Method for analyzing evolution of defects caused by fracture and electromigration based on phase field method

Abstract

The embodiment of the invention provides an evolution analysis method for defects caused by fracture and electromigration based on a phase field method, which comprises the following steps of: determining parameter information and multi-physical field load information of a defect-containing sample, and establishing a simplified model; wherein the multi-physical field load information comprises a force-heat-electric field load and a boundary condition; constructing a defect evolution phase field model based on the simplified model; the defect evolution phase field model comprises a force-heat-electric field coupled electromigration phase field model and a thermoelastic fracture phase field model; and solving the defect evolution phase field model. According to the scheme, the electrostatic model, the electrothermal model, the thermoelastic solid mechanical model and the thermoelastic fracture phase field model are solved for the defect morphology of each time step in the electromigration phase field evolution process, so that cracks penetrating through the defect pattern are classified into the final defect morphology, and the complete process of evolution of the defect morphology along with time is obtained.

Description

Technical Field

[0001] The present application relates to the field of component electromigration, and to a defect evolution analysis method caused by fracture and electromigration based on a phase field method. Background Art

[0002] A large number of engineering practices have shown that the performance degradation and failure of printed circuit board assemblies are caused by the fracture of intermetallic compounds at the solder joint interface, which means that solder joints are critical to the reliability of printed circuit board assemblies. Solder joints in service are subjected to multi-physics loads of electricity, heat, and force. Under these loads, internal defects such as microcracks and microvoids in intermetallic compounds will gradually evolve and expand to eventually form through cracks. Some studies have found that the mechanism driving crack evolution is not only electromigration but also fracture mechanics.

[0003] At present, the research on defect evolution in solder joints mainly includes two categories. One category assumes that defect evolution is only controlled by solid-state diffusion induced by electromigration, ignoring the possibility of defects initiating cracks at stress concentration points. The other category only considers crack propagation caused by fracture mechanics, ignoring the evolution of hole morphology caused by electromigration, resulting in an incomplete and objective understanding of the evolution of defects inside solder joints.

[0004] Therefore, it is necessary to study a defect evolution analysis method that considers both defect evolution mechanisms at the same time and investigates the interaction between the final fracture of the solder joint and the mass diffusion caused by electromigration to make the defect evolution within the solder joint more complete. Summary of the invention

[0005] The purpose of the embodiment of the present application is to provide a defect evolution analysis method based on the phase field method caused by fracture and electromigration to address the deficiencies of the existing model, combining the two different physical processes of electromigration and fracture to simulate the complete destruction process of intermetallic compounds at the solder joint interface from the early electromigration mass diffusion to the final fracture destruction. The specific technical solution is as follows:

[0006] In a first aspect of the present application, a defect evolution analysis method based on fracture and electromigration induced by a phase field method includes:

[0007] Determine the parameter information and multi-physical field load information of the defective sample and establish a simplified model; wherein the multi-physical field load information includes: force-heat-electric field load and boundary conditions;

[0008] Based on the simplified model, a defect evolution phase field model is constructed; the defect evolution phase field model includes a force-heat-electric field coupled electromigration phase field model and a thermoelastic fracture phase field model;

[0009] The defect evolution phase field model is solved.

[0010] Optionally, the force-heat-electric field coupled electromigration phase field model includes: an electrostatic model, an electrothermal model, a thermoelastic solid mechanics model and an electromigration solid diffusion model;

[0011] In the mechanical-thermal-electric field coupled electromigration phase field model, in the simulation domain The phase field variable ψ (ψ∈[-1,1]) is introduced to distinguish metal materials from holes, where ψ=-1 represents the hole defect area, ψ=1 represents the metal area; ψ∈(1,1) represents the hole interface. Contains hole areas;

[0012] In the thermoelastic fracture phase field model, in the metal region of the specimen Introducing fracture phase field variables Distinguish between metal materials and cracks, and Respectively represent the state of complete destruction and intactness of the material; Representing different degrees of damage state of the material, the metal area of ​​the specimen The hole area is not included.

[0013] Optionally, the electrostatic model includes:

[0014]

[0015] Among them, ζ(ψ) = h(ψ)·ζ is the effective conductivity, and the material performance parameter interpolation function It satisfies h(1)=1 in the metal region and h(-1)=0 in the hole region, ζ is the metal conductivity, and φ is the electric potential field.

[0016] Optionally, the electrothermal model includes:

[0017]

[0018] Among them, k(ψ)=h(ψ)·k is the effective thermal conductivity, k is the thermal conductivity of the metal, and T is the temperature field.

[0019] Optionally, the thermoelastic solid mechanics model includes:

[0020]

[0021] Among them, C(ψ) = h(ψ)·C is the effective fourth-order elastic tensor, C is the fourth-order elastic tensor of the metal, ε e is the elastic strain tensor.

[0022] Optionally, the electromigration solid-state diffusion model includes:

[0023]

[0024] Among them, the electromigration chemical potential μ is:

[0025]

[0026] Where t is time, ε is the phase field interface control parameter, σ is the stress tensor, Ω is the atomic volume, γ s is the surface energy density, It represents the effective charge number of surface electromigration, e represents the electron charge, Representing the heat transferred by surface electromigration, the surface diffusivity M can be written as:

[0027]

[0028] Among them, 1-ψ 2 Characterizes that restricted diffusion occurs only on the pore surface, and the solid-state diffusion coefficient D s for:

[0029]

[0030] Where D s is the pre-index coefficient, Q s is the surface diffusion activation energy, δ s represents the width of the diffusion layer, k B Refers to the Boltzmann constant.

[0031] Optionally, the thermoelastic fracture phase field model includes a control equation group for crack initiation and propagation, and the control equation group for crack initiation and propagation is:

[0032]

[0033] Among them, l 0 G is the characteristic width of the phase field model that controls the degree of crack diffusion. c is the critical energy release rate, the constant p<<1 avoids numerical singularity, and in order to prevent crack self-healing, the elastic energy density history variable is introduced:

[0034]

[0035] The above formula indicates Elastic strain energy density function The historical maximum value in the time period [0, t].

[0036] Optionally, the electrostatic model, the electrothermal model, the thermoelastic solid mechanics model and the thermoelastic fracture phase field model are all steady-state models without time terms.

[0037] Optionally, solving the defect evolution phase field model includes:

[0038] For the simulation domain Discretize in time and space dimensions, input the initial phase field variable ψ and the electric potential boundary conditions into the electrostatic model to obtain the electric potential field φ output by the electrostatic model; input the initial phase field variable ψ, the temperature boundary conditions and the output electric potential field φ into the electrothermal model to obtain the temperature field T output by the electrothermal model; input the displacement boundary conditions and the output temperature field T into the thermoelastic solid mechanics model to obtain the displacement field u output by the thermoelastic solid mechanics model; input the initial phase field variable ψ and the obtained electric potential field φ, temperature field T and displacement field u information into the electromigration solid diffusion model to obtain the phase field ψ of the next time layer; perform mapping on the output phase field ψ Output mapping result phase field The displacement boundary condition, temperature boundary condition and output phase field Information is input into the elastic fracture phase field model to obtain the phase field variables after fracture The output phase field Execute the inverse mapping ψ(r) and output the inverse mapping result phase field ψ; repeat the above steps for the output phase field ψ until the crack penetrates. In terms of numerical methods for solving the model, the electrostatic model, electrothermal model, and thermoelastic solid mechanics model all use the finite volume method, the electromigration solid diffusion model uses the finite difference method, and the thermoelastic fracture phase field model uses the finite element method.

[0039] In another aspect of the implementation of the present application, an embodiment of the present application provides an electronic device, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus;

[0040] Memory, used to store computer programs;

[0041] The processor is used to implement a defect evolution analysis method caused by fracture and electromigration based on a phase field method when executing a program stored in the memory.

[0042] Beneficial effects of the embodiments of the present application:

[0043] The defect evolution analysis method caused by fracture and electromigration based on the phase field method provided in the embodiment of the present application determines the parameter information and multi-physical field load information of the defective sample and establishes a simplified model; wherein the multi-physical field load information includes: force-heat-electric field load and boundary conditions; based on the simplified model, a defect evolution phase field model is constructed; the defect evolution phase field model includes an electromigration phase field model coupled with force-heat-electric field, and a thermoelastic fracture phase field model; the defect evolution phase field model is solved. In this scheme, the electrostatic model, electrothermal model, thermoelastic solid mechanics model and thermoelastic fracture phase field model are solved for the defect morphology at each time step in the electromigration phase field evolution process, so that the cracks that penetrate the defect pattern are classified into the final defect morphology, and the complete process of the evolution of the defect morphology over time is obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art are briefly introduced below.

[0045] Figure 1 Flow chart of a defect evolution analysis method caused by fracture and electromigration based on a phase field method according to an embodiment of the present application.

[0046] Figure 2 It is a schematic diagram of the evolution mechanism of the sample containing hole defects driven by the dual physical mechanism under the high-density current and uniaxial tensile load of the present application;

[0047] Figure 3 It is a schematic diagram of the geometric structure and boundary conditions of the defective specimen of the present application.

[0048] Figure 4 It is a simulation flow chart of the brittle fracture of the sample caused by the evolution of holes caused by electromigration in the present application;

[0049] Figure 5 This is a result diagram of the crack initiation evolution process of the sample containing a circular hole defect under horizontal uniaxial tension and electric field load in the present application. DETAILED DESCRIPTION

[0050] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0051] In order to solve the problems in the prior art, the present application provides a defect evolution analysis method caused by fracture and electromigration based on the phase field method, which combines the two different physical processes of electromigration and fracture to simulate the complete destruction process of intermetallic compounds at the solder joint interface from the early electromigration mass diffusion to the final fracture destruction.

[0052] It should be noted that the defect evolution analysis method caused by fracture and electromigration based on the phase field method provided in the embodiment of the present application can be applied to electronic devices. In practical applications, the electronic device can be: smart phones, tablet computers, laptop computers and other devices, which is reasonable.

[0053] The following first introduces the defect evolution analysis method caused by fracture and electromigration based on the phase field method provided in the embodiment of the present application.

[0054] like Figure 1 As shown, the defect evolution analysis method caused by fracture and electromigration based on the phase field method provided in the embodiment of the present application may include the following steps:

[0055] S101, determining parameter information and multi-physical field load information of a defective sample, and establishing a simplified model; wherein the multi-physical field load information includes: loads and boundary conditions of mechanical-thermal-electric fields.

[0056] The parameter information of the defective material may include defect geometry and position information, and may also include mechanical, thermal and electrical material parameter information of the material. For example, the defect geometry may include the width and height of the defect, as well as the diameter of the defect, etc. In addition, the defective pattern may be any defective pattern in a pre-collected pattern library, or any designated defective pattern.

[0057] The load of the force-heat-electric field can be a uniaxial load in a single direction, for example, a uniaxial tensile load in the horizontal direction, and the boundary condition can be a natural boundary condition, etc.

[0058] S102, constructing a defect evolution phase field model based on the simplified model; the defect evolution phase field model includes a force-heat-electric field coupled electromigration phase field model and a thermoelastic fracture phase field model.

[0059] For example, in the electromigration phase field model of mechanical-thermal-electric field coupling, in the simulation domain The phase field variable ψ (ψ∈[-1,1]) is introduced to distinguish metal materials from holes, where ψ=-1 represents the hole defect area, ψ=1 represents the metal area; ψ∈(1,1) represents the hole interface, and the simulation domain Including the hole area; introducing the phase field and considering the degradation of interface material performance parameters, the above models are as follows:

[0060] (1) Electrostatic model:

[0061]

[0062] Among them, ζ(ψ)=h(ψ)·ζ is the effective conductivity, and the material performance parameter interpolation function h(ψ)=(1+ψ) 3 [20-15(1+ψ)+3(1+ψ) 2 ]16, which satisfies h(1)=1 in the metal region and h(-1)=0 in the hole region, ζ is the metal conductivity, and φ is the electric potential field.

[0063] (2) Electric heating model:

[0064]

[0065] Among them, k(ψ)=h(ψ)·k is the effective thermal conductivity, k is the thermal conductivity of the metal, and T is the temperature field.

[0066] (3) Thermoelastic solid mechanics model:

[0067]

[0068] Among them, C(ψ) = h(ψ)·C is the effective fourth-order elastic tensor, C is the fourth-order elastic tensor of the metal, ε e is the elastic strain tensor.

[0069] (4) Electromigration solid-state diffusion model:

[0070]

[0071] Among them, the electromigration chemical potential μ is:

[0072]

[0073] Where t is time, ε is the phase field interface control parameter, σ is the stress tensor, Ω is the atomic volume, γ s is the surface energy density, It represents the effective charge number of surface electromigration, e represents the electron charge, Representing the heat transferred by surface electromigration, the surface diffusivity M can be written as:

[0074]

[0075] Among them, 1-ψ 2 Restricted diffusion occurs only on the pore surface, and the solid-state diffusion coefficient D s for:

[0076]

[0077] Where D sis the pre-index coefficient, Q s is the surface diffusion activation energy, δ s represents the width of the diffusion layer, k B Refers to the Boltzmann constant.

[0078] For example, in the thermoelastic fracture phase field model, in the metal region of the specimen Introducing fracture phase field variables Distinguish between metal materials and cracks, and Respectively represent the state of complete destruction and intactness of the material; Represents different degrees of damage to the material, the metal area of ​​the specimen The hole area is not included.

[0079] Exemplarily, the thermoelastic fracture phase field model includes a set of control equations for crack initiation and propagation, which are:

[0080]

[0081] Among them, l 0 G is the characteristic width of the phase field model that controls the degree of crack diffusion. c is the critical energy release rate, the constant p<<1 avoids numerical singularity, and in order to prevent crack self-healing, the elastic energy density history variable is introduced:

[0082]

[0083] The above formula indicates Elastic strain energy density function The historical maximum value in the time period [0, t].

[0084] For example, when constructing a defect evolution phase field model, in addition to the electromigration solid diffusion model, it can be assumed that the electrostatic model, the electrothermal model, the thermoelastic solid mechanics model and the thermoelastic fracture phase field model are all steady-state models, that is, the control equation is a steady-state equation (without time term). Then, both defect evolution mechanisms involve bidirectional coupling: the displacement field, the temperature field and the electric field jointly regulate the evolution of the defect, and the change in the defect morphology reversely redistributes the three fields.

[0085] S103, solving the defect evolution phase field model.

[0086] In one implementation, solving the defect evolution phase field model may include:

[0087] For the simulation domain Discretize in time and space dimensions, input the initial phase field variable ψ and the electric potential boundary conditions into the electrostatic model to obtain the electric potential field φ output by the electrostatic model; input the initial phase field variable ψ, the temperature boundary conditions and the output electric potential field φ into the electrothermal model to obtain the temperature field T output by the electrothermal model; input the displacement boundary conditions and the output temperature field T into the thermoelastic solid mechanics model to obtain the displacement field u output by the thermoelastic solid mechanics model; input the initial phase field variable ψ and the obtained electric potential field φ, temperature field T and displacement field u information into the electromigration solid diffusion model to obtain the phase field ψ of the next time layer; perform mapping on the output phase field ψ Output mapping result phase field The displacement boundary condition, temperature boundary condition and output phase field Information is input into the elastic fracture phase field model to obtain the phase field variables after fracture The output phase field Execute the inverse mapping ψ(r) and output the inverse mapping result phase field ψ; execute the above steps repeatedly on the output phase field ψ until the crack penetrates.

[0088] Exemplarily, the numerical method for solving the phase field model may include:

[0089] The electrostatic model, electrothermal model, and thermoelastic solid mechanics model all use the finite volume method, the electromigration solid diffusion model uses the finite difference method, and the thermoelastic fracture phase field model uses the finite element method.

[0090] In the embodiment of the present application, the parameter information and multi-physical field load information of the defective sample are determined to establish a simplified model; wherein the multi-physical field load information includes: loads and boundary conditions of force-heat-electric field; based on the simplified model, a defect evolution phase field model is constructed; the defect evolution phase field model includes an electromigration phase field model coupled with force-heat-electric field, and a thermoelastic fracture phase field model; the defect evolution phase field model is solved. In this scheme, the electrostatic model, electrothermal model, thermoelastic solid mechanics model and thermoelastic fracture phase field model are solved for the defect morphology at each time step during the electromigration phase field evolution process, so that the cracks that penetrate the defect pattern are classified into the final defect morphology, and the complete process of the evolution of the defect morphology over time is obtained.

[0091] In order to further illustrate the solution of the present application, the defect evolution analysis method of the present application caused by fracture and electromigration based on the phase field method is introduced below with reference to specific examples.

[0092] like Figure 2-5 As shown, the defect evolution analysis method caused by fracture and electromigration based on the phase field method may include the following steps:

[0093] like Figure 2 As shown in the figure, the defective sample is subjected to potential difference ΔV and uniaxial tension at the same time. When the hole edge is not only electromigration, but also crack initiation occurs. The model in this embodiment takes into account both the physical processes of mass migration caused by electromigration and crack extension induced by stress concentration at the hole edge, and can simulate the complete destruction process of intermetallic compounds at the solder joint interface from early electromigration mass diffusion to final fracture destruction. The mechanism of electromigration of hole defects on the fracture of intermetallic compounds along the hole is revealed.

[0094] Step 1: Determine the sample parameters and boundary conditions. Specifically, the sample geometry and boundary conditions are as follows: Figure 3 As shown in the figure, the sample has a width of L = 5 μm and a height of H = 5 μm. There is a circular hole defect with a radius of R = 0.5 μm in the center. The left edge of the specimen is grounded, and a uniform potential ΔV=5×10 -4 V, while the top and bottom boundaries are both insulating. The phase field ψ and Natural boundary conditions are used. The temperature of all boundaries of the sample is fixed at 473K. The simulated metal material is AuAl 2 Its material parameters and phase field model parameters are shown in Table 1.

[0095] Table 1 Model parameters

[0096]

[0097] Step 2: Construct a phase field model of defect evolution driven by dual physical mechanisms, including an electromigration phase field model of force-heat-electric multi-field coupling and a thermoelastic fracture phase field model, and numerically solve the electromigration-thermoelastic fracture phase field model.

[0098] Discretization of the field variable solution space of the phase field model. Since the control equations in the model contain terms related to time, it is necessary to discretize the simulation domain not only in space but also in time. Specifically, a uniform grid with a step size of Δx = Δy = 0.01 μm is used to discretize the simulation area. Discretize; time is discretized into multiple equal time periods, and the time step is Δt = 1×10 -2 s.

[0099] The control equation of the phase field variable ψ of the electromigration phase field model is a non-steady-state equation (the control equation contains time-related terms), while the control equations of the electrostatic model, electrothermal model, thermoelastic solid mechanics model and thermoelastic fracture phase field model reach equilibrium relaxation in a time much shorter than the diffusion time, so they are all steady-state equations. This means that while the phase field variable ψ evolves with time, other physical processes always maintain equilibrium.

[0100] Figure 4The specific process of model solution is demonstrated. The distribution of phase field ψ updated at each time step is solved for electrostatic model, electrothermal model, thermoelastic solid mechanics model and thermoelastic fracture phase field model. The field variables related to phase field ψ in the model (potential field φ, temperature field T, displacement field u and fracture phase field ) is also updated accordingly. The control equation of the electromigration phase field variable ψ is solved by the difference method, using the forward difference format; the control equations of the electrostatic model, electrothermal model, and thermoelastic solid mechanics model are solved by the finite volume method; the fracture phase field variable The solution adopts the finite element method and a one-step staggered iteration format; before executing the thermoelastic fracture model, the phase field variable ψ of the electromigration model needs to be mapped:

[0101]

[0102] If no crack initiation occurs, the phase field ψ before the input fracture model is directly inherited into the phase field ψ evolution equation of the next time step; otherwise, the fracture phase field variable after the fracture phase field model is executed Do the mapping:

[0103]

[0104] Step 3: Simulation results. Figure 5 It shows that when the stress magnitude is The evolution process of circular holes under uniaxial tension. 5(a) is the initial defect morphology. Figure 5 (b) It can be seen that the void drifts along the direction of the electric field. In addition, due to the concentration of elastic strain energy and local high temperature caused by the "current crowding" effect, sharp corners appear at the top and bottom of the hole, respectively. However, at the apex of the sharp corner, the fracture mechanism does not work because the crack growth criterion has not been met. In order to better characterize the stress accumulation effect during electromigration, a proportionality factor based on the first principal stress can be defined in and Respectively represent the time t=t n and the maximum first principal stress of the intermetallic compound at t = 0. The proportionality factor Starting from 1.0 at t = 0, it gradually increases with the development of mass diffusion and reaches 1.417 at 80000s, which means that the maximum first principal stress increases by more than 40%. As the mass diffusion caused by electromigration proceeds, the development of the two sharp corners amplifies the stress concentration at the top and bottom of the cavity. Figure 5As shown in (c), electromigration drives the two sharp corners to extend continuously in the vertical direction, eventually leading to the initiation and expansion of cracks. The time scale of the brittle fracture process is much smaller than the time scale of the diffusion of materials induced by electromigration. In the simulation, when t = 80100s, the initiation and expansion of the crack are completed within one time step. The crack expansion process within this time step is shown in Figure 5 (d)-(f) As shown in the figure, it can be seen that the crack starts from the upper and lower sharp corners formed during the electromigration process and expands upward and downward respectively. This is consistent with the experience of fracture mechanics, that is, when subjected to uniaxial tensile loading, the crack tends to expand perpendicular to the loading direction.

[0105] The embodiment of the present application also provides an electronic device, including a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory communicate with each other through the communication bus.

[0106] Memory, used to store computer programs;

[0107] The processor is used to implement the defect evolution analysis method caused by fracture and electromigration based on the phase field method provided in the embodiment of the present application when executing the program stored in the memory.

[0108] The communication bus mentioned in the above terminal can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. The communication bus can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, only one thick line is used in the figure, but it does not mean that there is only one bus or one type of bus.

[0109] The communication interface is used for communication between the above terminal and other devices.

[0110] The memory may include a random access memory (RAM) or a non-volatile memory, such as at least one disk memory. Optionally, the memory may also be at least one storage device located away from the aforementioned processor.

[0111] The above-mentioned processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0112] In another embodiment provided in the present application, a computer-readable storage medium is also provided, in which a computer program is stored. When the computer program is executed by a processor, the defect evolution analysis method caused by fracture and electromigration based on the phase field method described in any of the above embodiments is implemented.

[0113] In another embodiment provided in the present application, a computer program product comprising instructions is also provided. When the computer is run on the computer, the computer executes the defect evolution analysis method caused by fracture and electromigration based on the phase field method as described in any of the above embodiments.

[0114] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions may be transmitted from a website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) mode to another website site, computer, server or data center. The computer-readable storage medium may be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrated. The available medium may be a magnetic medium, (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state drive Solid State Disk (SSD)), etc.

[0115] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0116] Each embodiment in this specification is described in a related manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the device embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0117] The above description is only a preferred embodiment of the present application and is not intended to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application are included in the protection scope of the present application.

Claims

1. A phase-field method based defect evolution analysis method induced by fracture and electromigration, characterized in that: include: Determine the parameter information and multi-physical field load information of the defective sample and establish a simplified model; wherein the multi-physical field load information includes: force-heat-electric field load and boundary conditions; Based on the simplified model, a defect evolution phase field model is constructed; the defect evolution phase field model includes a force-heat-electric field coupled electromigration phase field model and a thermoelastic fracture phase field model; The defect evolution phase field model is solved.

2. The method according to claim 1, characterized in that The force-heat-electric field coupled electromigration phase field model includes: an electrostatic model, an electrothermal model, a thermoelastic solid mechanics model and an electromigration solid diffusion model; In the mechanical-thermal-electric field coupled electromigration phase field model, in the simulation domain The phase field variable ψ (ψ∈[-1,1]) is introduced to distinguish metal materials from holes, where ψ=-1 represents the hole defect area, ψ=1 represents the metal area; ψ∈(1,1) represents the hole interface. Contains hole areas; In the thermoelastic fracture phase field model, in the metal region of the specimen Introducing fracture phase field variables Distinguish between metal materials and cracks, and Respectively represent the state of complete destruction and intactness of the material; Representing different degrees of damage state of the material, the metal area of ​​the specimen The hole area is not included.

3. The method according to claim 2, characterized in that The electrostatic model includes: ▽·[ζ(ψ)▽φ]=0 Among them, ζ(ψ) = h(ψ)·ζ is the effective conductivity, and the material performance parameter interpolation function It satisfies h(1)=1 in the metal region and h(-1)=0 in the hole region, ζ is the metal conductivity, and φ is the electric potential field.

4. The method according to any one of claims 2 or 3, characterized in that: The electrothermal model includes: ▽·[k(ψ)▽T]+ζ(ψ)|▽φ| 2 =0 Among them, k(ψ)=h(ψ)·k is the effective thermal conductivity, k is the thermal conductivity of the metal, and T is the temperature field.

5. The method according to any one of claims 2 or 3, characterized in that: The thermoelastic solid mechanics model includes: ▽·[C(ψ)e e ]=0 Among them, C(ψ) = h(ψ)·C is the effective fourth-order elastic tensor, C is the fourth-order elastic tensor of the metal, ε e is the elastic strain tensor.

6. The method according to claim 2 or 3, characterized in that: The electromigration solid-state diffusion model includes: Among them, the electromigration chemical potential μ is: Where t is time, ε is the phase field interface control parameter, σ is the stress tensor, Ω is the atomic volume, γ s is the surface energy density, It represents the effective charge number of surface electromigration, e represents the electron charge, Q s * Representing the heat transferred by surface electromigration, the surface diffusivity M can be written as: Among them, 1-ψ 2 Characterizes that restricted diffusion occurs only on the pore surface, and the solid-state diffusion coefficient D s for: Where D s is the pre-exponential coefficient, Q s is the surface diffusion activation energy, δ s represents the width of the diffusion layer, k B Refers to the Boltzmann constant.

7. The method according to claim 2, characterized in that: The thermoelastic fracture phase field model includes a set of control equations for crack initiation and propagation, and the set of control equations for crack initiation and propagation is: ▽·σ=0 Among them, l0 is the characteristic width of the phase field model that controls the degree of crack diffusion, G c is the critical energy release rate, the constant p<<1 avoids numerical singularity, and in order to prevent crack self-healing, the elastic energy density history variable is introduced: The above formula indicates The historical maximum value of the elastic strain energy density function W in the time period [0, t].

8. The method according to claim 2, characterized in that: The electrostatic model, electrothermal model, thermoelastic solid mechanics model and thermoelastic fracture phase field model are all steady-state models without time terms.

9. The method according to claim 2, characterized in that: The step of solving the defect evolution phase field model comprises: For the simulation domain Discretize in time and space dimensions, input the initial phase field variable ψ and the electric potential boundary conditions into the electrostatic model to obtain the electric potential field φ output by the electrostatic model; input the initial phase field variable ψ, the temperature boundary conditions and the output electric potential field φ into the electrothermal model to obtain the temperature field T output by the electrothermal model; input the displacement boundary conditions and the output temperature field T into the thermoelastic solid mechanics model to obtain the displacement field u output by the thermoelastic solid mechanics model; input the initial phase field variable ψ and the obtained electric potential field φ, temperature field T and displacement field u information into the electromigration solid diffusion model to obtain the phase field ψ of the next time layer; perform mapping on the output phase field ψ Output mapping result phase field The displacement boundary condition, temperature boundary condition and output phase field Information is input into the elastic fracture phase field model to obtain the phase field variables after fracture The output phase field Execute the inverse mapping ψ(r) and output the inverse mapping result phase field ψ; execute the above steps repeatedly on the output phase field ψ until the crack penetrates.

10. An electronic device, characterized in that: It includes a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory communicate with each other through the communication bus; Memory, used to store computer programs; A processor, for implementing the method steps described in any one of claims 1 to 9 when executing a program stored in a memory.

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