determining whether the material includes the crack or other defect based on the adjusted voltage difference.

Clause 34: A system comprising: a set of N electrodes electrically coupled to a material; an electrical signal source; and a computing device configured to: cause the electrical signal source to apply a first electrical signal to a plurality of current injection electrodes electrically coupled to the material, wherein the plurality of current injection electrodes are positioned substantially symmetrically with reference to a symmetry of the material and are from the set of N electrodes; cause the first electrical signal to be extracted through a first current extraction electrode, wherein the first current extraction electrode is positioned at a first location of the material and is from the set of N electrodes; while the electrical signal source is applying the first electrical signal to the plurality of current injection electrodes, determine a first voltage difference between a first voltage measured using a first measurement electrode and a second voltage measured using a second measurement electrode, wherein the first and second measurement electrodes are positioned substantially symmetrically with reference to the symmetry of the material; cause the electrical signal source to apply a second electrical signal to the plurality of current injection electrodes electrically coupled to the material; cause the second electrical signal to be extracted through a second current extraction electrode, wherein the second current extraction electrode is positioned at a second location of the material and is from the set of N electrodes, and wherein the first and second locations are substantially symmetric with reference to the symmetry of the material; while the electrical signal source is applying the second electrical signal to the plurality of current injection electrodes, determine a second voltage difference between a third voltage measured using the first measurement electrode and a fourth voltage measured using the second measurement electrode; and determine whether the material includes a crack or other defect based on the first voltage difference and the second voltage difference.

Clause 35 : The system of clause 34, wherein: the computing device is configured to determine the first voltage difference between the first voltage measured using the first measurement electrode and the second voltage measured using the second measurement electrode by at least, while the electrical signal source is applying the first electrical signal to the plurality of current injection electrodes, determining the first voltage difference between a first differential voltage determined using the first measurement electrode and a third measurement electrode and a second differential voltage determined using the second measurement electrode and a fourth measurement electrode, wherein the third measurement electrode and the fourth measurement electrode are positioned substantially symmetrically with reference to the symmetry of the material and are from the set of N electrodes; and the computing device is configured to determine the second voltage difference between the third voltage measured using the third measurement electrode and the fourth voltage measured using the fourth measurement electrode by at least, while the electrical signal source is applying the second electrical signal to the plurality of current injection electrodes, determining a second voltage difference between a third differential voltage determined using the first measurement electrode and the third measurement electrode and a fourth differential voltage determined using the second measurement electrode and the fourth measurement electrode.

Clause 36: The system of clause 34 or 35, wherein the symmetry of the material is a point, a line, a plane, a curve, or a manifold, and wherein a single mathematical operation made with reference to the symmetry maps each electrode of the set of N electrodes to another of the electrodes of the set of N electrodes.

Clause 37: The system of any one of clauses 34 to 36, wherein the plurality of current injection electrodes is a first current injection electrode and a second current injection electrode.

Clause 38: The system of any one of clauses 34 to 37, wherein the first voltage is a first single- ended voltage measured using the first measurement electrode and a reference electrode, wherein the second voltage is a second single-ended voltage measured using the second measurement electrode and the reference electrode, wherein the third voltage is a third single-ended voltage measured using the first measurement electrode and the reference electrode, and wherein the fourth voltage is a fourth single- ended voltage measured using the second measurement electrode and the reference electrode.

Clause 39: The system of clause 38, wherein the reference electrode is electrically connected to a non-grounded node of a resistor electrically connected between the first and second current extraction electrodes and electrical ground.

Clause 40: The system of any one of clauses 34 to 39, wherein the computing device is configured to determine whether the material includes the crack or other defect based on the first voltage difference and the second voltage difference by at least determining that the material includes the crack or other defect in response to a difference between the first voltage difference and the second voltage difference being a non-zero value.

Clause 41 : The system of clause 40, wherein the computing device is configured to determine that the material includes the crack or other defect in response to the voltage difference being a non-zero value by at least determining that the material includes the crack or other defect in response to an absolute value of the difference between the first voltage difference and the second voltage difference being greater than a threshold voltage value .

Clause 42: The system of any one of clauses 34 to 41, wherein: the computing device is configured to determine the first voltage difference between the first voltage measured using the first measurement electrode and the second voltage measured using the second measurement electrode by at least, while the electrical signal source is applying the first electrical signal to the plurality of current injection electrodes, determining, for each respective measurement electrode set of a plurality of respective measurement electrode sets, a respective first voltage difference between a respective first voltage measured using a respective first measurement electrode from the respective measurement electrode set and a respective second voltage measured using a respective second measurement electrode from the respective measurement electrode set; for each respective measurement electrode set, the respective first measurement electrode and the respective second measurement electrodes are positioned substantially symmetrically with reference to the symmetry of the material; the computing device is configured to determine the second voltage difference between the third voltage measured using the first measurement electrode and the fourth voltage measured using the second measurement electrode by at least, while the electrical signal source is applying the second electrical signal to the plurality of current injection electrodes, determining, for each respective measurement electrode set of the plurality of respective measurement electrode sets, a respective third voltage difference between a respective third voltage measured using the respective first measurement electrode from the respective measurement electrode set and a respective fourth voltage measured using the respective second measurement electrode from the respective measurement electrode set; and the computing device is configured to determine whether the material includes a crack or other defect based on the respective voltage differences.

Clause 43 : The system of clause 42, wherein the set of N electrodes are distributed around a perimeter of the material, and wherein the set of N electrodes includes the current extraction electrodes, the plurality of current injection electrodes, and the plurality of respective measurement electrode sets. Clause 44: The system of any one of clauses 34 to 43, wherein the computing device is configured to determine whether the material includes the crack or other defect based on the first voltage difference and the second voltage difference by at least: determining a first adjusted voltage difference based on the first voltage difference and a control voltage difference associated with the first and second measurement electrodes and the first current extraction electrode; determining a second adjusted voltage difference based on the second voltage difference and a control voltage difference associated with the first and second measurement electrodes and second current extraction electrode; and determining whether the material includes the crack or other defect based on the first adjusted voltage difference and the second adjusted voltage difference.

Various examples have been described. These and other examples are within the scope of the following claims.

Claims

WHAT IS CLAIMED IS:

1. A method for detecting a crack or defect in a material, the method comprising:

applying an electrical signal to a plurality of current injection electrodes electrically coupled to the material, wherein the plurality of current injection electrodes are positioned substantially

symmetrically with reference to a symmetry of the material;

extracting the electrical signal through a single current extraction electrode, wherein the single current extraction electrode is positioned on the symmetry of the material;

while applying the electrical signal to the plurality of current injection electrodes, determining a voltage difference between a first voltage measured using a first measurement electrode and a second voltage measured using a second measurement electrode, wherein the first and second measurement electrodes are positioned substantially symmetrically with reference to the symmetry of the material; and determining whether the material includes a crack or other defect based on the voltage difference.

2. The method of claim 1, wherein:

determining the voltage difference between the first voltage measured using the first

measurement electrode and the second voltage measured using the second measurement electrode comprises, while applying the electrical signal to the plurality of current injection electrodes, determining a voltage difference between a first differential voltage determined using the first measurement electrode and a third measurement electrode and a second differential voltage determined using the second measurement electrode and a fourth measurement electrode, wherein the third measurement electrode and the fourth measurement electrode are positioned substantially symmetrically with reference to the symmetry of the material.

3. The method of claim 1, wherein the symmetry of the material is a point, a line, a plane, a curve, or a manifold, and wherein a single mathematical operation made with reference to the symmetry maps the first electrode to the second electrode.

4. The method of claim 1, wherein the plurality of current injection electrodes is a first current injection electrode and a second current injection electrode.

5. The method of claim 1, wherein the first voltage is a first single-ended voltage measured using the first measurement electrode and a reference electrode, and wherein the second voltage is a second single-ended voltage measured using the second measurement electrode and the reference electrode.

6. The method of claim 5, wherein the reference electrode is electrically connected to a non- grounded node of a resistor electrically connected between the single current extraction electrode and electrical ground.

7. The method of claim 1, wherein determining whether the material includes the crack or other defect based on the voltage difference comprises determining that the material includes the crack or other defect in response to the voltage difference being a non-zero value.

8. The method of claim 7, wherein determining that the material includes the crack or other defect in response to the voltage difference being a non-zero value comprises determining that the material includes the crack or other defect in response to an absolute value of the voltage difference being greater than a threshold voltage value.

9. The method of claim 1, wherein:

measurement electrode and the second voltage measured using the second measurement electrode comprises, while applying the electrical signal to the plurality of current injection electrodes, determining, for each respective measurement electrode set of a plurality of respective measurement electrode sets, a respective voltage difference between a respective first voltage measured using a respective first measurement electrode from the respective measurement electrode set and a respective second voltage measured using a respective second measurement electrode from the respective measurement electrode set;

for each respective measurement electrode set, the respective first measurement electrode and the respective second measurement electrode are positioned substantially symmetrically with reference to the symmetry of the material; and

determining whether the material includes a crack or other defect based on the respective voltage differences.

10. The method of claim 9, wherein a plurality of electrodes are distributed around a perimeter of the material, and wherein the plurality of electrodes include the plurality of current injection electrodes, the single current extraction electrode, and the plurality of respective measurement electrode sets.

1 1. The method of claim 1, wherein determining whether the material includes the crack or other defect based on the voltage difference comprises:

determining an adjusted voltage difference based on the voltage difference and a control voltage difference associated with the first and second measurement electrodes; and

determining whether the material includes the crack or other defect based on the adjusted voltage difference.

12. A method for detecting a crack or defect in a material, the method comprising: applying a first electrical signal to a plurality of current injection electrodes electrically coupled to the material, wherein the plurality of current injection electrodes are positioned substantially symmetrically with reference to a symmetry of the material;

extracting the first electrical signal through a first current extraction electrode, wherein the first current extraction electrode is positioned at a first location of the material;

while applying the first electrical signal to the plurality of current injection electrodes, determining a first voltage difference between a first voltage measured using a first measurement electrode and a second voltage measured using a second measurement electrode, wherein the first and second measurement electrodes are positioned substantially symmetrically with reference to the symmetry of the material;

applying a second electrical signal to the plurality of current injection electrodes;

extracting the second electrical signal through a second current extraction electrode, wherein the second current extraction electrode is positioned at a second location of the material, wherein the first and second locations are substantially symmetric with reference to the symmetry of the material;

while applying the second electrical signal to the plurality of current injection electrodes, determining a second voltage difference between a third voltage measured using the first measurement electrode and a fourth voltage measured using the second measurement electrode; and

determining whether the material includes a crack or other defect based on the first voltage difference and the second voltage difference.

13. The method of claim 12, wherein:

determining the first voltage difference between the first voltage measured using the first measurement electrode and the second voltage measured using the second measurement electrode comprises, while applying the first electrical signal to the plurality of current injection electrodes, determining the first voltage difference between a first differential voltage determined using the first measurement electrode and a third measurement electrode and a second differential voltage determined using the second measurement electrode and a fourth measurement electrode, wherein the third measurement electrode and the fourth measurement electrode are positioned substantially symmetrically with reference to the symmetry of the material; and

determining the second voltage difference between the third voltage measured using the first measurement electrode and the fourth voltage measured using the second measurement electrode comprises, while applying the second electrical signal to plurality of current injection electrodes, determining a second voltage difference between a third differential voltage determined using the first measurement electrode and the third measurement electrode and a fourth differential voltage determined using the second measurement electrode and the fourth measurement electrode.

14. The method of claim 12, wherein the symmetry of the material is a point, a line, a plane, a curve, or a manifold, and wherein a single mathematical operation made with reference to the symmetry maps the first electrode to the second electrode.

15. The method of claim 12, wherein the plurality of current injection electrodes is a first current injection electrode and a second current injection electrode.

16. The method of claim 12, wherein the first voltage is a first single-ended voltage measured using the first measurement electrode and a reference electrode, wherein the second voltage is a second single- ended voltage measured using the second measurement electrode and the reference electrode, wherein the third voltage is a third single-ended voltage measured using the first measurement electrode and the reference electrode, and wherein the fourth voltage is a fourth single-ended voltage measured using the second measurement electrode and the reference electrode.

17. The method of claim 16, wherein the reference electrode is electrically connected to a non- grounded node of a resistor electrically connected between the first and second current extraction electrodes and electrical ground.

18. The method of claim 12, wherein determining whether the material includes the crack or other defect based on the first voltage difference and the second voltage difference comprises determining that the material includes the crack or other defect in response to a difference between the first voltage difference and the second voltage difference being a non-zero value.

19. The method of claim 18, wherein determining that the material includes the crack or other defect in response to the voltage difference being a non-zero value comprises determining that the material includes the crack or other defect in response to an absolute value of the difference between the first voltage difference and the second voltage difference being greater than a threshold voltage value.

20. The method of claim 12, wherein:

determining the first voltage difference between the first voltage measured using the first measurement electrode and the second voltage measured using the second measurement electrode comprises, while applying the first electrical signal to the plurality of current injection electrodes, determining, for each respective measurement electrode set of a plurality of respective measurement electrode sets, a respective first voltage difference between a respective first voltage measured using a respective first measurement electrode from the respective measurement electrode set and a respective second voltage measured using a respective second measurement electrode from the respective measurement electrode set; for each respective measurement electrode set, the respective first measurement electrode and the respective second measurement electrodes are positioned substantially symmetrically with reference to the symmetry of the material;

determining the second voltage difference between the third voltage measured using the first measurement electrode and the fourth voltage measured using the second measurement electrode comprises, while applying the second electrical signal to the plurality of current injection electrodes, determining, for each respective measurement electrode set of the plurality of respective measurement electrode sets, a respective third voltage difference between a respective third voltage measured using the respective first measurement electrode from the respective measurement electrode set and a respective fourth voltage measured using the respective second measurement electrode from the respective measurement electrode set; and

21. The method of claim 20, wherein a plurality of electrodes are distributed around a perimeter of the material, and wherein the plurality of electrodes include the plurality of current injection electrodes, the first and second current extraction electrodes, and the plurality of respective measurement electrode sets.

22. The method of claim 12, wherein determining whether the material includes the crack or other defect based on the first voltage difference and the second voltage comprises:

determining a first adjusted voltage difference based on the first voltage difference and a control voltage difference associated with the first and second measurement electrodes and the first current extraction electrode;

determining a second adjusted voltage difference based on the second voltage difference and a control voltage difference associated with the first and second measurement electrodes and second current extraction electrode; and

determining whether the material includes the crack or other defect based on the first adjusted voltage difference and the second adjusted voltage difference.

23. A system comprising:

a set of N electrodes electrically coupled to a material;

an electrical signal source; and

a computing device configured to:

cause the electrical signal source to apply an electrical signal to a plurality of current injection electrodes, wherein the plurality of current injection electrodes are positioned substantially symmetrically with reference to a symmetry of the material and are from the set of N electrodes; cause the electrical signal to be extracted through a single current extraction electrode, wherein the single current extraction electrode is positioned on the symmetry of the material and is from the set of N electrodes;

while the electrical signal source is applying the electrical signal to the plurality of current injection electrodes, determine a voltage difference between a first voltage measured using a first measurement electrode and a second voltage measured using a second measurement electrode, wherein the first and second measurement electrodes are positioned substantially symmetrically with reference to the symmetry of the material; and

determine whether the material includes a crack or other defect based on the voltage difference.

24. The system of claim 23, wherein:

the computing device is configured to determine the voltage difference between the first voltage measured using the first measurement electrode and the second voltage measured using the second measurement electrode by at least, while the electrical signal source is applying the electrical signal to the plurality of current injection electrodes, determining a voltage difference between a first differential voltage determined using the first measurement electrode and a third measurement electrode and a second differential voltage determined using the second measurement electrode and a fourth measurement electrode, wherein the third measurement electrode and the fourth measurement electrode are positioned substantially symmetrically with reference to the symmetry of the material.

25. The system of claim 23, wherein the symmetry of the material is a point, a line, a plane, a curve, or a manifold, and wherein a single mathematical operation made with reference to the symmetry maps each electrode of the set of N electrodes to another of the electrodes of the set of N electrodes.

26. The system of claim 23, wherein the plurality of current injection electrodes is a first current injection electrode and a second current injection electrode.

27. The system of claim 23, wherein the first voltage is a first single-ended voltage measured using the first measurement electrode and a reference electrode, and wherein the second voltage is a second single-ended voltage measured using the second measurement electrode and the reference electrode.

28. The system of claim 27, wherein the reference electrode is electrically connected to a non- grounded node of a resistor electrically connected between the single current extraction electrode and electrical ground.

29. The system of claim 23, wherein the computing device is configured to determine whether the material includes the crack or other defect based on the voltage difference by at least determining that the material includes the crack or other defect in response to the voltage difference being a non-zero value.

30. The system of claim 29, wherein the computing device is configured to determine that the material includes the crack or other defect in response to the voltage difference being a non-zero value by at least determining that the material includes the crack or other defect in response to an absolute value of the voltage difference being greater than a threshold voltage value.

31. The system of claim 23, wherein:

the computing device is configured to determine the voltage difference between the first voltage measured using the first measurement electrode and the second voltage measured using the second measurement electrode by at least, while the electrical signal source is applying the electrical signal to the plurality of current injection electrodes, determining, for each respective measurement electrode set of a plurality of respective measurement electrode sets, a respective voltage difference between a respective first voltage measured using a respective first measurement electrode from the respective measurement electrode set and a respective second voltage measured using a respective second measurement electrode from the respective measurement electrode set;

for each respective measurement electrode set, the respective first measurement electrode and the respective second measurement electrodes are positioned substantially symmetrically with reference to the symmetry of the material; and

the computing device is configured to determine whether the material includes a crack or other defect based on the respective voltage differences.

32. The system of claim 31, wherein the set of N electrodes are distributed around a perimeter of the material, and wherein the set of N electrodes includes the plurality of current injection electrodes, the single current extraction electrode, and the plurality of respective measurement electrode sets.

33. The system of claim 23, wherein the computing device is configured to determine whether the material includes the crack or other defect based on the voltage difference by at least:

34. A system comprising:

a set of N electrodes electrically coupled to a material;

an electrical signal source; and a computing device configured to:

cause the electrical signal source to apply a first electrical signal to a plurality of current injection electrodes electrically coupled to the material, wherein the plurality of current injection electrodes are positioned substantially symmetrically with reference to a symmetry of the material and are from the set of N electrodes;

cause the first electrical signal to be extracted through a first current extraction electrode, wherein the first current extraction electrode is positioned at a first location of the material and is from the set of N electrodes;

while the electrical signal source is applying the first electrical signal to the plurality of current injection electrodes, determine a first voltage difference between a first voltage measured using a first measurement electrode and a second voltage measured using a second measurement electrode, wherein the first and second measurement electrodes are positioned substantially symmetrically with reference to the symmetry of the material;

cause the electrical signal source to apply a second electrical signal to the plurality of current injection electrodes electrically coupled to the material;

cause the second electrical signal to be extracted through a second current extraction electrode, wherein the second current extraction electrode is positioned at a second location of the material and is from the set of N electrodes, and wherein the first and second locations are substantially symmetric with reference to the symmetry of the material;

while the electrical signal source is applying the second electrical signal to the plurality of current injection electrodes, determine a second voltage difference between a third voltage measured using the first measurement electrode and a fourth voltage measured using the second measurement electrode; and

determine whether the material includes a crack or other defect based on the first voltage difference and the second voltage difference.

35. The system of claim 34, wherein:

the computing device is configured to determine the first voltage difference between the first voltage measured using the first measurement electrode and the second voltage measured using the second measurement electrode by at least, while the electrical signal source is applying the first electrical signal to the plurality of current injection electrodes, determining the first voltage difference between a first differential voltage determined using the first measurement electrode and a third measurement electrode and a second differential voltage determined using the second measurement electrode and a fourth measurement electrode, wherein the third measurement electrode and the fourth measurement electrode are positioned substantially symmetrically with reference to the symmetry of the material and are from the set of N electrodes; and

the computing device is configured to determine the second voltage difference between the third voltage measured using the first measurement electrode and the fourth voltage measured using the second measurement electrode by at least, while the electrical signal source is applying the second electrical signal to the plurality of current injection electrodes, determining a second voltage difference between a third differential voltage determined using the first measurement electrode and the third measurement electrode and a fourth differential voltage determined using the second measurement electrode and the fourth measurement electrode.

36. The system of claim 34, wherein the symmetry of the material is a point, a line, a plane, a curve, or a manifold, and wherein a single mathematical operation made with reference to the symmetry maps each electrode of the set of N electrodes to another of the electrodes of the set of N electrodes.

37. The system of claim 34, wherein the plurality of current injection electrodes is a first current injection electrode and a second current injection electrode.

38. The system of claim 34, wherein the first voltage is a first single-ended voltage measured using the first measurement electrode and a reference electrode, wherein the second voltage is a second single- ended voltage measured using the second measurement electrode and the reference electrode, wherein the third voltage is a third single-ended voltage measured using the first measurement electrode and the reference electrode, and wherein the fourth voltage is a fourth single-ended voltage measured using the second measurement electrode and the reference electrode.

39. The system of claim 38, wherein the reference electrode is electrically connected to a non- grounded node of a resistor electrically connected between the first and second current extraction electrodes and electrical ground.

40. The system of claim 34, wherein the computing device is configured to determine whether the material includes the crack or other defect based on the first voltage difference and the second voltage difference by at least determining that the material includes the crack or other defect in response to a difference between the first voltage difference and the second voltage difference being a non-zero value.

41. The system of claim 40, wherein the computing device is configured to determine that the material includes the crack or other defect in response to the voltage difference being a non-zero value by at least determining that the material includes the crack or other defect in response to an absolute value of the difference between the first voltage difference and the second voltage difference being greater than a threshold voltage value.

42. The system of claim 34, wherein:

the computing device is configured to determine the first voltage difference between the first voltage measured using the first measurement electrode and the second voltage measured using the second measurement electrode by at least, while the electrical signal source is applying the first electrical signal to the plurality of current injection electrodes, determining, for each respective measurement electrode set of a plurality of respective measurement electrode sets, a respective first voltage difference between a respective first voltage measured using a respective first measurement electrode from the respective measurement electrode set and a respective second voltage measured using a respective second measurement electrode from the respective measurement electrode set;

for each respective measurement electrode set, the respective first measurement electrode and the respective second measurement electrodes are positioned substantially symmetrically with reference to the symmetry of the material;

the computing device is configured to determine the second voltage difference between the third voltage measured using the first measurement electrode and the fourth voltage measured using the second measurement electrode by at least, while the electrical signal source is applying the second electrical signal to the plurality of current injection electrodes, determining, for each respective measurement electrode set of the plurality of respective measurement electrode sets, a respective third voltage difference between a respective third voltage measured using the respective first measurement electrode from the respective measurement electrode set and a respective fourth voltage measured using the respective second measurement electrode from the respective measurement electrode set; and

43. The system of claim 42, wherein the set of N electrodes are distributed around a perimeter of the material, and wherein the set of N electrodes includes the current extraction electrodes, the plurality of current injection electrodes, and the plurality of respective measurement electrode sets.

44. The system of claim 34, wherein the computing device is configured to determine whether the material includes the crack or other defect based on the first voltage difference and the second voltage by at least: