Numerical calculation method of multi-scale residual stress and application

Abstract

The invention discloses a numerical calculation method for multi-scale residual stress and application, and belongs to the technical field of residual stress analysis. The calculation method comprises the following steps: (1) according to the structure and the manufacturing process of a component sample, establishing a temperature field calculation model, respectively setting corresponding moving heat source models, and calculating the macroscopic temperature field distribution of the whole component through finite element simulation; (2) establishing a multi-physical mechanism macroscopic residual stress calculation model based on temperature-stress-microstructure coupling, and calculating a macroscopic stress field by using an indirect thermal-mechanical coupling method; and (3) establishing a multi-mechanism mesoscopic and microcosmic residual stress calculation model based on temperature-stress-microstructure coupling by utilizing a sub-model technology, and calculating mesoscopic and microcosmic stress fields. According to the method, microstructure evolution characteristics and macroscopic thermal boundary conditions in the component manufacturing process are coupled, a multi-scale residual stress calculation method based on a multi-physical mechanism is established, and the distribution rule of residual stress is researched from multiple scales.

Description

Technical Field

[0001] The present invention relates to the technical field of residual stress, and in particular to a numerical calculation method and application of multi-scale residual stress. Background Art

[0002] Welding, heat treatment, additive manufacturing, etc. are important manufacturing processes in modern industry, but components will inevitably produce complex residual stresses after processing. Generally speaking, non-uniform plastic deformation, temperature distribution and phase change process will cause macroscopic residual stress. Component deformation is the shape and position response of the evolution behavior of macroscopic residual stress, which will not only reduce the strength, stiffness and stability of the structure, but also may have a serious impact on structural fatigue, corrosion resistance and stress crack damage and processing accuracy; and the result of the performance difference between grains will lead to the generation of mesoscopic residual stress. Microscopic residual stress is a comprehensive reflection of local defects such as dislocations. Mesoscopic and microscopic residual stresses are the source of early creep, fatigue and other fracture damage and crack initiation, which can easily induce failure problems such as stress corrosion cracking and fatigue rupture. Whether in welding, heat treatment or additive manufacturing, accurate characterization of multi-scale residual stress distribution is of great significance to the high-reliability manufacturing and operation of components.

[0003] However, if the entire component is to be tested for the distribution of multi-scale residual stress, it is costly and difficult to sustain development. Therefore, a numerical calculation method for multi-scale residual stress is proposed to accurately and effectively predict and evaluate the residual stress distribution characteristics of different scales during the component manufacturing process. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides a numerical calculation method and application of multi-scale residual stress, which can be used for residual stress analysis in welding, post-weld heat treatment or additive manufacturing, accurately and effectively predict the distribution characteristics of residual stress at different scales in components, and then analyze the influence of residual stress on the mechanical properties and service life of components.

[0005] The technical solution adopted by the present invention is:

[0006] The present invention provides a numerical calculation method for multi-scale residual stress, comprising the steps of:

[0007] S1. According to the structure and manufacturing process of the component sample, a temperature field calculation model is established, and the corresponding mobile heat source model, thermal physical parameters, initial conditions, and boundary conditions are set respectively, and the macroscopic temperature field distribution of the entire component is calculated through finite element simulation;

[0008] S2. Using the indirect thermal-mechanical coupling method, the temperature field distribution obtained in step (1) is coupled as a temperature load to the calculation of the stress field, and a corresponding phase change model, a phase size calculation model, and a yield strength calculation model of phase content-element composition-grain size coupling are set to establish a multi-physical mechanism macro residual stress calculation model based on temperature-stress-microstructure coupling, and calculate the macro residual stress distribution through finite element simulation;

[0009] S3. Establish a micro-mesoscopic geometric model, and use the sub-model technology to calculate the temperature field of the micro-mesoscopic geometric area with the macroscopic temperature field model as the boundary. The sub-model temperature field result is used as the predefined field for the calculation of the mesoscopic and microscopic stress fields. Then, a variety of microscopic mechanism characteristics including dislocation slip, twinning, and phase change are coupled to establish a multi-physical mechanism mesoscopic and microscopic residual stress calculation model based on temperature-stress-microstructure coupling. Combined with the calibrated crystal plasticity parameters, three types of stress separation models are established, and the mesoscopic and microscopic residual stress distributions are calculated through finite element simulation.

[0010] Furthermore, the phase change model in step S2 needs to be set according to the material properties and manufacturing process of the component. If the component does not undergo phase change during the manufacturing process, there is no need to set the phase change model. If the component undergoes phase change during the manufacturing process, the corresponding phase change model is selected according to the phase change type.

[0011] The phase change model in step S2 includes:

[0012] During the heating process, the austenite volume fraction is calculated using the lever principle during the austenite phase transformation, namely:

[0013]

[0014] Among them, X A represents the volume fraction of austenite, A c1 Indicates the austenitization start temperature, A c3 Indicates the complete austenitization temperature, T indicates the real-time temperature;

[0015] During the cooling process, the phase transformation from austenite to ferrite is calculated using the classic JMAK equation for diffusion-type phase transformation, namely:

[0016] X F =1-exp(-ut F m )

[0017] Among them, X F represents the ferrite phase transformation fraction, t F represents the time from the phase transition temperature, u and m represent time-independent constants for the specific reaction, which depend on the nucleation, growth rate and activation energy used to determine the phase formation, calculated from the TTT curve;

[0018] The phase transformation from austenite to bainite adopts the bainite phase transformation mathematical model, namely:

[0019]

[0020] Among them, X B is the volume fraction of bainite, T represents the real-time temperature, and the variables a1, b1, c1, a2, b2, and c2 are the parameters of the function fitting;

[0021] The KM model is used for the phase transformation from austenite to martensite, namely:

[0022] X M =X r (1-exp(-κ·(Ms-T)))

[0023] Among them, X M is the volume fraction of martensite, X r is the volume fraction of retained austenite, T is the real-time temperature, Ms is the starting temperature of martensitic transformation, and K is a constant reflecting the martensitic transformation process;

[0024] The calculation formula of the phase size calculation model in step S2 is:

[0025]

[0026] in, is the grain size growth rate of the kth phase, A k , B k , C k is the material parameter of the kth phase, T is the real-time temperature, T 1k is the nose temperature of the TTT curve of the kth phase; the material constants in the above formula are solved by Matlab genetic algorithm toolbox to obtain the full phase transformation kinetic model to predict the phase ratio and grain size;

[0027] The yield strength calculation model in step S2 is:

[0028] σ s =σ PN +σ ss +σ gd

[0029]

[0030]

[0031]

[0032] Among them, σ s is the yield strength, σ PN , σss and σ gd are the contributions of lattice Penta force, solid solution elements and grain boundaries to yield strength; k is the serial number, X k is the volume fraction of the kth phase; K HP is the magnitude of the hindering effect of grain boundaries and phase boundaries.

[0033] Furthermore, in the stress field analysis process in step S2, the influence of temperature on component stress and strain is analyzed using thermoelastic-plastic theory and phase change theory;

[0034] When the component does not undergo phase change, the calculation formula for its total strain increment is:

[0035]

[0036] When a component undergoes phase change, the calculation formula for its total strain increment is:

[0037]

[0038] in, They are elastic strain increment, plastic strain increment, thermal strain increment, phase change strain increment and phase change plastic strain increment respectively.

[0039] Furthermore, the step S3 is specifically as follows:

[0040] S31, establish a micro-mesoscopic geometry sub-model, use the sub-model technology, take the macroscopic temperature field calculation model of step S2 as its global model, the thermophysical parameters when calculating the temperature field of the sub-model are consistent with those when calculating the macroscopic temperature field, restrict the degree of freedom of temperature of the overall sub-model, and calculate the temperature field of the sub-model through finite element simulation;

[0041] S32. Establish a micro-mesoscopic geometric model at the initial moment according to the actual microstructure morphology of the parent material, obtain the actual Euler angle corresponding to each grain according to the Realistic model calculated by DREAM.3D combined with the MATLAB script program, and assign the actual grain orientation to each grain through the Python script program;

[0042] S33. Based on nanoindentation experiments, obtain and assign microscopic crystal plasticity parameters of different phases, and establish a stress-strain curve relationship;

[0043] S34, based on the micro-mesoscopic geometric sub-model when calculating the temperature field of the sub-model in step S31, introduce a variety of microscopic mechanism characteristics including dislocation slip, twinning, and phase transformation of each phase, and establish a multi-mechanism plastic deformation constitutive model of coupled dislocation slip-twinning-phase transformation; use the sub-model temperature field result as a predefined field for mesoscopic and microscopic stress field calculation, use displacement boundaries to constrain each node around the model, transfer the boundary conditions of the sub-model at the corresponding position of the global model to the sub-model stress field calculation, and obtain the full stress distribution of the area to be tested by calculation;

[0044] S35. Establish a separation model for the three types of stresses, and write a subroutine to perform cloud map processing and analysis on the three types of stresses to obtain the distribution law of meso- and micro-scale residual stresses in the area to be tested.

[0045] Furthermore, the multi-mechanism plastic deformation constitutive model of coupled dislocation slip-twinning-phase transformation in step S34 is:

[0046]

[0047] Among them, k, α, β are serial numbers, N k is the total number of metallographic structures involved in the phase transformation, N α is the total number of slip systems in the kth phase, X k is the volume fraction of the kth phase, is the slip shear rate of the αth slip system in the kth phase, is the orientation tensor of the αth slip system in the kth phase. If the material has twinning behavior, N β is the total number of twin systems in the kth phase, is the twin shear rate of the β-th twin system in the k-th phase, is the orientation tensor of the β-th twin system in the k-th phase.

[0048] The above slip shear rate is expressed as:

[0049]

[0050] The above twin shear rate is expressed as:

[0051]

[0052] in, is the reference shear strain rate, w is the sensitivity coefficient, is the shear strain component on the αth slip system in the kth phase, is the slip resistance of the αth slip system in the kth phase; is the shear strain component on the β-th twin system in the k-th phase, is the slip resistance of the β-th twin system in the k-th phase.

[0053] Furthermore, the separation model of the three types of stress established in step S35 is:

[0054]

[0055]

[0056] σ J II =σ J II+III -σ J III

[0057] Where J is any node in the microscopic representative volume unit model, n is the total number of nodes, σ J I+II+III is the total stress at a specific node, σ J I , σ J II , σ J III They represent type I, II and III residual stresses respectively.

[0058] The present invention also provides an application of a multi-scale residual stress numerical simulation calculation method in analyzing residual stress in welding, post-weld heat treatment, arc additive manufacturing and selective laser melting additive manufacturing processes.

[0059] Furthermore, for a component sample prepared by welding, post-weld heat treatment or arc additive manufacturing process, step S1 is specifically as follows:

[0060] According to the structure of the component sample, a finite element model is established using ABAQUS software, and the corresponding mobile heat source model is set according to the actual morphology of the weld. The ABAQUS heat source subroutine is independently developed in combination with the mobile heat source model. The temperature field distribution during welding or arc additive manufacturing is obtained through finite element simulation. For post-weld heat treatment, the post-weld stress field is calculated based on the temperature field distribution of the welding process, and then the temperature amplitude curve is set according to the heat treatment process parameters on the basis of the post-weld stress field to perform heat treatment temperature field simulation and obtain the temperature field distribution of the post-weld heat treatment.

[0061] Furthermore, for a component sample manufactured by selective laser melting additive manufacturing, step S1 is specifically as follows:

[0062] S11. Use FLUENT software to establish a finite volume model based on a single-pass scanning area, set up a double ellipsoid heat source model that takes into account the reduction effect between the laser beam and the powder material, and write a UDF program that reflects the surface tension, recoil pressure, and convective and radiative heat transfer during temperature changes. Calculate the molten pool changes, temperature field distribution, and thermal cycle curves in the single-pass scanning area through fluid dynamics simulation;

[0063] S12. Based on the calculation results of the single-channel scanning area, a finite element model of a single-layer powder deposition layer consisting of a powder deposition layer and a substrate is established using ABAQUS software, and a corresponding equivalent heat source model is set to calculate the temperature field distribution and thermal cycle curve of the single-layer powder deposition layer through finite element simulation;

[0064] S13. A finite element model is established for the overall structure of the selective laser melting additively manufactured component, and the equivalent heat source model established in step S12 is introduced. Based on the calculation result of step S12, the heating-melting-cooling-solidification cycle is repeated until the entire macroscopic component is deposited to obtain the temperature field distribution of the overall component.

[0065] Furthermore, the double ellipsoid heat source model of the reduction effect between the laser beam and the powder material established in step S11 is:

[0066]

[0067] in, is the fraction of laser power consumed by powder particles, (1-η p ) is the reduction coefficient of the laser, η s is the material absorption rate, and the orthogonal coordinates x, y, and z represent the trajectory of the laser when melting the powder layer, respectively, and a, b, and c f , c r are the shape parameters of the heat source model, f f and f r is the distribution coefficient of heat source energy, f f +f r =2, use Ensure the continuity of heat source when z=0 for q(x, y, z, t), V is the cladding rate, t is the cladding time, and P is the cladding power;

[0068] In step S12, when establishing the equivalent heat source model, the ellipsoidal heat source is simplified to a rectangular parallelepiped heat source, the energy density of the body heat source in the single-channel simulation calculation is defined as the power density of the unit volume heat input, and the reduction factor considering the effects of laser and powder particles is introduced into the calculation of the unit volume power density to obtain the calculation model of the equivalent heat source model:

[0069]

[0070] Among them, d s is the diameter of the laser spot, H is the scanning width during single-channel scanning, d m is the thickness of a single powder deposition layer, the diameter of the laser spot, the scanning width during single-pass scanning, and the thickness of a single powder deposition layer are the length, width, and height of the simplified cuboid, respectively.

[0071] The beneficial effects of the present invention are:

[0072] (1) The present invention proposes a numerical calculation method for multi-scale residual stress. In the stress calculation process, the microstructural evolution characteristics such as dislocation slip, grain orientation, and dislocation density are coupled with macroscopic thermal boundary conditions, and corresponding phase change models, phase size calculation models, and yield strength calculation models coupled with phase content-element composition-grain size are set. A multi-scale residual stress calculation method based on physical mechanisms is established, and a separation model of macroscopic, mesoscopic, and microscopic multi-scale residual stresses is constructed. The distribution law of multi-scale residual stresses during welding and post-weld heat treatment or additive manufacturing is revealed, and the distribution characteristics of residual stresses of different scales in components can be accurately and effectively predicted, thereby analyzing the influence of residual stress on the mechanical properties and service life of components;

[0073] (2) The present invention proposes a numerical calculation method for multi-scale residual stress. For selective laser melting additively manufactured components, a laser selective melting cross-scale temperature field calculation model is established in the order of single-channel scanning area, single-layer powder deposition layer, and overall component during the temperature field calculation process. The mobile heat source model set in the temperature field calculation process of the single-channel scanning area introduces a reduction factor representing the interaction between the laser beam and the powder material, and takes into account the influence of fluid flow such as surface tension and recoil pressure that changes with the temperature gradient. It can accurately characterize and control the temperature change of the molten pool on the analysis of residual stress and improve the performance of the component. In the temperature field calculation of the single-layer powder deposition layer and the overall component, an equivalent heat source model is established. On the basis of ensuring the accuracy of the calculation results, the calculation time and cost are greatly reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] In order to clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0075] Figure 1 is a flow chart of the present invention;

[0076] Figure 2 It is a finite volume model of a single-channel scanning area in an embodiment of the present invention;

[0077] Figure 3 The thermal cycle curve of the center point of a single-channel scanning area in an embodiment of the present invention;

[0078] Figure 4 is a finite element model of a single powder deposition layer in an embodiment of the present invention;

[0079] Figure 5 is a finite element model of the overall component in the embodiment of the present invention;

[0080] Figure 6 It is a macro residual stress distribution cloud diagram of the integral component in the embodiment of the present invention;

[0081] Figure 7 A micro-mesoscopic residual stress test area diagram of an integral component in an embodiment of the present invention;

[0082] Figure 8 for Figure 7 The lateral, normal and longitudinal total stress distribution cloud diagrams of area A shown in FIG;

[0083] Fig. 9 for Figure 7 The lateral, normal and longitudinal total stress distribution cloud diagrams of a single grain in area A shown in FIG. DETAILED DESCRIPTION

[0084] The present invention provides a numerical calculation method and application of multi-scale residual stress. In order to make the purpose, technical solution and effect of the present invention clearer and more specific, the present invention is further described in detail below. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0085] The present invention is described in detail below with reference to the accompanying drawings.

[0086] Reference Figure 1 The present invention provides a numerical calculation method for multi-scale residual stress, comprising the following steps:

[0087] S1. According to the structure and manufacturing process of the component sample, a temperature field calculation model is established, and the corresponding mobile heat source model, thermal physical parameters, initial conditions, and boundary conditions are set respectively, and the macroscopic temperature field distribution of the entire component is calculated through finite element simulation;

[0088] S2. Using the indirect thermal-mechanical coupling method, the temperature field distribution obtained in step (1) is coupled as a temperature load to the calculation of the stress field, and a corresponding phase change model, a phase size calculation model, and a yield strength calculation model of phase content-element composition-grain size coupling are set to establish a multi-physical mechanism macro residual stress calculation model based on temperature-stress-microstructure coupling, and calculate the macro residual stress distribution through finite element simulation;

[0089] In step S2, the phase change model needs to be set according to the material properties and manufacturing process of the component. If the component does not undergo phase change during the manufacturing process, there is no need to set the phase change model. If the component undergoes phase change during the manufacturing process, the corresponding phase change model is selected according to the phase change type.

[0090] The phase change model in step S2 includes:

[0091] During the heating process, the austenite volume fraction is calculated using the lever principle during the austenite phase transformation, namely:

[0092]

[0093] Among them, X A represents the volume fraction of austenite, A c1 Indicates the austenitization start temperature, A c3 Indicates the complete austenitization temperature, T indicates the real-time temperature;

[0094] During the cooling process, the phase transformation from austenite to ferrite is calculated using the classic JMAK equation for diffusion-type phase transformation, namely:

[0095] X F =1-exp(--ttt F mm )

[0096] Among them, X F represents the ferrite phase transformation fraction, t F represents the time from the phase transition temperature, u and n represent time-independent constants for the specific reaction, which depend on the nucleation, growth rate and activation energy used to determine the phase formation, calculated from the TTT curve;

[0097] The phase transformation from austenite to bainite adopts the bainite phase transformation mathematical model, namely:

[0098]

[0099] Among them, X B is the volume fraction of bainite, T represents the real-time temperature, and the variables a1, b1, c1, a2, b2, and c2 are the parameters of the function fitting;

[0100] The KM model is used for the phase transformation from austenite to martensite, namely:

[0101] X M =X r (1-exp(-κ·(Ms-T)))

[0102] Among them, X M is the volume fraction of martensite, X r is the volume fraction of retained austenite, T is the real-time temperature, Ms is the starting temperature of martensitic transformation, and κ is a constant reflecting the martensitic transformation process;

[0103] The calculation formula of the phase size calculation model in step S2 is:

[0104]

[0105] Where k is a serial number, k = 1, 2, 3, 4, 5 represent austenite, ferrite, bainite, pearlite and martensite respectively. is the grain size growth rate of the kth phase, A k , B k , C k is the material parameter of the kth phase, T is the real-time temperature, T 1k is the nose temperature of the TTT curve of the kth phase; the material constants in the above formula are solved by Matlab genetic algorithm toolbox to obtain the full phase transformation kinetic model to predict the phase ratio and grain size;

[0106] The yield strength calculation model in step S2 is:

[0107] σ s =σ PN +σ ss +σ gd

[0108]

[0109]

[0110]

[0111] Among them, σ s is the yield strength, σ PN , σ ss and σ gd are the contributions of lattice Penta force, solid solution elements and grain boundaries to yield strength; k is the serial number, X k is the volume fraction of the kth phase; K HP is the magnitude of the hindering effect of grain boundaries and phase boundaries;

[0112] In the stress field analysis process in step S2, the influence of temperature on the stress and strain of the component is analyzed using the thermoelastic-plastic theory and the phase change theory;

[0113] When the component does not undergo phase change, the calculation formula for its total strain increment is:

[0114]

[0115] When a component undergoes phase change, the calculation formula for its total strain increment is:

[0116]

[0117] in, They are elastic strain increment, plastic strain increment, thermal strain increment, phase change strain increment and phase change plastic strain increment respectively;

[0118] S3. A micro-mesoscopic geometric model is established according to the microstructure morphology of the test area of ​​the component specimen. The temperature field of the micro-mesoscopic geometric area is calculated by using the sub-model technology with the macroscopic temperature field model as the boundary, and the sub-model temperature field result is used as a predefined field for calculating the mesoscopic and microscopic stress fields. Then, a multi-physical mechanism feature including dislocation slip, twinning, and phase change is coupled to establish a multi-physics mechanism mesoscopic and microscopic residual stress calculation model based on temperature-stress-microstructure coupling, and three types of stress separation models are established in combination with the calibrated crystal plasticity parameters. The mesoscopic and microscopic residual stress distributions are calculated by finite element simulation. The specific steps of step S3 are as follows:

[0119] S31, establish a micro-mesoscopic geometry sub-model, use the sub-model technology, take the macroscopic temperature field calculation model of step S2 as its global model, the thermophysical parameters when calculating the temperature field of the sub-model are consistent with those when calculating the macroscopic temperature field, restrict the degree of freedom of temperature of the overall sub-model, and calculate the temperature field of the sub-model through finite element simulation;

[0120] S32. Establish a micro-mesoscopic geometric model at the initial moment according to the actual microstructure morphology of the parent material, obtain the actual Euler angle corresponding to each grain according to the Realistic model calculated by DREAM.3D combined with the MATLAB script program, and assign the actual grain orientation to each grain through the Python script program;

[0121] S33. Based on nanoindentation experiments, obtain and assign microscopic crystal plasticity parameters of different phases, and establish a stress-strain curve relationship;

[0122] S34, based on the micro-mesoscopic geometric sub-model when calculating the temperature field of the sub-model in step S31, introduce a variety of microscopic mechanism characteristics including dislocation slip, twinning, and phase transformation of each phase, and establish a multi-mechanism plastic deformation constitutive model of coupled dislocation slip-twinning-phase transformation; use the sub-model temperature field result as a predefined field for mesoscopic and microscopic stress field calculation, use displacement boundaries to constrain each node around the model, transfer the boundary conditions of the sub-model at the corresponding position of the global model to the sub-model stress field calculation, and obtain the full stress distribution of the area to be tested by calculation;

[0123] The above-mentioned multi-mechanism plastic deformation constitutive model of coupled dislocation slip-twinning-phase transformation is:

[0124]

[0125] Among them, k, α, β are serial numbers, N k is the total number of metallographic structures involved in the phase transformation, N α is the total number of slip systems in the kth phase, X k is the volume fraction of the kth phase, is the slip shear rate of the αth slip system in the kth phase, is the orientation tensor of the αth slip system in the kth phase. If the material has twinning behavior, N β is the total number of twin systems in the kth phase, is the twin shear rate of the β-th twin system in the k-th phase, is the orientation tensor of the β-th twin system in the k-th phase.

[0126] The above slip shear rate is expressed as:

[0127]

[0128] The above twin shear rate is expressed as:

[0129]

[0130] in, is the reference shear strain rate, w is the sensitivity coefficient, is the shear strain component on the αth slip system in the kth phase, is the slip resistance of the αth slip system in the kth phase; is the shear strain component on the β-th twin system in the k-th phase, is the slip resistance of the β-th twin system in the k-th phase;

[0131] S35. Establish a separation model for the three types of stresses, and write a subroutine to perform cloud map processing and analysis on the three types of stresses to obtain the distribution law of mesoscopic and microscopic residual stresses in the area to be tested; the separation model for the above three types of stresses is:

[0132]

[0133]

[0134] σ J II =σ J II+III -σ J III

[0135] Where J is any node in the microscopic representative volume unit model, n is the total number of nodes, σ J I+II + III is the total stress at a specific node, σ J I , σ J II , σ J III They represent type I, II and III residual stresses respectively.

[0136] The above method can be used to analyze the residual stresses in welding, post-weld heat treatment, arc additive manufacturing and selective laser melting additive manufacturing processes from macroscopic, mesoscopic and microscopic perspectives.

[0137] Example

[0138] In this example, an Inconel 718 specimen made by selective laser melting additive manufacturing technology was used as the research object, and a multi-scale residual stress analysis was performed on it.

[0139] In the preparation process of Inconel 718 specimens made by selective laser melting additive manufacturing technology, 45 steel was selected for the substrate, and the cladding material was Inconel 718 powder particles with a particle size of 10-65μm; the process parameters used in selective laser melting additive manufacturing were: scanning speed of 1000mm / s, laser power of 260W, single-layer powder thickness of 40μm, and laser diameter of 100μm; the specimen structure mainly consisted of a substrate and several layers of powder deposition layers, the deposition layer was located in the middle position above the substrate, the substrate size was 250mm×250mm×42mm (x×y×z), the deposition layer size formed after cladding was 100mm×15mm×20mm (x×y×z), with a total of 500 layers and 75,000 scanning paths.

[0140] The steps of performing multi-scale residual stress analysis on Inconel 718 specimens in this embodiment are as follows:

[0141] S1. According to the structure and manufacturing process of the selective laser melting additive manufacturing component, the laser selective melting cross-scale temperature field calculation model for the single-pass scanning area, single-layer powder deposition layer, and overall component is established in sequence, and the corresponding heat source model, thermophysical property parameters, initial conditions, and boundary conditions are set respectively. The macroscopic temperature field distribution of the overall component is calculated through finite element simulation. The above-mentioned overall component is a component composed of several layers of powder deposition layers.

[0142] The step S1 specifically includes temperature field calculation of a single-channel scanning area, temperature field calculation of a single-layer powder deposition layer, and temperature field calculation of an entire component.

[0143] S11. The temperature field calculation process of the single-channel scanning area is as follows:

[0144] (1) Use Fluent software to establish a finite volume model based on a single-channel scanning area;

[0145] A physical model consisting of an argon protective layer and an Inconel 718 powder deposition layer is established, such as Figure 2 As shown, the size of the argon protective layer is 0.5mm×0.4mm×20mm(x×y×z), and the size of the single-pass powder deposition layer is 0.5mm×0.8mm×20mm(x×y×z). Then the mesh is divided, and after mesh independence analysis, the mesh size is determined to be 0.25mm×0.02mm×0.02mm.

[0146] (2) A double ellipsoid heat source model is set up to consider the reduction effect between the laser beam and the powder material, and a UDF program is written to reflect the surface tension, recoil pressure, and convective heat transfer and radiation heat transfer during the temperature change process. It is compiled into the model calculation in the form of energy source phase and momentum source phase, and a single-channel scanning area molten pool and temperature field calculation model is established. The molten pool change, temperature field distribution and thermal cycle curve of the single-channel scanning area are calculated through fluid dynamics simulation. The thermal cycle curve of the center point of the single-channel scanning area is as follows: Figure 3 shown.

[0147] The double ellipsoid heat source model established above considering the reduction effect between the laser beam and the powder material is:

[0148]

[0149] Among them, q(x, y, z, t) is the heat source energy, is the fraction of laser power consumed by powder particles, Q P is the laser energy consumed by the powder particles, (1-η p ) is the reduction coefficient of the laser, η s is the material absorption rate, and the orthogonal coordinates x, y, and z represent the trajectory of the laser when melting the powder layer, respectively, and a, b, and cf , c r are the shape parameters of the heat source model, f f and f r is the distribution coefficient of heat source energy, f f +f r =2, use Ensure the continuity of the heat source when z=0 for q(x, y, z, t), V is the cladding rate, t is the cladding time, and P is the cladding power.

[0150] S12. The temperature field calculation process of a single-layer powder deposition layer is as follows:

[0151] (1) Based on the calculation results of the single-channel scanning area, a finite element model consisting of a single-layer powder deposition layer and a substrate was established using ABAQUS software; that is:

[0152] The 2D finite element model was established using ABAQUS calculation software. The model consists of a powder deposition layer and a substrate. Figure 4 As shown, the size of the powder deposition layer is 15 mm × 0.04 mm (x × y), and the size of the substrate is 250 mm × 42 mm (x × y). Then, the finite element mesh is divided, the unit type is DC2D4, and the mesh is encrypted in the powder deposition layer and the substrate near the powder deposition layer;

[0153] (2) Based on the calculation results of the single-channel scanning area, the ellipsoidal heat source is simplified into a rectangular heat source, where the length, width, and height are the diameter of the laser spot, the scanning width during single-channel scanning, and the thickness of a single-layer powder deposition layer, respectively. The energy density of the body heat source during the single-channel simulation calculation is defined as the power density of the heat input per unit volume. The reduction factor considering the effects of laser and powder particles is introduced into the calculation of the power density per unit volume, and an equivalent heat source model is established.

[0154] The calculation formula of the above equivalent heat source model is:

[0155]

[0156] Among them, q is the equivalent heat source energy, d s is the diameter of the laser spot, H is the scanning width during single-channel scanning, d m is the thickness of a single powder deposition layer, the diameter of the laser spot, the scanning width during single-pass scanning, and the thickness of a single powder deposition layer are the length, width, and height of the simplified cuboid, respectively;

[0157] S13. The specific calculation process of the temperature field of the overall component is as follows:

[0158] (1) Use ABAQUS calculation software to establish a two-dimensional model of the entire macro specimen, such as Figure 5As shown, the size of the powder deposition layer is 15mm×20mm (x×y), and the size of the substrate is 250mm×42mm (x×y). Then the finite element mesh is divided. The density of the mesh unit near the deposition layer is relatively high, and the density of the mesh unit at the substrate is relatively low. The unit type is DC2D4. According to the multi-layer and multi-channel characteristics of selective laser melting additive manufacturing, the birth and death unit technology is used to realize its real deposition process.

[0159] (2) Introduce the equivalent heat source model established in step S12, and based on the calculation result of step S12, repeat the cycle process of heating melting-cooling solidification until the entire macro component is deposited, and obtain the macro temperature field distribution and thermal cycle curve of the entire component.

[0160] S2. Using the indirect thermal-mechanical coupling method, the macroscopic temperature field distribution of the overall component obtained in step S1 is coupled to the calculation of the stress field as a temperature load, and the corresponding phase change model, phase size calculation model, phase content-element composition-grain size coupled yield strength calculation model are set, and a multi-physical mechanism macroscopic residual stress calculation model based on temperature-stress-microstructure coupling is established, and the macroscopic residual stress distribution is calculated by finite element simulation.

[0161] The macroscopic residual stress distribution cloud diagram obtained in this step is as follows Figure 6 shown.

[0162] Specifically, the phase change model in the above step S2, specifically the Inconel 718 material in this embodiment is an austenite structure during the selective laser melting additive manufacturing process, and does not involve a phase change process. Therefore, there is no need to set a related phase change model in this step.

[0163] The phase size calculation model in the above step S2 is based on the free energy theory in the continuous cooling process, and is obtained according to the nucleation activation energy and growth activation energy required for grain growth. The phase size calculation model is used to calculate the grain size growth rate, and the calculation formula is:

[0164]

[0165] in, is the grain size growth rate, A1, B1, C1 are material parameters, T is the real-time temperature, T 11 is the nose temperature of the TTT curve; the material constants in the above formula are solved using the Matlab Genetic Algorithm Toolbox to predict the phase ratio and grain size.

[0166] The yield strength calculation model in the above step S2 is:

[0167] σ s =σ PN +σ ss+σ gd

[0168]

[0169]

[0170]

[0171] Among them, σ s is the yield strength, σ PN , σ ss and σ gd are the contributions of lattice Penta force, solid solution elements and grain boundaries to yield strength; X1 is the volume fraction of austenite phase; K HP is the magnitude of the hindering effect of grain boundaries and phase boundaries.

[0172] In the stress field analysis process in the above step S2, the thermoelastic-plastic theory and the phase change theory are used to analyze the influence of temperature on the stress and strain of the component. Specifically, the Inconel 718 material in this embodiment does not involve a phase change process during the selective laser melting additive manufacturing process, and the calculation formula for its total strain increment is:

[0173]

[0174] In addition, for the above Figure 6 The macroscopic residual stress distribution diagram shown in the figure is analyzed, where (a), (b), and (c) are the residual stress distribution cloud diagrams of the transverse, normal, and longitudinal directions of the integral component, respectively. It can be seen from the figure that: there is a large stress concentration at the connection between the substrate and the integral component, where cracks are prone to occur; the transverse residual stress is manifested as a large compressive stress state in the central area of ​​the connection between the substrate and the integral component, that is, the bottom of the integral component, and as a tensile stress state in the upper central area of ​​the integral component. The component as a whole shows a balanced "tension-compression-tension" trend; the maximum normal residual stress still exists at the connection between the integral component and the substrate, where there is a certain stress concentration, and the center of the integral component shows a large compressive stress state; the longitudinal residual stress is manifested as a tensile stress state on the integral component, and the residual stress at the outer edge of the integral component is greater than the residual stress in the central area. There is also a sudden change in stress at the connection between the substrate and the integral component. In the substrate area, except for a certain tensile stress at the connection with the integral component, other areas show a small compressive stress or even a stress-free state.

[0175] S3. Establish a micro-mesoscopic geometric model, and use the sub-model technology to calculate the temperature field of the micro-mesoscopic geometric area with the macroscopic temperature field model as the boundary. The sub-model temperature field result is used as the predefined field for the calculation of the mesoscopic and microscopic stress fields. Then, a variety of microscopic mechanism characteristics including dislocation slip are coupled to establish a multi-physical mechanism mesoscopic and microscopic residual stress calculation model based on temperature-stress-microstructure coupling. Combined with the calibrated crystal plasticity parameters, three types of stress separation models are established, and the mesoscopic and microscopic residual stress distributions are calculated through finite element simulation.

[0176] The specific steps of step S3 are:

[0177] S31. Establish a micro-mesoscopic geometry sub-model according to the microstructure morphology of the test area of ​​the component sample, that is, use the EBSD test to test the microstructure of the test area, and then use the DREAM.3D software to generate a Realistic model to obtain the micro-mesoscopic geometry sub-model, and then use the sub-model technology to use the macroscopic temperature field calculation model of step S2 as its global model. The thermophysical parameters when calculating the temperature field of the sub-model are consistent with those when calculating the macroscopic temperature field. The degree of freedom of temperature is restricted for the overall sub-model, and the temperature field of the sub-model is calculated by finite element simulation;

[0178] S32. According to the actual microstructure morphology of the parent material (i.e., Inconel 718 alloy), a micro-mesoscopic geometric model at the initial moment is established, and the actual Euler angle corresponding to each grain is obtained according to the Realistic model calculated by DREAM.3D combined with the MATLAB script program, and the actual grain orientation of each grain is given by the Python script program;

[0179] S33. Based on the nanoindentation experiment, microscopic crystal plastic parameters are obtained and assigned, and a stress-strain curve relationship is established; specifically, for obtaining the crystal plastic material parameters, the stress-strain curve obtained by the macroscopic tensile test is compared with the stress-strain result obtained by uniaxial tensile calculation of the crystal plastic finite element, and the required crystal plastic material parameters are fitted;

[0180] S34, based on the micro-mesoscopic geometry sub-model when calculating the temperature field of the sub-model in step S31, introduce microscopic mechanism characteristics including dislocation slip, and establish a plastic deformation constitutive model of coupled dislocation slip; use the sub-model temperature field result as a predefined field for mesoscopic and microscopic stress field calculations, use displacement boundaries to constrain the nodes around the model, and transfer the boundary conditions of the sub-model at the corresponding position of the global model to the sub-model stress field calculation, and obtain the full stress distribution of the area to be tested by calculation; the plastic deformation constitutive model established in this step is:

[0181] The separation model of three types of stress is established to obtain the distribution law of mesoscopic and microscopic residual stress in the tested area. The separation model of three types of stress is:

[0182]

[0183]

[0184] σ J II =σ J II+III -σ J III .

[0185] Reference Figure 7 , the residual stress of area A of the overall component is simulated, and the simulation results are as follows Figure 8 , 9 shown. Figure 8 It is the total stress distribution cloud diagram of the transverse, normal and longitudinal sub-models in area A. Figure 8 It can be seen that due to the different grain morphologies and grain orientations in each region, the distribution of residual stress in the sub-model is significantly uneven, and there are stress concentrations and mutations at some grain boundaries. These areas are dangerous areas that are prone to intergranular microcracks.

[0186] In addition, due to the influence of grain orientation, dislocation slip, lattice distortion, etc., the residual stress not only changes at the grain boundaries at the mesoscopic scale, but also has an uneven stress distribution inside most grains. Fig. 9 The single grain in the area with the largest residual stress distribution density is analyzed. Fig. 9 It is the total stress distribution cloud diagram of the transverse, normal and longitudinal directions of a single grain in area A. Fig. 9 It can be seen that there are also non-uniform residual stresses and certain stress concentration phenomena in a single grain, which will cause certain non-uniform deformation of the grain. On the one hand, it may be due to the slip of dislocations on specific slip planes in the grains, lattice distortion and rigid torsion. On the other hand, it may be caused by the different grain orientations of adjacent grains and their interaction.

[0187] In addition, from Figure 6 The data of type I residual stress can be obtained from the macroscopic stress distribution cloud map. Figure 8 and Fig. 9 The data of residual stresses of types I, II and III can be obtained from the full stress distribution cloud map. Using the separation model of the above three types of stress, Figure 8 or Fig. 9 The total stress in is separated to obtain the type II and type III residual stresses, that is, the distribution law of meso- and micro-scale residual stresses is obtained.

[0188] The above-mentioned multi-scale residual stress numerical simulation analysis method can be used for residual stress analysis in selective laser melting additive manufacturing, as well as residual stress analysis in welding or post-weld heat treatment or arc additive manufacturing. The main difference between residual stress analysis in welding, post-weld heat treatment or arc additive manufacturing and residual stress analysis in selective laser melting additive manufacturing is that the temperature field calculation process in step S1 is different. The temperature field calculation process is relatively simple, and the subsequent residual stress calculation steps are the same, but it is necessary to set the corresponding phase change model according to the material properties and manufacturing process of the component. The temperature field calculation process is as follows: a finite element model is established using ABAQUS software according to the structure of the component sample, a corresponding mobile heat source model is set according to the actual morphology of the weld, and an ABAQUS heat source subroutine is independently developed in combination with the mobile heat source model. The temperature field distribution during welding or arc additive manufacturing is obtained through finite element simulation; for post-weld heat treatment, it is necessary to first calculate the welding temperature field, and then calculate the post-weld stress field based on the welding temperature field distribution, and then, based on the post-weld stress field, set the temperature amplitude curve according to the heat treatment process parameters to simulate the heat treatment temperature field to obtain the temperature field distribution of the post-weld heat treatment.

[0189] It should be noted that some parts not described in the present invention can be implemented by adopting or drawing on existing technologies.

[0190] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A numerical calculation method for multi-scale residual stress, characterized in that: Includes steps: S1. According to the structure and manufacturing process of the component sample, a temperature field calculation model is established, and the corresponding mobile heat source model, thermal physical parameters, initial conditions, and boundary conditions are set respectively, and the macroscopic temperature field distribution of the entire component is calculated through finite element simulation; S2. Using the indirect thermal-mechanical coupling method, the temperature field distribution obtained in step (1) is coupled as a temperature load to the calculation of the stress field, and a corresponding phase change model, a phase size calculation model, and a yield strength calculation model of phase content-element composition-grain size coupling are set to establish a multi-physical mechanism macro residual stress calculation model based on temperature-stress-microstructure coupling, and calculate the macro residual stress distribution through finite element simulation; S3. Establish a micro-mesoscopic geometric model, and use the sub-model technology to calculate the temperature field of the micro-mesoscopic geometric area with the macroscopic temperature field model as the boundary. The sub-model temperature field result is used as the predefined field for the calculation of the mesoscopic and microscopic stress fields. Then, a variety of microscopic mechanism characteristics including dislocation slip, twinning, and phase change are coupled to establish a multi-physical mechanism mesoscopic and microscopic residual stress calculation model based on temperature-stress-microstructure coupling. Combined with the calibrated crystal plasticity parameters, three types of stress separation models are established, and the mesoscopic and microscopic residual stress distributions are calculated through finite element simulation.

2. The numerical calculation method of multi-scale residual stress according to claim 1 is characterized in that: The phase change model in step S2 needs to be set according to the material properties and manufacturing process of the component. If the component does not undergo phase change during the manufacturing process, there is no need to set the phase change model. If the component undergoes phase change during the manufacturing process, the corresponding phase change model is selected according to the phase change type. The phase change model in step S2 includes: During the heating process, the austenite volume fraction is calculated using the lever principle during the austenite phase transformation, namely: Among them, X A represents the volume fraction of austenite, A c1 Indicates the austenitization start temperature, A c3 Indicates the complete austenitization temperature, T indicates the real-time temperature; During the cooling process, the phase transformation from austenite to ferrite is calculated using the classic JMAK equation for diffusion-type phase transformation, namely: X F =1-exp(-out f m ) Among them, X F represents the ferrite phase transformation fraction, t F represents the time from the phase transition temperature, u and m represent time-independent constants for the specific reaction, which depend on the nucleation, growth rate and activation energy used to determine the phase formation, calculated from the TTT curve; The phase transformation from austenite to bainite adopts the bainite phase transformation mathematical model, namely: Among them, X B is the volume fraction of bainite, T represents the real-time temperature, and the variables a1, b1, c1, a2, b2, and c2 are the parameters of the function fitting; The KM model is used for the phase transformation from austenite to martensite, namely: X M =X r (1-exp(-κ·(Ms-T))) Among them, X M is the volume fraction of martensite, X r is the volume fraction of retained austenite, T is the real-time temperature, Ms is the starting temperature of martensitic transformation, and κ is a constant reflecting the martensitic transformation process; The calculation formula of the phase size calculation model in step S2 is: Among them, k is the sequence number, is the grain size growth rate of the kth phase, A k , B k , C k is the material parameter of the kth phase, T is the real-time temperature, T 1k is the nose temperature of the TTT curve of the kth phase; The yield strength calculation model in step S2 is: s s =s PN +s ss +s gd Among them, σ s is the yield strength, σ PN , σ ss and σ gd are the contributions of lattice Penta force, solid solution elements and grain boundaries to yield strength; k is the serial number, X k is the volume fraction of the kth phase; K HP is the magnitude of the hindering effect of grain boundaries and phase boundaries.

3. The numerical calculation method of multi-scale residual stress according to claim 1, characterized in that: In the stress field analysis process in step S2, the influence of temperature on component stress and strain is analyzed using thermoelastic-plastic theory and phase change theory; When the component does not undergo phase change, the calculation formula for its total strain increment is: When a component undergoes phase change, the calculation formula for its total strain increment is: in, They are elastic strain increment, plastic strain increment, thermal strain increment, phase change strain increment and phase change plastic strain increment respectively.

4. The numerical calculation method of multi-scale residual stress according to claim 1, characterized in that: The step S3 is specifically as follows: S31, establish a micro-mesoscopic geometry sub-model, use the sub-model technology, take the macroscopic temperature field calculation model of step S2 as its global model, the thermophysical parameters when calculating the temperature field of the sub-model are consistent with those when calculating the macroscopic temperature field, restrict the degree of freedom of temperature of the overall sub-model, and calculate the temperature field of the sub-model through finite element simulation; S32. Establish a micro-mesoscopic geometric model at the initial moment according to the actual microstructure morphology of the parent material, obtain the actual Euler angle corresponding to each grain according to the Realistic model calculated by DREAM.3D combined with the MATLAB script program, and assign the actual grain orientation to each grain through the Python script program; S33. Based on nanoindentation experiments, obtain and assign microscopic crystal plasticity parameters of different phases, and establish a stress-strain curve relationship; S34, based on the micro-mesoscopic geometric sub-model when calculating the temperature field of the sub-model in step S31, introduce a variety of microscopic mechanism characteristics including dislocation slip, twinning, and phase transformation of each phase, and establish a multi-mechanism plastic deformation constitutive model of coupled dislocation slip-twinning-phase transformation; use the sub-model temperature field result as a predefined field for mesoscopic and microscopic stress field calculation, use displacement boundaries to constrain each node around the model, transfer the boundary conditions of the sub-model at the corresponding position of the global model to the sub-model stress field calculation, and obtain the full stress distribution of the area to be tested by calculation; S35. Establish a separation model of three types of stresses to obtain the distribution law of mesoscopic and microscopic residual stresses in the area to be tested.

5. The numerical calculation method of multi-scale residual stress according to claim 4 is characterized in that: The multi-mechanism plastic deformation constitutive model of coupled dislocation slip-twinning-phase transformation in step S34 is: Among them, k, α, β are serial numbers, N k is the total number of metallographic structures involved in the phase transformation, N α is the total number of slip systems in the kth phase, X k is the volume fraction of the kth phase, is the slip shear rate of the αth slip system in the kth phase, is the orientation tensor of the αth slip system in the kth phase. If the material has twinning behavior, N β is the total number of twin systems in the kth phase, is the twin shear rate of the β-th twin system in the k-th phase, is the orientation tensor of the β-th twin system in the k-th phase. The slip shear rate is expressed as: The twin shear rate is expressed as: in, is the reference shear strain rate, w is the sensitivity coefficient, is the shear strain component on the αth slip system in the kth phase, is the slip resistance of the αth slip system in the kth phase; is the shear strain component on the β-th twin system in the k-th phase, is the slip resistance of the β-th twin system in the k-th phase.

6. The method for numerical calculation of multi-scale residual stress according to claim 4, characterized in that: The separation model of the three types of stress established in step S35 is: s J Ⅱ =s J Ⅱ+Ⅲ -s J Ⅲ Where J is any node in the microscopic representative volume unit model, n is the total number of nodes, σ J Ⅰ+Ⅱ+Ⅲ is the total stress at a specific node, σ J Ⅰ , σ J Ⅱ , σ J Ⅲ They represent type I, II and III residual stresses respectively.

7. Application of a multi-scale residual stress numerical simulation calculation method as described in any one of claims 1 to 6 in analyzing residual stress in welding, post-weld heat treatment, arc additive manufacturing and selective laser melting additive manufacturing processes.

8. The use according to claim 7, characterized in that: For a component sample prepared by welding, post-weld heat treatment or arc additive manufacturing process, step S1 is specifically as follows: According to the structure of the component sample, a finite element model is established using ABAQUS software, and the corresponding mobile heat source model is set according to the actual morphology of the weld. The ABAQUS heat source subroutine is independently developed in combination with the mobile heat source model. The temperature field distribution during welding or arc additive manufacturing is obtained through finite element simulation. For post-weld heat treatment, the post-weld stress field is calculated based on the temperature field distribution of the welding process, and then the temperature amplitude curve is set according to the heat treatment process parameters on the basis of the post-weld stress field to perform heat treatment temperature field simulation and obtain the temperature field distribution of the post-weld heat treatment.

9. The use according to claim 7, characterized in that: For a component sample manufactured by selective laser melting additive manufacturing, step S1 is specifically as follows: S11. Use FLUENT software to establish a finite volume model based on a single-pass scanning area, set up a double ellipsoid heat source model that takes into account the reduction effect between the laser beam and the powder material, and write a UDF program that reflects the surface tension, recoil pressure, and convective and radiative heat transfer during temperature changes. Calculate the molten pool changes, temperature field distribution, and thermal cycle curves in the single-pass scanning area through fluid dynamics simulation; S12. Based on the calculation results of the single-channel scanning area, a finite element model of a single-layer powder deposition layer consisting of a powder deposition layer and a substrate is established using ABAQUS software, and a corresponding equivalent heat source model is set to calculate the temperature field distribution and thermal cycle curve of the single-layer powder deposition layer through finite element simulation; S13. A finite element model is established for the overall structure of the selective laser melting additively manufactured component, and the equivalent heat source model established in step S12 is introduced. Based on the calculation result of step S12, the heating-melting-cooling-solidification cycle is repeated until the entire macroscopic component is deposited to obtain the temperature field distribution of the overall component.

10. The use according to claim 9, characterized in that: The double ellipsoid heat source model of the reduction effect between the laser beam and the powder material established in step S11 is: in, is the fraction of laser power consumed by powder particles, (1-η p ) is the reduction coefficient of the laser, η s is the material absorption rate, and the orthogonal coordinate system x, y, and z represent the trajectory of the laser when melting the powder layer, respectively, and a, b, and c f ,c r are the shape parameters of the heat source model, f f and f r is the distribution coefficient of heat source energy, f f +f r =2, use Ensure the continuity of heat source when z=0 for q(x,y,z,t), V is the cladding rate, t is the cladding time, and P is the cladding power; In step S12, when establishing the equivalent heat source model, the ellipsoidal heat source is simplified to a rectangular parallelepiped heat source, the energy density of the body heat source in the single-channel simulation calculation is defined as the power density of the unit volume heat input, and the reduction factor considering the effects of laser and powder particles is introduced into the calculation of the unit volume power density to obtain the calculation model of the equivalent heat source model: Among them, d s is the diameter of the laser spot, H is the scanning width during single-channel scanning, d m is the thickness of a single powder deposition layer, the diameter of the laser spot, the scanning width during single-pass scanning, and the thickness of a single powder deposition layer are the length, width, and height of the simplified cuboid, respectively.

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