WO1999063315A1

WO1999063315A1 - A sensor for embedding in a cast material which transfers a pressure in the cast material to an electrical signal and a method to measure pressure in a cast material

Info

Publication number: WO1999063315A1
Application number: PCT/DK1999/000295
Authority: WO
Inventors: Henrik Stang; Birgitte Friis Dela; Helge Fredslund-Hansen; John Forbes Olesen
Original assignee: Henrik Stang; Birgitte Friis Dela; Fredslund Hansen Helge; John Forbes Olesen
Priority date: 1998-06-04
Filing date: 1999-06-04
Publication date: 1999-12-09
Also published as: AU4133499A

Abstract

A sensor for embedding in a cast material which transfers a pressure in the cast material to an electrical signal comprising a volumetric body (2, 3; 9, 10; 17, 18), and a pressure sensitive electrical conductor (4, 6; 11; 19) which changes resistance as a function of pressure. The volumetric body (2, 3; 9, 10; 17, 18) is constructed in such a way that a hydrostatic pressure acting on the volumetric body is transferred to an approximately hydrostatic pressure acting on the pressure sensitive electrical conductor. The invention furthermore relates to a method of determining eigenstresses from a measured pressure using the sensor.

Description

A SENSORFOREMBEDDING IN A CAST MATERIALWHICH TRANSFERS A

PRESSURE IN THE CAST MATERIAL TO AN ELECTRICAL SIGNAL AND A

METHOD TO MEASURE PRESSURE IN A CAST MATERIAL

This invention relates to a sensor for embedding in a cast material which transfers pressure in the cast material to an electrical signal and comprises a volumetric body and an electrical conductor made from a material which changes resistance as a function of pressure.

Furthermore, the invention relates to a procedure for determination of eigenstresses in a first specimen cast of a first material undergoing shrinkage during the hardening process when part of this shrinkage causes mechanical stresses to arise.

During casting of specimens to be used in mechanical and civil engineering structures documentation for the reliability of the cast specimen is often required. In order to be able to document the reliability of a specific spe- cimen which e.g. constitutes a critical part of a larger structure it is particularly advantageous if this documentation can be based on a non-destructive measurement. In the assessment of the reliability of a cast specimen an evaluation of the probability of crack formation is typically included. This is particularly important since crack formation gives rise to a strength reduction and accelerated deterioration of the cast specimen caused by penetration of aggressive substances.

When formation of eigenstresses during casting and subsequent hardening is an issue, reliability can be documented when a measure of the eigenstresses in the specimens is at hand and when the critical stress level for crack initiation is known. However, it can be difficult to pro- vide such a documentation in a practical way. The traditional measurement techniques in this field are based on deformation measurement in the cast material, e.g. using strain gauges or simply by measuring the vol- ume change during hardening. These measurements are used as indicators for the shrinkage of the cast material du^¬ ring the hardening process. However, it is not possible to relate these measurements to corresponding mechanical stresses occurring in the cast specimen, since part (typically a very large part) of the shrinkage does not produce stresses, as the shrinkage takes place at a time when the stiffness of the material is negligible or very low. Typically, the stiffness of the cast material is negligible or very low in the beginning of the hardening process and changes in a non-linear fashion over the hardening period. These stiffness changes are difficult to measure, which means that in practice it is not possible (or very difficult) to determine the mechanical stresses arising from the hardening and shrinkage process. Thus, an assessment of the eigenstresses in relation to the critical stress level is impossible or at least very difficult.

In cement-based materials such as concrete and mortar and in polymeric materials such as epoxy and polyester great volume changes take place during the hardening process. These volume changes can cause large and critical eigenstresses where the volume changes are restrained. The restraint can be due to the casting mould or the aggregates in mortar and concrete.

When restrained shrinkage takes place, the simultaneous creep (change in deformation under constant load) and relaxation (change in load under constant deformation) will make prediction of eigenstresses from known shrinkage even more difficult. High strength concrete m general exhibits greater shrinkage during the hardening process compared to ordinary concrete due to the low water/cement ratio and the addi- tion of microsilica. This greater shrinkage increases the eigenstresses m the concrete, particularly around aggregates and other elements which constitute a restraint. Consequently, the risk of crack formation is increased which will typically reduce strength and durability sig- mficantly. Owing to this increased risk of crack formation it is particularly important to document eigenstresses m specimens made from high strength concrete.

From the paper internal Eigenstresses m Concrete Due to Autogenous Shrinkage' by B. F. Dela og H. Stang published m

of an International Research Seminar m Lund, June 10, 1997' a sensor for measurement of eigenstresses m cement paste is known. The sensor comprises a sphere of porcelain with a pressure sensitive electrical conducting wire wrapped around. When measuring eigenstresses m cement paste the sensor is embedded m the cement paste and the pressure sensitive electrical conducting wire is connected to a suitable measuring instrument - typically based on a Wheatstone bridge.

When calibrating the sensor and the measuring instrument the sensor is placed m a pressure chamber filled with fluid. The pressure m this chamber is varied and corresponding values of pressure and electrical signal are re- corded. In this calibration setup the sensor is loaded with a hydrostatic pressure due to the fluid m the pressure chamber.

Since the pressure sensitive electrical conductor is placed outside the sphere it cannot be expecred that a hydrostatic pressure acts on the electrical conductor when the sensor is embedded in a solid material undergoing shrinkage. In this case the electrical conductor will be placed in a complicated non-homogeneous non-hydrostatic stresss field.

This means that the conditions in the sensor in practical applications are significantly different from the conditions in the sensor during calibration, and this gives rise to measuring errors.

It is therefore an object of the invention to provide a sensor which can be embedded in a material and which, due to the volume changes in this material, will introduce an eigenstress state. This eigenstress state is transferred to a measurable electrical signal, which, on the other hand, through a calibration can give information about the exact magnitude of the eigenstress state acting on the sensor.

This is achieved by constructing the mentioned sensor such that a volumetric body surrounds the electrical conductor in such a way that the pressure acting on the volumetric body is transferred to a hydrostatic pressure acting on the electrical conductor, irrespectively of whether the sensor is surrounded by a fluid or cast into a solid material.

When the sensor is cast into a solid material which shrinks and when (and only when) the sensor has the shape of a sphere, a hydrostatic stress state is created inside the sphere, and this can be detected by a pressure sensitive electrical conductor placed inside the sphere itself. Thus, it is possible to calibrate the sensor under hydrostatic conditions (typically in a fluid) and use the result of the calibration to determine the magnitude of the eigenstresses around the sensor in the cast material m spite of the fact that the cast material undergoes unknown and non-linear deformations over time. Furthermore, the pressure sensitive electrical conductor is well protected against corrosion and mechanical abrasion which could be caused by the cast material.

Often temperature variations occur in the cast material m which the sensor is embedded. These variations often occur m connection with the same process (typically hardening and shrinkage) which gives rise to volume changes. These temperature changes can be considerable, in cement-based or polymeric materials a temperature rise of the order of 20-40 C often occurs during nardemng depending of the size of the specimens and the msula- tion. Since electrical conductors typically change resis^¬ tance with change of temperature and since the resistance change associated with such a temperature change will be significant (of the same order of magnitude as the resis^¬ tance change due to the pressure which should be eas- ured) , then a temperature change can be measured as a false pressure. In sucn cases it is necessary to use a temperature compensated sensor.

A temperature compensated sensor can be established ac- cording to the same principles as the non-compensated sensor using two identical electrical conductors. The first electrical conductor should be placed such that the volumetric body encloses the electrical conductor and such that a hydrostatic pressure acting on the volumetric body is transferred to a hydrostatic pressure acting on the first electrical conductor. The second electrical conductor should be placed m such a way that no pressure is transferred to the second electrical conductor when a pressure acts on the sensor. The two electrical conduc- tors should be placed so that both experience the same temperature at any time. The desired temperature compen- sated pressure related resistance change can be determined at any time by subtracting the two resistance changes in the two conductors. (This is typically done in a Wheatstone bridge by placing the two conductors in a so-called half-bridge) .

Prior art for pressure sensors e.g. US A 3,933,034 and ΞU 935,727 is characterized by the fact that the sensors work independently of the stiffness of the sensors. Ei- ther the sensors are relatively soft or work according to a deformation principle. This is in contrast to the sensor according to the present invention which should be as stiff as possible - preferably 'infinitely' stiff relative to the cast material in which it is embedded. Thereby the sensor according to the invention becomes a stress sensor measuring the stresses occurring when the material in which it is embedded undergoes volume changes under restraint established by the sensor itself.

In a suitable design the volumetric body has the shape of a sphere and the electrical conductor is placed on a mid- sectional area of the sphere. Thereby the sensor can be produced as two half-spheres which are e.g. glued together .

When the volumetric body is made of a sphere surrounded by a spherical shell and when the electrical conductor is placed on the surface of this sphere in contact with the spherical shell, the electrical conductor can be kept in contact with the volumetric body without any use of other adhesives .

When the volumetric body has a high homogeneous stiffness a particularly precise determination of the hydrostatic pressure is achieved. In a suitable embodiment the volumetric body is made of a spherical shell which encloses a fluid in such a way that the hydrostatic pressure in the fluid is transferred to the pressure sensitive electrical conductor. In this way particularly precise measurements can be achieved.

A particularly suitable embodiment is achieved when the volumetric body has a stiffness which is significantly larger than the stiffness of the material in which it is embedded at any time. In this case the stress related shrinkage can be determined. This stress related shrinkage can then be used to predict the eigenstresses in specimens with other restraints than the restraint estab- lished by the sensor. Another restraint could e.g. be a casting mould. Furthermore, the sensor could be perceived as equivalent to aggregates in the cast material in which the sensor is to be placed.

In a suitable embodiment the temperature compensated sensor comprises a sphere with the first electrical conductor placed on a mid-section of the sphere. The second electrical conductor is placed on the surface of or in a cavity in the sphere. Thereby the sensor can be produced as two half-spheres. The first electrical conductor is placed on the plane surface of the first half-sphere. The second electrical conductor is placed in the cavity, made in the plane section of the first or the second half- sphere. Hereafter the two half-spheres can e.g. be glued together.

In the temperature compensated sensor the first electrical conductor can also be placed on a sphere enclosed by a spherical shell while the second electrical conductor is placed in a cavity inside the sphere. In the temperature compensated sensor the first electrical conductor can also be placed m a fluid surrounded by a spherical shell with the second electrical conductor placed on the inside surface of or inside an empty (preferably rigid) container surrounded by the fluid.

When the electrical conductor comprises an alloy consisting of 86% copper, 12% manganese and 2% nickel, the elec- trical conductor is particularly pressure sensitive.

It is furthermore an object of the invention to be able to determine the eigenstress state m a cast first specimen with a given geometrical restraint without having to place the sensor in the mentioned specimen.

This can be achieved when the mentioned method comprises the following steps: Measurement of the hydrostatic pressure m a second specimen made of a material which is identical to the first material using a sensor placed m the second specimen followed by a calculation of the magnitude of the eigenstress state m the cast first specimen from the measured hydrostatic pressure m the second specimen.

By this method the eigenstress state m a cast specimen with any geometrical restraint can be determined without actually having to cast the sensor into the specimen m question. Consequently, the specimen can be designed without taking into consideration the placing of the sensor m the specimen.

A suitable method comprises the following steps: determination of a formula for the stress related shrinkage m the second body as the product between the measured pressure and a factor which contains the stiffness modulus for the cast material during hardening. Determination of a formula for the magnitude of the eigenstress field m the first specimen based on the stiffness modulus for the cast material during hardening and the stress related shrinkage in the second specimen. Determination of the magnitude of the stress field m the first specimen from the measured hydrostatic pressure and the stress related shrinkage m the second specimen and the formula for the magnitude of the eigenstress field m the first specimen. By this method the magnitude of the eigenstress field from one restraint can be calculated from the hydrostatic pressure due to the restraint of the sensor by means of simple linear considerations .

The invention will now be explained with reference to figures, where

fig. 1 shows a first cross-section through the first embodiment of a sensor according to the invention;

fig. 2 shows a second cross-section through the first embodiment of the sensor;

fig. 3 shows the second embodiment of a sensor according to the invention;

fig. 4 shows the third embodiment of a sensor according to the invention;

fig. 5. shows an outline of the radial and tangential stress variation around the sensor with radius R embedded m a material which shrinks;

fig. 6 shows a sensor according to the invention embedded m a material undergoing a volume change; fig. 7 shows an example of a temperature compensated sensor according to the invention.

fig. 8 shows an example of a cast specimen in the form of a bar and the stress in the bar.

Fig. 1 shows a first cross-section through the first embodiment of a sensor according to the invention. In this embodiment the sensor comprises a first half-sphere 2 and a second half-sphere 3. The plane surfaces of the half spheres (not shown) are in contact with a pressure sensitive electrical conductor in the shape of a wire 4 such that the pressure sensitive electrical conductor 4 and the half spheres 2 and 3 form a sphere. The pressure sensitive electrical conductor 4 and the half spheres 2 and 3 are held together by means of an adhesive which fills the space 1. The pressure acting on the sphere i.e. the sensor will in this way be transferred to a pressure act- ing on the pressure sensitive electrical conductor 4.

The pressure sensitive conductor 4 can comprise an alloy consisting of 86% copper, 12% manganese og 2% nickel. The pressure sensitive conductor 4 can be constructed in the shape of a wire with a diameter of 0.05 mm and a length of 550 mm. Electrical leakage from one part of the wire to another should be prevented e.g. by the use of insulated wire. The electrical resistance of the wire will change inter alia as a function of hydrostatic pressure acting on the wire.

The half spheres 2 and 3 can be made of e.g. glass, ceramics, porcelain or another relatively stiff material. The material should be stiff only relative to the ate- rial in which the sensor is embedded. The half spheres are glued together with e.g. an epoxy resin.

Fig. 2 shows a second cross-section through the first embodiment of the sensor. In this section the circumference 5 of the sensor is seen together with the wire-shaped pressure sensitive conductor 6 placed m a winding pattern 6. The pressure sensitive electrical conductor 6 is connected to the terminals 7 and 8 at both ends. The terminals can be placed inside or outside the circumference 5. The terminals are used to connect the sensor to measuring equipment so that the electrical resistance change of the electrical conducting wire, which is a function of the hydrostatic pressure acting on the wire, can be meas^¬ ured. The resistance change can be measured by means of a Wheatstone bridge.

Fig. 3 shows a second embodiment of a sensor according to the invention. In this embodiment the sensor comprises a sphere 10 enclosed in a spherical shell 9. The pressure sensitive electrical conductor 11 is wound around the sphere 10 and connected to the terminals 12 and 13 so that the terminals can be used to connect the sensor to the measuring equipment.

In the production of the sensor of this second embodiment the sphere 10 can be cast. When the sphere is sufficiently hardened, the pressure sensitive conductor wire 11 can be wound around the sphere. Hereafter the spherical shell 9 can be cast around the sphere 10 and the electrical pressure sensitive conducting wire 11. Thereby it will be possible to obtain full physical contact between the sphere 10, the pressure sensitive wire 11 and the spherical shell 9. The material used for the sphere and the spherical shell could be e.g. Portland cement, a cementitious material, a technical ceramic material, a ceramic composite material, a polymer or a polymer based composite material.

Fig. 4 shows a third embodiment of a sensor according to the invention. In this embodiment the sensor comprises a spherical shell 18 enclosing a space 17 containing a fluid. The pressure sensitive conductor 19 is placed in the fluid and could be wound in the shape of a spiral. Electrical contact to a measuring device is established through the terminals 14 and 15.

In this way it is ensured that a pure hydrostatic pressure acts on the pressure sensitive conductor.

Fig. 5 shows an outline of the radial and tangential stress variation around the sensor with radius R cast in a material which shrinks. The material shrinks from a volume VI to a volume V2. Both the radial and the tangential stress σ_rr og σ_φφ are identical and constant (negative) inside the sphere. On the boundary of the sphere the tangential stress σ_φφ has a discontinuity and outside the sphere - in the cast material - the magnitude of the positive tangential stresses decreases with increasing distance from the sphere. On the boundary of the sphere the radial stresses are continuous and outside the sphere - in the cast material - the magnitude of the negative radial stresses decreases with increasing distance from the sphere.

It follows that it is possible to measure the radial stresses acting on the boundary between the cast material and the sensor by placing the pressure sensitive electrical conductor inside the sphere.

Fig. 6 shows a sensor according to the invention cast m a material undergoing a volume change. When the sensor 20 is cast m the material 21, the material and the sensor have a volume VI. During hardening the material 21 undergoes a volume change so that the volume VI is reduced to the volume V2. This means that the material 21 shrinks with the linear shrinkage ε„ corresponding to a volume change per volume amounting to 3ε . The material 21 is not restrained. Before, during and after the hardening process it is possible to measure the pressure P acting on the sensor 20 by means of the same sensor.

Fig. 7 shows an embodiment of the temperature compensated sensor based on two half-spheres (1,2) with the first electrical conductor (3) placed on the plane surface of one of the half-spheres. The second electrical conductor (4) is placed on the surface of a cylindrical cavity m the two half-spheres. Only the first electrical conductor will be sensitive to pressure changes acting on the sensor, while both will be sensitive to temperature changes. The first electrical conductor can be placed m a cavity m sphere. The cavity can have the form of a slot or groove that has a cross-sectional dimension larger than the cross-sectional dimension of the second electrical conductor. The slot or groove can, at least partially, be filled with a heat conducting pasta.

In the following it is assumed that the cast material 21 has a stiffness modulus E_]η which varies with time and a

Poisson' s ratio v_m (the positive ratio between transverse and axial strain under uni-axial stress) . Furthermore it is assumed that the sensor has a stiffness modulus E_ and a Poisson' s ratio v_ which are independent of time.

The expected pressure P acting on the sensor can be calculated as follows according to the theory of linear elasticity:

If the sensor is very stiff relative to the cast material

E E then — -— 0. For —r^~ - 0 the following expression for P

is obtained:

^{p = ~}. ^ε,

At a given measured P,_n information about the stress related shrinkage ε^* can be obtained. The stress related shrinkage ε] is a theoretical value for the shrinkage which is obtained assuming a value Ε_m. Thus,

_* 2E

P = ε — ^{m s} \ + v m

7Λn example will now be considered where this result can be used to determine the eigenstress state in a cast specimen with a geometrical restraint other than the re- straint provided by the sensor.

Fig. 8 shows an example of a cast specimen in the shape of a bar and the stresses in that bar. The bar 22 is cast between two anchorages 23 and 24. A sensor according to the invention is embedded in an identical material. This material is not otherwise restrained. The pressure acting on the sensor can now be determined based on a calibration of the sensor and a measured resistance change in the pressure sensitive conductor in the sensor. The uni-axial stress field in the bar σ, can be determined according to: σ s - E m ε s^* where ε^* is the stress related shrinkage in the bar under the assumption of the stiffness modulus E_m in the bar. Inserting the expression for P_m/ it is possible to determine the magnitude of the stress field σ_s from knowledge of the product between E_m and ε^* :

σ. = —-— P_m = E_mε.

This expression requires knowledge of v_m, however this quantity is typically known and varies only by a small amount during hardening, typically v,_n takes values between 0.2 and 0.4 which introduces a maximum error in the determination of the eigenstress field of the order of 10%.

Claims

PATENT CLAIMS

1. A sensor for embedding in a cast material which transfers a pressure in the cast material to an electrical signal comprising

a volumetric body (2,3; 9,10; 17,18), and

a pressure sensitive electrical conductor (4,6; 11; 19) which changes resistance as a function of pressure,

characteri zed in that

the volumetric body (2,3; 9,10; 17,18) encloses the elec- trical conductor (4,6; 11; 19) in such a way that a hydrostatic pressure acting on the volumetric body is transferred to an approximately hydrostatic pressure acting on the pressure sensitive electrical conductor.

2. A sensor according to claim 1, characteri zed in that the volumetric body (2,3) substantially has the shape of a sphere (5) ,

3. A sensor according to claim 1-2, characteri zed in that the volumetric body (2, 3) has the shape of a sphere (5) , and in that the pressure sensitive electrical conductor (4,6) is placed in a cross section (1) in the sphere.

4. A sensor according to claims 1, characterized in that the volumetric body (9,10) comprises a sphere

(10) enclosed by a spherical shell (9) and in that the pressure sensitive electrical conductor (11) is placed on the surface of the sphere (10) in contact with the spherical shell.