JP2023005229A - Damage simulation method - Google Patents

Abstract

To provide a damage simulation method for performing evaluation by considering macroscopic dynamic behavior when deforming a structure composed of a heterogeneous material, such as a diploid material containing a metal material by operating a load to it, dynamic behavior regarding micro organization, and behavior of occurrence and development of damage.SOLUTION: In a damage simulation method for evaluating damage behavior of a diploid material by using an arithmetic circuit, the arithmetic circuit executes the processes of: creating a micro organization finite element model of a diploid material; setting and acquiring strength characteristics and damage criteria for each constituent phase of a diploid material; creating a macro structure finite element model and calculating a deformation history by executing analysis by using the macro structure finite element model assuming a homogeneous material; executing analysis by granting a deformation history to the micro organization finite element model and calculating deformation behavior; performing damage determination by comparing deformation behavior with the damage criteria; and changing a calculation formula of analysis by the damage determination.SELECTED DRAWING: Figure 2

Description

The present invention relates to a damage simulation method for evaluating damage behavior of multiphase materials including metallic materials.

Many metal materials can receive a large load, for example, during plastic working in the manufacturing process or when using a structure formed of the metal material. When a large strain exceeding the breaking strain amount of the metal material is generated by receiving a large load, the metal material breaks, resulting in a manufacturing defect in the manufacturing process and loss of its function when used as a structure. Therefore, it is very important to know the rupture properties of metallic materials in advance, for example, to evaluate whether the material will rupture under the occurrence of a certain strain.

On the other hand, since the metal materials are heterogeneous at the microstructure level, attempts have been made to develop excellent properties on a macroscopic scale in consideration of the morphology of the microstructure. For example, Non-Patent Document 1 shows an example of multi-scale simulation for analyzing the relationship between the microstructure morphology inside the material and the macroscopic strength characteristics. Non-Patent Document 2 proposes direct evaluation of the microvoid generation behavior of a material by stress analysis using a microstructure analysis model to which continuum damage mechanics is applied.

Eisuke Kurosawa et al., "Multiscale Strength Analysis of Dual-Phase Steel", Proc. Shigeru Yonemura et al., "Finite element analysis of deformation and fracture at the mesoscale", Nippon Steel & Sumitomo Metal Technical Report, No. 410 (2018), page 47-56

A multi-phase material including a metallic material develops heterogeneity in structure and strength inside due to the influence of its component composition and manufacturing conditions. Such inhomogeneity greatly affects the mechanical properties of the material. Non-Patent Document 1 proposes a multi-scale strength analysis that predicts the mechanical properties of the macrostructure using a microstructure model based on SEM observation images as the actual structure of the DP steel sample. In order to develop materials with excellent characteristics and quality, it was necessary to evaluate the damage initiation and propagation at the microstructural level in inhomogeneous materials in relation to the deformation of members at the macrostructural level. In Non-Patent Document 2, although damage simulation at the microstructure level is realized, it is necessary to set a damage model for each damage form, and the analysis is complicated. In other words, multi-scale simulations that are easy to analyze and that correlate damage initiation and propagation at the microstructural level with deformation of members at the macrostructural level have not been realized so far.

The present invention has been made in view of the above circumstances, and is easier to analyze than conventional, macroscopic mechanical behavior of inhomogeneous materials, mechanical behavior related to microstructure, behavior of damage occurrence and propagation. To provide a damage simulation method for evaluation in consideration of

Aspect 1 of the present invention is
A damage simulation method for evaluating the damage behavior of a multi-phase material composed of a plurality of phases having different strength properties, including a metallic material, using an arithmetic circuit, the arithmetic circuit comprising:
creating a microstructure finite element model for microanalysis based on the structure observation results of the multiphase material;
obtaining and setting different strength properties and damage criteria for each phase constituting the multiphase material;
A macro structural finite element model is created for the macro region of the multiphase material to be analyzed, and assuming that it is a homogeneous material, finite element analysis is performed using the macro structural finite element model, and the evaluation target region is a step of calculating a deformation history;
a step of applying the deformation history to each integration point of the microstructure finite element model and calculating the deformation behavior of the microstructure finite element model by finite element analysis based on a homogenization method;
a step of determining damage by comparing the deformation behavior with the damage criteria;
a step of releasing the stress at the integration point determined to cause damage in the microstructure finite element model by the damage determination, and reducing the element stiffness to zero or a predetermined value;
is a damage simulation method that evaluates the damage behavior of a multiphase material composed of multiple phases with different strength properties, including metallic materials.

Aspect 2 of the present invention is
Aspect 1. The damage simulation method of aspect 1, wherein the damage criteria are functions of equivalent plastic strain and stress triaxiality.

Aspect 3 of the present invention is
In the damage determination, if the value calculated based on the equivalent plastic strain and stress triaxiality calculated as the damage behavior at a specific integration point of the microstructure finite element model is greater than the damage criteria, the specific The damage simulation method according to aspect 2, wherein damage occurrence is determined with respect to the integration point of .

Aspect 4 of the present invention is
The damage simulation method according to any one of aspects 1 to 3, wherein the predetermined value is 1/50 or less of the initial value of the element stiffness.

Aspect 5 of the present invention is
The damage simulation method according to any one of aspects 1 to 4, wherein the multi-phase material is a metallic material.

According to the present invention, when a structure composed of heterogeneous materials such as multi-phase materials including metal materials is deformed by applying a load, the macroscopic mechanical behavior, the mechanical behavior related to the microstructure, the occurrence of damage, and the It is possible to provide a damage simulation method that considers and evaluates the behavior of propagation.

FIG. 1 is a block diagram of an evaluation system according to this embodiment. FIG. 2 is a flow chart for numerical analysis evaluation of the damage behavior of the metal material according to the present embodiment. FIG. 3 is a diagram showing an example of the procedure for creating an FEM analysis model that simulates the microstructure of the metal material according to this embodiment. FIG. 4 is a flow chart for acquiring macro-distortion. FIG. 5 is a stress-strain curve of a duplex steel obtained by tensile testing. FIG. 6 is an enlarged view of a portion of the stress-strain curve of FIG. FIG. 7 is a log-log graph of the stress-strain curve of FIG. FIG. 8 is a stress-strain curve for explaining the second stress Δσ. FIG. 9 is a stress-strain curve of a hard phase that can be regarded as an elastic perfect plastic body. FIG. 10 is a log-log graph plotting the relationship between stress and strain of a duplex steel with ln(σ−Δσ) on the vertical axis and ln(1+ε/α) on the horizontal axis. FIG. 11 is a schematic diagram showing the relationship between the macrostructure finite element model and the microstructure finite element model. FIG. 12A is a stress-strain curve calculated by FEM analysis for the damage-weighted macrostructural finite element model. FIG. 12B is a graph showing the evolution of the number of integration points determined to be damaged by FEM analysis for the microstructure finite element model. FIG. 13A is a microstructure finite element model calculated when a predetermined macro strain is applied in FEM analysis. FIG. 13B is a microstructure finite element model calculated when applying macro strain larger than that in FIG. 13A.

The present inventors have conducted extensive research to realize a method capable of evaluating the damage behavior of multiphase materials including metallic materials. As a result, the present inventors created an FE model of the macrostructure based on the FE model of the microstructure created based on the microstructure shape of the material, and performed an FEM analysis in which they were associated with each other. Found it. Specifically, the present inventors performed FEM analysis using a macrostructure FE model assuming that it is a homogeneous material to calculate a deformation history, and added the deformation history to the microstructure FE model was used to perform FEM analysis. Then, in the FEM analysis of the microstructure, the present inventors determined the presence or absence of damage based on a predetermined criterion, and changed the calculation formula for the FEM analysis of the site determined to be damaged. By associating the FEM analysis on the macrostructure and the FEM analysis on the microstructure in this way, the present inventors can simulate the decrease in deformation resistance on the macrostructure side due to the occurrence and progression of damage on the microstructure side during deformation. I found that it can be reproduced. In this specification, unless otherwise specified, "stress" refers to true stress (σ), and "strain" refers to true strain (ε). In addition, hereinafter, a metal material composed of a plurality of phases with different strength characteristics will be described as an example of a multi-phase material containing the metal material, but the method according to the present embodiment is not limited to this, and will be described later. As shown, it can be applied to various multi-phase materials.

An evaluation system 1, which is an example for executing a damage simulation method for evaluating the damage behavior of a multi-phase material (a metallic material composed of a plurality of phases with different strength characteristics) according to this embodiment, will be described. FIG. 1 is a block diagram of an evaluation system 1 according to this embodiment. The evaluation system 1 includes an imaging device 10 and a control device 20 . The imaging device 10 includes an imaging unit 11 and a communication circuit 12 . The control device 20 includes an arithmetic circuit 21, a storage device 22, and an interface device (input/output device 23 and communication circuit 24).

The photographing unit 11 is, for example, a scanning electron microscope (SEM) or the like, and can photograph a microstructure image in which at least part of the metal material is partially enlarged. The photographing unit 11 transmits data of the photographed microstructure image to the control device 20 via the communication circuit 12 . As will be described later, the arithmetic circuit 21 of the control device 20 stores the received microstructure image data in the storage device 22 .

The arithmetic circuit 21 of the control device 20 executes model creation processing, parameter setting processing, analysis processing, damage determination processing, and the like. Arithmetic circuit 21 includes a general-purpose processor such as a CPU or MPU that implements a predetermined function by executing a program. The arithmetic circuit 21 can implement model creation processing, parameter setting processing, analysis processing, damage determination processing, and the like by calling and executing, for example, arithmetic programs stored in the storage device 22 . Arithmetic circuit 21 is not limited to one that achieves a predetermined function through cooperation of hardware and software, and may be a hardware circuit that is exclusively designed to achieve a predetermined function. That is, the arithmetic circuit 21 can be realized by various processors such as GPU, FPGA, DSP, ASIC, etc., in addition to CPU and MPU. Such an arithmetic circuit 21 can be configured by, for example, a signal processing circuit that is a semiconductor integrated circuit.

In the model creation process, a microstructure finite element model (microstructure FE model), which is an FEM analysis model of the microstructure to be used in the FEM analysis, is generated from the microstructure image of the metal material captured by the imaging device 10. create. Programs, parameters, and the like for creating a microstructure finite element model are stored, for example, in the storage device 22, and are read by the arithmetic circuit 21 as necessary and used for model creation. As will be described later, the arithmetic circuit 21 can create a microstructure finite element model by, for example, image-based modeling. When performing image-based modeling, the arithmetic circuit 21 applies any image processing filter to at least a partial region of the microstructure image to form shape data based on the microstructure shape of that region of the metallic material. . Then, in the parameter setting process to be described later, the arithmetic circuit 21 calculates the region based on the set parameters of the microstructure finite element model (for example, the type of element of the model to be created, the number of elements, the number of nodes, etc.). It is possible to create a microstructure finite element model simulating the The created microstructure finite element model is output to the storage device 22 and stored.

In addition, the model creation process can create a macrostructure finite element model (macrostructure FE model) that simulates an area larger than the area simulated by the microstructure finite element model. A macrostructural finite element model may be created with arbitrary dimensions, and the model is constructed as a homogeneous material.

The parameter setting process sets various parameters. The parameters may include, for example, the type of elements, the number of elements, and the number of nodes of the microstructure finite element model and the macrostructure finite element model created by the arithmetic circuit 21 by the model creation process. In addition, the parameters include the characteristics of the metal material to be analyzed by FEM analysis (Young's modulus, yield stress and yield strength, work hardening index and crystal orientation of the metal material, etc.), boundary conditions when performing FEM analysis by analysis processing, etc. may be included. In addition, the parameter setting process can set, as one of the parameters, a damage criterion, which is a criterion for determining damage in the damage determination process, which will be described later. As will be described later, the damage criteria can be set as a function with the equivalent plastic strain and the stress triaxiality calculated for each integration point in the FEM analysis as variables. Damage criteria can be set for each phase that constitutes the metallic material. The parameters are output to storage device 22 and stored. Then, each component reads the parameters from the storage device 22 and uses them as necessary.

Analysis processing can use the created microstructure finite element model to perform FEM analysis for simulating shape deformation when stress or strain is applied to the metal material. In addition, the analysis process uses the created macrostructure finite element model to perform FEM analysis for simulating the history of stress or strain generated in the metal material when a load is applied or a displacement occurs in the metal material. It can be carried out. A microstructural finite element model or macrostructural finite element model used for analysis, a program for performing simulation, boundary conditions, etc. are stored, for example, in the storage device 22 and used for analysis. The arithmetic circuit 21 of the control device 20 of the evaluation system 1 according to the present embodiment performs analysis processing, for each stress or strain applied to the microstructure finite element model, stress triaxiality and equivalent Plastic strain can be calculated and output. In addition, the arithmetic circuit 21 performs analysis processing to simulate the deformation of the macro structural finite element model for each load or displacement applied to the model, and calculates and outputs the deformation history (macro strain history) of the model. be able to. In this embodiment, the macro strain calculated by the FEM analysis for the macrostructure finite element model is used as input information for the FEM analysis for the microstructure finite element model. The macro strain, stress triaxiality and equivalent plastic strain may be output to the input/output device 23 and displayed on the input/output device 23, or may be output to the storage device 22 and stored. The macrostrain and stress triaxiality and equivalent plastic strain may also be output to communication circuitry 24 and transmitted to another controller.

The damage determination process can determine whether or not the integration point is damaged based on the equivalent plastic strain and stress triaxiality for each integration point calculated by the FEM analysis and the set damage criteria. can. When the arithmetic circuit 21 determines that a certain integration point is damaged, when performing FEM analysis by further applying stress or strain in the analysis process, considering that the integration point is damaged, the microscopic Simulation of the deformation of the textured finite element model is performed. More specifically, when performing the FEM analysis, the arithmetic circuit 21 changes part of the calculation formula regarding the integration point, and performs simulation of microstructure finite element model deformation due to stress or strain (details will be described later). ).

The storage device 22 is a storage medium capable of storing various information. The storage device 22 is realized by, for example, memories such as DRAM, SRAM, flash memory, HDD, SSD, other storage devices, or an appropriate combination thereof. The storage device 22 can store images captured by the imaging device 10, microstructural finite element models and macrostructural finite element models created in the model creation process. In addition, the storage device 22 can store parameters such as material properties and boundary conditions used in the analysis set in the parameter setting process, analysis result data calculated and output in the analysis process, and the like. Furthermore, the storage device 22 can transmit the stored information to each component such as the arithmetic circuit 21, the input/output device 23, the communication circuit 24, etc., as necessary. Each component may transmit and receive information directly between each component without going through the storage device 22 .

The input/output device 23 functions as an input device for inputting information from the user and as an output device for outputting information to the user. Input/output device 23 comprises one or more human-machine interfaces. Examples of human-machine interfaces include keyboards, pointing devices (mouse, trackball, etc.), input devices such as touch pads, output devices such as displays and speakers, and input/output devices such as touch panels. The input/output device 23 can display arbitrary information such as microstructure images of metal materials, microstructure finite element models, macrostructure finite element models, and parameters such as material properties and boundary conditions used for analysis. .

The communication circuit 24 is an interface device for connecting to a device or system via a communication line by wire or wirelessly. The interface device can perform communication conforming to a wired communication standard such as USB (registered trademark) or Ethernet (registered trademark). Further, the interface device is capable of performing communication conforming to wireless communication standards such as Wi-Fi (registered trademark), Bluetooth (registered trademark), and mobile phone lines.

In addition, the evaluation system 1 should just have the control apparatus 20 at least. For example, the arithmetic circuit 21 may receive a separately captured microstructure image via an interface device (the input/output device 23 and the communication circuit 24) and execute various processes.

A method for evaluating the damage behavior of a multi-phase material according to the present embodiment will be described with reference to the flowchart of damage behavior evaluation of a metallic material in FIG. 2 as an example. FIG. 2 is a flow chart for numerical analysis evaluation of the damage behavior of metal materials.

[Step 100: Acquisition of Microstructure Image of Multiphase Material]
First, as in step 100 (S100) of FIG. 2, the arithmetic circuit 21 acquires a microstructure image of the multiphase material. The arithmetic circuit 21 may acquire, for example, by reading out the microstructure image stored in the storage device 22 , or acquire it from another device or system via the communication circuit 24 .

The microstructure image is, for example, an image observed with a scanning electron microscope (SEM), an optical microscope (OM), electron beam backscatter diffraction (EBSD), computed tomography (CT), ultrasonic inspection (UT), or the like. You can use it. For the above observation, pretreatment such as etching may be carried out in advance depending on the type of constituent phases constituting the microstructure. The size, magnification, etc. of the microstructure image may be appropriately set according to the evaluation region, evaluation position, and the like.

In the above, as a method of acquiring a microstructure image of a metal material, a method of observing the microstructure of the metal structure and acquiring an image is shown, but the method is not limited to this, and the microstructure of the metal structure is not observed. First, a simulated geometric model may be formed, and a microstructure finite element model may be created based on this simulated geometric model.

The target multi-phase material may be any material as long as it contains a metal material. The type and strength level of the target metal material do not matter. The metal material is not limited to steel, and includes aluminum, titanium, copper, and magnesium pure metals or alloys. When the metal material is steel, the type of microstructure, structure shape, and phase fraction are not limited. Constituent phases constituting the microstructure include, for example, one or more of ferrite, martensite, bainite, pearlite, retained austenite, MA (Martensite-Austenite constituent, also referred to as "island martensite"), cementite, etc. may contain precipitates of The structure shape refers to the shape of crystals, and examples thereof include branch-like, granular, needle-like, and the like. The chemical composition of the steel is also not limited. The method for producing the metal material is not limited, either, and production conditions such as hot rolling conditions and heat treatment conditions can be appropriately set so as to obtain a desired microstructure. When evaluating a plurality of metal materials, for example, when comparing a plurality of metal materials, it is possible to prepare a plurality of metal materials that differ in one or more of, for example, the type of constituent phase of the microstructure, the shape of the structure, and the phase fraction. mentioned.

The target multi-phase material may contain ceramics in addition to the metal material. Ceramics include metal oxides such as silica, alumina, zirconia, titania, magnesia, cerium oxide, zinc oxide, barium titanate, hexaferrite, and mullite, silicon nitride, titanium nitride, aluminum nitride, silicon carbide, titanium carbide, and carbide. Non-oxide ceramics such as tungsten, boron carbide, and titanium boride are included.

The target multiphase material is, for example, a material composed of a metal material and composed of a plurality of steels in which one or more of the types of constituent phases that make up the microstructure, the shape of the structure, and the phase fraction are different. , materials composed of steel and non-ferrous metals such as aluminum other than steel, materials composed of non-ferrous metals of different metal types, and materials composed of metal materials and ceramics.

For the sake of simplicity, in the damage simulation method described below, a metal material having different types of constituent phases constituting a microstructure as a multiphase material, specifically, ferrite as a soft phase and martensite as a hard phase. The dual-phase steels, which are manufactured in the same field, are targeted to evaluate the microstructural damage behavior of metallic materials.

[Step 110: Step of creating a finite element model for microanalysis]
As shown in step 110 (S110) of FIG. 2, the arithmetic circuit 21 executes a model creation process to generate a mesh model as a microstructure finite element model, which is an FEM analysis model of a microstructure to be used in FEM analysis. to create The analysis model can be created, for example, by image-based modeling using acquired microstructure images of the metal material. An example of the model creation method is described in FIG. FIG. 3A shows the acquired microstructure image. Arithmetic circuit 21 sets a predetermined threshold value for the density or luminance of a pixel in such a microstructure image, and sets a value for the pixel depending on whether the density or the like at an arbitrary pixel position exceeds the threshold value. A binary image is created by performing binarization processing. FIG. 3B is a binary image created from the microstructure image of FIG. 3A. This allows the martensite phase to be extracted and separated from the other phases.

Next, the arithmetic circuit 21 acquires the contour of the region corresponding to the martensite phase from the binary image. The contour can be obtained, for example, by using an image processing filter (eg, Sobel filter, Laplacian filter, etc.) that detects edges. FIG. 3C represents the contour of the region corresponding to the martensite phase (hard phase) obtained from the binary image.

Next, the arithmetic circuit 21 creates shape data of the region corresponding to the martensite phase and shape data of the region corresponding to the ferrite phase (soft phase) from the contours. FIG. 3D shows shape data for creating a region M corresponding to the martensite layer and a region F corresponding to the ferrite phase. After that, the arithmetic circuit 21 creates a two-dimensional mesh model by dividing the shape data into meshes set based on predetermined conditions. The mesh model according to this embodiment is divided into meshes of quadrilateral elements. FIG. 3E shows a partial enlargement of a region in the upper right. The shape of the mesh is exemplified. A quadrilateral element need not be rectangular. Moreover, it is not essential to be a quadrilateral, and it is sufficient if the polygon is a triangle or more.

As the FEM analysis model in this embodiment, the above mesh model is created as a 2D model with a total number of elements of 40,279 and a total number of nodes of 40,507 by setting 4-node isoparametric elements. Then, the 2D model is expanded by one layer in the depth direction of the image, and a 3D model with a total number of elements of 40,279 and a total number of nodes of 81,014 is created by 8-node isoparametric elements, and the 3D model is used. FEM analysis is performed by The conditions of the model are not limited to those described above, and for example, elements with different numbers of constituent nodes may be used with respect to the types of elements. In addition, FEM analysis may be performed by creating 3D models with different total number of elements and total number of nodes. Also, instead of the 3D model, a 2D model may be created and used as the FEM analysis model.

[Step 120: Obtain Material Properties, Determine Damage Criteria]
As shown in step 120 (S120) of FIG. 2, the arithmetic circuit 21 acquires the characteristics of each material related to each phase that constitutes the metal material and sets them as parameters in order to perform the FEM analysis by the parameter setting process. Here, the material properties to be obtained are, for example, Young's modulus, yield stress and yield strength, work hardening index and crystal orientation of each of the ferrite phase and the martensite phase. In addition, the arithmetic circuit 21 acquires a stress-strain curve (in this embodiment, a stress-strain curve for ferrite and a stress-strain curve for martensite) for each phase material constituting the metal material as material characteristics. . As a result, when the arithmetic circuit 21 performs the FEM analysis described later in the analysis process, the stress or strain applied to the microstructure finite element model is based on the shape and characteristics of each phase that constitutes the model. The stress or strain applied to each integration point is calculated.

The arithmetic circuit 21 can set the boundary conditions when performing the FEM analysis using the microstructure finite element model by the parameter setting process. In this embodiment, the arithmetic circuit 21 assumes that the microstructure finite element model is arranged periodically, and gives periodic boundary conditions to the disturbance displacement components. As a result, as will be described later, the arithmetic circuit 21 uses, as input information, the history of macro strain calculated by performing FEM analysis on the macro structure finite element model based on the so-called homogenization method, and the micro structure finite element model can be performed for FEM analysis.

In addition, the arithmetic circuit 21 performs parameter setting processing to determine whether or not damage has occurred in each element of the model when stress or strain is applied in the FEM analysis using the microstructure finite element model. Set the damage criteria that are the criteria. By setting the damage criteria, the arithmetic circuit 21 determines the presence or absence of damage to each element of the microstructure finite element model based on the damage criteria and the equivalent plastic strain and stress triaxiality calculated by the FEM analysis described later. can be determined. As a result, the arithmetic circuit 21 can perform FEM analysis taking into consideration local damage to the metal material that occurs when a certain amount of stress or strain is applied to the metal material. Damage criteria can be represented by, for example, equations (1) and (2).
f _i =ε ^p (η+A) (1)
f _i >f _cr (2)

where f _i is a parameter for determining damage. _fcr is a reference value for determining damage and is an arbitrary constant. ε ^p is the equivalent plastic strain. η is the stress triaxiality. A is an arbitrary constant. _fcr and A can be set to different values for each phase that constitutes the metal material. By setting for each constituent phase, the arithmetic circuit does not need to create an FEM analysis model for each constituent phase, and the FEM analysis model can be simplified. Values of _fcr and A may be determined empirically or based on experimental data.

The damage criteria can be expressed as a function represented by Equation (3) with ^εp and η as variables.
f _cr =ε ^p (η+A) (3)
The function is a predetermined _curve (more specifically, an ^{inversely proportional} curve). Therefore, when the arithmetic circuit 21 plots the stress triaxiality ^η and the equivalent plastic strain ε ^p at a certain integration point on the graph, η or ε If at least one of ^p takes a large value, it may be determined that the integration point is damaged. The damage criteria are not limited to functions expressed in inverse proportion as described above, and may be set as arbitrary linear functions, for example.

When defining damage criteria based on experimental data, for example, the damage criteria can be defined as follows. An FEM analysis model is created based on a tissue image of an arbitrary test piece, a tensile test is performed on the test piece, and the arithmetic circuit 21 applies stress or strain equivalent to that of the tensile test to the FEM analysis model. FEM analysis is performed by giving a history. During execution of the tensile test, the arithmetic circuit 21 acquires a tissue image of the test piece at an arbitrary timing and associates it with the strain occurring in the test piece at that timing. Then, when confirming the tissue image and microvoids are generated, the arithmetic circuit 21 determines the microvoids in the tissue image from the FEM analysis result when the strain associated with the tissue image is applied to the FEM analysis model. Calculate the equivalent plastic strain and stress triaxiality of the integration point corresponding to the position where When the arithmetic circuit 21 obtains the equivalent plastic strain and the stress triaxiality, it plots them on a graph. Arithmetic circuit 21 plots combinations of equivalent plastic strain and stress triaxiality for a plurality of microvoids on a graph to determine _fcr and A where the plotted points satisfy equations (1) and (2). , whereby the damage criteria can be defined.

The arithmetic circuit 21 determines that damage has occurred when the parameter _fi calculated based on the equivalent plastic strain, the stress triaxiality, and an arbitrary constant is greater than a certain reference value _fcr , as shown in Equation (2). I can judge. The equivalent plastic strain and the stress triaxiality are calculated by analysis processing described later. Details of acquisition of material properties and setting of damage criteria for setting parameters in the parameter setting process will be described later.

[Step 130: Acquisition of Macro Strain]
As shown in step 130 (S130) of FIG. 2, the arithmetic circuit 21 acquires the macro strain given when performing the FEM analysis on the microstructure finite element model. For example, the arithmetic circuit 21 performs steps 131 to 133 described below to create a macro structural finite element model, perform FEM analysis on the model, and calculate and obtain macro strain.
FIG. 4 is a flow chart for acquiring macro-distortion. Further, the arithmetic circuit 21 may acquire the macro strain by reading out the macro strain calculated in advance and stored in the storage device 22 , or may acquire the macro strain via the communication circuit 24 .

[Step 131: Creation of macrostructural finite element model]
As shown in step 131 (S131) of FIG. 4, the arithmetic circuit 21 executes the model creation process, and for use in the FEM analysis, the mesh model is used as the macrostructure finite element model, which is the FEM analysis model to be analyzed for the macrostructure. to create The mesh model may have any size.

[Step 132: Acquisition of strength characteristics as homogeneous material]
As shown in step 132 (S132) in FIG. 4, the arithmetic circuit 21 executes parameter setting processing to acquire the properties of the metal material for the macro structural finite element model for FEM analysis and set them as parameters. Here, the material properties to be acquired are, for example, Young's modulus, Poisson's ratio, stress-strain curve, yield stress and proof stress, work hardening index, crystal orientation, etc. of the metal material. The parameters can be obtained through experiments. For example, stress-strain curves and yield stresses for metallic materials can be obtained by performing tensile tests on specimens constructed of the material. Young's modulus and Poisson's ratio can be obtained by a tensile test, a resonance method, an ultrasonic method, or the like. Since the metallic material can be separated into each phase that constitutes the metallic material in the microscopic structure, the arithmetic circuit 21 sets the parameters for each phase in the microscopic structure, but in the macroscopic structure, the parameters are the same regardless of the phase structure. Set parameters as a material.

[Step 133: Execution of FEM analysis using macrostructural finite element model (calculation of strain)]
As shown in step 133 (S133) in FIG. 4, the arithmetic circuit 21 performs FEM analysis using the created macrostructure finite element model by analysis processing. In the FEM analysis, by applying a predetermined load or displacement to the created macrostructure finite element model, the history of stress or strain generated in the metal material can be analyzed by simulation. For example, in the analysis process, load or displacement conditions corresponding to uniaxial tension are applied to the macrostructural finite element model, the deformation of the macrostructural finite element model is simulated, and the deformation history of the macrostructural finite element model (macro strain history). The calculated deformation history is output and stored in the storage device 22, for example. The deformation field applied to the macrostructure finite element model is not limited to uniaxial tension, and may be a composite deformation field in which tension, compression and shear deformation occur simultaneously.

In this manner, the arithmetic circuit 21 can create a macrostructure finite element model and calculate and acquire macroscopic strain using the model. In this embodiment, the arithmetic circuit 21 calculates the macro strain after acquiring the material properties of the microstructure finite element model and determining the damage criteria (that is, step 120), but is not limited to this. For example, arithmetic circuitry 21 may calculate macrostrain prior to acquiring a microtissue image (ie, step 100). In addition, as will be described later, the arithmetic circuit 21 performs FEM analysis in a microstructure finite element model for each macro strain by giving a history of macro strain. Therefore, the macro strain should be calculated when performing the FEM analysis of the microstructure finite element model. For example, the arithmetic circuit 21 may first execute steps 131 and 132 and then execute step 133 as appropriate. That is, the arithmetic circuit 21 may execute step 133 after execution of step 160 described later and before execution of step 140 described later, and calculate the macro distortion used in step 140 at that timing.

[Step 140: Execution of FEM analysis using microstructure finite element model (calculation of equivalent plastic strain and stress triaxiality)]
As shown in step 140 (S140) of FIG. 2, the arithmetic circuit 21 performs FEM analysis using the created microstructure finite element model by analysis processing. As described above, as a boundary condition for the FEM analysis of the microstructural finite element model, a periodic boundary condition is given to the disturbance displacement component, assuming that the model is arranged periodically. Therefore, in the FEM analysis, the arithmetic circuit 21 gives the macro strain history obtained in step 130 as a macro strain increment to the created microstructure finite element model. Thereby, the arithmetic circuit 21 can simulate how the metallic material behaves when macro-strain increments are applied, based on the so-called homogenization method. The arithmetic circuit 21 can calculate the equivalent plastic strain and the stress triaxiality of each element as the deformation behavior of the microstructure finite element model for each macro strain applied to each element of the microstructure finite element model by the analysis processing. . The calculated equivalent plastic strain and stress triaxiality can be output to and stored in the storage device 22 . Each element of the microstructure finite element model has preset integration points for performing integration during analysis. Equivalent plastic strain and stress triaxiality are calculated for each strain applied to the integration points. In addition to the integration point of each element of the microstructure finite element model, for example, the equivalent plastic strain and stress triaxiality may be calculated using element solutions or nodal solutions calculated from the solutions calculated for the integration points. .

[Step 150: Damage determination at each integration point of the microstructure finite element model]
As shown in step 150 (S150) of FIG. 2, the arithmetic circuit 21 determines whether damage (that is, microvoids) has occurred at each integration point of the microstructure finite element model by the damage determination process. The damage determination process determines the presence or absence of damage based on the damage criteria set in step 120 and the equivalent plastic strain and stress triaxiality calculated by the FEM analysis performed in step 140 . In the damage determination process, in step 140, the presence or absence of damage is determined each time the equivalent plastic strain and stress triaxiality are calculated. Details of the damage determination process will be described later.

[Step 160: Determining whether to continue FEM analysis]
As in step 160 (S160) in FIG. 2, the arithmetic circuit 21 determines whether to continue the FEM analysis. Specifically, the arithmetic circuit 21 determines whether or not the deformation of the microstructure finite element model has reached a predetermined deformation rate through the damage determination process. If the deformation of the microstructure finite element model has not reached the predetermined deformation rate, the arithmetic circuit 21 changes the macro strain given to the microstructure finite element model and further executes the FEM analysis (S140) (S160: Yes). Then, the equivalent plastic strain and stress triaxiality in the microstructure finite element model when the macro strain is applied are calculated. When the deformation of the microstructure finite element model reaches the predetermined deformation rate, the arithmetic circuit 21 terminates the FEM analysis by the analysis process (S160: No). In addition, since the element determined to be damaged in the microstructure finite element model reduces the element rigidity of the element, as the number of elements determined to be damaged increases, the damage caused by the microvoids progresses, and the microstructure Deformation resistance of the finite element model is reduced. The arithmetic circuit 21 may end the FEM analysis by the analysis process when the deformation resistance drops below a predetermined value.

As described above, the damage simulation method according to the present embodiment can perform FEM analysis using a finite element model that simulates the macrostructure of a metal material, and can calculate the history of macroscopic strain. In addition, in the damage simulation method, FEM analysis is performed using a finite element model that simulates the microstructure of the metal material and the calculated macro strain history, and the equivalent plastic strain and stress triaxiality can be calculated. . In the damage simulation method, the presence or absence of damage is determined based on the calculated equivalent plastic strain and stress triaxiality. A decrease in deformation resistance in the tensile direction can be reproduced. In the damage simulation method, on the microstructure side, damage to the microstructure occurs as the macroscopic deformation of the metal material progresses, and it is possible to simultaneously analyze the behavior in which the damage to the microstructure connects and progresses. can.

(Acquisition of stress-strain curves, etc. of each constituent phase)
A material characteristic setting process for performing an FEM analysis, which is set in the parameter setting process, will be described. A stress-strain curve for each material for each phase that makes up the metallic material can be obtained, for example, by performing a tensile test on a test piece made up of that material. Also, the stress-strain curve and yield stress for each material can be obtained, for example, by analytical techniques such as those described below. Incidentally, the method of acquiring the stress-strain curve and yield stress for each material is not limited to this method, and may be determined based on a predetermined formula such as the Swift's law formula, or may be obtained in advance in the storage device 22 You may use the curve etc. which were memorize|stored in .

First, the arithmetic circuit 21 acquires the area fraction of each phase (the ferrite phase and the martensite phase in FIG. 3A) constituting the metal material from the microstructure image as shown in FIG. 3A. The arithmetic circuit 21 can separate the microstructure image of the metal material into each phase, for example, by the method described in step 110, so that the area fraction of each phase can be obtained. Next, the arithmetic circuit 21 calculates the volume fraction of each phase based on the area fraction. For example, assuming that of the two constituent phases, the constituent phase having the smaller area fraction (constituent phase A) is uniformly dispersed in the duplex steel, the arithmetic circuit 21 calculates the The volume fraction VA of the constituent phase A can be obtained by multiplying the area fraction SA to the power of 3/2. The volume fraction VB of the other constituent phase (constituent phase B) can be obtained by subtracting the volume fraction VA of constituent phase A from 100%.

In the example of FIG. 3A, the arithmetic circuit 21 can obtain the ferrite phase area fraction of 85% and the martensite phase area fraction of 15%. The arithmetic circuit 21 raises the area fraction (15%) of the martensite phase having a smaller area fraction to the power of 3/2 (that is, 0.15 ^3/2 ) to obtain the volume fraction of the martensite phase (approximately 6 %). The arithmetic circuit 21 can calculate the volume fraction of the ferrite phase by subtracting the volume fraction of the martensite phase (6%) from the total (100%). For example, if the martensite phase volume fraction is 6%, the ferrite phase volume fraction is 100%-6%=94%.

Arithmetic circuitry 21 then obtains the stress-strain curve for the duplex steel of interest. The stress-strain curve can be obtained, for example, by preparing a tensile test specimen from a duplex steel and conducting a uniaxial tensile test. Although the test method of the uniaxial tensile test and the shape of the test material are not particularly limited, for example, JIS Z2241:2011 can be referred to. FIG. 5 is an example of measured data of a stress-strain curve of a duplex steel.

Next, the arithmetic circuit 21 obtains the yield stress σ _yDP of the duplex steel from the obtained stress-strain curve measurement data. FIG. 6 is an enlarged view of the vicinity of the boundary line between the elastic region and the plastic region in the stress-strain curve of FIG. The stress-strain curve is linear in the elastic region, but once the duplex steel begins to deform plastically (ie, enters the plastic region), the stress-strain curve loses linearity. The stress value when the linearity is lost is defined as the yield stress _σyDP of the duplex steel. In the example of FIG. 6, σ _yDP =220 MPa.

In a duplex steel composed of a soft phase and a hard phase, the soft phase, ie the ferrite phase in this embodiment, begins to plastically deform first, followed by the hard phase, ie the martensite phase in this embodiment, begins to plastically deform. it is conceivable that. That is, it is considered that the yield stress σ _yDP of the duplex steel depends only on the yield stress σ _ySP of the ferrite phase. Therefore, the yield stress of the ferrite phase can be obtained from the yield stress _σyDP of the dual-phase steel and the volume fraction of the ferrite phase as shown in the following formula (4).
σ _ySP =σ _yDP ÷ {(volume fraction of ferrite phase (%))/100} (4)

For example, if the yield stress σ _yDP of the duplex steel is 220 MPa and the volume fraction of the ferrite phase is 94% (0.94), the yield stress σ _ySP of the ferrite phase is 220 ÷ (94 (%) / 100) = 234 MPa becomes. Thus, the yield stress _σySP of the ferrite phase is calculated.

Next, the arithmetic circuit 21 generates a graph showing the relationship between stress and strain from the measured data of the stress-strain curve (for example, the vertical axis is the natural logarithm of the stress, and the horizontal axis is the natural logarithm of the strain). create. FIG. 7 is a log-log graph of the stress-strain curve shown in FIG. Then, the arithmetic circuit 21 determines the part where the log-log graph is a straight line within the plastic region of the stress-strain curve. The range including the straight line portion is defined as "range LA". The range LA is a range that follows the multiplier (nth power) on the right side in the Swift's law formula (5) that shows the stress-strain curve of the ferrite phase.
σ ₁ =σ _{y SP} (1+ε/α) ⁿ (5)

where σ1 is the _first stress borne by the ferrite phase. _σySP is the yield stress of the ferrite phase. ε is the strain of the ferrite phase. α is the intrinsic constant of the ferrite phase. n is the work hardening index of the ferrite phase. In FIG. 7, the solid line indicates a log-log graph of the stress-strain curve. When an approximation straight line (dashed line) is drawn along the straight line portion (the portion within the area LA) of the solid line, the slope of the approximation straight line correlates with the work hardening index n of the ferrite phase.

As used herein, the term “linear portion” refers to part or all of the portion that can be regarded as a straight line in the double-logarithmic graph of the stress-strain curve. The range LA may be a range including "part or all of the portion that can be regarded as a straight line". In this specification, the "portion that can be regarded as a straight line" also includes a portion that is not perfectly straight, but is almost straight. Specifically, when an approximate straight line is drawn on the double-logarithmic graph of the stress-strain curve by the method of least squares, the "deviation" in the vertical axis direction (natural logarithm direction of stress) between the double-logarithmic graph and the approximate straight line is , If the value is equal to or less than 1 MPa on the double logarithmic graph, it is regarded as "the part that can be regarded as a straight line".

The stress σ experienced by the duplex steel can be divided into a first stress σ ₁ borne by the ferrite phase and a second stress Δσ borne by the martensite phase. FIG. 8 is a stress-strain curve for explaining the second stress Δσ. In the stress-strain curve shown in FIG. 8, the solid line is actually measured data of the stress-strain curve of the duplex steel, and the dashed line is an image of the stress-strain curve of the ferrite phase. The first stress σ ₁ borne by the ferrite phase can be read from the stress-strain curve of the ferrite phase. The distance between the solid line and the dashed line in the vertical axis direction corresponds to the second stress Δσ borne by the martensite phase.

Based on this, a range C-LA (see FIG. 8) corresponding to the range LA specified on the log-log graph is defined on the stress-strain curve, and the stress σ of the duplex steel in that range is calculated as the first The procedure for dividing the stress into the _first stress σ1 and the second stress Δσ will be described. The corresponding range on the stress-strain curve is sometimes simply referred to as "Range C-LA."

FIG. 9 is a schematic diagram of a stress-strain curve of a martensite phase that can be regarded as an elastic perfect plastic body. Since the martensite phase can be regarded as an elastic perfect plastic body, the stress-strain curve in the case of only the martensite phase has the shape shown in FIG. Therefore, the stress σ _HP within the range C-LA is constant and equal to the yield stress σ _yHP . Also, the second stress Δσ borne by the martensite phase corresponds to a value obtained by multiplying the stress σ _HP by the volume fraction. From these, the second stress Δσ is constant within the range C-LA (that is, in FIG. 8, the separation distance in the vertical axis direction between the solid line and the broken line is constant within the range C-LA ). Also, the second stress Δσ is equal to the yield stress σ _yHP of the martensitic phase multiplied by the volume fraction. The first stress σ ₁ borne by the ferrite phase corresponds to a value obtained by multiplying the stress σ _SP in the case of only the ferrite phase by the volume fraction.

The above contents can be represented by the following formulas (6) to (9). The volume fraction of the ferrite phase is, for example, 94% (0.94), and the volume fraction of the martensite phase is, for example, 6% (0.06).
σ=σ ₁ +Δσ (6)
_σHP = _σyHP (7)
Δσ = σ _HP × (volume fraction of martensite phase)
= σ _yHP × (volume fraction of martensite phase) (8)
σ ₁ = σ _SP × (volume fraction of ferrite phase) (9)

As described above, the Swift's law represented by Equation (5) can be applied to the ferrite phase. The relationship between the ferrite phase and the martensite phase can be represented by one equation by transforming the equation (5) according to the following procedures (i) to (ii).
Procedure (i) Take the natural logarithm of both sides and transform the formula.
lnσ ₁ = lnσ y _SP (1+ε/α) ⁿ
=ln(1+ε/α) ⁿ + _lnσySP
=n ln(1+ε/α)+ _lnσySP (5-1)
Procedure (ii) Transform equation (6) into equation (10) and substitute it into equation (5-1) σ ₁ =σ−Δσ (10)
ln(σ-Δσ)=n ln(1+ε/α)+ _lnσySP (5-2)

Plotting equation (5-2) with ln(σ−Δσ) on the vertical axis and ln(1+ε/α) on the horizontal axis can produce a graph of a linear function. The graph has a slope of n and an intercept of lnσ _ySP . FIG. 10 is a log-log graph plotting the relationship between stress and strain of a duplex steel with ln(σ−Δσ) on the vertical axis and ln(1+ε/α) on the horizontal axis. Here, since the yield stress σ _ySP of the ferrite phase can be obtained as described above (for example, 234 MPa), the value of α is determined so that the intercept lnσ _ySP =ln234=5.45. When the value of α is determined, the slope n is also uniquely determined. In FIG. 10, the slope n=0.23.

Substituting the obtained values of α and n into equation (5-2), the variables in the equation are the stress σ and strain ε of the duplex steel and the second stress Δσ. Since the stress σ and the strain ε of the dual-phase steel can be specified from the actual measurement data of the tensile test of the dual-phase steel, the only variables in practice are the second stress Δσ. Therefore, the arithmetic circuit 21 sets an appropriate initial value (for example, 200 MPa) for the second stress Δσ, and performs reverse analysis of the finite element method from the actual measurement data of the duplex steel tensile test to obtain Δσ. be able to. Since the value of Δσ finally obtained does not depend on the initial value, any value may be set as the initial value.

The arithmetic circuit 21 obtains the first stress σ1 by substituting the obtained _second stress Δσ into the equation (10). As a result, the arithmetic circuit 21 can divide the stress σ of the stress-strain curve into the first stress σ ₁ borne by the ferrite phase and the second stress Δσ borne by the martensite phase. .

In this way, by processing the variable to be one of the second stresses Δσ, the arithmetic circuit 21 can reduce the calculation load on the inverse analysis of the finite element method. The arithmetic circuit 21 performs inverse analysis of the finite element method while also treating the intrinsic constant α of the ferrite phase and the work hardening exponent n in the Swift's law equation (5) as variables in the same manner as the second stress Δσ. is also possible. However, it is not easy to uniquely determine the combination of multiple variables. Therefore, by using only the second stress Δσ as a variable, the arithmetic circuit 21 can relatively easily identify Δσ by inverse analysis.

The arithmetic circuit 21 transforms the equation (8) into the following equation (11), and substitutes the second stress Δσ obtained as described above to obtain the yield stress σ _yHP of the martensite phase. can. As described above, the value of the martensite phase volume fraction of 6% is just an example, and the value is not limited to this.
σ _yHP =Δσ/(volume fraction of martensite phase)
=Δσ/0.06 (11)

Next, the arithmetic circuit 21 calculates the stress-strain curve of the ferrite phase using the yield stress σ _ySP of the ferrite phase, the work hardening exponent n, and the intrinsic constant α of the ferrite phase obtained as described above. The stress-strain curve of the ferrite phase can be drawn by substituting the values obtained as described above for σ _ySP , α, and n in equation (5) of Swift's law.

Next, the arithmetic circuit 21 obtains the stress-strain curve of the martensite phase by calculation using the yield stress σ _yHP of the martensite phase obtained as described above. Since the martensite phase can be regarded as an elastic perfect plastic body, the stress-strain curve becomes a stress-strain curve of the form shown in FIG. In the elastic region the stress σ is proportional to the strain ε, and in the plastic region the stress σ is constant regardless of the value of the strain ε. The stress and strain in the elastic region satisfy the relationship of Equation (12) below.
Stress = Young's modulus x Strain (12)

Therefore, in the martensite phase, the stress (yield stress σ _yHP ) and strain (yield strain ε _yHP ) at the boundary point (yield point YP) between the elastic region and the composition region can be obtained by the following equation (13). can be done. A known value can be used for the Young's modulus of the martensite phase, and is, for example, about 200 GPa.
σ _yHP =Young's modulus of martensite phase×ε _yHP (13)

Based on these, when the stress-strain curve of the martensite phase is created, up to the yield point YP, it becomes a straight line whose slope is the "Young's modulus of the martensite phase". A graph shown in FIG. 9 is obtained, which is constant at σ _yHP .

As described above, the arithmetic circuit 21 can acquire the stress-strain curve of the ferrite phase and the stress-strain curve of the martensite phase. As noted above, the technique is not limited to duplex steels composed of ferritic and martensitic phases, but can be used for duplex steels composed of any soft and hard phases.

(Processing by FEM analysis and damage determination)
The damage determination and damage determination processing performed by the FEM analysis and the damage determination processing executed in the analysis processing will be described. A micro-element stiffness equation used in FEM analysis is represented by the following equation (14). Here, x (x is a dot code above x) represents a characteristic displacement at each node, and F (F is a dot code above F) represents a nodal load for each node.

Regarding the formula (14), [K], {x}, and {F} are represented by the following formulas (15) to (17), respectively.

Here, [B _D ] is a matrix that associates displacement velocity-deformation velocity. [B _L ] is a matrix relating displacement velocity-velocity gradient. [C _ep ] is the microelastic-plastic constitutive law matrix, and [σ _L ] is the stress matrix due to geometric nonlinearity. These are specifically represented by the following equations (18) to (21) in a three-dimensional problem.

where N ⁱ denotes the shape function for node i. {j} in the right side of equation (17) is a column vector in which only the j component is 1 and the other components are zero. I in the right side of Equation (21) is a 3×3 identity matrix. Equation (15) is the elasto-plastic stiffness matrix, and if the load velocity vectors corresponding to the six deformation modes given by Equation (17) can be separately calculated, the microstructural properties can be determined using a regular FEM solver (i.e. software) It becomes possible to calculate the displacement speed. A periodic boundary condition must be given as a geometric boundary condition when solving equation (14), and an MPC (multipoint constraint) function is required. When calculating the elastoplastic stiffness matrix represented by the formula (15) and the load velocity vector represented by the formula (17), using all known quantities (various quantities at time t), static explicit method The characteristic displacement velocity is obtained by

As described above, the analysis process is performed by applying the macro strain history obtained by executing the FEM analysis on the macro structure finite element model as a macro strain increment to the micro structure finite element model, so that deformation of the metal material Simulate behavior. For example, the analysis process provides a microstructure finite element model with six components of macro strain increments equivalent to uniaxial tension. Assuming that the tensile direction is the 11th direction and the directions orthogonal to the 11th direction are the 22nd and 33rd directions, the analysis processing is as follows: 11 components: 22 components: 33 components: 12 components: 23 components: 31 components = 1: -0.5: A ratio of strain increments such as −0.5:0:0:0 may be applied to all integration points. The 12th, 23rd and 31st components mean shear components. The ratio is not limited to the above. For example, in the analysis process, when the deformation field given to the macrostructure finite element model is a multiaxial strain field instead of a uniaxial tension, FEM analysis is performed by giving a strain increment of a ratio different from the above ratio to all integration points can be executed.

As described above, when it is determined in the damage determination process that damage has occurred at a certain integration point, the analysis process changes the calculation formula for the element stiffness and performs FEM analysis. For example, in the analysis processing, all components of [σ _L ] in Equation (15) are set to zero, and the value of [C _ep ] is changed to 1/100 of the initial value. As a result, the analysis process can perform FEM analysis with the stress released and the element stiffness reduced to 1/100 with respect to the integration point where it is determined that damage has occurred. As a result, the analysis processing can perform FEM analysis taking into consideration the occurrence of damage at each integration point. The value of [C _ep ] after change is not limited to the above numerical value, and can be any value, for example, 1/50 or less of the initial value. More specifically, the value of [C _ep ] can be changed to 1/50, 1/200, 1/500, 1/1000, zero, and so on.

[Example]
EXAMPLES Hereinafter, the present invention will be described more specifically with reference to examples. The present invention is not limited by the following examples, and can be implemented with appropriate modifications within the scope that can match the spirit described above and below. subsumed in That is, although the examples using the duplex steel composed of the two phases of the ferrite phase as the soft phase and the martensite phase as the hard phase are shown below, the present invention is not limited to this. Moreover, although the deformation field given to the macrostructure finite element model is given by uniaxial tension below, it is not limited to this. In addition, although damage criteria represented by a certain function are given below as criteria for determining the presence or absence of damage, the present invention is not limited to this.

In this example, as a dual-phase material, a dual-phase steel composed of two phases of a ferrite phase and a martensite phase is targeted. was evaluated as follows.

1. Preparation of dual-phase material (metal material) Steel containing 0.063% by mass of C, 0.50% by mass of Si, and 1.46% by mass of Mn (actual results) is melted as a dual-phase steel, and an ingot is obtained. A martensitic and ferritic dual phase steel was prepared by forging after obtaining and heat treating. Using the dual-phase steel, a model for FEM analysis simulating the microstructure was created by the following procedure.

2. Acquisition of microstructure image of metal material The above material is cut into a size of about 10 mm × 10 mm with a microscopic observation surface, etched with nital, and then photographed with a scanning electron microscope at a magnification of 1000 times. Images of tissues were acquired. A photomicrograph of the above material is shown in FIG. 3A. In FIG. 3A, the white portion indicates the martensite phase, which is the hard phase, and the gray portion indicates the ferrite phase, which is the soft phase. In FIG. 3A, image analysis of the micrograph revealed that the area fraction of martensite, which is a hard phase, was about 15%.

3. Creation of microstructure finite element model Next, the arithmetic circuit 21 of the evaluation system 1 is caused to execute a model creation process to simulate an image of the microstructure of the material in order to create a microstructure finite element model to be used for FEM analysis. A mesh model was created. A mesh model may be created in a manner similar to step 110 described above. In this example, similar to the model described in step 110, the mesh model was created as a 2D model with a total number of elements of 40,279 and a total number of nodes of 40,507 by setting 4-node isoparametric elements. there is By causing the arithmetic circuit 21 to execute the model creation process, the 2D model is expanded by one layer in the depth direction of the image, and the total number of elements is 40,279 and the total number of nodes is 81 with 8-node isoparametric elements. , 014 was created.

The created 2D mesh model is created so that the area fraction of the region corresponding to martensite, which is the hard phase, is approximately 15%. Similarly, a 3D mesh model is created such that the volume fraction of the region corresponding to the hard phase martensite is approximately 15%.

4. Acquisition of Material Properties and Setting of Damage Criteria Next, the arithmetic circuit 21 of the evaluation system 1 was caused to execute a parameter setting process to acquire material properties of each phase constituting the metal material. Known values were used for the Young's modulus and Poisson's ratio of each phase, and the Young's modulus of the ferrite phase was set to 206 GPa and the Poisson's ratio to 0.3, and the Young's modulus of the martensite phase was set to 206 GPa and the Poisson's ratio of 0.3. . Also, as a stress-strain curve, curve data expressed by Swift's law equation (22) was given. The relationship between stress and strain for ferrite and martensite phases can be expressed by the following equation (22). Here, _σy is the yield stress (subsequent yield stress) of each phase when the equivalent plastic strain becomes ^εp . σ ₀ is the initial yield stress of each phase (the yield stress when the equivalent plastic strain is zero). ε ^p is the equivalent plastic strain. a is a constant specific to each phase. n is the work hardening index of each phase. Parameters for each phase were calculated by the above method and input as material properties by parameter setting processing. In this example, each parameter regarding the ferrite phase was calculated as σ ₀ =230 MPa, a=7×10 ⁻³ , and n=0.23. Parameters for the martensite phase were calculated as σ ₀ =2100 MPa, a=1×10 ⁻⁵ , n=0.015.
σ _y =σ ₀ (1+ε ^p /a) ⁿ (22)

Also, the arithmetic circuit 21 was caused to execute parameter setting processing to set damage criteria for each phase constituting the metal material. Based on the formulas (1) and (2), when the ferrite phase satisfies the formula (23) and the martensite phase satisfies the formula (24), it is determined that the structure related to the integration point is damaged. We set the damage criteria as follows. where ε ^p is the equivalent plastic strain. η is the stress triaxiality. For ε ^p and η, the equivalent plastic strain and stress triaxiality for each integration point calculated by FEM analysis, which will be described later, are input.
ε ^p (η+4.5)>5 (23)
ε ^p (η+1.4)>2.2 (24)

5. Creation of Macro Structure Finite Element Model Next, the arithmetic circuit 21 was caused to execute model creation processing to create a macro structure finite element model. FIG. 11 is a schematic diagram showing the relationship between the macrostructure finite element model and the microstructure finite element model. FIG. 11(a) is a schematic diagram of a macrostructure finite element model. FIG. 11(b) is a schematic diagram in which microstructure finite element models are arranged periodically. FIG. 11(c) is an example of a microstructure finite element model. The schematic diagram shown in FIG. 11(b) shows how the microstructure finite element model shown in FIG. 11(c) is arranged periodically. FIG. 11(b) corresponds to a partial region of FIG. 11(a), and the partial region of the macrostructure finite element model corresponds to the region in which the microstructure finite element model is periodically arranged. indicates that

6. Acquisition of Material Properties as Homogeneous Material Next, the arithmetic circuit 21 is caused to execute parameter setting processing to acquire material properties for executing FEM analysis on the macrostructure finite element model, and as uniform material properties set the parameters. As described above, the stress-strain curves for metallic materials were obtained by subjecting specimens composed of metallic materials to uniaxial tensile tests. Moreover, the yield stress of the metal material was obtained in the uniaxial tensile test.

7. Execution of FEM analysis on macrostructural finite element model (calculation of macro strain history)
Next, the arithmetic circuit was caused to perform analysis processing, and FEM analysis was performed using the macrostructure finite element model. In the FEM analysis, a load or displacement condition equivalent to a uniaxial tensile test is applied to the macrostructural finite element model, the deformation behavior of the macrostructural finite element model is simulated, and the deformation history of the macrostructural finite element model is analyzed. was calculated. The tensile direction in the uniaxial tensile test corresponds to the direction indicated by the arrow in FIG. 11(a). Hereinafter, the pulling direction is appropriately referred to as "11 directions". In this embodiment, as shown in FIG. 11A, the left-right direction of the macrostructure finite element model is the 11th direction, and the directions perpendicular to the tensile direction are the 22nd and 33rd directions. In this example, boundary conditions were set as shown in FIG. 11(a). Specifically, the left lower end of the macrostructure finite element model was fully constrained, and the left end of the model excluding the right end and the left lower end was constrained in 11 directions. Under the boundary conditions, a forced displacement that pulls the right end in 11 directions is applied to the macrostructure finite element model, and an FEM analysis equivalent to a uniaxial tensile test is performed to obtain a predetermined macrostrain in an arbitrary evaluation area. Calculated. In the present embodiment, the ratio macro strain is calculated such that 11 components: 22 components: 33 components: 12 components: 23 components: 31 components = 1: -0.5: -0.5: 0: 0: 0 was done. Then, the macro strain calculated for each set load in the uniaxial tension was output as the macro strain history. In the following description, "macro strain" means strain in the above 11 directions, unless otherwise specified. The 12th, 23rd and 31st components mean shear components.

8. Setting of Boundary Conditions Next, the boundary conditions given to the microstructure finite element model were set by causing the arithmetic circuit 21 to execute parameter setting processing. More specifically, we assume that the microstructure finite element model is arranged periodically and give periodic boundary conditions to the disturbance displacement components.

9. Performing FEM analysis on the microstructure finite element model (calculation of equivalent plastic strain and stress triaxiality)
Next, the arithmetic circuit 21 was caused to perform analysis processing, and FEM analysis was performed using the created microstructure finite element model. In the FEM analysis, the obtained macro strain history was given to all integration points of the microstructure finite element model as input information for the boundary value problem. Then, when macro strain increment based on macro strain history is applied to the microstructural finite element model, the deformation behavior of the model is analyzed by simulation to see how the model deforms under periodic boundary conditions for the disturbance displacement component. . As a result, the equivalent plastic strain and stress triaxiality at each position were calculated and output as the deformation behavior of the model for each macro strain. In this example, as each position, the value at the integration point of each element of the microstructure finite element model was used.

10. Continuation of damage determination and FEM analysis at each integration point of the microstructure finite element model Based on plastic strain and stress triaxiality, it was determined whether damage had occurred at each integration point. Damage criteria for determining damage are given by equations (1) and (2), as described above. In this example, as shown in formulas (23) and (24), A = 4.5 and f _cr = 5 for the ferrite phase, and A = 1.4 and f _cr = 2.2 for the martensite phase. The presence or absence of damage was determined based on the phases constituting each integration point. That is, the equivalent plastic strain and stress triaxiality calculated at a certain integration point are substituted into formulas (1) and (2), and if f _i ≤ f _cr , it is determined that no damage has occurred at that integration point. do. If f _i >f _cr , it is determined that damage has occurred at the integration point. In the present embodiment, it is determined that no damage has occurred with respect to the integration point where f _i =f _cr , but the present invention is not limited to this, and damage has occurred with respect to the integration point where f _i =f _cr . It may be determined that When it was determined that damage had occurred at a certain integration point, the calculation circuit 21 released the stress at that integration point and lowered the element stiffness to 1/100 of the initial value. Further FEM analysis was then performed with increasing macro strain increments.

When the strain in the microstructure finite element model reaches a given deformation rate, or when the integration points at which damage is determined to have occurred increase to such an extent that the equivalent plastic strain and stress triaxiality cannot be calculated by the FEM analysis, the FEM analysis is performed. finished.

FIG. 12A shows stress-strain curves of 11 directional components obtained by calculating volume averages at all integration points for the stresses and strains calculated by the above FEM analysis for the microstructure finite element model. FIG. 12B shows changes in the number of integration points of the microstructure finite element model determined to be damaged based on the damage criteria according to the applied strain in the FEM analysis for the microstructure finite element model.

FIG. 12B shows that the number of integration points determined to be damaged increases sharply from around when the macrostrain in the tensile direction component exceeds about 27%. Also, FIG. 12A shows that the stress required for deformation decreases from around when the macro strain in the tensile direction exceeds about 27%, and thus the deformation resistance decreases. FIG. 12A reproduces the same trend as the measured data of the stress-strain curve obtained by the uniaxial tensile test performed on the test piece made of the metal material.

FIG. 13A is a microstructure finite element model calculated by simulation when a macro strain of 30% in the tensile direction component is applied in the FEM analysis. FIG. 13B is a microstructure finite element model calculated by simulation when applying a macro strain of 35% in the tensile direction component in the FEM analysis. In each of FIGS. 13A and 13B, the solid-line circled regions indicate microvoids occurring in each microstructure finite element model. In FIG. 13B, the area surrounded by the dashed circle shows that the microvoids generated when 30% macro strain is applied grow by increasing the macro strain, and multiple microvoids are connected. indicates that

As shown in FIGS. 12A to 13B, the analysis results obtained by this simulation method can reproduce the data obtained by the experiment, and can be analyzed with high accuracy. As described above, according to the present invention, it is possible to reproduce by simulation the decrease in deformation resistance in the direction of tension on the macrostructure side that accompanies the occurrence and progression of damage on the microstructure side during tensile deformation. In addition, on the microstructure side, it is possible to simultaneously analyze the behavior in which microstructural damage occurs as macroscopic deformation progresses, and these damages are linked and propagated. Therefore, it is possible to realize a multi-scale simulation that considers and evaluates the mechanical behavior of the macrostructure, the mechanical behavior of the microstructure, and the behavior of damage initiation and damage progression.

By executing such a simulation, a person skilled in the art can predict the properties of a material accompanying the progress of deformation taking into account the occurrence and progress of microstructural damage, and make judgments by comparing multiple materials. This allows a person skilled in the art to predict by analysis which material will satisfy the required quality and material properties. Also, those skilled in the art can determine by analysis which of the multiple materials is superior.

In recent years, as the component composition and manufacturing process of metallic materials have become more complex, on the scale of the microstructure of metallic materials, the distribution (heterogeneity) of the structure and strength inevitably tends to occur. Inhomogeneity greatly affects macroscopic strength properties. Furthermore, the strength characteristics required for structures formed from the above metal materials have become more and more severe in recent years. However, according to the method according to the present embodiment, it is possible to accurately evaluate the macro-strength characteristics of a practical-scale structure (member) by accurately considering the influence of the inhomogeneity of the structure and the like.

The damage simulation method for evaluating the damage behavior of multiphase materials including metallic materials of the present disclosure is realized by cooperation of hardware resources, such as processors, memories, and software resources (computer programs). .

The method according to the present embodiment can be effectively utilized in the development of metal materials that constitute structures such as buildings, ships, offshore structures, bridges, tanks, etc., which require stricter strength characteristics.

REFERENCE SIGNS LIST 1 evaluation system 10 imaging device 11 imaging unit 12 communication circuit 20 control device 21 arithmetic circuit 22 storage device 23 input/output device 24 communication circuit

Claims (5)

A damage simulation method for evaluating the damage behavior of a multi-phase material composed of a plurality of phases having different strength properties, including a metallic material, using an arithmetic circuit, the arithmetic circuit comprising:
creating a microstructure finite element model for microanalysis based on the structure observation results of the multiphase material;
setting and obtaining different strength characteristics and damage criteria for each phase constituting the multiphase material;
A macro structural finite element model is created for the macro region of the multiphase material to be analyzed, and assuming that it is a homogeneous material, finite element analysis is performed using the macro structural finite element model, and the evaluation target region is a step of calculating a deformation history;
a step of applying the deformation history to each integration point of the microstructure finite element model and calculating the deformation behavior of the microstructure finite element model by finite element analysis based on a homogenization method;
a step of determining damage by comparing the deformation behavior with the damage criteria;
a step of releasing the stress at the integration point determined to cause damage in the microstructure finite element model by the damage determination, and reducing the element stiffness to zero or a predetermined value;
damage simulation method. 2. The damage simulation method of claim 1, wherein the damage criteria are functions of equivalent plastic strain and stress triaxiality. In the damage determination, if the value calculated based on the equivalent plastic strain and stress triaxiality calculated as the damage behavior at a specific integration point of the microstructure finite element model is greater than the damage criteria, the specific 3. The damage simulation method according to claim 2, wherein damage occurrence is determined with respect to an integration point of . 4. The damage simulation method according to any one of claims 1 to 3, wherein said predetermined value is 1/50 or less of the initial value of said element stiffness. 5. A damage simulation method according to any one of claims 1 to 4, wherein the multi-phase material is a metallic material.

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