JP2021156686A - Heat treatment simulation method, heat treatment simulation device, and program - Google Patents

Abstract

To accurately analyze behavior of a member where segregation is present by heat treatment in a heat treatment simulation.SOLUTION: A heat treatment simulation method includes: step S1 of reading model data in which a member to be analyzed is represented by a plurality of elements; step S2 of setting an anisotropy parameter showing anisotropy of distortion caused by phase transformation as a parameter used for calculating strain of an integration point of each of the plurality of elements; step S3 of calculating temperature of each node of the plurality of elements; step S4 of calculating strain of an integration point of each of the plurality of elements using a tissue fraction determined according to change in at least one of temperature and time and an anisotropic parameter; and step S5 of outputting analysis results based on temperature and calculated strain of the plurality of elements.SELECTED DRAWING: Figure 2

Description

The present invention relates to a technique for performing a simulation of a heat treatment involving a phase transformation of a member by using a computer.

Heat treatment is widely used in steel products to improve their properties. For example, steel members such as gears and shafts used in automobiles and industrial machines that are repeatedly exposed to high stress are subjected to quenching treatment to improve wear resistance and fatigue strength. However, when the member is hardened, thermal stress due to the temperature difference between the surface portion and the inside of the member and transformation stress due to the volume change accompanying the phase transformation are generated. As a result, the member is distorted. In recent years, computer simulations have been used to predict deformation or residual stress of members due to such heat treatment.

For example, Japanese Patent Application Laid-Open No. 2017-53807 (Patent Document 1) discloses a method for simulating a heat treatment of steel. In this method, the time change of temperature at each node of the finite element model is calculated by the finite element method. Further, at least the transformation plastic strain and the creep strain are calculated as the amount of strain at the integration point of each element, and the change in the internal stress of the steel is calculated based on the sum of these. This makes it possible to accurately estimate the strain and stress of a large forged steel product during heat treatment.

Japanese Patent Laying-Open No. 2017-193777 (Patent Document 2) describes in advance the heat treatment conditions of the heating rate, the heating temperature, and the cooling rate, and the amount of dimensional change in the plate thickness direction, the plate width direction, and the plate length direction due to the heat treatment. It is disclosed that the correlation between the above is obtained by measurement and the heat treatment of the steel plate is performed using these correlations. It is said that this correlation may be obtained by numerical simulation.

JP-A-2017-53807 JP-A-2017-193777

In a general heat treatment simulation, the member is treated as a continuum of homogeneous materials. However, the actual material has a microscopic structure such as crystal grains. For example, the bias of the chemical composition in the steel material generated during casting becomes a microsegregation. The presence of microsegregation in the steel member increases the amount of deformation during quenching. In the conventional heat treatment simulation, it is difficult to analyze macroscopic deformation and residual stress in consideration of microsegregation. Therefore, the effect of microsegregation on the deformation and residual stress of the member due to heat treatment could not be evaluated by analysis.

The inventors have found that microsegregation in a member has a relatively large effect on the strain generated due to the phase transformation of the member during heat treatment. Then, a method of analyzing the strain generated due to the phase transformation in consideration of microsegregation was examined.

The present application discloses a heat treatment simulation method, a heat treatment simulation apparatus, and a program capable of accurately analyzing the behavior associated with phase transformation due to heat treatment of a member having microsegregation.

The heat treatment simulation method according to the embodiment of the present invention is a method of executing a heat treatment simulation accompanied by a phase transformation of a member by using a computer. In the heat treatment simulation method, the strain caused by the phase transformation is used as a parameter used in the step of reading the model data in which the member to be analyzed is represented by a plurality of elements and the strain of the integration point of each of the plurality of elements. The step of setting the anisotropic parameter indicating the anisotropy, the step of calculating the temperature of each node of the plurality of elements, and the strain of the integration point of each of the plurality of elements are subjected to the temperature and time change. It includes a step of calculating using the microstructure fraction determined according to at least one of them and the anisotropic parameter, and a step of outputting an analysis result based on the calculated temperature and strain of the plurality of elements.

According to the present invention, in a heat treatment simulation using a computer, it is possible to accurately analyze the behavior of a member in which microsegregation exists, which is accompanied by a phase transformation due to heat treatment.

FIG. 1 is a functional block diagram showing a configuration example of the heat treatment simulation apparatus according to the present embodiment. FIG. 2 is a flowchart showing an operation example of the heat treatment simulation apparatus shown in FIG. FIG. 3 is a flowchart showing an example of processing of the anisotropic parameter generation unit shown in FIG. FIG. 4 is a diagram showing a representative volume element that reproduces the microsegregation in the embodiment of the present invention. FIG. 5 is a diagram showing a homogeneous macro model in the examples. FIG. 6 is a diagram showing the shape of microsegregation applied to the representative volume element in the example. FIG. 7 is a diagram showing the distribution of the chemical components of microsegregation in the examples. FIG. 8 is a diagram showing transformational plastic strain in each direction when stress is applied to each of the representative volume element and the macro model (uniform model). FIG. 9 is a diagram showing a comparison between the transformation plastic strain in each direction when stress is applied to the anisotropic macro model and the result of the representative volume element. FIG. 10 is a diagram showing an isotropic macro model and strains in the x, y, and z directions of a representative volume element that reproduces microsegregation when stress is not applied. FIG. 11 is a diagram showing a three-dimensional analysis model of the members of the embodiment. FIG. 12 is a diagram showing the heat transfer coefficient of the quenching oil used in the examples. FIG. 13 is a diagram showing the amount of bending deformation of the hollow round bar obtained by the quenching analysis of the examples.

The inventors have focused on the fact that the microsegregation in the member affects the strain generated due to the phase transformation of the member during the heat treatment, and the heat treatment accompanied by the phase transformation of the member in which the microsegregation is present. We examined the simulation. In such a heat treatment simulation, in addition to the usual thermal elasto-plastic analysis for analyzing the temperature and displacement, the change in the microstructure fraction due to the phase transformation and the strain due to the phase transformation are calculated.

Distortions caused by phase transformation include transformation strain and transformation plastic strain. The transformation strain is a strain generated by a volume change due to a phase transformation. The transformation plastic strain is an inelastic strain generated in proportion to the stress (for example, deviation stress) when a stress is applied during the phase transformation. Metamorphic plastic strain also occurs below the yield stress. The transformational plastic strain can be calculated by, for example, the following equation (1).

When the concentration of the alloy component is distributed due to segregation in the steel material, the timing of phase transformation changes depending on the site, and internal stress is generated due to the volume difference between the segregated portion and the non-segregated portion. When the microsegregation is unevenly distributed in a specific direction, the stress distribution changes depending on the direction, and anisotropic deformation occurs. The inventors have found that the anisotropy generated by segregation can be calculated by considering the anisotropy of the strain caused by the transformation. From this, it was found that the amount of deformation of a member having microsegregation during quenching can be calculated.

Conventionally, when there is a local distribution of chemical components in a member such as microsegregation, it is considered that it has almost no effect on the yield behavior, so anisotropy is rarely considered in the calculation of plastic strain. There wasn't. Similarly, in the heat treatment simulation considering the phase transformation, anisotropy was not considered for the transformation plastic strain, and an isotropic constitutive equation was used. That is, in the general finite element method, since the member is treated as a continuum of homogeneous materials, the microscopic structure in the member such as crystal grains and microsegregation cannot be considered. In the conventional analysis, when a plurality of structures exist, the plurality of structures are treated as a uniform structure having material properties averaged by a linear mixing law of the material properties of each structure.

In order to consider the effect of microsegregation, it is conceivable to create a minute model that reproduces the microscopic structure and analyze how it behaves during phase transformation. In this way, when reproducing the microscopic structure with a plurality of elements, for example, it becomes necessary to divide a region on the order of several tens of μm with a sufficient number of elements. Therefore, when simulating heat treatment on a real member scale and evaluating deformation such as bending using a model that reproduces the microscopic structure with a plurality of minute elements, the number of elements becomes enormous and practical analysis is performed. Is difficult.

Therefore, the inventors examined a method of performing heat treatment analysis in consideration of the influence of the microscopic structure of microsegregation without subdividing the elements. As a result of the examination, an anisotropy parameter indicating the anisotropy of the strain caused by the phase transformation was set at the integration point of each element, and the change in the structure fraction due to the temperature change or the time change and this anisotropy parameter were set. It was found that by calculating the distortion of the integration point of each element using the above, it is possible to calculate the macroscopic deformation in the same way as when calculating with a model that reproduces the microscopic structure by subdividing the elements. Based on this finding, the inventors came up with the following embodiments.

The heat treatment simulation method according to the embodiment of the present invention is a method of executing a heat treatment simulation accompanied by a phase transformation of a member by using a computer. In the heat treatment simulation method, the strain caused by the phase transformation is used as a parameter used in the step of reading the model data in which the member to be analyzed is represented by a plurality of elements and the strain of the integration point of each of the plurality of elements. The step of setting the anisotropic parameter indicating the anisotropy, the step of calculating the temperature of each node of the plurality of elements, and the strain of the integration point of each of the plurality of elements are subjected to the temperature and time change. It includes a step of calculating using the microstructure fraction determined according to at least one of them and the anisotropic parameter, and a step of outputting an analysis result based on the calculated temperature and strain of the plurality of elements.

According to the above method, an anisotropy parameter indicating the anisotropy of the strain caused by the phase transformation is set at the integration point of each element, and the structure fraction is set according to at least one of the calculated temperature and time changes. , The distortion of the integration point of each element is calculated using this anisotropy parameter. Here, the inventor has found that the influence of the microscopic structure on the strain due to the microsegregation in the element can be reflected in the anisotropy parameter. Therefore, the strain caused by the phase transformation in consideration of microsegregation is calculated. As a result, it is possible to accurately analyze the behavior of a member in which microsegregation exists, which is accompanied by a phase transformation due to heat treatment.

The present embodiment relates to a computer simulation of a heat treatment involving a phase transformation of a member. In the simulation, in order to calculate the strain caused by the phase transformation in consideration of the microsegregation of the member, for example, it is conceivable to use finely divided elements to express the microscopic structure of the microsegregation. In this case, the number of elements increases and the amount of computer calculation also increases. By introducing anisotropy parameters into the calculation of strain caused by phase transformation as in the above method, the inventors can perform analysis considering the effects of microsegregation without using fine elements representing microsegregation. I found it possible. According to the above method, it is possible to simulate a heat treatment accompanied by a phase transformation of a member in which microsegregation exists, while avoiding an increase in the amount of calculation due to an increase in the number of elements. That is, in the simulation of the heat treatment accompanied by the phase transformation, the processing efficiency of the computer with respect to the analysis accuracy can be improved.

The model data may include material data showing the characteristics of the phase transformation of the member. Transformation characteristics are represented by changes in tissue with temperature and time, such as the Time-Temperature-Transformation (TTT) curve or the Continuous-Cooling-Trancformation (CCT) curve. The transformation characteristic data showing the characteristics of the phase transformation of the member may be, for example, data showing the relationship between at least one of the temperature and time changes and the change in the structure. The transformation characteristic data can be used to determine the tissue fraction according to at least one of the calculated temperature and temporal changes.

In the heat treatment simulation, as an analysis result, information on the behavior accompanied by the phase transformation in the heat treatment of the member is output. For example, information indicating at least one distribution of displacement, stress, strain, and temperature of a member due to heat treatment may be output as an analysis result.

The anisotropy parameter may include a transformation plastic strain anisotropy parameter indicating the anisotropy of the transformation plastic strain generated in proportion to the stress when a stress is applied during the phase transformation of the member. The heat treatment simulation method may further include a step of calculating the stress at the integration point of each of the plurality of elements. In the step of calculating the strain at the integration point of each of the plurality of elements, the transformational plastic strain of the integration point of each of the plurality of elements is determined as a tissue fraction determined according to at least one of the temperature and time changes. , The step of calculating using the stress of the integration point and the transformation plastic strain anisotropy parameter may be included.

The inventors have found that the transformation plastic strain accounts for a large proportion of the strain caused by the phase transformation and is susceptible to microsegregation. As described above, the transformation plastic strain anisotropic parameter is set at the integration point of each element, and the microstructural fraction corresponding to at least one of the temperature and time changes of each element, the stress at each integration point, and this transformation plastic strain. By calculating the transformational plastic strain of the integration point of each element using the anisotropy parameter, the behavior of the member in which microsegregation exists due to heat treatment can be analyzed more accurately.

The transformation plastic strain at each integration point may be calculated using a function that inputs the tissue fraction and the stress and outputs the strain with respect to the input tissue fraction and the stress. The function may include a transformational plastic strain anisotropy parameter as a coefficient. In this case, the tissue fraction input to the function is a tissue fraction determined according to at least one of the temperature and time changes. The stress input to the function is the stress at each of the calculated integration points. As a result, the transformational plastic strain at each integration point can be calculated accurately in consideration of the influence of microsegregation.

The function may be a function that can be set so that the strain with respect to the tensile stress and the strain with respect to the compressive stress having the same magnitude as the tensile stress are different depending on the transformation plastic strain anisotropy parameter. This makes it possible to express the asymmetry of strain with respect to tensile stress and compressive stress as a function. The inventors have observed the asymmetry of strain with respect to tensile stress and strain with respect to compressive stress in metamorphic plastic strain. By using a function that can reproduce the asymmetry of tensile compression, it is possible to analyze the behavior of a member with phase transformation due to heat treatment more accurately.

As an example, the transformation plastic strain may be calculated using the following equation.

The anisotropy parameter may include a transformation strain anisotropy parameter indicating the anisotropy of the transformation strain generated by the volume change due to the phase transformation of the member. The step of calculating the strain of each integration point of the plurality of elements is to determine the transformation strain of each integration point of the plurality of elements with a tissue fraction determined according to at least one of the temperature and time changes. A step of calculating using the transformation strain anisotropy parameter may be included. Thereby, the transformation strain generated by the volume change due to the phase transformation of the member can be calculated in consideration of the influence of the microsegregation. As a result, the behavior of the member having microsegregation due to heat treatment can be analyzed more accurately.

As an example, the transformation strain may be calculated using the following equation.

The heat treatment simulation method is based on the anisotropy of strain caused by phase transformation calculated using microsegregation model data representing the state of microsegregation in a unit volume by a plurality of elements. It may further have a step of generating sex parameters. As a result, anisotropy parameters that reflect the effect on strain caused by phase transformation due to microsegregation in the elements of the model data can be obtained.

In the heat treatment simulation method, different anisotropic parameters may be set in the plurality of elements. Thereby, for example, when the state of microsegregation is different for each part of the member to be analyzed, the influence of these microsegregations can be reflected in the anisotropy parameter. As a result, the analysis accuracy can be further improved.

An embodiment of the present invention also includes a heat treatment simulation apparatus that uses a computer to simulate a heat treatment involving a phase transformation of a member. The heat treatment simulation device uses an input unit for reading model data representing a member to be analyzed by a plurality of elements and a strain at the integration point of each of the plurality of elements as parameters used for calculation, and is caused by a phase transformation. The parameter setting unit for setting the anisotropic parameter indicating the anisotropy of the plurality of elements, the temperature calculation unit for calculating the temperature of each node of the plurality of elements, and the distortion of the integration point of each of the plurality of elements are described. A strain calculation unit that calculates using the tissue fraction determined according to at least one of the temperature and time changes and the anisotropy parameter, and an analysis result based on the calculated temperature and strain of the plurality of elements are output. It is provided with an output unit. The strain calculation unit may be configured to calculate the displacement of the node at each of the plurality of elements and the strain of the integration point.

An embodiment of the present invention also includes a program for causing a computer to perform a simulation of a heat treatment involving a phase transformation of a member. In the program, the distortion caused by the phase transformation is different as a parameter used for the process of reading the model data in which the member to be analyzed is represented by a plurality of elements and the calculation of the strain at the integration point of each of the plurality of elements. The process of setting the anisotropic parameter indicating the property, the process of calculating the temperature of each node of the plurality of elements, and the strain of the integration point of each of the plurality of elements are set to at least one of the temperature and the time change. A computer is made to execute a process of calculating using the tissue fraction determined according to the above and the anisotropic parameter and a process of outputting an analysis result based on the calculated temperature and strain of the plurality of elements. ..

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. The same or corresponding parts in the drawings are designated by the same reference numerals, and the description thereof will not be repeated. The dimensional ratio between the constituent members shown in each figure does not necessarily indicate the actual dimensional ratio.

[Heat treatment simulation device]
FIG. 1 is a functional block diagram showing a configuration example of the heat treatment simulation apparatus according to the present embodiment. The heat treatment simulation device 1 shown in FIG. 1 is a device that executes a simulation of heat treatment of a member accompanied by a phase transformation by using a computer. The heat treatment simulation device 1 includes an input unit 11, a parameter setting unit 12, a temperature calculation unit 13, a strain calculation unit 14, and an output unit 15.

The heat treatment simulation device 1 can be configured by a computer having a processor and a memory. By executing the program stored in the memory by the processor, the functions of the input unit 11, the parameter setting unit 12, the temperature calculation unit 13, the strain calculation unit 14, the output unit 15, and the anisotropic parameter generation unit 16 can be realized. .. Non-transitory recording media on which such programs and programs are recorded are also included in the embodiments of the present invention. Each part of the heat treatment simulation apparatus 1 may be realized by a plurality of processors.

The input unit 11 reads model data in which the member to be analyzed is represented by a plurality of elements. The input unit 11 expands the model data in the memory so that the processor of the heat treatment simulation apparatus 1 can access the model data. The input unit 11 may accept the input of the model data from the user, or may read the model data from another storage medium. The elements of the model data are, for example, the elements of the mesh data used in the finite element method. Each element is represented by a node. The element is provided with at least one integration point. In the simulation using the finite element method, for example, the displacement and temperature at the node and the stress and strain at the integration point are calculated.

As described above, the model data includes data of a plurality of elements indicating the shape of the member to be analyzed, that is, data indicating the positions of the nodes and integration points. In addition, the model data may include data indicating the material properties of the member. The model data can be generated, for example, based on the design data of the member to be analyzed.

The parameter setting unit 12 sets an anisotropy parameter indicating the anisotropy of the strain caused by the phase transformation as a parameter used for calculating the strain at the integration point of each of the plurality of elements of the model data. The parameter setting unit 12 sets the anisotropic parameter based on the input from the user or the data recorded in advance. Alternatively, the input unit 11 may read the model data in which the anisotropic parameter is set at each integration point. In this case, the parameter setting unit 12 becomes a part of the input unit 11. The anisotropy parameter can be, for example, a coefficient of a function that calculates the strain caused by the phase transformation of each integration point. As a specific example, an anisotropy parameter can be set as a coefficient included in the tensor element included in the function for calculating the strain caused by the phase transformation of each integration point.

The temperature calculation unit 13 calculates the temperature of each node of the plurality of elements. For example, the temperature calculation unit 13 calculates the temperature at each node using a value indicating the material property of the member. The tissue fraction of each phase (each structure) of the member is determined according to the calculated temperature. As a result, the phase transformation is calculated. The phase transformation can also occur when there is no temperature change and the time changes. Therefore, the tissue fraction may be determined according to changes over time rather than temperature. Here, the time change is the time change in the simulation. The temperature calculation unit 13 can calculate, for example, the temperature at each time in the time series. The tissue fraction may be determined according to the temperature at each time. Alternatively, the tissue fraction may be determined to change over time, even if the temperature does not change over time. Also, the tissue fraction may be determined based on both temperature and time variation.

The strain calculation unit 14 calculates the displacement at each node of the plurality of elements and the stress and strain at the integration point. The strain calculation unit 14 calculates the strain at the integration point of each of the plurality of elements using the tissue fraction and the anisotropy parameter determined according to at least one of the temperature and time changes. The strain calculation unit 14 can calculate at least one of transformation plasticity and transformation strain at each integration point. The metamorphic plastic strain changes according to the stress. Therefore, the transformation plastic strain can be calculated using the stress calculated at each integration point. Since the transformation strain is a strain generated by a volume change due to a phase transformation, it can be calculated using, for example, a value indicating a volume change due to a phase transformation of each element, for example, a value indicating a change in density.

The strain calculation unit 14 may calculate the strain that is not caused by the phase transformation. Examples of strains not caused by phase transformation include elastic strains, plastic strains and thermal strains. For example, the strain calculation unit 14 may be configured to calculate the transformation strain and the transformation plastic strain, which are the strains associated with the phase transformation, in addition to the elastic strain, the plastic strain, and the thermal strain. For the calculation of elastic strain, plastic strain and thermal strain, a known calculation method of thermal elasto-plastic analysis can be used.

By using the anisotropy parameter, the strain calculation unit 14 can calculate the strain caused by the phase transformation at each integration point as different values in a plurality of directions. That is, the strain having anisotropy can be calculated at each integration point. The anisotropy parameter is a parameter that exhibits different strain behavior depending on the direction. For example, at each integration point, different strain values may be calculated in multiple directions. Further, the strain calculation unit 14 can calculate the transformation plastic strain for compressive stress and the transformation plastic strain for tensile stress at each integration point by using different anisotropic parameters. As a result, at the integration point, the strain for compressive stress and the strain for tensile stress of the same magnitude may be calculated with different values even in the same direction. In this way, the strain calculation unit 14 can calculate the strain caused by the phase transformation reflecting the anisotropy due to microsegregation.

When both the transformation plastic strain and the transformation strain are calculated at one integration point, the strain calculation unit 14 may calculate, for example, the sum of these values as the strain caused by the phase transformation of the integration point. In this case, the strain due to the phase transformation can be calculated in a plurality of directions at one integration point. That is, the strain having anisotropy at one integration point can be calculated.

As in the above example, the temperature calculation of each node by the temperature calculation unit 13 and the strain calculation due to the phase transformation of each integration point by the strain calculation unit 14 are combined, and further, the displacement of each node and the displacement of each integration point are combined. The stress can be calculated. Thereby, in addition to the thermal elasto-plastic analysis for calculating the displacement with respect to the temperature change, the change in the microstructure fraction due to the phase transformation and the strain and stress due to the phase transformation can be analyzed.

The output unit 15 outputs an analysis result based on the calculated temperature and strain of the plurality of elements. The analysis result is not particularly limited as long as it is based on the temperature and strain of a plurality of elements. An example of the analysis result is the distribution of at least one of the temperature and strain in the member, or the time variation of the distribution. In addition to temperature and strain, for example, member deformation, stress, structure distribution, or structure fraction may be output as an analysis result. The form of output is not particularly limited. Examples of the output form include displaying the analysis result on a display, transmitting the analysis result to a designated place via a network, or saving the analysis result in a designated place.

In the example shown in FIG. 1, the heat treatment simulation device 1 includes an anisotropic parameter generation unit 16. The anisotropic parameter generation unit 16 generates the anisotropic parameter set by the parameter setting unit 12. The anisotropy parameter generation unit 16 can generate anisotropy parameters based on the data showing the anisotropy of the strain caused by the phase transformation calculated using the microsegregation model data. The microsegregation model data is data representing the state of microsegregation in a unit volume by a plurality of elements. The anisotropic parameter generation unit 16 may be provided in a computer outside the heat treatment simulation apparatus 1. Specific examples of the anisotropy parameter will be described later.

[Calculation example of transformation plastic strain]
In the calculation of the transformation plastic strain by the strain calculation unit 14, the transformation plastic strain anisotropy parameter is used. The transformation plastic strain anisotropy parameter is a parameter indicating the anisotropy of the transformation plastic strain generated in proportion to the stress when a stress is applied during the phase transformation of the member. The metamorphic plastic strain anisotropy parameter is set at each integration point by the parameter setting unit 12. The strain calculation unit 14 determines the transformation plastic strain at each integration point according to at least one of the temperature and time changes calculated by the temperature calculation unit 13, the stress at the integration point, and the transformation plastic strain. Calculated using directional parameters. The transformation plastic strain at each integration point can be calculated using a function. The function may be, for example, a function in which the structure fraction and stress are input and the transformation plastic strain is output. Here, the tissue fraction is determined according to at least one of temperature and time change. The function may include the transformational plastic strain anisotropy parameter as a coefficient. The metamorphic plastic strain anisotropy parameter may be, for example, a coefficient included in the element of the tensor included in the function.

Next, a specific example of calculation of the transformation plastic strain using the transformation plastic strain anisotropy parameter at each integration point will be described.

By using a function that can consider anisotropy instead of the yield function of isotropic Mises shown in the above equation (A1), the transformation plastic strain that considers anisotropy can be calculated. Examples of the function considering anisotropy include Hill's anisotropy function and other equations. A function that matches the microscopic structure of the material can be used as a function that can take into account the above anisotropy. Tension-compression asymmetry has been experimentally observed in metamorphic plastic strain. Therefore, it is preferable to use a function that can simultaneously reproduce the asymmetry of tension and compression as a function that can consider anisotropy. For example, as a function that can reproduce the asymmetry of tension and compression, the following equation consisting of the first, second, and third invariants of linearly transformed stress can be used. Regarding the following formula, the description in the following documents is incorporated by reference.
JW Yoon, Y. Lou, J. Yoon, MV Glazoff, Int. J. Plasticity, 56 (2014) 184-202.

The following equation may be used as a function considering the anisotropy that can express the asymmetry of other tensile compression. For the following equations, the description in the following literature is incorporated by reference.
O. Cazacu, B. Plunkett, F. Barlat, Int. J. Plasticity, 22 (2006) 1171-1194.

[Calculation example of transformation strain]
In the calculation of the transformation strain by the strain calculation unit 14, the transformation strain anisotropy parameter is used. The transformation strain anisotropy parameter is a parameter indicating the anisotropy of the transformation strain generated by the volume change due to the phase transformation of the member. The transformation strain anisotropy parameter is set at each integration point by the parameter setting unit 12. The strain calculation unit 14 calculates the transformation strain at each integration point using the tissue fraction determined according to the temperature calculated by the temperature calculation unit 13 and the transformation strain anisotropy parameter. The transformation strain at each integration point can be calculated using a function. The function may be, for example, a function that inputs a value indicating a density change due to phase transformation and outputs transformation strain. Here, the value indicating the density change due to the phase transformation is determined based on the tissue fraction. The function may include the transformation strain anisotropy parameter as a coefficient. The transformation strain anisotropy parameter may be a coefficient included in the element of the tensor included in the function.

As an example, the following equation (13) can be used as a function for calculating the transformation strain at each integration point. The following equation (13) is based on the finding that the transformation strain can be calculated from the volume change before and after the phase transformation.

The formulas used for the function for calculating the transformation plastic strain and the function for calculating the transformation strain are not limited to the above examples.

[Operation example]
FIG. 2 is a flowchart showing an operation example of the heat treatment simulation apparatus shown in FIG. In the example shown in FIG. 2, first, the input unit 11 reads the model data (S1). The model data is data in which the member to be analyzed is represented by a plurality of elements. The parameter setting unit 12 sets an anisotropic parameter as a parameter used for calculating the distortion of the integration point of each of the plurality of elements (S2).

The temperature calculation unit 13 calculates the temperature of each node of the plurality of elements (S3). In addition, a value indicating a tissue fraction corresponding to at least one of the temperature and time changes may be calculated. The material properties of the members included in the model data can be used for the calculation of temperature and structure fraction. The calculation of S3 can be a heat transfer analysis that calculates the change in temperature using the finite element method.

The strain calculation unit 14 calculates the displacement at each node of the plurality of elements and the strain and stress at the integration point of each of the plurality of elements (S4). The strain at the integration point is calculated using a tissue fraction and anisotropy parameters that are determined in response to at least one of temperature and temporal changes. In S4, as an example, the transformation plastic strain and the transformation strain at each integration point are calculated. The transformation plastic strain is calculated using the microstructural fraction, the stress at the integration point, and the transformation plastic strain anisotropy parameters. The transformation strain is calculated using the tissue fraction and the transformation strain anisotropy parameters. At each integration point, the sum of the transformation plastic strain and the transformation strain is calculated as the strain due to the phase transformation at each integration point.

The output unit 15 outputs the analysis result based on the temperature and strain calculated in S3 and S4 (S5). For example, the output unit 15 can generate and output a visible image of at least one of the temperature distribution, stress distribution, displacement distribution, and strain distribution of the member.

[Processing example of anisotropic parameter generation]
FIG. 3 is a flowchart showing an example of anisotropic parameter generation processing by the anisotropic parameter generation unit 16 shown in FIG. In the example shown in FIG. 3, first, a microsegregation model is acquired (S11). The microsegregation model is data representing the state of microsegregation in a unit volume by a plurality of elements. The unit volume of the microsegregation model may be a size that can express the periodic structure of microsegregation.

For example, as a microsegregation model, a model is created in which a plurality of minute hexahedral elements given a distribution of chemical components simulating the shape of microsegregation are gathered to form a representative volume element of a unit volume. The distribution of the chemical components represented by the minute elements in the representative volume element can be determined, for example, by observing the microsegregation of the actual member and obtaining the average shape of the segregation.

The dimensions of the representative volume element shall be such that the periodic symmetry of microsegregation can be reproduced. The representative volume element is divided by the number of elements that can sufficiently reproduce the chemical composition distribution of segregation. The volume of the representative volume element, that is, the unit volume, does not have to match the volume of the element of the model data.

In S12, a uniform model of a uniform chemical composition having the same dimensions as the representative volume element is obtained. The uniform model can be an isotropic model composed of one element.

In S13, the microsegregation model generated in S11 and the uniform model generated in S12 are subjected to heat treatment analysis (heat treatment simulation) under the condition that no stress is applied, and the transformation strain is calculated. The heat treatment analysis of S13 is performed under typical heat treatment conditions using isotropic transformational plastic strain. The transformation strain can be calculated from the difference in the amount of deformation between the start of transformation and the completion of transformation. The transformation strain in the microsegregation model and the transformation strain in the uniform model are calculated respectively.

In S14, the transformation strain anisotropy parameter is generated based on the relative value of the transformation strain of the uniform model to the transformation strain of the microsegregation model. In the analysis using the representative volume element of the microsegregation model, anisotropy appears in the transformation strain depending on the segregation shape. That is, in the microsegregation model, different transformation strains are calculated in a plurality of directions. On the other hand, in the uniform model, the same transformation strain is calculated in a plurality of directions. For example, the ratio of the transformation strain in the corresponding direction in the representative volume element to the transformation strain in each direction of the uniform model is obtained as the transformation strain parameter.

In S15, the heat treatment analysis is executed on the microsegregation model under the condition that stress is applied in a plurality of directions, and the transformation plastic strain is calculated. For example, a heat treatment analysis is performed by applying a constant stress (for example, 10 MPa in the x direction) to a representative volume element of the microsegregation model in a specific direction. The amount of deformation at the completion of transformation can be obtained, and the transformation plastic strain can be calculated from the difference between the amount of deformation and the amount of deformation of the representative volume element when no stress is applied in S14. By carrying out this in a plurality of directions including the shearing direction, the transformation plastic strain in each direction can be calculated. In addition, when considering the asymmetry of tensile compression, the case of stress load of compression in addition to tension is also calculated. Further, not only uniaxial and pure shear stresses but also multiaxial stresses may be applied to the analysis.

In S16, an anisotropy model using the transformation plastic strain anisotropy parameter is generated. The anisotropy model is a model in which a transformation plastic strain having anisotropy for stress in a plurality of directions is defined by using a transformation plastic strain anisotropy parameter with respect to a uniform model. This anisotropy model is a model that defines the characteristics of the transformation plastic strain in consideration of anisotropy with respect to the uniform model.

In S17, the transformation plastic strain when stress is applied in the above-mentioned plurality of directions to the anisotropic model is calculated. In S17, the heat treatment analysis is performed under the same stress load as in S15, and the transformation plastic strain is calculated. In the case of a uniform simple shape model with a constant stress load, it is possible to obtain the transformation plastic strain at the completion of transformation by theoretical calculation without performing finite element analysis. In this case, the transformation plastic strain may be obtained by theoretical calculation without analysis using the finite element method.

In S18, the transformational plastic strain calculated by the anisotropic model in S17 is compared with the transformational plastic strain calculated by the microsegregation model in S15 and evaluated. When the evaluation result satisfies a predetermined condition (YES in S19), the transformation plastic strain anisotropy parameter set in the anisotropy model is determined as an optimum value. If the evaluation result does not satisfy the predetermined conditions, the transformation plastic strain parameter of the anisotropic model is updated (S20), and the processes of S16 to S18 are repeated. The processing of S16 to S20 is repeated until the optimum value of the transformation plastic strain anisotropy parameter is obtained.

As an example of S18, S19, and S20, the transformation plastic strain of the anisotropic model calculated in S17 under stress load in each direction is compared with the transformation plasticity of the microsegregation model calculated in S15 under stress load in the corresponding direction. It is possible to calculate the sum of squares of the error with the strain and execute the process of determining the transformation-plastic anisotropy parameter so that the sum of squares of the error is minimized.

When the segregation state is different for each part of the member, the treatments S11 to S20 can be carried out at each part of the member. As a result, it is possible to generate a transformational plastic strain anisotropy parameter that reflects each segregation state at each site. As a result, different anisotropic parameters can be set for the elements of the parts whose deformation states are different from each other. In this way, by giving the anisotropy parameters a distribution in the plurality of elements of the model data to be analyzed, more accurate heat treatment analysis becomes possible.

The process of generating anisotropic parameters is not limited to the example shown in FIG. For example, in FIG. 3, the transformation plastic strain anisotropy parameter generation processing of S15 to S20 may be executed before the transformation strain anisotropy parameter generation processing of S13 to S14. Further, in the example shown in FIG. 3, the anisotropy of strain in microsegregation is calculated by a simulation using a representative volume element, but instead of the simulation, the anisotropy of strain in microsegregation is calculated by an experiment. You may measure. In this case, the anisotropy parameter can be determined by comparing the anisotropy of the strain obtained by the measurement with the anisotropy of the strain calculated by the anisotropy macro model.

[Example]
(1. Calculation of anisotropic parameters)
In this example, in order to express microsegregation by macro material properties, a homogenization method using representative volume elements was used. A representative volume element is the smallest unit of repetition in a material with a periodic microstructure. A representative volume element is a model of a microstructure that repeats periodically. Numerical material tests were carried out on this representative volume element, and it was found that the material having a micro-repetitive structure can be replaced with a macro-homogeneous material by using the obtained material property as a macro-material response.

FIG. 4 is a diagram showing a representative volume element that reproduces the microsegregation in this embodiment. FIG. 5 is a diagram showing a homogeneous macro model in this embodiment. In the representative volume element, the microstructure was reproduced by simulating microsegregation and locally changing the chemical composition. In the macro model, the entire model has a uniform chemical composition. By using a constitutive law that considers anisotropy in the transformation plasticity for the macro model, it is possible to output the same result as the analysis using the representative volume element. The representative volume element is configured to include a plurality of elements by evenly dividing each side of the hexahedron. The macro model consisted of one element of the hexahedron. Hexahedron primary elements were used as the elements. At the nodes on the plane of symmetry that are periodic symmetry, the boundary conditions are given so that the displacements from the reference nodes are the same. The representative volume element and the chemical composition of the macro model used in this example were the chemical composition of chromium molybdenum steel. Mechanical properties such as Young's modulus and stress-strain curve were calculated using actual measurement data, and thermal properties and transformation properties were calculated using prediction formulas based on chemical composition. All heat treatment conditions were maintained at a constant temperature of 500 ° C for 1000 s with austenite. During the phase transformation of these models, a constant stress was applied in a specific direction, and the strain in each direction at the completion of the analysis was calculated to obtain the transformation plastic strain.

FIG. 6 is a diagram showing the shape of microsegregation applied to the representative volume element in this embodiment. The segregated portion has a cylindrical shape with the z direction as the axial direction. The microsegregation was directly reproduced from the histological observation results obtained in the past. FIG. 7 shows the distribution of the chemical components of microsegregation in this example. The concentration distribution of segregation was approximated by a quadratic function so that the central part was the highest. In the representative volume element, since the chemical composition differs depending on the site, the phase transformation and the timing of expansion due to the phase transformation differ. As a result, internal stress and strain are generated, and anisotropic strain is generated according to the shape and direction of segregation.

FIG. 8 shows the transformation plastic strain in each direction when a stress of 10 MPa is applied in the x-direction or the z-direction while maintaining the isothermal temperature for each of the representative volume element and the macro model (uniform model). The transformation plastic strain constitutive equation used and the average deviation stress applied to the model are the same, but the transformation plastic strain changes greatly depending on the direction by reproducing the distribution of chemical components that simulate microsegregation inside the model. It was confirmed that asymmetry appears even in tension and compression. In order to express the deformation behavior under stress load due to microsegregation only by the macroscopic constitutive law, it is impossible with the equivalent stress of Mises, and it is considered necessary to use an equation considering anisotropy.

FIG. 9 shows that the stress in the x-direction or the z-direction is 10 MPa or − A comparison between the transformation plastic strain in each direction when a load of 10 MPa is applied and the result of the representative volume element is shown. It was confirmed that the anisotropy-plastic behavior due to microsegregation reproduced by giving a distribution to the chemical components can be reproduced by an anisotropy macro model to which anisotropy is applied in consideration of anisotropy.

In this example, anisotropy was imparted not only to the transformation plastic strain but also to the transformation strain. FIG. 10 shows an isotropic macro model and strains in the x, y, and z directions of a representative volume element that reproduces microsegregation under no stress. An isotropic transformation distortion was obtained in the macro model. It was confirmed that the transformation strain has anisotropy due to microsegregation in the representative volume element. The ratio of the strain of the representative volume element to the strain of the isotropic macro model in each of the x, y, and z directions can be used as the transformation strain anisotropy parameter. In the calculation of transformation strain, the anisotropy of transformation strain is calculated by multiplying the expansion amount in each of the x, y, and z directions by a coefficient based on the transformation strain anisotropy parameters in each of the x, y, and z directions. Can be expressed.

(2. Quenching analysis)
Quenching analysis (heat treatment simulation) was performed using the above anisotropy parameters. The target member was a hollow round bar. FIG. 11 shows a three-dimensional analysis model of the members of this embodiment. Due to the symmetry of the members, the shape was made 1/4. FIG. 12 shows the heat transfer coefficient of the quenching oil (hot oil) used in this example. The oil was charged so that the model central axis of the member was horizontal to the oil level. In order to reproduce the difference in cooling rate depending on the part, the model surface was divided into regions above and below the center of the model, and the heat transfer coefficient on the lower side was multiplied by 0.7.

FIG. 13 shows the amount of bending deformation of the hollow round bar obtained by quenching analysis. The amount of deformation was defined as the displacement in the direction perpendicular to the axis at the end of the model. The amount of deformation obtained by an analysis in which anisotropy was imparted to the metamorphic plastic strain and microsegregation was taken into consideration was about 30% larger than the amount of deformation obtained by ordinary quenching analysis. The actual phenomenon that quenching deformation increases due to microsegregation could be reproduced by simulation.

1 Heat treatment simulation device 11 Input unit 12 Parameter setting unit 13 Temperature calculation unit 14 Strain calculation unit 15 Output unit 16 Anisotropy parameter generation unit

Claims (11)

A heat treatment simulation method that uses a computer to simulate a heat treatment that involves phase transformation of a member.
The process of reading model data that represents the member to be analyzed with multiple elements, and
As a parameter used for calculating the strain at the integration point of each of the plurality of elements, a step of setting an anisotropy parameter indicating the anisotropy of the strain caused by the phase transformation, and a step of setting the anisotropy.
The step of calculating the temperature of each node of the plurality of elements, and
A step of calculating the strain of the integration point of each of the plurality of elements using the tissue fraction determined according to at least one of the temperature and the time change and the anisotropy parameter.
A heat treatment simulation method including a step of outputting an analysis result based on the calculated temperature and strain of the plurality of elements. The heat treatment simulation method according to claim 1.
The anisotropy parameter includes a transformation plastic strain anisotropy parameter indicating the anisotropy of the transformation plastic strain generated in proportion to the stress when a stress is applied during the phase transformation of the member.
The heat treatment simulation method further includes a step of calculating the stress at the integration point of each of the plurality of elements.
The step of calculating the distortion of the integration point of each of the plurality of elements is
The transformational plastic strain at the integration point of each of the plurality of elements is determined by the microstructure fraction determined according to at least one of the temperature and time changes, the stress at the integration point, and the transformation plastic strain anisotropic parameter. A heat treatment simulation method that includes a step of calculating using. The heat treatment simulation method according to claim 2.
The transformation plastic strain at each integration point is calculated using a function that inputs the tissue fraction and the stress and outputs the input strain with respect to the tissue fraction and the stress.
The function is a heat treatment simulation method including a transformation plastic strain anisotropy parameter as a coefficient. The heat treatment simulation method according to claim 3.
The heat treatment simulation method, wherein the function is a function that can be set so that the strain with respect to the tensile stress and the strain with respect to the compressive stress having the same magnitude as the tensile stress are different depending on the transformation plastic strain anisotropy parameter. The heat treatment simulation method according to claim 4.
The transformation plastic strain is obtained using the following equation.

The heat treatment simulation method according to any one of claims 1 to 5.
The anisotropy parameter includes a transformation strain anisotropy parameter indicating the anisotropy of the transformation strain generated by the volume change due to the phase transformation of the member.
The step of calculating the distortion of the integration point of each of the plurality of elements is
The step of calculating the transformation strain at the integration point of each of the plurality of elements is calculated using the microstructure fraction determined according to at least one of the temperature and time changes and the transformation strain anisotropic parameter. Heat treatment simulation method. The heat treatment simulation method according to claim 6.
The transformation strain is calculated using the following equation.

The heat treatment simulation method according to any one of claims 1 to 7.
A step of generating the anisotropy parameter based on data showing the anisotropy of strain due to phase transformation calculated using microsegregation model data representing the state of microsegregation in a unit volume by a plurality of elements. Further, a heat treatment simulation method. The heat treatment simulation method according to any one of claims 1 to 8.
A heat treatment simulation method in which different anisotropic parameters are set in the plurality of elements. A heat treatment simulation device that uses a computer to simulate heat treatment involving phase transformation of members.
An input unit that reads model data that represents the member to be analyzed with multiple elements,
As a parameter used for calculating the strain at the integration point of each of the plurality of elements, a parameter setting unit for setting anisotropy parameters indicating the anisotropy of the strain caused by the phase transformation, and a parameter setting unit.
A temperature calculation unit that calculates the temperature of each node of the plurality of elements,
A strain calculation unit that calculates the strain at the integration point of each of the plurality of elements using the tissue fraction determined according to at least one of the temperature and time changes and the anisotropy parameter.
A heat treatment simulation apparatus including an output unit that outputs an analysis result based on the calculated temperature and strain of the plurality of elements. A program that causes a computer to simulate a heat treatment involving phase transformation of a member.
Processing to read model data representing the member to be analyzed with multiple elements,
As a parameter used for calculating the strain at the integration point of each of the plurality of elements, a process of setting an anisotropy parameter indicating the anisotropy of the strain caused by the phase transformation and
The process of calculating the temperature of each node of the plurality of elements, and
A process of calculating the strain of the integration point of each of the plurality of elements using the tissue fraction determined according to at least one of the temperature and the time change and the anisotropy parameter.
A program that causes a computer to execute a process of outputting an analysis result based on the calculated temperature and strain of the plurality of elements.

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