Welding thermal stress finite element calculation method and device based on temperature gradient vector, equipment and medium

Abstract

The invention discloses a welding thermal stress finite element calculation method, device and equipment based on a temperature gradient vector and a medium, and relates to the technical field of welding thermal stress calculation. And S2, temperature field data in the welding process are obtained. And S3, extracting a temperature gradient vector. And S4, establishing an anisotropic constitutive model. And S5, loading the anisotropic constitutive model based on the temperature gradient vector. According to the method, a temperature gradient dependent elastic stiffness matrix calculation method and a dynamic hardening criterion are developed by establishing a dynamic coupling relationship between the temperature field gradient and the mechanical property of the material, the problem of misalignment of material anisotropic response simulation caused by a directional heat source and a non-uniform temperature field in the welding process is solved, and compared with a traditional isotropic model, the method has the advantage that the material anisotropic response simulation accuracy is greatly improved. Cooperative improvement of precision and efficiency is achieved, and a breakthrough simulation tool is provided for welding process optimization and defect prevention and control.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of welding thermal stress calculation, in particular to a welding thermal stress finite element calculation method, device, equipment and medium based on temperature gradient vector. BACKGROUND

[0002] Welding thermal stress finite element calculation is a technology that uses finite element method to simulate and analyze the thermal stress distribution caused by temperature change during welding process. It establishes the geometric model of the welded structure, divides the finite element mesh, defines the thermal physical and mechanical properties of the material, applies load and boundary conditions, performs thermal analysis to obtain temperature field distribution, and then uses the temperature field results for structural analysis to calculate the thermal stress distribution, so as to evaluate the influence of welding thermal stress on the structure and provide scientific basis for the optimization of welding process and structural design.

[0003] The existing welding thermal stress finite element calculation method usually establishes a geometric model, divides the mesh, defines the material properties, applies load and boundary conditions, performs thermal analysis to simulate the temperature field distribution during the welding process, and then uses the temperature field results for structural analysis to calculate the thermal stress distribution. Finally, through the result analysis, the influence of welding thermal stress on the structure is evaluated and the welding process is optimized. However, in actual use, there is a problem of inaccurate simulation of material anisotropic response caused by directional heat source and non-uniform temperature field during the welding process. SUMMARY

[0004] The present application provides a welding thermal stress finite element calculation method, device, equipment and medium based on temperature gradient vector to improve at least one of the above technical problems.

[0005] In a first aspect, the present application provides a welding thermal stress finite element calculation method based on temperature gradient vector, which includes steps S1 to S5.

[0006] S1, according to the parameter scale in the actual welding process, a thermoelastic plastic model is constructed by a finite element model.

[0007] S2, the thermoelastic plastic model is constructed as a three-dimensional unstable state, and temperature field analysis is performed to obtain temperature field data.

[0008] S3, the temperature gradient vector of each element of the thermoelastic plastic model, the welding process parameters and the key size characteristics are determined by analyzing the temperature field data. The key size characteristics include the penetration and the width.

[0009] S4, based on the anisotropic constitutive model, the SPPARKS open source module is used to calculate the grain distribution during the welding process combined with the key feature size and the welding process parameters to obtain the constitutive matrix at different positions.

[0010] S5, the constitutive matrix is combined with the temperature gradient vector by a temperature gradient-anisotropy constitutive model loading algorithm to construct a final constitutive model. The final constitutive model can be used to calculate stiffness.

[0011] Preferably, the elastothermoplastic model is constructed as a three-dimensional non-steady state, and temperature field analysis is performed to obtain temperature field data, specifically including: The elastothermoplastic model is constructed as a three-dimensional non-steady state. The heat conduction differential equation of the three-dimensional non-steady state is: Wherein, is the density, is the specific heat capacity, is the thermal conductivity, is the temperature, is the time, is the internal heat source, , and are three coordinate directions of the elastothermoplastic model, denotes the partial derivative.

[0012] Temperature field analysis is performed to obtain temperature field data. In the analysis of the temperature field, the initial condition of the object is the initial temperature itself, which is represented as: In the formula, is the temperature, is the initial temperature, is the time.

[0013] Preferably, when the temperature field data corresponding to the analyzed elastothermoplastic model is a triangular element: let the temperatures of the three vertices of the triangle be , and , the centroid of the triangle is the point. Then the following definitions are made: .

[0014] .

[0015] .

[0016] .

[0017] .

[0018] In the formula, is the temperature of the centroid of the triangle, is the vector from the centroid to the first vertex, is the vector from the centroid to the second vertex, is the vector from the centroid to the third vertex, , and are temperature gradients of three vertices, respectively, is a temperature gradient of a triangular element.

[0019] Preferably, when the temperature field data analyzed corresponds to an element of the elastic-thermo plastic model which is a polyhedral element: the average temperature of the element is defined as: .

[0020] wherein is the average temperature of the element, is the number of nodes of the element, is the number of the node of the element, is the global node number corresponding to the node of the element, is the temperature value at the global node number .

[0021] The temperature gradient vector of the node is obtained according to .

[0022] .

[0023] wherein is the temperature gradient vector of the node, is the position vector of the node relative to the center of gravity of the element.

[0024] The average temperature gradient of the element is obtained according to the temperature gradient vector of the node.

[0025] .

[0026] wherein is the average temperature gradient vector of the element.

[0027] Preferably, because the temperature of a certain point on the welding piece is constantly changing with time, two time points and are introduced.

[0028] The temperature of the element is higher than the liquidus at the time , and the temperature is lower than the liquidus at the time , that is: .

[0029] .

[0030] wherein, is the temperature of the th unit at the th time, is the initial temperature, is the temperature of the th unit at the th time, is the final temperature.

[0031] Then, the temperature gradient vector of the th unit at the solidification time is: .

[0032] wherein, is the grain growth vector direction of the th unit during the welding process, is the time difference, is the temperature of one time difference, is the temperature of two time differences.

[0033] Preferably, based on the anisotropic constitutive model, the SPPARKS open source module is used to calculate the grain distribution during the welding process combined with the key feature size and the welding process parameters, to obtain the constitutive matrix at different positions, specifically including: The expression of the stress tensor and the strain tensor of the solid constitutive equation is: .

[0034] .

[0035] wherein, is the stress tensor, is the elastic stiffness tensor, is the strain tensor, is the first index symbol of the tensor component, is the second index symbol of the tensor component, is the third index symbol of the tensor component, is the fourth index symbol of the tensor component, is the partial derivative of the coordinate direction, is the vector of the displacement vector in the direction, is the partial derivative of the coordinate direction, is the vector of the displacement vector in the direction, is the vector of the displacement vector in the wherein each index i ranges from 1 to 3, corresponding to the coordinate directions in three-dimensional space.

[0036] Based on the symmetry of stress and strain tensors, the constitutive equation in tensor form is expressed in matrix form: .

[0037] wherein , and respectively represent the normal stress of the material in directions. , and respectively represent the shear stress of the material in plane, plane and plane. , and respectively represent the normal strain of the material in directions. , and respectively represent the shear strain of the material in plane, plane and plane. is the elastic elastic constant, the subscript rule is: is the corresponding normal stress response, is the corresponding shear stress response, is the corresponding normal strain influence, is the corresponding shear strain influence.

[0038] When the anisotropic constitutive model has three orthogonal elastic symmetry planes, it is an orthotropic anisotropic constitutive model: the normal stress and shear strain of the orthotropic anisotropic material are not coupled, the shear stress and normal strain are not coupled, and the shear stress and shear strain in different planes also have no interaction, then the stress and strain satisfy the following relationship: .

[0039] According to the relationship between stress and strain, the 6x6 constitutive matrix of the orthotropic anisotropic constitutive model is obtained:

[0040] wherein is the orthotropic anisotropic constitutive model, is the material along stiffness of the material along the direction, stiffness of the material along the direction, stiffness of the material along the direction, stiffness of the material along the direction, stiffness of the material along the direction, in-plane shear stiffness, in-plane shear stiffness, in-plane shear stiffness, contribution of the direction to the stress, contribution of the direction to the stress, contribution of the direction to the stress, contribution of the direction to the stress, contribution of the direction to the stress, contribution of the direction to the stress, contribution of the direction to the stress, contribution of the direction to the stress, contribution of the direction to the stress, contribution of the direction to the stress, contribution of the direction to the stress, contribution of the direction to the stress.

[0041] Preferably, the final constitutive model is constructed by combining the constitutive matrix with the temperature gradient vector through the temperature gradient-anisotropy constitutive model loading algorithm, and specifically includes: the orthotropic anisotropy constitutive model is constructed as: on the axis, it is expressed as an independent parameter, axis and axis, it is expressed as the same parameter.

[0042] the temperature gradient of the element of the elastothermoplastic model is set as , and and and are selected to obtain a custom coordinate system.

[0043] the mapping relationship is obtained according to the included angle between the custom coordinate system and the natural coordinate system.

[0044]

[0045] the conversion matrix of the constitutive model is constructed according to the mapping relationship.

[0046] .

[0047] .

[0048] wherein, ​​​​​​constitutive model for final loading into the global structure. is a transformation matrix. denotes the transpose. , and are the sizes of the projections of , and onto . , and are the sizes of the projections of , and onto . , and are the sizes of the projections of , and onto .

[0049] The stiffness matrix of the construction unit is constructed according to : ; in the formula, is the stiffness matrix, is the integral operation, is the strain displacement matrix.

[0050] In a second aspect, the application provides a welding thermal stress finite element calculation device based on a temperature gradient vector, which comprises a model construction module, a temperature field module, a feature module, a matrix module and an updating module.

[0051] The model construction module is used to construct an elastic-thermal plasticity model through a finite element model according to the parameter scale in the actual welding process.

[0052] The temperature field module is used to construct the elastic-thermal plasticity model into a three-dimensional non-steady state and perform temperature field analysis to obtain temperature field data.

[0053] The feature module is used to analyze the temperature field data to determine the temperature gradient vector of each unit of the elastic-thermal plasticity model, the welding process parameters and the key size features. The key size features include the penetration and the width.

[0054] The matrix module is used to perform grain distribution calculation in the welding process based on the anisotropic constitutive model, adopt the SPPARKS open source module, combine the key feature size and the welding process parameters, and obtain the constitutive matrix at different positions.

[0055] An updating module is configured to combine the constitutive matrix and the temperature gradient vector by a temperature gradient-anisotropy constitutive model loading algorithm to construct a final constitutive model, wherein the final constitutive model can be used to calculate the stiffness.

[0056] In a third aspect, the present application provides a temperature gradient vector-based welding thermal stress finite element calculation device, which comprises a processor, a memory and a computer program stored in the memory. The computer program can be executed by the processor to implement the temperature gradient vector-based welding thermal stress finite element calculation method according to any one of the first aspect.

[0057] In a fourth aspect, the present application provides a computer readable storage medium comprising a stored computer program, wherein the computer readable storage medium controls the device where the computer readable storage medium is located to execute the temperature gradient vector-based welding thermal stress finite element calculation method according to any one of the first aspect when the computer program is running.

[0058] The temperature gradient vector-based welding thermal stress finite element calculation method has the following beneficial effects: Compared with the traditional isotropic model, the anisotropic constitutive model based on the temperature gradient vector can more accurately simulate the anisotropic response of the material during the welding process, improve the accuracy of the welding thermal stress finite element calculation, and more truly reflect the physical phenomena in the welding process by establishing the dynamic coupling relationship between the temperature field gradient and the mechanical properties of the material, thereby further improving the accuracy of the simulation.

[0059] By developing the temperature gradient-dependent elastic stiffness matrix calculation method and the dynamic hardening criterion, the calculation process is optimized, the calculation efficiency is improved, the parallel computing capability of the SPPARKS open source module is utilized, the efficiency of large-scale simulation can be significantly improved, and the model is suitable for complex welding structures and large-scale simulation tasks. At the same time, the model provides a more accurate simulation tool for welding process optimization, which can help engineers better design welding process parameters, reduce welding defects, and predict possible defects such as cracks and pores in the welding process through more accurate simulation results, so as to take effective prevention and control measures. BRIEF DESCRIPTION OF DRAWINGS

[0060] In order to more clearly illustrate the technical solutions of the present application, the following will briefly introduce the drawings needed to be used in the specific embodiments of the present application. It should be understood that the following drawings only show some specific embodiments of the present application, and therefore should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can also be obtained without creative labor on the basis of these drawings.

[0061] Fig. 1 An example schematic diagram of a triangular element of the present application.

[0062] Fig. 2 An example schematic diagram of a triangular element temperature gradient natural coordinate system of the present application.

[0063] Fig. 3 An example schematic diagram of a user-defined coordinate system and a natural coordinate system. DETAILED DESCRIPTION

[0064] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application.

[0065] In the prior art, welding thermal stress finite element calculation is performed by establishing a geometric model, dividing a mesh, defining material properties, applying a thermal load and a boundary condition, simulating a welding temperature field distribution and calculating a thermal stress. However, a directional heat source and a non-uniform temperature field cause the material to present an anisotropic response, and the existing method causes the constitutive model to be unable to accurately reflect the spatial variation of the mechanical properties of the material due to the neglect of the relevance of the grain growth direction and the temperature gradient vector. For example, in a multi-layer welding process of a thick plate, the grains near the molten pool grow preferentially along the temperature gradient direction, and the traditional isotropic assumption causes a significant deviation between the predicted value and the measured value of the stress, which affects the optimization of the process parameters.

[0066] In order to solve the above problems, first, the source of the inaccuracy of the existing model needs to be clarified: the anisotropic constitutive relationship is not coupled with the temperature gradient vector. Through analysis, it is found that the temperature gradient direction in the solidification stage of the molten pool directly affects the grain orientation, and the grain arrangement direction determines the anisotropy of the mechanical properties of the material. Based on this, a model is proposed to be constructed in stages: first, an elastoplastic model is established to describe the thermal-mechanical coupling behavior, then the gradient vector in the temperature field is extracted as the reference for the grain growth direction, and finally the anisotropic constitutive matrix is associated with the gradient direction. The key is to map the Monte Carlo grain simulation results to the finite element unit, and to realize the global loading of the local anisotropic properties through coordinate transformation.

[0067] Referring to Figs. 1 to 3 The embodiment provides a welding thermal stress finite element calculation method based on a temperature gradient vector. The method comprises the following steps: establishing an elastoplastic model of a welding process, obtaining temperature field data and extracting a penetration, a width and a temperature gradient vector, combining welding process parameters to calculate grain distribution through a Monte Carlo algorithm, constructing an orthogonal anisotropic constitutive matrix, establishing a user-defined coordinate system to realize directional coupling of the temperature gradient direction and the constitutive model, and finally loading the anisotropic constitutive model into finite element calculation.

[0068] The elastic-thermal-plastic model refers to a coupling model for describing the thermal expansion, phase change and plastic deformation of a material during welding, which can be specifically implemented by using an incremental constitutive equation containing a temperature-dependent yield criterion and hardening law to represent the stress-strain evolution caused by thermal cycles. The temperature gradient vector refers to a spatial vector of the temperature change rate of a node of an element, which can be specifically calculated by solving the temperature field of the node through the derivative method of shape functions after obtaining the temperature field of the node by solving the heat conduction differential equation, and the direction of the temperature gradient vector determines the preferred growth direction of the grains during the solidification of the molten pool. The anisotropic constitutive model refers to a constitutive relationship reflecting the direction dependence of the mechanical properties of a material, which can be specifically described by using a 6*6 stiffness matrix based on the crystal plasticity theory, and the matrix elements are determined by volume-weighted averaging according to the grain orientation distribution. The temperature gradient-anisotropic constitutive loading algorithm refers to a coordinate transformation method for aligning the local coordinate system with the direction of the temperature gradient, which can be specifically implemented by converting the material principal axis coordinate system to the global coordinate system through a direction cosine matrix to ensure the accurate matching of the anisotropic properties and the gradient direction.

[0069] Specifically, first, a three-dimensional elastic-thermal-plastic finite element model is established based on actual welding parameters, and the temperature space-time distribution data are obtained by solving the unsteady heat conduction equation. Then, the geometric characteristics such as the penetration and the width are extracted, and the temperature gradient vector of each element is calculated. For a three-dimensional eight-node hexahedral element, the temperature gradient components can be obtained by summing the products of the partial derivatives of the shape functions with respect to the local coordinates and the node temperatures. Next, the SPPARKS module is used to simulate the grain growth process in the heat-affected zone, the grain principal axis orientation is determined according to the temperature gradient direction, and the orthogonal anisotropic stiffness matrix is generated. Finally, a local coordinate system is created for each element in the finite element calculation, so that the axis coincides with the direction of the temperature gradient, and the anisotropic constitutive relationship is embedded into the global stiffness matrix through coordinate transformation, realizing the spatial anisotropy representation of the material properties.

[0070] Compared with the prior art, the existing method adopts a uniform isotropic assumption, ignores the grain orientation change caused by the temperature gradient, and causes the stress prediction error to accumulate. The present scheme solves the defect that the traditional model cannot reflect the heterogeneity of the welding zone performance by introducing the temperature gradient vector as the reference of the anisotropic principal axis, directly relating the grain growth direction to the mechanical properties of the material. At the same time, the Monte Carlo algorithm is used to simulate the grain distribution, so that the constitutive matrix is closer to the actual microstructure evolution law, and the coordinate transformation algorithm ensures the correct transmission of the anisotropic properties in the global model.

[0071] Through the above technical scheme, the present application can accurately represent the anisotropic mechanical behavior of the heat-affected zone of the welding, improve the simulation accuracy of the thermal stress distribution, and provide a reliable basis for the optimization of the welding process parameters. By coupling the temperature gradient and the grain growth direction, the stress prediction deviation problem caused by the traditional method due to the neglect of the direction dependence of the material performance is effectively solved, and the accuracy of the residual stress field calculation can be significantly improved, especially in complex conditions such as multi-layer and multi-pass welding.

[0072] On the basis of the above-mentioned embodiments, in an optional embodiment of the present application, the welding thermal stress finite element calculation method based on the temperature gradient vector can be executed by a welding thermal stress finite element calculation device based on the temperature gradient vector (hereinafter referred to as: calculation device). In particular, it is executed by one or more processors in the calculation device to realize steps S1 to S5.

[0073] S1, establish an elastoplastic model of the welding process: according to the parameter scale in the actual welding process, an elastoplastic model is constructed by a finite element model. Specifically, the elastoplastic model in S1 can be a computational fluid dynamics (CFD), a finite element (FEM) or a CFD-FEM coupling model, and the FEM model is used in this embodiment.

[0074] S2, obtain temperature field data in the welding process: the elastoplastic model is constructed as a three-dimensional unstable state, and temperature field analysis is performed to obtain temperature field data. Specifically, the finite element model in S1 is analyzed to obtain the corresponding temperature field data changing with time. The finite element model used in this embodiment is a three-dimensional unstable state.

[0075] Preferably, step S2 includes steps S21 to S22.

[0076] S21, construct the elastoplastic model as a three-dimensional unstable state.

[0077] The heat conduction differential equation of the three-dimensional unstable state is: .

[0078] In the formula, is the density, is the specific heat capacity, is the thermal conductivity, is the temperature, is the time, is the internal heat source, , and are three coordinate directions of the elastoplastic model, denotes the partial derivative.

[0079] S22, perform temperature field analysis to obtain temperature field data.

[0080] In the analysis of the temperature field, the initial condition of the object is the initial temperature itself, which is represented as: .

[0081] In the formula, is the temperature, is the initial temperature, is time.

[0082] Specifically, a heat source model in the welding process can be selected according to actual conditions, such as a Gaussian surface heat source model, a rotating Gaussian body heat source model, and a double-ellipsoid heat source model.

[0083] By the technical solution, the present application effectively solves the misalignment problem of temperature field simulation caused by directional movement and non-uniform heating of the heat source in the welding process, provides high-precision temperature gradient data basis for loading of the subsequent anisotropic constitutive model, thereby improving the prediction accuracy of the material anisotropic response in the thermal stress calculation, and at the same time, the present application realizes accurate quantization of the initial condition of the temperature field analysis in the welding process, eliminates the prediction deviation of the grain growth direction caused by unreasonable initial temperature assumption in the traditional method, so that the subsequent anisotropic constitutive model based on the temperature gradient vector can more truly reflect the mechanical response characteristics of the material in the non-uniform temperature field.

[0084] S3, extracting key feature size and temperature gradient vector: analyzing the temperature field data to determine the temperature gradient vector, welding process parameters and key size features of each element of the thermoelastic-plastic model. Among them, the key size features include the penetration and the width. Specifically, the temperature gradient vector and the key size features such as the penetration and the width and the welding process related parameters at the solidification time of each element are obtained according to the temperature field data in S2.

[0085] Specifically, the specific way of obtaining the key size data such as the penetration and the width from the weld temperature data (i.e., the temperature field data) is: the key size data such as the penetration and the width are calculated by substituting the existing metallographic experimental data of different positions of the weld into the simulation calculation.

[0086] As shown in Fig. 1 , in the embodiment, a two-dimensional case is described, and a triangular element is taken as an example (i.e., when the element of the thermoelastic-plastic model corresponding to the analyzed temperature field data is a triangular element): let the temperatures of the three vertices of the triangle be , and , , and the center of gravity of the triangle is

[0087] Then the following definitions are made: .

[0088] .

[0089] .

[0090] .

[0091] .

[0092] In the formula, The temperature of the centroid of the triangle. The vector from the centroid to the first vertex. The vector from the centroid to the second vertex. The vector from the centroid to the third vertex. , and These are the temperature gradients at the three vertices. The temperature gradient is represented by the triangular element.

[0093] It should be noted that when the simulation model is a three-dimensional tetrahedral unit, the above can be deduced by analogy.

[0094] Based on the above embodiments, in an optional embodiment of the present invention, when the element of the elasto-thermo-plastic model corresponding to the analyzed temperature field data is... When defining a solid element: Define the first The average temperature of each unit is: .

[0095] In the formula, For the first Average temperature of each unit For the number of nodes in the unit, For the numbering of unit nodes, For the first The first unit The global node number corresponding to each node Number the global nodes The temperature value at that location.

[0096] according to Obtain the temperature gradient vector of the node.

[0097] .

[0098] In the formula, For the first Temperature gradient vector of each node, For the first The position vector of each node relative to the centroid of the element.

[0099] The average temperature gradient of the cell is obtained based on the temperature gradient vector of the node.

[0100] .

[0101] In the formula, For the first The average temperature gradient vector of each unit.

[0102] During welding, due to the heat source, the temperature at a point on the workpiece changes continuously over time. This change is characterized by rapid heating, a short dwell time at the highest temperature, and subsequent cooling at different rates at different points. The closer to the weld, the higher the temperature at each point; conversely, the farther from the weld, the lower the temperature.

[0103] Preferably, two time points are introduced. and . No. Each unit in At any given time, the temperature is above the liquidus line. The temperature is below the liquidus line at any given time. That is: .

[0104] .

[0105] In the formula, For the first Each unit in Temperature at any moment For the initial temperature, For the first Each unit is in Temperature at any moment The final temperature.

[0106] No. The temperature gradient vector of each element at the time of solidification is: .

[0107] in, For the first step in the welding process The grain growth vector direction of each unit For time difference, Temperature for a time difference The temperature represents the two time differences.

[0108] Through the above technical solution, this application effectively solves the problem of material anisotropic response simulation deviation caused by inaccurate temperature gradient characterization in welding thermal stress calculation. By accurately calculating the element-level temperature gradient vector, the spatial correspondence between grain growth direction and constitutive matrix is ​​ensured, significantly improving the engineering applicability of welding thermal stress finite element analysis. At the same time, this application can accurately characterize the grain orientation distribution characteristics of the welding heat-affected zone, effectively improving the simulation accuracy of material anisotropic response in thermal stress calculation, and providing accurate crystallographic parameter input for the mechanical property evaluation of welded joints.

[0109] S4, establishing an anisotropic constitutive model: based on the anisotropic constitutive model, the SPPARKS open source module is used to calculate the grain distribution in the welding process combined with the key feature size and the welding process parameters, and the constitutive matrix at different positions is obtained. Specifically, in the embodiment, the SPPARKS open source module based on the Monte Carlo algorithm is used, the key feature sizes such as the penetration and the width and the welding process related parameters are introduced, and the grain distribution calculation in the welding process is carried out. Through the grain distribution simulation calculation, the anisotropic constitutive matrix of the material at different positions is obtained.

[0110] The orthogonal anisotropic constitutive model is used in the embodiment.

[0111] The expressions of the stress tensor and the strain tensor of the solid constitutive equation are: .

[0112] .

[0113] In the formula, is the stress tensor, is the elastic stiffness tensor, is the strain tensor, is the first index symbol of the tensor component, is the second index symbol of the tensor component, is the third index symbol of the tensor component, is the fourth index symbol of the tensor component, is the partial derivative of the coordinate direction, is the vector of the displacement vector in the direction, is the partial derivative of the coordinate direction, is the vector of the displacement vector in the direction.

[0114] The value range of each index symbol is 1 to 6; wherein 1 to 3 correspond to the coordinate directions of the three-dimensional space respectively. 4 to 6 correspond to the three coordinate planes of the three-dimensional space respectively.

[0115] Based on the symmetry of the stress tensor and the strain tensor, the constitutive equation in the tensor form is expressed in the matrix form: .

[0116] In the formula, , and respectively represent the normal stress of the material in the direction. , and represent the shear stress of the material in the plane, plane and plane respectively. , and represent the normal strain of the material in the direction respectively. , and represent the shear strain of the material in the plane, plane and plane respectively. is the elastic elastic constant, the subscript rule is: is the corresponding normal stress response, is the corresponding shear stress response, is the corresponding normal strain influence, is the corresponding shear strain influence.

[0117] When the anisotropic constitutive model has three orthogonal elastic symmetry planes, it is an orthotropic anisotropic constitutive model: there is no coupling between the normal stress and the shear strain of the orthotropic anisotropic material, there is no coupling between the shear stress and the normal strain, and there is also no interaction between the shear stress and the shear strain in different planes.

[0118] Therefore, the relationship between stress and strain satisfies the following relationship: .

[0119] According to the relationship between stress and strain, the 6x6 constitutive matrix of the orthotropic anisotropic constitutive model is obtained:

[0120] In the formula, is the orthotropic anisotropic constitutive model, is the stiffness of the material along the direction, is the stiffness of the material along the direction, is the stiffness of the material along the direction, is the shear stiffness in the plane, is the shear stiffness in the plane, is the shear stiffness in the plane, are the stiffnesses of the material along the direction respectively direction and The direction is correct Contribution of stress in the direction, They are respectively The direction is correct direction and The direction is correct Contribution of stress in the direction, They are respectively The direction is correct direction and The direction is correct The contribution of stress in the direction.

[0121] Through the above technical solutions, this application achieves accurate characterization of the anisotropic behavior of materials in welding thermal stress calculation, effectively improves the accuracy of thermal stress distribution prediction, and provides a reliable mechanical analysis basis for welding process optimization. At the same time, this application can accurately reflect the influence of grain growth direction on material anisotropic behavior during welding, ensuring that the spatial correspondence between temperature gradient vector and grain orientation is accurately expressed in the finite element model, thereby improving the accuracy of welding thermal stress distribution simulation and providing a reliable calculation basis for optimizing welding process parameters.

[0122] S5. Loading the anisotropic constitutive model based on the temperature gradient vector: The constitutive matrix is ​​combined with the temperature gradient vector using the temperature gradient-anisotropic constitutive model loading algorithm to construct the final constitutive model. This final constitutive model can be used to calculate stiffness.

[0123] Specifically, the constitutive model established in this embodiment is The parameters are independent on the axis. shaft and The same parameters are observed on the axis. That is, the grain growth direction in the weld is determined in space. Axis, according to The axial vectors are chosen to be perpendicular to each other and with Orthogonal axis shaft and Axis, define the custom coordinate system.

[0124] Preferably, step S5 specifically includes steps S51 to S55.

[0125] S51. Construct the orthogonal anisotropic constitutive model as follows: The parameters are independent on the axis. shaft and The same parameters are displayed on the axis.

[0126] S52, Set the temperature gradient of the elements in the elasto-thermo-plastic model to... Select perpendicular to of and , the custom coordinate system is obtained. Specifically, as shown in Fig. 2 , is the natural coordinate system; the temperature gradient of the unit of the elastic-plastic model is set as .

[0127] Taking as the x-axis, an arbitrary coordinate system perpendicular to the x-axis is selected, as shown in Fig. 3 , the following can be obtained: .

[0128] S53, according to the included angle between the custom coordinate system and the natural coordinate system, a mapping relationship is obtained.

[0129] Table 1 mapping relationship between custom coordinate system and natural coordinate system

[0130] Specifically, let the included angle between the extension line of and the natural coordinate system axis be . Then: . Similarly, , can be obtained. Then the coordinate system can be converted into three-dimensional point coordinates ( , , ), and Table 1 is obtained.

[0131] S54, according to the mapping relationship, a conversion matrix of the constitutive model is constructed.

[0132] .

[0133] .

[0134] wherein, is the constitutive model finally loaded into the overall structure. is the conversion matrix. represents transposition. , and are the sizes of , and projected onto . , and are the sizes of , and projected onto . , and are respectively , and projected onto .

[0135] S55, according to , the stiffness matrix of the evolution unit is: ; wherein, is the stiffness matrix, is the integral operation, is the strain displacement matrix.

[0136] Through the above technical scheme, the application can accurately characterize the spatial correspondence relationship between the temperature gradient vector direction in the welding process and the anisotropic mechanical behavior of the material, effectively improve the accuracy of the thermal stress finite element calculation, provide a reliable anisotropic constitutive model loading method for welding process parameter optimization, and then realize the accurate spatial matching of the anisotropic constitutive model and the temperature gradient vector, significantly improve the simulation accuracy of the anisotropic behavior of the material in the welding thermal stress calculation, provide a reliable theoretical basis for the welding process optimization, and realize the accurate spatial matching of the anisotropic constitutive model and the temperature gradient vector, effectively avoid the distortion of the material response simulation caused by the deviation of the coordinate system, and significantly improve the accuracy of the welding thermal stress finite element calculation.

[0137] Embodiment two, the application provides a welding thermal stress finite element calculation device based on a temperature gradient vector, which comprises a model construction module, a temperature field module, a feature module, a matrix module and an updating module.

[0138] The model construction module is used for constructing an elastic-thermal plasticity model through a finite element model according to the parameter scale in the actual welding process.

[0139] The temperature field module is used for constructing the elastic-thermal plasticity model into a three-dimensional unstable state, and performing temperature field analysis to obtain temperature field data.

[0140] The feature module is used for analyzing the temperature field data to determine the temperature gradient vector, the welding process parameters and the key size features of each unit of the elastic-thermal plasticity model. The key size features include the penetration and the width.

[0141] The matrix module is used for performing grain distribution calculation in the welding process based on the anisotropic constitutive model, combining the key feature size and the welding process parameters, and obtaining the constitutive matrix at different positions by using the SPPARKS open source module.

[0142] An updating module is configured to combine the constitutive matrix and the temperature gradient vector to construct a final constitutive model by using a temperature gradient-anisotropy constitutive model loading algorithm, wherein the final constitutive model can be used to calculate stiffness.

[0143] In the third embodiment, the present application provides a temperature gradient vector based welding thermal stress finite element calculation device, which comprises a processor, a memory and a computer program stored in the memory. The computer program can be executed by the processor to implement the temperature gradient vector based welding thermal stress finite element calculation method according to any one of the first embodiment.

[0144] In the fourth embodiment, the present application provides a computer readable storage medium, which comprises a stored computer program. When the computer program is executed, the computer readable storage medium controls the device where the computer readable storage medium is located to execute the temperature gradient vector based welding thermal stress finite element calculation method according to any one of the first embodiment.

[0145] Obviously, the above described embodiments are only some but not all of the embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative efforts should fall into the scope of the present application.

[0146] In the several embodiments of the present application provided in the embodiments of the present application, it should be understood that the disclosed device and method can also be implemented in other manners. The person skilled in the art should understand that the described device and method embodiments are only illustrative, and the present application is not limited thereto. For example, the flowchart and block diagram in the accompanying drawings merely show the possible implementation modes of the device, method and computer program product according to the embodiments of the present application. In this regard, each block in the flowchart or block diagram can represent a module, a program segment or a part of code, which contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementation modes, the functions noted in the blocks can occur in different orders from those noted in the accompanying drawings. For example, two consecutive blocks can actually be executed in parallel, and sometimes they can be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, and the combination of blocks in the block diagram and / or flowchart, can be implemented by a dedicated hardware-based system for implementing the specified function or action, or can be implemented by a combination of dedicated hardware and computer instructions.

[0147] In addition, the function modules in each embodiment of the present application can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.

[0148] The functions described can be implemented in software, firmware, hardware, or any combination thereof. If implemented in software and as an independent application in a computing environment, the functions described can be stored in one or more of the storage devices, which can also be used to store files and other data related to the application function implementation. A storage device can be any available medium or memory or combination thereof adapted to store programming code in the form of computer readable instructions and / or data. Examples of storage devices include a read-only memory (ROM), a random-access memory (RAM), a magnetic disk, or an optical disk or tape. Further, the storage device can be integral to, or removable from, the computing device. As used herein, the term "memory" refers to both removable and non-removable storage devices.

[0149] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. The terms "comprises", "comprising", "including", and "having" used herein are specifically intended to be interpreted as "including, but not limited to".

[0150] It should be understood that the term "and / or" as used herein is merely an associative relationship of the associated objects, and means that there can be three relationships, for example, A and / or B, which means that there are three cases of A alone, A and B together, and B alone. In addition, the character " / " in this paper generally represents that the front and rear associated objects are a "or" relationship.

[0151] Depending on the context, the word "if" as used herein can be interpreted to mean "when" or "upon" or "in response to determining" or "in response to detecting." Similarly, the phrase "if it is determined" or "if [a stated condition or event] is detected" can be interpreted to mean "upon determining" or "in response to determining" or "upon detecting [the stated condition or event]" or "in response to detecting [the stated condition or event]."

[0152] The "first / second" mentioned in the embodiments only distinguishes similar objects, and does not represent a specific order for the objects. Understandably, the "first / second" can be interchanged in a specific order or sequence as appropriate. It should be understood that the objects distinguished by "first / second" can be interchanged as appropriate, so that the embodiments described herein can be implemented in an order other than those illustrated or described herein.

[0153] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. Various modifications and changes can be made to the present application by those skilled in the art. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A finite element method for calculating welding thermal stress based on temperature gradient vectors, characterized in that, Specifically, it includes: Based on the parameter scale in the actual welding process, an elastic-thermo-plastic model is constructed using the finite element model. The elasto-thermo-plastic model is constructed as a three-dimensional unstable state, and temperature field analysis is performed to obtain temperature field data. Analyzing temperature field data determines the temperature gradient vector, welding process parameters, and critical dimensional features of each element in the elasto-thermo-plastic model; among which, critical dimensional features include weld penetration and weld width. Based on the anisotropic constitutive model, the SPPARKS open-source module is used to calculate the grain distribution during the welding process by combining key feature dimensions and welding process parameters, and to obtain the constitutive matrix at different locations. The constitutive matrix is ​​combined with the temperature gradient vector using the temperature gradient-anisotropic constitutive model loading algorithm to construct the final constitutive model, which can be used to calculate stiffness.

2. The finite element method for calculating welding thermal stress based on temperature gradient vectors according to claim 1, characterized in that: The elasto-thermo-plastic model is constructed as a three-dimensional unstable state, and temperature field analysis is performed to obtain temperature field data, specifically including: The elasto-thermo-plastic model is constructed as a three-dimensional unsteady state; the differential equation for heat conduction in the three-dimensional unsteady state is: ;in, For density, For specific heat capacity, Thermal conductivity, For temperature, For time, For internal heat source, , and These represent the three coordinate directions of the elasto-thermo-plastic model. Represents partial derivatives; Temperature field analysis is performed to obtain temperature field data; in the temperature field analysis, the initial condition of the object is its initial temperature, expressed as: In the formula, For temperature, The initial temperature. For time.

3. The finite element method for calculating welding thermal stress based on temperature gradient vectors according to claim 1, characterized in that: When the element of the elasto-thermo-plastic model corresponding to the analyzed temperature field data is a triangular element: let the temperatures of the three vertices of the triangle be respectively... , and , If point is the centroid of the triangle, then the following definition applies: ； ； ； ； ； In the formula, The temperature of the centroid of the triangle. The vector from the centroid to the first vertex. The vector from the centroid to the second vertex. The vector from the centroid to the third vertex. , and These are the temperature gradients at the three vertices. The temperature gradient is represented by the triangular element.

4. The finite element method for calculating welding thermal stress based on temperature gradient vectors according to claim 1, characterized in that: When the element of the elasto-thermo-plastic model corresponding to the analyzed temperature field data is When using solid elements: Definition of the first The average temperature of each unit is: ； In the formula, For the first Average temperature of each unit For the number of nodes in the unit, For the numbering of unit nodes, For the first The first unit The global node number corresponding to each node Number the global nodes Temperature value at that location; according to Obtain the temperature gradient vector of the node; ； In the formula, For the first Temperature gradient vector of each node, For the first The position vector of each node relative to the centroid of the element; The average temperature gradient of the cell is obtained based on the temperature gradient vector of the node. ； In the formula, For the first The average temperature gradient vector of each unit.

5. The finite element method for calculating welding thermal stress based on temperature gradient vectors according to claim 4, characterized in that: Because the temperature at a certain point on the weldment changes continuously over time, two time points are introduced. and ; No. Each unit in At any given time, the temperature is above the liquidus line. The temperature is below the liquidus line at any given time, that is: ； ； In the formula, For the first Each unit in Temperature at any moment For the initial temperature, For the first Each unit is in Temperature at any moment The final temperature; Then, the first The temperature gradient vector of each element at the time of solidification is: ； in, For the first step in the welding process The grain growth vector direction of each unit For time difference, Temperature for a time difference The temperature represents the two time zones.

6. A finite element method for calculating welding thermal stress based on temperature gradient vectors according to any one of claims 1 to 5, characterized in that: Based on an anisotropic constitutive model, the SPPARKS open-source module is used, combined with key feature dimensions and welding process parameters, to calculate the grain distribution during the welding process and obtain the constitutive matrix at different locations, specifically including: The expressions for the stress tensor and strain tensor in the constitutive equation of a solid are: ； ； In the formula, For stress tensor, For elastic stiffness tensor, For strain tensor, The first index of the tensor component, The second index of the tensor component, The third index of the tensor component. The fourth index of the tensor component. for coordinates Partial derivatives of direction, For the displacement vector in Directional vector for coordinates Partial derivatives of direction, For the displacement vector in A vector of direction; Based on the symmetry of the stress tensor and strain tensor, the constitutive equation in tensor form is expressed in matrix form: ； In the formula, , and They respectively represent the materials in Normal stress in the direction; , and They respectively represent the materials in flat, plane and Shear stress in a plane; , and They respectively represent the materials in The positive strain in the direction; , and They respectively represent the materials in flat, plane and Shear strain in a plane; Where is the elastic constant. The subscript rules are as follows: To correspond to the normal stress response, To correspond to the shear stress response, To correspond to the effects of normal strain, To correspond to the influence of shear strain; An anisotropic constitutive model is an orthotropic constitutive model when it has three orthogonal elastic symmetry planes: In orthotropic materials, there is no coupling between normal stress and shear strain, no coupling between shear stress and normal strain, and no interaction between shear stress and shear strain in different planes. Therefore, the stress and strain satisfy the following relationship: ； Based on the relationship between stress and strain, the 6×6 constitutive matrix of the orthogonal anisotropic constitutive model is obtained: In the formula, For orthogonal anisotropic constitutive models, For materials along Stiffness in direction, For materials along Stiffness in direction, For materials along Stiffness in direction, for in-plane shear stiffness for in-plane shear stiffness for in-plane shear stiffness They are respectively The direction is correct direction and The direction is correct Contribution of stress in the direction, They are respectively The direction is correct direction and The direction is correct Contribution of stress in the direction, They are respectively The direction is correct direction and The direction is correct The contribution of stress in the direction.

7. The finite element method for calculating welding thermal stress based on temperature gradient vectors according to claim 6, characterized in that: The temperature gradient-anisotropic constitutive model loading algorithm combines the constitutive matrix with the temperature gradient vector to construct the final constitutive model, which specifically includes: The orthogonal anisotropic constitutive model is constructed as follows: The parameters are independent on the axis. shaft and The same parameters are observed on the axis; Set the temperature gradient of the elements in the elasto-thermo-plastic model to Select perpendicular to of and Get a custom coordinate system; Obtain the mapping relationship based on the angle between the custom coordinate system and the natural coordinate system; Based on the mapping relationship, construct the transformation matrix of the constitutive model; ； ； in, This is the constitutive model that is ultimately loaded into the overall structure; This is the transformation matrix; Indicates transpose; , and They are respectively , and Projected to Size on; , and They are respectively , and Projected to Size on; , and They are respectively , and Projected to Size on; according to Stiffness matrix of the building element: In the formula, For stiffness matrix, For integration operations, This is the strain-displacement matrix.

8. A finite element calculation device for welding thermal stress based on temperature gradient vector, characterized in that, Include: The model building module is used to construct an elastic-thermo-plastic model based on the parameter scale in the actual welding process using a finite element model. The temperature field module is used to construct the elasto-thermo-plastic model into a three-dimensional unstable state and perform temperature field analysis to obtain temperature field data. The feature module is used to analyze temperature field data to determine the temperature gradient vector, welding process parameters, and critical dimensional features of each element in the elasto-thermo-plastic model; among which, critical dimensional features include weld penetration and weld width. The matrix module is used to calculate the grain distribution during the welding process based on the anisotropic constitutive model, using the SPPARKS open-source module, combined with key feature dimensions and welding process parameters, to obtain the constitutive matrix at different locations; The update module is used to combine the constitutive matrix with the temperature gradient vector through the temperature gradient-anisotropic constitutive model loading algorithm to construct the final constitutive model, which can be used to calculate stiffness.

9. A finite element method for calculating welding thermal stress based on temperature gradient vectors, characterized in that, It includes a processor, a memory, and a computer program stored in the memory; the computer program can be executed by the processor to implement the finite element method for calculating welding thermal stress based on temperature gradient vectors as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored computer program, wherein, when the computer program is executed, it controls the device containing the computer-readable storage medium to perform the finite element calculation method for welding thermal stress based on any one of claims 1 to 7.

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