JP2011137667A - Method and apparatus for testing indentation - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a new indentation testing apparatus. <P>SOLUTION: The indentation testing apparatus is employed to push an indenter in a sample and has a corresponding indentation strain calculator for calculating the corresponding indentation strain of the sample using the thickness of the sample and a non-linear physical property calculator for calculating the non-linear physical property values of the sample using the corresponding indentation strain. Herein, a viscoelastic material can be employed as the sample. Further, non-linear physical property values in a three-element solid model can be calculated as the non-linear physical property values. That is, the Young's modulus of an elastic part, the viscosity compliance of the viscoelastic part and the Young's modulus of the elastic part in the viscoelastic part can be calculated as the non-linear physical property values. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a novel indentation test method. The present invention also relates to a novel indentation test apparatus using the above indentation test method.

  Standard material testing methods have been applied to the tests to determine the mechanical properties of various organs in the living body, but in order to solve ethical problems, in-situ measurement methods suitable for human physical property measurement have been developed. Development is expected.

  Therefore, in the ball indenter indentation test that can measure the physical property value without cutting out the sample, the inventor proposed a method that introduced the concept of equivalent indentation strain that measures the Young's modulus regardless of the thickness of the sample. It was shown that minimally invasive measurement is possible with soft materials such as materials and soft tissues of living organisms (see Non-Patent Document 1).

  Here, regarding the case of evaluating the viscoelastic behavior of these soft materials, the effectiveness of a multi-element mechanical model such as a generalized viscoelastic model is known, and various other constitutive models have been studied. ing. Among them, the three-element solid model has few components and is relatively easy to apply to FEM, and is an effective model for highly accurate numerical simulation of a living body (see Non-Patent Documents 2 and 3).

  As a method for improving the accuracy of this simulation, a method for identifying nonlinear physical property values from uniaxial tensile test results at three different strain rates in a three-element solid model has been proposed. Has been confirmed (see Non-Patent Document 4).

M. Tani, A. Sakuma and M. Shinomiya, Evaluation of Thickness and Young's Modulus of Soft Materials by using Spherical Indentation Testing, Transactions of the Japan Society of Mechanical Engineers, Series A, Vol.75, No.755, (2009) , pp.901-908. (in Japanese) E. Nakamachi, K. Furukawa, N. Shiomura and Y. Itou, Development of a Multi-Scale Finite Element Analysis Code by Using a Micro Nerve Cell Model for Brain Injury Prediction, Transactions of the Japan Society of Mechanical Engineers, Series A, Vol.73, No.733, (2007), pp.1087-1094. (In Japanese) H. Kuramae, Y. Itou, Y. Uetsuji and E. Nakamachi, A Multi-Scale Finite Element Crash Analysis for Head Injury Prediction by Employing a Micro Blood Vessel Model, Transactions of the Japan Society of Mechanical Engineers, Series A, Vol. 74, No.741, (2008), pp.749-756. (In Japanese) M. Ogasawara, A. Sakuma, T. Tadomi, E. Yanagisawa and M. Tani, Valuation Technique of Nonlinear Parameters in Three-Element Solid Model and Its Application to Biological Soft Tissue, Transactions of the Japan Society of Mechanical Engineers, Series A , Vol.75, No.750, (2009), pp.251-258. (In Japanese)

  However, the method described in Non-Patent Document 4 has a problem that it is difficult to perform measurement with minimal invasiveness because the most standard tensile test is used.

  Therefore, development of a novel indentation test method and indentation test apparatus that solves such problems is desired.

The present invention has been made in view of such problems, and an object thereof is to provide a novel indentation test method.
Another object of the present invention is to provide a novel indentation test apparatus using the above indentation test method.

  In order to solve the above problems and achieve the object of the present invention, the indentation test method of the present invention calculates the equivalent indentation strain of the sample using the sample thickness in the indentation test method of indenting the sample into the sample, The nonlinear physical property value of the sample is calculated using the equivalent indentation strain.

  Here, although not necessarily limited, the sample is preferably a viscoelastic body. Moreover, although not necessarily limited, it is preferable that the nonlinear physical property value is a nonlinear physical property value in a three-element solid model. Moreover, although not necessarily limited, it is preferable that a nonlinear physical property value is the Young's modulus of an elastic part, the viscosity compliance of a viscoelastic part, and the Young's modulus of the elastic part in a viscoelastic part.

  The indentation test apparatus according to the present invention is an indentation test apparatus for indenting an indenter into a sample, an equivalent indentation strain calculating unit for calculating an equivalent indentation strain of the sample using the sample thickness, and a nonlinear of the sample using the equivalent indentation strain. It has a non-linear property value calculation unit for calculating a property value.

  Here, although not necessarily limited, the sample is preferably a viscoelastic body. Moreover, although not necessarily limited, it is preferable that the nonlinear physical property value is a nonlinear physical property value in a three-element solid model. Moreover, although not necessarily limited, it is preferable that a nonlinear physical property value is the Young's modulus of an elastic part, the viscosity compliance of a viscoelastic part, and the Young's modulus of the elastic part in a viscoelastic part.

  The present invention has the following effects.

  In the indentation test method of the present invention, in the indentation test method in which an indenter is indented into a sample, the equivalent indentation strain of the sample is calculated using the sample thickness, and the nonlinear physical property value of the sample is calculated using the equivalent indentation strain. A new indentation test method can be provided.

  The indentation test apparatus according to the present invention is an indentation test apparatus for indenting an indenter into a sample, an equivalent indentation strain calculating unit for calculating an equivalent indentation strain of the sample using the sample thickness, and a nonlinear of the sample using the equivalent indentation strain. Since it has the nonlinear physical property value calculation part which calculates a physical property value, a novel indentation test apparatus can be provided.

It is a figure explaining that indentation deformation | transformation is considered to be a superposition of contact deformation and compression deformation. It is a figure which shows the 3 element solid model used for this invention. It is a figure which shows the stress increase in a load process, and the stress relaxation after a stop in the tension test of a viscoelastic material which stops a deformation | transformation when it reaches a fixed strain. It is a figure explaining the method of correct | amending the influence of the stress relaxation contained in the reference data obtained from the experiment on very low speed conditions. It is a figure which shows the outline of an indentation testing machine. (a) is a figure which shows the result of having identified the nonlinear physical property value in the 3 element solid model of a test material by a ball indenter indentation test and a tensile test, (b) is a figure which shows two elastic elements in a 3 element solid model It is a figure which shows what was evaluated only by the identification result of the elastic part Young's modulus and the viscoelastic part Young's modulus, considering only the serial connection model. It is a figure which shows the stress curve of the experiment and numerical simulation which also observed the stress relaxation process after tension | pulling stop, after carrying out the tension load to the predetermined strain at three different strain rates.

  Hereinafter, embodiments for carrying out the invention relating to the indentation test method and the indentation test apparatus will be described.

  The indentation test method is a method of calculating the equivalent indentation strain of the sample using the sample thickness and calculating the nonlinear physical property value of the sample using the equivalent indentation strain in the indentation test method in which an indenter is indented into the sample.

  The indentation test apparatus is an indentation test apparatus that indents an indenter into a sample, an equivalent indentation strain calculation unit that calculates the equivalent indentation strain of the sample using the sample thickness, and a nonlinear physical property value of the sample using the equivalent indentation strain. It is an apparatus having a nonlinear physical property value calculation unit for calculating.

  A viscoelastic body can be adopted as the sample. As the nonlinear physical property value, the Young's modulus of the elastic part, the viscosity compliance of the viscoelastic part, and the Young's modulus of the elastic part in the viscoelastic part in the three-element solid model can be adopted.

  In the text of this specification, “(English character symbol) hat” refers to an English character symbol with a hat symbol, and “(English character symbol) overline” refers to an English character symbol with an overline. The one with an overdot in an English character symbol is described as “(English character symbol) overdot”, and the one with an overdot line in an English character symbol is described as “(English character symbol) overdot line”. To do.

  The ball indenter indentation test and viscoelastic behavior evaluation will be described. First, the Young's modulus measurement by the ball indenter indentation test is explained [1]. As shown in FIG. 1, indentation deformation by a ball indenter indentation test to a finite sample fixed on a rigid body is considered as superposition of contact deformation and compression deformation. At this time, an equivalent indentation strain ε overline representing an equivalent uniaxial strain at the center of the contact portion is defined by the following equation.

  This first term expresses contact deformation due to the ball indenter, and is expressed as the following equation as Hertz strain according to Hertz's elastic contact theory.

  Here, φ and δ are the diameter and indentation amount of the ball indenter, respectively, and ν is the Poisson's ratio of the sample. The second term expresses the rate of change of the area volume of the compressive deformation that occurs between the ball indenter and the rigid body, and is expressed by the following equation using the sample thickness h.

  At this time, the Young's modulus E of the sample is obtained by the following equation from Hertz's elastic contact theory and Hooke's law.

  Here, the indentation load F-hat on the finite sample with the sample thickness h placed on the rigid body is larger than that on the semi-infinite sample, and this effect is considered by considering the equivalent indentation strain ε overline. The Young's modulus E can be measured regardless of the thickness h. In addition, this measurement method suggests the possibility of measuring the strain dependence in which the Young's modulus changes with the indentation amount δ [1].

The identification [2] of the nonlinear physical property value of the three-element solid model will be described. The problem of deformation in a polymer material or a solid containing a solution is a problem in which a viscous phenomenon and an elastic phenomenon coexist. In the present invention, a constitutive equation is considered in the three-element solid model shown in FIG. The subscripts e, v, and ve in this figure represent an elastic part, a viscoelastic part, and an elastic part in the viscoelastic part, respectively, where Young's modulus is E and viscous compliance is C. First as a relational expression of this model, the total strain rate epsilon over dots as the sum of the elastic portions strain rate epsilon ^e over dots and viscoelastic unit strain rate epsilon ^v over dots can be illustrated as follows.

  In addition, the following relationships are established for each component.

However, σ, σ overdot, ^σve and σve ^overdot respectively represent stress, stress rate, stress in the viscoelastic part and its rate. In addition, the physical property values used here are expressed in a function form of a state quantity for the purpose of expressing a complicated nonlinear behavior of the viscoelastic material. As this state quantity, an amount corresponding to a storage force related to deformation should be adopted, but strains ε ^e and ε ^v are considered in the present invention for simplicity. In other words, each physical quantity has a function form having dependence on these strains ε ^e and ε ^v, and elastic Young's modulus E ^e (ε ^e ), viscoelastic Young's modulus E ^ve (ε ^v ) and viscous compliance C, respectively. It shall be represented by (ε ^v ).

In the case of a viscoelastic material whose behavior can be expressed by equations (5) to (8), in a tensile test where the deformation stops when a certain strain is reached, the stress rise in the loading process as shown by the solid line in FIG. Can be assumed to relax the stress after a stop. Here, as a physical property identification procedure, three strain rates ε _I overdots (I = α, β, γ) having the following relationship are considered.

This relationship is made from a relatively fast two different strain rates epsilon _alpha over dots, and epsilon _beta over dot, very low strain rate epsilon _gamma-over dot compared thereto. At this time, although the stress response curve becomes high stress peak at stop as strain rate epsilon _I over dot becomes higher, the very slow strain rate epsilon _gamma-over dots can not be observed stress peaks and stress relaxation, i.e. the viscosity The conditions that can be ignored are ideal. In the present invention, the relationship between the ideal conditions of extremely low speed that is close to 0 but not 0 is shown as follows.

Stress curves obtained from three strain rate epsilon _I over dots in FIG. 3, consider these relationships in incremental process of separated by a dotted line in such a stress level from sigma _k and σ _{k + 1.} In the process of this stress level from σ _k to σ _{k + 1} , the strain rate ε _I overdot is calculated from the constitutive equation (5) as follows: Elastic part strain rate ε ^e _{Ik overdot} and viscoelastic part strain rate ε ^v Can be expressed as the sum of _{Ik overdots} .

The elastic part strain ε ^e _Ik and the viscoelastic part strain ε ^v _Ik are defined by the following relationship using the time increment Δt _{Ik + 1} in this process.

Here, the relationship of ε ^e _αk = ε ^e _βk = ε ^e _γk is established from the characteristics of the three-element solid model in which the elastic portion strain ε ^e _Ik does not depend on the strain rate ε _{I overdot} . At this time, the following relationship holds for the Young's modulus E ^e .

For this Young's modulus E ^e (ε ^e _Ik ), the stress rate σ _{Ik overdot} defined by the stress increment Δσ _{k + 1} and time increment Δt _{Ik + 1} : = Δσ _{k + 1} / Δt _{Ik + 1} Thus, the following equation can be derived by substituting equations (5) and (8) into equation (6).

In the present invention, the stress σ _{k + 1} overline is the reference stress in the increment interval, and the average stress σ _{k + 1} overline = (σ _{k + 1} + σ assuming a linear relationship in the process of the stress increment Δσ _{k + 1} is used. _k ) / 2. This reference stress σ _{k + 1} overline is a value that does not depend on the strain rate ε _I overdot. Furthermore, the stress σ ^ve _Ik of the viscoelastic part has a relationship that can be derived from Equation (7).

Here, a condition is considered in which the stress level Δσ ₁ is given to the state of the load start k = 0 to change the stress level from σ ₀ to σ ₁ . For first elastic portion Young's modulus E ^e, respectively it can be defined the following equation with respect to strain rate epsilon _alpha over dot, epsilon _beta over dots.

At the beginning of this load, since there is no strain or ε = 0, the relationship of ε ^e _α0 = ε ^e _β0 = 0 holds in the elastic portion strain, and accordingly, the elastic portion Young's modulus E ^e The following relationship holds.

Further, since the relationship of ε ^v _α0 = ε ^v _β0 = 0 holds in the viscoelastic part strain, the following relationship holds in the viscosity compliance C.

  Here, by substituting Equations (16), (17), and (19) into Equation (18), the viscous compliance C (0) can be derived as follows.

On the other hand, by substituting Equations (16), (19), and (20) into Equation (18), the elastic Young's modulus E ^e (0) can be derived from the following relationship.

These results, viscous compliance C (0) and the elastic portion Young's modulus E ^e (0), it is seen derivable from a relatively fast strain rate epsilon _alpha over dot, two experimental results of epsilon _beta over dot . Furthermore, for the viscoelastic part Young's modulus E ^ve , the relationship of σ ≒ σ ^ve obtained from the extremely low speed condition ε _γ overdot ~ 0 and equation (8), that is, σ over dot ≒ σ ^{ve overdot} , and equation (21) The following equation can be defined by applying the elastic part Young's modulus E ^e (0) obtained in (5) to the relationships of equations (5) to (7).

Here, E _γ0 is the slope of the stress-strain curve of the very low strain rate ε _γ overdot obtained from the experiment, and the strain increment Δε _γ1 : = ε _{γ overdot} Δt _γ1 to E _γ0 : = Let Δσ ₁ / Δε _γ1 . This equation (22) represents the property that the three-element solid model can be approximated by a series model of two elements of an elastic part Young's modulus E ^e and a viscoelastic part Young's modulus E ^{ve at} a very low speed. From the above results, the physical property values E ^e (0), E ^ve (0), C (0) at the start of loading are derived from the experimental results of three strain rates ε _I overdots (I = α, β, γ).・ Can be defined.

Next, consider a section where the load process k ≧ 1. At this time, with regard to the elastic portion, E ^e (ε ^e _αk ) = E ^e (ε ^e _βk ) holds for the Young's modulus E ^e from the relationship shown in Expression (14). For one viscoelastic unit, viscous compliance _C (ε ^v αk) of the following stress levels sigma _k obtained from the two conditions of strain rate epsilon _alpha over dots and epsilon _beta over _dot, C (ε ^v βk) and reference If the relationship of the viscous compliance C (ε ^v _k-1 ) is clarified, the value of the viscosity compliance C can be obtained from the relationship and the equations (15) and (16). Here, the value obtained from the condition of the maximum strain rate ε _α overdot is adopted as the reference viscoelastic part strain ε ^v _k-1 at the k-1th stress level σ _k-1.

And the viscous compliance C (ε ^v _k ) at the viscoelastic part strain ε ^v _k as the next standard is defined. In the present invention this time, assuming a linear relationship in the viscous compliance C for the two strain rate epsilon _alpha over dots and epsilon _beta over dot from simplicity, consider the relationship shown in the following equation.

  For this equation (24), the relationship obtained from equations (14) and (15)

By substituting into, the viscous compliance C (ε ^v _k ) can be defined as follows.

Here, the coefficient R _k has the following relationship.

The Young's modulus E ^e (ε ^e _k ) of the elastic part can be defined by the following equation by using the relationships of equations (14), (15), and (26).

Further viscoelastic portion Young's modulus E ^ve (ε ^v _k) is also to determine its value by clarifying the relationship between a plurality of strain rate conditions, two strain rate epsilon _alpha over dots, values for epsilon _gamma-over dot E Consider the following relationship assuming a simple linear relationship for ^ve (ε ^v _αk ) and E ^ve (ε ^v _γk ).

From the very low speed condition ε _γ overdot to 0, the viscoelastic section Young's modulus E ^ve (ε ^v _γk ) is the slope of the stress-strain curve E _γk : = Δσ _{k + 1} / Δε _γk by the same procedure as described above. _The following equation can be defined using ₊₁ .

From the relationship between the equations (29) and (30), the viscoelastic part Young's modulus E ^ve (ε ^v _k ) can be defined by the following equation.

Here, when the experimental data is considered divided by a plurality of stresses σ _k , the increment interval k is derived from the result of the interval k−1, and ε ^v _Ik is derived by the following equation.

With respect to the value obtained from each strain rate of the stress σ _k, the present invention adopts the value obtained from the condition of the maximum strain rate ε _α overdot as the reference value, and the viscoelastic part strain ε ^v _k-1 is And

However, since no strain is generated at the start of loading, ε ^v ₀ = 0 holds for the viscoelastic portion strain.
The strain rate ε _I overdot is derived for each incremental section k and applied to the identification method as shown in the following equation in order to deal with the speed fluctuation in the test process.

The stress rate sigma _Ik over dots using the relation sigma _Ik over dot _{= Δσ k + 1 / Δt Ik} + 1.
The elastic part stress σ ^ve _Ik in the viscoelastic part is derived using the following equation.

In this physical property value identification method, as described above, the initial value at k = 0 is used to derive the value of k = 1, and this result is used to repeat the procedure for deriving the value at k = 2. Get the value. Note that Δε ^v _Ik uses the following equation. The first term “σ _k overline” in the right parenthesis is the reference stress in the increment interval.

  In the case of I = β, γ, the equations (21), (22), (28), (31) are as follows. The nonlinearity of each physical property value of the three-element solid model is expressed by strain dependence. Assuming that no distortion occurs at k = 0 when the load starts, the following equation can be considered at k = 0.

Therefore, E ^e and E ^{ve at} I = β and γ are also derived by equations (21) and (22).
Next, for the equations (28), (31), in order to identify each physical property value at the same stress level even at k = 1, 2, 3,..., The elastic strain ε ^e _{IK at} the stress level k is the total strain rate ε _Since ε ^e _αK = ε ^e _βK = ε ^e _γK = ε ^e _K regardless of the _{I overdot} , the following equation is established.

However, since the viscoelastic part strain ε ^v _IK differs depending on the total strain rate ε _I overdot, the viscosity compliance C and the viscoelastic part Young's modulus E ^ve are identified for each strain rate. ^{Eve at} I = β is expressed by the following equation according to the description of Equation (31).

I = γ is identified by equation (30).
Here, when I = α for E ^ve (ε ^v _IK-1 ), Equation (22) for k = 1, Equations (29), (30), for k = 2, 3, 4. (31), but for I = β, the first term on the left-hand side molecule is

And the first term on the left side denominator

It is supposed to derive in the same way.
E _γk is the slope of the stress-strain curve at an extremely low strain rate ε _{γ overdot. From} the incremental relationship between stress and strain, E _γk = Δσ _{k + 1} / Δε _{γk + 1} = Δσ _{k + 1} / (ε _{γ overdot} Δt _{γk + 1} ).

From the experimental results of the three strain rates ε _I overdot, the physical properties E ^e (ε ^e _k ), E ^ve (ε ^v _k ), C (ε ^v _k ) in the increment interval of the stress increment Δσ _{k + 1} Are sequentially determined from the start to the end of the load to identify the elastic part strain ε ^e _k and the viscoelastic part strain ε ^v _k as functions. Furthermore, by sufficiently finely dividing the elastic part strain ε ^e _k and the viscoelastic part strain ε ^v _k which are discrete variables, these physical property values are handled as functions of continuous values ε ^e and ε ^v .

A method for correcting the reference data will be described. As a correction method for simply reducing the influence of stress relaxation included in the reference data E _γ (ε) obtained from the experiment under the extremely low speed condition ε _γ overdot, in the present invention, as shown in FIG. 4, the reference data E _γ (ε ) _{Shows a} method of applying a correction coefficient so as to pass the stress after stress relaxation σ _γrx . In this case, if the stress when the load is stopped is σ _γmx , the reference data E ′ _γ (ε) corrected for the stress relaxation can be expressed by the following equation.

The spherical indenter indentation test to viscoelastic body, the deformation resistance due to the viscosity occurs, indentation load F hat to the sample is larger than that of the elastic body sample according to pushing speed [delta] _I over dots. In the present invention, push the viscous by considering deformation resistance, addition thinking of generalizing the equation (4) so that it can be evaluated dependent strain, increases in accordance with pushing speed [delta] _I over dot loading process defining a load F _I deformation resistance ratio D _I of the formula as a function of the corresponding push strain ε overline per hat.

Using this deformation resistivity D _I (ε overline), when the experimental data is divided into a plurality of stress levels σ _k and considered, the stress increment from the stress level σ _k to σ _{k + 1} is increased to Δσ _{k + 1} . On the other hand, the following relationship using the relationship between the stress increment Δσ _{k + 1} and the equivalent indentation strain increment Δε _{Ik + 1} overline is assumed.

Ie

That is, with respect to one stress increment Δσ _{k + 1} , three equivalent indentation strain increments Δε _{Ik + 1} overline corresponding to the three deformation resistivities D _I are obtained. From this equivalent indentation strain increment Δε _{Ik + 1} overline and the time increment Δt _{Ik + 1} required for this increment, the equivalent indentation strain rate ε _{Ik overdot} line

Ie

It is defined as
In response to this, the three stress rates σ _{Ik overdots} are also incremented from the time increment Δt _{Ik + 1}

Ie

Can be defined.
Substituting the equivalent indentation strain rate ε _{Ik overdot} line and stress rate σ _{Ik overdot} line in these indentation indentation tests into equations (26) and (28) of the identification method, the viscoelastic property values of the three-element solid model Identification becomes possible.

  The application of the ball indenter indentation test to the nonlinear property value identification method will be described. First, test methods and test conditions will be described. Here, the ball indenter indentation test is applied to the method of identifying the non-linear physical property value of the three-element solid model, and the effectiveness is evaluated by comparing the result with that obtained by the tensile test.

First, the outline of the ball indenter indentation test system is shown in FIG. This system uses a load shaft attached to an actuator 1 (NSK, XY-HRS400-RH202) with a maximum indentation speed δ _max overdot = 1200 mm / s for sample 7 placed on an aluminum table 8. 5 Acrylic ball indenter 6 having a diameter φ = 20 mm above 5 is pushed in. Load F _I load cell 2 (Kyowa Electronic Instruments Co., LUR-A100NSA1) attached to the load axis 5 for hat obtained from, depression depth δ is a potentiometer 3 as the movement amount of the stage 4 of the actuator, fitted with a loading axis 5 (Alps Electric Measured with a slide volume RSA0N11S9002). Each resolution is load 6.15 × 10 ⁻³ N and displacement 1.53 × 10 ⁻⁶ m.

Also, when applying to the identification method, the indentation speed δ _I overdot is considered to be two relatively high speeds δ _α overdot, δ _β overdot and extremely low speed δ _γ overdot, especially extremely low speed δ _γ overdot Is 0.01 mm / s which is the minimum speed specification of the testing machine. For convenience but when a constant these indentation velocity [delta] _I over dot loading process corresponding indentation strain rate epsilon _I over dot line changes, a relationship among the strain rate epsilon _I over dot line in the identification process again is maintained. Table 1 shows initial values ε _{I0 overdot} lines of the corresponding indentation strain rates in this loading process. In addition, the viscous behavior that cannot be eliminated ideally at very low speed δ _γ overdots can be eliminated by applying the correction method [2] based on the stress relaxation measured by holding the indenter for 60 s after stopping the indentation. To do.

  Regarding the indentation into the sample, the indentation amount δ is set to a load up to 10N, and the indentation number N is set once for each condition for the purpose of error evaluation of the test method. The environmental conditions during the indentation test were temperature 26.5-27.0 ° C and humidity 62-63%.

  The indentation test system uses the load value F sent from the load cell of the indentation tester and the indentation amount δ sent from the potentiometer, the Young's modulus of the elastic part, the viscosity compliance of the viscoelastic part in the three-element solid model, And the Young's modulus of the elastic part in the viscoelastic part is calculated. All the data handled by the CPU unit is recorded by the storage unit.

The tensile test system uses a testing machine [2] for soft materials such as biological soft tissue having almost the same configuration as the system of FIG. This drive unit has a mechanism for starting the load axis of the sample after the stage part of the actuator reaches a predetermined speed ε _I overdot and further stops the load shaft when the set maximum strain ε _mx is reached. As a result, strain rate dependence and stress relaxation phenomenon in a wide strain rate region can be observed. The actuator uses NSK's mechatronic actuator XY-HRS063-RS204 with a speed of 0.1 to 1200 mm / s, and the amount of displacement is obtained by measuring the amount of movement of the load axis with the KEYENCE laser displacement meter LB-62. Yes. The load cell is a measurement system using a micro load cell LST-1KA manufactured by Kyowa Denki Co., Ltd., with a resolution of 6.25 × 10 ⁻⁶ m and a load of 3.28 × 10 ⁻³ N.

Regarding the identification of nonlinear physical property values, three different tensile strain rates ε _I overdots will be considered, but since the equivalent indentation strain rate ε _I overdot line cannot be unified with the indentation test in which the load process changes, this The values in Table 2 are used in the invention. The ultra-low speed condition is the minimum speed specification of the testing machine as well as the indentation test. However, in order to improve the identification accuracy, the stress relaxation amount is measured for 60 s after stopping the tension and used to correct the viscous behavior [2]. The number of tensile tests is N = 5 for each condition, and an average value is calculated and used as a criterion for identification method evaluation. The environmental conditions at the time of the tensile test were air temperature 23.2-27.0 ° C and humidity 62-68%.

  As a test material of the present invention, a commercially available silicone rubber sheet having a stable characteristic and low anisotropy is used, and a sample is cut out from a material having a high viscosity of hardness A20 and used.

  In the indentation test, a sample with a sheet thickness of 5.1 mm was prepared with both a vertical and horizontal dimension of 100 mm, and talc powder for reducing friction was applied to the contact surface of the sample with the indenter. Measure.

On the other hand, in the tensile test, a square column specimen with a side of about 2.5mm cut out from the same specimen as the indentation specimen was prepared, and in particular, a load shaft connecting both ends of the specimen with a chuck distance of 10mm to the drive unit. The sensor axis connected to the load cell is connected to each by an instantaneous adhesive, and the physical property value is measured.
In the evaluation of the measurement result of the present invention, the Poisson's ratio ν uses a unified value of 0.48.

  The identification results and discussion will be described. FIG. 6 (a) shows the result of identifying nonlinear physical property values in a three-element solid model of the specimen by a ball indenter indentation test and a tensile test.

These physical properties are elastic part Young's modulus E ^e , viscoelastic part Young's modulus E ^ve and viscous compliance C, but viscosity compliance C and elastic part Young's modulus E ^e decrease as strains ε ^e and ε ^v increase. The tendency and the viscoelastic part Young's modulus E ^ve are almost constant. Comparing the results of the ball indenter indentation test with the tensile test, all the physical property values identified by the ball indenter indentation test shown in bold lines are higher than those in the tensile test, and the difference is particularly noticeable in the viscosity compliance C .

In order to investigate the cause of this difference, we considered a series connection model of only two elastic elements ignoring the effect of viscous compliance C in the three-element solid model, and the identification results of elastic Young's modulus E ^e and viscoelastic Young's modulus E ^ve FIG. 6 (b) shows the results evaluated only with FIG. The curve shown here is the Young's modulus E = E ^e calculated from the series connection of two elastic elements, elastic Young's modulus E ^e and viscoelastic Young's modulus E ^ve identified from the ball indenter indentation test and tensile test. E ^ve / (E ^e + E ^ve ) and the corresponding stress-strain curve, and the stress-strain curve obtained by a tensile test under extremely low speed conditions corresponding to this series connection model and its slope E _γ However, the difference here is significantly smaller than that in FIG. 6 (a).

This indicates that the difference between the ball indenter indentation test and the tensile test is small in the case of an elastic body that can be evaluated by Young's modulus, as already reported [1]. On the other hand, as shown by the result of the large difference between the three physical property values identified in Fig. 6 (a), the physical properties of the tensile test and the ball indenter indentation test were used in the evaluation of the deformation process where the viscous behavior acts. The difference is large in the identification result of the value, and the influence is particularly noticeable in the identification result of the viscosity compliance C. There are also differences in the identification results of the elastic Young's modulus E ^e and the viscoelastic Young's modulus E ^ve , but the results of ignoring the effect of viscosity are similar to those reported in the previous report [1] between the ball indenter indentation test and the tensile test. It can be considered that this is caused by the difference in viscous compliance C, since it is getting smaller.
Therefore, in the identification of nonlinear physical property values, it can be said that the result of the ball indenter indentation test shows a difference in the effect of viscosity.

Here, regarding the viscous effect that appears in the identification of the nonlinear physical property value observed in FIG. 6 (a) by the ball indenter indentation test, the effect of this on the viscoelastic behavior is confirmed from the application to the numerical simulation. FIG. 7 is a stress curve of an experiment and a numerical simulation in which a tensile load is applied up to a strain ε _mx = 0.2 set with three different strain rates ε _I overdots and a stress relaxation process is observed after the suspension of tension. First, the simulation using the physical property values by the tensile test and the experimental results are almost the same in the course of each strain rate from the start of loading to the stress peak, and the stress level after relaxation is also a close value. On the other hand, the simulation results using the physical property values from the ball indenter indentation test indicated by the thick line show that the stress peak is high, and the relaxation process converges to a constant stress immediately after the rapid stress relaxation. Yes. As a result, the viscosity effect was estimated to be low due to the high viscosity compliance C identified, and along with this, the Young's modulus E ^e and E ^ve of each part were calculated to be high, resulting in a more agile stress response. It is considered a thing. From these, it is considered necessary to investigate the viscosity effect in the process of pushing the ball indenter into the viscoelastic body in detail and to formulate the identification method based on this.

  According to the present embodiment, if a method based on a ball indenter indentation test that can be performed without cutting out a sample can be established, it becomes possible to identify nonlinear physical property values in viscoelastic behavior of human soft tissue by minimally invasive in situ measurement.

  Samples to be subjected to the indentation test method and indentation test apparatus of the present invention include polyurethane, silicone rubber, polyolefin rubber, natural rubber, polymer materials including soft vinyl, biological tissue including skin and muscle, jelly and gelatin. Foods containing can be used.

  The Young's modulus E of the sample is preferably in the range of 100 Pa to 100 MPa. When the Young's modulus E of the sample is 100 Pa or more, there is an advantage that the sample does not collapse or break with the indentation. When the Young's modulus E of the sample is 100 MPa or less, there is an advantage that a soft indenter can be used.

In the nonlinear physical property value of the sample in the three-element solid model, the viscosity compliance of the viscoelastic part is preferably in the range of 10 ⁻¹⁴ to 10 ³ (PaS) ⁻¹ . If the viscosity compliance of the viscoelastic part is 10 ⁻¹⁴ (PaS) ⁻¹ or more, there is an advantage that the viscous behavior can be identified. When the viscosity compliance of the viscoelastic part is 10 ³ (PaS) ⁻¹ or less, there is an advantage that measurement can be performed without breaking the sample.

  In the nonlinear property value of the sample in the three-element solid model, the Young's modulus of the elastic part in the viscoelastic part is preferably in the range of 100 Pa to 100 MPa. When the Young's modulus E of the sample is 100 Pa or more, there is an advantage that the sample does not collapse or break with the indentation. When the Young's modulus E of the sample is 100 MPa or less, there is an advantage that a soft indenter can be used.

  Although the spherical indenter has been described as the shape of the indenter, it is not limited to this. In addition, as the shape of the indenter, a cylindrical shape or a cubic shape can be employed.

  As the material of the indenter, a metal and / or a resin material can be employed.

When the indenter is a ball indenter, the diameter of the ball indenter is preferably in the range of 1 × 10 ⁻⁸ to 1 m. If the thickness of the sample is larger than the diameter of the spherical indenter, there is an advantage that a result equivalent to the theoretical solution of Hertz can be obtained. If the thickness of the sample is equal to or less than the diameter of the ball indenter, there is an advantage that the Young's modulus, which was difficult to obtain by Hertz's theory, can be identified.

  When the indenter is a ball indenter, the relatively high indentation speed of the ball indenter is preferably in the range of 1 nm / s to 10 m / s. When the indentation speed of the ball indenter is 1 nm / s or more, there is an advantage that it does not take time for measurement. When the indentation speed of the ball indenter is 10 m / s or less, there is an advantage that the apparatus can be operated safely.

  When the indenter is a ball indenter, the extremely low indentation speed of the ball indenter is preferably in the range of 1 nm / s to 0.001 m / s. When the indentation speed of the ball indenter is 1 nm / s or more, there is an advantage that it does not take time for measurement. If the indentation speed of the ball indenter is 0.001 m / s or less, there is an advantage that a ready-made testing machine can be used.

  As a method for reducing the adhesion at the contact surface between the ball indenter and the sample, a method of applying talc powder to the sample contact surface, a method of applying oil, or the like can be employed. In addition, when the adhesiveness at the contact surface between the ball indenter and the sample is small, these treatments can be omitted.

  It is to be noted that the present invention is not limited to the embodiment for carrying out the above-described invention, and various other configurations can be adopted without departing from the gist of the present invention.

[References]
[1] M. Tani, A. Sakuma and M. Shinomiya, Evaluation of Thickness and Young's Modulus of Soft Materials by using Spherical Indentation Testing, Transactions of the Japan Society of Mechanical Engineers, Series A, Vol.75, No.755, (2009), pp.901-908. (In Japanese)
[2] M. Ogasawara, A. Sakuma, T. Tadomi, E. Yanagisawa and M. Tani, Valuation Technique of Nonlinear Parameters in Three-Element Solid Model and Its Application to Biological Soft Tissue, Transactions of the Japan Society of Mechanical Engineers , Series A, Vol.75, No.750, (2009), pp.251-258. (In Japanese)

DESCRIPTION OF SYMBOLS 1 ... Actuator, 2 ... Load cell, 3 ... Potentiometer, 4 ... Stage, 5 ... Load axis, 6 ... Ball indenter, 7 ... Sample, 8 ... Table

Claims (8)

In the indentation test method in which an indenter is pushed into the sample,
Using the sample thickness, calculate the equivalent indentation strain of the sample,
Using the equivalent indentation strain, the nonlinear physical property value of the sample is calculated. The indentation test method according to claim 1, wherein the sample is a viscoelastic body. The indentation test method according to claim 2, wherein the nonlinear property value is a nonlinear property value in a three-element solid model. 4. The indentation test method according to claim 3, wherein the nonlinear physical property values are Young's modulus of the elastic part, viscous compliance of the viscoelastic part, and Young's modulus of the elastic part in the viscoelastic part. In an indentation testing device that pushes an indenter into a sample,
An equivalent indentation strain calculation unit for calculating the equivalent indentation strain of the sample using the sample thickness;
An indentation test apparatus comprising: a non-linear property value calculation unit that calculates a non-linear property value of a sample using the equivalent indentation strain. The indentation test apparatus according to claim 5, wherein the sample is a viscoelastic body. The indentation test apparatus according to claim 6, wherein the nonlinear property value is a nonlinear property value in a three-element solid model. The indentation test apparatus according to claim 7, wherein the nonlinear physical property values are Young's modulus of the elastic part, viscous compliance of the viscoelastic part, and Young's modulus of the elastic part in the viscoelastic part.

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