A method for predicting moisture-induced interfacial fracture failure of reflow soldered electronic packages

Abstract

The application discloses a kind of moisture-induced reflow soldering electronic packaging interface fracture failure prediction methods, it is related to fracture failure prediction technical field, comprising the following steps: S1, according to the energy contribution of elastic deformation, humidity effect, material interface and material damage to electronic packaging system, determine several energy density parameters;S2, according to several energy density parameters, calculate total potential energy;S3, according to total potential energy, obtain several control equations;S4, according to several control equations, obtain weak form control model;S5, weak form control model is solved, and prediction result is obtained.The application can be deployed in local server to carry out packaging reliability analysis, reduce design data upload demand, improve the security of packaging structure sensitive data from source, meet the high requirement of chip packaging enterprise to information security, with good engineering popularization value.

Description

Technical Field

[0001] This invention relates to the field of fracture failure prediction technology, and specifically to a method for predicting moisture-induced fracture failure at the interface of reflow soldering electronic packaging. Background Technology

[0002] In the electronic packaging industry, reflow soldering is an indispensable part of surface mount technology (SMT), its main function being to fix electronic components onto printed circuit boards (PCBs) by soldering. During reflow soldering, the packaging materials are often exposed to high temperature and high humidity environments, posing a severe challenge to the reliability of the material interface. Because packaging materials use a large amount of polymer materials (such as epoxy molding compounds, chip adhesives, and underfill materials), these polymers are hygroscopic and absorb moisture from the air in humid environments. When the packaging materials undergo rapid heating during reflow soldering (typically reaching around 260°C), the absorbed moisture evaporates quickly, forming high vapor pressure. This internal vapor pressure generates enormous stress at the interface, easily leading to interface delamination and crack propagation, and even the "popcorn effect," severely impacting the reliability of electronic packaging products. Furthermore, the significant difference in the coefficients of thermal expansion and hygroscopic expansion between the polymers and inorganic materials (such as silicon wafers and metal substrates) in the packaging materials also causes additional stress at the material interface, further increasing the risk of interface failure.

[0003] To improve the reliability of electronic packaging materials, accurately predicting moisture-induced interfacial fracture failure during reflow soldering is of significant engineering importance. Current research focuses on moisture diffusion behavior, vapor pressure evolution, and the coupling effect of hygroscopic expansion and thermal stress. However, research on interfacial fracture behavior mainly relies on the finite element method (FEM), virtual crack closure technology, molecular dynamics, and crack tip opening displacement method. However, all these methods have drawbacks. The FEM, virtual crack closure technology, and crack tip opening displacement method require pre-setting and tracking the crack path, making it unable to simulate complex crack paths. Molecular dynamics can simulate relatively small time and spatial scales but cannot simulate interfacial fracture problems in packaged components. Currently, there is a lack of methods to accurately predict the interfacial fracture failure behavior of electronic packaging materials caused by humidity during reflow soldering. Therefore, exploring an effective technique for predicting interfacial fracture failure under multi-field coupling of moisture, vapor, and force has significant technical value and application prospects for improving the long-term reliability of electronic packaging materials. Summary of the Invention

[0004] To address the above problems, this invention proposes a method for predicting moisture-induced interface fracture failure in reflow soldering electronic packaging.

[0005] The technical solution of this invention is: a method for predicting moisture-induced interface fracture failure in reflow soldering electronic packaging, comprising the following steps:

[0006] S1. Determine several energy density parameters based on the energy contribution of elastic deformation, humidity effect, material interface and material damage to the electronic packaging system;

[0007] S2. Calculate the total potential energy based on several energy density parameters;

[0008] S3. Based on the total potential energy, several governing equations are obtained;

[0009] S4. Based on several control equations, a weak form control model is obtained;

[0010] S5. Solve the weak form control model to obtain the prediction results.

[0011] Furthermore, in S1, the energy density parameters include elastic energy density, energy density of the moisture contained in the material, energy density of internal fracture dissipation, energy density of interface fracture dissipation, energy density of interface opening dissipation, and the work done by the vapor pressure at the interface crack as an external force.

[0012] Furthermore, elastic energy density The expression is:

[0013] ;

[0014] ;

[0015] ;

[0016] In the formula, Represents the elastic degradation function. Represents damage variables, This represents the compensation coefficient to prevent numerical non-convergence after complete fracture. The tensile portion representing elastic performance. This represents the compressible portion of elastic energy. Indicates the bulk elastic modulus. Denotes the first Lamé constant. This represents the second Lamé constant. Indicates trace, Represents the elastic strain tensor. Indicates the elastic strain deviation;

[0017] Energy density of water contained in a material The expression is:

[0018] ;

[0019] In the formula, Indicates the porosity of the material. Indicates the compressibility of water. Represents the equivalent stress coefficient. Indicates water content;

[0020] Energy density dissipation during fracture within the material The expression is:

[0021] ;

[0022] In the formula, This represents the critical energy release rate at which the material fractures. This represents the characteristic length of the crack regularization within the material. Represents the left gradient of the phase field variable;

[0023] Interfacial fracture dissipation energy density The expression is:

[0024] ;

[0025] In the formula, This represents the critical fracture energy release rate of the i-th type of interface. This represents the characteristic length of the i-th type of interface crack. Indicates the number of interfaces;

[0026] Interface opening dissipation energy density The expression is:

[0027] ;

[0028] ;

[0029] ;

[0030] ;

[0031] ;

[0032] ;

[0033] ;

[0034] In the formula, This represents a new energy degradation function. This represents the interface parameters related to the critical value of interface separation peak. This represents the interface parameters related to the peak limit of interface separation. Indicates the relative displacement along the specified interface. The volume expansion component represents the energy density dissipated at the interface. The deviatoric component representing the interfacial dissipation energy density The volumetric compressibility component represents the interfacial dissipation energy density. The coefficients of the degenerate function are represented. This indicates the stiffness of the interface in the normal direction. This indicates the stiffness of the interface in the tangential direction. Represents the normal components of the interface. This represents the tangential component of the interface. Indicates interface displacement. This represents the thickness of the finite element mesh along the specified interface. The left gradient represents the interface displacement. The unit vector representing the normal direction of the interface. The unit vector representing the tangential direction of the interface. Represents the dot product symbol;

[0035] Work done by the vapor pressure at the interface crack as an external force The expression is:

[0036] ;

[0037] ;

[0038] In the formula, This represents the vapor pressure at the interface crack based on Henry's theorem. Indicates saturated vapor pressure. Indicates relative humidity. This represents the Heaviside approximation function. Represents a standardized unit volume. This represents the independent variable that controls the Heaviside approximation function. Indicates temperature. .

[0039] Furthermore, in S2, the total potential energy The expression is:

[0040] ;

[0041] In the formula, Indicates the material medium region. Represents the elastic degradation function. Represents damage variables, Indicates the bulk elastic modulus. Indicates trace, Represents the elastic strain tensor. This represents the elastic strain deviator. This represents the second Lamé constant. Indicates the porosity of the material. Indicates the compressibility of water. Represents the equivalent stress coefficient. Indicates water content, Indicates volume, This represents the critical energy release rate at which the material fractures. This represents the characteristic length of the crack regularization within the material. Represents the left gradient of the phase field variables. Indicates a sharp interface of materials. Indicates the number of interfaces. This represents a new energy degradation function. The volume expansion component represents the energy density dissipated at the interface. The deviatoric component representing the interfacial dissipation energy density The volumetric compressibility component represents the interfacial dissipation energy density. This represents the interface area after regularization. Indicates the relative displacement along the specified interface. This represents the critical fracture energy release rate of the i-th type of interface. This represents the characteristic length of the i-th type of interface crack. This represents the vapor pressure at the interface crack based on Henry's theorem. Represents the normal components of the interface. Indicates surface.

[0042] Furthermore, in S3, the governing equations include the governing equations for the stress field, the damage field, temperature, and humidity.

[0043] Furthermore, the governing equations of the stress field are expressed as follows:

[0044] ;

[0045] In the formula, This represents the first-order partial derivative of the degenerate function. This represents the first historical field variable representing the replacement crack driving force. Represents damage variables, This represents the critical energy release rate at which the material fractures. This represents the characteristic length of the crack regularization within the material. Represents the left gradient of the phase field variable;

[0046] The governing equation of the damage field is expressed as follows:

[0047] ;

[0048] In the formula, Describing degenerate functions The first-order partial derivative, This represents the second historical field variable that replaces the crack driving force. This represents the critical fracture energy release rate of the i-th type of interface. This represents the characteristic length of the i-th type of interface crack. This represents the first-order partial derivative of the vapor pressure at the interface crack with respect to d. Represents the normal components of the interface;

[0049] The governing equation for temperature is expressed as follows:

[0050] ;

[0051] In the formula, Indicates density, Indicates the compressibility of water. Indicates the rate of change of temperature. Denotes divergence, Indicates the coefficient of thermal expansion. Represents the left gradient of temperature;

[0052] The governing equation for humidity is expressed as follows:

[0053] ;

[0054] In the formula, Indicates the density of the fluid. Indicates the rate of change in humidity. Indicates the diffusion coefficient. Indicates the porosity of the material. Indicates trace, Represents the equivalent stress coefficient. Indicates water content, It represents the elastic strain tensor.

[0055] Furthermore, in S4, the expression for the weakly formal control model is:

[0056] ;

[0057] ;

[0058] ;

[0059] ;

[0060] ;

[0061] In the formula, Indicates the material medium region. Denotes divergence, Indicates interface displacement. Represents the effective stress tensor. Represents the elastic strain tensor. Represents the equivalent stress coefficient. Indicates the increase in pressure. Indicates temperature. Represents damage variables, Represents a unit tensor. Indicates volume, Represents volume force. Indicates the body part. Indicates surface, Indicates boundary traction force. Indicates surface, This represents the first-order partial derivative of the degenerate function. This represents the first historical field variable representing the replacement crack driving force. This represents the critical energy release rate at which the material fractures. This represents the characteristic length of the crack regularization within the material. This represents the left gradient of the phase field variable d. This represents the first-order partial derivative of a new energy degradation function. This represents the second historical field variable that replaces the crack driving force. This represents the first-order partial derivative of the interface crack vapor pressure with respect to the damage variable. Represents the normal components of the interface. This represents the critical fracture energy release rate of the i-th type of interface. This represents the characteristic length of the i-th type of interface crack. Indicates density, Indicates the porosity of the material. Indicates the compressibility of water. Indicates water content, Indicates the rate of temperature change. Indicates the coefficient of thermal expansion. Represents the left gradient of temperature. Indicates the density of the fluid. Indicates the rate of change in humidity. Indicates the diffusion coefficient. Indicates a trace.

[0062] Furthermore, in S5, the finite element method is used to solve the weak formal control model to obtain a numerical solution, which is then used as the prediction result.

[0063] The beneficial effects of this invention are:

[0064] (1) The crack path of the present invention does not need to be preset and evolves automatically, which is suitable for complex interface failure simulation. The present invention uses the phase field method to model the interface crack propagation process, which avoids the problem of manually preset crack path and track evolution in the traditional finite element method, and significantly improves the intelligence level and adaptability of the simulation.

[0065] (2) This invention fully considers the interfacial vapor pressure effect caused by humidity, and the prediction is more accurate. This invention introduces an interfacial vapor pressure expression based on Henry's law, which effectively describes the stress loading caused by the rapid evaporation of moisture during reflow soldering, and improves the accuracy of fracture prediction from the perspective of multiple fields of heat, humidity and force.

[0066] (3) The present invention constructs a unified energy variational framework, which facilitates numerical solution and algorithm porting. Through the unified processing of the total potential energy functional, the control equations under multi-field coupling can be directly derived. It has good numerical stability and finite element solution compatibility, and is easy to embed into commercial simulation platforms or integrate as a module into the EDA design process.

[0067] (4) This invention can improve the localization capability of data processing, save network resources and ensure data security. Compared with some fracture simulation tools that rely on cloud platform computing, this invention can be deployed on local servers for packaging reliability analysis, reduce the need to upload design data, improve the security of sensitive data of packaging structure from the source, meet the high requirements of chip packaging companies for information security, and has good engineering promotion value. Attached Figure Description

[0068] Figure 1 This is a flowchart of a method for predicting moisture-induced interface fracture failure in reflow soldering electronic packages. Detailed Implementation

[0069] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0070] like Figure 1 As shown, this invention provides a method for predicting moisture-induced interface fracture failure in reflow soldering electronic packages, comprising the following steps:

[0071] S1. Determine several energy density parameters based on the energy contribution of elastic deformation, humidity effect, material interface and material damage to the electronic packaging system;

[0072] S2. Calculate the total potential energy based on several energy density parameters;

[0073] S3. Based on the total potential energy, several governing equations are obtained;

[0074] S4. Based on several control equations, a weak form control model is obtained;

[0075] S5. Solve the weak form control model to obtain the prediction results.

[0076] In this embodiment of the invention, we first consider a spatially occupied area as... The medium, whose outer boundary is denoted as By introducing a continuous phase field variable. A discrete crack can be approximated as a diffusion crack zone. The phase field variable ranges from 0 to 1, i.e. ,in and These correspond to the states of intact material and completely fractured material, respectively. Through five steps from S1 to S5, this invention can predict moisture-induced reflow soldering electronic packaging interface fracture failure.

[0077] In S1, the energy density parameters include elastic energy density, the energy density of the water contained in the material, the energy density of internal fracture dissipation, the energy density of interfacial fracture dissipation, the energy density of interfacial opening dissipation, and the work done by the vapor pressure at the interfacial crack as an external force.

[0078] In an embodiment of the invention, elastic energy density The expression is:

[0079] ;

[0080] ;

[0081] ;

[0082] In the formula, Represents the elastic degradation function. Represents damage variables, This represents the compensation coefficient to prevent numerical non-convergence after complete fracture. The tensile portion representing elastic performance. This represents the compressible portion of elastic energy. Indicates the bulk elastic modulus. Denotes the first Lamé constant. This represents the second Lamé constant. Indicates trace, Represents the elastic strain tensor. Indicates the elastic strain deviation;

[0083] Energy density of water contained in a material The expression is:

[0084] ;

[0085] In the formula, Indicates the porosity of the material. Indicates the compressibility of water. Represents the equivalent stress coefficient. Indicates water content;

[0086] Energy density dissipation during fracture within the material The expression is:

[0087] ;

[0088] In the formula, This represents the critical energy release rate at which the material fractures. This represents the characteristic length of the crack regularization within the material. Represents the left gradient of the phase field variable;

[0089] Interfacial fracture dissipation energy density The expression is:

[0090] ;

[0091] In the formula, This represents the critical fracture energy release rate of the i-th type of interface. This represents the characteristic length of the i-th type of interface crack. Indicates the number of interfaces;

[0092] Interface opening dissipation energy density The expression is:

[0093] ;

[0094] ;

[0095] ;

[0096] ;

[0097] ;

[0098] ;

[0099] ;

[0100] In the formula, This represents a new energy degradation function. This represents the interface parameters related to the critical value of interface separation peak. This represents the interface parameters related to the peak limit of interface separation. Indicates the relative displacement along the specified interface. The volume expansion component represents the energy density dissipated at the interface. The deviatoric component representing the interfacial dissipation energy density The volumetric compressibility component represents the interfacial dissipation energy density. The coefficients of the degenerate function are represented. This indicates the stiffness of the interface in the normal direction. This indicates the stiffness of the interface in the tangential direction. Represents the normal components of the interface. This represents the tangential component of the interface. Indicates interface displacement. This represents the thickness of the finite element mesh along the specified interface. The left gradient represents the interface displacement. The unit vector representing the normal direction of the interface. The unit vector representing the tangential direction of the interface. Represents the dot product symbol;

[0101] Work done by the vapor pressure at the interface crack as an external force The expression is:

[0102] ;

[0103] ;

[0104] In the formula, This represents the vapor pressure at the interface crack based on Henry's theorem. Indicates saturated vapor pressure. Indicates relative humidity. This represents the Heaviside approximation function. Represents a standardized unit volume. This represents the independent variable that controls the Heaviside approximation function. Indicates temperature. .

[0105] The expression for the Heaviside approximation function is:

[0106] ;

[0107] , used to control the width of the transition zone.

[0108] In this embodiment of the invention, in S2, the total potential energy The expression is:

[0109] ;

[0110] In the formula, Indicates the material medium region. Represents the elastic degradation function. Represents damage variables, Indicates the bulk elastic modulus. Indicates trace, Represents the elastic strain tensor. This represents the elastic strain deviator. This represents the second Lamé constant. Indicates the porosity of the material. Indicates the compressibility of water. Represents the equivalent stress coefficient. Indicates water content, Indicates volume, This represents the critical energy release rate at which the material fractures. This represents the characteristic length of the crack regularization within the material. Represents the left gradient of the phase field variables. Indicates a sharp interface of materials. Indicates the number of interfaces. This represents a new energy degradation function. The volume expansion component represents the energy density dissipated at the interface. The deviatoric component representing the interfacial dissipation energy density The volumetric compressibility component represents the interfacial dissipation energy density. This represents the interface area after regularization. Indicates the relative displacement along the specified interface. This represents the critical fracture energy release rate of the i-th type of interface. This represents the characteristic length of the i-th type of interface crack. This represents the vapor pressure at the interface crack based on Henry's theorem. Represents the normal components of the interface. Indicates surface.

[0111] In this embodiment of the invention, S3 includes the control equations for the stress field, the damage field, the temperature, and the humidity.

[0112] In this embodiment of the invention, the governing equation of the stress field is expressed as follows:

[0113] ;

[0114] In the formula, This represents the first-order partial derivative of the degenerate function. This represents the first historical field variable representing the replacement crack driving force. Represents damage variables, This represents the critical energy release rate at which the material fractures. This represents the characteristic length of the crack regularization within the material. Represents the left gradient of the phase field variable;

[0115] The governing equation of the damage field is expressed as follows:

[0116] ;

[0117] In the formula, Describing degenerate functions The first-order partial derivative, This represents the second historical field variable that replaces the crack driving force. This represents the critical fracture energy release rate of the i-th type of interface. This represents the characteristic length of the i-th type of interface crack. This represents the first-order partial derivative of the vapor pressure at the interface crack with respect to d. Represents the normal components of the interface;

[0118] The governing equation for temperature is expressed as follows:

[0119] ;

[0120] In the formula, Indicates density, Indicates the compressibility of water. Indicates the rate of change of temperature. Denotes divergence, Indicates the coefficient of thermal expansion. Represents the left gradient of temperature;

[0121] The governing equation for humidity is expressed as follows:

[0122] ;

[0123] In the formula, Indicates the density of the fluid. Indicates the rate of change in humidity. Indicates the diffusion coefficient. Indicates the porosity of the material. Indicates trace, Represents the equivalent stress coefficient. Indicates water content, It represents the elastic strain tensor.

[0124] In this embodiment of the invention, in S4, the expression of the weakly formal control model is:

[0125] ;

[0126] ;

[0127] ;

[0128] ;

[0129] ;

[0130] In the formula, Indicates the material medium region. Denotes divergence, Indicates interface displacement. Represents the effective stress tensor. Represents the elastic strain tensor. Represents the equivalent stress coefficient. Indicates the increase in pressure. Indicates temperature. Represents damage variables, Represents a unit tensor. Indicates volume, Represents volume force. Indicates the body part. Indicates surface, Indicates boundary traction force. Indicates surface, This represents the first-order partial derivative of the degenerate function. This represents the first historical field variable representing the replacement crack driving force. This represents the critical energy release rate at which the material fractures. This represents the characteristic length of the crack regularization within the material. This represents the left gradient of the phase field variable d. This represents the first-order partial derivative of a new energy degradation function. This represents the second historical field variable that replaces the crack driving force. This represents the first-order partial derivative of the interface crack vapor pressure with respect to the damage variable. Represents the normal components of the interface. This represents the critical fracture energy release rate of the i-th type of interface. This represents the characteristic length of the i-th type of interface crack. Indicates density, Indicates the porosity of the material. Indicates the compressibility of water. Indicates water content, Indicates the rate of temperature change. Indicates the coefficient of thermal expansion. Represents the left gradient of temperature. Indicates the density of the fluid. Indicates the rate of change in humidity. Indicates the diffusion coefficient. Indicates a trace.

[0131] , .

[0132] In this embodiment of the invention, in step S5, the finite element algorithm is used to solve the weak formal control model to obtain a numerical solution, which is used as the prediction result.

[0133] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for predicting moisture-induced interface fracture failure in reflow soldering electronic packages, characterized in that, Includes the following steps: S1. Determine several energy density parameters based on the energy contribution of elastic deformation, humidity effect, material interface and material damage to the electronic packaging system; S2. Calculate the total potential energy based on several energy density parameters; S3. Based on the total potential energy, several governing equations are obtained; S4. Based on several control equations, a weak form control model is obtained; S5. Solve the weak form control model to obtain the prediction results.

2. The method for predicting moisture-induced reflow soldering electronic packaging interface fracture failure according to claim 1, characterized in that, In S1, the energy density parameters include elastic energy density, the energy density of the moisture contained in the material, the energy density of internal fracture dissipation, the energy density of interface fracture dissipation, the energy density of interface opening dissipation, and the work done by the vapor pressure at the interface crack as an external force.

3. The method for predicting moisture-induced reflow soldering electronic packaging interface fracture failure according to claim 2, characterized in that, The elastic energy density The expression is: ； ； ； In the formula, Represents the elastic degradation function. Represents damage variables, This represents the compensation coefficient to prevent numerical non-convergence after complete fracture. The tensile portion representing elastic performance. This represents the compressible portion of elastic energy. This represents the bulk elastic modulus. Denotes the first Lamé constant. This represents the second Lamé constant. Indicates trace, Represents the elastic strain tensor. Indicates the elastic strain deviation; The energy density of the water contained in the material The expression is: ； In the formula, Indicates the porosity of the material. Indicates the compressibility of water. Represents the equivalent stress coefficient. Indicates water content; The internal fracture energy dissipation density of the material The expression is: ； In the formula, This represents the critical energy release rate at which the material fractures. This represents the characteristic length of the crack regularization within the material. Represents the left gradient of the phase field variable; The energy dissipation density of the interface fracture The expression is: ； In the formula, Let represent the critical fracture energy release rate of the i-th type of interface. This represents the characteristic length of the i-th type of interface crack. Indicates the number of interfaces; The interface opening dissipates energy density The expression is: ； ； ； ； ； ； ； In the formula, This represents a new energy degradation function. This represents the interface parameters related to the critical value of interface separation peak. This represents the interface parameters related to the peak limit of interface separation. Indicates the relative displacement along the specified interface. The volume expansion component represents the energy density dissipated at the interface. The deviatoric component representing the interfacial dissipation energy density The volumetric compressibility component represents the interfacial dissipation energy density. The coefficients of the degenerate function are represented. This indicates the stiffness of the interface in the normal direction. This indicates the interface stiffness in the tangential direction. Represents the normal components of the interface. This represents the tangential component of the interface. Indicates interface displacement. This represents the thickness of the finite element mesh along the specified interface. The left gradient represents the interface displacement. The unit vector representing the normal direction of the interface. The unit vector representing the tangential direction of the interface. Represents the dot product symbol; The work done by the vapor pressure at the interface crack as an external force The expression is: ； ； In the formula, This represents the vapor pressure at the interface crack based on Henry's theorem. Indicates saturated vapor pressure. Indicates relative humidity. This represents the Heaviside approximation function. Represents a standardized unit volume. This represents the independent variable that controls the Heaviside approximation function. Indicates temperature.

4. The method for predicting moisture-induced reflow soldering electronic packaging interface fracture failure according to claim 1, characterized in that, In S2, the total potential energy The expression is: ； In the formula, Indicates the material medium region. Represents the elastic degradation function. Represents damage variables, This represents the bulk elastic modulus. Indicates trace, Represents the elastic strain tensor. This represents the elastic strain deviator. This represents the second Lamé constant. Indicates the porosity of the material. Indicates the compressibility of water. Represents the equivalent stress coefficient. Indicates water content, Indicates volume, This represents the critical energy release rate at which the material fractures. This represents the characteristic length of the crack regularization within the material. This represents the left gradient of the phase field variables. Indicates a sharp interface of materials. Indicates the number of interfaces. This represents a new energy degradation function. The volume expansion component represents the energy density dissipated at the interface. The deviatoric component representing the interfacial dissipation energy density The volumetric compressibility component represents the interfacial dissipation energy density. This represents the interface area after regularization. Indicates the relative displacement along the specified interface. Let represent the critical fracture energy release rate of the i-th type of interface. This represents the characteristic length of the i-th type of interface crack. This represents the vapor pressure at the interface crack based on Henry's theorem. Represents the normal components of the interface. Indicates surface.

5. The method for predicting moisture-induced reflow soldering electronic packaging interface fracture failure according to claim 1, characterized in that, In S3, the governing equations include the governing equations for the stress field, the damage field, the temperature, and the humidity.

6. The method for predicting moisture-induced reflow soldering electronic packaging interface fracture failure according to claim 5, characterized in that, The governing equation of the stress field is expressed as follows: ； In the formula, This represents the first-order partial derivative of the degenerate function. This represents the first historical field variable representing the replacement crack driving force. Represents damage variables, This represents the critical energy release rate at which the material fractures. This represents the characteristic length of the crack regularization within the material. Represents the left gradient of the phase field variable; The governing equation of the damage field is expressed as follows: ； In the formula, Describing degenerate functions The first-order partial derivative, This represents the second historical field variable that replaces the crack driving force. Let represent the critical fracture energy release rate of the i-th type of interface. This represents the characteristic length of the i-th type of interface crack. This represents the first-order partial derivative of the vapor pressure at the interface crack with respect to d. Represents the normal components of the interface; The expression for the temperature control equation is: ； In the formula, Indicates density, Indicates the compressibility of water. Indicates the rate of change of temperature. Denotes divergence, Indicates the coefficient of thermal expansion. Represents the left gradient of temperature; The expression for the humidity control equation is: ； In the formula, Indicates the density of the fluid. Indicates the rate of change in humidity. Indicates the diffusion coefficient. Indicates the porosity of the material. Indicates trace, Represents the equivalent stress coefficient. Indicates water content, It represents the elastic strain tensor.

7. The method for predicting moisture-induced reflow soldering electronic packaging interface fracture failure according to claim 1, characterized in that, In S4, the expression for the weak-form control model is: ； ； ； ； ； In the formula, Indicates the material medium region. Denotes divergence, Indicates interface displacement. Represents the effective stress tensor. Represents the elastic strain tensor. Represents the equivalent stress coefficient. Indicates the increase in pressure. Indicates temperature. Represents damage variables, Represents a unit tensor. Indicates volume, Represents volume force. Indicates the body part. Indicates surface, Indicates boundary traction force. Indicates surface, This represents the first-order partial derivative of the degenerate function. This represents the first historical field variable representing the replacement crack driving force. This represents the critical energy release rate at which the material fractures. This represents the characteristic length of the crack regularization within the material. This represents the left gradient of the phase field variable d. This represents the first-order partial derivative of a new energy degradation function. This represents the second historical field variable that replaces the crack driving force. This represents the first-order partial derivative of the interface crack vapor pressure with respect to the damage variable. Represents the normal components of the interface. Let represent the critical fracture energy release rate of the i-th type of interface. This represents the characteristic length of the i-th type of interface crack. Indicates density, Indicates the porosity of the material. Indicates the compressibility of water. Indicates water content, Indicates the rate of temperature change. Indicates the coefficient of thermal expansion. Represents the left gradient of temperature. Indicates the density of the fluid. Indicates the rate of change in humidity. Indicates the diffusion coefficient. Indicates a trace.

8. The method for predicting moisture-induced reflow soldering electronic packaging interface fracture failure according to claim 1, characterized in that, In step S5, the finite element method is used to solve the weak form control model to obtain a numerical solution, which is then used as the prediction result.

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