Fracture failure prediction method for solid-state lithium battery electrolyte materials based on phase field method

Abstract

The present invention discloses a method for predicting fracture failure of solid-state lithium battery electrolyte materials based on a phase field method, which relates to the technical field of battery failure prediction. The method comprises the following steps: S1, constructing a reference configuration and an instantaneous configuration for the lithium battery electrolyte material; S2, constructing a transformation between the reference configuration and the instantaneous configuration to generate a deformation map; S3, constructing 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 potential distribution and the reference configuration; S4, constructing phase field variables for the lithium battery electrolyte material; S5, obtaining a thermodynamic constitutive model; S6, obtaining the governing equations of the solid-state lithium battery electrolyte material; S7, constructing boundary conditions for the governing equations; and S8, using the weak form of the governing equations to complete fracture failure prediction. The present invention provides a basis for parameter setting and safety assessment of solid-state batteries.

Description

Technical Field

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

[0002] Solid-state lithium metal batteries are considered the ultimate choice for future energy storage systems due to their high theoretical energy density and safety. However, severe interfacial issues such as 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 building safe solid-state lithium batteries.

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

[0004] However, despite the many advantages mentioned above, solid-state lithium metal batteries still face challenges in practical applications, mainly including: the strong polarization of solid electrolytes, which will generate more polarization heat during operation, affecting the safety performance and ion conductivity of the battery; lithium deposition on the electrode surface eventually develops into lithium dendrites and hollow "dead lithium", which reduces the ion conductivity of the electrolyte, thereby affecting the capacity of the battery; and stress concentration at the tips of lithium dendrites leads to the generation of mechanical cracks, which also leads to a decrease in ion 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 causing interface stratification and hindering ion transport; and the deposition and dissolution of lithium will generate large stress 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, in which heat, current, chemical reactions, and mechanical deformation and damage all play an important role. Therefore, in order to more comprehensively evaluate the impact 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-physics 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 fracture failure of solid-state lithium battery electrolyte materials based on a phase field method comprises the following steps:

[0007] S1. Construct reference configurations and real-time configurations for lithium battery electrolyte materials;

[0008] S2, constructing the transformation between the reference configuration and the instant configuration to generate a deformation map;

[0009] S3, constructing 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 potential distribution and the reference configuration;

[0010] S4. Construct phase field variables for lithium battery electrolyte materials;

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

[0012] S6. Obtain the governing equations of the solid-state lithium battery electrolyte material based on 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 potential distribution and the reference configuration, the phase field equation corresponding to the phase field variables, and the thermodynamic constitutive model;

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

[0014] S8. According to the control equation and boundary conditions of the solid-state lithium battery electrolyte material, the weak form of the control equation is determined, and the weak form of the control equation is used to complete the fracture failure prediction.

[0015] Furthermore, deformation mapping The expression is:

[0016] ;

[0017] Where, represents the spatial region occupied by the reference configuration, Indicates the time period taken by the deformation and destruction process of the configuration, represents the spatial region occupied by the instantaneous configuration, Variables representing the reference configuration, Indicates time, Variables representing instant configurations, represents the deformation field.

[0018] Furthermore, the mapping between the temperature field and the reference configuration The expression is:

[0019] ;

[0020] Where, represents the spatial region occupied by the reference configuration, Indicates the time period taken by the deformation and destruction process of the configuration, represents the set of all positive real numbers, Variables representing the reference configuration, Indicates time, Represents the temperature field.

[0021] Furthermore, in S4, the mapping between the concentration field and the reference configuration The expression is:

[0022] ;

[0023] Where, represents the spatial region occupied by the reference configuration, Indicates the time period taken by the deformation and destruction process of the configuration, represents the set of all positive real numbers, Variables representing the reference configuration, Indicates time, Indicates the The number of moles of nuclides per unit undeformed volume of the component, Indicates the total number of nuclides.

[0024] Furthermore, the mapping between the potential distribution and the reference configuration The expression is:

[0025] ;

[0026] Where, represents the spatial region occupied by the reference configuration, Indicates the time period taken by the deformation and destruction process of the configuration, represents the field of real numbers, Variables representing the reference configuration, Indicates time, Indicates electric potential.

[0027] Furthermore, energy dissipation The expression is:

[0028] ;

[0029] Where, represents the spatial region occupied by the reference configuration, represents the Piola–Kirchhoff stress of the first kind, represents the time derivative of the deformation gradient tensor, represents the density in the reference configuration, Represents the internal microscopic force, represents the time derivative of the phase field variable, represents the microscopic traction within the damaged area, represents the gradient operator, represents the gradient of the time derivative of the phase field variable, represents the heat flow inside the material described by Lagrangian, Indicates temperature, represents the temperature gradient, represents the electric field strength, represents the time derivative of the electric displacement vector, represents the current density, represents the total number of nuclides, Indicates the The chemical potential of the components, Indicates the The number of moles of nuclides per unit undeformed volume of the component, Indicates the The mass flow of particles of the species, Indicates the The gradient of the chemical potential of the species, represents the time derivative of the Helmholtz free energy density, represents entropy, Represents the derivative of temperature with respect to time.

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

[0031] ;

[0032] Where, represents the Piola–Kirchhoff stress of the first kind, represents the stress decay function, represents the phase field variable, represents the shear modulus, represents the mechanical deformation caused by macroscopic stress, represents the transpose of a tensor, represents the Lamé constant, represents the third invariant of the mechanical deformation tensor, represents the expansion and contraction deformation caused by changes in local chemical concentration, represents the expansion and contraction due to local temperature changes, Indicates temperature, represents the logarithmic function, Represents the internal microscopic force, represents the density in the reference configuration, represents the tensile strain energy density, represents the fracture toughness, is a vector of moles of each nuclide per unit undeformed volume, represents fixed parameters, represents the characteristic length, represents the microscopic traction within 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, Indicates the maximum temperature, represents the first undetermined constant, represents the second undetermined constant, represents the total number of nuclides, Indicates the The fracture toughness decay function related to the concentration of the species, Indicates the The number of moles of nuclides per unit undeformed volume of the component, Indicates the The chemical potential of the components, represents the chemical expansion rate, Indicates the The molar salt volume of the components, Represents parameters related to chemistry, represents the first The standard chemical potential of the components, represents the ideal gas constant, Indicates the The fugacity coefficient of the species, Indicates the The reference concentration of the components, represents the temperature-dependent fracture toughness decay function, Indicates the The maximum concentration of the component, Indicates the The first undetermined constant related to the concentration of the species, Indicates the The second unknown constant related to the concentration of the species, Indicates the The fracture toughness decay function related to the concentration of the species, Indicates the The number of moles of nuclides per unit undeformed volume of the component, represents the electric field strength, represents the dielectric constant of vacuum, represents the relative dielectric constant, represents the electric displacement vector, Represents the third invariant of the deformation gradient tensor.

[0033] Furthermore, the expression of the control equation is:

[0034] ;

[0035] Where, 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, Indicates an external heat source, represents the damage-related thermal conductivity decay function, represents the deformation-dependent thermal conductivity tensor, represents the temperature gradient, Indicates an internal heat source, Indicates the The derivative of the number of moles of nuclides per unit undeformed volume of a component with respect to time, Indicates the The mass flow of particles of the species, The first The particle concentration of the species, represents the time derivative of the charge density, Represents 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] Where, represents the displacement vector, represents a fixed displacement at the boundary, represents the position vector of a point on the boundary, represents the displacement boundary, represents the Piola–Kirchhoff stress of the first kind, represents the normal vector outside the boundary, Indicates fixed traction, Indicates force boundaries;

[0040] The thermal boundary condition is expressed as:

[0041] ;

[0042] Where, Indicates temperature, Indicates a fixed temperature, represents the temperature boundary, represents the heat flow inside the material described by Lagrangian, represents the normal vector outside the boundary, represents a fixed heat flow, represents the heat flow boundary;

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

[0044] ;

[0045] Where, Indicates the The number of moles of nuclides per unit undeformed volume of the component, Indicates the The fixed concentration of the components, Indicates the The fixed concentration boundary of the species, Indicates the The mass flow of particles of the species, Indicates the A fixed mass flow of particles of the same species, Indicates the Fixed mass flow boundaries of the species;

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

[0047] ;

[0048] Where, represents the electric potential, represents a fixed potential, represents the electric potential boundary, represents the current density, represents a fixed current, Represents the current boundary.

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

[0050] ;

[0051] Where, represents the spatial region occupied by the reference configuration, represents the Piola–Kirchhoff stress of the first kind, represents the deformation gradient tensor, represents the density in the reference configuration, represents the volumetric force per unit mass in the reference configuration, represents displacement, represents the force boundary, Indicates fixed traction, represents the phase field variable, Represents a historical 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, Indicates temperature, represents the heat flow inside the material described by Lagrangian, represents the temperature gradient, Indicates an internal heat source, represents the heat flow boundary, represents a fixed heat flow, represents the electrode and electrolyte interface, represents the heat generated at the interface by the instantaneous current density at the interface between the electrode and the electrolyte, Indicates the The derivative of the number of moles of nuclides per unit undeformed volume of a component with respect to time, Indicates the The number of moles of nuclides per unit undeformed volume of the component, Indicates the The concentration gradient of the number of moles of nuclides per unit undeformed volume of the species, Indicates the The mass flow of particles of the species, The first The particle concentration of the species, represents the current boundary, Indicates the A fixed mass flow of particles of the same species, 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 a fixed current density, It represents the instantaneous current density at the interface between electrode and electrolyte.

[0052] The beneficial effect of the present invention is that the present invention takes into account the full coupling effects of electric field, chemical concentration field, temperature field and displacement field to predict the distribution and changes of various physical fields and the initiation and expansion of cracks during the operation of solid-state batteries, providing a basis for parameter setting and safety assessment of solid-state batteries. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 This is a flow chart of the fracture failure prediction method for solid-state lithium battery electrolyte materials based on the phase field method. DETAILED DESCRIPTION

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

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

[0056] S1. Construct reference configurations and real-time configurations for lithium battery electrolyte materials;

[0057] S2, constructing the transformation between the reference configuration and the instant configuration to generate a deformation map;

[0058] S3, constructing 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 potential distribution and the reference configuration;

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

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

[0061] S6. Obtain the governing equations of the solid-state lithium battery electrolyte material based on 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 potential distribution and the reference configuration, the phase field equation corresponding to the phase field variables, and the thermodynamic constitutive model;

[0062] S7, construct boundary conditions for the governing equations;

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

[0064] In the embodiment of the present invention, first consider an occupied space region in the reference configuration The isotropic solid material, whose external boundary is , the variables in the reference configuration are all material coordinates The spatial area occupied by the instantaneous configuration is recorded as , whose outer boundary is denoted as , that is, the variables in the configuration are all spatial coordinates In order to describe the deformation of the material and establish the transformation between the reference configuration and the instantaneous configuration, deformation mapping is introduced. The expression is:

[0065] ;

[0066] Where, represents the spatial region occupied by the reference configuration, Indicates the time period taken by the deformation and destruction process of the configuration, represents the spatial region occupied by the instantaneous configuration, Variables representing the reference configuration, Indicates time, Variables representing instant configurations, 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 a temperature field and a reference configuration is established. The expression is:

[0068] ;

[0069] Where, represents the spatial region occupied by the reference configuration, Indicates the time period taken by the deformation and destruction process of the configuration, represents the set of all positive real numbers, Variables representing the reference configuration, Indicates time, Represents the temperature field.

[0070] In the embodiment of the present invention, in order to describe the change of the concentration of each component in the material, a mapping between the concentration field and the reference configuration is established. It is assumed that there is Mapping between different particles, concentration fields and reference configurations The expression is:

[0071] ;

[0072] Where, represents the spatial region occupied by the reference configuration, Indicates the time period taken by the deformation and destruction process of the configuration, represents the set of all positive real numbers, Variables representing the reference configuration, Indicates time, Indicates the The number of moles of nuclides per unit undeformed volume of the component, Indicates the total number of nuclides.

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

[0074] ;

[0075] Where, represents the spatial region occupied by the reference configuration, Indicates the time period taken by the deformation and destruction process of the configuration, represents the field of real numbers, Variables representing the reference configuration, Indicates time, Indicates electric potential.

[0076] In the embodiment of the present invention, first, according to the first law of thermodynamics, in the reference configuration, Where, represents the total internal energy, Indicates kinetic energy, represents the external force power, represents the thermal power, represents the rate of change of chemical energy, Represents electrical power. Substituting the above energy expression into the first law of thermodynamics and applying the equilibrium equation, combined with the second law of thermodynamics, we get the energy dissipation expression. Energy dissipation The expression is:

[0077] ;

[0078] Where, represents the spatial region occupied by the reference configuration, represents the Piola–Kirchhoff stress of the first kind, represents the time derivative of the deformation gradient tensor, represents the density in the reference configuration, Represents the internal microscopic force, represents the time derivative of the phase field variable, represents the microscopic traction within the damaged area, represents the gradient operator, represents the gradient of the time derivative of the phase field variable, represents the heat flow inside the material described by Lagrangian, Indicates temperature, represents the temperature gradient, represents the electric field strength, represents the time derivative of the electric displacement vector, represents the current density, represents the total number of nuclides, Indicates the The chemical potential of the components, Indicates the The number of moles of nuclides per unit undeformed volume of the component, Indicates the The mass flow of particles of the species, Indicates the The gradient of the chemical potential of the species, represents the time derivative of the Helmholtz free energy density, represents entropy, Represents the derivative of temperature with respect to time.

[0079] In the embodiment of the present invention, the expression of the thermodynamic constitutive model is:

[0080] ;

[0081] Where, represents the Piola–Kirchhoff stress of the first kind, represents the stress decay function, represents the phase field variable, represents the shear modulus, represents the mechanical deformation caused by macroscopic stress, represents the transpose of a tensor, represents the Lamé constant, represents the third invariant of the mechanical deformation tensor, represents the expansion and contraction deformation caused by changes in local chemical concentration, represents the expansion and contraction due to local temperature changes, Indicates temperature, represents the logarithmic function, Represents the internal microscopic force, represents the density in the reference configuration, represents the tensile strain energy density, represents the fracture toughness, is a vector of moles of each nuclide per unit undeformed volume, represents fixed parameters, represents the characteristic length, represents the microscopic traction within 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, Indicates the maximum temperature, represents the first undetermined constant, represents the second undetermined constant, represents the total number of nuclides, Indicates the The fracture toughness decay function related to the concentration of the species, Indicates the The number of moles of nuclides per unit undeformed volume of the component, Indicates the The chemical potential of the components, represents the chemical expansion rate, Indicates the The molar salt volume of the components, Represents parameters related to chemistry, represents the first The standard chemical potential of the components, represents the ideal gas constant, Indicates the The fugacity coefficient of the species, Indicates the The reference concentration of the components, represents the temperature-dependent fracture toughness decay function, Indicates the The maximum concentration of the component, Indicates the The first undetermined constant related to the concentration of the species, Indicates the The second unknown constant related to the concentration of the species, Indicates The fracture toughness decay function related to the concentration of the species, Indicates the The number of moles of nuclides per unit undeformed volume of the component, represents the electric field strength, represents the dielectric constant of vacuum, represents the relative dielectric constant, represents the electric displacement vector, Represents the third invariant of the deformation gradient tensor.

[0082] In the embodiment of the present invention, the control equation of the temperature field is obtained 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 situation, and finally obtaining the differential form of the control equation. The expression of the control equation is:

[0083] ;

[0084] Where, 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, Indicates an external heat source, represents the damage-related thermal conductivity decay function, represents the deformation-dependent thermal conductivity tensor, represents the temperature gradient, Indicates an internal heat source, Indicates the The derivative of the number of moles of nuclides per unit undeformed volume of a component with respect to time, Indicates the The mass flow of particles of the species, The first The particle concentration of the species, represents the time derivative of the charge density, Represents the current density.

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

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

[0087] ;

[0088] Where, represents the displacement vector, represents a fixed displacement at the boundary, represents the position vector of a point on the boundary, represents the displacement boundary, represents the Piola–Kirchhoff stress of the first kind, represents the normal vector outside the boundary, Indicates fixed traction, Indicates force boundaries;

[0089] The thermal boundary condition is expressed as:

[0090] ;

[0091] Where, Indicates temperature, Indicates a fixed temperature, represents the temperature boundary, represents the heat flow inside the material described by Lagrangian, represents the normal vector outside the boundary, represents a fixed heat flow, represents the heat flow boundary;

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

[0093] ;

[0094] Where, Indicates the The number of moles of nuclides per unit undeformed volume of the component, Indicates the The fixed concentration of the components, Indicates the The fixed concentration boundary of the species, Indicates the The mass flow of particles of the species, Indicates the A fixed mass flow of particles of the same species, Indicates the Fixed mass flow boundaries of the species;

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

[0096] ;

[0097] Where, represents the electric potential, represents a fixed potential, represents the electric potential boundary, represents the current density, represents a fixed current, Represents the current boundary.

[0098] In the embodiments of the present invention, for the instantaneous current density at the interface between the electrode and the electrolyte, 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 BV equation is used to describe the relationship between the electrode potential and the current density in this process. When all components are completely transported in equilibrium, or the current through the battery is very small, and is approximately 1; when the reaction rates of the anode and cathode are equal, , especially for lithium batteries, there are , then the BV equation can be simplified, and the weak form of the control equation can be obtained by combining the boundary conditions and the differential form of the control equation. represents the charge transfer coefficient of the anodic reaction, represents the charge transfer coefficient of the cathode reaction and satisfies , is a function of the anode surface concentration, is a function of the cathode surface concentration.

[0099] The weak form of the governing equation is expressed as:

[0100] ;

[0101] Where, represents the spatial region occupied by the reference configuration, represents the Piola–Kirchhoff stress of the first kind, represents the deformation gradient tensor, represents the density in the reference configuration, represents the volumetric force per unit mass in the reference configuration, represents displacement, represents the force boundary, Indicates fixed traction, represents the phase field variable, Represents a historical 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, Indicates temperature, represents the heat flow inside the material described by Lagrangian, represents the temperature gradient, Indicates an internal heat source, represents the heat flow boundary, represents a fixed heat flow, represents the electrode and electrolyte interface, represents the heat generated at the interface by the instantaneous current density at the interface between the electrode and the electrolyte, Indicates the The derivative of the number of moles of nuclides per unit undeformed volume of a component with respect to time, Indicates the The number of moles of nuclides per unit undeformed volume of the component, Indicates the The concentration gradient of the number of moles of nuclides per unit undeformed volume of the species, Indicates the The mass flow of particles of the species, The first The particle concentration of the species, represents the current boundary, Indicates the A fixed mass flow of particles of the same species, 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 a fixed current density, It represents the instantaneous current density at the interface between electrode and electrolyte.

[0102] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the present invention.

Claims

1. A method for predicting fracture failure of solid-state lithium battery electrolyte materials based on phase field method, characterized in that: The following steps are involved: S1. Construct reference configurations and real-time configurations for lithium battery electrolyte materials; S2, constructing the transformation between the reference configuration and the instant configuration to generate a deformation map; S3, constructing 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 potential distribution and the reference configuration; S4. Construct phase field variables for lithium battery electrolyte materials; S5. Calculate energy dissipation and obtain a thermodynamic constitutive model based on the energy dissipation; S6. Obtain the governing equations of the solid-state lithium battery electrolyte material based on 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 potential distribution and the reference configuration, the phase field equation corresponding to the phase field variables, and the thermodynamic constitutive model; S7, construct boundary conditions for the governing equations; S8. Determine the weak form of the governing equation based on the governing equation and boundary conditions of the solid-state lithium battery electrolyte material, and use the weak form of the governing equation to complete fracture failure prediction; The expression of the control equation is: ； Where, 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, Indicates an external heat source, represents the damage-related thermal conductivity decay function, represents the deformation-dependent thermal conductivity tensor, represents the temperature gradient, Indicates an internal heat source, Indicates the The derivative of the number of moles of nuclides per unit undeformed volume of a component with respect to time, Indicates the The mass flow of particles of the species, The first The particle concentration of the species, represents the time derivative of the charge density, represents the current density; The weak form of the governing equation is expressed as: ； Where, represents the spatial region occupied by the reference configuration, represents the Piola–Kirchhoff stress of the first kind, represents the deformation gradient tensor, represents the density in the reference configuration, represents the volumetric force per unit mass in the reference configuration, represents displacement, represents the force boundary, Indicates fixed traction, represents the phase field variable, Represents a historical 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, Indicates temperature, represents the heat flow inside the material described by Lagrangian, represents the temperature gradient, Indicates an internal heat source, represents the heat flow boundary, represents a fixed heat flow, represents the electrode and electrolyte interface, represents the heat generated at the interface by the instantaneous current density at the interface between the electrode and the electrolyte, Indicates the The derivative of the number of moles of nuclides per unit undeformed volume of a component with respect to time, Indicates the The number of moles of nuclides per unit undeformed volume of the component, Indicates the The concentration gradient of the number of moles of nuclides per unit undeformed volume of the species, Indicates the The mass flow of particles of the species, The first The particle concentration of the species, represents the current boundary, Indicates the A fixed mass flow of particles of the same species, 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 a fixed current density, It represents the instantaneous current density at the interface between electrode and electrolyte.

2. The method for predicting fracture failure of solid-state lithium battery electrolyte materials based on the phase field method according to claim 1, characterized in that: The deformation map The expression is: ； Where, represents the spatial region occupied by the reference configuration, Indicates the time period taken by the deformation and destruction process of the configuration, represents the spatial region occupied by the instantaneous configuration, Variables representing the reference configuration, Indicates time, Variables representing instant configurations, represents the deformation field.

3. The method for predicting fracture failure of solid-state lithium battery electrolyte materials based on the phase field method according to claim 1, characterized in that: The mapping between the temperature field and the reference configuration The expression is: ； Where, represents the spatial region occupied by the reference configuration, Indicates the time period taken by the deformation and destruction process of the configuration, represents the set of all positive real numbers, Variables representing the reference configuration, Indicates time, Represents the temperature field.

4. The method for predicting fracture failure of solid-state lithium battery electrolyte materials based on phase field method according to claim 1, characterized in that: Mapping between the concentration field and the reference configuration The expression is: ； Where, represents the spatial region occupied by the reference configuration, Indicates the time period taken by the deformation and destruction process of the configuration, represents the set of all positive real numbers, Variables representing the reference configuration, Indicates time, Indicates the The number of moles of nuclides per unit undeformed volume of the component, Indicates the total number of nuclides.

5. The method for predicting fracture failure of solid-state lithium battery electrolyte materials based on phase field method according to claim 1, characterized in that: The mapping between the potential distribution and the reference configuration The expression is: ； Where, represents the spatial region occupied by the reference configuration, Indicates the time period taken by the deformation and destruction process of the configuration, represents the field of real numbers, Variables representing the reference configuration, Indicates time, Indicates electric potential.

6. The method for predicting fracture failure of solid-state lithium battery electrolyte materials based on phase field method according to claim 1, characterized in that: The energy dissipation The expression is: ； Where, represents the spatial region occupied by the reference configuration, represents the Piola–Kirchhoff stress of the first kind, represents the time derivative of the deformation gradient tensor, represents the density in the reference configuration, Represents the internal microscopic force, represents the time derivative of the phase field variable, represents the microscopic traction within the damaged area, represents the gradient operator, represents the gradient of the time derivative of the phase field variable, represents the heat flow inside the material described by Lagrangian, Indicates temperature, represents the temperature gradient, represents the electric field strength, represents the time derivative of the electric displacement vector, represents the current density, represents the total number of nuclides, Indicates the The chemical potential of the components, Indicates the The number of moles of nuclides per unit undeformed volume of the component, Indicates the The mass flow of particles of the species, Indicates the The gradient of the chemical potential of the species, represents the time derivative of the Helmholtz free energy density, represents entropy, Represents the derivative of temperature with respect to time.

7. The method for predicting fracture failure of solid-state lithium battery electrolyte materials based on phase field method according to claim 1, characterized in that: The expression of the thermodynamic constitutive model is: ； Where, represents the Piola–Kirchhoff stress of the first kind, represents the stress decay function, represents the phase field variable, represents the shear modulus, represents the mechanical deformation caused by macroscopic stress, represents the transpose of a tensor, represents the Lamé constant, represents the third invariant of the mechanical deformation tensor, represents the expansion and contraction deformation caused by changes in local chemical concentration, represents the expansion and contraction due to local temperature changes, Indicates temperature, represents the logarithmic function, Represents the internal microscopic force, represents the density in the reference configuration, represents the tensile strain energy density, represents the fracture toughness, is a vector of moles of each nuclide per unit undeformed volume, represents fixed parameters, represents the characteristic length, represents the microscopic traction within 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, Indicates the maximum temperature, represents the first undetermined constant, represents the second undetermined constant, represents the total number of nuclides, Indicates the The fracture toughness decay function related to the concentration of the species, Indicates the The number of moles of nuclides per unit undeformed volume of the component, Indicates the The chemical potential of the components, represents the chemical expansion rate, Indicates the The molar salt volume of the components, Represents parameters related to chemistry, represents the first The standard chemical potential of the components, represents the ideal gas constant, Indicates the The fugacity coefficient of the species, Indicates the The reference concentration of the components, represents the temperature-dependent fracture toughness decay function, Indicates the The maximum concentration of the component, Indicates the The first undetermined constant related to the concentration of the species, Indicates the The second unknown constant related to the concentration of the species, Indicates the The fracture toughness decay function related to the concentration of the species, Indicates the The number of moles of nuclides per unit undeformed volume of the component, represents the electric field strength, represents the dielectric constant of vacuum, represents the relative dielectric constant, represents the electric displacement vector, Represents the third invariant of the deformation gradient tensor.

8. The method for predicting fracture failure of solid-state lithium battery electrolyte materials based on phase field method according to claim 1, characterized in that: 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 condition is: ； Where, represents the displacement vector, represents a fixed displacement at the boundary, represents the position vector of a point on the boundary, represents the displacement boundary, represents the Piola–Kirchhoff stress of the first kind, represents the normal vector outside the boundary, Indicates fixed traction, Indicates force boundaries; The thermal boundary condition is expressed as: ； Where, Indicates temperature, Indicates a fixed temperature, represents the temperature boundary, represents the heat flow inside the material described by Lagrangian, represents the normal vector outside the boundary, represents a fixed heat flow, represents the heat flow boundary; The expression of the chemical concentration boundary condition is: ； Where, Indicates the The number of moles of nuclides per unit undeformed volume of the component, Indicates the The fixed concentration of the components, Indicates the The fixed concentration boundary of the species, Indicates the The mass flow of particles of the species, Indicates the A fixed mass flow of particles of the same species, Indicates the Fixed mass flow boundaries of the species; The expression of the electric field boundary condition is: ； Where, represents the electric potential, represents a fixed potential, represents the electric potential boundary, represents the current density, represents a fixed current, Represents the current boundary.

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