JP5932290B2 - Mechanical property creation method considering parameters related to plastic volume change - Google Patents

Description

In the present invention, in addition to the measurement of the mechanical properties of the elastic region, the “parameter related to true strain-volume change” including the plastic region in the measurement range is obtained by a digital image correlation method or the like, and using these results, Mechanical properties of various materials, relating to the method of obtaining mechanical properties input to the elasto-plastic material constitutive law (hereinafter referred to as material constitutive law) of the type in which the elastic strain increment and the plastic strain increment are connected in series from the "nominal strain-nominal stress" relationship It is.

          In the simulation by the finite element method (hereinafter, simulation), in order to express the plastic deformation behavior of a certain material, it is necessary to input the mechanical characteristics.

Many material constitutive laws are formulated assuming that elastic strain and plastic strain are coupled in series, and the plastic deformation behavior of the material is expressed. Here, attention should be paid to the parameter related to the volume change in terms of Poisson's ratio. Note that Poisson's ratio is a physical quantity applied to elastic strain and not plastic strain. In the case of a metal material, since plastic deformation is shear deformation, a plastic strain increment (a tensor amount) such that the volume plastic strain increment becomes 0 is determined. For convenience, if the aspect ratio (Equation 1) of the plastic strain increment is defined as the plastic Poisson's ratio, the plastic Poisson's ratio can be considered to be 0.5 in the case of a metal material. On the other hand, in the tensile deformation of the resin material, a phenomenon that the volume expands is observed. There has been proposed a method for expressing this phenomenon by assuming that the plastic Poisson's ratio varies depending on the amount of plastic deformation (Non-patent Document 1).

Conventionally, the “true strain-true stress” relationship has been estimated from the “nominal strain-nominal stress” relationship and Poisson's ratio (Equations 2 and 3). Here, Formula 2 is a conversion formula for uniaxial tension and uniaxial compression, and Formula 3 is a conversion formula for biaxial tension and biaxial compression. However, since this estimation method does not take into account the plastic Poisson's ratio, the volume change accompanying plastic deformation cannot be expressed with high accuracy. For this reason, for delicate problems such as buckling behavior (Non-Patent Document 2) where the solution branches due to contact / deformation between parts, contact that differs from the actual phenomenon is necessary unless deformation due to volume change of the part is taken into account. As a result, there arises a problem that the complicated deformation behavior of the resin material part cannot be reproduced by simulation.

          For example, in Patent Document 1, by fitting an arbitrary slope to a curve of a plastic region in which a void is induced, that is, a yielded curve of a “true stress-logarithmic plastic strain” curve, and reflecting the effect of void generation, Re-analyze the elasto-plastic model analysis using the newly estimated constitutive equation, and obtain the analysis “true stress-nominal strain” curve and analysis “volume strain-nominal strain” curve from the analysis results. Attempts have been made to use a true “true stress-logarithmic plastic strain” curve as a constitutive equation from the matched data. The operation | work which calculates | requires has performed the process of passing through 7 processes. However, since it tries to determine both the analysis "volume strain-nominal strain" curve and the "true stress-logarithmic plastic strain" curve simultaneously, the degree of fitting freedom increases, and the number of fitting trials is The number of trial and error times of the “strain” curve is multiplied by the number of trial and error times h of the “true stress-logarithmic plastic strain” curve (g × h times). . For this reason, there has been a problem of identifying with enormous effort and time. Moreover, since a local plastic region such as necking cannot be handled in order to handle a wide range of volume strain measured values, the fitting target becomes a measured value with a large error and accuracy is low. In addition, there is a problem that it is necessary to allow a reduction in accuracy together with reducing the number of repeated operations to obtain a convergent solution.

JP 2006-337343 A

S. Kolling et al., 4th German LS-DYNA Users Conf., A-II-27 / 57, 2005 P. A. Du Bois et al., 10th Int. LS-DYNA Users Conf., 19-35 / 42, 2008

          In determining the mechanical properties input to an arbitrary material constitutive law to be used, the present invention obtains a “nominal strain-nominal stress” relationship, a “displacement-load” relationship, and a “true strain-volume change” obtained by testing an actual material. For the "parameters related to the relationship" and those relationships obtained by simulation simulating the test, the task of obtaining the mechanical properties should be performed easily and quickly so that the consistency between the two is high.

          In order to obtain the mechanical characteristics having high coincidence, it is necessary to increase the measurement accuracy of the plastic region by using a finer test method of the actual material.

          The present invention is dramatically lessTrialCreate appropriate mechanical properties to input into material constitutive law through repeated mistakesMethodHowever, paying attention to the fact that it is difficult to measure parameters related to volume changes accompanying plasticity, which is one of the factors that require a great deal of effort to create appropriate mechanical properties. Using a measurement method that sorts and handles, obtains "true strain-parameter related to volume change" relationshipProcessTheIncludeAnd that the second factor is an algorithm involving multiple estimations in series, there is a temporary “true strain-true stress (SS)” relationship.TrialThe relationship between the error process 1 and the provisional "equivalent plastic strain-parameter related to volume change accompanying plasticity" TrialUsing the error-and-error process 2, the two estimations can be performed with an algorithm that uses independent circuits.Craft AboutTheIncludeIt is characterized byMethodAnd
It is composed of Step 1 to Step 10 described later as a detailed algorithmProcessThe IncludeIt is characterized byMethodIt is.
There are various parameters related to the volume change, such as Poisson's ratio, volume plastic strain, void ratio accompanying plastic deformation, etc., but Poisson's ratio is used in the following explanation.

How definitive to the present invention includes the steps of setting the necessary conditions in relation to the simulation defines the material constitutive model for operating the first, it performs material tested using the materials of interest, fine by digital image correlation method Acquire high-precision 2D or 3D deformation data including the plastic region of the region, acquire data such as longitudinal strain, lateral strain, stress, etc., `` displacement-load '' relationship (A1) and `` nominal strain-nominal stress '' In addition to the relationship (C1), a step (step 1) of obtaining a “true strain-apparent Poisson ratio” relationship (B1) including a plastic region is included .

How definitive to the present invention, the C1 obtained by step 1, including using a number 2 or number 3, the temporary step of converting the "S-S" relationship (A2) (Step 2).

How definitive to the present invention, by applying the conditions set in the step 1 to A2, a simulation to simulate the material testing by entering it in the material constitutive model, "displacement - load" relationship (A3-i, i = 1, 2, ..., number of trials n) a step of obtaining (step 3-i, i = 1, 2, ..., includes a number of trials n).

How definitive to the present invention compares the A3-i obtained in A1 and Step 3-i obtained in step 1, the difference obtained is determined whether within the range of target accuracy, the determination is YES By now, the temporary "S-S" relationship (A2 or A5-i) the step of defining the A4 (step 4-i, i = 1, 2, ..., number of trials n) including.

How definitive to the present invention, Step 4-i Thus obtained comparative estimated to exceed the target accuracy reference, "S-S" relationship provisional (A5-i, i = 2,3 , ..., trial as engineering to create a number of times n) (step 5-i, i = 2,3, ..., including the number of attempts n).

How definitive to the present invention, trial and error steps 4-i Therefore YES determination exits to step 5-i and Step 3-i and performing at repeat step 4-i (tentative "S-S" relation acquiring including the legal process of trying and error method) 1.

How definitive to the present invention estimates and the B1 obtained by Step 1 reference, provisional - the "equivalent plastic strain plastic Poisson's ratio (S-P)" step of creating relationships (B6) (Step 6) Including .

How definitive to the present invention, Step 4-i Therefore A4 obtained a B6 or B10-j (j = 2,3, ..., attempts m) True corresponding to "S-S" relationship (A7-j , j = 1, 2, ... , is converted using the formula in attempts m) (step 7-j, j = 1, 2, ..., includes a number of trials m) step. The mathematical formula used for the conversion is Equation 2, Equation 4, Equation 5, Equation 6, Equation 7, Equation 8 for the conversion equation of uniaxial tension and uniaxial compression, and the number for the conversion equation of biaxial tension and biaxial compression. 3, Equation 6, Equation 7, Equation 8, Equation 9, Equation 10, Equation 11, and Equation 12.

How definitive to the present invention performs a simulation to simulate the input to material testing A7-j and B6 or B10-j in the material constitutive model, "true strain - Apparent Poisson ratio" relationship (B8-j, j = 1 ,
2, ..., to obtain a number of trials m) (Step 8-j, j = 1, 2, ..., includes a number of trials m).

How definitive to the present invention judges whether the step difference that is obtained by comparing the B8-j obtained in 1 Thus obtained B1 and Step 8-j is in the range of the target accuracy, the determination is the YES became temporary "S-P" relationship (B6 or B10-j) the step of defining the B9 (step 9-j, j = 1, 2, ..., number of trials m) including.

How definitive to the present invention, Step 9-j Hence YES determination exits to step 10-j and the step 7-j and Step 8-j and step 9-j a step for repetition of trial and error method (tentative " including the trial-and-error method process) 2 S-P "relationship.

How definitive to the present invention, in the case of setting to assert the "S-P" relationship provisional and those known in the process of Step 6, is omitted Step 8-j, the determination in Step 9-j Step 9-j, including the steps of short circuit process 3 in which B6 is defined as B9.

How definitive to the present invention, the structure of the above steps, the proper mechanical properties A9 for inputting the material constitutive model comprising the step of outputting the B9.

While parameters relating how definitive the present invention change in volume has been described with reference to Poisson's ratio, "true strain - Apparent Poisson ratio" relationship and "S-P" relationship, Step 3-i, in step 8-j according to the input of the material constitutive model for operating, (strain volume plastic, such as void ratio due to plastic deformation) parameters related to the volume change includes the step of operating the relationship replaced giving a correlation condition.

One of the direct effects of the present invention is to introduce a test method capable of measuring parameters related to volume change, and obtain a highly accurate comparison reference “SP” relationship from measurement data including local plasticity in the necking state. it is, in fact capable of even small number of trial and error to obtain the mechanical properties significantly accurate than conventional approaches.
Second, by dividing the estimation trial-and-error circuit into two, each circuit is shortened, and by making the estimation easier, the number of trial-and-error repetitions is reduced.
Thirdly, the circuit of the trial and error of estimation by the independent trial and error divided into two, the number of repetitions of trial and error becomes significantly less to the number in the case of performing the two trial and error in the same circuit That is. G> n and h> m are clear from the ease of estimation, and the number of trial and error iterations is (g × h)> (n × m)> (n + m) (where g, h, m, n are All are 2 or more).
The Fourth, since the repetition of trial and error is reduced is to be promoted automated mechanical characterization by the introduction of such a genetic algorithm.
Fifth, there is versatility that can be applied to all types of elastoplastic material constitutive law in which elastic strain increments and plastic strain increments are connected in series, and the volume plastic strain increment can be set to 0 and can also be applied to metal material constitutive laws.
These comprehensive effects can be applied to a wide variety of elastoplastic material constitutive laws, and high-precision mechanical properties can be created quickly.

It is a flow diagram showing a specific algorithm of the method definitive to the present invention. The “displacement-load” relationship A1 obtained from Example Step 1 according to the present invention is shown. Fig. 4 shows the "nominal strain-nominal stress" relationship C1 obtained from Example Step 1 according to the present invention. The position of the measurement point α and β of the apparent Poisson's ratio on the test piece in the digital image correlation method used in Example Step 1 of the present invention is shown. The "true strain-apparent Poisson's ratio" relationship (B1-α, B1-β) obtained from Example Step 1 according to the present invention is shown. The provisional “SS” relationship A2 obtained from Example Step 2 according to the present invention is shown. A comparison between the “displacement-load” relationship A3-1 and A1 determined No in the embodiment step 4-1 according to the present invention is shown. The temporary “SS” relationship A5-n obtained by repeating trial and error n-1 times of the embodiment step 5-i according to the present invention is shown. A comparison between the “displacement-load” relationship A1 and A3-n, in which YES is obtained in Example step 3-n according to the present invention, is shown. A4 is shown in which the provisional “SS” relationship A5-n for which a YES determination is obtained in the embodiment step 4-n according to the present invention is positive. The temporary “SP” relationship B6 created in the embodiment step 6 according to the present invention is shown. The “SS” relationship A7-1 corresponding to B6, obtained from Example Step 7-1 according to the present invention, is shown. The comparison of the “true strain-apparent Poisson ratio” relationship B8-α-1 and B1-α determined No in Example Step 9-1 of the present invention is shown. A comparison of the “true strain-apparent Poisson ratio” relationship B8-β-1 and B1-β determined No in Example Step 9-1 of the present invention is shown. The provisional “SP” relationship B10-m obtained by repeating trial and error of Example Step 10-j according to the present invention m−1 times is shown. The “SS” relationship A7-m corresponding to B10-m, obtained from Example step 7-m according to the present invention is shown. In addition, the comparison with A7-1 is also shown. A comparison of the “true strain-apparent Poisson ratio” relationship B8-α-m and B1-α determined YES in Example step 9-m according to the present invention is shown. A comparison of the “true strain-apparent Poisson's ratio” relationship B8-β-m and B1-β obtained as YES in Example Step 9-m of the present invention is shown. B9 which makes positive B10-m which obtained YES determination in Example step 9-m according to the present invention is shown. A9 in which A7-m obtained as YES in Example Step 9-m according to the present invention is positive. The comparison with A4 is also shown.

A mode for carrying out the present invention will be described along the algorithm flow shown in FIG.
How definitive to the present invention, set the required correlation condition in relation to the simulation defines the material constitutive model to operate initially. Next, in step 1, using the target material, obtain data such as longitudinal strain, lateral strain, and stress. As a material test method, any one of a uniaxial tensile test method, a biaxial tensile test method, a uniaxial compression test method, and a biaxial compression test method can be applied. From the test data using the digital image correlation method to obtain the aspect ratio of the total strain, the "displacement-load" relationship (A1) and the "true strain-apparent Poisson ratio" relationship (B1), "nominal strain-nominal stress" Output relationship (C1).

How definitive to the present invention, the A1, B1 output from Step 1, was operated in a trial and error method processes 1 to A1, to operate the B1 trial and error method the process 2.

How definitive to the present invention, in step 2, under the condition that Poisson's ratio and the plastic Poisson's ratio were considered equally constant, for converting the A1 to the "S-S" relationship provisional (A2).

How definitive to the present invention, in step 3-i, by applying the set correlation condition in step 1 to A2, and inputs it to the material constitutive law, a simulation to simulate the material testing of Step 1 "displacement Obtain the “load” relationship (A3-i).

How definitive to the present invention, in step 4-i, the difference resulting A3-i obtained in step 3-i as compared to the A1 obtained in Step 1 is the same for tolerances target accuracy Or, if it is small, a determination of YES is made. If the difference obtained by the comparison is larger than the tolerance of the target accuracy, NO is determined. The target accuracy may be determined in advance or may be set at this stage.
When the determination is YES, a temporary “SS” relationship (A4) with A2 being positive is obtained.
Determination makes a repetition of determination and estimation using process 1 of trial and error method, if No.

How definitive to the present invention, the determination in Step 4-i and the A3-i, which is compared in step 4-i as a reference in the case of No, the provisional estimated to exceed again target accuracy in Step 5-i Create an “SS” relationship (A5-i).

How definitive to the present invention, anew Step 3-i, by applying the conditions set in step 1 to the A5-i, by entering it in the material constitutive law, a simulation to simulate the material tests performed Obtain the “displacement-load” relationship (A3-i).

How definitive to the present invention, anew Step 4-i, a difference obtained by comparing A3-i and A1 obtained in the material testing obtained the same or smaller than the allowable error of the target accuracy in the simulation In that case, a determination of YES is made. If the difference obtained by the comparison is larger than the tolerance of the target accuracy, NO is determined.
When the determination is YES, a temporary “SS” relationship (A4) with A2 or A5-i as positive is obtained.
If the determination is No, the estimation and determination using the trial and error process 1 is repeated.

How definitive to the present invention, the step determination in 4-i until the YES, a step 5-i, Step 3-i, repeated n-1 times trial and error method processes the first step 4-i by trial and error method Do. In this trial and error, n-1 estimations are made in advance in the process of step 5-1, and n-1 "displacement-load" relations are simultaneously compared in the process of step 4-1. The “SS” relationship (A4) can also be selected. The repetition of trial and error a judgment automatically calculated by the genetic algorithm or the like, can also be selected A4.

How definitive to the present invention, in step 6, the "S-P" relationship (B6) estimated provisional using the output B1 of the step 1. B6 can be determined to be known and set.

How definitive to the present invention, in step 7-j, to convert the "S-S" relationship A4 mock "S-S" relationship (A7-j) with B6. If the provisional “SP” relationship (B6) is determined to be known, it is converted to the “SS” relationship (A7-j), and then B6 and B7-j are short circuit processes. In step 3, step 8-j is omitted, and processing is performed in step B9-j.

How definitive to the present invention, in step 8-j, enter the set correlation condition in step 1 to the material constitutive model with application to A7-j in B6, to simulate to simulate the material experimental "apparent Poisson The ratio-true strain relationship (B8-j) is output.

How definitive to the present invention, in step 9-j, the B8-j obtained in the simulation, the difference obtained by comparing the B1 obtained in materials testing are the same or smaller than the allowable error of the target accuracy In that case, a determination of YES is made. If the difference obtained by the comparison is larger than the tolerance of the target accuracy, NO is determined. The target accuracy may be determined in advance or may be set at this stage.
When the determination is YES, a provisional “SP” relationship (B9) with B6 or B10-j as positive is obtained. At the same time, A9 with A7-j as positive is obtained.
If the determination is No, the estimation and determination using the trial and error method process 2 is repeated.

How definitive to the present invention, the determination in Step 9-j to the B8-j, which is compared in step 8-j as a reference in the case of No, the provisional estimated to exceed again target accuracy in step 10-j The “SP” relationship (B10-j) is created.

How definitive to the invention, again in step 7-j, to convert the "S-S" relationship A4 mock "S-S" relationship (A7-j) with B10-j.

How definitive to the present invention, in step 8-j, is input to the material constitutive model with A7-j by applying the set correlation condition in step 1 in B10-j, a simulation to simulate the material experiments " The “apparent Poisson ratio−true strain” relationship (B8-j) is output.

How definitive to the present invention, anew Step 8-j, the difference obtained by comparing the B1 obtained the B8-j in materials testing obtained the same or smaller than the allowable error of the target accuracy in the simulation In that case, a determination of YES is made. If the difference obtained by the comparison is larger than the tolerance of the target accuracy, NO is determined.
When the determination is YES, an “SP” relationship (B9) with B10-j as positive is obtained. At the same time, A9 is obtained with A7 being positive.
If the determination is No, the estimation and determination using the trial and error method process 2 is repeated.

How definitive to the present invention, until the determination in Step 9-j becomes to YES, repeat step 10-j, Step 7-j, Step 8-j, the process 2 of step 9-j by trial and error method m- Perform once. In this trial and error, m-1 is estimated in the process of step 10-1, and m-1 "true strain-apparent Poisson ratio" relations are simultaneously compared in the process of step 9-1. The “SP” relationship (B9) can also be selected. The repetition of trial and error a judgment automatically calculated by the genetic algorithm or the like, can also be selected B9. At the same time, A9 with A7-j as positive is obtained.

How definitive to the present invention, in step 9-j, in step 6 if the "S-P" relationship provisional (B6) is set to conclude that those known, and B6 passing through a short process 3 The A7- B9 and A9 with 1 being positive are obtained.

Through the above implementation, the mechanical properties A9 and B9 necessary for the material constitutive law are output.

Polycarbonate, which is an amorphous resin material, is known to cause craze in a tensile test and cause a volume change during plasticity. “SS” curve and “SP” curve used for the material constitutive law Semi-Anakytycal Model for Polymers with C1-differentiable yeald (hereinafter referred to as SAMP-1) developed by S. Kolling et al. The example which calculated | required is demonstrated. 2 to 20 show outputs obtained in the respective steps.

In step 1, the material constitutive law to be used was set to SAMP1.
The resin material constitutive law SAMP-1 handled in this example is described by an unrelated plastic constitutive equation (Non-patent Document 1). Equation 10 shows the yield function f and Equation 7 shows the plastic potential g. The coefficient shown in Equation 10 is determined from three types of static material test results. For example, the coefficients are determined by inputting a “true stress-plastic strain” curve of tensile / compressive / shear characteristics. The plastic Poisson's ratio is a parameter that determines the volume plastic strain increment. For example, in the uniaxial tension state, the volume plastic strain increment is proportional as shown in Equation 12. When the plastic Poisson's ratio is 0.5, the volumetric strain increment is 0, that is, the plastic deformation is incompressible. On the other hand, when the plastic Poisson's ratio is larger than 0 and smaller than 0.5, the volume strain becomes larger than 0, so the volume changes with plastic deformation. The void expansion of the Craze phenomenon can be expressed by the plastic Poisson's ratio in this material constitutive law.
Accordingly, the correlation condition related to the simulation is a condition for directly inputting the temporary “true strain-true stress” relationship and the temporary “equivalent plastic strain-plastic Poisson ratio”.

In Step 1, a static tensile test (JISK7113-2 compliant, tensile speed 5 mm / min) was performed, and the “displacement-load” relationship A1 (FIG. 2) and the “nominal strain-nominal stress” relationship C1 (FIG. 3) Obtained. At the same time, the digital image correlation method was used to measure the longitudinal strain and lateral strain near the center of the specimen shown in (Fig. 4), and the "true strain-apparent Poisson's ratio" relationship (B1-α, B1-β) (FIG. 5) was obtained.

Provisional “SS” relationship A2 (FIG. 6) was obtained by carrying out the process of step 2.

A “displacement-load” relationship A3-1 by simulation is obtained by performing the process of step 3-1, and a comparison with the “displacement-load” relationship A1 by the test of step 1 by performing the process of step 4-1 (FIG. 7). To No.

Step 5-i was performed 24 times, and the temporary “SS” relationship A5-n, (n = 24) (FIG. 8) was estimated again.

Process 1 of trial and error to obtain a decision of YES 24 iterations trial and error result "Load - Strain" was obtained relationship A3-n (n = 24) ( Fig. 9). At the same time, a temporary “SS” relationship A5-n, (n = 24) (FIG. 10), which was determined positive by the YES determination, was obtained. A5-n is called A4 after determination.

Step 6 is performed. An “SP” relationship B6 (FIG. 11) was created in which the plastic Poisson's ratio was constant at 0.5.

Step 7-1 is performed, and the temporary “SS” relationship A4 when the plastic Poisson's ratio and the Poisson's ratio are constant is converted, and the “SS” relationship A7-1 corresponding to B6 (FIG. 12) Got.

In the process of step 9-1, the "apparent Poisson ratio-true strain" relationship (B8-α-1) obtained by the simulation of the process of step 8-1 was obtained by the test of step 1. Compared to the “apparent Poisson ratio-true strain” relationship (B1-α) (FIG. 13), the process of step 8-1 was also performed, and (B8-β-1) obtained by simulation was In the process of 9-1, it was compared with (B1-β) obtained by the test of Step 1 (FIG. 14), and No determination was made.

In response to the No determination of the step 9-1, the trial and error process 2 is repeatedly performed 19 times, and the provisional “SP” estimated in the execution of the step 10-m, (m = 19) is performed. The relationship B10-m, (m = 19) (FIG. 15) was obtained.

The trial and error of process 2 was performed 19 times, and in the process of step 9-m (m = 19), the “true strain-apparent Poisson ratio” relationship B8-α-m was compared with B1-α (FIG. 16), and B8 -1-β was compared with B1-β (FIG. 17), and a determination of YES was made, and a provisional “SP” relationship (B10-m) was obtained as a true “SP” relationship. B10-m is called after determination B9. In addition, an “SS” relationship corresponding to B9 was obtained as A9 (FIG. 18).

The accuracy of the “SS” relationship obtained in this example was within 1% and partially within 3% for a target error of 5% in the “displacement-load” relationship.
The result was much higher than the 30% error of the conventional method.

The number of repetitions was actually performed 43 times, and the required mechanical characteristics could be created with a very small number of times compared to the estimated conventional method of 457 times or more.

As an effect that the present invention contributes to the industry, it is possible to create mechanical characteristics that accurately represent and reproduce volume changes accompanying plasticity, such as resin materials and foamed metals, even without an experienced expert. . Since the threshold for creating high-accuracy mechanical properties has been lowered, it is expected that the operation of simulation using high-accuracy mechanical properties can be widely extended to engineering.

1: Temporary “true strain-true stress” relationship estimation trial-and-error process 2: Temporary “equivalent plastic strain-plastic Poisson ratio” trial-error process 3: Temporary “equivalent plastic strain-plastic Poisson ratio” Short circuit process when the relationship is determined to be known

Claims (1)

Plastic Poisson's ratio is a structure made of a material different from the Poisson's ratio from - - "parameter relating to the volume change associated with the plastic corresponding to the material constitutive model where to operate equivalent plastic strain" relationship "true strain true stress" associated with A method for obtaining mechanical characteristics used in simulation such as a finite element method ,
1) A step of obtaining a “displacement-load” relationship and a “true strain- parameter related to volume change ” relationship by measurement in a material tensile test or compression test ,
2) Converting the “displacement-load” relationship (“nominal strain-nominal stress” relationship) obtained in the step 1) to obtain a temporary “true strain-true stress” relationship;
3) the two), or below 5), the provisional obtained in step "true strain - true stress" relationship by simulation to simulate the material tensile test or compression test using a "displacement - load" give relationship Ru step ,
4) The coincidence between the “displacement- load” relationship obtained in the step 1) and the “displacement-load” relationship obtained in the step 3) is determined, and the provisional “true” used in the later step 7) strain - a process that determine the true stress "relationship,
5) A step of obtaining a new temporary “ true strain-true stress” relationship by using the determination of the coincidence of the “displacement-load” relationship obtained in the step 4) .
6) wherein 1) the obtained in the step "true strain - parameters related to the volume change" relationship, or obtained in step described later 8) "true strain - parameters related to the volume change" match of the relationship from the determination of the provisional "equivalent plastic strain - parameters related to the volume change associated with the plastic" process give Ru relationships,
7) From the provisional “true strain-true stress” relationship obtained in the step 4) and from the provisional “equivalent plastic strain—parameter related to volume change accompanying plasticity” obtained in the step 6). Obtaining a "true strain- parameter related to volume change " relationship obtained by simulation simulating a material tensile test or compression test ;
8) Determine the coincidence between the “parameters related to true strain-volume change ” relationship obtained in the step 1) and the “parameters related to true strain-volume change” relationship obtained in the step 7). And determining the “parameters related to equivalent plastic strain-volume change” relationship and the “true strain-true stress” relationship.

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