Crystal plasticity constitutive model construction method based on density characteristics

Abstract

The invention relates to the field of power module reliability evaluation, and particularly discloses a crystal plasticity constitutive model construction method based on density characteristics, and the method comprises the steps: S1, correcting an initial value and a saturation value of critical decomposition shear stress through a correction coefficient; s2, taking the initial value and the saturation value of the corrected critical decomposition shear stress obtained in the step S1 as parameters, substituting the parameters into a hardening law of a crystal plasticity constitutive model, and establishing the crystal plasticity constitutive model based on density characteristics; and S3, based on the crystal plasticity constitutive model established in the step S2, performing simulation in finite element software, and calculating and outputting a mechanical property prediction result of the material by inputting values of different density characteristic parameters and a macroscopic shear strain rate. According to the method, the influence of the manufacturing process uncertainty on the mechanical property of the packaging interconnection material is effectively quantified by introducing the density characteristic parameters, and the accuracy of simulation analysis is improved.

Description

Technical Field

[0001] This invention relates to the field of power module reliability assessment, and in particular to a method for constructing a crystal plastic constitutive model based on density characteristics. Background Technology

[0002] Power modules, as core components for efficient power conversion and control, play a crucial role in numerous scenarios, including photovoltaic inverters and wind power converters in the new energy field, motor drives and fast charging for electric vehicles, variable frequency speed regulation and servo control in industry, and frequency conversion in home appliances and traction in rail transit, effectively promoting energy efficiency improvements across multiple industries. However, process uncertainty is a significant factor in their manufacturing process. Currently, reliability assessment of power modules mainly revolves around two core stages: simulation and damage assessment. Simulation provides parameters needed for damage assessment, such as stress-strain at weak points in the power module, while subsequent damage assessment can predict the module's failure life. However, existing reliability assessment methods have significant shortcomings, failing to incorporate manufacturing process uncertainty into their considerations. During power module production, variations in manufacturing processes are inevitable, and even seemingly minor differences can significantly impact the module's actual performance.

[0003] In particular, the constitutive model relied upon in the simulation phase has significant limitations. Because this model does not account for differences in manufacturing processes, simulations based on it struggle to accurately simulate the actual operating state of the power module, leading to errors in the simulation results. Since damage assessment often relies on simulation results, these errors propagate like dominoes, making the damage assessment results inaccurate as well, severely impacting the accurate assessment of the power module's reliability. In actual design and production, to ensure stable and reliable operation of the power module, given the shortcomings of the aforementioned assessment methods, only a relatively conservative redundancy design strategy can be adopted. This not only increases product costs but may also affect the overall performance and market competitiveness of the product to some extent, becoming a bottleneck restricting the further development of power modules. Summary of the Invention

[0004] This invention aims to address the problem in existing power module reliability assessments where constitutive models fail to consider manufacturing process uncertainties (especially density variations), leading to insufficient simulation accuracy and consequently affecting lifetime prediction accuracy. To this end, this invention provides a method for constructing a crystal plastic constitutive model based on density characteristics. This method corrects the critical decomposition shear stress using density characteristic parameters, thereby quantifying the impact of process differences on material mechanical properties, significantly improving simulation accuracy, and providing a reliable basis for the optimized design of packaging interconnect materials.

[0005] This invention provides a method for constructing a crystal plastic constitutive model based on density characteristics, characterized by comprising: S1: Correct the initial and saturation values ​​of the critical decomposition shear stress using a correction factor. A correction coefficient is constructed by comparing the current density characteristic parameter with the reference density characteristic parameter, and this correction coefficient is adjusted using an exponential function. When the density characteristic parameter is less than the reference value, the correction coefficient is greater than 1, causing the initial and saturation values ​​of the critical decomposition shear stress to increase simultaneously. When the density characteristic parameter is greater than the reference value, the correction coefficient is less than 1, causing the initial and saturation values ​​of the critical decomposition shear stress to decrease simultaneously. This correction coefficient introduces the influence of density on crystal plastic behavior into the critical decomposition shear stress. S2: Using the initial and saturation values ​​of the corrected critical decomposition shear stress obtained in step S1 as parameters, substitute them into the hardening law of the crystal plastic constitutive model to establish a crystal plastic constitutive model based on density characteristics. S3: Based on the crystal plastic constitutive model established in step S2, simulation is performed in finite element software. By inputting the values ​​of macroscopic shear strain rate and material density characteristic parameters, the predicted results of the material's mechanical properties are calculated and output.

[0006] Furthermore, the initial and saturation values ​​of the critical decomposition shear stress are corrected using density characteristic parameters: in, This represents the initial value of the corrected critical decomposed shear stress. This is the corrected saturation value of the critical decomposed shear stress. To reference the initial value of the critical decomposition shear stress under the density characteristics, To reference the saturation value of the critical decomposition shear stress under the density characteristics, For density characteristic parameter values, For reference density characteristic parameter values, The density characteristic influence index.

[0007] Furthermore, a crystal plastic constitutive model based on density characteristics is established, the specific process of which includes: S21: The total deformation gradient is decomposed into elastic deformation gradient and plastic deformation gradient. The total deformation gradient describes the overall deformation of the crystal from the initial configuration to the current configuration. The elastic deformation gradient characterizes the elastic stretching and rotation of the crystal lattice. The plastic deformation gradient is determined by the plastic deformation caused by crystal slip. S22: Based on elastic deformation gradient and the first The unit slip direction vector of the slip system is used to calculate the slip direction vector of the deformed slip system; based on the first... The normal vector of the slip plane of the slip system is the inverse of the elastic deformation gradient. The normal vector of the slip plane after deformation is calculated, where... This serves as the index for the slip system, from which the relevant parameters of the slip system after deformation are calculated; S23: Based on the determinant of the total deformation gradient and the Cauchy stress, the Kirchhoff stress is calculated; based on the deformation of the first... The slip surface normal vector of the slip system, Kirchhoff stress, and the first deformation after deformation. The slip direction vector of the slip system is used to calculate the decomposed shear stress of the slip system. S24: Based on reference shear strain rate, the first Given the decomposed shear stress of the slip system, the back stress of the slip system, the critical decomposed shear stress of the slip system, the velocity sensitivity index, and the sign function, calculate the first... Shear strain rate of the slip system; S25: Based on direct hardening modulus, the first Calculate the shear strain rate, dynamic restitution coefficient, back stress of the slip system at the start of the current time step t, and the absolute value of the shear strain rate at the current time step. The rate of change of back stress of the slip system; based on the back stress, the rate of change of back stress and the time step length of the slip system at the beginning of the time step, calculate and update the back stress at the end of the time step. S26: Based on the sum of the products of the shear strain rate, unit slip direction vector and slip plane normal vector of each slip system, determine the product relationship between the derivative of plastic deformation gradient with respect to time and the inverse of plastic deformation gradient; calculate and update the plastic deformation gradient through time integration, and then update the elastic deformation gradient using the product of the total deformation gradient and the inverse of plastic deformation gradient. S27: Based on the sum of the integral results of the absolute values ​​of the shear strain rates of each slip system over the time interval [0,t], calculate the sum of the cumulative plastic slip of all slip systems; S28: Using the initial and saturation values ​​of the critical decomposition shear stress corrected in step S1, combined with the initial hardening modulus and the sum of cumulative plastic slip, the hardening modulus is calculated; then, based on this hardening modulus, combined with the ratio of potential hardening to self-hardening modulus and the Kronecker sign, the hardening coefficient of the multi-slip system coupling is obtained to characterize the degree of influence of the shear strain rate between different slip systems on the critical decomposition shear stress. S29: The evolution of critical decomposition shear stress is determined in the multi-slip system coupled update mode. The rate of change of critical decomposition shear stress for each slip system is obtained by summing the products of the hardening coefficient of each slip system and the absolute value of the corresponding shear strain rate. Then, the critical decomposition shear stress at the current moment, the rate of change, and the time step are combined to update the critical decomposition shear stress value at the next moment. The updated value must satisfy the Voce-type saturation evolution law after density correction. Based on the critical decomposition shear stress saturation value and initial value after correction by the density characteristic parameter, combined with the initial hardening modulus and the cumulative plastic slip of all slip systems, the critical decomposition shear stress of the α-slip system is calculated. S210: Iteration and convergence judgment. The updated critical decomposition shear stress, back stress, elastic deformation gradient and plastic deformation gradient are fed back to steps S22 to S29. The calculation is repeated until the Cauchy stress and the shear strain rate of each slip system meet the preset convergence conditions.

[0008] Furthermore, in step S24, the formula for calculating the shear strain rate is: in, For the first Shear strain rate of slip system For reference shear strain rate, For the first Decomposed shear stress of a slip system For the first Back stress of a slip system For the first Critical decomposed shear stress of the slip system, where n is the velocity sensitivity index. It is a symbolic function.

[0009] Furthermore, in step S25, the back stress update formula is: in, For the first Rate of change of back stress in a slip system For direct hardening modulus, The coefficient of recovery is the dynamic recovery factor. This represents the absolute value of the shear strain rate at the current time step. For the current moment, For time step, For the first The sliding system at the end of the time step Back stress at any moment For the first The slip frame at the start of the time step Back stress at any given moment.

[0010] Furthermore, in step S28, the evolution of the critical decomposition shear stress is analyzed, and the hardening modulus is calculated using the following formula: in, For hardening modulus, The initial hardening modulus, This represents the initial value of the corrected critical decomposed shear stress. This is the corrected saturation value of the critical decomposed shear stress. This is the sum of the cumulative plastic slip of all slip systems.

[0011] Furthermore, in step S29, the evolution of the critical decomposition shear stress is calculated within the multi-slip system coupled update framework. The rate of change of the critical decomposition shear stress in each slip system is calculated and updated via time integration. in, For the first The rate of change of critical decomposition shear stress in a slip system For potential hardening modulus, For the first Shear strain rate of slip system for exist The value at time, for At the present moment The value of , For time step, For the first Starting point of time step of the sliding system Critical decomposition of shear stress at time; The evolution of the critical decomposition shear stress must also satisfy the Voce-type saturation evolution law: in, For the first Critical decomposition shear stress of slip system This represents the initial value of the corrected critical decomposed shear stress. This is the corrected saturation value of the critical decomposed shear stress. The initial hardening modulus, This is the sum of the cumulative plastic slip of all slip systems, used to verify the consistency of the macroscopic saturation trend in the multi-slip system coupling update results.

[0012] Furthermore, in step S210, the Cauchy stress iteration residual is less than MPa and the iterative residual of the shear strain rate of each slip system is less than The iteration stops once the preset convergence condition is met.

[0013] Furthermore, in step S3, the macroscopic shear strain rate is set to 0.01. .

[0014] Furthermore, the density characteristic parameter is the porosity of the power module packaging interconnect material. The porosity is adjusted by sintering process parameters, including sintering temperature, sintering time, and sintering pressure.

[0015] The above-described one or more technical solutions in the embodiments of the present invention have at least one of the following technical effects: This invention quantifies the impact of manufacturing process uncertainties on the mechanical properties of packaged interconnect materials by introducing density characteristic parameters, significantly improving simulation accuracy. The density characteristic parameters can be flexibly selected according to the characteristics of different power module packaged interconnect materials, expanding the applicability of the model. Combined with crystal plasticity theory, it achieves high-precision simulation of micro-deformation mechanisms such as slip and twinning, providing a reliable reference for material design optimization.

[0016] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0018] Figure 1 This is a flowchart of the method provided by the present invention.

[0019] Figure 2 This is a comparison chart of shear stress-shear strain data from simulation and experimentation under process A provided by the present invention.

[0020] Figure 3 This is a comparison chart of shear stress-shear strain data from simulation and experiment under process B provided by the present invention.

[0021] Figure 4 This is a comparison chart of shear stress-shear strain data from simulation and experimentation under process C provided by the present invention.

[0022] Figure 5 This is a comparison chart of shear stress-shear strain data from simulation and experimentation under process D provided by the present invention.

[0023] Figure 6 This is a comparison chart of shear stress-shear strain data from simulation and experimentation under process E provided by the present invention. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention. The following embodiments are used to illustrate this invention but should not be used to limit the scope of this invention.

[0025] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0026] The following is combined Figures 1 to 6 The present invention will be further described in detail below, including a method for constructing a crystal plastic constitutive model based on density characteristics. The constitutive model of crystal plasticity is a mathematical model used to describe the relationship between microscopic mechanisms (such as slip system initiation and hardening) and macroscopic mechanical response (shear stress-shear strain relationship) during plastic deformation of crystalline materials. It can quantitatively characterize the evolution law of crystal from elastic to plastic deformation.

[0027] In this embodiment, as Figure 1 As shown, a method for constructing a crystal plastic constitutive model based on density characteristics is provided. This method takes the total deformation gradient (describing the overall deformation of the crystal from the initial configuration to the current configuration), the geometric parameters of the slip system (unit slip direction vector, slip plane normal vector), the plastic deformation dynamic parameters (reference shear strain rate, velocity sensitivity index, direct hardening modulus, dynamic restitution coefficient, initial hardening modulus, and the ratio of potential hardening modulus to self-hardening modulus), and density characteristic parameters reflecting the compactness of the microstructure related to the internal pores of the material as inputs.

[0028] The total deformation gradient can be determined in the following way: first, the velocity gradient is determined by the macroscopic shear strain rate; then, the evolution equation is established by using the relationship between the deformation gradient rate and the velocity gradient; finally, the total deformation gradient, which varies with time or deformation process, is obtained by integral solution, taking into account the condition that the total deformation gradient is a unit tensor in the initial undeformed state.

[0029] The method includes the following steps: S1: Correct the initial and saturation values ​​of the critical decomposition shear stress using a correction factor. A correction coefficient is constructed by comparing the current density characteristic parameter with the reference density characteristic parameter, and this correction coefficient is adjusted using an exponential function. When the density characteristic parameter is less than the reference value, the correction coefficient is greater than 1, causing the initial and saturation values ​​of the critical decomposition shear stress to increase simultaneously. When the density characteristic parameter is greater than the reference value, the correction coefficient is less than 1, causing the initial and saturation values ​​of the critical decomposition shear stress to decrease simultaneously. Through this correction coefficient, the influence of density on crystal plastic behavior is introduced into the critical decomposition shear stress.

[0030] The initial and saturation values ​​of the critical decomposition shear stress are corrected using density characteristic parameters: in, This is the initial value of the critical decomposition shear stress. This represents the saturation value of the critical decomposition shear stress. To reference the initial value of the critical decomposition shear stress under the density characteristics, To reference the saturation value of the critical decomposition shear stress under the density characteristics, For density characteristic parameter values, For reference density characteristic parameter values, The density characteristic influence index.

[0031] The invention is further illustrated by simulating the shear stress-strain response of sintered silver under different processes. In this embodiment, porosity is used as a density characteristic parameter of sintered silver. The reference value was set at 5.42%. The sintering parameters and the obtained porosity under different processes are shown in Table 1.

[0032] Table 1

[0033] In this embodiment, five different sintering processes (A to E) and their corresponding material porosities were selected, as shown in Table 1. Using the parameters of process A (sintering temperature 265℃, time 10 min, pressure 20 MPa) as a baseline, processes B to E and their corresponding porosities were obtained by adjusting the temperature and time using a single-variable method. In practical applications, other combinations of process parameters can be selected as needed to establish different process-porosity correspondences.

[0034] S2: Using the initial and saturation values ​​of the corrected critical decomposition shear stress obtained in step S1 as parameters, substitute them into the hardening law of the crystal plastic constitutive model to establish a crystal plastic constitutive model that considers density characteristics.

[0035] The specific process of establishing a crystal plastic constitutive model based on density characteristics includes: S21: The total deformation gradient is decomposed into elastic deformation gradient and plastic deformation gradient. The total deformation gradient describes the overall deformation of the crystal from its initial configuration to its current configuration. The elastic deformation gradient characterizes the elastic stretching and rotation of the crystal lattice. The plastic deformation gradient is determined by the plastic deformation caused by crystal slip. The formula is as follows: in, To describe the total deformation gradient of a crystal from its initial configuration to its current configuration, To characterize the elastic deformation gradient of the lattice under elastic stretching and rotation, This represents the plastic deformation gradient caused by crystal slip.

[0036] S22: Based on elastic deformation gradient and the first The unit slip direction vector of the slip system is used to calculate the slip direction vector of the deformed slip system, based on the first... The normal vector of the slip plane of the slip system is the inverse of the elastic deformation gradient. The normal vector of the slip plane after deformation is calculated, where... The index of the slip system is used to calculate the relevant parameters of the slip system after deformation. The formula is as follows: in, For the glide system index, For the deformed first The slip direction vector of the slip system. For the first The unit slip direction vector of a slip system. The first in the deformed lattice The normal vector of the slip surface of the slip system. For the first The normal vector of the slip plane of the slip system. It is the inverse of the elastic deformation gradient.

[0037] S23: Based on the determinant of the total deformation gradient and the Cauchy stress, the Kirchhoff stress is calculated, based on the deformation of the first... The slip surface normal vector of the slip system, Kirchhoff stress, and the first deformation after deformation. The slip direction vector of the slip system is used to calculate the decomposed shear stress of the slip system, using the following formula: in, Here, det represents the Kirchhoff stress, and det is the determinant. This refers to Cauchy stress.

[0038] The formula for calculating the decomposed shear stress of a slip system is: in, For the first Decomposed shear stress of a slip system.

[0039] S24: Based on reference shear strain rate, the first Given the decomposed shear stress of the slip system, the back stress of the slip system, the critical decomposed shear stress of the slip system, the velocity sensitivity index, and the sign function, calculate the first... The shear strain rate of the slip system is given by the following formula: in, For the first Shear strain rate of slip system For reference shear strain rate, For the first Decomposed shear stress of a slip system For the first Back stress of a slip system For the first Critical decomposed shear stress of the slip system, where n is the velocity sensitivity index. It is a symbolic function.

[0040] S25: Based on direct hardening modulus, the first Calculate the shear strain rate, dynamic restitution coefficient, back stress of the slip system at the start of the current time step t, and the absolute value of the shear strain rate at the current time step. The rate of change of back stress in the slip system is calculated and updated based on the back stress, the rate of change of back stress, and the time step size at the beginning of the time step. The formula is as follows: in, For the first Rate of change of back stress in a slip system For direct hardening modulus, The coefficient of recovery is the dynamic recovery factor. This represents the absolute value of the shear strain rate at the current time step. For the current moment, For time step, For the first The sliding system at the end of the time step Back stress at any moment For the first The slip frame at the start of the time step Back stress at any given moment.

[0041] S26: Based on the sum of the products of the shear strain rate, unit slip direction vector, and slip plane normal vector of each slip system, determine the product relationship between the derivative of the plastic deformation gradient with respect to time and the inverse of the plastic deformation gradient. Calculate and update the plastic deformation gradient through time integration, and then update the elastic deformation gradient using the product of the total deformation gradient and the inverse of the plastic deformation gradient. The formulas for the rate of change of the plastic deformation gradient and the shear strain rate of each slip system are as follows: in, Let be the derivative of the plastic deformation gradient with respect to time. It is the inverse of the plastic deformation gradient. This represents the number of slip systems.

[0042] Update the plastic deformation gradient by time integration. , and by Update the elastic deformation gradient.

[0043] S27: Based on the sum of the integral results of the absolute values ​​of the shear strain rates of each slip system over the time interval [0,t], calculate the sum of the cumulative plastic slip of all slip systems, using the following formula: in, This is the sum of the cumulative plastic slip of all slip systems.

[0044] S28: Using the initial and saturation values ​​of the critical decomposition shear stress corrected in step S1, combined with the initial hardening modulus and the sum of cumulative plastic slip, the hardening modulus is calculated using the following formula: in, For hardening modulus, The initial hardening modulus, This represents the initial value of the corrected critical decomposed shear stress. This is the corrected saturation value of the critical decomposed shear stress. This is the sum of the cumulative plastic slip of all slip systems.

[0045] Based on this hardening modulus, and combining the ratio of potential hardening to self-hardening modulus and the Kronecker sign, the hardening coefficient of the multi-slip coupling is calculated to characterize the influence of the shear strain rate between different slip systems on the critical decomposition shear stress. The formula is as follows: in, Let be the hardening coefficient, describing the th The shear strain rate of the slip system on the first The degree of influence of the critical decomposition shear stress of the slip system. It is the ratio of potential hardening modulus to self-hardening modulus. For Kronecker symbols.

[0046] S29: The evolution of the critical decomposition shear stress, under the multi-slip system coupled update mode, is obtained by summing the products of the hardening coefficient of each slip system and the absolute value of the corresponding shear strain rate. Then, combining the current critical decomposition shear stress, this rate of change, and the time step, the critical decomposition shear stress value for the next time step is updated. The formula is as follows: in, For the first The rate of change of critical decomposition shear stress in a slip system For potential hardening modulus, For the first Shear strain rate of slip system for exist The value at time, for At the present moment The value of , For time step, For the first Starting point of time step of the sliding system The critical decomposition shear stress at a given moment.

[0047] The updated values ​​must satisfy the Voce-type saturation evolution law corrected for density. Based on the critical decomposition shear stress saturation value and initial value corrected for density characteristic parameters, combined with the initial hardening modulus and the sum of cumulative plastic slip of all slip systems, the critical decomposition shear stress of the α-slip system is calculated, as follows: in, For the first Critical decomposition shear stress of slip system This represents the initial value of the corrected critical decomposed shear stress. This is the corrected saturation value of the critical decomposed shear stress. The initial hardening modulus, This is the sum of the cumulative plastic slip of all slip systems, used to verify the consistency of the macroscopic saturation trend in the multi-slip system coupling update results.

[0048] S210: Perform iteration and convergence judgment, and feed back the updated critical decomposition shear stress, back stress, elastic deformation gradient, and plastic deformation gradient to steps S22 to S29. Repeat the calculation until the preset convergence condition is met. Cauchy stress iteration residual is less than MPa, the iterative residuals of the shear strain rate of each slip system are less than The iteration stops once the conditions are met.

[0049] After stopping the iteration, the output model solution results include: macroscopic Cauchy stress (characterizing the overall stress state of the material), shear strain rate of each slip system (reflecting the activity of plastic deformation of a single slip system), cumulative plastic slip sum (quantifying the total degree of plastic deformation of all slip systems), and dynamically updated internal state variables (such as back stress of each slip system, critical decomposition shear stress, and elastic deformation gradient and plastic deformation gradient used to decompose elastoplastic deformation).

[0050] The logic for obtaining the macroscopic Cauchy stress is as follows: First, the total deformation is decomposed into elastic deformation and plastic deformation. The stress tensor is calculated from the elastic deformation using the elastic constitutive relation. Under the framework of the plastic model, the stress is continuously recalculated in combination with the update of the internal state variables during the iteration process. After the stress residual satisfies the convergence condition, the stable macroscopic Cauchy stress is finally obtained.

[0051] S3: Based on the crystal plastic constitutive model established in step S2, perform finite element simulation and output application results for real-world scenarios, as follows: S31: Finite element platform embedding. This involves embedding the model into the ABAQUS finite element platform and implementing numerical calculations of the model through the UMAT user subroutine.

[0052] S32: Model parameters are determined. The complete parameter system required for simulation is divided into two categories: The fundamental constants of the crystal plastic constitutive model under the reference state. These fundamental constants have been determined independently through experiments, and their specific values ​​are shown in Table 2.

[0053] Table 2

[0054] The density characteristic influence index quantifies the degree to which density deviation affects the critical decomposition shear stress. It is determined by the reverse calibration method. Based on the shear stress-strain experimental data of process D (porosity of sintered silver is 8.38%), the material constant parameters under the reference density (porosity 5.42%) in Table 2 are substituted into the model. The density characteristic influence index is adjusted by iterative optimization, and finally the density characteristic influence index is determined to be 0.43.

[0055] S33: Set simulation boundary conditions, with the macroscopic shear strain rate fixed at 0.01. Numerical simulations were performed on sintered silver using different sintering processes, and the shear stress-shear strain curves corresponding to each process were output, where: Shear stress: The tangential component of the macroscopic Cauchy stress output by the model directly reflects the internal force density of the material in the shear direction. Its value dynamically evolves with the initiation (initial yielding stage), hardening (stress rise stage), and saturation (stress plateau stage) of the slip system. Shear strain: The total strain in the shear direction calculated by the model "total deformation gradient decomposition algorithm" consists of two parts: elastic shear strain (originating from crystal lattice deformation) and plastic shear strain (originating from the cumulative slip of each slip system). The two accumulate synchronously with the loading process and together determine the shape of the shear stress-strain curve.

[0056] To evaluate the superiority of the model of this invention, the results of the improved simulation (based on the density correction model), the original simulation (the model without considering density correction), and experimental data were compared systematically (results are shown in the figure). Figures 2 to 6 As shown in the figure, the improved model significantly improves the prediction accuracy under different process conditions.

[0057] Analysis shows that the improved simulation curves and experimental curves exhibit a higher degree of agreement under all process conditions. It should be noted that, in the appendix... Figure 2 In the simulation, corresponding to reference process A (i.e., reference density state), the curves of the original simulation and the improved simulation completely overlap. This phenomenon is consistent with the expectations of the model construction. When the material density parameter equals the reference value, the density correction factor is 1, and the improved model naturally degenerates into the baseline model, ensuring the continuity and rationality of the model across different states.

[0058] The improvement effect of the model is particularly significant under process conditions that deviate from the reference state (as shown in the attached figure). Figures 2 to 5(As shown). Taking a process with high porosity as an example, the original simulation, which did not consider the influence of density, showed a significant deviation between its predictions and experimental data; while the improved simulation can more accurately reflect the changes in material mechanical properties caused by manufacturing process uncertainties, thus significantly improving the accuracy of the simulation results.

[0059] The above results fully demonstrate that by introducing the density characteristic parameter, the impact of manufacturing process uncertainty on the mechanical properties of packaged interconnect materials can be effectively quantified, significantly improving the accuracy of simulation analysis and providing a more reliable theoretical tool for the reliability assessment of power modules.

[0060] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for constructing a crystal plastic constitutive model based on density characteristics, characterized in that, include: S1: Correct the initial and saturation values ​​of the critical decomposition shear stress using a correction factor. A correction coefficient is constructed by comparing the current density characteristic parameter with the reference density characteristic parameter, and this correction coefficient is adjusted using an exponential function. When the density characteristic parameter is less than the reference value, the correction coefficient is greater than 1, causing the initial and saturation values ​​of the critical decomposition shear stress to increase simultaneously. When the density characteristic parameter is greater than the reference value, the correction coefficient is less than 1, causing the initial and saturation values ​​of the critical decomposition shear stress to decrease simultaneously. This correction coefficient introduces the influence of density on crystal plastic behavior into the critical decomposition shear stress. S2: Using the initial and saturation values ​​of the corrected critical decomposition shear stress obtained in step S1 as parameters, substitute them into the hardening law of the crystal plastic constitutive model to establish a crystal plastic constitutive model based on density characteristics. S3: Based on the crystal plastic constitutive model established in step S2, simulation is performed in finite element software. By inputting the values ​​of macroscopic shear strain rate and material density characteristic parameters, the predicted results of the material's mechanical properties are calculated and output.

2. The method for constructing a crystal plastic constitutive model based on density characteristics as described in claim 1, characterized in that, The initial and saturation values ​​of the critical decomposition shear stress are corrected using density characteristic parameters: in, This represents the initial value of the corrected critical decomposed shear stress. This is the corrected saturation value of the critical decomposed shear stress. To reference the initial value of the critical decomposition shear stress under the density characteristics, To reference the saturation value of the critical decomposition shear stress under the density characteristics, For density characteristic parameter values, For reference density characteristic parameter values, The density characteristic influence index.

3. The method for constructing a crystal plastic constitutive model based on density characteristics as described in claim 1, characterized in that, The specific process of establishing a crystal plastic constitutive model based on density characteristics includes: S21: The total deformation gradient is decomposed into elastic deformation gradient and plastic deformation gradient. The total deformation gradient describes the overall deformation of the crystal from the initial configuration to the current configuration. The elastic deformation gradient characterizes the elastic stretching and rotation of the crystal lattice. The plastic deformation gradient is determined by the plastic deformation caused by crystal slip. S22: Based on elastic deformation gradient and the first The unit slip direction vector of the slip system is used to calculate the slip direction vector of the deformed slip system; based on the first... The normal vector of the slip plane of the slip system is the inverse of the elastic deformation gradient. The normal vector of the slip plane after deformation is calculated, where... This serves as the index for the slip system, from which the relevant parameters of the slip system after deformation are calculated; S23: Based on the determinant of the total deformation gradient and the Cauchy stress, the Kirchhoff stress is calculated; based on the deformation of the first... The slip surface normal vector of the slip system, Kirchhoff stress, and the first deformation after deformation. The slip direction vector of the slip system is used to calculate the decomposed shear stress of the slip system. S24: Based on reference shear strain rate, the first Given the decomposed shear stress of the slip system, the back stress of the slip system, the critical decomposed shear stress of the slip system, the velocity sensitivity index, and the sign function, calculate the first... Shear strain rate of the slip system; S25: Based on direct hardening modulus, the first Calculate the shear strain rate, dynamic restitution coefficient, back stress of the slip system at the start of the current time step t, and the absolute value of the shear strain rate at the current time step. The rate of change of back stress of the slip system; based on the back stress, the rate of change of back stress and the time step length of the slip system at the beginning of the time step, calculate and update the back stress at the end of the time step. S26: Based on the sum of the products of the shear strain rate, unit slip direction vector and slip plane normal vector of each slip system, determine the product relationship between the derivative of plastic deformation gradient with respect to time and the inverse of plastic deformation gradient; calculate and update the plastic deformation gradient through time integration, and then update the elastic deformation gradient using the product of the total deformation gradient and the inverse of plastic deformation gradient. S27: Based on the sum of the integral results of the absolute values ​​of the shear strain rates of each slip system over the time interval [0,t], calculate the sum of the cumulative plastic slip of all slip systems; S28: Using the initial and saturation values ​​of the critical decomposition shear stress corrected in step S1, combined with the initial hardening modulus and the sum of cumulative plastic slip, the hardening modulus is calculated; then, based on this hardening modulus, combined with the ratio of potential hardening to self-hardening modulus and the Kronecker sign, the hardening coefficient of the multi-slip system coupling is obtained to characterize the degree of influence of the shear strain rate between different slip systems on the critical decomposition shear stress. S29: The evolution of critical decomposition shear stress is determined in the multi-slip system coupled update mode. The rate of change of critical decomposition shear stress for each slip system is obtained by summing the products of the hardening coefficient of each slip system and the absolute value of the corresponding shear strain rate. Then, the critical decomposition shear stress at the current moment, the rate of change, and the time step are combined to update the critical decomposition shear stress value at the next moment. The updated value must satisfy the Voce-type saturation evolution law after density correction. Based on the critical decomposition shear stress saturation value and initial value after correction by the density characteristic parameter, combined with the initial hardening modulus and the cumulative plastic slip of all slip systems, the critical decomposition shear stress of the α-slip system is calculated. S210: Iteration and convergence judgment. The updated critical decomposition shear stress, back stress, elastic deformation gradient and plastic deformation gradient are fed back to steps S22 to S29. The calculation is repeated until the Cauchy stress and the shear strain rate of each slip system meet the preset convergence conditions.

4. The method for constructing a crystal plastic constitutive model based on density characteristics as described in claim 3, characterized in that, In step S24, the formula for calculating the shear strain rate is: in, For the first Shear strain rate of slip system For reference shear strain rate, For the first Decomposed shear stress of a slip system For the first Back stress of a slip system For the first Critical decomposed shear stress of the slip system, where n is the velocity sensitivity index. It is a symbolic function.

5. The method for constructing a crystal plastic constitutive model based on density characteristics as described in claim 3, characterized in that, In step S25, the back stress update formula is: in, For the first Rate of change of back stress in a slip system For direct hardening modulus, The coefficient of recovery is the dynamic recovery factor. This represents the absolute value of the shear strain rate at the current time step. For the current moment, For time step, For the first The sliding system at the end of the time step Back stress at any moment For the first The slip frame at the start of the time step Back stress at any given moment.

6. The method for constructing a crystal plastic constitutive model based on density characteristics as described in claim 3, characterized in that, In step S28, the evolution of the critical decomposition shear stress is calculated, and the hardening modulus is determined using the following formula: in, For hardening modulus, The initial hardening modulus, This represents the initial value of the corrected critical decomposed shear stress. This is the corrected saturation value of the critical decomposed shear stress. This is the sum of the cumulative plastic slip of all slip systems.

7. The method for constructing a crystal plastic constitutive model based on density characteristics as described in claim 3, characterized in that, In step S29, the evolution of the critical decomposition shear stress is calculated within the multi-slip system coupled update framework. The rate of change of the critical decomposition shear stress for each slip system is calculated and updated via time integration. in, For the first The rate of change of critical decomposition shear stress in a slip system For potential hardening modulus, For the first Shear strain rate of slip system for exist The value at time, for At the present moment The value of , For time step, For the first Starting point of time step of the sliding system Critical decomposition of shear stress at time; The evolution of the critical decomposition shear stress must also satisfy the Voce-type saturation evolution law: in, For the first Critical decomposition shear stress of slip system This represents the initial value of the corrected critical decomposed shear stress. This is the corrected saturation value of the critical decomposed shear stress. The initial hardening modulus, This is the sum of the cumulative plastic slip of all slip systems, used to verify the consistency of the macroscopic saturation trend in the multi-slip system coupling update results.

8. The method for constructing a crystal plastic constitutive model based on density characteristics as described in claim 3, characterized in that, In step S210, the Cauchy stress iteration residual is less than MPa and the iterative residual of the shear strain rate of each slip system is less than The iteration stops once the preset convergence condition is met.

9. The method for constructing a crystal plastic constitutive model based on density characteristics as described in claim 1, characterized in that, In step S3, the macroscopic shear strain rate is set to 0.

01. .

10. The method for constructing a crystal plastic constitutive model based on density characteristics as described in claim 1, characterized in that, The density characteristic parameter is the porosity of the power module packaging interconnect material. The porosity is adjusted by sintering process parameters, including sintering temperature, sintering time, and sintering pressure.

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