JP5354287B2 - Crack area ratio calculation method and apparatus - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a cracked area rate calculation method and device, which can quantitatively and continuously measure a cracked area rate of a conductive part having electric conductivity such as a joint. <P>SOLUTION: The cracked area rate calculation method for calculating the cracked area rate of the conductive part having electric conductivity includes: a relational expression setting step of setting a relational expression between a resistance change and the cracked area rate based on a specific resistance value of the conductive part determined beforehand; a resistance change measuring step of measuring a resistance change of the conductive part; and a cracked area rate calculation step of calculating the cracked area rate of the conductive part from the resistance change measured in the resistance change measuring step, based on the relational expression set in the relational expression setting step. <P>COPYRIGHT: (C)2011,JPO&amp;INPIT

Description

  The present invention relates to a method and apparatus for measuring the crack area ratio of a conductive part such as solder.

  Conventionally, for example, various methods for evaluating the life of a solder joint in a circuit have been proposed. The joining portion has electrical conductivity for joining, for example, an element and a substrate in a circuit. The joint may crack due to thermal fatigue and break. A temperature cycle test, life evaluation, and the like are performed on the joint.

  As an evaluation method or an evaluation apparatus for a joint portion, for example, there are those disclosed in Japanese Unexamined Patent Application Publication No. 2007-255925 (Patent Document 1) and Japanese Unexamined Patent Application Publication No. 2007-255926 (Patent Document 2). In these joint evaluation methods, the resistance value of the joint can be measured, and the life close to fracture can be measured from a significant change (inflection point) of the resistance value.

JP 2007-255925 A JP 2007-255926 A

  However, the above evaluation method cannot quantitatively detect the crack growth characteristics before the inflection point. In addition, in order to investigate the growth characteristics of this crack, it is necessary to conduct post-evaluation (actual measurement) by measuring the crack length and crack area by cross-sectional observation and fracture surface observation after the test. Labor and time were required. Furthermore, in the above evaluation method, the data obtained as a result of the ex-post evaluation is only one point data of a specific number of cycles, and it is extremely difficult to measure the continuous crack propagation behavior during the test.

  Here, in the measurement object, the crack progresses in a planar shape, and the degree of progress of the crack can be represented by a crack area ratio (crack progress ratio). The crack area ratio is the ratio of the crack area to the total cross-sectional area of the cross section cut along the crack path. The larger the crack area ratio, the more the crack is developed.

  The present invention has been made in view of such circumstances, and a crack area ratio measuring method capable of quantitatively and continuously measuring the crack area ratio of a conductive portion having electrical conductivity such as a solder joint. And an object to provide an apparatus.

The crack area ratio calculation method of the present invention is a crack area ratio calculation method for calculating the crack area ratio of a measurement object having electrical conductivity, and is a portion where a crack propagation of the measurement object is expected. A specific resistance value calculating step for obtaining a specific resistance value when there is no crack , and a relational equation setting step for setting a relational expression between the resistance change and the crack area ratio based on the specific resistance value when there is no crack in the crack propagation portion When the resistance change measurement step of measuring the resistance change of the crack growth unit, based on a relationship formula set in relation setting step, a crack area ratio of the crack propagation portion from the measured change in resistance resistance change measurement steps And calculating a crack area ratio calculation step.

By using the relational expression between the resistance change and the crack area ratio, the crack area ratio from time to time can be obtained simply by actually measuring the resistance change of the measurement object . That is, according to this method, the crack area ratio of the measurement object can be measured quantitatively and continuously. It should be noted that the specific resistance value of the crack propagation part necessary for the relational expression is a value corresponding to the initial resistance value of the crack propagation part in a state where there is no crack, and is a preliminary experiment (calculation by the relational expression or direct measurement) A value obtained in advance by calculation from the value is used.

Here, the relational expression is preferably F = 1 / (1 + Ro / ΔR) where F is the crack area ratio, ΔR is the resistance change, and Ro is the specific resistance value when there is no crack in the crack propagation portion. . This formula is an original formula that quantitatively clarifies the relationship between the resistance change and the crack area ratio by theoretical calculation using an equivalent circuit model and experimental support. This makes it possible to calculate the crack area ratio more accurately.

Here, when a plurality of measurement objects (n: n is a natural number of 2 or more) are electrically connected in series in one circuit, it is preferable to calculate the effective crack area ratio as the crack area ratio. The effective crack area ratio is a crack area ratio calculated by assuming that all measurement objects connected in series in the circuit are one virtual conductive portion. The resistance of the virtual conductive portion is a value equivalently representing the resistance of a plurality of measurement objects connected in series with one resistance, that is, the total resistance of the measurement objects . Therefore, when calculating the effective crack area ratio, in the above relational expression, ΔR is the total resistance change of each measurement object in the circuit, and Ro is the crack of each crack propagation portion in the circuit. It is the sum of the specific resistance values when there is no. Note that the total ΣRoi of the specific resistance values Roi (i = 1 to n) when there is no crack in each crack propagation portion in the circuit is also referred to as an effective specific resistance value Roe. In the above method, the effective specific resistance value Roe can be obtained from the specific resistance value when there is no crack in each crack propagation portion , regardless of whether or not the materials of the respective measurement objects are the same. In this method, when a plurality of measurement objects are connected in series , the resistance change uses the total value of the resistance changes of all the measurement objects .

Here, when the specific resistance value when there is no crack of one crack progressing portion is obtained, the specific resistance value when there is no crack of another crack progressing portion made of the same material as the measurement object is the crack path It is preferable to obtain using the ratio of the cross-sectional area of the cross section along the line. That is, the present method, the cross-sectional area of the cross section along the crack path of the first measurement object A1, the resistivity of the absence crack crack growth of the first measurement object Ro1, first If the cross-sectional area of the cross section along the crack path of the second measurement object made of the same material as the measurement object is A2, there is no crack in the crack propagation portion of the second measurement object in the specific resistance value calculating step. The specific resistance value Ro2 at that time is preferably calculated as Ro2 = Ro1 × (A1 / A2). Thus, for the measurement object of the same material as the measuring object already known, we found there is no need to determine the specific resistance value when there is no crack crack growth unit by greatly reduces the work effort and time be able to.

Here, a case is considered in which a plurality of measurement objects exist in a circuit in a state of being electrically connected in series, and the measurement objects are all of the same material and the same connection state. The same connection state means, for example, a state in which a plurality of measurement objects are bonded to the same (same type) chip on the same substrate, and each measurement object has the same bonding area to bond the substrate and the chip. means. In this case, if the crack area ratio of each crack propagation portion is obtained by actual measurement, the effective crack area ratio can be obtained using the crack area ratio, and the effective specific resistance value can be calculated from the effective crack area ratio.

That is, wood charge and the measurement object in the same n number connection state are electrically connected in series in the circuit, the crack growth of the crack area ratio Fi (i = 1~n) are been determined by actual measurement In this case, the specific resistance value calculating step calculates the effective crack area ratio Fe by calculating the effective crack area ratio Fe by n / (1-Fe) = Σ {1 / (1-Fi)}, (i = 1 to n). From the effective crack area ratio Fe calculated in the step, the effective crack area ratio calculation step, and the resistance change ΔR (actually measured value) that is the sum of the resistance changes of all the crack propagation portions in the circuit, the effective specific resistance value Roe is And an effective specific resistance value calculating step of calculating using Fe = 1 / (1 + Roe / ΔR). Thereby, the effective specific resistance value can be calculated from the crack area ratio measured.

In addition, the measurement object should just have an electrical conductivity, and this method can be used for the crack growth evaluation of everything which has an electrical conductivity. The measurement object may be a junction in a circuit. For example, a solder crack growth test can be performed by this method on a wiring board on which a semiconductor chip or the like is mounted by solder.

By the way, this invention can be described also as an apparatus which calculates a crack area ratio using the above-mentioned method. That is, the crack area ratio calculation apparatus of the present invention is a crack area ratio calculation apparatus that calculates the crack area ratio of a measurement object having electrical conductivity, and is a crack that is a portion where crack propagation of the measurement object is expected. A resistance change measurement unit that measures the resistance change of the progressing part , and a relational expression between the resistance change and the crack area ratio, which is set using a specific resistance value obtained when there is no crack of the crack progressing part obtained in advance. And a crack area rate calculation unit that calculates a crack area rate of the crack propagation portion from the resistance change measured by the resistance change measurement unit. The relational expression is preferably F = 1 / (1 + Ro / ΔR). This also exhibits the same effect as described above.

The crack area ratio calculation method and apparatus according to the present invention calculate a crack area ratio (crack progress rate) based on a change in electrical resistance, but thermal resistance may be used instead of electrical resistance. That is, in this case, the specific resistance value is the specific resistance value of the thermal resistance, and the resistance change is a thermal resistance change. According to this, the measurement object (crack generation site, thermal resistance measurement site) is not limited to having conductivity. In addition, a general method can be used for the measurement of the thermal resistance, and for example, it can be measured from a temperature change of a part sandwiching the crack part. The relational expression here is preferably F = 1 / (1 + Ro / ΔR), where Ro is the specific resistance value of the thermal resistance when there is no crack in the crack propagation portion, and ΔR is the change in thermal resistance.

According to the crack area ratio calculation method and apparatus of the present invention, the crack area ratio of a measurement object having electrical conductivity such as a joint can be quantitatively and continuously measured. Moreover, in the said method and apparatus, it can replace with an electrical resistance, and can determine the crack area ratio of all the measurement objects by using a thermal resistance.

It is a graph which shows the relationship between a junction area ratio and resistance change. It is a graph which shows the relationship between a crack area ratio and resistance change. It is a graph which shows the relationship between a crack area ratio and resistance change (logarithm). It is a flowchart which shows the flow of the crack area ratio calculation method of 1st embodiment. It is a schematic diagram which shows the crack area ratio calculation apparatus of 1st embodiment. 3 is a schematic diagram showing a solder joint component Z. FIG. It is a flowchart which shows the flow of the crack area ratio calculation method of 2nd embodiment. It is a graph which shows the relationship between the crack area ratio and resistance change in 2nd embodiment.

  Next, the present invention will be described in more detail with reference to embodiments.

First, a relational expression between resistance change and crack area ratio will be described with reference to FIGS. 1 to 3, taking a solder joint as an example of a conductive part having electrical conductivity (corresponding to “measurement object”) . FIG. 1 is a graph showing the relationship between the junction area ratio and the resistance change. FIG. 2 is a graph showing the relationship between the crack area ratio and the resistance change. FIG. 3 is a graph showing the relationship between the crack area ratio and resistance change (logarithm).

  In general, the resistance R is proportional to the length of the current path and inversely proportional to the cross-sectional area. From this relationship, when a crack occurs, the resistance is expected to increase because the cross-sectional area decreases accordingly. However, the length of the current path interrupted by the crack cannot be obtained because the width of the crack is unknown. In addition, since the width of the crack is usually extremely small, it is assumed that the electric flow around the crack is complicated. Therefore, it was unclear whether the above general relationship regarding resistance could be applied to a current path having a crack.

  Therefore, in the present invention, a new concept of the specific resistance value of the conductive portion (crack propagation portion) is introduced, and the following equation (1) is obtained, in which the resistance value is obtained even if the width of the crack is unknown.

R = Ro × (Ao / A) (1)
Here, Ro is a specific resistance value of the solder joint, A is a cross-sectional area of the solder joint along the crack path, and Ao is a cross-sectional area of the solder joint along the crack path when there is no crack. It is. When a crack occurs, A becomes smaller by the cross-sectional area of the crack portion. The path of the crack can be assumed in advance by the joining state of the solder joint portion, a preliminary experiment, or the like.

And resistance change (DELTA) R is (DELTA) R = R-Ro, This Formula is from Formula (1),
ΔR = Ro / (A / Ao) −Ro (2)
And can be transformed. Here, A / Ao represents the junction area ratio, and the relationship between the junction area ratio and the resistance change is illustrated in FIG.

Here, the relationship between the crack area ratio F and the cross-sectional areas A and Ao is as follows:
F = 1−A / Ao (3)
It becomes. From the equations (2) and (3), between the crack area ratio F and the resistance change ΔR,
F = 1 / (1 + Ro / ΔR) (4)
The following relational expression holds. That is, the relational expression between the resistance change and the crack area ratio can be expressed by Expression (4). This relationship is illustrated in FIG. In FIGS. 1 and 2, Ro is 0.8 mΩ.

  Also, the change in resistance on the vertical axis in FIG. 2 is expressed in logarithm, and the above relationship is illustrated for various specific resistance values Ro (0.8 mΩ, 0.2 mΩ, 0.05 mΩ) as shown in FIG. As shown in FIG. 3, it can be seen that there is almost a linear relationship between the logarithmic value (vertical axis) of the resistance change indicating a minute resistance change and the crack area ratio (horizontal axis). Therefore, the crack area ratio can be obtained from the measurement value of this minute resistance change. FIG. 3 illustrates a case where the specific resistance values differ by 16 times. From this, it can be seen that the relationship between the resistance change and the crack area ratio depends on the specific resistance value, but a slight difference in the specific resistance value does not make a large difference in the calculation accuracy of the crack area ratio. That is, the above relationship is insensitive to slight differences in Ro, and it is not necessary to use a specific resistance value measured with high accuracy. In addition, for example, even when the crack path of the joint has changed, the error of the crack area ratio is small.

  The specific resistance value Ro of the solder joint can be obtained by using equation (4) from the relationship between the crack area ratio F and the measured data of the resistance change ΔR. For simplicity, it can also be obtained directly by actual measurement. From the viewpoint of error, it is preferable to obtain from equation (4).

In addition, when measuring the resistance of a plurality of solder joints connected in series, the effective crack area ratio Fe,
Fe = 1 / (1 + Roe / ΔR) (5)
It becomes. Here, Roe is an effective value of the specific resistance value (effective specific resistance value), and since it is connected in series,
Roe = ΣRoi, (i = 1 to n) (6)
The relationship holds. These effective values Fe and Roe mean values when a circuit having a plurality of resistors (junction portions) connected in series is replaced with one resistance circuit (virtual junction portion). The effective specific resistance value Roe of the entire joint used in Expression (5) can be obtained from each specific resistance value Roi of the joint based on Expression (6). Each specific resistance value Roi can be obtained by direct measurement or by using equation (4) from the relationship between crack area ratio and measured data of resistance change.

  In addition, when a plurality of joints having the same material and joint state are connected in series, the effective specific resistance value Fe obtained from the crack area ratio Fi (actually measured value) of each joint using the following formula (7): The effective specific resistance value Roe may be obtained from the relationship (equation (5)) of the actually measured value of the resistance change ΔR.

n / (1-Fe) = Σ {1 / (1-Fi)}, (i = 1 to n) (7)
In addition, for joints of the same material that differ only in cross-sectional area along the crack path, the specific resistance value Roj is not actually measured,
Roj = Roi × (A1 / A2) (8)
Can be used to calculate.

  As described above, the crack area ratio of the joint can be calculated quantitatively and continuously by the above relational expression. In addition, the said relational expression is applicable not only to a junction part but to what has electrical conductivity.

<First embodiment>
Here, the case where this invention is applied to the crack growth test of a test piece is demonstrated with reference to FIG. 4 and FIG. FIG. 4 is a flowchart showing the flow of the crack area ratio calculation method of the first embodiment. FIG. 5 is a schematic diagram showing the crack area ratio calculation apparatus 1.

The test piece (corresponding to the “ measurement object ” in the present invention) has electrical conductivity and is made of aluminum here. The calculation method of the crack area ratio of the test piece is as follows.

  As shown in FIG. 4, first, the specific resistance value Ro of the test piece is obtained in advance by actual measurement (S401). Specifically, the specific resistance value is obtained from Equation (4) by actually measuring the crack area ratio and resistance change of the test piece by a preliminary test. In addition, for simplicity, the initial resistance value of a portion where crack growth of a test piece without a crack is expected may be actually measured to obtain a specific resistance value. Here, it calculates | requires using Formula (4) from the relationship between the measurement data of the crack area ratio F and resistance change (DELTA) R.

  The initial resistance value of the test piece without cracks may be measured, or the crack area ratio and resistance change of the test piece may be measured by a preliminary test and calculated from the equation (5). Here, the resistance when a current is passed from one end of the test piece to the other end is measured.

Subsequently, the Motoma' intrinsic resistance Ro into equation (4), to set the relationship of the resistance change and crack area ratio (S402). Subsequently, a thermal cycle test is applied to the test piece, and the resistance change ΔR of the test piece is measured (S403). Subsequently, the crack area ratio F is calculated from the resistance change ΔR based on the equation (4) (S404). When the calculation of the crack area ratio is continued (S405: No), the resistance change is continuously monitored, and the crack area ratio is calculated from the resistance change. The crack area ratio can be calculated as long as the resistance change of the test piece is known, for example, during a cooling cycle test or during actual use as a part. However, if the resistance value has temperature dependence, it is naturally necessary to obtain a resistance change under the same temperature.

  According to this method, the crack area ratio can be calculated continuously and quantitatively. Note that once the specific resistance value Ro is obtained, the value can be used for the same test piece, and it is not necessary to perform S401. Further, when only the cross-sectional areas along the crack path are different, the specific resistance value can be calculated using Expression (8).

  The crack area ratio can be calculated by a crack area ratio calculation apparatus using the above method. As shown in FIG. 5, the crack area ratio calculation device 1 includes a resistance change measurement unit 2 and a crack area ratio calculation unit 3. The resistance change measuring unit 2 measures a resistance change of a measurement target (here, a test piece), and is a known measuring instrument. The crack area ratio calculation unit 3 is an arithmetic device such as a computer, and is set to calculate the above relational expression. According to the crack area ratio calculation apparatus 1, this method can be executed, and the same effect as described above is exhibited.

<Second embodiment>
Next, the present invention will be described with reference to FIGS. 6 to 8 by taking an example of crack propagation measurement due to thermal fatigue of a solder joint. FIG. 6 is a schematic diagram showing the solder joint component Z. As shown in FIG. FIG. 7 is a flowchart showing the flow of the crack area ratio calculation method of the second embodiment. FIG. 8 is a graph showing the relationship between the crack area ratio and the resistance change in the second embodiment.

  As shown in FIG. 6, the solder joint component Z includes a substrate 4, copper wirings 51 and 52 disposed on the substrate 4, solder joint portions 61 and 62, and a chip resistor 7.

  The solder joint portion 61 is solder, and joins the copper wiring 51 and the chip resistor 7. The solder joint portion 62 is solder, and joins the copper wiring 52 and the chip resistor 7. That is, the solder joint portions 61 and 62 are made of the same material and are in the same connection state. Specifically, the solder joints 61 and 62 are in contact with the lower surface and side surfaces of the end of the chip resistor 7, and are in contact with the upper surface of the copper wirings 51 and 52. The joint areas of the solder joint portions 61 and 62 to the other members are substantially the same.

  Similarly, each of the solder joint portions 61 and 62 has a shape having a portion under the chip resistor 7 and a half-mountain fillet portion. Further, in the solder joint component Z, the solder joint portion 61 and the solder joint portion 62 are electrically connected in series. As an example, a crack path assumed in the solder joint portion 61 is indicated by a broken line.

  In the second embodiment, the resistance is measured over the entire circuit (solder joint component Z) in which the solder joint portions 61 and 62 are connected in series. Other than the solder joints 61 and 62, since no crack is generated, other resistance components in the wiring path are considered to be constant. Therefore, by measuring the resistance change of the entire circuit, the sum of the resistance changes of the solder joints 61 and 62 can be measured.

  Specifically, assuming that the resistance of the copper wiring 51 (52) is Ra (Rb), the resistance of the solder joint 61 (62) is R1 (R2), and the resistance Rc of the chip resistor 7, the resistance of the solder joint component Z is R = Ra + R1 + Rc + R2 + Rb. The resistance changes ΔR1 and ΔR2 of the solder joint portions 61 and 62 can be measured by the resistance change ΔR of the solder joint component Z (ΔR = ΔR1 + ΔR2). In addition, when cracks may occur in parts other than the solder joints 61 and 62 (for example, copper wiring) and the resistance may change, the resistance is measured at both ends of the solder joints 61 and 62 (that is, R1, R2 may be measured) and the resistance changes may be summed.

  In the second embodiment, a description will be given of a cooling / heating cycle test as an example. When a cooling cycle is applied to the solder joint component Z, cracks due to thermal fatigue may occur in the solder joint portions 61 and 62 due to the difference in thermal expansion between the substrate 4 and the chip resistor 7.

  Here, the flow of this method will be described with reference to FIG. In obtaining the crack area ratio of the solder joint component Z, first, a preliminary test is performed, and the effective specific resistance value Roe is obtained as follows. The crack area ratio Fi of each of the solder joints 61 and 62 is obtained by observing the fracture surface (S701).

  Since the solder joints 61 and 62 are composed of the lower part of the chip and the fillet part, the fracture surface is observed at both parts. For each of the solder joint portions 61 and 62, crack area ratios F1 and F2 with respect to the entire solder joint portion including the two portions (chip lower portion and fillet portion) are obtained. Then, using these measured values F1 and F2, an effective crack area ratio Fe is obtained based on Expression (7) (S702). The formula at this time is 2 / (1-Fe) = Σ {1 / (1-Fi)}, (i = 1, 2).

  Subsequently, the resistance change ΔR of the solder joint component Z is obtained by the AC four-terminal method (S703). From the obtained actual measurement data of Fe and ΔR, an effective specific resistance value Roe is calculated based on the equation (5) (S704). Thus, the effective specific resistance value Roe can be obtained from the preliminary test. As shown in FIG. 8, the relationship (calculation formula) of Formula (5) using this Roe and the actual measurement value of Fe actually measured in the preliminary test are almost the same. Here, Roe is 0.09 mΩ.

  By the above preliminary test, first, the effective specific resistance value Roe is obtained. And the following steps are performed when calculating the effective crack area ratio of a solder joint part in a thermal cycle test or actual use.

  First, a relational expression between the resistance change ΔR and the effective crack area ratio Fe is set using the effective specific resistance value Roe (S705). Specifically, it is set based on the formula (5). Subsequently, the resistance change ΔR of the solder joint component Z is measured (S706). Subsequently, the effective crack area ratio Fe is calculated from the resistance change ΔR based on the formula (5) (S707). Thereby, the effective crack area ratio Fe of the solder joint portions 61 and 62 can be obtained continuously and quantitatively. In addition, about S701-S704, since the same value Roe can be used with respect to the same thing (here soldering component) as what was calculated | required once effective fixed resistance value Roe, it can abbreviate | omit.

  By the way, in the above method, when only the cross-sectional areas along the crack path of the solder joint portion are different, if the specific resistance value of one solder joint portion is obtained, the specific resistance value of the other solder joint portion is expressed by the equation (8). ) Can be obtained by calculation. Thus, the crack area ratio calculated using the specific resistance value converted by correcting the cross-sectional area and the crack area ratio obtained by the fracture surface observation were almost the same.

  As described above, according to the second embodiment, the crack area ratio of the measurement target can be calculated continuously and quantitatively. Note that the measurement target (joint part) in the circuit is not limited to the solder joint part, and may be any conductive part that may cause a crack, such as a conductive adhesive or silver solder. The crack includes interfacial peeling (interface crack) and the like. Further, by using thermal resistance instead of electrical resistance, the crack area ratio can be calculated by the above method even for an object having no electrical conductivity.

1: crack area ratio calculation device, 2: resistance change measurement section, 3: crack area ratio calculation section,
4: Board, 51, 52: Copper wiring, 61, 62: Solder joint, 7: Chip resistance,
Z: Solder joint parts

Claims (10)

A crack area ratio calculation method for calculating a crack area ratio of a measurement object having electrical conductivity,
A specific resistance value calculating step for obtaining a specific resistance value when there is no crack in a crack progressing portion which is a portion where crack progress of the measurement object is expected;
Based on the specific resistance value when there is no crack in the crack propagation part, a relational expression setting step for setting a relational expression between resistance change and crack area ratio;
A resistance change measuring step for measuring a resistance change of the crack propagation portion ;
Based on the relational expression set in the relational expression setting step, a crack area ratio calculating step for calculating a crack area ratio of the crack propagation portion from the resistance change measured in the resistance change measuring step;
The crack area ratio calculation method characterized by including. When the crack area ratio is F, the resistance change is ΔR, and the specific resistance value when there is no crack in the crack propagation portion is Ro,
The crack area ratio calculation method according to claim 1, wherein the relational expression is F = 1 / (1 + Ro / ΔR). When a plurality of the measurement objects are electrically connected in series in a circuit, and the effective crack area ratio obtained by assuming that all the measurement objects are one virtual conductive part for the circuit,
In the equation, [Delta] R is the sum of the resistance change of each said crack growth portion located in said circuit, Ro is the sum of the specific resistance value when there are no cracks in the said crack growth portion located on the circuit The crack area ratio calculation method according to claim 2. The cross-sectional area of the cross section along the crack path of the first measurement object A1, the specific resistance value when there are no cracks crack growth portion of the first measurement object Ro1, said first measurement object When the cross-sectional area of the cross section along the crack path of the second measurement object made of the same material is A2,
In the specific resistance value calculating step, the specific resistance value Ro2 when there is no crack in the crack propagation portion of the second object to be measured is calculated by Ro2 = Ro1 × (A1 / A2). The crack area calculation method of description. The measurement object wood charge and the connection state is the same n (n is a natural number of 2 or more) are electrically connected in series in the circuit, each said crack growth of the crack area ratio Fi (i = 1~ n) is obtained by actual measurement,
The specific resistance value calculating step includes:
The effective crack area ratio Fe obtained on the assumption that all the measurement objects of the circuit are one virtual conductive part is n / (1-Fe) = Σ {1 / (1-Fi)}, (i = 1 to n), the effective crack area ratio calculating step,
From the effective crack area ratio Fe calculated in the effective crack area ratio calculating step and the resistance change ΔR that is the sum of the resistance changes of all the crack progressing portions in the circuit, an effective specific resistance value Roe is calculated as Fe = 1 / (1 + Roe). Effective specific resistance value calculating step using / ΔR),
Including
In the relational expression setting step, a relational expression between the resistance change ΔR and the effective crack area ratio Fe is set based on the effective specific resistance value calculated in the effective specific resistance value calculating step,
The crack area ratio calculation step calculates the effective crack area ratio Fe from the resistance change ΔR measured in the resistance change measurement step based on the relational expression set in the relational expression setting step. The crack area ratio calculation method of description. The crack area ratio calculation method according to claim 1, wherein the measurement object is a joint in a circuit. A crack area ratio calculation device for calculating a crack area ratio of a measurement object having electrical conductivity,
A resistance change measuring unit for measuring a resistance change of a crack progressing portion which is a portion where crack progress of the measurement object is expected ;
It is a relational expression between the resistance change and the crack area ratio, and is measured by the resistance change measuring unit based on the relational expression set using a specific resistance value obtained when there is no crack of the crack progressing part obtained in advance. A crack area ratio calculation unit for calculating a crack area ratio of the crack propagation part from a resistance change;
A crack area ratio calculation device comprising: When the crack area ratio is F, the resistance change is ΔR, and the specific resistance value when there is no crack in the crack propagation portion is R ₀ ,
The crack area ratio calculation apparatus according to claim 7, wherein the relational expression is F = 1 / (1 + R ₀ / ΔR). A crack area ratio calculation method for calculating a crack area ratio of a measurement object,
A specific resistance value calculating step for obtaining a specific resistance value of a thermal resistance when there is no crack in a crack progressing portion which is a portion where crack progress of the measurement object is expected;
Based on the specific resistance value of the thermal resistance when there is no crack in the crack propagation part, a relational expression setting step for setting a relational expression between the thermal resistance change and the crack area ratio;
A thermal resistance change measuring step for measuring a thermal resistance change of the measurement object;
Based on the relational expression set in the relational expression setting step, a crack area ratio calculation step for calculating a crack area ratio of the crack propagation part from the thermal resistance change measured in the thermal resistance change measurement step;
The crack area ratio calculation method characterized by including. When the crack area ratio is F, the thermal resistance change is ΔR, and the specific resistance value of the thermal resistance when there is no crack in the crack propagation portion is Ro,
The crack area ratio calculation method according to claim 9, wherein the relational expression is F = 1 / (1 + Ro / ΔR).

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