JP7353639B2 - Viscoelastic coefficient measurement method, viscoelastic coefficient measurement device and program - Google Patents

Description

The present invention relates to a viscoelastic coefficient measuring method, a viscoelastic coefficient measuring apparatus, and a program.

The viscoelasticity of a substance is a property of a substance that combines elasticity and viscosity. In order to understand the viscoelastic properties of a substance, it is necessary to identify the elastic coefficient and viscous coefficient. As a method for identifying the elastic modulus, a method using a so-called tensile test has also been proposed (see, for example, Patent Document 1). Further, as a method for identifying the elastic modulus, a method using a so-called indentation test has also been proposed (see, for example, Patent Documents 2 and 3). These methods assume a constitutive model, ie a physical model for the deformation of a material that has multiple components. For example, in the methods described in Patent Documents 2 and 3, a so-called three-element solid model is employed as a configuration model. Then, a tensile test or an indentation test is performed under multiple types of conditions that exceed the number of multiple components described above, and the mechanical property values (so-called physical property values) of each component are determined from the test results under each of the multiple types of conditions. ). For example, in the method described in Patent Document 3, when a material is pushed at three different pushing speeds, the correlation between the amount of deformation of the material and the force is measured, and the elasticity for each of the two elastic elements in the three-element solid model is measured. The coefficient and the viscosity coefficient regarding one viscosity element are determined.

JP2011-257321A Japanese Patent Application Publication No. 2011-137667 International Publication No. 2015/059878

However, in the methods described in Patent Documents 1 to 3, it is necessary to perform a tensile test or an indentation test under multiple types of conditions equal to or greater than the number of constituent elements included in the constituent model. For this reason, there is a risk that the test content may become complicated or that the time required to determine the elastic coefficient and viscosity coefficient becomes long.

The present invention has been made in view of the above reasons, and an object of the present invention is to provide a viscoelastic coefficient calculation method, a viscoelastic coefficient calculation device, and a program that can easily and quickly determine the viscosity coefficient and elastic coefficient of a substance. shall be.

In order to achieve the above object, the viscoelastic coefficient measuring method according to the present invention includes:
deforming the sample over time;
acquiring a history of a first physical quantity that reflects the amount of strain of the sample when deforming the sample over time and a history of a second physical quantity that reflects the stress acting on the sample;
calculating a history of the rate of change of the first physical quantity based on the history of the first physical quantity;
The history of the first physical quantity and the history of the second physical quantity are determined using a relational expression that includes the viscosity coefficient and the elastic coefficient of the sample and expresses the relationship between the first physical quantity, the second physical quantity, and the rate of change. calculating an approximate solution for the viscosity coefficient and an approximate solution for the elastic coefficient from the history of the rate of change;
outputting information indicating the calculated approximate solution of the viscosity coefficient and the calculated approximate solution of the elastic coefficient as viscosity coefficient information indicating the viscosity coefficient and elastic coefficient information indicating the elastic coefficient of the sample ; ,
The relational expression is a first-order differential equation with respect to time between the stress acting on the sample and the amount of strain in the sample, which represents the behavior of the viscoelastic model of the sample, and the change in the stress when the amount of strain changes. It is derived from the relational expression obtained by substituting the deformation resistivity representing the quantity .

The viscoelastic coefficient measuring device according to the present invention seen from another point of view is as follows:
A viscoelastic coefficient measuring device that measures the viscosity coefficient and elastic coefficient of a sample by deforming the sample over time,
a physical quantity history acquisition unit that acquires a history of a first physical quantity that reflects an amount of strain of the sample when deforming the sample over time and a history of a second physical quantity that reflects stress acting on the sample;
a speed calculation unit that calculates a history of the rate of change of the first physical quantity based on the history of the first physical quantity;
The history of the first physical quantity and the history of the second physical quantity are determined using a relational expression that includes the viscosity coefficient and the elastic coefficient of the sample and expresses the relationship between the first physical quantity, the second physical quantity, and the rate of change. a coefficient calculation unit that calculates an approximate solution of the viscosity coefficient and an approximate solution of the elastic coefficient from the history of the rate of change;
an output unit that outputs information indicating the calculated approximate solution of the viscosity coefficient and the calculated approximate solution of the elastic coefficient as viscosity coefficient information indicating the viscosity coefficient and elastic coefficient information indicating the elastic coefficient of the sample. picture,
The relational expression is a first-order differential equation with respect to time between the stress acting on the sample and the amount of strain in the sample, which represents the behavior of the viscoelastic model of the sample, and the change in the stress when the amount of strain changes. It is derived from the relational expression obtained by substituting the deformation resistivity representing the quantity .

The program according to the present invention seen from another point of view is
computer,
a physical quantity history acquisition unit that acquires a history of a first physical quantity that reflects the amount of strain of the sample when deforming the sample over time and a history of a second physical quantity that reflects the stress acting on the sample;
a speed calculation unit that calculates a history of the rate of change of the first physical quantity based on the history of the first physical quantity;
The history of the first physical quantity and the history of the second physical quantity are determined using a relational expression that includes the viscosity coefficient and the elastic coefficient of the sample and expresses the relationship between the first physical quantity, the second physical quantity, and the rate of change. a coefficient calculation unit that calculates an approximate solution of the viscosity coefficient and an approximate solution of the elastic coefficient from the history of the rate of change;
an output unit that outputs information indicating the calculated approximate solution of the viscosity coefficient and the calculated approximate solution of the elastic coefficient as viscosity coefficient information indicating the viscosity coefficient and elastic coefficient information indicating the elastic coefficient of the sample;
It is a program to function as
The relational expression is a first-order differential equation with respect to time between the stress acting on the sample and the amount of strain in the sample, which represents the behavior of the viscoelastic model of the sample, and the change in the stress when the amount of strain changes. It is derived from the relational expression obtained by substituting the deformation resistivity representing the quantity .

According to the present invention, the history of the first physical quantity that reflects the amount of strain on the sample when deforming the sample over time and the history of the second physical quantity that reflects the stress acting on the sample are acquired, and the history of the first physical quantity that reflects the stress acting on the sample is obtained. A history of the rate of change of the first physical quantity is calculated based on the history. Then, using a relational expression that includes the viscosity coefficient and elastic coefficient of the sample and expresses the relationship between the first physical quantity, the second physical quantity, and the rate of change, the history of the first physical quantity, the history of the second physical quantity, and the history of the rate of change are used. An approximate solution for the viscosity coefficient and an approximate solution for the elastic coefficient are calculated from This makes it possible to calculate an approximate solution to the viscosity coefficient and elastic modulus of the sample by changing the sample only once over time. The contents can be simplified and the time required to obtain the elastic coefficient and viscosity coefficient can be shortened.

3 is a diagram showing a three-element solid model that is an example of a viscoelastic model of a sample according to Embodiment 1. FIG. 3 is a stress strain diagram of a sample according to Embodiment 1. FIG. FIG. 3 is a diagram showing a state of contact between an indenter and a sample according to the first embodiment. FIG. 3 is a diagram showing an example of the relationship between the indentation amount and the strain rate according to the first embodiment. (A) is a diagram showing an example of the relationship between indentation speed and deformation resistivity according to Embodiment 1, and (B) is a diagram showing an example of the relationship between indentation amount and deformation resistivity according to Embodiment 1. It is a diagram. FIG. 3 is a diagram showing an example of the relationship between the pushing load and the pushing amount according to the first embodiment. 1 is a schematic configuration diagram of a viscoelastic coefficient measuring device according to Embodiment 1. FIG. 1 is a block diagram of a viscoelastic coefficient measuring device according to Embodiment 1. FIG. FIG. 3 is a diagram showing an example of the relationship between the pushing amount and the pushing load according to the first embodiment. 5 is a flowchart illustrating an example of the flow of analysis processing according to the first embodiment. (A) is a diagram showing a two-element solid model that is a viscoelastic model of the sample according to Comparative Example 1, and (B) is a diagram showing the relationship between the indentation load and the indentation amount obtained by the analysis process according to Comparative Example 1. It is a figure which shows the approximate curve and measurement data shown. FIG. 3 is a diagram showing an approximate curve showing the relationship between the indentation load and the indentation amount obtained by the analysis process according to the first embodiment, and measurement data. FIG. 6 is a diagram showing an approximate curve showing the relationship between the indentation load and the indentation amount obtained by the analysis process according to the first embodiment and the analysis process according to Comparative Examples 1 and 2. 7 is a diagram showing an example of a time profile of strain amount and stress according to Embodiment 2. FIG. (A) is a diagram showing the angular velocity dependence of the phase delay amount according to the second embodiment, and (B) is a diagram showing the angular velocity dependence of the loss tangent according to the second embodiment. 7 is a diagram showing the angular velocity dependence of deformation resistivity according to Embodiment 2. FIG. FIG. 2 is a schematic configuration diagram of a viscoelastic coefficient measuring device according to a second embodiment. FIG. 2 is a block diagram of a viscoelastic coefficient measuring device according to a second embodiment. 7 is a flowchart illustrating an example of the flow of analysis processing according to Embodiment 2. FIG. (A) is a diagram showing an example of a time profile of strain rate according to Embodiment 3, and (B) is a diagram showing an example of a time profile of strain amount according to Embodiment 3. FIG. 3 is a schematic configuration diagram of a viscoelastic coefficient measuring device according to a third embodiment. FIG. 3 is a block diagram of a viscoelastic coefficient measuring device according to a third embodiment. 7 is a flowchart illustrating an example of the flow of analysis processing according to Embodiment 3.

(Embodiment 1)
Embodiments according to the present invention will be described below with reference to the drawings. First, a method for measuring a viscoelastic coefficient according to this embodiment will be explained.

In the viscoelastic coefficient measuring method according to the present embodiment, when the sample is deformed over time by pushing the indenter into the sample, the history of the indentation amount of the indenter, the history of the indentation load acting on the indenter, The viscosity coefficient value and the elastic coefficient value of the sample are calculated based on the history of the indentation speed of the indenter. In the viscoelastic coefficient measuring method according to the present embodiment, the sample includes an elastic part having a spring element and a viscoelastic part having a spring element and a dashpot element, as shown in FIG. It is assumed that it is expressed by a three-element solid model, which is a viscoelastic model consisting of and . Here, the strain amount ε ^e of the elastic part, the elastic coefficient E ^e , the elastic coefficient E ^ve of the spring element of the viscoelastic part, the stress σ ^ve generated in the spring element of the viscoelastic part, and the viscous compliance of the dashpot element of the viscoelastic part (Hereinafter, referred to as "viscosity coefficient.") Regarding C, the stress σ v generated in the dashpot element, the amount of strain ε ^v , and the sum σ of the stress ^{σ ve and} the stress σ ^v , the following formulas (1) to (7) are used. The relationship holds true. In addition, regarding the following formulas (1) to (7), the overdot attached to the symbol indicating each physical quantity indicates time differentiation, which is represented by a superscript "." in the text below.

Here, for example, after substituting equations (6) and (7) into equation (5), based on equations (1) and (2), ε ^v , ε ^v・are changed to ε, ε^・, ε ^e , ε ^e・. Then, by substituting equations (3) and (4) into ε ^e and ε ^e , a relational expression representing the behavior of the viscoelastic model of sample SP1 as shown in equation (8) below is derived. .

The relational expression expressed by equation (8) is a first-order differential equation with respect to time between the stress σ acting on the sample and the amount of strain ε of the sample. On the other hand, the relationship between the amount of strain of a sample having viscoelasticity and the magnitude of stress acting on the sample is expressed, for example, by a stress-strain curve as shown in FIG. This is due to the influence of the viscosity of the sample. Here, if the amount obtained by partially differentiating the magnitude of the stress acting on the sample with the strain amount ε is the deformation resistivity D, the deformation resistivity D is expressed by the following formula (9).

Here, the constitutive equation of the three-element solid model shown in FIG. 1 is expressed by the following equation (10).

Then, by substituting the relational expression of equation (9) into equation (10), the following relational expressions of equation (11) and equation (12) are derived.

Here, regarding equation (12), consider a differential equation expressed by equation (13) below.

Then, by solving the differential equation of equation (13) above, the relational expression of equation (14) below is derived.

Here, it is assumed that the following relational expression (15) is substituted into the relational expression (14).

Then, the following relational expression (16) is derived.

Here, k ₁ is a constant. By partially differentiating both sides of the relational expression (16) with respect to ε, a relational expression expressed by the following equation (17) is derived.

Here, D indicates deformation resistivity. In order to easily realize the analysis, it is assumed that the relational expressions from Equation (17) to Equation (18) below approximately hold true.

Then, by substituting the relational expression (18) into the above-mentioned relational expression (8), the following relational expression (19) is derived. At this time, the deformation resistivity D corresponds to the so-called apparent Young's modulus at the strain amount ε. In this case, the deformation resistivity D is expressed by the relational expression shown in Equation (19) from the relational expressions of Equation (8) and Equation (18).

Furthermore, in the viscoelastic coefficient measuring method according to the present embodiment, it is assumed that, for example, as shown in FIG. 3, a spherical indenter 15 is pushed into the sample SP1. In this case, in the relational equation derived from Hertz's elastic contact theory, the following relational equation (20) can be calculated by replacing Young's modulus with deformation resistivity D, which corresponds to the so-called apparent Young's modulus.

Here, F1 is the indentation load acting on the indenter 15 (see white arrow AR2 in Fig. 3), E is Young's modulus of sample SP1, ν is Poisson's ratio of sample SP1, φ is the diameter of the indenter 15, and δ is the indentation amount. It is. Further, the sample SP1 is a semi-infinite body with a flat surface, and the indenter 15 is sufficiently hard with respect to the sample SP1. The indentation amount δ corresponds to a first physical quantity that reflects the amount of distortion of the sample SP1 when the sample SP1 is deformed over time. Further, the indentation load F1 corresponds to a second physical quantity that reflects the stress acting on the sample SP1.

Further, in the process of pressing the sample SP1 with the indenter 15, a phenomenon occurs in which the surface shape of the load surface of the sample SP1 changes significantly, that is, the deformation area of the sample SP1 changes significantly due to the pressing of the indenter 15. The indentation load applied to the finite body sample SP1 placed on the rigid body is greater than the indentation load applied to the semi-infinite body sample SP1. Here, considering the influence of the fact that the actual sample SP1 is a finite body, the deformation of the sample SP1 due to the indentation of the indenter 15 is calculated by combining the contact deformation of the indenter 15 with the compressive deformation that occurs when the material is soft. Express in combination. In this case, the following relational expression (21) holds true. Note that the overline attached to the symbol indicating each physical quantity in the following formula (21) is represented by a superscript "-" in the following text.

Here, ε _H ⁻ represents the amount of Hertzian strain due to contact deformation by the indenter 15, and ε _V ⁻ represents the amount of volumetric strain indicating compressive deformation occurring between the indenter 15 and the sample SP1. This equation (21) expresses the distribution of the three-dimensional strain amount that occurs in the sample SP1 during the indentation process of the indenter 15 in terms of the equivalent uniaxial strain amount. Further, ε _I ⁻ is referred to as “equivalent indentation strain amount”. The Hertzian strain amount ε _H ⁻ and the volumetric strain amount ε _V ⁻ are expressed by the following relational expressions (22) and (23), respectively.

Note that ν, φ, and δ in equation (22) have the same meanings as ν, φ, and δ in equations (11) to (13).

Note that φ and δ in equation (23) have the same meanings as ν, φ, and δ in equations (11) to (13). Moreover, h indicates the thickness of sample SP1. Then, by substituting the relational expressions of equation (22) and equation (23) into equation (21), the relational equation shown in equation (24) below is obtained.

Note that ν, φ, and δ in formula (24) have the same meanings as ν, φ, and δ in formulas (11) to (13), and h in formula (24) has the same meaning as h in formula (23). indicate the same meaning. Here, the following relational expression (25) holds true for the time differential ε _I ^· of the equivalent indentation strain amount ε _I ⁻ .

Here, the following relational expression (26) is derived from the relational expression (21).

Then, by substituting the relational expressions of equation (22) and equation (23) into equation (26), the relational equation shown in equation (27) below is derived.

Here, assuming that the sample SP1 is a semi-infinite body sample ^whose thickness h is infinite, the time differential of the equivalent indentation strain amount ε _I ^- , that is, the strain rate ε _I ) is approximately expressed by the relational expression.

Regarding equation (28), the dependence of the strain rate ε _I on the indentation amount δ when the Poisson's ratio ν of the sample SP1 is 0.45, the diameter φ of ^the indenter 15 is 30 mm, and the indentation speed ^δ is 2 mm/sec. The theoretical curve shown in FIG. 4 is shown in FIG. From the results shown in FIG. 4, the strain rate tends to decrease as the indentation amount increases. Furthermore, in equation (27), assuming that the sample SP1 is a semi-infinite body sample whose thickness h is infinite, the equivalent indentation strain amount ε _I ^- is expressed by the following equation (29).

Then, by substituting Equation (29) regarding the equivalent indentation strain amount ε _I ^- for ε in Equation (19), and substituting Equation (28) regarding the strain rate ε _I ^{for ε} , the following relational expression (30) is obtained. is obtained.

Regarding equation (30), FIG. 5A shows a theoretical curve showing the dependence of the deformation resistivity D on the indentation speed ^δ· when the indentation amount of the indenter 15 is set to 0.1 mm, 1 mm, and 3 mm. As shown in FIG. 5(A), the behavior of the deformation resistivity D with respect to the strain rate changes depending on the amount of indentation. Regarding equation (30), when the indentation speed of the indenter 15 is set to 0.1 mm/sec, 1 mm/sec, 10 mm/sec, 20 mm/sec, 50 mm/sec, 100 mm/sec, 1000 mm/sec, and 10000 mm/sec A theoretical curve showing the dependence of the deformation resistivity D on the indentation amount δ is shown in FIG. 5(B). As shown in FIG. 5(B), the behavior of the deformation resistivity D with respect to the strain amount δ of the sample SP1 changes depending on the indentation speed of the indenter 15. Then, by substituting the relational expression of Equation (30) to the deformation resistivity D of Equation (20), the relational expression shown in Equation (31) is derived.

The relational expression expressed by this equation (31) includes the viscosity coefficient C and the elastic coefficients E ^e and E ^ve of the sample SP1, and represents the relationship between the indentation amount and the indentation load. Regarding formula (31), calculation when the indentation speed of the indenter 15 is 0.1 mm/sec, 1 mm/sec, 10 mm/sec, 20 mm/sec, 50 mm/sec, 100 mm/sec, 1000 mm/sec, 10000 mm/sec The results are shown in FIG. As shown in FIG. 6, the relationship between the indentation load F1 and the strain amount δ of the sample SP1 changes depending on the indentation speed of the indenter 15. In the viscoelastic coefficient measuring method according to the present embodiment, fitting is performed using the least squares method on the measurement data of the indentation load and indentation amount using the above-mentioned relational expression (31). Approximate solutions for the elastic coefficients E ^e and E ^ve and approximate solutions for the viscosity coefficient C are calculated.

Next, a viscoelastic coefficient measuring device according to this embodiment will be explained. As shown in FIG. 7, the viscoelastic coefficient measuring device 100 according to the present embodiment includes a measurement unit 10, a control unit 20, and an analysis unit 30. The measurement unit 10 includes an indenter 15, a load shaft 14, a stage 12, a load cell 13, an actuator 11, and a potentiometer 17. The actuator 11 drives the stage 12 in a preset direction (downward of arrow AR3 in FIG. 7). The load shaft 14 is attached to the stage 12, and when the actuator 11 drives the stage 12, the position of the load shaft 14 is also changed accordingly. The indenter 15 has a spherical shape and is attached to the tip of the load shaft 14. When the actuator 11 moves the stage 12 in a direction approaching the sample SP1 placed on the table 16 (downward of arrow AR3), the indenter 15 comes into contact with the sample SP1 and is pushed in.

The load cell 13 is attached to the load shaft 14 and measures the load acting on the indenter 15 from the load shaft 14. The load cell 13 measures the load acting on the indenter 15 from the sample SP1 and outputs this load information to the analysis unit 30. Potentiometer 17 measures the amount of movement of stage 12. The amount of movement of the stage 12 corresponds to the amount of pushing of the indenter 15 into the sample SP1. The potentiometer 17 outputs pushing amount information indicating the measured pushing amount of the indenter 15 to the control unit 20.

The control unit 20 controls the actuator 11 by outputting a control signal to the actuator 11. The control unit 20 includes a CPU (Central Processing Unit) and a storage section. Furthermore, when outputting a control signal to the actuator 11, the control unit 20 outputs a test start signal to the analysis unit 30, which notifies the start of the pushing operation of the indenter 15 into the sample SP1. When the control unit 20 pushes the indenter 15 to a preset pushing amount, it outputs a test end signal to the analysis unit 30 to notify that the pushing operation of the indenter 15 is finished. Furthermore, the control unit 20 outputs the pushing amount information input from the potentiometer 17 to the analysis unit 30. The control unit 20 is realized by the CPU executing a program for controlling the actuator 11 stored in a storage section.

The analysis unit 30 includes a CPU 31, a storage section 32, and a display section 33, as shown in FIG. The display section 33 is, for example, a liquid crystal display device. The CPU 31 functions as a data acquisition section 311, a correction section 312, a speed calculation section 313, a coefficient calculation section 314, and a coefficient information output section 315 by executing the analysis program stored in the storage section 32. Furthermore, the storage unit 32 includes a measurement information storage unit 321 that stores load information indicating the indentation load acquired from the measurement unit 10 and indentation amount information indicating the indentation amount in chronological order. Furthermore, the storage unit 32 includes a relational expression storage unit 322 that stores information on the relational expression shown in the above-mentioned equation (31), and a coefficient storage unit 323 that stores information that indicates the calculated elastic coefficient and viscosity coefficient. have

The data acquisition unit 311 is a physical quantity history acquisition unit that sequentially acquires load information and pushing amount information from the measurement unit 10 when a test start signal is input from the control unit 20 . Here, the indentation amount information is information indicating the indentation amount of the indenter 15, and the load information is information indicating the indentation load acting on the indenter 15. Then, the data acquisition unit 311 stores the push amount information and load information in the measurement information storage unit 321 in the order in which they are acquired. Furthermore, when the test end signal is input from the control unit 20, the data acquisition unit 311 stops acquiring data.

The correction unit 312 specifies a reference push amount that is an initial value of the push amount. Here, as shown in FIG. 9, the reference indentation amount is the point at which the indentation load first becomes larger than the 0 level when the indentation amount is increased from a state where the indenter 15 is not in contact with the sample SP1. This corresponds to the pushing amount δ0 in . Then, the correction unit 312 updates the push amount information where the push amount is the reference push amount δ0 or more with information indicating the push amount δ obtained by subtracting the reference push amount δ0 from the push amount δ1 indicated by the push. The pushing amount information stored in the measurement information storage unit 321 is corrected.

The speed calculation unit 313 calculates the change rate of the push amount, that is, the history of the push speed, based on the history of the push amount indicated by the push amount information stored in the measurement information storage unit 321. The speed calculation unit 313 notifies the coefficient calculation unit 314 of information indicating the history of the calculated pushing speed.

The coefficient calculation unit 314 uses the above-mentioned relational expression (31) to perform fitting by the least squares method on the history of the indentation load, the history of the indentation amount, and the history of the indentation speed notified from the speed calculation unit 313. Execute. At this time, the coefficient calculation unit 314 acquires information indicating the relational expression of equation (31) described above from the relational expression storage unit 322, and performs fitting using the least squares method. Thereby, the coefficient calculation unit 314 calculates approximate solutions for the elastic coefficients E ^e and E ^ve and approximate solutions for the viscosity coefficient C. The coefficient calculation unit 314 stores information indicating approximate solutions for the calculated elastic coefficients Ee and Eve and information indicating an approximate solution for the viscosity coefficient C in the coefficient storage unit 323.

The coefficient information output unit 315 converts the information indicating the approximate solution of the viscosity coefficient C and the information indicating the approximate solutions of the elastic coefficients E ^e and E ^ve stored in the coefficient storage unit 323 into the viscosity coefficient indicating the viscosity coefficient C of the sample SP1. The information and elastic coefficients E ^e and E ^ve are outputted to the display section 33 as elastic coefficient information. At this time, the display unit 33 displays the viscosity coefficient information and elastic coefficient information input from the coefficient information output unit 315.

Next, the analysis process executed by the analysis unit 30 of the viscoelastic coefficient measuring device 100 according to the present embodiment will be described with reference to FIG. 10. This analysis process is executed, for example, when a test start signal is input from the control unit 20.

First, the data acquisition section 311 sequentially acquires load information and push amount information from the measurement unit 10, and stores them in the measurement information storage section 321 (step S1). Then, when the test end signal is input from the control unit 20, the data acquisition section 311 stops acquiring data.

Next, the correction unit 312 reads a series of load information and indentation amount information acquired for the sample SP1 from the measurement information storage unit 321 (step S2). Subsequently, the correction unit 312 specifies a reference push amount using the read series of load information and push amount information, and corrects the push amount information based on the specified reference push amount (step S3). Here, when the indenter 15 increases the indentation amount from a state where it is not in contact with the sample SP1, the correction unit 312 sets the indentation amount δ ₀ as a reference at the time when the indentation load becomes larger than the 0 level for the first time. Specify as the amount of push.

Thereafter, the speed calculation unit 313 calculates the history of the pushing speed based on the history of the pushing amount indicated by the pushing amount information stored in the measurement information storage unit 321 (step S4).

Next, the coefficient calculation unit 314 uses the above-mentioned relational expression (31) to perform fitting by the least squares method on the history of the indentation load, the history of the indentation amount, and the history of the indentation speed. , approximate solutions for the elastic coefficients E ^e and E ^ve and approximate solutions for the viscosity coefficient C are calculated. Then, the coefficient calculation unit 314 causes the coefficient storage unit 323 to store information indicating approximate solutions for the calculated elastic coefficients Ee and Eve and information indicating an approximate solution for the viscosity coefficient C. (Step S5).

Subsequently, the coefficient information output unit 314 uses the information indicating the approximate solution of the viscosity coefficient C and the information indicating the approximate solutions of the elastic coefficients E ^e and E ^ve stored in the coefficient storage unit 323 to the viscosity coefficient C of the sample SP1. The viscosity coefficient information and the elastic coefficient information indicating the elastic coefficients E ^e and E ^ve are output to the display section 33 (step S6).

Next, the results of executing the analysis process according to the present embodiment will be explained while comparing with the viscoelastic coefficient measuring method according to Comparative Examples 1 and 2. In the viscoelastic coefficient measuring method according to Comparative Example 1, the elastic coefficient E ^e and the viscous coefficient C are calculated based on Vigot's theory. Specifically, the sample SP1 is composed of an elastic part having a spring element and a viscoelastic part having a dashpot element, as shown in FIG. 11(A). Assume that it is represented by an elemental solid model. Note that in FIG. 11(A), ε ^e , E ^e , C, σ ^v and ε ^v have the same meanings as ε ^e , E ^e , C, σ ^v and ε ^v shown in FIG. 1 above.

In FIG. 11(B), a curve C10 shows the measurement results when a bilinear flexible material (superelastic polymer material SMP Foam manufactured by SMP Technologies Co., Ltd.) was used as the sample SP1. Here, as the measurement unit 10, SoftMeasure HG1003 manufactured by Horiuchi Electric Manufacturing Co., Ltd. was used. Further, the diameter of the indenter 15 was 10 mm, and the pushing speed of the indenter 15 was 2.0 mm/s. Further, a curve C91 in FIG. 11(B) shows an approximate curve showing the relationship between the indentation load and the indentation amount obtained by the analysis process according to the comparative example. As shown in FIG. 11(B), in the curve C91 obtained by the analysis process according to the comparative example, deviations from the measured data can be confirmed in the region where the indentation amount is close to 0.

Here, FIG. 12 shows the results of executing the analysis process according to this embodiment. A curve C11 in FIG. 12 is an approximate curve showing the relationship between the indentation load and the indentation amount obtained by the analysis process according to the present embodiment. As shown in FIG. 12, it can be confirmed that the curve C11 obtained by the analysis process according to the present embodiment matches the measurement data in the entire region of the indentation amount. From this, it can be seen that by performing the analysis process according to the present embodiment, the deformation behavior of the sample SP1 can be appropriately reproduced, and the viscosity coefficient C and the elastic coefficients E ^e and E ^ve can be calculated with high accuracy. In addition, calculation results obtained by the viscoelastic coefficient measuring method according to Comparative Example 1 and calculations obtained by the viscoelastic coefficient measuring method according to Comparative Example 2, which calculates the elastic coefficient E ^e and the viscous coefficient C based on Maxwell's theory. The results and the calculation results obtained by the viscoelastic coefficient measuring method according to the present embodiment are shown in FIG. In FIG. 13, a curve C12 shows an approximate curve according to the present embodiment, a curve C92 shows an approximate curve according to Comparative Example 1, and a curve C93 shows an approximate curve according to Comparative Example 2. In addition, in FIG. 13, the pushing speed was 10 mm/sec in all cases.

As explained above, according to the viscoelastic coefficient measuring method and the viscoelastic coefficient measuring apparatus 100 according to the present embodiment, the history of the indentation amount of the sample SP1 and the effect on the sample SP1 when deforming the sample SP1 over time. The history of the pushing load is acquired, and the history of the pushing speed is calculated based on the history of the pushing amount. Then, using the relational expression shown in equation (31) above, approximate solutions for the elastic coefficients E ^e and E ^ve and approximate solutions for the viscosity coefficient C are obtained from the history of the indentation amount, the history of the indentation load, and the history of the indentation speed. Calculate. Thereby, approximate solutions for the elastic coefficients E ^e and E ^ve and approximate solutions for the viscous coefficient C of the sample SP1 can be calculated by changing the sample SP1 only once over time. Therefore, the content of the test for measuring the elastic coefficients E ^e , E ^ve and viscosity coefficient C of sample SP1 can be simplified, and the time required to determine the elastic coefficients E ^e , E ^ve and viscosity coefficient C can be shortened. can.

(Embodiment 2)
In the viscoelastic coefficient measuring method according to the present embodiment, the value of the sample is determined based on the history of the amount of strain of the sample and the history of the magnitude of stress acting on the sample when the sample is periodically deformed. Calculate the value of the viscosity coefficient and the value of the elastic coefficient. In the viscoelastic coefficient measuring method according to the present embodiment, it is also assumed that the sample is represented by the three-element solid model described in Embodiment 1 using FIG. 1.

When a sample having viscoelasticity is periodically deformed, the amount of strain on the sample and the magnitude of stress acting on the sample exhibit temporal behavior as shown in, for example, FIG. 14. In FIG. 14, ε(t) indicates the amount of strain on the sample, and σ(t) indicates the stress response that can be observed when the sample is deformed, that is, the magnitude of the stress acting on the sample. . Further, ε ₀ and σ ₀ respectively indicate the amount of strain of the sample and the amplitude value of stress acting on the sample. As shown in FIG. 14, the waveform of the strain amount of the sample is out of phase by Δ/ω with respect to the waveform of the stress acting on the sample. This is due to the influence of the viscosity of the sample. Further, the strain amount ε(t) corresponds to a first physical quantity when periodically deforming the sample, and the stress σ(t) corresponds to a second physical quantity. Here, the amount of strain ε(t) of the sample and the magnitude of stress σ(t) acting on the sample are expressed by the following equations (32) and (33), respectively.

Here, ω indicates the angular velocity when periodically deforming the sample, and Δ indicates the amount of phase delay due to the influence of the viscosity of the sample having viscoelasticity. Further, the time differential of the strain amount ε(t) of the sample and the time differential of the magnitude σ(t) of the stress acting on the sample are expressed by the following equations (34) and (35), respectively.

Then, by substituting the relational expressions (32) to (35) into the equation (8) described in Embodiment 1 and transforming it using the law of sine, the following relational expression (36) is obtained. derived.

Here, the following relational expression (37) is derived from the condition that equation (36) holds true at all times t.

Then, by transforming equation (37), the following relational expression (38) is obtained.

FIG. 15(A) shows an example of a theoretical curve showing the dependence of the phase delay amount Δ on the frequency ω, which is shown in Equation (38). Further, by transforming the equation (38), the following relational expression (39) representing the loss tangent is obtained.

An example of a theoretical curve showing the dependence of the loss tangent tanΔ on the frequency ω, which is shown in Equation (39), is shown in FIG. 15(B). Furthermore, if the relational expressions shown in equations (37) to (39) hold true, equation (36) can be expressed as the relational equation shown in equation (40) below.

Further, the deformation resistivity explained in Embodiment 1 is expressed by the relational expression shown in the following equation (41) from the relational expression of equation (40).

Here, D(ω) represents deformation resistivity. FIG. 16 shows an example of a theoretical curve showing the dependence of the deformation resistivity D(ω) on the frequency ω, which is shown in Equation (41). Then, for the relational expression (33), by replacing the amplitude σ ₀ and the phase delay amount Δ based on the relational expression (38) and the relational expression (40), the following equation (42) can be obtained. A relational expression is obtained.

In the viscoelastic coefficient measuring method according to the present embodiment, elasticity is Approximate solutions for the coefficients E ^e and E ^ve and an approximate solution for the viscosity coefficient C are calculated.

Next, a viscoelastic coefficient measuring device according to this embodiment will be explained. As shown in FIG. 17, a viscoelastic coefficient measuring device 2100 according to the present embodiment includes a measurement unit 2010, a control unit 2020, and an analysis unit 2030. The measurement unit 2010 includes two plates 2142 and 2152 that sandwich the sample SP2, shaft parts 2141 and 2151 with one end fixed to the center of each of the plates 2142 and 2152, a stress measurement section 2013, an actuator 2011, and an encoder. 2017. The actuator 2011 rotates the plate 2142 by rotating the shaft portion 2141 around its central axis. Here, the actuator 2011 alternately rotates the shaft portion 2141 by a preset angle in a rotation direction shown by an arrow AR203 and a rotation direction shown by an arrow AR204, which is opposite to the rotation direction shown by the arrow AR203. The stress measurement unit 2013 is attached to the shaft portion 2151 and measures the stress acting on the plate 2152 from the sample SP2 via the shaft portion 2151. Further, the stress measurement unit 2013 outputs stress information obtained by measuring stress to the analysis unit 2030. The encoder 2017 outputs to the control unit 2020 distortion amount information indicating the amount of distortion of the sample SP2 on which the measured rotation angle of the shaft portion 2141 is reflected.

Control unit 2020 controls actuator 2011 by outputting a control signal to actuator 2011. Control unit 2020 has a CPU and a storage section. Furthermore, when outputting a control signal to the actuator 2011, the control unit 2020 outputs a test start signal to the analysis unit 2030, which notifies the start of the rotational drive of the plate 2142. Then, when a preset test time has elapsed since the start of the rotational drive of the plate 2142, the control unit 2020 outputs a test end signal to the analysis unit 30 to notify that the pushing operation of the indenter 15 is to be ended. Further, the control unit 2020 outputs the distortion amount information input from the encoder 2017 to the analysis unit 2030. The control unit 2020 is realized by the CPU executing a program for controlling the actuator 11 stored in a storage section.

Similar to the analysis unit 30 according to the first embodiment, the analysis unit 2030 includes a CPU 31, a storage section 32, and a display section 33, as shown in FIG. Note that in FIG. 18, the same components as in Embodiment 1 are given the same reference numerals as in FIG. 10. The CPU 31 functions as a data acquisition section 2311, a time measurement section 2312, a speed calculation section 2313, a coefficient calculation section 2314, and a coefficient information output section 315 by executing the analysis program stored in the storage section 32. The storage unit 32 also stores measurement information in which stress information acquired from the measurement unit 2010 and strain amount information acquired from the control unit 2020 are associated with time information indicating the time measured by the time measurement unit 2312. It has a storage section 2321. Furthermore, the storage unit 32 includes a relational expression storage unit 2322 that stores information about the relational expression shown in the above-mentioned equation (33), and a coefficient storage unit 323.

The data acquisition unit 2311 is a physical quantity history acquisition unit that sequentially acquires stress information and strain amount information from the measurement unit 2010 and the control unit 2020 in response to input of a test start signal from the control unit 20. The clock unit 2312 clocks the time when the data acquisition unit 2311 acquires stress information and strain amount information. Then, the data acquisition unit 2311 stores the pushing amount information and the load information in the measurement information storage unit 2321 in association with time information indicating the time measured by the clock unit 2312.

The speed calculating unit 2313 calculates the angular velocity when periodically changing the sample SP2 based on the history of the amount of strain of the sample SP2 indicated by the amount of strain information stored in the measurement information storage unit 321. The velocity calculation unit 2313 notifies the coefficient calculation unit 2314 of information indicating the calculated angular velocity.

The coefficient calculation unit 2314 calculates the history of the stress acting on the sample SP2 and the amount of strain of the sample SP2 based on the relational expression (42) described above and the angular velocity indicated by the information notified from the velocity calculation unit 2313. Perform least squares fitting on the history. At this time, the coefficient calculation unit 2314 acquires information indicating the relational expression of the above-mentioned equation (42) from the relational expression storage unit 2322, and performs fitting using the least squares method. Thereby, the coefficient calculation unit 2314 calculates approximate solutions for the elastic coefficients E ^e and E ^ve and approximate solutions for the viscosity coefficient C. The coefficient calculation unit 2314 stores information indicating approximate solutions for the calculated elastic coefficients Ee and Eve and information indicating an approximate solution for the viscosity coefficient C in the coefficient storage unit 323. The coefficient information output unit 314 then converts the information indicating the approximate solution of the viscosity coefficient C and the information indicating the approximate solution of the elastic coefficients E ^e and E ^ve stored in the coefficient storage unit 323 to the information indicating the viscosity coefficient C of the sample SP1. It is output to the display unit 33 as elastic coefficient information indicating viscosity coefficient information and elastic coefficients E ^e and E ^ve .

Next, the analysis process executed by the analysis unit 2030 of the viscoelastic coefficient measuring device 2100 according to this embodiment will be described with reference to FIG. 19. This analysis process is started, for example, when a test start signal is input from the control unit 20.

First, the data acquisition unit 2311 sequentially acquires stress information and strain amount information from the measurement unit 2010 and the control unit 2020, and stores them in the measurement information storage unit 2321 (step S201). At this time, the data acquisition unit 2311 stores the pushing amount information and the load information in the measurement information storage unit 2321 in association with time information indicating the time measured by the clock unit 2312. Then, when the test end signal is input from the control unit 2020, the data acquisition unit 2311 stops acquiring data.

Next, the speed calculation unit 2313 calculates the angular velocity when periodically changing the sample SP2 based on the history of the amount of strain of the sample SP2 indicated by the amount of strain information stored in the measurement information storage unit 321 (step S202 ).

Subsequently, the coefficient calculating unit 2314 calculates the history of stress acting on the sample SP2 and the history of the stress acting on the sample SP2 based on the above-mentioned relational expression (42) and the angular velocity indicated by the information notified from the velocity calculating unit 2313. Approximate solutions for the elastic coefficients E ^e and E ^ve and approximate solutions for the viscosity coefficient C are calculated from the history of the amount of strain. Then, the coefficient calculation unit 2314 causes the coefficient storage unit 323 to store information indicating approximate solutions for the calculated elastic coefficients Ee and Eve and information indicating an approximate solution for the viscosity coefficient C. (Step S203).

Thereafter, the coefficient information output unit 315 converts the information indicating the approximate solution of the viscosity coefficient C and the information indicating the approximate solution of the elastic coefficients E ^e and E ^ve stored in the coefficient storage unit 323 to the information indicating the viscosity coefficient C of the sample SP2. The viscosity coefficient information and the elastic coefficients E ^e and E ^ve are output to the display section 33 as elastic coefficient information indicating the elastic coefficients E e and E ve (step S204).

As explained above, according to the viscoelastic coefficient measuring method and the viscoelastic coefficient measuring apparatus 2100 according to the present embodiment, based on the history of the strain amount of the sample SP2 when the sample SP2 is periodically deformed, , calculate the angular velocity when periodically deforming the sample SP2. Then, based on the relational expression shown in the above-mentioned equation (42) and the calculated angular velocity, the elastic coefficients E ^e and E ^ve are calculated from the history of the strain amount of the sample SP2 and the history of the stress acting on the sample SP2. An approximate solution and an approximate solution for the viscosity coefficient C are calculated. Thereby, by periodically deforming the sample SP2, approximate solutions for the elastic coefficients E ^e and E ^ve and an approximate solution for the viscosity coefficient C of the sample SP2 can be calculated. Therefore, the content of the test for measuring the elastic coefficients E ^e , E ^ve and viscosity coefficient C of sample SP2 can be simplified, and the time required to determine the elastic coefficients E ^e , E ^ve and viscosity coefficient C can be shortened. can.

(Embodiment 3)
In the viscoelastic coefficient measuring method according to the present embodiment, the sample is measured based on the history of the amount of strain on the sample and the history of the magnitude of stress acting on the sample when tensile strain is applied to the sample. The values of the viscosity coefficient and the elastic coefficient are calculated. In the viscoelastic coefficient measuring method according to the present embodiment, it is also assumed that the sample is represented by the three-element solid model described in Embodiment 1 using FIG. 1.

In this embodiment, similarly to Embodiment 1, the deformation resistivity D is expressed by the relational expression shown in Equation (19). Further, in the process of pulling the sample, the relationship between the strain rate of the sample and the pulling rate of the sample is expressed by the following relational expression (43).

Here, e ^· represents the pulling speed of the sample, and e ₀ ^- represents the initial value of the amount of pulling of the sample. Further, ε ^· indicates the rate of change in the amount of strain, that is, the rate of strain. Regarding equation (43), a theoretical straight line showing the time dependence of the strain rate ^ε is shown in FIG. 20(A). Here, the straight line C31 shows the case where the strain rate increases with the passage of time, and the straight line C32 shows the case where the strain rate is constant regardless of the passage of time. Then, by time-integrating the relational expression (43), the following relational expression (44) is derived.

Here, ε0 indicates the initial value of the amount of distortion, and ε indicates the amount of distortion. Note that e ^· , e ₀ ^- represent the same physical quantities as those in equation (43). Regarding equation (44), a theoretical straight line showing the time dependence of the amount of strain ε is shown in FIG. 20(B). Here, the straight line C33 shows the case where the strain rate increases with the passage of time, and the straight line C34 shows the case where the strain rate is constant regardless of the passage of time. Then, by substituting the relational expressions of equation (43) and equation (44) into equation (19) described in the first embodiment, the relational equation of equation (45) below is derived.

Here, assuming that the tensile load is represented by the product of the deformation resistivity D and the amount of tension, the following relational expression (46) is derived.

Here, F2 indicates the tensile load, and e ^- indicates the amount of tension. The amount of tension e ^- corresponds to a first physical quantity that reflects the amount of distortion of the sample when the sample is deformed over time. Further, the tensile load F2 corresponds to a second physical quantity that reflects the stress acting on the sample. In the viscoelastic coefficient measuring method according to the present embodiment, by using the above-mentioned relational expression (46) and performing fitting by the least squares method on the measured data of the tensile amount and the tensile load, Approximate solutions for the elastic coefficients E ^e and E ^ve and approximate solutions for the viscosity coefficient C are calculated.

Next, a viscoelastic coefficient measuring device according to this embodiment will be explained. As shown in FIG. 21, a viscoelastic coefficient measuring device 3100 according to the present embodiment includes a measurement unit 3010, a control unit 3020, and an analysis unit 3030. The measurement unit 3010 includes two chucks 3014 and 3015 that grip the sample SP3, a load cell 3013, an actuator 3011, and a potentiometer 3017. Chuck 3014 and load cell 3013 are fixed to a base (not shown). Actuator 3011 applies a tensile load to sample SP3 by moving chuck 3014 in the direction shown by arrow AR303. The load cell 3013 is attached to the chuck 3015 and measures the tensile load acting on the sample SP3 via the chuck 3015. Further, the load cell 3013 outputs load information obtained by measuring the tensile load to the analysis unit 3030. Potentiometer 3017 measures the amount of movement of chuck 3014. The amount of movement of the chuck 3014 corresponds to the amount of pulling of the sample SP3. Potentiometer 3017 outputs tension amount information indicating the measured amount of tension of sample SP3 to control unit 3020.

Control unit 3020 controls actuator 3011 by outputting a control signal to actuator 3011. Control unit 3020 has a CPU and a storage section. Further, when outputting a control signal to the actuator 3011, the control unit 3020 outputs a test start signal to the analysis unit 3030, which notifies the start of the pulling operation of the sample SP3 by the chuck 3014. When the control unit 3020 moves the chuck 3014 until the amount of pulling of the sample SP3 reaches a preset amount of pulling, the control unit 3020 sends a test end signal to the analysis unit 3030 to notify that the pulling operation by the chuck 3014 is finished. Output. Further, the control unit 3020 outputs the tension amount information input from the potentiometer 3017 to the analysis unit 3030. The control unit 3020 is realized by the CPU executing a program for controlling the actuator 3011 stored in a storage section.

Similar to the analysis unit 30 according to the first embodiment, the analysis unit 3030 includes a CPU 31, a storage section 32, and a display section 33, as shown in FIG. Note that in FIG. 22, the same components as in Embodiment 1 are given the same reference numerals as in FIG. The CPU 31 functions as a data acquisition section 3311, a time measurement section 3312, a speed calculation section 3313, a coefficient calculation section 3314, and a coefficient information output section 315 by executing the analysis program stored in the storage section 32. The storage unit 32 also stores measurement information in which the load information acquired from the measurement unit 3010 and the tension amount information acquired from the control unit 3020 are associated with time information indicating the time measured by the clock unit 3312. It has a storage section 3321. Furthermore, the storage unit 32 includes a relational expression storage unit 3322 that stores information on the relational expression shown in the above-mentioned equation (46), and a coefficient storage unit 323.

The data acquisition unit 3311 is a physical quantity history acquisition unit that sequentially acquires load information and tension amount information from the measurement unit 3010 and the control unit 3020 when a test start signal is input from the control unit 3020. The clock section 3312 clocks the time when the data acquisition section 3311 acquires the load information and the amount of tension information. Then, the data acquisition unit 3311 stores the tension amount information and the load information in the measurement information storage unit 3321 in association with time information indicating the time measured by the clock unit 3312.

The speed calculating unit 3313 calculates the pulling speed of the sample SP3 based on the history of the pulling amount of the sample SP2 indicated by the pulling amount information stored in the measurement information storage unit 3321. The speed calculation unit 3313 notifies the coefficient calculation unit 3314 of information indicating the calculated pulling speed.

The coefficient calculating unit 3314 calculates the history of the tensile load acting on the sample SP3 and the tensile force of the sample SP3 based on the above-mentioned relational expression (46) and the pulling speed indicated by the information notified from the speed calculating unit 3313. Perform least squares fitting on the history of quantities. At this time, the coefficient calculation unit 3314 acquires information indicating the relational expression of the above-mentioned equation (46) from the relational expression storage unit 3322, and performs fitting using the least squares method. Thereby, the coefficient calculation unit 3314 calculates approximate solutions for the elastic coefficients E ^e and E ^ve and approximate solutions for the viscosity coefficient C. The coefficient calculation unit 3314 stores information indicating approximate solutions for the calculated elastic coefficients Ee and Eve and information indicating an approximate solution for the viscosity coefficient C in the coefficient storage unit 323. The coefficient information output unit 314 then converts the information indicating the approximate solution of the viscosity coefficient C and the information indicating the approximate solution of the elastic coefficients E ^e and E ^ve stored in the coefficient storage unit 323 to the information indicating the viscosity coefficient C of the sample SP1. It is output to the display unit 33 as elastic coefficient information indicating viscosity coefficient information and elastic coefficients E ^e and E ^ve .

Next, the analysis process executed by the analysis unit 3030 of the viscoelastic coefficient measuring device 3100 according to the present embodiment will be described with reference to FIG. 23. This analysis process is started, for example, when a test start signal is input from the control unit 3020.

First, the data acquisition section 3311 sequentially acquires load information and tension amount information from the measurement unit 3010 and the control unit 3020, and stores them in the measurement information storage section 3321 (step S301). At this time, the data acquisition unit 3311 causes the measurement information storage unit 3321 to store the tension amount information and the load information in association with time information indicating the time measured by the clock unit 3312. Then, when the test end signal is input from the control unit 3020, the data acquisition unit 3311 stops acquiring data.

Next, the speed calculating unit 3313 calculates the pulling speed of the sample SP3 based on the history of the pulling amount of the sample SP3 indicated by the pulling amount information stored in the measurement information storage unit 3321 (step S302).

Next, the coefficient calculating unit 3314 calculates the history of the tensile load acting on the sample SP3 and the sample based on the relational expression (46) described above and the pulling speed indicated by the information notified from the speed calculating unit 3313. Approximate solutions for the elastic coefficients E ^e and E ^ve and approximate solutions for the viscosity coefficient C are calculated from the history of the amount of tension of SP3. Then, the coefficient calculation unit 3314 causes the coefficient storage unit 323 to store information indicating approximate solutions for the calculated elastic coefficients Ee and Eve and information indicating an approximate solution for the viscosity coefficient C. (Step S303).

Thereafter, the coefficient information output unit 315 converts the information indicating the approximate solution of the viscosity coefficient C and the information indicating the approximate solution of the elastic coefficients E ^e and E ^ve stored in the coefficient storage unit 323 to the information indicating the viscosity coefficient C of the sample SP2. The viscosity coefficient information and the elastic coefficients E ^e and E ^ve are output to the display unit 33 as elastic coefficient information indicating the elastic coefficients E e and E ve (step S304).

As explained above, according to the viscoelastic coefficient measuring method and the viscoelastic coefficient measuring apparatus 3100 according to the present embodiment, the sample Calculate the pulling speed of SP3. Based on the relational expression shown in the above-mentioned equation (46) and the calculated pulling speed, the elastic modulus E ^e is determined from the history of the amount of pulling of the sample SP3 and the history of the tensile load applied to the sample SP3 An approximate solution for E ^ve and an approximate solution for the viscosity coefficient C are calculated. Thereby, approximate solutions for the elastic coefficients E ^e and E ^ve and approximate solutions for the viscosity coefficient C of the sample SP3 can be calculated by applying a tensile load to the sample SP3 only once and changing the load over time. Therefore, the content of the test for measuring the elastic coefficients E ^e , E ^ve and viscosity coefficient C of sample SP3 can be simplified, and the time required to determine the elastic coefficients E ^e , E ^ve and viscosity coefficient C can be shortened. can.

Although each embodiment of the present invention has been described above, the present invention is not limited to the configuration of each of the above-described embodiments. For example, a viscoelastic coefficient measurement system is constructed from a measurement device including measurement units 10, 2010, 3010 and control units 20, 2020, 3020, and an analysis device including analysis units 30, 2030, 3030 separate from the measurement device. may be configured.

Further, various functions of the control units 20, 2020, 3020 and the analysis units 30, 2030, 3030 according to the present invention may be realized by software, firmware, or a combination of software and firmware. In this case, the software or firmware is written as a program and stored in the storage unit 32. Moreover, the various functions of the control units 20, 2020, 3020 and the analysis units 30, 2030, 3030 according to the present invention can be realized using a computer system without relying on a dedicated system. For example, a computer connected to a network can store a program for executing the above operations on a non-temporary recording medium (flexible disk, CD-ROM (Compact Disc Read-Only Memory), DVD) that can be read by the computer system. (Digital Versatile Disc), MO (Magneto-Optical Disc), etc.) and installs the program on a computer system to execute the above-mentioned processing. , 2030, and 3030 may be configured.

Further, the method of providing the program to the computer is arbitrary. For example, the program may be uploaded to a server on a communication line and distributed to a computer via the communication line. Then, the computer starts this program and executes it like other applications under the control of the OS (Operating System). Thereby, the computer functions as a control unit 20, 2020, 3020 and an analysis unit 30, 2030, 3030 that execute the above-described processing.

Although the embodiments and modifications of the present invention (including those described in the notes; the same applies hereinafter) have been described above, the present invention is not limited to these. The present invention includes combinations of the embodiments and modifications as appropriate, and modifications as appropriate.

The present invention is suitable for evaluating the viscosity coefficient and elastic coefficient of a viscoelastic body.

10, 2010, 3010: Measurement unit, 11, 2011, 3011: Actuator, 12: Stage, 13, 3013: Load cell, 14: Load axis, 15: Indenter, 16: Table, 17, 3017: Potentiometer, 20, 2020, 3020: control unit, 30, 2030, 3030: analysis unit, 31: CPU, 32: storage section, 33: display section, 100, 2100, 3100: viscoelastic coefficient measuring device, 311, 2311, 3311: data acquisition section, 312: Correction section, 313, 2313, 3313: Speed calculation section, 314, 2314, 3314: Coefficient calculation section, 315: Coefficient information output section, 321, 2321, 3321: Measurement information storage section, 322, 2322, 3322: Relationship Formula storage unit, 323: Coefficient storage unit, 2013: Stress measurement unit, 2017: Encoder, 2312, 3312: Time measurement unit, SP1, SP2, SP3: Sample

Claims (10)

deforming the sample over time;
acquiring a history of a first physical quantity that reflects the amount of strain of the sample when deforming the sample over time and a history of a second physical quantity that reflects the stress acting on the sample;
calculating a history of the rate of change of the first physical quantity based on the history of the first physical quantity;
The history of the first physical quantity and the history of the second physical quantity are determined using a relational expression that includes the viscosity coefficient and the elastic coefficient of the sample and expresses the relationship between the first physical quantity, the second physical quantity, and the rate of change. calculating an approximate solution for the viscosity coefficient and an approximate solution for the elastic coefficient from the history of the rate of change;
outputting information indicating the calculated approximate solution of the viscosity coefficient and the calculated approximate solution of the elastic coefficient as viscosity coefficient information indicating the viscosity coefficient and elastic coefficient information indicating the elastic coefficient of the sample ; ,
The relational expression is a first-order differential equation with respect to time between the stress acting on the sample and the amount of strain in the sample, which represents the behavior of the viscoelastic model of the sample, and the change in the stress when the amount of strain changes. Derived from the relational expression obtained by substituting the deformation resistivity representing the quantity,
Method for measuring viscoelastic coefficient. In the step of deforming the sample over time, deforming the sample over time by pushing an indenter into the sample,
The first physical quantity is the amount of pushing of the indenter when pushing the indenter into the sample,
The second physical quantity is an indentation load acting on the indenter,
The rate of change is the indentation rate of the indenter,
The viscoelastic coefficient measuring method according to claim 1 . deforming the sample over time;
acquiring a history of a first physical quantity that reflects the amount of strain of the sample when deforming the sample over time and a history of a second physical quantity that reflects the stress acting on the sample;
calculating a history of the rate of change of the first physical quantity based on the history of the first physical quantity;
The history of the first physical quantity and the history of the second physical quantity are determined using a relational expression that includes the viscosity coefficient and the elastic coefficient of the sample and expresses the relationship between the first physical quantity, the second physical quantity, and the rate of change. calculating an approximate solution for the viscosity coefficient and an approximate solution for the elastic coefficient from the history of the rate of change;
outputting information indicating the calculated approximate solution of the viscosity coefficient and the calculated approximate solution of the elastic coefficient as viscosity coefficient information indicating the viscosity coefficient and elastic coefficient information indicating the elastic coefficient of the sample,
In the step of deforming the sample over time, deforming the sample over time by pushing an indenter into the sample,
The first physical quantity is the amount of pushing of the indenter when pushing the indenter into the sample,
The second physical quantity is an indentation load acting on the indenter,
The rate of change is the indentation rate of the indenter,
The indenter is spherical,
The relational expression is expressed by the following formula (A),
Here, F is the indentation load, δ is the indentation amount, δ^・is the indentation speed, E ^e and ^Eve are the elastic coefficients, C is the viscosity coefficient, ν is the Poisson's ratio of the sample, and φ is the indenter diameter of,
Method for measuring viscoelastic coefficient. deforming the sample over time;
acquiring a history of a first physical quantity that reflects the amount of strain of the sample when deforming the sample over time and a history of a second physical quantity that reflects the stress acting on the sample;
calculating a history of the rate of change of the first physical quantity based on the history of the first physical quantity;
The history of the first physical quantity and the history of the second physical quantity are determined using a relational expression that includes the viscosity coefficient and the elastic coefficient of the sample and expresses the relationship between the first physical quantity, the second physical quantity, and the rate of change. calculating an approximate solution for the viscosity coefficient and an approximate solution for the elastic coefficient from the history of the rate of change;
outputting information indicating the calculated approximate solution of the viscosity coefficient and the calculated approximate solution of the elastic coefficient as viscosity coefficient information indicating the viscosity coefficient and elastic coefficient information indicating the elastic coefficient of the sample,
In the step of deforming the sample over time, holding the sample with a chuck and applying periodic vibrations to the sample, deforming the sample over time,
The first physical quantity is a strain amount of the sample,
The second physical quantity is stress acting on the chuck,
The rate of change is the angular velocity of the periodic vibration.
Method for measuring viscoelastic coefficient. The relational expression is a first-order differential equation with respect to time between the stress acting on the sample and the amount of strain in the sample, which represents the behavior of the viscoelastic model of the sample, and the change in the stress when the amount of strain changes. Derived from the relational expression obtained by substituting the deformation resistivity representing the quantity,
The viscoelastic coefficient measuring method according to claim 3 or 4. The viscoelastic model is a three-element solid model,
The viscoelastic coefficient measuring method according to claim 1, 2 or 5 . In the step of deforming the sample over time, both sides of the sample in one preset direction are gripped by two chucks, and the two chucks are moved away from each other to deform the sample over time. transform it into
The first physical quantity is the amount of tension of the sample,
The second physical quantity is a tensile load acting on the chuck,
The rate of change is the pulling rate of the chuck.
The viscoelastic coefficient measuring method according to claim 1 . A viscoelastic coefficient measuring device that measures the viscosity coefficient and elastic coefficient of a sample by deforming the sample over time,
a physical quantity history acquisition unit that acquires a history of a first physical quantity that reflects an amount of strain of the sample when deforming the sample over time and a history of a second physical quantity that reflects stress acting on the sample;
a speed calculation unit that calculates a history of the rate of change of the first physical quantity based on the history of the first physical quantity;
The history of the first physical quantity and the history of the second physical quantity are determined using a relational expression that includes the viscosity coefficient and the elastic coefficient of the sample and expresses the relationship between the first physical quantity, the second physical quantity, and the rate of change. a coefficient calculation unit that calculates an approximate solution of the viscosity coefficient and an approximate solution of the elastic coefficient from the history of the rate of change;
an output unit that outputs information indicating the calculated approximate solution of the viscosity coefficient and the calculated approximate solution of the elastic coefficient as viscosity coefficient information indicating the viscosity coefficient and elastic coefficient information indicating the elastic coefficient of the sample. picture,
The relational expression is a first-order differential equation with respect to time between the stress acting on the sample and the amount of strain in the sample, which represents the behavior of the viscoelastic model of the sample, and the change in the stress when the amount of strain changes. Derived from the relational expression obtained by substituting the deformation resistivity representing the quantity,
Viscoelastic coefficient measuring device. An indenter and
an actuator that drives the indenter and deforms the sample over time by pushing the indenter into the sample;
a potentiometer that detects the amount of pushing of the indenter when pushing the indenter into the sample;
further comprising a load cell that detects an indentation load acting on the indenter,
The first physical quantity is the amount of pushing of the indenter when pushing the indenter into the sample,
The second physical quantity is an indentation load acting on the indenter,
The rate of change is the indentation rate of the indenter,
The viscoelastic coefficient measuring device according to claim 8 . computer,
a physical quantity history acquisition unit that acquires a history of a first physical quantity that reflects the amount of strain of the sample when deforming the sample over time and a history of a second physical quantity that reflects the stress acting on the sample;
a speed calculation unit that calculates a history of the rate of change of the first physical quantity based on the history of the first physical quantity;
The history of the first physical quantity and the history of the second physical quantity are determined using a relational expression that includes the viscosity coefficient and the elastic coefficient of the sample and expresses the relationship between the first physical quantity, the second physical quantity, and the rate of change. a coefficient calculation unit that calculates an approximate solution of the viscosity coefficient and an approximate solution of the elastic coefficient from the history of the rate of change;
an output unit that outputs information indicating the calculated approximate solution of the viscosity coefficient and the calculated approximate solution of the elastic coefficient as viscosity coefficient information indicating the viscosity coefficient and elastic coefficient information indicating the elastic coefficient of the sample;
It is a program to function as
The relational expression is a first-order differential equation with respect to time between the stress acting on the sample and the amount of strain in the sample, which represents the behavior of the viscoelastic model of the sample, and the change in the stress when the amount of strain changes. Derived from the relational expression obtained by substituting the deformation resistivity representing the quantity,
program .

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