A method for constructing a crystal plasticity constitutive model based on a compactness characteristic

Abstract

The application relates to the field of power module reliability evaluation, and particularly discloses a crystal plasticity constitutive model construction method based on a density characteristic, which comprises the following steps: S1: modifying the initial value and the saturation value of a critical decomposed shear stress through a correction coefficient; S2: taking the initial value and the saturation value of the corrected critical decomposed shear stress obtained in the step S1 as parameters and substituting the parameters into a hardening law of a crystal plasticity constitutive model to establish the crystal plasticity constitutive model based on the density characteristic; and S3: simulating in finite element software based on the crystal plasticity constitutive model established in the step S2, inputting values of different density characteristic parameters and macroscopic shear strain rates, and calculating and outputting the mechanical performance prediction result of the material. The application effectively quantifies the influence of manufacturing process uncertainty on the mechanical performance of a packaging interconnection material by introducing the density characteristic parameter, and improves the accuracy of simulation analysis.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of power module reliability evaluation, in particular to a crystal plasticity constitutive model construction method based on density characteristics. BACKGROUND

[0002] As the core component of efficient conversion and control of electric energy, power modules play a key role in many scenarios such as photovoltaic inverter, wind power conversion, motor drive and fast charging of electric vehicles, frequency conversion and servo control in industry, and variable frequency of household appliances and rail transit traction, and effectively promote the energy efficiency of multiple industries. However, in its manufacturing process, process uncertainty is a key factor that cannot be ignored. At present, the reliability evaluation of power modules mainly focuses on two core links: simulation and damage evaluation. Through the simulation link, stress-strain and other damage evaluation parameters of the weak position of the power module can be obtained, and the subsequent damage evaluation link can predict the failure life of the power module. However, the existing reliability evaluation method has obvious defects and fails to consider manufacturing process uncertainty. In the production process of power modules, manufacturing process differences are inevitable, and even if these differences are small, they will significantly affect the actual performance of the module.

[0003] In particular, the constitutive model relied on by the simulation link has obvious limitations. Since the model does not consider manufacturing process difference factors, the simulation based on it cannot accurately simulate the actual operating state of the power module, resulting in errors in the simulation results. Damage evaluation often takes simulation results as the basis, and errors will be transmitted like a domino effect, making the damage evaluation results inaccurate, and thus seriously affecting the accurate judgment of the reliability of the power module. In actual design and production, in order to ensure that the power module can operate stably and reliably, due to the shortcomings of the above evaluation method, only a conservative redundancy design strategy can be adopted. This not only increases the cost of the product, but also may affect the overall performance and market competitiveness of the product to some extent, becoming a bottleneck restricting the further development of power modules. SUMMARY

[0004] The present application aims to solve the problem that in the existing reliability evaluation of power modules, the constitutive model does not consider manufacturing process uncertainty (especially density difference), which leads to insufficient simulation accuracy and further affects the accuracy of life prediction. Therefore, the present application provides a crystal plasticity constitutive model construction method based on density characteristics. This method corrects the critical resolved shear stress through the density characteristic parameter, thereby quantifying the influence of process differences on the mechanical properties of materials, significantly improving the simulation accuracy, and providing a reliable basis for the optimization design of packaging interconnection materials.

[0005] The present application provides a crystal plasticity constitutive model construction method based on density characteristics, characterized by comprising:

[0006] S1: modifying the initial value and the saturation value of the critical resolved shear stress by a correction coefficient:

[0007] The correction coefficient is constructed by the deviation of the current density characteristic parameter and the reference density characteristic parameter, and is adjusted in the form of an exponential function. When the density characteristic parameter is less than the reference value, the correction coefficient is greater than 1, so that the initial value and the saturation value of the critical resolved shear stress are increased synchronously. When the density characteristic parameter is greater than the reference value, the correction coefficient is less than 1, so that the initial value and the saturation value of the critical resolved shear stress are decreased synchronously. Through the correction coefficient, the influence of the density on the plastic behavior of the crystal is introduced into the critical resolved shear stress;

[0008] S2: the initial value and the saturation value of the critical resolved shear stress obtained in step S1 are substituted into the hardening law of the crystal plasticity constitutive model as parameters, and a crystal plasticity constitutive model based on the density characteristic is established;

[0009] S3: based on the crystal plasticity constitutive model established in step S2, simulation is performed in the finite element software, the mechanical property prediction results of the material are calculated and output by inputting the values of the macroscopic shear strain rate and the density characteristic parameter of the material.

[0010] Further, the initial value and the saturation value of the critical resolved shear stress are modified by the density characteristic parameter:

[0011]

[0012]

[0013] wherein, is the initial value of the modified critical resolved shear stress, is the saturation value of the modified critical resolved shear stress, is the initial value of the critical resolved shear stress under the reference density characteristic, is the saturation value of the critical resolved shear stress under the reference density characteristic, is the value of the density characteristic parameter, is the value of the reference density characteristic parameter, is the density characteristic influence index.

[0014] Further, a crystal plasticity constitutive model based on the density characteristic is established, and the specific process includes:

[0015] S21: decomposing the total deformation gradient into an elastic deformation gradient and a plastic deformation gradient, wherein the total deformation gradient is used to describe the overall deformation of the crystal from the initial configuration to the current configuration, the elastic deformation gradient represents the elastic stretching and rotation of the crystal lattice, and the plastic deformation gradient is determined by the plastic deformation caused by the crystal slip;

[0016] S22: based on the elastic deformation gradient and the unit slip direction vector of the slip system, the slip direction vector of the slip system after deformation is calculated; based on the slip plane normal vector of the slip system and the inverse of the elastic deformation gradient, the slip plane normal vector of the slip system after deformation is calculated, wherein is the slip system index, and the related parameters of the slip system after deformation are calculated in this way;

[0017] S23: based on the determinant of the total deformation gradient and the Cauchy stress, the Kirchhoff stress is calculated; based on the slip plane normal vector of the slip system after deformation, the Kirchhoff stress, the slip direction vector of the slip system after deformation, the resolved shear stress of the slip system is calculated;

[0018] S24: based on the reference shear strain rate, the resolved shear stress of the slip system, the back stress of the slip system, the critical resolved shear stress of the slip system, the velocity sensitivity index and the sign function, the shear strain rate of the slip system is calculated;

[0019] S25: based on the direct hardening modulus, the shear strain rate of the slip system, the dynamic recovery coefficient, the back stress of the slip system at time t at the beginning of the current time step and the absolute value of the shear strain rate at the current time step, the back stress change rate of the slip system is calculated; based on the back stress of the slip system at the beginning of the time step, the back stress change rate and the time step length, the back stress of the slip system at the end of the time step is calculated and updated;

[0020] S26: based on the sum of the product of the shear strain rate, the unit slip direction vector and the slip plane normal vector of each slip system, the derivative of the plastic deformation gradient with respect to time and the product of the inverse of the plastic deformation gradient are determined; the plastic deformation gradient is calculated and updated by time integration, and the elastic deformation gradient is updated by the product of the total deformation gradient and the inverse of the plastic deformation gradient;

[0021] S27: based on the sum of the absolute value of the shear strain rate of each slip system in the time interval [0, t], the total sum of the cumulative plastic slip of all slip systems is calculated;

[0022] ​​​​​​​​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.

[0023] 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.

[0024] 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.

[0025] Furthermore, in step S24, the formula for calculating the shear strain rate is:

[0026]

[0027] 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.

[0028] Furthermore, in step S25, the back stress update formula is:

[0029]

[0030]

[0031] in, For the first Rate of change of back stress in a slip system is the direct hardening modulus, is the dynamic recovery coefficient, is the absolute value of the shear strain rate at the current time step, is the current time, is the time step, is the back stress of the i-th slip system at the end of the time step, is the back stress of the i-th slip system at the start of the time step. is the back stress of the i-th slip system at the end of the time step, is the back stress of the i-th slip system at the start of the time step.

[0032] Further, in step S28, the evolution of the critical resolved shear stress is calculated, and the hardening modulus is calculated by the formula:

[0033]

[0034] wherein, is the hardening modulus, is the initial hardening modulus, is the initial value of the corrected critical resolved shear stress, is the saturation value of the corrected critical resolved shear stress, is the sum of the cumulative plastic slip of all slip systems.

[0035] Further, in step S29, the evolution of the critical resolved shear stress is calculated, and the change rate of the critical resolved shear stress of each slip system is calculated under the multi-slip system coupling update framework, and is updated by time integration:

[0036]

[0037]

[0038] wherein, is the change rate of the critical resolved shear stress of the i-th slip system, is the potential hardening modulus, is the shear strain rate of the i-th slip system, is the value of the i-th slip system at the end of the time step, is the value of the i-th slip system at the start of the time step. is the value of the i-th slip system at the end of the time step, is the value of the i-th slip system at the start of the time step, is the value of the i-th slip system at the end of the time step, is the value of the i-th slip system at the start of the time step, is the value of the i-th slip system at the end of the time step, is the time step, is the critical resolved shear stress of the i-th slip system at the start of the time step, is the critical resolved shear stress of the i-th slip system at the start of the time step.

[0039] ​​​​The evolution of the critical resolved shear stress also needs to satisfy the Voce type saturation evolution rule:

[0040]

[0041] wherein, is the initial value of the critical resolved shear stress of the first slip system, is the critical resolved shear stress of the slip system, is the initial value of the corrected critical resolved shear stress, is the saturation value of the corrected critical resolved shear stress, is the initial hardening modulus, is the sum of the cumulative plastic slip of all slip systems, used to verify the macroscopic saturation trend consistency of the multi-slip system coupling update result.

[0042] Further, in step S210, the Cauchy stress iteration residual is less than 0.1 MPa and the iteration residual of the shear strain rate of each slip system is less than 0.001, the preset convergence condition is met, and the iteration is stopped.

[0043] Further, in step S3, the macroscopic shear strain rate is set to 0.01 .

[0044] Further, the density characteristic parameter is the porosity of the power module packaging interconnection material, and the porosity is adjusted by the sintering process parameters, including sintering temperature, sintering time and sintering pressure.

[0045] The one or more technical solutions in the embodiments of the present application have at least one of the following technical effects:

[0046] The present application introduces the density characteristic parameter, quantifies the influence of manufacturing process uncertainty on the mechanical properties of the packaging interconnection material, significantly improves the simulation accuracy, flexibly selects the density characteristic parameter according to the characteristics of different power module packaging interconnection materials, expands the application range of the model, and realizes high-precision simulation of slip, twinning and other micro deformation mechanisms by combining with the crystal plasticity theory, and provides a reliable reference for material design optimization.

[0047] Additional aspects and advantages of the application will be described in part below, some will become apparent from the following description, or will be learned by practice of the application. BRIEF DESCRIPTION OF DRAWINGS

[0048] ​​In order to make the technical solutions in the present application or prior art clearer, the accompanying drawings needed in the embodiments or prior art description will be briefly introduced. Obviously, the accompanying drawings in the following description are only some embodiments of the present application, and all other drawings obtained by those of ordinary skill in the art without creative effort based on these drawings belong to the protection scope of the present application. The following embodiments are used to illustrate the present application, but cannot be used to limit the scope of the present application.

[0049] Figure 1 is a flow chart of the method provided by the present application.

[0050] Figure 2 is a comparison chart of the shear stress-shear strain data of simulation and test under Process A provided by the present application.

[0051] Figure 3 is a comparison chart of the shear stress-shear strain data of simulation and test under Process B provided by the present application.

[0052] Figure 4 is a comparison chart of the shear stress-shear strain data of simulation and test under Process C provided by the present application.

[0053] Figure 5 is a comparison chart of the shear stress-shear strain data of simulation and test under Process D provided by the present application.

[0054] Figure 6 is a comparison chart of the shear stress-shear strain data of simulation and test under Process E provided by the present application. DETAILED DESCRIPTION

[0055] In order to make the technical solutions in the present application or prior art clearer, the accompanying drawings needed in the embodiments or prior art description will be briefly introduced. Obviously, the accompanying drawings in the following description are only some embodiments of the present application, and all other drawings obtained by those of ordinary skill in the art without creative effort based on these drawings belong to the protection scope of the present application. The following embodiments are used to illustrate the present application, but cannot be used to limit the scope of the present application.

[0056] In the description of the present specification, the description referring to the terms "one embodiment", "some embodiments", "an example", "a specific example", or "some examples" and the like means that the specific features, structures, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Also, the specific features, structures, or characteristics described can be combined in any appropriate manner in any one or more embodiments or examples. Furthermore, the person skilled in the art can combine and combine the different embodiments or examples described in the present specification and the features of the different embodiments or examples, without contradiction.

[0057] The following will be described in conjunction with Figures 1 to 6 Further detailed description of the present application, a method for constructing a crystal plasticity constitutive model based on density characteristics,

[0058] The crystal plasticity constitutive model is a mathematical model for describing the correlation between the microscopic mechanism (such as slip system activation, hardening) and the macroscopic mechanical response (shear stress-shear strain relationship) when the crystal material is plastically deformed, which can quantitatively describe the evolution law of the crystal from elastic to plastic deformation.

[0059] In the present embodiment, as Figure 1 shown, a method for constructing a crystal plasticity constitutive model based on density characteristics is provided, which takes the total deformation gradient (describing the overall deformation of the crystal from the initial configuration to the current configuration), the slip system geometric parameters (unit slip direction vector, slip plane normal vector), plastic deformation dynamics parameters (reference shear strain rate, velocity sensitivity index, direct hardening modulus, dynamic recovery coefficient, initial hardening modulus, and the ratio of potential hardening modulus to self-hardening modulus), and density characteristic parameters reflecting the density of the internal pores of the material The microstructure is input.

[0060] Among them, the total deformation gradient can be determined by the following method: first, determine the velocity gradient from the macroscopic shear strain rate, then establish the evolution equation by using the relationship between the deformation gradient rate and the velocity gradient, and finally combine the condition that the total deformation gradient is a unit tensor in the initial un-deformed state. The total deformation gradient varying with time or deformation process is obtained by integration.

[0061] The method comprises the following steps:

[0062] S1: correcting the initial value and saturation value of the critical resolved shear stress by the correction coefficient:

[0063] The correction coefficient is constructed by the deviation of the current density characteristic parameter and the reference density characteristic parameter, and the correction coefficient is adjusted in the form of an exponential function; when the density characteristic parameter is less than the reference value, the correction coefficient is greater than 1, so that the initial value and the saturation value of the critical resolved shear stress are increased synchronously; when the density characteristic parameter is greater than the reference value, the correction coefficient is less than 1, so that the initial value and the saturation value of the critical resolved shear stress are decreased synchronously; the influence of the density on the plastic behavior of the crystal is introduced into the critical resolved shear stress through the correction coefficient.

[0064] The initial value and the saturation value of the critical resolved shear stress are corrected by the density characteristic parameter:

[0065]

[0066]

[0067] wherein, is the initial value of the critical resolved shear stress, is the saturation value of the critical resolved shear stress, is the initial value of the critical resolved shear stress under the reference density characteristic, is the saturation value of the critical resolved shear stress under the reference density characteristic, is the density characteristic parameter value, is the reference density characteristic parameter value, is the density characteristic influence index.

[0068] The simulation process of the shear stress-strain response of sintered silver under different processes is used to further illustrate the present application. In the present embodiment, the porosity is taken as the density characteristic parameter of the sintered silver , and the reference value thereof is set to 5.42%. The sintering parameters and the obtained porosities under different processes are shown in Table 1.

[0069] Table 1

[0070]

[0071] In the present embodiment, five different sintering processes (A to E) and the corresponding material porosities are selected, and the specific values are shown in Table 1. Among them, the parameters of the reference process A (sintering temperature 265℃, time 10 min, pressure 20 MPa) are taken as the benchmark, and the temperature and time are adjusted respectively by the single variable method to obtain processes B to E and the corresponding porosities. In actual application, other process parameter combinations can be selected according to needs to establish different process-porosity corresponding relationships.

[0072] S2: taking the initial value and the saturation value of the revised critical resolved shear stress obtained in step S1 as parameters, substituting into the hardening law of the crystal plasticity constitutive model, and establishing the crystal plasticity constitutive model considering the density characteristics.

[0073] The crystal plasticity constitutive model based on the density characteristics is established, and the specific process includes:

[0074] S21: decomposing the total deformation gradient into an elastic deformation gradient and a plastic deformation gradient, wherein the total deformation gradient is used to describe the overall deformation of the crystal from the initial configuration to the current configuration, the elastic deformation gradient represents the elastic stretching and rotation of the lattice, and the plastic deformation gradient is determined by the plastic deformation caused by the crystal slip, and the formula is:

[0075]

[0076] wherein, is the total deformation gradient for describing the overall deformation of the crystal from the initial configuration to the current configuration, is the elastic deformation gradient for representing the elastic stretching and rotation of the lattice, is the plastic deformation gradient caused by the crystal slip.

[0077] S22: based on the elastic deformation gradient and the unit slip direction vector of the first slip system, the slip direction vector of the slip system after deformation is calculated, and based on the slip plane normal vector of the first slip system and the inverse of the elastic deformation gradient, the slip plane normal vector of the slip system after deformation is calculated, wherein is the slip system index, and the related parameters of the slip system after deformation are calculated, and the formula is:

[0078]

[0079]

[0080] wherein, is the slip system index, is the slip direction vector of the first slip system after deformation, is the unit slip direction vector of the first slip system, is the slip plane normal vector of the first slip system in the lattice after deformation, is the slip plane normal vector of the first slip system, is the inverse of the elastic deformation gradient.

[0081] S23: based on the determinant of the total deformation gradient and the Cauchy stress, the Kirchhoff stress is calculated, and based on the slip direction vector of the first Normal vector of slip plane of slip system, Kirchhoff stress, the Slip direction vector of slip system, the resolved shear stress of the slip system is calculated, and the formula is:

[0082]

[0083] , wherein, Kirchhoff stress, det is determinant, Cauchy stress.

[0084] The formula for calculating the resolved shear stress of the slip system is:

[0085]

[0086] , wherein, The resolved shear stress of the first slip system.

[0087] S24: Based on the reference shear strain rate, the resolved shear stress of the first slip system, the back stress of the slip system, the critical resolved shear stress of the slip system, the velocity sensitivity index and the sign function, the shear strain rate of the first slip system is calculated, and the formula is:

[0088]

[0089] , wherein, The shear strain rate of the first slip system, The reference shear strain rate, The resolved shear stress of the first slip system, The back stress of the first slip system, The critical resolved shear stress of the first slip system, n is the velocity sensitivity index, The sign function.

[0090] S25: Based on the direct hardening modulus, the shear strain rate of the first slip system, the dynamic recovery coefficient, the back stress of the slip system at time t at the beginning of the current time step and the absolute value of the shear strain rate at the current time step, the back stress of the first slip system is calculated, and the back stress of the slip system at the end of the time step is calculated and updated based on the back stress of the slip system at the beginning of the time step, the back stress change rate and the time step length, and the formula is:

[0091]

[0092]

[0093] wherein, is the back stress rate of the slip system, is the direct hardening modulus, is the dynamic recovery coefficient, is the absolute value of the shear strain rate of the current time step, is the current time, is the time step, is the back stress of the slip system at the end of the time step is the back stress of the slip system at the beginning of the time step is the back stress of the slip system at the beginning of the time step.

[0094] S26: Based on the sum of the product of the shear strain rate of each slip system, the unit slip direction vector and the slip plane normal vector, the derivative of the plastic deformation gradient with respect to time and the product of the inverse of the plastic deformation gradient are determined, the plastic deformation gradient is calculated and updated by time integration, and the elastic deformation gradient is updated by the product of the total deformation gradient and the inverse of the plastic deformation gradient, the change rate of the plastic deformation gradient and the shear strain rate formula of each slip system is:

[0095]

[0096] wherein, is the derivative of the plastic deformation gradient with respect to time, is the inverse of the plastic deformation gradient, is the number of slip systems.

[0097] The plastic deformation gradient is updated by time integration , and the elastic deformation gradient is updated by .

[0098] S27: Based on the sum of the integral results of the absolute value of the shear strain rate of each slip system in the time interval [0, t], the total sum of the cumulative plastic slip of all slip systems is calculated, and the formula is:

[0099]

[0100] wherein, is the total sum of the cumulative plastic slip of all slip systems.

[0101] S28: The initial value and the saturation value of the critical resolved shear stress corrected by step S1 are used to calculate the hardening modulus combined with the initial hardening modulus and the total sum of the cumulative plastic slip, and the formula is:

[0102]

[0103] wherein, is the hardening modulus, is the initial hardening modulus, is the initial value of the modified critical resolved shear stress, is the saturation value of the modified critical resolved shear stress, is the summation of the cumulative plastic slips of all slip systems.

[0104] Based on the hardening modulus, the hardening coefficient of multi-slip system coupling is calculated by combining the ratio of potential hardening modulus and self-hardening modulus, Kronecker symbol, to represent the influence degree of shear strain rate between different slip systems on the critical resolved shear stress, and the formula is:

[0105]

[0106] wherein, is the hardening coefficient, describing the influence degree of the shear strain rate of the slip system on the critical resolved shear stress of the slip system, is the ratio of potential hardening modulus and self-hardening modulus, is the Kronecker symbol.

[0107] S29: The evolution of the critical resolved shear stress, under the multi-slip system coupling update mode, the change rate of the critical resolved shear stress of each slip system is obtained by the summation of the product of the hardening coefficient of each slip system and the absolute value of the corresponding shear strain rate, and then the critical resolved shear stress value at the next time is updated by combining the critical resolved shear stress at the current time, the change rate and the time step, and the formula is:

[0108]

[0109]

[0110] wherein, is the change rate of the critical resolved shear stress of the slip system, is the potential hardening modulus, is the shear strain rate of the slip system, is the value of at the time, is the value of at the current time , is the time step, is the start time of the slip system time step Critical resolved shear stress.

[0111] The updated value needs to satisfy the Voce-type saturation evolution law corrected by the densification degree, and the critical resolved shear stress saturation value and initial value of the αth slip system are calculated based on the corrected critical resolved shear stress saturation value and initial value of the densification degree characteristic parameter, combined with the initial hardening modulus and the total sum of the cumulative plastic slip of all slip systems, and the critical resolved shear stress of the αth slip system is calculated, and the formula is as follows:

[0112]

[0113] wherein, is the initial value of the critical resolved shear stress of the αth slip system, is the critical resolved shear stress of the αth slip system, is the initial value of the corrected critical resolved shear stress, is the saturation value of the corrected critical resolved shear stress, is the initial hardening modulus, is the total sum of the cumulative plastic slip of all slip systems, which is used to verify the consistency of the macroscopic saturation trend of the multi-slip system coupling update result.

[0114] S210: iteration and convergence judgment are performed, and the updated critical resolved shear stress, back stress, elastic deformation gradient and plastic deformation gradient are fed back to steps S22 to S29, and the calculation is repeated until the preset convergence condition is met:

[0115] the Cauchy stress iteration residual is less than 0.1 MPa, and the iteration residual of the shear strain rate of each slip system is less than 0.001, and the iteration is stopped when the conditions are met.

[0116] After stopping the iteration, the model solving result is output, including: macroscopic Cauchy stress (representing the overall stress state of the material), shear strain rate of each slip system (reflecting the activity degree of single slip system plastic deformation), total sum of cumulative plastic slip (quantifying the total degree of plastic deformation of all slip systems), and dynamically updated internal state variables (such as back stress, critical resolved shear stress of each slip system, and elastic deformation gradient and plastic deformation gradient for decomposing elastic-plastic deformation).

[0117] wherein, the acquisition logic of the macroscopic Cauchy stress is: first, the total deformation is decomposed into elastic deformation and plastic deformation, and the stress tensor is calculated from the elastic deformation by using the elastic constitutive relationship; under the plastic model framework, the stress is continuously recalculated combined with the update of the internal state variables in the iteration process, and the stable macroscopic Cauchy stress is finally obtained when the stress residual meets the convergence condition.

[0118] S3: based on the crystal plastic constitutive model established in step S2, finite element simulation is carried out, and application results facing actual scenes are output, as follows: ​​

[0119] S31: Finite element platform embedding, embedding it in the ABAQUS finite element platform, realizing the numerical calculation function of the model through the UMAT user subroutine.

[0120] S32: Model parameter determination, the complete parameter system required for simulation is divided into two categories:

[0121] The basic constants of the crystal plasticity constitutive model under the reference state. Among them, the basic constants have been determined through independent experiments, and the specific values are as shown in Table 2.

[0122] Table 2

[0123]

[0124] Density characteristic influence index, quantifying the adjustment degree of density deviation on the critical decomposition shear stress, determined by the inverse calibration method, taking the shear stress-strain experimental data of process D (the porosity of sintered silver is 8.38%) as the benchmark, the material constant parameters under the reference density (porosity 5.42%) in Table 2 are brought into the model, and the density characteristic influence index is adjusted through iterative optimization, and finally the density characteristic influence index is determined as 0.43.

[0125] S33: Set the simulation boundary condition, the macroscopic shear strain rate is fixed at 0.01 Carry out numerical simulation on sintered silver of different sintering processes, and output the shear stress-shear strain curves corresponding to each process, wherein:

[0126] Shear stress: the tangential component of the macroscopic Cauchy stress output by the model, which directly reflects the internal force density of the material in the shear direction, and its value evolves dynamically with the start of the slip system (initial yield stage), hardening (stress rising stage), and saturation (stress platform stage);

[0127] Shear strain: the total strain in the shear direction calculated by the model "total deformation gradient decomposition algorithm", which consists of elastic shear strain (derived from crystal lattice deformation) and plastic shear strain (derived from the cumulative slip of each slip system), both of which accumulate synchronously with the loading process, and together determine the shape of the shear stress-strain curve.

[0128] In order to evaluate the superiority of the model of the present application, the results of the improved simulation (based on the density correction model), the original simulation (without considering the density correction model), and the test data are compared (as shown in Figures 2 to 6 It is verified that the prediction accuracy of the improved model under different process conditions has been significantly improved.

[0129] The analysis shows that the improved simulation curve and the test curve show higher consistency under all process conditions. It needs to be specially pointed out that in the attached Figure 2In the case of reference process A (i.e. reference density state), the curves of the original simulation and the improved simulation are completely coincident. This phenomenon is consistent with the expectation of the model construction. When the material density parameter is equal to the reference value, the density correction factor is 1, and the improved model naturally degenerates into the benchmark model, ensuring the continuity and rationality of the model between different states.

[0130] The improvement effect of the model is particularly significant under process conditions deviating from the reference state (as shown in the accompanying drawings). Figures 2 to 5 For example, in the case of a process with high porosity, the prediction results of the original simulation deviate significantly from the experimental data due to the failure to consider the influence of the density. However, the improved simulation can more accurately reflect the changes in the mechanical properties of the material caused by the manufacturing process uncertainty, thereby significantly improving the accuracy of the simulation results.

[0131] The above results fully demonstrate that by introducing the density characteristic parameter, the influence of the manufacturing process uncertainty on the mechanical properties of the packaging interconnection material is effectively quantified, the accuracy of the simulation analysis is significantly improved, and a more reliable theoretical tool is provided for the reliability evaluation of the power module.

[0132] Finally, it should be noted that the above examples are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing examples, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing examples, or make equivalent substitutions for some of the technical features; and these modifications or substitutions do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for constructing a crystal plasticity constitutive model based on a densification feature, characterized by, The method comprises the following steps: S1: modifying the initial value and the saturation value of the critical resolved shear stress by a correction coefficient: The correction coefficient is constructed by the deviation of the current density characteristic parameter from the reference density characteristic parameter, and is adjusted in the form of an exponential function. When the density characteristic parameter is less than the reference value, the correction coefficient is greater than 1, so that the initial value and the saturation value of the critical resolved shear stress are increased synchronously. When the density characteristic parameter is greater than the reference value, the correction coefficient is less than 1, so that the initial value and the saturation value of the critical resolved shear stress are decreased synchronously. The influence of the density on the plastic behavior of the crystal is introduced into the critical resolved shear stress through the correction coefficient; S2: substituting the initial value and the saturation value of the critical resolved shear stress obtained in step S1 into the hardening law of the crystal plasticity constitutive model to establish the crystal plasticity constitutive model based on the density characteristic; S3: simulating the crystal plasticity constitutive model established in step S2 in the finite element software, inputting the macroscopic shear strain rate and the value of the density characteristic parameter of the material, and calculating and outputting the prediction result of the mechanical property of the material.

2. The method of claim 1, wherein the method is based on a density characteristic of a crystal plasticity constitutive model. The initial value and the saturation value of the critical resolved shear stress are modified by the density characteristic parameter: wherein is an initial value of the critical resolved shear stress, is a saturation value of the critical resolved shear stress, is an initial value of the critical resolved shear stress at a reference density feature, is a saturation value of the critical resolved shear stress at a reference density feature, is a density feature parameter value, is a reference density feature parameter value, is a density feature influence exponent.

3. The method of claim 1, wherein the method is characterized by: The crystal plasticity constitutive model based on the density characteristic is established, and the specific process comprises: S21: decomposing the total deformation gradient into an elastic deformation gradient and a plastic deformation gradient, wherein the total deformation gradient is used to describe the overall deformation of the crystal from the initial configuration to the current configuration, the elastic deformation gradient represents the elastic stretching and rotation of the crystal lattice, and the plastic deformation gradient is determined by the plastic deformation caused by the slip of the crystal; S22: based on the elastic deformation gradient and the first the unit slip direction vector of the slip system, the slip direction vector of the slip system after deformation is calculated; based on the inverse of the normal vector of the slip plane of the slip system and the elastic deformation gradient the normal vector of the slip plane of the slip system and the inverse of the elastic deformation gradient, the normal vector of the slip plane of the slip system after deformation is calculated, wherein is the slip system index, and 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: calculating the first shear strain rate of the slip system based on the reference shear strain rate, the resolved shear stress of the slip system, the back stress of the slip system, the critical resolved shear stress of the slip system, the velocity sensitivity index, and the sign function. S24: calculating the first shear strain rate of the slip system based on the reference shear strain rate, the resolved shear stress of the slip system, the back stress of the slip system, the critical resolved shear stress of the slip system, the velocity sensitivity index, and the sign function. S24: calculating the first shear strain rate of the slip system based on the reference shear strain rate, the resolved shear stress of the slip system, the back stress of the slip system, the critical resolved shear S25: based on the direct hardening modulus, the first the shear strain rate of the slip system, the dynamic recovery coefficient, the back stress of the slip system at the time t at the beginning of the current time step, and the absolute value of the shear strain rate of the current time step, the first the back stress change rate of the slip system; based on the back stress of the slip system at the time t at the beginning of the time step, the back stress change rate, and the time step length, the back stress of the slip system at the time t at the end of the time step is calculated and updated. S26: determining the product relationship between the derivative of the plastic deformation gradient with respect to time and the inverse of the plastic deformation gradient based on the sum of the products of the shear strain rate of each slip system, the unit slip direction vector and the slip plane normal vector; the plastic deformation gradient is calculated and updated by time integration, and the elastic deformation gradient is updated by the product of the total deformation gradient and the inverse of the plastic deformation gradient; S27: calculating the total sum of the cumulative plastic slip of all slip systems based on the sum of the absolute values of the shear strain rates of all slip systems in the time interval [0, t]; S28: calculating the hardening modulus by using the initial value and the saturation value of the critical resolved shear stress modified in step S1, combining the initial hardening modulus and the total sum of the cumulative plastic slip; and obtaining the hardening coefficient of the multi-slip system coupling based on the hardening modulus, combining the ratio of the latent hardening to the self-hardening modulus and the Kronecker symbol, so as to represent the influence degree of the shear strain rate of different slip systems on the critical resolved shear stress. S29: Evolution of critical resolved shear stress, under the framework of multi-slip system coupled updating mode, the change rate of critical resolved shear stress of each slip system is obtained by the sum of the product of hardening coefficient of each slip system and the absolute value of corresponding shear strain rate; then the critical resolved shear stress value at next time is updated by combining the critical resolved shear stress at current time, the change rate and time step; the updated value needs to meet the Voce type saturation evolution rule after the density correction, and the critical resolved shear stress saturation value and initial value after the density characteristic parameter correction, combined with the initial hardening modulus and the total sum of cumulative plastic slip of all slip systems, the critical resolved shear stress of the alpha slip system is calculated; S210: Iteration and convergence judgment, the updated critical resolved shear stress, back stress, elastic deformation gradient and plastic deformation gradient are fed back to steps S22 to S29, and the calculation is repeated until the Cauchy stress and the shear strain rate of each slip system meet the preset convergence condition.

4. The method of claim 3, wherein the density-based crystal plasticity constitutive model is constructed by, In step S24, the shear strain rate calculation formula is: wherein is the first slip system shear strain rate, is the reference shear strain rate, is the first resolved shear stress of the slip system, is the first back stress of the slip system, is the first critical resolved shear stress of the slip system, n is the velocity sensitivity exponent, is the sign function.

5. The method of claim 3, wherein the density-based crystal plasticity constitutive model is constructed by, In step S25, the back stress updating formula is: wherein, is the first back stress of the slip system, is the direct hardening modulus, is the dynamic recovery coefficient, is the absolute value of the shear strain rate of the current time step, is the current time, is the time step, is the first back stress of the slip system at the end of the time step, is the back stress of the slip system at the end of the time step, is the first back stress of the slip system at the beginning of the time step, is the back stress of the slip system at the beginning of the time step.

6. The method of claim 3, wherein the method is characterized by: In step S28, the evolution of critical resolved shear stress, the hardening modulus is calculated, and the formula is: wherein, is the hardening modulus, is the initial hardening modulus, is the initial value of the modified critical resolved shear stress, is the saturation value of the modified critical resolved shear stress, is the sum of the cumulative plastic slip of all slip systems.

7. The method of claim 3, wherein the method further comprises: In step S29, the evolution of critical resolved shear stress, under the framework of multi-slip system coupled updating mode, the change rate of critical resolved shear stress of each slip system is calculated, and is updated by time integration: wherein, is the first slip system critical resolved shear stress, is the potential hardening modulus, is the first slip system shear strain rate, is the at the current time step, is the value of the at the current time step, is the value of the at the current time step, is the time step, is the first slip system time step start time critical resolved shear stress; The evolution of critical resolved shear stress also needs to meet the Voce type saturation evolution rule: wherein, is the initial value of the critical resolved shear stress, is the initial value of the critical resolved shear stress, is the initial value of the critical resolved shear stress, is the initial value of the critical resolved shear stress, is the initial value of the critical resolved shear stress, is the initial value of the critical resolved shear stress, 8. The method of claim 3, wherein the method is characterized by: In step S210, the Cauchy stress iteration residual is less than MPa and the iteration residual of the shear strain rate of each slip system is less than , the preset convergence condition is met and the iteration is stopped.

9. The method of claim 1, wherein, In step S3, the macroscopic shear strain rate is set to 0.01 . 10.The method of claim 1, wherein The density characteristic parameter is the porosity of the power module packaging interconnection material, and the porosity is adjusted by the sintering process parameters, including sintering temperature, sintering time and sintering pressure.

Images