WO2013042600A1

WO2013042600A1 - Stress-strain relation simulation method, stress-strain relation simulation system, and stress-strain relation simulation program which use chaboche model

Info

Publication number: WO2013042600A1
Application number: PCT/JP2012/073392
Authority: WO
Inventors: 正博石橋
Original assignee: 日本電気株式会社
Priority date: 2011-09-19
Filing date: 2012-09-06
Publication date: 2013-03-28
Also published as: JPWO2013042600A1

Abstract

In this simulation method, a plastic strain is calculated from stress data and strain data, and a plastic strain rate is calculated from the temporal change of the plastic strain. A viscosity function with the plastic strain rate as a parameter is set, and an isotropic hardening model with the plastic strain as a parameter is set. Further, in this simulation method, the viscosity function and the isotropic hardening model are introduced into a yield stress of a dynamic constitutive equation of the Chaboche model, and a material constant of the dynamic constitutive equation is determined by a global nonlinear numerical optimization method. Furthermore, in this simulation method, a stress and a strain are calculated using the determined dynamic constitutive equation.

Description

Stress-strain relationship simulation method, stress-strain relationship simulation system, stress-strain relationship simulation program using Chaboche model

The present invention relates to a method, a system, and a program for simulating a stress-strain relationship of a material using a Chaboche model.

Resin materials are greatly inferior to metal materials in rigidity, strength, and temperature characteristics, and their deformation behavior is complex and difficult to predict. Therefore, resin materials are often used only in parts regions with relatively low strength requirements. However, in recent years, the demand for fiber reinforced resin has been increased for reducing the weight of automobiles and home appliances, and it has become important to predict strength characteristics and deformation characteristics.
Conventionally, linear viscoelasticity analysis has been performed on resin materials. However, plastic strain cannot be calculated by linear viscoelastic analysis. For this reason, there is a drawback in that it is impossible to simulate the phenomenon of a resin material that yields or constricts and breaks depending on the application.
On the other hand, for a metal material, a stress-strain relationship simulation by a finite element method using various mechanical constitutive equations in consideration of plastic strain is generally performed and used for design of a structure. Finite element method analysis is to divide an object into small and finite regions (elements) where force, heat, magnetic field, etc. are uniform, and calculate the balance of forces, thereby calculating stress and strain at each position of the object. It is a technique to do. Examples of main general-purpose software include ABAQUS (registered trademark), LS-DYNA (registered trademark), ANSYS (registered trademark), and the like.
Non-Patent Document 1 (JL Chaboche, G. Rousselier, Journal of Pressure Vessel Technology, Vol. 105, p.153-158 1983) is a mechanical constitutive equation for simulating the stress-strain relationship. J. L. Chaboche and G. A plastic constitutive equation (hereinafter referred to as a Chaboche model) by Rousselier is known. ABAQUS, LS-DYNA, ANSYS, etc. are mentioned as general purpose finite element method analysis software which can calculate the plastic constitutive equation by the Chaboche model. The Chaboche model is an Armstrong-Frederick type nonlinear kinematic hardening theory and can calculate the Bauschinger effect at the time of load reversal. Further, it is possible to apply an isotropic hardening rule to a yield function to develop a composite hardening model.
Here, isotropic hardening is a yield curved surface centered on stress 0, which represents the yield condition at which the material starts plastic deformation as a curved surface. The center does not move and the radius increases by the amount of increased stress. Curing, which represents work hardening of a material caused by plastic deformation.
In addition, kinematic hardening is hardening in which the center moves in that direction without changing the radius by the amount of increase in stress after yielding or the amount of increase in back stress in the above-described yield surface. A decrease in yield stress, that is, the Bauschinger effect can be represented.
In Patent Document 1 (Japanese Patent No. 3897477), the characteristic of the first back stress component α ₁ is shown in FIG. 10A with respect to a large strain of a metal such as 20% strain. A means for analyzing the characteristics of the second back stress component α ₂ by dividing it into the low strain region b and dividing it into the low strain region c, the medium strain region d and the high strain region e is disclosed. In addition, as shown in FIG. 10B, a means for sequentially determining an isotropic hardening constant, a kinematic hardening constant during tension, and a kinematic hardening constant during compression when the stress-strain relationship is accurately simulated is disclosed.
In Patent Document 2 (Japanese Patent Application Laid-Open No. 2008-142774), as shown in FIG. 11, a part of material constants are determined first, and the remaining material constants are calculated from the calculation results using the plastic constitutive equation in which the results are input. A method for improving the convergence of the calculation of the material constant determination by determining is disclosed.
Further, in Patent Document 1 and Patent Document 2, it is possible to predict a springback deformation amount in which the metal material is deformed by elastic recovery after plastic deformation in consideration of the Bauschinger effect.
Unlike metal materials, resin materials have viscous properties, and it is known that the stress caused by a load varies with strain rate. It is also known that various plastic properties are exhibited depending on the type of resin material and load conditions. That is, in the resin material, it is necessary to consider the strain rate dependency of the stress, which is not necessary in the metal material.
For this reason, when simulating the stress-strain relationship by the finite element method, it is necessary to accurately represent the stress change due to the strain rate. However, in general methods as disclosed in Patent Document 1 and Patent Document 2, although metal materials can be accurately simulated, there are various types of deformation and stress-strain of resin materials ranging from rubber to hard plastic. There is a problem that it is difficult to accurately and easily simulate the relationship.
Also, when simulating the stress-strain relationship, the Bauschinger effect can be expressed by using the Chaboche model as a dynamic constitutive equation. However, there is a problem that there is no specific method for applying the Chaboche model to a resin material and an efficient method for determining a material constant.
An object of the present invention is to disclose a method for calculating the strain rate dependence of stress generated in a material by applying the Chaboche model, and a method for efficiently determining a material constant therefor, and to simulate a stress-strain relationship of the material. To provide a method, a simulation system, and a program.

The stress-strain relationship simulation method in the present invention is a mechanical constitutive equation in which a material constant is determined by a global nonlinear numerical optimization method, in which a viscosity function and an isotropic hardening model are introduced into the yield stress of the Chaboche model. Is used.
The stress-strain relationship simulation system according to the present invention includes an improved Chaboche model setting means for introducing a viscosity function and an isotropic hardening model into a yield stress calculation part of the Chaboche model, and a dynamic configuration of the improved Chaboche model by a global nonlinear numerical optimization method. A global nonlinear numerical optimization approximating means for determining a material constant of the equation; and a stress-strain calculating means for calculating stress and strain using a dynamic constitutive equation.
The stress-strain relationship simulation program according to the present invention includes a process for setting a mechanical constitutive equation in which a viscosity function and an isotropic hardening model are introduced to the yield stress of the Chaboche model, and a dynamics in which material constants are determined by a global numerical nonlinear optimization method It has a process of constitutive formula and a process of calculating stress and strain using a dynamic constitutive formula.

It is a block diagram which shows the structure of the stress-strain relationship simulation of embodiment of this invention. It is a flowchart of the stress-strain relationship simulation of embodiment of this invention. It is a conceptual diagram which shows the function of the Chaboche model of embodiment of this invention. It is a flowchart which shows the flow of the process of material constant determination of embodiment of this invention. It is a figure which shows the isotropic hardening model of embodiment of this invention. It is a figure which shows an example of material constant determination of Example 1 of this invention. It is a figure which shows an example of the stress-strain curve display of Example 1 of this invention. It is a figure which shows an example of material constant determination of Example 2 of this invention. It is a figure which shows an example of the stress-strain curve display which is Example 2 of this invention. It is the figure which showed dividing | segmenting the distortion area | region of patent document 1. FIG. It is a flowchart which shows a plastic constitutive equation identification program. 10 is a flowchart showing a flow of parameter identification processing of Patent Document 2.

[Embodiment] An embodiment of the present invention will be described below with reference to the drawings. However, the preferred embodiments described below are technically preferable for carrying out the present invention, but the scope of the invention is not limited to the following.
FIG. 1 is a block diagram showing the configuration of the stress-strain relationship simulation of this embodiment. First, with respect to the target material, measurement data is obtained by performing various material tests such as uniaxial and biaxial tests such as tension, compression, stress relaxation, and creep.
The plastic strain calculation means 1 performs a process of calculating the plastic strain from the measurement data. In the case where the plastic strain cannot be obtained directly, a means for calculating the elastic modulus from the measurement data and calculating the plastic strain is included. The plastic strain rate calculating means 2 performs a process of calculating the plastic strain rate from the time change of the plastic strain.
The viscosity function setting means 3 sets a viscosity function using the plastic strain rate as a parameter. The set viscosity function expresses the strain rate dependence of stress. The isotropic hardening model setting means 4 sets a stress function of an isotropic hardening model using plastic strain as a parameter. The improved Chaboche model setting means 5 introduces the viscosity function and the stress function of the isotropic hardening model into the yield stress term of the dynamic constitutive equation of the Chaboche model. Generally, the back stress is expressed by a function having a plastic strain as a parameter. In the embodiment of the present invention, the improved Chaboche model means a model in which a viscosity function and an isotropic hardening model are introduced into the yield stress term of the Chaboche model.
The material constant determination means 6 determines the material constant of the mechanical constitutive equation using a global nonlinear numerical optimization method. The global nonlinear numerical optimization method (hereinafter referred to as global optimization approximation) is a kind of nonlinear least square method that can minimize the difference between data and an approximate value over a wide range without being limited to a local minimum point. The stress-strain calculation means 7 sets a load condition when obtaining measurement data, calculates a stress and strain using a finite element method stress analysis method using a mechanical constitutive equation to which material constants are applied. The display means 8 plots the measurement data as data points, and displays the stress-strain curves obtained by the simulation in a superimposed manner.
FIG. 2 is a flowchart of the stress-strain relationship simulation of this embodiment.
First, measurement data is acquired (step 10). The measurement data is converted into data to determine the material constant (step 20), is applied to a dynamic constitutive equation for which the material constant is not determined, and the material constant is determined by global optimization approximation (step 30). The determined material constant is applied to the dynamic constitutive equation to determine the dynamic constitutive equation (step 40). A stress analysis by the finite element method is performed using the determined mechanical constitutive equation (step 50), and the result is displayed as a stress-strain curve (step 60).
FIG. 3 is a conceptual diagram of an improved Chaboche model 50 showing that an additional extended function 54 including a viscosity function 55 and an isotropic hardening model 56 is added to the yield stress 52 of the Chaboche model. In the present embodiment, the Chaboche model 51 is adopted as the base of the dynamic constitutive equation, and an additional extended function 54 is given thereto. The dynamic constitutive equation used here may be a self-made program, or the additional extended function 54 may be incorporated into a general-purpose finite element method analysis software by a user subroutine.
In general, the Chaboche model 51 calculates the stress as the sum of the yield stress 52 and the back stress 53. Here, the back stress 53 is used for calculating the Bauschinger effect in a kinematic hardening model. Usually, the yield stress 52 is a constant, but various functions can be further expanded. In this embodiment, a model in which various isotropic hardening models 56 and a viscosity function 55 having a strain rate as a variable are added to the calculation portion of the yield stress 52 is used.
FIG. 4 is a flowchart showing the flow of processing for determining the material constant according to the present embodiment. In the present embodiment, the (stress, strain) measurement data group obtained by the measurement is converted into a (stress, plastic strain) data group in the plastic strain calculation means 1, and further in the plastic strain rate calculation means 2 (stress, plasticity). Strain, plastic strain rate) data group, and the data is taken into a mechanical constitutive equation whose plastic strain material constant is not determined (step 31). Based on the acquired data, the material constant is estimated by global optimization approximation (step 32). When the global optimization approximation is used, a plurality of material constants that minimize the error between the measurement data and the approximate value can be determined simultaneously (step 33).
Therefore, the material constant can be determined at a time, and the calculation steps can be reduced and the calculation time can be reduced. The approximate portion may be a self-made program or commercially available mathematical expression processing software such as Maple (registered trademark) or Mathematica (registered trademark). The dynamic constitutive equation is determined by this flow (step 34).
FIG. 5 is a diagram illustrating an example of the isotropic hardening model of the present embodiment. This is an example in which an isotropic hardening model is defined as the sum of these two stress functions, where the stress function for converging the stress against the plastic strain is the convergence type and the diverging stress function is the divergent type. For example, a convergent stress function is suitable when the stress gradient is substantially constant at large strains, such as rubber materials. Also, a divergent stress function is suitable when the stress gradient with respect to strain does not decrease, as with some hard plastics. If the convergent stress function and the divergent stress function are each linearly combined with a coefficient, the coefficient can be determined as a material constant. As a result, an optimal isotropic hardening model is selected and used for the stress-strain relationship simulation.
Furthermore, the stress expressed as a function of the plastic strain rate is added to the yield stress calculation part as a viscosity function. In the viscosity function, the ratio of the stress that changes with the strain rate corresponds to the material constant. By using a mechanical constitutive equation in which these functions are additionally expanded, it becomes possible to accurately simulate deformations and stress-strain relationships of various resin materials.

Example 1 according to the present invention will be described in detail. In Example 1, a material test was performed using a resin material containing 30% glass fiber as a reinforcing fiber in an ABS resin material which is a thermoplastic resin material. Here, a uniaxial tensile test was performed under the condition of a strain rate of 1 [1 / s]. However, the strain rate of 1 [1 / s] means a tensile test rate at which a test piece having a certain length is doubled in one second.
As a result of the resin material test, measurement data of stress σ and strain ε for each time were obtained in pairs. That is, a measurement data group (time, strain, stress) was obtained.
Next, the plastic strain ε _p was calculated from the (time, strain, stress) measurement data group. The plastic strain ε _p was calculated using Equation 1.
ε _p = ε−ε _e = ε−σ / E (1)
In Equation 1, E is the elastic modulus and ε _e is the elastic strain.
Herein, the elastic modulus E is the ratio of stress σ and the elastic strain epsilon _e, in the small strain range of elastic strain epsilon _e can be considered as equivalent to the strain epsilon. Therefore, the elastic modulus E can be calculated from Equation 2 by obtaining the stress change amount δσ in the minute strain range δε from the (time, strain, stress) measurement data group.
E = δσ / δε (2)
(Time, strain, stress) If there is a measurement data group and an elastic modulus E, the plastic strain ε _p is calculated using Equation 1.
Also, the time variation of the plastic strain epsilon _p, plastic strain rate (Equation 3) is calculated. The plastic strain rate means the amount of change in plastic strain per unit time.

That is, a data group (time, strain, plastic strain, plastic strain rate, stress) was obtained. From the obtained (time, strain, plastic strain, plastic strain rate, stress) data group, the (plastic strain, stress) data group was extracted and indicated by ○ in FIG.
Further, the (time, strain, stress) data group obtained from the material test was converted into a (plastic strain, stress) data group, and the material constants were determined by global optimization approximation using these as data points. The data points obtained by approximation are indicated by solid lines in FIG.
The mechanical constitutive equation in the first embodiment is based on the Chaboche model, and the stress σ is calculated as the sum of the yield stress σ _y and the back stress α as shown in Equation 4.
σ = σ _y + α (4)
The viscosity function of the additional extended function is a function for expressing the strain rate dependency of stress.

A and B are material constants for expressing the strain rate dependence of the stress which differs for each material.
In Example 1, Formula 6 was used as an isotropic hardening model of an extended function.
C [1-exp (−Dε _p )] + Fε _p (6)
C, D, F is a material constant, representing that the stress is changed by plastic strain epsilon _p.
Equation 7, which is the first term of Equation 6, is a convergent stress function that converges to stress C at a rate determined by D as the plastic strain ε _p increases.
C [1-exp (−Dε _p )] (7)
Efuipushiron _p of the second term of Equation 6 is a stress function of diverging. To the proportionality coefficient F, the stress is increased in proportion to the plastic strain epsilon _p. In this way, if it is in the form of a linear combination of a convergent stress function and a divergent stress function, an optimal isotropic hardening model can be obtained by determining the material constant so that it matches the test data. it can.
If the initial yield stress of the Chaboche model is k, the yield stress σ _y of the mechanical constitutive equation of Example 1 is expressed by Equation 8.

In Example 1, the back stress α was defined by Equation 9.
α = a (1−exp (−bε _p )) + c (1−exp (−dε _p )) (9)
a, b, c, and d are material constants.
In Example 1, the data constant (plastic strain, plastic strain rate, stress) data group obtained by converting the (time, strain, stress) measurement data group is used as a data point, and the material constants of the above mechanical constitutive equation are calculated at once by global optimization approximation. Were determined. In the first embodiment, the global optimization approximation is performed using the programming function of the mathematical formula processing software Maple. The material constant obtained in this way is substituted into the mechanical constitutive equation and used for the finite element method stress analysis.
Here, for confirmation, the test conditions and constraint conditions of the material test when the measurement data was obtained were given as load conditions, and an analysis model of the resin material test piece shape was created. For stress analysis, general-purpose finite element method analysis software ANSYS was used to calculate a (stress, strain) data group. The calculation result was transferred from ANSYS to Maple, and a stress-strain curve was displayed on Maple.
FIG. 7 shows the material test result data and the simulation result superimposed.
The stress-strain curve of the resin material simulated by the method of Example 1 based on the Chaboche model was in good agreement with the original material test results.

Example 2 according to the present invention will be described in detail. In the same manner as in Example 1, a material test was performed using a resin material containing 30% glass fiber as a reinforcing fiber in an ABS resin material which is a thermoplastic resin material. Here, the uniaxial tensile test was performed by changing the strain rate in four ways of 1, 0.1, 0.01, and 0.001 [1 / s]. Here, the strain rate of 0.001 [1 / s] means a tensile test rate at which a test piece having a certain length becomes 1.001 times longer after 1 second. Similarly, 0.01 [1 / s], 0.1 [1 / s], and 1 [1 / s] mean that a test piece having a certain length is 1.01 times and 1.1 times after 1 second, respectively. It means a tensile test speed that is twice as long.
As a result of the resin material test, data groups (time, strain, stress) for each test speed were obtained as measurement data. In the measurement data of four kinds of test speeds, the plastic strain ε _p was calculated using Equation 1 for each time. Moreover, to calculate the plastic strain rate from the change in the plastic strain epsilon _p with time (equation (3)), (time, strain, plastic strain, plastic strain rate, stress) data group is obtained. Among the obtained data, a (plastic strain, stress) data group for each test speed is indicated by ◯ in FIG.
In Example 2, the viscosity function of the additional extension function is represented by Equation 10.

A and B are material constants.
In Example 2, Formula 11 was used as an isotropic hardening model of an extended function.
C × In (Dε _p −F) (11)
C, D, and F are material constants.
In Example 2, the back stress α was defined by Expression 12.
α = a (1-exp (−bε _p )) (12)
a and b are material constants.
In Example 2, the material constants of the above mechanical constitutive equation were determined by global optimization approximation using data groups of four types of test speeds (plastic strain, plastic strain rate, stress) obtained by converting the material test data as data points. . In the second embodiment, mathematical expression processing software Maple is used for approximation by global optimization approximation. The material constant obtained in this way is substituted into the previous mechanical constitutive equation and used for finite element method stress analysis.
Here, for confirmation, the test conditions and restraint conditions of the resin material test were given as load conditions, and an analysis model of the resin material test piece shape was created. For stress analysis, general-purpose finite element method analysis software ANSYS was used to calculate a (stress, strain) data group. The calculation result was written from ANSYS to a file and read with Maple to display a stress-strain curve.
FIG. 9 shows the material test data for each test speed. As shown in FIG. 9, both the measurement data and the simulation result agreed well. That is, according to the method of Example 2, the stress-strain curve of the fiber reinforced resin material could be calculated accurately and easily.
In the embodiment of the present invention, a specific example of a resin material in which an ABS resin is reinforced with glass fiber is given. However, the simulation according to the embodiment of the present invention is not limited to the resin material. Other than the resin material, the simulation according to the embodiment of the present invention can be used for a metal material, for example.
According to the present invention, it is possible to efficiently simulate the stress-strain relationship of a material whose stress increases as the strain rate increases. In addition, the stress-strain relationship can be accurately simulated for various materials.
Although the present invention has been described with reference to the exemplary embodiments and examples, the present invention is not limited to the above exemplary embodiments and examples. Various changes that can be understood by those skilled in the art can be made to the configuration and details of the present invention within the scope of the present invention.
This application claims the priority on the basis of Japanese application Japanese Patent Application No. 2011-203948 for which it applied on September 19, 2011, and takes in those the indications of all here.

According to the present invention, the stress-strain relationship of various resin materials can be obtained efficiently and accurately. Therefore, a simulation result close to the actual use condition can be obtained even for a product that has not been used due to the characteristics of the resin material, and it is possible to estimate whether or not it can be applied. In addition, even in products that have been used for resin materials, it is possible to accurately estimate the difference in material properties by replacing another resin material through simulation. Therefore, the quality of the product can be improved simply and at low cost.

DESCRIPTION OF SYMBOLS 1 Plastic strain calculation means 2 Plastic strain rate calculation means 3 Viscosity function setting means 4 Isotropic hardening model setting means 5 Improved Chaboche model setting means 6 Material constant determination means 7 Stress-strain calculation means 8 Display means 50 Improved Chaboche model 51 Chaboche model 52 Yield stress 53 Back stress (kinematic hardening model)
54 Additional extended functions 55 Viscosity function 56 Isotropic hardening model

Claims

Stress-strain, characterized by setting a mechanical constitutive equation in which a viscosity function and an isotropic hardening model are introduced to the yield stress of the Chaboche model, and using the mechanical constitutive equation whose material constants are determined by a global nonlinear numerical optimization method Relationship simulation method.
Calculate plastic strain from stress data and strain data,
2. The stress-strain relationship simulation method according to claim 1, wherein the plastic strain is set in the isotropic hardening model.
Calculate plastic strain from stress data and strain data,
Calculate the plastic strain rate from the time variation of the plastic strain,
3. The stress-strain relationship simulation method according to claim 1, wherein the plastic strain rate is set in the viscosity function.
Calculate elastic modulus from stress data and strain data,
4. The stress-strain relationship simulation method according to claim 1, wherein a plastic strain is calculated from the elastic modulus.
5. The stress-strain relationship simulation method according to claim 1, wherein a linear combination of a convergent stress function and a divergent stress function is used as the isotropic hardening model.
The isotropic hardening model is
C [1-exp (-D [epsilon] p )] + F [epsilon] p
However,
6. The stress-strain relationship simulation method according to claim 1, wherein C, D, F: constant ε p : plastic strain.
The isotropic hardening model is
C x In (Dε p -F)
However,
5. The stress-strain relationship simulation method according to claim 1, wherein the stress-strain relationship simulation method is expressed by an equation: C, D, F: constant ε p : plastic strain.
8. The stress-strain relationship simulation method according to claim 1, wherein the viscosity function is set using stress data and strain data obtained from a plurality of resin material tests with different test speeds.
Improved Chaboche model setting means for introducing a viscosity function and an isotropic hardening model into the yield stress calculation part of the Chaboche model;
A global nonlinear numerical optimization approximation means for determining a material constant of a mechanical constitutive equation of the improved Chaboche model by a global nonlinear numerical optimization method;
A stress-strain relationship simulation system comprising stress-strain calculation means for calculating stress and strain using the mechanical constitutive equation.
A process of setting a mechanical constitutive equation in which a viscosity function and an isotropic hardening model are introduced into the yield stress of the Chaboche model;
Processing of the mechanical constitutive equation in which material constants are determined by a global numerical nonlinear optimization method;
A stress-strain relationship simulation program comprising a process of calculating stress and strain using the mechanical constitutive equation.