JP7343788B2 - Heat treatment simulation method, heat treatment simulation device, and program - Google Patents

Description

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

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 machinery that are repeatedly exposed to high stress are subjected to quenching treatment to improve their wear resistance and fatigue strength. However, when a member is hardened, thermal stress due to a temperature difference between the surface and inside of the member and transformation stress due to volume change accompanying phase transformation occur. As a result, distortion occurs in the member. In recent years, computer simulations have been used to predict the deformation or residual stress of members due to such heat treatment.

For example, JP2017-53807A (Patent Document 1) discloses a steel heat treatment simulation method. In this method, the temporal change in temperature at each node of the finite element model is calculated using the finite element method. Furthermore, 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. Thereby, it is possible to accurately estimate the strain and stress when a large steel forged product is heat treated.

JP 2017-193777 A (Patent Document 2) describes in advance the heat treatment conditions of heating rate, heating temperature, and cooling rate, and the amount of dimensional change in the plate thickness direction, plate width direction, and plate length direction due to heat treatment. It is disclosed that the correlations between the two are determined by measurement, and the steel plate is heat-treated using these correlations. It is said that this correlation may be determined by numerical simulation.

JP2017-53807A Japanese Patent Application Publication No. 2017-193777

In general heat treatment simulations, components are treated as a continuous body of homogeneous material. However, actual materials have microscopic structures such as crystal grains. For example, the imbalance of chemical components in steel materials that occurs during casting results in micro-segregation. The presence of microsegregation in steel members increases the amount of deformation during quenching. With conventional heat treatment simulations, it is difficult to analyze macroscopic deformation and residual stress that take microscopic segregation into account. As a result, it has not been possible to analyze the effects of microsegregation on deformation and residual stress caused by heat treatment of components.

The inventors have discovered that microsegregation in a member has a relatively large effect on the strain generated due to phase transformation of the member during heat treatment. We then investigated a method for analyzing strain caused by phase transformation, taking into account microsegregation.

The present application discloses a heat treatment simulation method, a heat treatment simulation apparatus, and a program that can accurately analyze behavior involving phase transformation due to heat treatment of a member in which microsegregation exists.

A heat treatment simulation method according to an embodiment of the present invention is a method of using a computer to perform a simulation of heat treatment accompanied by phase transformation of a member. The heat treatment simulation method described above involves the process of reading model data representing the member to be analyzed using multiple elements, and using the strain caused by phase transformation as a parameter used to calculate the strain at the integration point of each of the multiple elements. a step of setting an anisotropy parameter indicating anisotropy, a step of calculating the temperature at the node of each of the plurality of elements, and a step of calculating the strain at the integration point of each of the plurality of elements based on the temperature and time change. The method includes a step of calculating using the anisotropy parameter and a tissue fraction determined according to at least one of the two, 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 micro-segregation exists, which is accompanied by phase transformation due to heat treatment.

FIG. 1 is a functional block diagram showing a configuration example of a heat treatment simulation apparatus in this embodiment. FIG. 2 is a flowchart showing an example of the operation of the heat treatment simulation apparatus shown in FIG. FIG. 3 is a flowchart illustrating an example of processing by the anisotropic parameter generation unit illustrated in FIG. FIG. 4 is a diagram showing representative volume elements for reproducing micro-segregation in an example of the present invention. FIG. 5 is a diagram showing a homogeneous macro model in the example. FIG. 6 is a diagram showing the shape of micro-segregation applied to representative volume elements in the example. FIG. 7 is a diagram showing the distribution of chemical components of micro-segregation in Examples. FIG. 8 is a diagram showing the transformation 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 results of the representative volume element. FIG. 10 is a diagram showing strains in the x-, y-, and z-directions when no stress is applied to an isotropic macro model and a representative volume element that reproduces micro-segregation. FIG. 11 is a diagram showing a three-dimensional analytical model of the member of the example. FIG. 12 is a diagram showing the heat transfer coefficient of the quenching oil used in the example. FIG. 13 is a diagram showing the amount of bending deformation of the hollow round bar obtained by the quenching analysis of the example.

The inventors focused on the fact that microsegregation in a member affects the strain that occurs due to phase transformation of the member during heat treatment, and developed heat treatment accompanied by phase transformation of a member in which microsegregation exists. We considered simulation. In such a heat treatment simulation, in addition to normal thermo-elasto-plastic analysis that analyzes temperature and displacement, changes in tissue fraction due to phase transformation and strain caused by phase transformation are calculated.

Strains caused by phase transformation include transformation strain and transformation plastic strain. Transformation strain is strain that occurs due to volume change due to phase transformation. Transformation plastic strain is inelastic strain that occurs in proportion to stress (eg, deviatoric stress) when stress is applied during phase transformation. Transformation plastic strain occurs even below the yield stress. The transformation plastic strain can be calculated using the following equation (1), for example.

When the concentration of alloy components is distributed due to segregation in the steel material, the timing of phase transformation changes depending on the region, and internal stress is generated due to the volume difference between the segregated part and the non-segregated part. When microsegregation is unevenly distributed in a specific direction, the stress distribution changes depending on the direction, resulting in anisotropic deformation. The inventors have discovered that anisotropic deformation caused by segregation can be calculated by considering anisotropy in strain caused by transformation. It was found that this allows calculation of the amount of deformation during quenching of a member with micro-segregation.

Conventionally, when there is a local distribution of chemical components in a member, such as micro-segregation, it is thought that it has little effect on yield behavior, so anisotropy is rarely taken into account when calculating plastic strain. There wasn't. Similarly, in heat treatment simulations that take phase transformation into consideration, an isotropic constitutive equation is used for transformation plastic strain without taking into account anisotropy. That is, in the general finite element method, a member is treated as a continuum of homogeneous materials, and therefore microscopic structures within the member, such as crystal grains and microsegregation, cannot be taken into account. In conventional analysis, when multiple structures exist, they are treated as a uniform structure with material properties averaged by a linear mixing law of the material properties of each structure.

In order to take into account the effects of microsegregation, it is possible to create a small model that reproduces the microscopic structure and analyze how it behaves during phase transformation. In this way, when reproducing a microscopic structure using a plurality of elements, it becomes necessary to divide a region on the order of several tens of micrometers into a sufficient number of elements, for example. Therefore, when evaluating deformation such as bending by simulating heat treatment on the scale of a real part using a model that reproduces the microscopic structure with multiple tiny elements, the number of elements becomes enormous, making practical analysis difficult. is difficult.

Therefore, the inventors investigated a method of performing heat treatment analysis that takes into account the influence of the microscopic structure of microsegregation without subdividing the elements. As a result of the study, an anisotropy parameter indicating the anisotropy of strain due to phase transformation was set at the integration point of each element, and the change in the tissue fraction due to temperature change or time change and this anisotropy parameter were set. We found that by calculating the distortion at the integration point of each element using Based on this knowledge, the inventors came up with the following embodiment.

A heat treatment simulation method according to an embodiment of the present invention is a method of using a computer to perform a simulation of heat treatment accompanied by phase transformation of a member. The heat treatment simulation method described above involves the process of reading model data representing the member to be analyzed using multiple elements, and using the strain caused by phase transformation as a parameter used to calculate the strain at the integration point of each of the multiple elements. a step of setting an anisotropy parameter indicating anisotropy, a step of calculating the temperature at the node of each of the plurality of elements, and a step of calculating the strain at the integration point of each of the plurality of elements based on the temperature and time change. The method includes a step of calculating using the anisotropy parameter and a tissue fraction determined according to at least one of the two, 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 strain due to phase transformation is set at the integration point of each element, and the texture fraction is determined according to at least one of the calculated temperature and time changes. , the distortion at the integration point of each element is calculated using this anisotropy parameter. Here, the inventor has discovered that the influence on strain due to the microscopic structure due to microsegregation within the element can be reflected in the anisotropy parameter. Therefore, strain due to phase transformation is calculated taking into account microsegregation. As a result, it is possible to accurately analyze the behavior associated with phase transformation due to heat treatment of a member in which microsegregation exists.

This embodiment relates to a simulation of heat treatment involving phase transformation of a member using a computer. In a simulation, in order to calculate the strain caused by phase transformation taking into account the micro-segregation of a member, it is conceivable to use finely divided elements to express the microscopic structure of the micro-segregation, for example. In this case, the number of elements increases and the amount of computer calculation also increases. The inventors believe that by introducing an anisotropic parameter into the calculation of strain caused by phase transformation as in the above method, it is possible to conduct an analysis that takes into account the effects of microsegregation without using detailed elements that represent microsegregation. I found out that it is possible. According to the above method, it is possible to simulate heat treatment accompanied by 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 heat treatment accompanied by phase transformation, it is possible to improve the processing efficiency of a computer with respect to analysis accuracy.

The model data may include material data indicating characteristics of phase transformation of the member. The transformation characteristics are expressed by changes in structure due to temperature and time, such as a Time-Temperature-Transformation (TTT) curve or a Continuous-Cooling-Transformation (CCT) curve. The transformation characteristic data representing the phase transformation characteristics of the member may be, for example, data representing the relationship between at least one of temperature and time changes and changes in structure. The transformation property data can be used to determine a tissue fraction in response to a calculated temperature and/or time change.

In the heat treatment simulation described above, information regarding the behavior of the member accompanied by phase transformation during heat treatment is output as an analysis result. 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 anisotropy of transformation plastic strain that occurs in proportion to stress when stress is applied during phase transformation of the member. The heat treatment simulation method may further include the step of calculating stress at an integration point of each of the plurality of elements. The step of calculating the strain at the integration point of each of the plurality of elements calculates the transformation plastic strain at the integration point of each of the plurality of elements with the tissue fraction determined according to at least one of the temperature and time change. , the method may include the step of calculating using the stress at the integration point and the transformation plastic strain anisotropy parameter.

The inventors have found that transformation plastic strain accounts for a large proportion of the strain caused by phase transformation and is susceptible to the influence of micro-segregation. As mentioned above, the transformation plastic strain anisotropy parameter is set at the integration point of each element, and the structure fraction according 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 transformation plastic strain at the integration point of each element using the anisotropy parameter, it is possible to more accurately analyze the behavior of a member in which microsegregation exists due to heat treatment.

The transformation plastic strain at each integration point may be calculated using a function that inputs the tissue fraction and the stress and outputs a strain corresponding to the input tissue fraction and stress. The function may include a transformation 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 change. The stress input to the function is the stress at each of the calculated integration points. Thereby, the transformation plastic strain at each integration point can be calculated with high accuracy while taking into account the influence of micro-segregation.

The function may be a function that can be set so that a strain for a tensile stress is different from a strain for a compressive stress having the same magnitude as the tensile stress, depending on the transformation plastic strain anisotropy parameter. Thereby, the asymmetry of strain with respect to tensile stress and compressive stress can be expressed as a function. The inventors have observed an asymmetry in transformation plastic strain with respect to tensile stress and strain with respect to compressive stress. By using a function that can reproduce the asymmetry of tension and compression, it is possible to more accurately analyze the behavior of members that undergo phase transformation due to heat treatment.

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

The anisotropy parameter may include a transformation strain anisotropy parameter indicating anisotropy of transformation strain caused by volume change due to phase transformation of the member. The step of calculating the strain at the integration point of each of the plurality of elements includes: calculating the transformation strain at the integration point of each of the plurality of elements with a tissue fraction determined according to at least one of the temperature and time change; The method may also include a step of calculating using the transformation strain anisotropy parameter. Thereby, the transformation strain caused by the volume change due to the phase transformation of the member can be calculated taking into account the influence of micro-segregation. As a result, the behavior of a member in which micro-segregation exists due to heat treatment can be analyzed with higher accuracy.

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

The heat treatment simulation method calculates the anisotropy based on data indicating the anisotropy of strain caused by phase transformation, which is calculated using microsegregation model data that represents the state of microsegregation in a unit volume by a plurality of elements. The method may further include the step of generating a gender parameter. This provides an anisotropy parameter that reflects the influence on strain caused by phase transformation due to microsegregation within the elements of the model data.

In the heat treatment simulation method, different anisotropy parameters may be set for the plurality of elements. Thereby, for example, when the state of micro-segregation differs depending on the part of the member to be analyzed, the influence of these micro-segregations can be reflected in the anisotropy parameter. As a result, analysis accuracy can be further improved.

Embodiments of the present invention also include a heat treatment simulation apparatus that uses a computer to simulate heat treatment involving phase transformation of a member. The heat treatment simulation device includes an input unit that reads model data representing a member to be analyzed using a plurality of elements, and a strain caused by phase transformation using strain at an integration point of each of the plurality of elements as a parameter for calculation. a parameter setting unit that sets an anisotropy parameter indicating the anisotropy of the plurality of elements; a temperature calculation unit that calculates the temperature of the node of each of the plurality of elements; and a temperature calculation unit that calculates the temperature of the node of each of the plurality of elements; a strain calculation unit that calculates using the anisotropy parameter and a tissue fraction determined according to at least one of temperature and time change; and outputs an analysis result based on the calculated temperature and strain of the plurality of elements. and an output section. The strain calculation unit may be configured to calculate displacements of nodes in each of the plurality of elements and distortions of integration points.

Embodiments of the present invention also include programs that cause a computer to execute a simulation of heat treatment involving phase transformation of a member. The program includes the process of reading model data representing the member to be analyzed using multiple elements, and the anisotropy of strain caused by phase transformation as a parameter used to calculate the strain at the integration point of each of the multiple elements. a process of setting an anisotropy parameter indicating the temperature, a process of calculating a temperature at a node of each of the plurality of elements, and a process of calculating a strain at an integration point of each of the plurality of elements, at least one of the temperature and time change. causing a computer to perform a process of calculating using the tissue fraction determined according to the anisotropy 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. Identical or corresponding parts in the drawings are denoted by the same reference numerals and their description will not be repeated. The dimensional ratios between the constituent members shown in each figure do not necessarily represent the actual dimensional ratios.

[Heat treatment simulation device]
FIG. 1 is a functional block diagram showing a configuration example of a heat treatment simulation apparatus in this embodiment. A heat treatment simulation apparatus 1 shown in FIG. 1 is an apparatus that uses a computer to perform a simulation of heat treatment of a member that involves phase transformation. The heat treatment simulation apparatus 1 includes an input section 11 , a parameter setting section 12 , a temperature calculation section 13 , a strain calculation section 14 , and an output section 15 .

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

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

In this way, the model data includes data on a plurality of elements indicating the shape of the member to be analyzed, that is, data indicating the positions of nodes and integration points. Further, the model data may include data indicating 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 anisotropy of strain due to phase transformation as a parameter used to calculate strain at an integration point of each of a plurality of elements of model data. The parameter setting unit 12 sets anisotropy parameters based on user input or prerecorded data. Alternatively, the input unit 11 may read model data in which anisotropy parameters are set at each integration point. In this case, the parameter setting section 12 becomes a part of the input section 11. The anisotropy parameter can be, for example, a coefficient of a function that calculates strain due to phase transformation at each integration point. As a specific example, an anisotropy parameter can be set as a coefficient included in a tensor element included in a function that calculates strain due to phase transformation at 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 values indicating material properties of the member. The tissue fraction of each phase (each structure) of the member is determined according to the calculated temperature. This calculates the phase transformation. Note that phase transformation can also occur when time changes without temperature change. Therefore, the tissue fraction may be determined in response to changes in time rather than temperature. Here, the time change is a change in time in the simulation. The temperature calculation unit 13 can calculate the temperature at each time in the time series, for example. 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. Additionally, tissue fraction may be determined based on both temperature and time changes.

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 anisotropy parameter determined according to at least one of temperature and time change. The strain calculation unit 14 can calculate at least one of transformation plasticity and transformation strain at each integration point. Transformation plastic strain changes depending on stress. Therefore, the transformation plastic strain can be calculated using the stress calculated at each integration point. Since the transformation strain is a strain that occurs due to a volume change due to phase transformation, it can be calculated using, for example, a value indicating a volume change due to phase transformation of each element, for example, a value indicating a change in density.

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

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

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

As in the above example, by combining the temperature calculation of each node by the temperature calculation unit 13 and the calculation of strain due to phase transformation of each integration point by the strain calculation unit 14, Stress can be calculated. Thereby, in addition to thermo-elastic-plastic analysis that calculates displacement with respect to temperature changes, it is possible to perform analysis of changes in tissue fraction due to phase transformation and strain and stress caused by phase transformation.

The output unit 15 outputs analysis results based on the calculated temperatures and strains of the plurality of elements. The analysis results are not particularly limited as long as they are based on the temperatures and strains of multiple elements. Examples of analysis results include the distribution of at least one of temperature and strain in the member, or changes in the distribution over time. In addition to temperature and strain, for example, deformation of the member, stress, tissue distribution, or tissue fraction may be output as the analysis result. The form of output is not particularly limited. Examples of output formats include displaying the analysis results on a display, transmitting the analysis results to a designated location via a network, or saving the analysis results at a designated location.

In the example shown in FIG. 1, the heat treatment simulation apparatus 1 includes an anisotropic parameter generation section 16. The anisotropic parameter generating section 16 generates the anisotropic parameter set by the parameter setting section 12. The anisotropy parameter generation unit 16 can generate an anisotropy parameter based on data indicating anisotropy of strain caused by phase transformation, which is calculated using microsegregation model data. Micro-segregation model data is data that expresses the state of micro-segregation in a unit volume using a plurality of elements. Note that the anisotropic parameter generation unit 16 may be provided in a computer outside the heat treatment simulation apparatus 1. A specific example of the anisotropy parameter will be described later.

[Example of calculation of transformation plastic strain]
In 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 transformation plastic strain that occurs in proportion to stress when stress is applied during phase transformation of a member. The transformation plastic strain anisotropy parameter is set at each integration point by the parameter setting unit 12. The strain calculation unit 14 calculates the transformation plastic strain at each integration point by calculating the structure fraction determined 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 difference. Calculate using the orientation parameter. The transformation plastic strain at each integration point can be calculated using a function. The function may be, for example, a function that inputs tissue fraction and stress and outputs transformation plastic strain. Here, the tissue fraction is determined according to at least one of temperature and time change. The function may include the transformation plastic strain anisotropy parameter as a coefficient. The transformation plastic strain anisotropy parameter may be, for example, a coefficient included in an element of a tensor included in the function.

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

By using a function that can take anisotropy into account instead of the isotropic Mises yield function shown in the above formula (A1), the transformation plastic strain can be calculated taking anisotropy into consideration. Examples of functions that take anisotropy into consideration include Hill's anisotropy function and other equations. A function adapted to the microscopic structure of the material can be used as a function that can take into account the above-mentioned anisotropy. An asymmetry in tension and compression has been experimentally observed in transformation plastic strain. Therefore, it is preferable to use a function that can simultaneously reproduce tension and compression asymmetries as a function that can take anisotropy into consideration. For example, the following equation consisting of the first, second, and third invariants of the linearly transformed stress can be used as a reproducible function of the tension and compression asymmetry. Regarding the following formulas, the descriptions of the following documents are 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 that takes into account anisotropy that can represent other tension-compression asymmetries. Regarding the following formulas, the descriptions of the following documents are incorporated by reference.
O. Cazacu, B. Plunkett, F. Barlat, Int. J. Plasticity, 22 (2006) 1171-1194.

[Example of calculation of transformation strain]
The transformation strain anisotropy parameter is used in the calculation of the transformation strain by the strain calculation unit 14. The transformation strain anisotropy parameter is a parameter indicating the anisotropy of transformation strain caused by volume change due to phase transformation of a member. The transformation strain anisotropy parameter is set at each integration point by the parameter setting section 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 a transformation strain. Here, the value indicating the density change due to 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 an element of a tensor included in the function.

As an example, the following equation (13) can be used as a function to calculate the transformation strain at each integration point. Equation (13) below is based on the knowledge that transformation strain can be calculated from volume changes before and after phase transformation.

Note that the function for calculating the transformation plastic strain and the expression used for the function for calculating the transformation strain are not limited to the above example.

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

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

The strain calculation unit 14 calculates the displacement at the node of each 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 the tissue fraction and anisotropy parameter determined according to at least one of temperature and time change. In S4, as an example, the transformation plastic strain and transformation strain at each integration point are calculated. The transformation plastic strain is calculated using the texture fraction, the stress at the integration point, and the transformation plastic strain anisotropy parameter. The transformation strain is calculated using the tissue fraction and the transformation strain anisotropy parameter. At each integration point, the sum of the transformation plastic strain and the transformation strain is calculated as the strain resulting from the phase transformation at each integration point.

The output unit 15 outputs analysis results based on the temperature and strain calculated in S3 and S4 (S5). For example, the output unit 15 can generate and output an image in which at least one of the temperature distribution, stress distribution, displacement distribution, and strain distribution of the member can be visually recognized.

[Processing example of anisotropic parameter generation]
FIG. 3 is a flowchart illustrating 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 micro-segregation model is acquired (S11). The micro-segregation model is data representing the state of micro-segregation in a unit volume using a plurality of elements. The unit volume of the micro-segregation model may be any size that can express the periodic structure of micro-segregation.

For example, as a micro-segregation model, a model is created in which a plurality of minute hexahedral elements each having a distribution of chemical components simulating the shape of micro-segregation are assembled to constitute a representative volume element of a unit volume. The distribution of chemical components represented by minute elements in a representative volume element can be determined, for example, by observing micro-segregation of an actual member and finding the average shape of the segregation.

The dimensions of the representative volume element are such that the periodic symmetry of microsegregation can be reproduced. The representative volume elements are divided into a number of elements that can sufficiently reproduce the chemical component 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 uniform chemical components having the same dimensions as the representative volume element is obtained. The homogeneous model can be an isotropic model made up of one element.

In S13, a heat treatment analysis (heat treatment simulation) is performed on the micro-segregation model generated in S11 and the uniform model generated in S12 under the condition that no stress is applied, and transformation strain is calculated. The heat treatment analysis in S13 is performed under typical heat treatment conditions using isotropic transformation plastic strain. The transformation strain can be calculated from the difference in the amount of deformation between the start of transformation and the end of transformation. The transformation strain in the micro-segregation model and the transformation strain in the homogeneous model are calculated respectively.

In S14, a transformation strain anisotropy parameter is generated based on the relative value of the transformation strain of the homogeneous model with respect to the transformation strain of the micro-segregation model. In the analysis using representative volume elements of the micro-segregation model, anisotropy appears in the transformation strain depending on the segregation shape. That is, in the micro-segregation model, different transformation strains are calculated in multiple directions. In contrast, in the uniform model, the same transformation strain is calculated in multiple directions. For example, the ratio of the transformation strain in each direction of the uniform model to the transformation strain in the corresponding direction in the representative volume element is determined as the transformation strain parameter.

In S15, a heat treatment analysis is performed on the micro-segregation model under the condition that stress is applied in a plurality of directions, and 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) in a specific direction to a representative volume element of a micro-segregation model. The amount of deformation upon completion of the transformation is determined, 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, which was performed in S14. By performing this in multiple directions including the shear direction, the transformation plastic strain in each direction can be calculated. In addition, if the asymmetry of tension and compression is also considered, calculations are made for the case of compressive stress loading in addition to tension. Furthermore, an analysis may be performed in which multiaxial stress is applied in addition to uniaxial or pure shear stress.

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

In S17, the transformation plastic strain when stress is applied to the anisotropic model in the plurality of directions described above is calculated. In S17, heat treatment analysis is performed under the same stress load conditions as in S15, and transformation plastic strain is calculated. In the case of a constant stress load on a uniform simple shape model, it is possible to determine 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 determined by theoretical calculation without performing analysis using the finite element method.

In S18, the transformation plastic strain based on the anisotropic model calculated in S17 is compared with the transformation plastic strain based on the micro-segregation model calculated in S15, and evaluated. If the evaluation result satisfies the predetermined condition (YES in S19), the transformation plastic strain anisotropy parameter set in the anisotropic model is determined as the optimum value. If the evaluation result does not satisfy the predetermined condition, the transformation plastic strain parameter of the anisotropic model is updated (S20), and the processes of S16 to S18 are repeated. The processes of S16 to S20 are repeated until the optimum value of the transformation plastic strain anisotropy parameter is obtained.

As an example of S18, S19, and S20, for the transformation plastic strain during stress loading in each direction of the anisotropic model calculated in S17, the transformation plastic strain during stress loading in the corresponding direction of the micro-segregation model calculated in S15. It is possible to perform a process of calculating the sum of squares of errors with respect to strain and determining the transformation plastic anisotropy parameter so that the sum of squares of the errors is minimized.

If the segregation state is different for each part of the member, the processes of S11 to S20 can be performed for each part of the member. This makes it possible to generate transformation plastic strain anisotropy parameters that reflect the respective segregation states at each site. As a result, different anisotropy parameters can be set for elements in portions whose deformation states are different from each other. In this way, by providing a distribution to the anisotropy parameters in multiple elements of the model data to be analyzed, more accurate heat treatment analysis becomes possible.

Note that the anisotropic parameter generation process is not limited to the example shown in FIG. 3. For example, in FIG. 3, the transformation plastic strain anisotropy parameter generation process in S15 to S20 may be performed before the transformation strain anisotropy parameter generation process in S13 to S14. In addition, in the example shown in Figure 3, the anisotropy of strain in micro-segregation is calculated by simulation using representative volume elements, but instead of simulation, the anisotropy of strain in micro-segregation is calculated by experiment. May be measured. In this case, the anisotropy parameter can be determined by comparing the strain anisotropy obtained through measurement and the strain anisotropy calculated using the anisotropic macro model.

[Example]
(1. Calculation of anisotropy parameter)
In this example, a homogenization method using representative volume elements was used to express micro segregation with macro material properties. A representative volume element is the smallest repeating unit in a material with a periodic microstructure. A representative volume element is a model of a periodically repeated microstructure. By conducting numerical material tests on this representative volume element and using the obtained material properties as macroscopic material responses, we found that it is possible to replace materials with microscopic repeating structures with macroscopic homogeneous materials.

FIG. 4 is a diagram showing representative volume elements that reproduce micro-segregation in this example. 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 components. In a macro model, the entire model is of uniform chemical composition. By using a constitutive law that takes into account anisotropy in transformation plasticity for the macro model, we were able to output results equivalent to analyzes using representative volume elements. Each side of the hexahedron was equally divided into representative volume elements, and each element was configured to include a plurality of elements. The macro model was composed of one hexahedral element. Hexahedral linear elements were used for the elements. A boundary condition was given in which the displacements from the reference node are the same at the nodes on the plane of periodic symmetry. The chemical composition of the representative volume element and macro model used in this example was the chemical composition of chrome-molybdenum steel. Mechanical properties such as Young's modulus and stress-strain diagram were calculated using actually measured data, while thermal properties and transformation properties were calculated using prediction formulas based on chemical components. The heat treatment conditions were all austenite and held at a constant temperature of 500°C for 1000 s. Transformation plastic strain was determined by applying a constant stress in a specific direction during the phase transformation of these models and determining the strain in each direction upon completion of the analysis.

FIG. 6 is a diagram showing the shape of micro-segregation applied to the representative volume element in this example. The segregated portion had a cylindrical shape with the axial direction in the z direction. Microsegregation was directly reproduced using the microstructural observation results obtained in the past. FIG. 7 shows the distribution of chemical components of micro-segregation in this example. The concentration distribution of segregation was approximated by a quadratic function so that the concentration was highest in the center. In the representative volume element, the timing of phase transformation and expansion caused by phase transformation differs because the chemical components differ depending on the region. This generates internal stress and strain, and anisotropic strain depending on the shape and direction of segregation.

FIG. 8 shows the transformation plastic strain in each direction when a stress of 10 MPa is applied to the representative volume element and the macro model (uniform model) in the x direction or the z direction during isothermal maintenance. The transformation plastic strain constitutive equation used and the average deviatoric stress loaded on the model are the same, but by reproducing the distribution of chemical components that simulates micro-segregation inside the model, the transformation plastic strain changes greatly depending on the direction. It was confirmed that asymmetry also appeared in tension and compression. In order to express the deformation behavior during stress loading due to micro-segregation using only macroscopic constitutive laws, it is impossible to use Mises' equivalent stress, and it is considered necessary to use a formula that takes anisotropy into consideration.

FIG. 9 shows a graph in which stress is applied to the A comparison between the transformation plastic strain in each direction when a load of 10 MPa is applied and the results of a representative volume element is shown. We were able to confirm that the anisotropic transformation plastic behavior due to micro-segregation, which was reproduced by giving a distribution to the chemical components, can be reproduced using an anisotropic macro model that applies transformation plasticity that takes anisotropy into consideration.

In this example, anisotropy was imparted to the transformation strain in addition to the transformation plastic strain. FIG. 10 shows the strains in the x, y, and z directions when no stress is applied to an isotropic macro model and a representative volume element that reproduces microsegregation. In the macro model, an isotropic transformation strain was obtained. It was confirmed that there is anisotropy in transformation strain due to micro-segregation 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 calculating the transformation strain, the anisotropy of the 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 parameter in each of the x, y, and z directions. can be expressed.

(2. Quenching analysis)
A quenching analysis (heat treatment simulation) was performed using the above anisotropic parameters. The target member was a hollow round bar. FIG. 11 shows a three-dimensional analytical model of the member of this example. Due to the symmetry of the members, the shape was set to 1/4. FIG. 12 shows the heat transfer coefficient of the quenching oil (hot oil) used in this example. The parts were placed in the oil so that the center axis of the model was parallel to the oil level. In order to reproduce the difference in cooling rate depending on the region, the model surface was divided into regions above and below the center of the model, and the heat transfer coefficient of the lower region 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 that gave anisotropy to the transformation plastic strain and took microsegregation into consideration was approximately 30% larger than the amount of deformation obtained by normal quenching analysis. We were able to reproduce the actual phenomenon in which quenching deformation increases due to microsegregation through simulation.

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

Claims (11)

A heat treatment simulation method for performing a heat treatment simulation involving phase transformation of a member using a computer, the method comprising:
A process of loading model data that represents the member to be analyzed using multiple elements,
setting an anisotropy parameter indicating anisotropy of strain due to phase transformation as a parameter used to calculate strain at an integration point of each of the plurality of elements;
calculating a temperature at a node of each of the plurality of elements;
calculating the strain at the integration point of each of the plurality of elements using the anisotropy parameter and a tissue fraction determined according to at least one of the temperature and time change;
A heat treatment simulation method comprising: outputting an analysis result based on the calculated temperatures and strains 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 anisotropy of transformation plastic strain that occurs in proportion to stress when stress is applied during phase transformation of the member,
The heat treatment simulation method further includes the step of calculating stress at an integration point of each of the plurality of elements,
The step of calculating the distortion at the integration point of each of the plurality of elements includes:
The transformation plastic strain at the integration point of each of the plurality of elements is determined by the texture fraction determined according to at least one of the temperature and time change, the stress at the integration point, and the transformation plastic strain anisotropy parameter. A heat treatment simulation method that includes a process 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 strain for the input tissue fraction and the stress,
The heat treatment simulation method, wherein the function includes 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 a strain for a tensile stress is different from a strain for a compressive stress having the same magnitude as the tensile stress, depending on the transformation plastic strain anisotropy parameter. The heat treatment simulation method according to claim 4,
The transformation plastic strain is determined using the following formula.

The heat treatment simulation method according to any one of claims 1 to 5,
The anisotropy parameter includes a transformation strain anisotropy parameter indicating anisotropy of transformation strain caused by a volume change due to phase transformation of the member,
The step of calculating the distortion at the integration point of each of the plurality of elements includes:
a step of calculating a transformation strain at an integration point of each of the plurality of elements using a tissue fraction determined according to at least one of the temperature and time change and the transformation strain anisotropy parameter; Heat treatment simulation method. The heat treatment simulation method according to claim 6,
Determine the transformation strain using the following formula.

The heat treatment simulation method according to any one of claims 1 to 7,
A step of generating the anisotropy parameter based on data indicating anisotropy of strain caused by phase transformation calculated using microsegregation model data that represents the state of microsegregation in a unit volume by a plurality of elements. A heat treatment simulation method further comprising: The heat treatment simulation method according to any one of claims 1 to 8,
A heat treatment simulation method, wherein different anisotropy parameters are set for the plurality of elements. A heat treatment simulation device that uses a computer to simulate heat treatment involving phase transformation of a member,
an input section that reads model data representing the member to be analyzed using multiple elements;
a parameter setting unit that sets an anisotropy parameter indicating anisotropy of strain due to phase transformation as a parameter used to calculate strain at an integration point of each of the plurality of elements;
a temperature calculation unit that calculates the temperature of each node of the plurality of elements;
a strain calculation unit that calculates strain at an integration point of each of the plurality of elements using the anisotropy parameter and a tissue fraction determined according to at least one of the temperature and time change;
A heat treatment simulation apparatus, comprising: an output section that outputs an analysis result based on the calculated temperatures and strains of the plurality of elements. A program that causes a computer to execute a simulation of heat treatment involving phase transformation of a member,
The process of loading model data that represents the member to be analyzed using multiple elements,
a process of setting an anisotropy parameter indicating anisotropy of strain caused by phase transformation as a parameter used to calculate strain at an integration point of each of the plurality of elements;
a process of calculating the temperature of each node of the plurality of elements;
a process of calculating a strain at an integration point of each of the plurality of elements using the anisotropy parameter and a tissue fraction determined according to at least one of the temperature and time change;
A program that causes a computer to execute a process of outputting an analysis result based on the calculated temperatures and strains of the plurality of elements.

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