Solid-state lithium battery electrolyte material fracture failure prediction method based on phase field method

Abstract

The invention discloses a solid-state lithium battery electrolyte material fracture failure prediction method based on a phase field method, and relates to the technical field of battery failure prediction, and the method comprises the following steps: S1, constructing a reference configuration and an instant configuration for a lithium battery electrolyte material; s2, constructing transformation between the reference configuration and the instant configuration, and generating deformation mapping; s3, establishing mapping between the temperature field and the reference configuration, mapping between the concentration field and the reference configuration, and mapping between the potential distribution and the reference configuration; s4, constructing a phase field variable for the lithium battery electrolyte material; s5, obtaining a thermodynamic constitutive model; s6, obtaining a control equation of the solid-state lithium battery electrolyte material; s7, constructing boundary conditions for the control equation; and S8, fracture failure prediction is completed by using the weak form of the control equation. According to the invention, a basis is provided for parameter setting and safety evaluation of the solid-state battery.

Description

Technical Field

[0001] The present invention relates to the technical field of battery failure prediction, and particularly relates to a method for predicting the fracture failure of a solid-state lithium battery electrolyte material based on the phase field method. Background Art

[0002] Solid-state lithium metal batteries are considered to be the ultimate choice for future energy storage systems due to their high theoretical energy density and safety. However, interface problems such as severe high interfacial resistance, poor chemical compatibility, and poor stability hinder the practical application of solid-state batteries. In addition, during repeated cycling, the growth and mechanical degradation of lithium dendrites caused by interfacial stress can also lead to the failure of solid-state batteries. Therefore, understanding the failure mechanism of solid-state lithium batteries is of great significance for constructing safe solid-state lithium batteries.

[0003] Traditional lithium metal batteries generally use organic liquid electrolytes, which have a narrow electrochemical window and are difficult to fully utilize the advantages of high energy density of lithium metal batteries. In addition, liquid electrolytes cannot restrain the growth of lithium dendrites originating from the anode surface, which easily leads to short-circuit faults inside the battery. On the other hand, organic liquid electrolytes have characteristics such as flammability, and the leakage of electrolytes and internal short circuits caused by dendrite growth are more likely to trigger safety accidents such as spontaneous combustion and explosion. While solid-state lithium metal batteries use solid electrolytes, which have good thermal stability and can effectively avoid the combustion and explosion of electrolytes. Secondly, solid electrolytes have shear resistance that liquid electrolytes do not have, and can better inhibit the growth and propagation of lithium dendrites. And solid electrolytes have a wider electrochemical window, which enables the battery to have a higher energy density. In addition, solid electrolytes also have advantages such as higher conductivity, better electrochemical and chemical stability.

[0004] However, despite the above-mentioned many advantages, solid-state lithium metal batteries still face challenges in practical applications, mainly including: the polarization degree of solid electrolytes is relatively strong, and more polarization heat will be generated during operation, which affects the safety performance and ionic conductivity of the battery; lithium deposition on the electrode surface eventually develops into lithium dendrites and hollow "dead lithium", and "dead lithium" reduces the ionic conductivity of the electrolyte, thereby affecting the battery capacity; the tip of the lithium dendrite undergoes stress concentration, resulting in the generation of mechanical cracks, which also reduces the ionic conductivity and further promotes the growth of lithium dendrites; during operation, the volume expansion of the anode reduces the stability of the anode-electrolyte interface, thereby triggering interface delamination and hindering ion transport; moreover, the deposition and dissolution of lithium will generate large stresses at the interface and inside the electrolyte, causing mechanical damage and increasing the internal resistance of the battery. Based on the above analysis, it can be seen that the failure of solid-state batteries involves multiple physical and chemical processes, and heat, current, chemical reactions, and mechanical deformation and damage all play important roles. Therefore, in order to more comprehensively evaluate the influence of various factors on the performance of solid-state batteries and predict the failure of solid-state batteries, it is necessary to study the various behaviors of solid-state batteries during operation from the perspective of multi-physical field coupling. Summary of the Invention

[0005] In order to solve the above problems, the present invention proposes a method for predicting the fracture failure of solid-state lithium battery electrolyte materials based on the phase field method.

[0006] The technical solution of the present invention is: a method for predicting the fracture failure of solid-state lithium battery electrolyte materials based on the phase field method includes the following steps:

[0007] S1. Construct a reference configuration and an instantaneous configuration for the lithium battery electrolyte material;

[0008] S2. Construct a transformation between the reference configuration and the instantaneous configuration to generate a deformation mapping;

[0009] S3. Construct a mapping between the temperature field and the reference configuration, a mapping between the concentration field and the reference configuration, and a mapping between the electric potential distribution and the reference configuration;

[0010] S4. Construct a phase field variable for the lithium battery electrolyte material;

[0011] S5. Calculate the energy dissipation, and obtain a thermodynamic constitutive model based on the energy dissipation;

[0012] S6. According to the momentum balance equation corresponding to the deformation mapping, the temperature control equation corresponding to the mapping between the temperature field and the reference configuration, the mass conservation equation corresponding to the mapping between the concentration field and the reference configuration, the charge conservation equation corresponding to the mapping between the electric potential distribution and the reference configuration, the phase field equation corresponding to the phase field variable, and the thermodynamic constitutive model, obtain the control equation of the solid-state lithium battery electrolyte material;

[0013] S7. Construct boundary conditions for the governing equations;

[0014] S8. Determine the weak form of the governing equations based on the governing equations and boundary conditions of the solid-state lithium battery electrolyte material, and complete the fracture failure prediction using the weak form of the governing equations.

[0015] Furthermore, the deformation mapping has the following expression:

[0016] ;

[0017] wherein, represents the spatial region occupied by the reference configuration, represents the time period occupied by the process of deformation and failure of the configuration, represents the spatial region occupied by the instantaneous configuration, represents the variable of the reference configuration, represents time, represents the variable of the instantaneous configuration, represents the deformation field.

[0018] Furthermore, the mapping between the temperature field and the reference configuration has the following expression:

[0019] ;

[0020] wherein, represents the spatial region occupied by the reference configuration, represents the time period occupied by the process of deformation and failure of the configuration, represents the set of all positive real numbers, represents the variable of the reference configuration, represents time, represents the temperature field.

[0021] Furthermore, in the above S4, the mapping between the concentration field and the reference configuration has the following expression:

[0022] ;

[0023] wherein, represents the spatial region occupied by the reference configuration, represents the time period occupied by the process of deformation and failure of the configuration, represents the set of all positive real numbers, represents the variable of the reference configuration, represents time, represents the The number of moles of nuclide per unit undeformed volume of each component represents the total number of nuclides.

[0024] Furthermore, the mapping between the electric potential distribution and the reference configuration is expressed as:

[0025] ;

[0026] wherein, represents the spatial region occupied by the reference configuration, represents the time period occupied by the process of deformation and damage of the configuration, represents the real number field, represents the variable of the reference configuration, represents time, represents the electric potential.

[0027] Furthermore, the energy dissipation is expressed as:

[0028] ;

[0029] wherein, represents the spatial region occupied by the reference configuration, represents the first Piola - Kirchhoff stress, represents the derivative of the deformation gradient tensor with respect to time, represents the density under the reference configuration, represents the internal microscopic force, represents the derivative of the phase - field variable with respect to time, represents the microscopic traction force within the damaged region, represents the gradient operator, represents the gradient of the derivative of the phase - field variable with respect to time, represents the heat flux within the material in Lagrangian description, represents the temperature, represents the temperature gradient, represents the electric field strength, represents the derivative of the electric displacement vector with respect to time, represents the current density, represents the total number of nuclides, represents the chemical potential of the th component, The number of moles of nuclide per unit undeformed volume of the th component, represents the mass flux of the particles of the th component, represents the gradient of the chemical potential of the represents the derivative of the Helmholtz free energy density with respect to time, represents entropy, represents the derivative of temperature with respect to time.

[0030] Furthermore, the expression of the thermomechanical constitutive model is:

[0031] ;

[0032] In the formula, represents the first Piola - Kirchhoff stress, represents the stress attenuation function, represents the phase - field variable, represents the shear modulus, represents the mechanical deformation caused by the macroscopic stress, represents the transpose of a tensor, represents the Lame constant, represents the third invariant of the mechanical deformation tensor, represents the expansion and contraction deformation caused by the local chemical concentration change, represents the expansion and contraction due to the local temperature change, represents temperature, represents the logarithmic function, represents the internal microscopic force, represents the density in the reference configuration, represents the Lagrangian strain energy density, represents the fracture toughness, represents the vector composed of the number of moles of each nuclide per unit undeformed volume, represents a fixed parameter, represents the characteristic length, represents the microscopic traction force in the damaged area, represents entropy, represents the coefficient of thermal expansion, represents the third invariant of the thermal deformation tensor, represents the deformation tensor, represents the standard entropy density per unit mass, represents the specific heat capacity at constant pressure, represents the reference temperature, represents the critical energy release rate at the reference temperature and reference concentration, represents the crack density function, represents the gradient of the phase - field variable, represents the maximum temperature, represents the first undetermined constant, represents the second undetermined constant, represents the total number of nuclides, represents with the Fracture toughness attenuation function related to the concentration of a component denotes the number of moles of nuclide per unit undeformed volume of the th component denotes the chemical potential of the th component denotes the chemical expansion rate denotes the molar salt volume of the th component denotes the parameter related to chemistry denotes the standard chemical potential of the th component independent of chemical concentration and deformation denotes the ideal gas constant denotes the fugacity coefficient of the th component denotes the reference concentration of the th component Fracture toughness attenuation function related to temperature denotes the maximum concentration of the th component denotes the first undetermined constant related to the concentration of the th component denotes the second undetermined constant related to the concentration of the th component denotes the fracture toughness attenuation function related to the concentration of the th component denotes the number of moles of nuclide per unit undeformed volume of the th component denotes the electric field strength denotes the vacuum permittivity denotes the relative permittivity denotes the electric displacement vector denotes the third invariant of the deformation gradient tensor

[0033] Furthermore, the expression of the governing equation is as follows:

[0034] ;

[0035] wherein denotes the gradient operator denotes the first Piola - Kirchhoff stress denotes the density in the reference configuration denotes the body force per unit mass in the reference configuration denotes the acceleration denotes the phase field variable denotes the history variable denotes the fracture toughness denotes the characteristic length, denotes the specific heat capacity at constant pressure, denotes the derivative of temperature with respect to time, denotes the external heat source, denotes the thermal conductivity decay function related to damage, denotes the thermal conductivity tensor related to deformation, denotes the temperature gradient, denotes the internal heat source, denotes the derivative with respect to time of the number of moles of nuclides per unit undeformed volume of the denotes the mass flux of the particles of the denotes the concentration of the particles of the component generated by the chemical reaction, denotes the derivative of the charge density with respect to time, denotes the current density.

[0036] Furthermore, the boundary conditions include force boundary conditions, thermal boundary conditions, chemical concentration boundary conditions, and electric field boundary conditions;

[0037] The expression of the force boundary condition is:

[0038] ;

[0039] wherein, denotes the displacement vector, denotes the fixed displacement at the boundary, denotes the position vector of the point on the boundary, denotes the displacement boundary, denotes the first Piola-Kirchhoff stress, denotes the outer normal vector of the boundary, denotes the fixed traction force, denotes the force boundary;

[0040] The expression of the thermal boundary condition is:

[0041] ;

[0042] wherein, denotes the temperature, denotes the fixed temperature, denotes the temperature boundary, denotes the heat flux inside the material in the Lagrangian description, denotes the outer normal vector of the boundary, denotes the fixed heat flux, denotes the heat flux boundary;

[0043] The expression of the chemical concentration boundary condition is as follows:

[0044] ;

[0045] In the formula, represents the nuclear mole number of the th component per unit undeformed volume, represents the fixed concentration of the th component, represents the fixed concentration boundary of the th component, represents the mass flow of the particles of the th component, represents the fixed mass flow of the particles of the th component, represents the fixed mass flow boundary of the th component;

[0046] The expression of the electric field boundary condition is as follows:

[0047] ;

[0048] In the formula, represents the electric potential, represents the fixed electric potential, represents the electric potential boundary, represents the current density, represents the fixed current, represents the current boundary.

[0049] Furthermore, the expression of the weak form of the governing equation is as follows:

[0050] ;

[0051] In the formula, represents the spatial region occupied by the reference configuration, represents the first Piola-Kirchhoff stress, represents the deformation gradient tensor, represents the density in the reference configuration, represents the body force per unit mass in the reference configuration, represents the displacement, represents the force boundary, represents the fixed traction, represents the phase field variable, represents the history variable, represents the fracture toughness, represents the characteristic length, represents the gradient of the phase field variable, represents the specific heat capacity at constant pressure, represents the derivative of temperature with respect to time, represents temperature, represents the heat flux within the material in the Lagrangian description, represents the temperature gradient, represents the internal heat source, represents the heat flux boundary, represents the fixed heat flux, represents the electrode and electrolyte interface, represents the heat generated at the interface by the instantaneous current density at the electrode and electrolyte interface, represents the derivative with respect to time of the nuclide mole number per unit undeformed volume of the represents the nuclide mole number per unit undeformed volume of the represents the concentration gradient of the nuclide mole number per unit undeformed volume of the represents the mass flux of the particles of the represents the particle concentration of the species generated by the chemical reaction, represents the current boundary, represents the fixed mass flux of the particles of the represents the derivative of the charge density with respect to time, represents the electric potential, represents the current density, represents the current boundary, represents the electrode and electrolyte interface, represents the electric potential gradient, represents the fixed current density, represents the instantaneous current density at the electrode and electrolyte interface.

[0052] The beneficial effects of the present invention are as follows: The present invention takes into account the full coupling effects of the electric field, chemical concentration field, temperature field, and displacement field to predict the distributions and changes of various physical fields and the initiation and propagation of cracks during the operation of a solid-state battery, providing a basis for the parameter setting and safety evaluation of the solid-state battery. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 is a flowchart of a method for predicting the fracture failure of an electrolyte material of a solid-state lithium battery based on the phase field method. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0054] The embodiments of the present invention will be further described below with reference to the drawings.

[0055] As Figure 1As shown, the present invention provides a method for predicting the fracture failure of a solid-state lithium battery electrolyte material based on the phase field method, including the following steps:

[0056] S1. Construct a reference configuration and an instant configuration for the lithium battery electrolyte material;

[0057] S2. Construct a transformation between the reference configuration and the instant configuration to generate a deformation mapping;

[0058] S3. Construct mappings between the temperature field and the reference configuration, between the concentration field and the reference configuration, and between the electric potential distribution and the reference configuration;

[0059] S4. Construct phase field variables for the lithium battery electrolyte material;

[0060] S5. Calculate the energy dissipation, and obtain a thermomechanical constitutive model based on the energy dissipation;

[0061] S6. According to the momentum balance equation corresponding to the deformation mapping, the temperature control equation corresponding to the mapping between the temperature field and the reference configuration, the mass conservation equation corresponding to the mapping between the concentration field and the reference configuration, the charge conservation equation corresponding to the mapping between the electric potential distribution and the reference configuration, the phase field equation corresponding to the phase field variables, and the thermomechanical constitutive model, obtain the control equation of the solid-state lithium battery electrolyte material;

[0062] S7. Construct boundary conditions for the control equation;

[0063] S8. According to the control equation and the boundary conditions of the solid-state lithium battery electrolyte material, determine the weak form of the control equation, and complete the fracture failure prediction using the weak form of the control equation.

[0064] In the embodiment of the present invention, first consider an isotropic solid material occupying a spatial region in the reference configuration, whose outer boundary is denoted as , and the variables in the reference configuration are all functions of the material coordinates . The spatial region occupied by the instant configuration is denoted as , whose outer boundary is denoted as , and the variables in the instant configuration are all functions of the spatial coordinates . To describe the deformation of the material, a transformation between the reference configuration and the instant configuration is established, and a deformation mapping is introduced. The expression of the deformation mapping is:

[0065] ;

[0066] In the formula, represents the spatial region occupied by the reference configuration, represents the time period occupied by the process of material deformation and damage, represents the spatial region occupied by the instantaneous configuration, a variable representing the reference configuration, represents time, a variable representing the instantaneous configuration, represents the deformation field.

[0067] In an embodiment of the present invention, in order to describe the temperature change of a material, a mapping between the temperature field and the reference configuration is established. The mapping between the temperature field and the reference configuration has the following expression:

[0068] ;

[0069] wherein, represents the spatial region occupied by the reference configuration, represents the time period occupied by the process of deformation and failure of the configuration, represents the set of all positive real numbers, a variable representing the reference configuration, represents time, represents the temperature field.

[0070] In an embodiment of the present invention, in order to describe the change in the concentration of each component in a material, a mapping between the concentration field and the reference configuration is established. Assuming that there are types of different particles in the system, the mapping between the concentration field and the reference configuration has the following expression:

[0071] ;

[0072] wherein, represents the spatial region occupied by the reference configuration, represents the time period occupied by the process of deformation and failure of the configuration, represents the set of all positive real numbers, a variable representing the reference configuration, represents time, represents the molar number of nuclides per unit undeformed volume of the th component,

[0073] In an embodiment of the present invention, in order to describe the electric potential distribution in a material, a mapping between the electric potential distribution and the reference configuration is established. The mapping between the electric potential distribution and the reference configuration has the following expression:

[0074] ;

[0075] wherein, Denotes the spatial region occupied by the reference configuration, Denotes the time period occupied by the process of deformation and failure of the configuration, Denotes the real number field, Denotes the variable of the reference configuration, Denotes time, Denotes the electric potential.

[0076] In the embodiment of the present invention, first, according to the first law of thermodynamics, on the reference configuration, there is ; In the formula, Denotes the total internal energy, Denotes the kinetic energy, Denotes the external power, Denotes the thermal power, Denotes the chemical energy change rate, Denotes the electric power. Substitute the above energy expressions into the first law of thermodynamics, apply the equilibrium equation, and combine with the second law of thermodynamics to obtain the energy dissipation expression. Energy dissipation The expression is:

[0077] ;

[0078] In the formula, Denotes the spatial region occupied by the reference configuration, Denotes the first Piola-Kirchhoff stress, Denotes the derivative of the deformation gradient tensor with respect to time, Denotes the density under the reference configuration, Denotes the internal microscopic force, Denotes the derivative of the phase field variable with respect to time, Denotes the microscopic traction force in the damaged area, Denotes the gradient operator, Denotes the gradient of the derivative of the phase field variable with respect to time, Denotes the heat flux inside the material in the Lagrangian description, Denotes the temperature, Denotes the temperature gradient, Denotes the electric field strength, Denotes the derivative of the electric displacement vector with respect to time, Denotes the current density, Denotes the total number of nuclides, Denotes the Chemical potential of the Denotes the Number of moles of nuclides per unit undeformed volume of the Denotes the Mass flux of the particles of the Denotes the The gradient of the chemical potential of the components, represents the derivative of the Helmholtz free energy density with respect to time, represents entropy, represents the derivative of temperature with respect to time.

[0079] In the embodiments of the present invention, the expression of the thermomechanical constitutive model is:

[0080] ;

[0081] In the formula, represents the first Piola-Kirchhoff stress, represents the stress attenuation function, represents the phase field variable, represents the shear modulus, represents the mechanical deformation caused by the macroscopic stress, represents the transpose of the tensor, represents the Lame constant, represents the third invariant of the mechanical deformation tensor, represents the expansion and contraction deformation caused by the local chemical concentration change, represents the expansion and contraction due to the local temperature change, represents temperature, represents the logarithmic function, represents the internal microscopic force, represents the density in the reference configuration, represents the strain energy density, represents the fracture toughness, represents the vector composed of the number of moles of each nuclide per unit undeformed volume, represents the fixed parameter, represents the characteristic length, represents the microscopic traction force in the damaged area, represents entropy, represents the coefficient of thermal expansion, represents the third invariant of the thermal deformation tensor, represents the deformation tensor, represents the standard entropy density per unit mass, represents the specific heat capacity at constant pressure, represents the reference temperature, represents the critical energy release rate at the reference temperature and reference concentration, represents the crack density function, represents the gradient of the phase field variable, represents the maximum temperature, represents the first undetermined constant, represents the second undetermined constant, represents the total number of nuclides, represents the fracture toughness attenuation function related to the concentration of the th component, represents the number of moles of nuclides per unit undeformed volume of the th component, represents the chemical potential of the th component, represents the chemical expansion rate, represents the molar salt volume of the th component, represents the chemical-related parameter, represents the standard chemical potential of the th component that is independent of chemical concentration and deformation, represents the ideal gas constant, represents the fugacity coefficient of the th component, represents the reference concentration of the th component, represents the fracture toughness attenuation function related to temperature, represents the maximum concentration of the th component, represents the first undetermined constant related to the concentration of the th component, represents the second undetermined constant related to the concentration of the th component, represents the fracture toughness attenuation function related to the concentration of the th component, represents the number of moles of nuclides per unit undeformed volume of the th component, represents the electric field strength, represents the vacuum permittivity, represents the relative permittivity, represents the third invariant of the deformation gradient tensor.

[0082] In the embodiments of the present invention, by combining the law of conservation of charge, the relationship between electric potential and electric field, and Fourier's law of heat conduction, and only considering the quasi-static case, the control equation of the temperature field is obtained, and finally the differential form of the control equation is obtained. The expression of the control equation is:

[0083] ;

[0084] In the formula, represents the gradient operator, represents the first Piola-Kirchhoff stress, represents the density in the reference configuration, represents the volume distribution force per unit mass under the reference configuration, represents the acceleration, represents the phase field variable, represents the history variable, represents the fracture toughness, represents the characteristic length, represents the specific heat capacity at constant pressure, represents the derivative of temperature with respect to time, represents the external heat source, represents the thermal conductivity attenuation function related to damage, represents the thermal conductivity tensor related to deformation, represents the temperature gradient, represents the internal heat source, represents the derivative with respect to time of the number of moles of nuclides per unit undeformed volume of the represents the mass flux of the particles of the represents the particle concentration of the represents the derivative with respect to time of the charge density, represents the current density.

[0085] In the embodiments of the present invention, based on the Dirichlet boundary condition and the Neumann boundary condition, the boundary conditions of the general form of force, heat, chemical concentration field and electric field are given. The damage field satisfies the Neumann condition of zero gradient on all boundaries, that is . The boundary conditions include force boundary conditions, heat boundary conditions, chemical concentration boundary conditions and electric field boundary conditions;

[0086] The expression of the force boundary condition is:

[0087] ;

[0088] In the formula, represents the displacement vector, represents the fixed displacement at the boundary, represents the position vector of the point on the boundary, represents the displacement boundary, represents the first Piola-Kirchhoff stress, represents the outer normal vector of the boundary, represents the fixed traction force, represents the force boundary;

[0089] The expression of the heat boundary condition is:

[0090] ;

[0091] In the formula, represents temperature, represents the fixed temperature, represents the temperature boundary, represents the heat flux inside the material in the Lagrangian description, represents the outer normal vector of the boundary, represents the fixed heat flux, represents the heat flux boundary;

[0092] The expression of the chemical concentration boundary condition is:

[0093] ;

[0094] In the formula, represents the number of moles of nuclides per unit undeformed volume of the th component, represents the fixed concentration of the th component, represents the fixed concentration boundary of the th component, represents the mass flux of the particles of the th component, represents the fixed mass flux of the particles of the th component, represents the fixed mass flux boundary of the th component;

[0095] The expression of the electric field boundary condition is:

[0096] ;

[0097] In the formula, represents the electric potential, represents the fixed electric potential, represents the electric potential boundary, represents the current density, represents the fixed current, represents the current boundary.

[0098] In the embodiment of the present invention, for the instantaneous current density at the electrode-electrolyte interface, in the battery system, the redox reaction (i.e., the transfer of electrons) occurs on the surface of the active particles in the electrode, and the B-V equation is used to describe the relationship between the electrode potential and the current density during this process. When all components are transported in a balanced state completely, or when the current passing through the battery is very small, and are approximately 1; when the reaction rates of the anode and the cathode are equal, there is , in particular, for a lithium battery, there is , at this time, the B-V equation can be simplified. By combining the boundary conditions and the differential form of the governing equations, the weak form of the governing equations can be obtained. Among them, represents the charge transfer coefficient of the anodic reaction, represents the charge transfer coefficient of the cathodic reaction, and satisfies , represents a function of the anodic surface concentration, represents a function of the cathodic surface concentration.

[0099] The expression of the weak form of the governing equations is:

[0100] ;

[0101] In the formula, represents the spatial region occupied by the reference configuration, represents the first Piola-Kirchhoff stress, represents the deformation gradient tensor, represents the density in the reference configuration, represents the body force per unit mass in the reference configuration, represents the displacement, represents the force boundary, represents the prescribed traction, represents the phase field variable, represents the history variable, represents the fracture toughness, represents the characteristic length, represents the gradient of the phase field variable, represents the specific heat capacity at constant pressure, represents the time derivative of the temperature, represents the temperature, represents the heat flux within the material in the Lagrangian description, represents the temperature gradient, represents the internal heat source, represents the heat flux boundary, represents the prescribed heat flux, represents the electrode and electrolyte interface, represents the heat generated by the instantaneous current density at the electrode and electrolyte interface on the interface, represents the time derivative of the number of moles of nuclides per unit undeformed volume of the th component, represents the number of moles of nuclides per unit undeformed volume of the th component, represents the concentration gradient of the number of moles of nuclides per unit undeformed volume of the th component, The mass flow of particles of a component represents the particle concentration of the species generated by the chemical reaction, represents the current boundary, the fixed mass flow of particles of the species, represents the derivative of the charge density with respect to time, represents the electric potential, represents the current density, represents the current boundary, represents the electrode - electrolyte interface, represents the electric potential gradient, represents the fixed current density, represents the instantaneous current density at the electrode - electrolyte interface.

[0102] Those of ordinary skill in the art will realize that the embodiments described herein are for helping the reader understand the principles of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific deformations and combinations without departing from the essence of the present invention according to the technical revelations disclosed in the present invention, and these deformations and combinations are still within the protection scope of the present invention.

Claims

1. A method for predicting the fracture failure of a solid-state lithium battery electrolyte material based on the phase field method, characterized in that It includes the following steps: S1. Construct a reference configuration and an instantaneous configuration for the lithium battery electrolyte material; S2. Construct the transformation between the reference configuration and the instantaneous configuration to generate a deformation mapping; S3. Construct the mappings between the temperature field and the reference configuration, between the concentration field and the reference configuration, and between the electric potential distribution and the reference configuration; S4. Construct the phase field variables for the lithium battery electrolyte material; S5. Calculate the energy dissipation and obtain the thermodynamic constitutive model based on the energy dissipation; S6. Obtain the governing equations for the solid-state lithium battery electrolyte material according to the momentum balance equation corresponding to the deformation mapping, the temperature control equation corresponding to the mapping between the temperature field and the reference configuration, the mass conservation equation corresponding to the mapping between the concentration field and the reference configuration, the charge conservation equation corresponding to the mapping between the electric potential distribution and the reference configuration, the phase field equation corresponding to the phase field variables, and the thermodynamic constitutive model; S7. Construct the boundary conditions for the governing equations; S8. Determine the weak form of the governing equations according to the governing equations for the solid-state lithium battery electrolyte material and the boundary conditions, and complete the fracture failure prediction using the weak form of the governing equations.

2. The method for predicting the fracture failure of the solid-state lithium battery electrolyte material based on the phase field method according to claim 1, wherein The deformation mapping has the following expression: ； In the formula, represents the spatial region occupied by the reference configuration, represents the time period occupied by the process of deformation and failure of the configuration, represents the spatial region occupied by the instantaneous configuration, represents the variable of the reference configuration, represents time, represents the variable of the instantaneous configuration, represents the deformation field.

3. The method for predicting the fracture failure of the solid-state lithium battery electrolyte material based on the phase field method according to claim 1, wherein The mapping between the temperature field and the reference configuration is expressed as: ； wherein, represents the spatial region occupied by the reference configuration, represents the time period occupied by the process of deformation and failure of the configuration, represents the set of all positive real numbers, represents the variable of the reference configuration, represents time, represents the temperature field.

4. The method for predicting the fracture failure of the solid-state lithium battery electrolyte material based on the phase field method according to claim 1, characterized in that, The mapping between the concentration field and the reference configuration is expressed as: ； wherein, represents the spatial region occupied by the reference configuration, represents the time period taken for the process of deformation and failure of the configuration, represents the set of all positive real numbers, represents the variable of the reference configuration, represents time, represents the molar number of nuclides per unit undeformed volume of the th component, and represents the total number of nuclides.

5. The method for predicting the fracture failure of the solid-state lithium battery electrolyte material based on the phase field method according to claim 1, wherein The mapping between the said potential distribution and the reference configuration has the expression: ； In the formula, represents the spatial region occupied by the reference configuration, represents the time period taken by the process of deformation and failure of the configuration, represents the real number field, represents the variable of the reference configuration, represents time, represents the electric potential.

6. The method for predicting the fracture failure of the solid-state lithium battery electrolyte material based on the phase field method according to claim 1, wherein The energy dissipation is expressed as: ； In the formula, represents the spatial region occupied by the reference configuration, represents the first Piola - Kirchhoff stress, represents the derivative of the deformation gradient tensor with respect to time, represents the density in the reference configuration, represents the internal microscopic force, represents the derivative of the phase - field variable with respect to time, represents the microscopic traction force in the damaged region, represents the gradient operator, represents the gradient of the derivative of the phase - field variable with respect to time, represents the heat flux inside the material in the Lagrangian description, represents the temperature, represents the temperature gradient, represents the electric field strength, represents the derivative of the electric displacement vector with respect to time, represents the current density, represents the total number of nuclides, represents the chemical potential of the th component, represents the number of moles of nuclides per unit undeformed volume of the th component, represents the mass flux of the particles of the th component, represents the gradient of the chemical potential of the th component, represents the derivative of the Helmholtz free energy density with respect to time, represents the derivative of the temperature with respect to time.

7. The method for predicting the fracture failure of the solid-state lithium battery electrolyte material based on the phase field method according to claim 1, wherein The expression of the thermodynamic constitutive model is: ； In the formula, represents the first Piola - Kirchhoff stress, represents the stress attenuation function, represents the phase - field variable, represents the shear modulus, represents the mechanical deformation caused by the macroscopic stress, represents the transpose of the tensor, represents the Lame constant, represents the third invariant of the mechanical deformation tensor, represents the expansion and contraction deformation caused by the local chemical concentration change, represents the expansion and contraction due to the local temperature change, represents the temperature, represents the logarithmic function, represents the internal microscopic force, represents the density in the reference configuration, represents the Lagrangian strain - energy density, represents the fracture toughness, represents the vector composed of the number of moles of each nuclide per unit undeformed volume, represents the fixed parameter, represents the characteristic length, represents the microscopic traction force in the damaged area, represents the entropy, represents the coefficient of thermal expansion, represents the third invariant of the thermal deformation tensor, represents the deformation tensor, represents the standard entropy density per unit mass, represents the specific heat capacity at constant pressure, represents the reference temperature, represents the critical energy release rate at the reference temperature and reference concentration, represents the crack density function, represents the gradient of the phase - field variable, represents the maximum temperature, represents the first undetermined constant, represents the second undetermined constant, represents the total number of nuclides, represents related to the fracture toughness attenuation function related to the concentration of the th component, represents the number of moles of nuclides per unit undeformed volume of the th component, represents the chemical potential of the th component, represents the chemical expansion rate, represents the molar salt volume of the th component. represents a chemical-related parameter, represents the standard chemical potential of the th component independent of chemical concentration and deformation, represents the ideal gas constant, represents the fugacity coefficient of the th component, represents the reference concentration of the th component, represents the temperature-dependent fracture toughness attenuation function, represents the maximum concentration of the th component, represents the first undetermined constant related to the concentration of the th component, represents the second undetermined constant related to the concentration of the th component, represents the fracture toughness attenuation function related to the concentration of the th component, represents the number of moles of nuclides per unit undeformed volume of the th component, represents the electric field strength, represents the vacuum permittivity, represents the relative permittivity, represents the third invariant of the deformation gradient tensor.

8. The method for predicting the fracture failure of the solid-state lithium battery electrolyte material based on the phase field method according to claim 1, wherein The expression of the governing equations is: ； In the formula, represents the gradient operator, represents the Piola–Kirchhoff stress of the first kind, represents the density in the reference configuration, represents the volumetric force per unit mass in the reference configuration, represents acceleration, represents the phase field variable, Represents a historical variable, represents the fracture toughness, represents the characteristic length, represents the specific heat capacity at constant pressure, represents the derivative of temperature with respect to time, Represents an external heat source, represents the damage-related thermal conductivity decay function, represents the deformation-dependent thermal conductivity tensor, represents the temperature gradient, Indicates internal heat source, Indicates The derivative of the number of moles of the nuclide per unit undeformed volume of the species with respect to time, Indicates The mass flow of particles of the components, The chemical reaction produces The particle concentration of the component, represents the time derivative of charge density, Represents the current density.

9. The method for predicting the fracture failure of the solid-state lithium battery electrolyte material based on the phase-field method according to claim 1, wherein The boundary conditions include force boundary conditions, thermal boundary conditions, chemical concentration boundary conditions, and electric field boundary conditions; The expression of the force boundary conditions is: ； In the formula, represents the displacement vector, represents the fixed displacement at the boundary, represents the position vector of a point on the boundary, represents the displacement boundary, represents the first Piola-Kirchhoff stress, represents the unit normal vector outside the boundary, represents the fixed traction force, represents the force boundary; The expression of the thermal boundary conditions is: ； In the formula, represents temperature, represents the fixed temperature, represents the temperature boundary, represents the heat flux inside the material described in the Lagrangian description, represents the outer normal vector of the boundary, represents the fixed heat flux, represents the heat flux boundary; The expression of the chemical concentration boundary conditions is: ； In the formula, represents the number of moles of nuclide per unit undeformed volume of the th component, represents the fixed concentration of the th component, represents the fixed concentration boundary of the th component, represents the mass flow of particles of the th component, represents the fixed mass flow of particles of the th component, represents the fixed mass flow boundary of the th component; The expression of the electric field boundary conditions is: ； Wherein, represents the electric potential, represents the fixed electric potential, represents the electric potential boundary, represents the current density, represents the fixed current, represents the current boundary.

10. The method for predicting the fracture failure of the solid-state lithium battery electrolyte material based on the phase field method according to claim 1, wherein The expression of the weak form of the governing equations is: ； In the formula, represents the spatial region occupied by the reference configuration, represents the first Piola-Kirchhoff stress, represents the deformation gradient tensor, represents the density under the reference configuration, represents the body force per unit mass under the reference configuration, represents the displacement, represents the force boundary, represents the prescribed traction, represents the phase field variable, represents the history variable, represents the fracture toughness, represents the characteristic length, represents the gradient of the phase field variable, represents the specific heat capacity at constant pressure, represents the time derivative of the temperature, represents the temperature, represents the heat flux within the material in the Lagrangian description, represents the temperature gradient, represents the internal heat source, represents the heat flux boundary, represents the prescribed heat flux, represents the electrode and electrolyte interface, represents the heat generated at the interface by the instantaneous current density at the electrode and electrolyte interface, represents the time derivative of the number of moles of nuclides per unit undeformed volume of the represents the number of moles of nuclides per unit undeformed volume of the represents the concentration gradient of the number of moles of nuclides per unit undeformed volume of the represents the mass flux of the particles of the represents the particle concentration of the represents the current boundary, represents the prescribed mass flux of the particles of the represents the time derivative of the charge density, represents the electric potential, represents the current density, represents the current boundary, represents the electrode and electrolyte interface, represents the electric potential gradient, represents the prescribed current density, Represents the instantaneous current density at the electrode-electrolyte interface.

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