Method for reducing interfacial stress between metal and epoxy resin based on molecular simulation

Abstract

The present invention discloses a method for reducing the interfacial stress between a metal and an epoxy resin based on molecular simulation, specifically as follows: Step 1) Establish a molecular dynamics model of an epoxy resin composite material; Step 2) Perform parameter calculations on the crosslinked model obtained in Step 1; Step 3) Obtain a modified molecular dynamics model; Step 4) By setting different target crosslinking degrees in the modified molecular dynamics model, use the method in Step 2 to obtain the thermal and mechanical parameters at different crosslinking degrees, and fit the thermal and mechanical calculation curves with the two curing parameters of the temperature and curing degree of the epoxy resin composite material; 5) Build a multi-physics field finite element simulation model; 6) The simulation can calculate the internal temperature, curing degree, stress, and strain distribution of the epoxy resin composite material; This method optimizes the stress at the interface between the metal and the resin-based insulating material through molecular simulation combined with finite element analysis means to minimize the residual stress at the interface, thereby optimizing the residual stress.

Description

Technical Field

[0001] The present invention belongs to the technical field of power equipment manufacturing, and particularly relates to a method for reducing the interfacial stress between metal and epoxy resin based on molecular simulation. Background Art

[0002] Solid-solid interface structures are commonly present in power equipment. Among them, the interface structure composed of a metal conductor and an epoxy resin insulating material is the most typical. There are solid-solid interface structures in which the central conductor is bonded to the epoxy-based composite material in power equipment such as power cables, dry-type bushings, gas-insulated metal-enclosed switchgear (GIS), and gas-insulated metal-enclosed transmission lines (GIL). The interface is often the weak position of the material insulation. In particular, the insulation defects caused by mechanical stress at the interface have become an issue that cannot be ignored in high-voltage power equipment. Different materials are used on both sides of the interface. Due to the differences in temperature and degree of cure distribution during the casting preparation process of power equipment, various residual stresses will be generated in the formed castings, mainly including curing shrinkage stress and thermal stress. These internal stresses will lead to insulation defects. In actual operation, taking the pot-type insulator as an example, electrical accidents such as insulation cracking and interface peeling at the interface between the metal insert and the epoxy insulation material have occurred. Such accidents will directly cause the failure of the pot-type insulator, thereby affecting the normal operation of the equipment. The interfacial stress concentration between the metal conductor and the resin insulation material is an important inducement for interfacial problems. Therefore, it is necessary to study the residual stress at the interface between the conductor and the solid insulation in power equipment.

[0003] Current research on numerical simulation of interfacial residual stress mainly focuses on finite element simulation calculations, and the method of combining molecular simulation with finite element analysis to reduce interfacial stress has not been involved. For example, the invention patent CN201810448171.9 discloses a multi-scale numerical simulation method for curing residual stress of composite materials, which mainly considers the change of residual stress inside the composite material, but does not consider optimizing the thermal and mechanical parameters of the curing process by molecular simulation. In this paper, the stress at the interface between the metal and the epoxy resin-based insulating material is optimized by combining molecular simulation with finite element analysis means to minimize the residual stress at the interface, and then the residual stress is optimized. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for reducing the interfacial stress between metal and epoxy resin based on molecular simulation, which takes into account optimizing the thermal and mechanical parameters of the curing process by molecular simulation. The stress at the interface between the metal and the resin-based insulating material is optimized by combining molecular simulation with finite element analysis means to minimize the residual stress at the interface, and then the residual stress is optimized.

[0005] The technical solution adopted by the present invention is: a method for reducing the interfacial stress between metal and epoxy resin based on molecular simulation, specifically: Step 1) Establish a molecular dynamics model of epoxy resin composite using Material Studio software; Step 2) Use the Forcite module in MS software to calculate the parameters of the crosslinked model obtained in Step 1; Step 3) Modify the molecular dynamics model in Step 1) to obtain a modified molecular dynamics model; Step 4) By setting different target crosslinking degrees in the modified molecular dynamics model, use the method in Step 2) to obtain the thermal and mechanical parameters under different crosslinking degrees, and fit the thermal and mechanical calculation curves with the two curing parameters of the temperature and curing degree of the epoxy resin composite; 5) Build a multi-physics field finite element simulation model, specifically including a heat transfer curing module, a flow compaction module, and a stress-strain module; 6) The simulation can calculate the internal temperature, curing degree, stress, and strain distribution of the epoxy resin composite; calculate the crosslinking degree of the modified molecular dynamics model until the minimum value of the interfacial stress is output.

[0006] The characteristics of the present invention also lie in that

[0007] Specifically, Step 1 is as follows:

[0008] Step 1.1) Use the amorphous cell tool in Material Studio software to construct a 3D box structure; initially create a molecular dynamics model at low density, and use the conjugate gradient method to relax through energy minimization, then use isothermal and isochoric MD simulations for geometric optimization and kinetic relaxation to obtain a molecular dynamics model with the lowest energy; finally, perform isobaric MD simulation at atmospheric pressure to obtain a configuration with the density and molecular arrangement closest to the actual distribution, so as to fully equilibrate the initial mixture before the chemical reaction starts. Based on the above operations, an uncured epoxy resin-curing agent amorphous cell structure model is obtained.

[0009] Step 1.2) Crosslinking process: Use the Perl programming language to perform MD simulation, set the crosslinking reaction temperature, crosslinking distance, and target crosslinking density of the epoxy resin composite; the uncured epoxy resin-curing agent amorphous cell structure model is equilibrated under the NPT system, and the cycle of chemical reaction is repeated, and then thermalization is carried out until the required curing degree is obtained; among them, the simulation force field is the COMPASSⅡ force field, the temperature control algorithm is Andersen, the pressure control algorithm is Berendsen, the electrostatic interaction is based on the Ewald method and the Atom based method, and the simulation accuracy is Medium;

[0010] Step 1.3) Annealing process: Anneal the models with different curing degrees in 1.2) to obtain the final crosslinked model for thermodynamic parameter calculation.

[0011] Specifically, Step 2 is as follows:

[0012] Step 2.1) The glass transition temperature T can be obtained by performing a quasi-static cooling simulation on the epoxy resin system, specifically: write a script using the Perl language, heat up the model obtained in Step 1, and perform a quasi-static cooling, gradually cooling down; at each temperature point, perform NPT / NVT molecular dynamics simulations on the model alternately; perform multiple rounds of simulations in total, and use the average value of the model density at each temperature to determine the glass transition temperature T g ; The glass transition temperature T of the epoxy resin composite is calculated based on the change in the slope of the density-temperature relationship during the constant-pressure cooling process; g The glass transition temperature T of the epoxy resin composite g is calculated based on the change in the slope of the density-temperature relationship during the constant-pressure cooling process;

[0013] Step 2.2) In this paper, the NEMD method is used to calculate the thermal conductivity; specifically: first, run the model obtained in Step 1 in the NVT system, then cancel the NVT global heat bath, and perform a local heat bath operation in the NVE ensemble. Divide the model finally obtained in Step 1 into multiple regions along the x-axis, and fix 2 regions at the left and right boundaries respectively as the fixed layers. Set the region adjacent to the fixed layer on the left as the heat sink, and the region adjacent to the fixed layer on the right as the heat source. Use the Langevin heat bath to set the temperature values of the heat source and the heat sink, so that energy exchange occurs continuously from the heat source to the heat sink until the temperature gradient reaches equilibrium and stability. Perform a linear fit on the temperature distribution to obtain the temperature gradient, and then based on Fourier's law, the thermal conductivity can be obtained; the specific heat capacity can be calculated according to Equation (1):

[0014]

[0015] where: J is the energy flux in the z direction; dT / dz is the temperature gradient, and the negative sign indicates that the direction of the energy flux is opposite to the gradient;

[0016] Step 2.3) The calculation formula for the coefficient of thermal expansion is:

[0017]

[0018] where: V is the volume of the model;

[0019] Step 2.4) Calculate the stiffness matrix of the model according to Equation (3), and its elements are the second-order derivatives of the potential energy with respect to the strain, that is

[0020]

[0021] where U is the potential energy; σ is the stress, which is the first-order derivative of the potential energy per unit volume with respect to the strain, the “+” represents tension, and the “-” represents compression; ε is the strain. For isotropic materials, the two Lame constants λ and μ are obtained from the stiffness matrix in Equation (4):

[0022]

[0023] Accordingly, the Young's modulus E, shear modulus G, bulk modulus B, and Poisson's ratio ν are as follows:

[0024]

[0025] Step 3 is specifically as follows:

[0026] Step 3.1) Measurement of thermal and mechanical test parameters: The thermal conductivity and specific heat capacity are important parameters affecting the heat transfer and exchange inside the composite material. Use the laser thermal conductivity meter NETZSCH LFA447 to measure the thermal conductivity and specific heat capacity of the epoxy resin composite material; use the differential scanning calorimeter of the Swiss Mettler DSC822 to measure the glass transition temperature of the epoxy resin composite material; measure the density of the epoxy resin composite material through the QL-300G / QL-300S density tester; use a linear thermal expansion instrument to measure the thermal expansion coefficient of the epoxy resin; use a dynamic universal testing machine Z250 to measure the storage modulus and Poisson's ratio;

[0027] Step 3.2) Correction of empirical and semi-empirical formulas: The calculation of the specific heat capacity needs to consider the quantum effect, that is, calculate the phonon density of states by performing a Fourier transform on the velocity autocorrelation function, and then obtain the quantum correction factor f according to the statistical relationship between classical and quantum:

[0028]

[0029] where x is the reduced energy commonly used in statistical physics; divide the area enclosed by the corrected density of states and the coordinate axis by the area enclosed by the density of states and the coordinate axis to obtain the correction factor k of the specific heat capacity c , and then the corrected specific heat capacity calculation formula can be obtained as:

[0030]

[0031] In the formula, T is the system temperature; E is the total energy of the system;

[0032] Step 3.3) Compare the experimental measurements obtained in Step 3.1) with the molecular dynamics simulation calculations obtained in Step 2), and use the empirical formula to correct the molecular dynamics model.

[0033] Step 5 is specifically as follows:

[0034] Step 5.1) Discretize the simulation model into finite element meshes. Select a suitable mesh generation method according to the complexity of the model and the calculation requirements;

[0035] Step 5.2) Establishment of the heat transfer and curing module: The specific building process is as follows:

[0036] (1) Define the mathematical equations for the heat transfer and curing problems, such as the heat conduction equation and the curing model;

[0037] (2) Discretize the equations into the finite element format and construct the finite element equation system at the grid nodes;

[0038] (3) Select a suitable numerical solution method, such as the iterative method or the direct solution method, to solve the finite element equation system;

[0039] (4) Analyze the temperature distribution and the curing state based on the solution results;

[0040] Step 5.3) Establishment of the flow compaction module: The specific construction process is as follows:

[0041] (1) Define the mathematical equations for the flow compaction problem, such as the fluid mechanics equation and the particle dynamics equation.

[0042] (2) Discretize the equations into the finite element format and construct the finite element equation system at the grid nodes.

[0043] (3) Select a suitable numerical solution method, such as the iterative method or the direct solution method, to solve the finite element equation system.

[0044] (4) Analyze the flow field and the mixing state based on the solution results.

[0045] Step 5.4) Establishment of the stress-strain module: The specific construction process is as follows:

[0046] (1) Define the mathematical equations for the stress-strain problem, such as the elasticity equation and the material constitutive relation.

[0047] (2) Discretize the equations into the finite element format and construct the finite element equation system at the grid nodes.

[0048] (3) Select a suitable numerical solution method, such as the iterative method or the direct solution method, to solve the finite element equation system.

[0049] (4) Analyze the stress distribution and the deformation situation based on the solution results.

[0050] Step 6 is specifically as follows:

[0051] Take the thermal and mechanical parameters that change with the degree of crosslinking in Step 4) as the initial material parameters of the interfacial stress finite element simulation model built in Step 5), and the simulation can calculate the temperature, degree of curing, stress, and strain distributions inside the epoxy resin composite material; taking the minimum value of the stress at the interface between the metal conductor and the epoxy resin composite material as the optimal target, if the calculated interfacial stress is not an extreme value, recalculate the degree of crosslinking of the modified molecular dynamics model until the minimum value of the interfacial stress is output.

[0052] The beneficial effects of the present invention are as follows: The method of the present invention takes into account that the interfacial stress concentration between the metal conductor and the resin insulating material is an important inducement for interfacial problems. By optimizing the thermal and mechanical parameters during the curing process through molecular simulation and combining with finite element analysis means to optimize the stress at the interface between the metal and the resin-based insulating material, it is possible to analyze the influence of material parameters on the stress during the curing process and then optimize the curing process formula to minimize the residual stress at the interface, thereby optimizing the residual stress. It can effectively improve the reliability of power equipment and has certain economic efficiency and practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 is the flowchart for building the model of the method of the present invention;

[0054] Figure 2 is the structural diagram of the bisphenol A epoxy resin monomer in the embodiment of the present invention;

[0055] Figure 3 is the flowchart of the crosslinking process in the embodiment of the present invention;

[0056] Figure 4 is the flowchart of the curing deformation of the composite material in the embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0057] The present invention will be described in detail below with reference to the drawings and specific embodiments.

[0058] Example 1

[0059] The present invention provides a method for reducing the interfacial stress between a metal and an epoxy resin based on molecular simulation, as Figures 1-4 shown, which specifically includes the following steps:

[0060] Step 1) Establish a molecular dynamics model of the epoxy resin composite material using Material Studio (MS) software. Step 1 is specifically as follows:

[0061] 1.1) Pre-crosslinking process: In this patent, bisphenol A epoxy resin commonly used in pot insulators is selected. As Figure 2 shown, its monomer and curing agent are bisphenol A diglycidyl ether (DGEBA) and 3,3'-diaminodiphenyl sulfone (33DDS) respectively. The structural diagram of the bisphenol A epoxy resin monomer is as Figure 2As shown, an amorphous cell tool in Material Studio (MS) software was used to construct a 3D box structure containing DGEBA, 33DDS, and Al2O3. The stoichiometric ratio of DGEBA and 33DDS in the box structure is 2:1. In the molecular dynamics model, the diameter of spherical Al2O3 nanoparticles with saturated surface hydroxyl groups is 1.00 nm (different diameters can be set). The volume fraction of Al2O3 is 20%. In the initial stage, a mixture of epoxy resin and curing agent was filled and equilibrated to a simulation cell with three-dimensional periodic boundary conditions in the required stoichiometry. Initially, the molecular dynamics model was created at a low density (0.5 - 10 g / cm 3 ) and relaxed by energy minimization using the conjugate gradient method. Then, isothermal and isochoric (NVT ensemble) MD simulations at 600 K for 50 ps were used for geometric optimization and kinetic relaxation to obtain the molecular dynamics model with the lowest energy. Finally, an isobaric (NPT) MD simulation at atmospheric pressure for 400 ps was performed to obtain a configuration with density and molecular arrangement closest to the actual distribution, so as to fully equilibrate the initial mixture before the chemical reaction started. Based on the above operations, an uncured epoxy resin - curing agent amorphous unit cell structure model was obtained.

[0062] 1.2) Crosslinking process: To ensure full reaction of the epoxy resin and curing agent in the above model, MD simulations were carried out using the Perl programming language. The crosslinking reaction temperature was set at 480 K, and the crosslinking distance was 0.35 - 0.75 nm. The target crosslinking density of the epoxy resin composite was set at 85% (different target crosslinking degrees can be set). The uncured epoxy resin - curing agent amorphous unit cell structure model was equilibrated in the NPT system at 298 K and 1.013×10 -4 GPa pressure, and the cycle of chemical reaction was repeated, followed by thermalization until the required degree of cure was obtained. The simulation force field was the COMPASSⅡ force field, the temperature control algorithm was Andersen, the pressure control algorithm was Berendsen, the electrostatic interaction was based on the Ewald method and the Atom based method, and the simulation accuracy was Medium.

[0063] 1.3) Annealing process: The models with different degrees of cure in 1.2) were annealed to obtain the final crosslinked model for thermodynamic parameter calculation.

[0064] Step 2) Use the Forcite module in MS software to calculate the parameters of the crosslinked model obtained in Step 1, specifically including the glass transition temperature T g , thermal conductivity, specific heat capacity, coefficient of thermal expansion, Young's modulus E, shear modulus G, bulk modulus B, and Poisson's ratio v.

[0065] 2.1) The glass transition temperature T can be obtained by quasi-static cooling simulation of the epoxy resin system g Specifically, a script was written in Perl language to heat the model obtained in step 1 to 700K and perform quasi-static cooling of 30K / 100ps-100ps, gradually cooling it to 250K. At each temperature point, the model was alternately simulated with NPT / NVT molecular dynamics for 100ps. A total of 5 rounds of simulations were performed, and the average value of the model density at each temperature was used to determine the glass transition temperature T g . Glass transition temperature T of epoxy resin composites g It is calculated based on the change in the slope of the density-temperature relationship during constant pressure cooling.

[0066] 2.2) This paper uses the NEMD method to calculate thermal conductivity; specifically: first, the model obtained in step 1 is run at 300K for 50ps in the NVT system, then the NVT overall heat bath is cancelled, and a local heat bath is run for 100ps in the NVE ensemble. The model finally obtained in step 1 is divided into 20 regions along the x-axis, and two regions are fixed on the left and right boundaries as fixed layers. The area close to the fixed layer on the left is set as a heat sink, and the area close to the fixed layer on the right is set as a heat source. The Langevin heat bath is used to set the temperature values ​​of the heat source and heat sink to 350K and 250K respectively. In this way, energy is continuously exchanged from the heat source to the heat sink, and finally the temperature gradient is balanced and stable. The temperature distribution is linearly fitted to obtain the temperature gradient, and then the thermal conductivity can be obtained based on Fourier's law. The thermal conductivity can be calculated according to the energy fluctuation method in the NVT system according to formula (1).

[0067]

[0068] Where: J is the energy flux in the z direction; dT / dz is the temperature gradient; the negative sign indicates that the direction of the energy flux is opposite to the gradient.

[0069] 2.3) The coefficient of thermal expansion (CTE) is one of the main physical properties of a material. It can be used to calculate the internal stress caused by thermal expansion and is an important indicator for measuring the thermal stability of a material. The calculation formula is:

[0070]

[0071] Where: V is the volume of the model;

[0072] 2.4) Using the static constant strain method, apply a small strain within the elastic limit in the crosslinking model obtained in 1.3, and then re - perform energy optimization. Apply this strain in different directions and repeat the above process multiple times. The stiffness matrix of the model can be calculated according to Equation (3), and its elements are the second - order derivatives of the potential energy with respect to the strain, that is

[0073]

[0074] where U is the potential energy; σ is the stress, which is the first - order derivative of the potential energy per unit volume with respect to the strain, “+” represents tension, and “ - ” represents compression; ε is the strain. For isotropic materials, the two Lame constants λ and μ are obtained from the stiffness matrix in Equation (4):

[0075]

[0076] Based on this, the Young's modulus E, shear modulus G, bulk modulus B, and Poisson's ratio v are:

[0077]

[0078] 3) Modify the molecular dynamics model in step 1) by experimentally measuring parameters, the thermal conductivity, specific heat capacity, glass transition temperature, density, coefficient of thermal expansion, storage modulus, Poisson's ratio measured by instruments, as well as empirical / semi - empirical formulas to obtain the modified molecular dynamics model.

[0079] 3.1) Measurement of thermal and mechanical test parameters: Thermal conductivity and specific heat capacity are important parameters affecting the heat transfer and exchange within the composite material. Use the laser thermal conductivity meter NETZSCH LFA447 to measure the thermal conductivity and specific heat capacity of the epoxy resin composite material; use the differential scanning calorimeter of the Swiss Mettler DSC822 to measure the glass transition temperature of the epoxy resin composite material; measure the density of the epoxy resin composite material through the QL - 300G / QL - 300S density tester; use a linear thermal expansion instrument to measure the coefficient of thermal expansion of the epoxy resin; use a dynamic universal testing machine Z250 to measure the storage modulus and Poisson's ratio;

[0080] 3.2) Modification by empirical and semi - empirical formulas: Taking the specific heat capacity parameter as an example for thermal parameters, for the epoxy resin composite material, the specific heat capacity obtained by the molecular dynamics model is larger than the result of the actual experimental measurement. The main reason is that the vibration energy levels of light - mass atoms are very high and cannot be fully excited at room temperature, while the molecular dynamics simulation assumes that all atoms are excited, so the calculated specific heat capacity is higher. Therefore, the calculation of the specific heat capacity needs to consider the quantum effect, that is, calculate the phonon density of states by performing a Fourier transform on the velocity autocorrelation function, and then obtain the quantum correction factor f according to the statistical relationship between classical and quantum:

[0081]

[0082] Among them, \(x\) is the reduced energy commonly used in statistical physics; dividing the area enclosed by the corrected density of states and the coordinate axes by the area enclosed by the density of states and the coordinate axes, the correction factor \(k\) of the specific heat capacity can be obtained. c , and then the formula for calculating the corrected specific heat capacity can be obtained as:

[0083]

[0084] In the formula, \(T\) is the system temperature; \(E\) is the total energy of the system (the sum of potential energy and kinetic energy);

[0085] For mechanical parameters, molecular dynamics (MD) simulation has high computational requirements and can only simulate phenomena on very small time scales (nanoseconds). If the MD simulation includes the simulated deformation of materials to calculate mechanical properties, the deformation must occur on the order of nanoseconds. Under typical laboratory conditions, experimental mechanical tests occur on higher time scales, such as seconds, minutes, or hours. Therefore, the time scales of MD simulation and experimental tests differ by several orders of magnitude, and so do their corresponding strain rates. Therefore, the mechanical properties calculated by simulation and measured should also be significantly different. This difference is usually referred to as the strain rate effect. Normalization reduces the strain rate effect by eliminating the corresponding errors from the values. Therefore, normalization is a very convenient method to minimize the errors in the predicted mechanical property values due to the strain rate effect.

[0086] 3.3) Compare the experimental measurements obtained in step 3.1) with the molecular dynamics simulation calculations obtained in step 2), and use an empirical formula to correct the molecular dynamics model.

[0087] 4) Through the corrected molecular dynamics model in step 3), simulate and calculate the thermal and mechanical parameters of epoxy resin composites with different crosslinking degrees, and obtain the expressions of the thermal and mechanical parameters changing with the curing process. By setting different target crosslinking degrees in the corrected molecular dynamics model, use the method in step 2) to obtain the thermal and mechanical parameters at different crosslinking degrees, and fit the thermal and mechanical calculation curves with the two curing parameters of the temperature and curing degree of the epoxy resin composites;

[0088] 5) Build a multi-physics finite element simulation model, specifically including a heat transfer curing module, a flow compaction module, and a stress-strain module.

[0089] 5.1) Discretize the simulation model into finite element meshes. According to the complexity of the model and the computational requirements, select a suitable mesh generation method;

[0090] 5.2) Establishment of heat transfer curing module: The distribution of the temperature field during the curing process is essentially a non-linear heat conduction problem with an internal heat source. This internal heat source is generated by the exothermic curing reaction of epoxy resin. This macroscopic dynamics can usually be characterized by the Fourier heat conduction law equation, and its specific form is shown in Equation (8):

[0091]

[0092] In the formula: ρ is the density of the composite material; C ρ is the specific heat capacity of the composite material; t is the time; k x 、k y 、k z are the thermal conductivities of the material in the three directions of the object; the left side of Equation (8) is the heat required for the microelement to increase in temperature, and the first, second, and third terms on the right side are the heat transferred into the microelement in the x, y, and z directions. Q is the heat generated inside the composite material, which is generated by the exothermic curing of the resin; this formula consists of two parts. One part is the heat conduction equation. For isotropic materials, the thermal conductivities of the object in the three directions are equal, that is, K xx =K yy =K zz ; the other part is the reaction exothermic equation Q of the resin, as shown in Equation (9):

[0093]

[0094] In the formula: ΔH r is the total reaction heat of resin curing, and dα / dt is the curing rate.

[0095] The total reaction heat is a constant value, which can be further measured by thermal analysis methods such as DSC and TGA; the heat flux density is proportional to the curing rate. The curing rate reflects the kinetic behavior during the resin curing process. Its research methods are divided into a phenomenological model at the macroscopic scale and a mechanism model at the microscopic scale. The phenomenological model focuses on the overall steps of the reaction, avoiding the details of chemical reactions. It uses the method of multiple linear regression and describes the reaction kinetics with a relatively simple rate equation, which has high engineering application value. Therefore, this paper uses the phenomenological model method to study the curing kinetics of epoxy resin. The general form of the phenomenological model is shown in Equation (10).

[0096]

[0097] In the formula: i is the curing reaction step; K(T) is the temperature rate correlation equation; f(α) is the resin curing reaction model; h(P) is the gas pressure correlation equation.

[0098] The specific construction process of the heat transfer curing module is as follows:

[0099] (1) Define the mathematical equations for the heat transfer curing problem, such as the heat conduction equation and the curing model;

[0100] (2) Discretize the equations into a finite element format and construct a finite element equation system at the grid nodes;

[0101] (3) Select a suitable numerical solution method, such as the iterative method or the direct solution method, to solve the finite element equation system;

[0102] (4) Analyze the temperature distribution and curing state based on the solution results;

[0103] 5.3) Establishment of the flow compaction module. The flow compaction of composite materials occurs in the initial curing stage, i.e., before the gel point. According to different mechanisms, the flow is mainly divided into two categories, namely seepage flow and shear flow. Seepage flow refers to the flow of the resin matrix in the porous medium, which reaches saturation under an external pressure and squeezes out the excess resin; shear flow occurs during the curing and forming process of thermoplastic composite materials and is generated by the shear force between the resin matrix and the filler. Generally, a flow-compaction coupling calculation model is established based on the effective stress principle and Darcy's seepage law to simulate the flow compaction process during the curing process of epoxy resin composites. The method of establishing the seepage equation and the effective stress principle by using the saturated flow of porous media is a commonly used research method at present, and its governing equations are as follows:

[0104]

[0105]

[0106] Equations (11) and (12) are respectively the basic seepage equation and the effective stress principle derived from Darcy's law; where: ν i is the flow velocity of the epoxy resin in the i direction, K i is the permeability of the filler in the i direction, η is the viscosity of the epoxy resin, is the externally applied pressure, p is the effective stress borne by the filler, and P is the pore pressure borne by the epoxy resin.

[0107] The specific construction process of the flow compaction module is as follows:

[0108] (1) Define the mathematical equations for the flow compaction problem, such as fluid mechanics equations and particle dynamics equations.

[0109] (2) Discretize the equations into a finite element format and construct a finite element equation system at the grid nodes.

[0110] (3) Select a suitable numerical solution method, such as the iterative method or the direct solution method, to solve the finite element equation system.

[0111] (4) Analyze the flow field and mixing state based on the solution results.

[0112] 5.4) Establishment of stress-strain module: The heat transfer and curing module obtained by coupling the heat conduction and curing kinetics equations can calculate the temperature and degree of cure at any time and space in the component. On this basis, the stress-deformation module, according to the obtained temperature field and degree of cure field, realizes the coupling of heat transfer and structural mechanics through the thermo-mechanical coupling module, and then establishes the relationship between stress and strain according to the constitutive equation to calculate the curing shrinkage strain and thermal strain generated during the resin curing deformation process. The linear elastic constitutive model is one of the commonly used methods for predicting the curing deformation of composites, and its general representation is:

[0113] {σ} = [E]({ε} - {ε0}) + {σ0} (13)

[0114] Where: {σ} and {σ0} are the residual stress and the initial stress value respectively, {ε} and {ε0} are the total strain and the total internal strain respectively, and [E] is the tensor of the elastic modulus.

[0115] The specific construction process of the stress-strain module is as follows:

[0116] (1) Define the mathematical equations of the stress-strain problem, such as the equations of elasticity and the material constitutive relationship.

[0117] (2) Discretize the equations into the finite element format and construct the finite element equations at the grid nodes.

[0118] (3) Select a suitable numerical solution method, such as the iterative method or the direct solution method, to solve the finite element equations.

[0119] (4) According to the solution results, analyze the stress distribution and deformation conditions.

[0120] 6) Take the thermal and mechanical parameters that change with the degree of crosslinking in step 4) as the initial material parameters of the interfacial stress finite element simulation model built in step 5). The simulation can calculate the temperature, degree of cure, stress, and strain distributions inside the epoxy resin composite material; taking the minimum value of the stress at the interface between the metal conductor and the epoxy resin composite material as the optimal target, if the calculated interfacial stress is not an extreme value, recalculate the degree of crosslinking of the corrected molecular dynamics model until the minimum value of the interfacial stress is output.

[0121] Example 2

[0122] Method for reducing interfacial stress between metal and epoxy resin based on molecular simulation, specifically: Step 1) Establish a molecular dynamics model of epoxy resin composite using Material Studio software; Step 2) Use the Forcite module in MS software to calculate parameters for the crosslinked model obtained in Step 1; Step 3) Modify the molecular dynamics model in Step 1) to obtain a modified molecular dynamics model; Step 4) By setting different target crosslinking degrees in the modified molecular dynamics model, use the method in Step 2) to obtain thermal and mechanical parameters at different crosslinking degrees, and fit the thermal and mechanical calculation curves with the two curing parameters of epoxy resin composite temperature and curing degree; 5) Build a multi-physics field finite element simulation model, specifically including a heat transfer curing module, a flow compaction module, and a stress-strain module; 6) The simulation can calculate the internal temperature, curing degree, stress, and strain distribution of the epoxy resin composite; perform crosslinking degree calculation on the modified molecular dynamics model until the minimum interfacial stress is output.

[0123] Example 3

[0124] Method for reducing interfacial stress between metal and epoxy resin based on molecular simulation, specifically: Step 1) Establish a molecular dynamics model of epoxy resin composite using Material Studio software; Step 2) Use the Forcite module in MS software to calculate parameters for the crosslinked model obtained in Step 1; Step 3) Modify the molecular dynamics model in Step 1) to obtain a modified molecular dynamics model; Step 4) By setting different target crosslinking degrees in the modified molecular dynamics model, use the method in Step 2) to obtain thermal and mechanical parameters at different crosslinking degrees, and fit the thermal and mechanical calculation curves with the two curing parameters of epoxy resin composite temperature and curing degree; 5) Build a multi-physics field finite element simulation model, specifically including a heat transfer curing module, a flow compaction module, and a stress-strain module; 6) The simulation can calculate the internal temperature, curing degree, stress, and strain distribution of the epoxy resin composite; perform crosslinking degree calculation on the modified molecular dynamics model until the minimum interfacial stress is output.

[0125] Step 1 is specifically as follows:

[0126] Step 1.1) Use the amorphous cell tool in Material Studio software to construct a 3D box structure; initially create a molecular dynamics model at low density, and use the conjugate gradient method to relax through energy minimization, then use isothermal and isochoric MD simulations for geometric optimization and kinetic relaxation to obtain a molecular dynamics model with the lowest energy; finally, perform isobaric MD simulation at atmospheric pressure to obtain a configuration with density and molecular arrangement closest to the actual distribution, so as to fully balance the initial mixture before the chemical reaction starts. Based on the above operations, an amorphous cell structure model of uncured epoxy resin-curing agent is obtained.

[0127] Step 1.2) Crosslinking process: MD simulation is carried out using the Perl programming language, setting the crosslinking reaction temperature, crosslinking distance, and target crosslinking density of the epoxy resin composite; the amorphous unit cell structure model of the uncured epoxy resin-curing agent is equilibrated under the NPT system, and the cycle of chemical reactions is repeated, and then thermalization is carried out until the required degree of cure is obtained; among them, the simulation force field is the COMPASSⅡ force field, the temperature control algorithm is Andersen, the pressure control algorithm is Berendsen, the electrostatic interaction is based on the Ewald method and the Atom based method, and the simulation accuracy is Medium;

[0128] Step 1.3) Annealing process: The models with different degrees of cure in 1.2) are annealed to obtain the final crosslinked model for thermodynamic parameter calculation.

Claims

1. A method for reducing the interfacial stress between a metal and an epoxy resin based on molecular simulation, characterized in that Specifically: Step 1) Establish a molecular dynamics model of epoxy resin composite using Material Studio software; Step 2) Use the Forcite module in MS software to calculate the parameters of the crosslinking model obtained in Step 1; Step 3) Modify the molecular dynamics model in Step 1) to obtain a modified molecular dynamics model; Step 4) By setting different target crosslinking degrees in the modified molecular dynamics model, use the method in Step 2) to obtain the thermal and mechanical parameters at different crosslinking degrees, and fit the thermal and mechanical calculation curves with the two curing parameters of the temperature and curing degree of the epoxy resin composite; 5) Build a multi-physics field finite element simulation model, specifically including a heat transfer curing module, a flow compaction module, and a stress-strain module; 6) Simulate and calculate the internal temperature, curing degree, stress, and strain distribution of the epoxy resin composite; Calculate the crosslinking degree of the modified molecular dynamics model until the minimum interfacial stress is output; Step 1 is specifically as follows: Step 1.1) Use the amorphous cell tool in Material Studio software to construct a 3D box structure; Initially create a molecular dynamics model at low density and relax it through energy minimization using the conjugate gradient method, then perform geometric optimization and kinetic relaxation using isothermal and isochoric MD simulations to obtain a molecular dynamics model with the lowest energy; Finally, perform isobaric MD simulations at atmospheric pressure to obtain a configuration with the density and molecular arrangement closest to the actual distribution, so as to fully equilibrate the initial mixture before the chemical reaction starts. Based on the above operations, an uncured epoxy resin-curing agent amorphous cell structure model is obtained; Step 1.2) Crosslinking process: Use the Perl programming language for MD simulation, set the crosslinking reaction temperature, crosslinking distance, and target crosslinking density of the epoxy resin composite; The uncured epoxy resin-curing agent amorphous cell structure model is equilibrated in the NPT system, and the cycle of chemical reactions is repeated, and then thermalization is performed until the required curing degree is obtained; Among them, the simulation force field is the COMPASSⅡ force field, the temperature control algorithm is Andersen, the pressure control algorithm is Berendsen, the electrostatic interaction is based on the Ewald method and the Atom based method, and the simulation accuracy is Medium; Step 1.3) Annealing process: Anneal the models with different curing degrees in 1.2) to obtain the final crosslinking model for thermodynamic parameter calculation.

2. The method for reducing the interfacial stress between a metal and an epoxy resin based on molecular simulation according to claim 1, wherein Step 2 is specifically as follows: Step 2.1) The glass transition temperature T can be obtained by performing a quasi-static cooling simulation on the epoxy resin system. g Specifically: Write a script using the Perl language to heat up the model obtained in Step 1 and perform quasi-static cooling, gradually cooling it; at each temperature point, perform NPT / NVT molecular dynamics simulations on the model alternately; perform multiple rounds of simulations in total, and use the average value of the model density at each temperature to determine the glass transition temperature T. g ; The glass transition temperature T of the epoxy resin composite g is calculated based on the change in the slope of the density-temperature relationship during the constant-pressure cooling process. Step 2.2) The NEMD method is adopted in this paper to calculate the thermal conductivity. Specifically, first, the model obtained in Step 1 is run under the NVT system. Then, the overall NVT heat bath is removed, and local heat bath operation is carried out under the NVE ensemble. The model finally obtained in Step 1 is divided into multiple regions along the x-axis. Two regions are taken at the left and right boundaries respectively for fixation as the fixed layers. The region adjacent to the fixed layer on the left is set as the heat sink, and the region adjacent to the fixed layer on the right is set as the heat source. The Langevin heat bath is used to set the temperature values of the heat source and the heat sink. In this way, energy exchange continuously occurs from the heat source to the heat sink until the temperature gradient reaches equilibrium and stability. The temperature distribution is linearly fitted to obtain the temperature gradient. Then, based on Fourier's law, the thermal conductivity can be obtained. The specific heat capacity is calculated according to Equation (1): where: J is the energy flux in the z direction; dT / dz is the temperature gradient. The negative sign indicates that the direction of the energy flux is opposite to the gradient; Step 2.3) The calculation formula for the coefficient of thermal expansion is: where: V is the volume of the model; Step 2.4) The stiffness matrix of the model is calculated according to Equation (3), and its elements are the second derivatives of the potential energy with respect to the strain, that is where, U is the potential energy; σ is the stress, which is the first derivative of the potential energy per unit volume with respect to the strain. The "+" represents tension, and the "-" represents compression; ε is the strain; for isotropic materials, the two Lame constants λ and μ are obtained from the stiffness matrix of Equation (4): Based on this, the Young's modulus E, shear modulus G, bulk modulus B, and Poisson's ratio v are obtained as follows:

3. The method for reducing the interfacial stress between a metal and an epoxy resin based on molecular simulation according to claim 2, wherein, Step 3 is specifically as follows: Step 3.1) Measurement of thermal and mechanical test parameters: The thermal conductivity and specific heat capacity are important parameters affecting the transfer and exchange of heat inside the composite material. A laser thermal conductivity meter NETZSCH LFA447 is used to test the thermal conductivity and specific heat capacity of the epoxy resin composite material; a differential scanning calorimeter of a Swiss Mettler DSC822 is used to test the glass transition temperature of the epoxy resin composite material; a QL-300G / QL-300S density tester is used to measure the density of the epoxy resin composite material; a linear thermal dilatometer is used to test the coefficient of thermal expansion of the epoxy resin; a dynamic universal testing machine Z250 is used to test the storage modulus and Poisson's ratio; Step 3.2) Correction of empirical and semi-empirical formulas: The calculation of the specific heat capacity needs to consider the quantum effect, that is, the phonon density of states is calculated by performing a Fourier transform on the velocity autocorrelation function, and then the quantum correction factor f is obtained according to the statistical relationship between classical and quantum: where x is the reduced energy commonly used in statistical physics; dividing the area enclosed by the corrected density of states and the coordinate axes by the area enclosed by the density of states and the coordinate axes gives the correction factor k for the specific heat capacity c , and then the corrected specific heat capacity calculation formula can be obtained as follows: where T is the system temperature; E is the total energy of the system; Step 3.3) Compare the experimental measurements obtained in Step 3.1) with the molecular dynamics simulation calculations obtained in Step 2), and use empirical formulas to correct the molecular dynamics model.

4. The method for reducing the interfacial stress between a metal and an epoxy resin based on molecular simulation according to claim 3, wherein Step 5 is specifically as follows: Step 5.1) Discretize the simulation model into finite element meshes; select an appropriate mesh generation method according to the complexity of the model and the calculation requirements; Step 5.2) Establishment of the heat transfer and curing module: The specific construction process is as follows: (1) Define the mathematical equation of the heat transfer and curing problem; (2) Discretize the equation into a finite element format and construct a finite element equation system at the mesh nodes; (3) Select an iterative method or a direct solution method to solve the finite element equation system; (4) Analyze the temperature distribution and curing state according to the solution results; Step 5.3) Establishment of the flow compaction module: The specific construction process is as follows: (1) Define the mathematical equation for the flow compaction problem; (2) Discretize the equation into a finite element format and construct a finite element equation system at the grid nodes; (3) Select an iterative method or a direct solution method to solve the finite element equation system; (4) Analyze the flow field and mixing state according to the solution results; Step 5.4) Establishment of the stress-strain module: The specific construction process is as follows: (1) Define the mathematical equations for the stress-strain problem, such as the equations of elasticity and material constitutive relations; (2) Discretize the equation into a finite element format and construct a finite element equation system at the grid nodes; (3) Select an iterative method or a direct solution method to solve the finite element equation system; (4) Analyze the stress distribution and deformation conditions according to the solution results.

5. The method for reducing the interfacial stress between a metal and an epoxy resin based on molecular simulation according to claim 4, wherein Step 6 is specifically as follows: Take the thermal and mechanical parameters that change with the degree of crosslinking in step 4) as the initial material parameters of the interfacial stress finite element simulation model built in step 5), and the simulation can calculate the temperature, degree of curing, stress, and strain distributions inside the epoxy resin composite material; taking the minimum value of the stress at the interface between the metal conductor and the epoxy resin composite material as the optimal target, if the calculated interfacial stress is not an extreme value, recalculate the degree of crosslinking of the modified molecular dynamics model until the minimum value of the interfacial stress is output.

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