Near-field dynamics and thermal coupling method for structural fracture analysis of pressure vessel

Abstract

The invention belongs to the field of computational mechanics, and provides a near-field dynamics thermal-mechanical coupling method for analyzing structural fracture of a pressure vessel, which adopts a forward Euler algorithm and a dynamic relaxation algorithm for staggered solution to avoid inconvenience of stiffness matrix change and the like caused by degree-of-freedom change of an implicit method. Meanwhile, according to the method, the axisymmetric near-field dynamic model and the elastoplasticity-creep coupling constitutive integral are combined, and the capacity of the near-field dynamic model in the aspect of analyzing and predicting the elastoplasticity-creep coupling fracture of the axisymmetric structure after ablation is effectively improved. According to the axial symmetry fracture model coupled with the elastoplasticity-creep effect, the fracture behavior of the structure is effectively represented, and the difficulty of fracture analysis under the elastoplasticity-creep coupling effect is overcome. As a new numerical solution format, the method provided by the invention can be realized through simple programming, the numerical implementation complexity is reduced, and favorable help is provided for the research under the serious loss accident of the nuclear reactor coolant.

Description

Technical Field

[0001] This application relates to the field of computational mechanics, and in particular to a near-field dynamics-thermal coupling method for fracture analysis of pressure vessel structures. Background Technology

[0002] The reactor pressure vessel (RPV), a core component of nuclear power facilities, is an essential part of the normal operation of the entire reactor. Studies have shown that in the event of a severe accident, when molten core material remains trapped in the lower head of the pressure vessel, the high heat flux density boundary acts directly on the inner wall of the pressure vessel. This inevitably leads to ablation and thinning of the inner wall, ultimately compromising the structural integrity of the pressure vessel. The thermal stress generated by the high temperature may exceed the yield limit of the structure, causing irreversible deformation. Furthermore, under prolonged high temperatures, unavoidable creep behavior will significantly impact the strength, stiffness, service life, and structural integrity of the components, potentially leading to structural damage and fracture. Due to the aforementioned thermo-mechanical coupling and nonlinear characteristics, the safety analysis of pressure vessels under severe accidents remains a significant challenge.

[0003] For the study of fracture and the deformation mechanism of materials during the process, experimental methods are not only difficult to implement and costly, but also difficult to simulate, especially the molten material in high-temperature reactor cores. In contrast, numerical simulation methods, as efficient numerical calculation tools in recent decades, provide a feasible solution for detailed investigation of the nonlinear response and fracture behavior of structures under extreme loads. By selecting appropriate constitutive and fracture models, the fracture behavior of pressure vessels can be predicted quickly and accurately. In engineering thermo-mechanical coupling analysis, numerical calculation methods such as the finite element method (FEM) based on continuum mechanics models are the most widely used, and commercial software based on FEM is basically mature. Nevertheless, FEM still faces many difficulties in characterizing crack propagation when dealing with both thermo-mechanical coupling effects and nonlinear material behavior. These difficulties, coupled with the discontinuity of the crack surface, further increase the difficulty of structural integrity analysis, thus seriously interfering with normal damage evolution and crack propagation calculations.

[0004] Over the past two decades, peridynamics (PD) has emerged as a novel nonlocal model, demonstrating superior performance in handling problems with discontinuities and interruptions. By transforming the differential form of physical equations in space into an integral form, it overcomes the challenge of non-differentiability at cracks in continuum-based mechanics models. Due to its advantages in handling discontinuous problems and the nonlocal integral properties of its equations, this invention will consider using peridynamics in space to study the fracture behavior of pressure vessels under extreme thermal loads.

[0005] Furthermore, pressure vessels possess highly axisymmetric characteristics and are often simplified into axisymmetric models in engineering to reduce computational scale and the difficulties associated with three-dimensional numerical calculations. Therefore, this invention employs unconventional state basis theory from peri-field dynamics to study the elasto-plastic and creep responses of pressure vessels under high temperature and pressure during thermal loading. To accurately simulate the fracture phenomenon of axisymmetric pressure vessels under extreme thermal loads, this invention proposes an axisymmetric elasto-plastic-creep coupled fracture model based on continuous damage mechanics theory and peri-field dynamics, expanding the application of peri-field dynamics models in the field of thermo-mechanical coupling in solid mechanics. By combining axisymmetric peri-field dynamics unconventional state basis theory with the elasto-plastic-creep coupled damage model, the elasto-plastic-creep coupled response and crack propagation behavior of pressure vessel structures under high temperature during ablation can be accurately simulated, while significantly reducing the difficulty of three-dimensional modeling and analysis. This provides an effective approach for the structural safety analysis of nuclear reactor pressure vessels. Summary of the Invention

[0006] In view of this, this application provides a near-field dynamic-thermal coupling method for fracture analysis of pressure vessel structures. The main purpose is to address the issue that thermal stress generated at high temperatures may exceed the yield limit of the structure, causing irreversible deformation. Furthermore, under prolonged high-temperature conditions, unavoidable creep behavior will significantly impact the strength, stiffness, service life, and structural integrity of components, ultimately potentially leading to structural damage and fracture. Due to the aforementioned thermo-mechanical coupling and nonlinear characteristics, the safety analysis of pressure vessels under severe accidents remains a significant challenge.

[0007] According to a first aspect of this application, a near-field dynamic-thermal coupling method for fracture analysis of pressure vessel structures is provided, the method comprising:

[0008] Step 1: Discretize the structure of the pressure vessel using a preset material point size, and set corresponding material properties for the material points. Based on the position coordinates of the discretized material points and the specified near-field dynamic neighborhood radius, determine the set of points in each material point and its neighborhood, and establish the interaction relationship between the material points. The material properties include physical properties and mechanical properties.

[0009] Step 2: Define the total computation time for the thermo-coupling problem, the time step for the transient heat conduction problem, the time interval for solving the mechanics problem, and the number of steps for the dynamic relaxation method;

[0010] Step 3: Calculate the thermal flow state of the structure based on the temperature field, and update the temperature by explicit time history integration using the forward Euler method. When the time meets the time interval for solving the mechanical problem, proceed to step 4.

[0011] Step 4: Based on the temperature field calculation results, the internal forces of the structure are calculated by introducing the classical plastic and creep constitutive relations. The displacement of the material point is calculated by using the dynamic relaxation method. After satisfying the convergence criterion, the displacement solution and velocity solution within this time interval are obtained. Then, return to step 3 to calculate the next time interval.

[0012] By employing the above technical solution, this application provides a near-field dynamic-thermal coupling method for fracture analysis of pressure vessel structures. The embodiments of this application have the following significant effects:

[0013] (1) The CA-PC-PD provided by this invention provides a simple numerical simulation method for thermo-mechanical coupling analysis of axisymmetric structures composed of metal materials such as pressure vessels, and broadens the application scope of peri-field dynamics in the field of thermo-mechanical coupling of solid materials. It effectively reduces the computational scale of the three-dimensional peri-field dynamics model when analyzing large structures with axisymmetric characteristics. In addition, the use of a meshless method to solve the equations in the axisymmetric peri-field dynamics thermo-mechanical coupling model reduces the complexity of the numerical implementation process and avoids problems such as stiffness singularity. (2) The CA-PC-PD provided by this invention provides a high-precision numerical simulation method for elastoplastic-creep coupling analysis of metal materials under high-temperature loads. It effectively introduces the classical metal elastoplastic material constitutive model and the time-hardening damage constitutive model containing the third stage of creep into peri-field dynamics, overcoming the difficulty of introducing various complex assumptions when simulating nonlinear material characteristics using traditional bond-based peri-field dynamics. In addition, by coupling the temperature field and displacement field in a sequential manner, and developing a thermo-mechanical coupling alternating solution algorithm using an explicit integral scheme, this invention can effectively simulate the elastoplastic and creep behavior of metal structures under high-temperature conditions. (3) The CA-PC-PD provided by the present invention provides an effective simulation of the CPC-FM of the structure under the elastic-plastic-creep coupling effect by coupling the critical equivalent plastic strain and the critical equivalent variable strain, so that the present invention can effectively predict the ablation behavior and the elastic-plastic-creep fracture phenomenon of the structure under the severe accident of the nuclear reactor pressure vessel.

[0014] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0015] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of this application. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0016] Figure 1 This paper illustrates a schematic diagram of a near-field dynamics-thermal coupling method for fracture analysis of a pressure vessel structure provided in an embodiment of this application.

[0017] Figure 2 This is a flowchart illustrating the operation of the axisymmetric near-field dynamic-thermal coupling method (CA-PC-PD) for pressure vessel ablation analysis according to the present invention.

[0018] Figure 3 This refers to the initial and current configurations of the axisymmetric unconventional basis precession dynamics of this invention.

[0019] Figure 4 This is a schematic diagram of the elastic-plastic-creep coupled fracture model (CPC-FM) of the present invention;

[0020] Figure 5 This is a schematic diagram of the thick-walled cylindrical structure and boundary conditions of Embodiment 1 of the present invention;

[0021] Figure 6 A comparison of the temperature, displacement, equivalent stress, and equivalent plastic strain solutions obtained using CA-PC-PD and FEM for the thick-walled cylinder of Embodiment 1 of the present invention;

[0022] Figure 7 This is a diagram showing the temperature, radial displacement, and equivalent stress distribution of a thick-walled cylinder along a certain path in Embodiment 1 of the present invention.

[0023] Figure 8 This is a geometric model and load diagram of Embodiment 2 of the present invention;

[0024] Figure 9 The equivalent stress, equivalent plastic strain, and equivalent creep strain curves obtained using CA-PC-PD and FEM respectively in Example 2 of the present invention;

[0025] Figure 10 This is a curve comparing the results obtained using CA-PC-PD with experimental data in Example 3 of the present invention;

[0026] Figure 11 This is a geometric model and thermal flow boundary load diagram of the spherical nuclear reactor pressure vessel according to Embodiment 4 of the present invention;

[0027] Figure 12 The temperature distribution diagrams before and after ablation obtained using CA-PC-PD and FEM are shown in Example 4 of the present invention.

[0028] Figure 13 The equivalent stress, equivalent plastic strain, and equivalent creep strain distribution diagrams at 72h under different internal pressures are obtained using CA-PC-PD in Example 4 of the present invention.

[0029] Figure 14 The displacement and overall damage distribution diagrams at 72h under different internal pressures obtained using CA-PC-PD in Example 4 of the present invention are shown.

[0030] Figure 15 The elastic-plastic-creep fracture phenomenon under an internal pressure of 7.75 MPa was simulated using CA-PC-PD in Example 4 of the present invention.

[0031] Figure 16 A schematic diagram of the device structure of a computer device provided in an embodiment of this application is shown. Detailed Implementation

[0032] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application.

[0033] This application provides a near-field dynamic-thermal coupling method for fracture analysis of pressure vessel structures, such as... Figure 1 As shown, the method includes:

[0034] Step 1: Discretize the structure of the pressure vessel using a preset material point size, and set corresponding material properties for the material points. Based on the position coordinates of the discretized material points and the specified near-field dynamic neighborhood radius, determine the set of points in each material point and its neighborhood, and establish the interaction relationship between the material points. The material properties include physical properties and mechanical properties.

[0035] Step 2: Define the total computation time for the thermo-coupling problem, the time step for the transient heat conduction problem, the time interval for solving the mechanics problem, and the number of steps for the dynamic relaxation method;

[0036] Step 3: Calculate the thermal flow state of the structure based on the temperature field, and update the temperature by explicit time history integration using the forward Euler method. When the time meets the time interval for solving the mechanical problem, proceed to step 4.

[0037] Step 4: Based on the temperature field calculation results, the internal forces of the structure are calculated by introducing the classical plastic and creep constitutive relations. The displacement of the material point is calculated by using the dynamic relaxation method. After satisfying the convergence criterion, the displacement solution and velocity solution within this time interval are obtained. Then, return to step 3 to calculate the next time interval.

[0038] This invention, based on the unconventional basis theory of peridynamics and combining continuum damage mechanics theory with peridynamics, innovatively proposes a coupled plastic-creep fracture model (CPC-FM) and a coupled daxisymmetric plastic-creep peridynamics (CA-PC-PD) method. Its purpose is to address several problems existing in current technologies: First, it uses a peridynamic model to overcome the inherent singularities in fracture behavior that are difficult to describe within the framework of traditional continuum mechanics. Second, it uses an axisymmetric peridynamic model to compensate for the low computational efficiency of traditional three-dimensional peridynamic analysis methods when performing large-scale analyses of structures with axisymmetric characteristics. Third, it uses an unconventional basis peridynamic model to overcome the limitations of Poisson's ratio in bond bases and the need to introduce complex assumptions to describe the nonlinear mechanical response of materials. Fourth, it combines rate-dependent and rate-independent nonlinear responses using an coupled plastic-creep fracture model, reducing the complexity of traditional fracture mechanics damage characterization and effectively improving the fracture prediction capability of the peridynamic model.

[0039] Furthermore, as a refinement and expansion of the above implementation, in order to accurately capture the mechanical behavior of axisymmetric structures under thermal shock loads and improve the accuracy of nonlinear analysis, this invention will analyze the elastoplastic-creep behavior of structures under thermal shock loads and study the fracture evolution behavior based on an unconventional state-based peri-field dynamics model, providing an axisymmetric elastoplastic-creep coupled peri-field dynamics analysis method, such as... Figure 2 As shown, the method includes:

[0040] The specific implementation process of the axisymmetric elastoplastic creep coupled near-field dynamics analysis method CA-PC-PD proposed in this invention will be shown in the following pseudocode form:

[0041] (1) Establish a discrete material point model, construct a neighborhood, define the interaction radius, and define the material physical properties (density ρ, thermal conductivity k). T Parameters including thermal expansion coefficient α, specific heat capacity c, and mechanical properties (elastic modulus E, Poisson's ratio ν; plastic hardening modulus K, initial yield stress). Creep parameters c1, c2, and c3, uniaxial fracture creep strain ε f Critical equivalent plastic strain Critical equivalent creep strain )parameter;

[0042] (2) Determine the total computation time t for the thermo-coupling problem TC Transient heat conduction problem with time step Δt T The time interval Δt for solving mechanical problemsd The number of steps in the dynamic relaxation method is n. max Apply loads and initialize variables such as temperature, velocity, and displacement;

[0043] (3) Enter the problem-solving process of mechanics, with the loop variable N d =0;

[0044] S1: Let N d =N d +1;

[0045] S2: Entering the solution of the heat conduction problem, loop variable N T =0;

[0046] S21: Let N T =N T +1, use the forward Euler method to solve the transient heat conduction equation to obtain the temperature field response T;

[0047] S22: According to scalar functions Determine the ablation state of material points and update the geometric model using MPDT;

[0048] S23: If N T Δt T ≥N d Δt d If the condition is met, proceed to step S3; otherwise, return to step S21 and continue the loop.

[0049] S3: Loop variable n = 0;

[0050] S31: Let n = n+1, and use the dynamic relaxation method to solve the momentum conservation equation discretization scheme to obtain the displacement field response u based on the temperature field information;

[0051] S32: Determine the damage state of material points based on CPC-FM and update crack propagation;

[0052] S33: If Proceed to step S4; otherwise, return to step S31 to continue the loop, where n is the loop variable for the dynamic relaxation method; n max The threshold value is the loop variable; N is the total number of material points discretized on the reference configuration; |u(x i | represents the magnitude of the displacement vector of material point i, and u represents the displacement field response; |u old (x i | represents the magnitude of the displacement vector of substance point i in the previous cycle step n, x i The position vector of the discretized material point i in the reference configuration is used to identify the material point i; u old is the displacement field response in the previous iteration step n; ∈ is a small quantity used to determine whether the calculation has converged;

[0053] S4: Output the calculation file for post-processing.

[0054] Understandably, based on the unconventional basis peri-field dynamics framework and combined with the characteristics of axisymmetric problems, Figure 3 The reference and current configurations of the unconventional ground peri-field dynamics model (NOSB-PD) in the axisymmetric plane are given, where x is the position vector of the matter point in the reference configuration, y is the position vector of the matter point in the current configuration, and u is the displacement vector of the matter point. T It is a force vector state. Y It is the deformation vector state. Let ξ be a circular neighborhood of radius δ around the material point x, ξ = x′ - x be the relative position vector in the reference configuration, and η = u′ - u be the relative displacement between the material points x and x′. It is worth noting that in the unconventional ground peridynamics, the force vector state... T With deformation vector state Y =y′-y=η+ξ is not necessarily in a parallel state.

[0055] In axisymmetric mode, the structural deformation gradient is decomposed into in-plane and out-of-plane parts based on the following formula 1:

[0056] Formula 1:

[0057] Where u r Here, r is the radial displacement component, and u is the radial coordinate. z Let F be the axial displacement component, and z be the axial coordinate. in Let F be the in-plane structural deformation gradient tensor. out This represents the deformation gradient of the structure within the axisymmetric plane.

[0058] Wherein, the in-plane structural deformation gradient F ib nonlocal form As shown in Formula 2 below:

[0059] Formula 2:

[0060] Where K is the shape tensor, This represents the product of two vectors. ω <ξ> represents a scalar state used to describe the degree of interaction between matter points. Y The state is the deformation vector state. X V represents the relative position vector state. x′ Let be the volume of the material point. The shape tensor can be calculated based on the following formula 3:

[0061] Formula 3:

[0062] The nonlocal form of the out-of-plane deformation gradient needs to be given by the spatial relationship between the relative positions, relative displacements, and deformation vector states of points in the neighborhood, as shown in Equation 4 below:

[0063] Formula 4: u=ξ+u′- Y

[0064] Where u is the displacement vector of substance point x, and u′ is the displacement vector of substance point x′. Y For the deformation vector state, ξ = x′ - x is the relative position vector in the reference configuration.

[0065] Integrating within the neighborhood yields the nonlocal form of the displacement. Specifically, as shown in Formula 5 below:

[0066] Formula 5:

[0067] in ω <ξ> represents a scalar state used to describe the degree of interaction between matter points, and u′ is the displacement vector of matter point x′. Y The state is the deformation vector state. Nonlocal form of out-of-plane deformation gradient As shown in Formula 6 below:

[0068] Formula 6:

[0069] in Nonlocal form The radial displacement component in the figure, where r is the radial coordinate.

[0070] After obtaining the nonlocal deformation gradient inside and outside the plane, the strain energy density W of the material point is expressed as shown in Equation 7 below:

[0071] Formula 7:

[0072] Where W(Y) is the strain energy density function with respect to the deformation vector state.

[0073] Substituting it into the Euler-Lagrange equation shown in Formula 8

[0074] Formula 8:

[0075] As shown in Formula 9 below, L is the Lagrange function containing the kinetic and potential energy of matter.

[0076] Where Ω represents the entire computational domain of the structure, and ρ represents the density. Let be the first derivative of displacement with respect to time, W be the strain energy density function, u be the displacement vector of material point x, and b be the body force. Substituting Equation 7 into Equation 8 above, and expanding at material point x, we obtain the following Equation 10:

[0077] Formula 10:

[0078]

[0079] in(*) ′ Representative point x ′ The corresponding variable, namely W ′ Let x be the material point ′ strain energy density, V is the second derivative of the displacement of point i at time t. x Let ρ(x) be the volume of the substance point, and ρ(x) be the density of the substance point, as shown in Formula 11 below. This is given by using Equation 7 above and the chain rule for differentiation:

[0080] Formula 11:

[0081] in Let W be the Frechet derivative of the strain energy W with respect to the deformed state Y, and I be the unit tensor. Similarly, it is calculated using the chain rule based on Equation 12 below.

[0082] Formula 12:

[0083] in and The component form of the Frechet derivative is shown in Equation 13 below:

[0084] Formula 13:

[0085] Where ω is a scalar state used to describe the degree of interaction between matter points, and δ ik The component notation for the unit tensor. For the nonlocal displacement of a material point, ξ p K is the component notation form of the relative position vector. pj This is the component notation form of the shape tensor. A significant advantage of unconventional basis peridynamics is that it can conveniently introduce classical material constitutive models into the peridynamics framework, thus integrating classical material constitutive relations in axisymmetric problems. The stress P of PK1 in the plane, as shown in Formula 14 below, is decomposed into two parts: in-plane and out-of-plane.

[0086] Formula 14:

[0087] Where θ is the circumferential coordinate of the cylindrical coordinate system, z is the axial coordinate, and r is the radial coordinate.

[0088] make and Finally, Equation 10 above simplifies to the integral-differential form of the momentum conservation equation, as shown in Equation 15 below:

[0089] Formula 15:

[0090] in T <ξ> and T ′<-ξ> represents the near-field dynamic force vector state, as shown in Equation 16 below:

[0091] Formula 16:

[0092] On the other hand, since temperature does not propagate outside the plane in axisymmetric problems, the temperature gradient in the axisymmetric mode is shown in Equation 17 below:

[0093] Formula 17:

[0094] Analogous to structural deformation problems, the temperature scalar state is considered under an axisymmetric near-field dynamic reference configuration. Based on this definition, the nonlocal form of the temperature gradient is shown in Equation 18 below:

[0095] Formula 18:

[0096] Where Q = T ′ -T represents the scalar temperature state, and X represents the vector relative position state. The thermal energy density Z of a point mass can be expressed as a function of the scalar temperature state, as shown in Equation 19 below:

[0097] Formula 19:

[0098] Substituting it into the Euler-Lagrange equation as shown in Equation 20,

[0099] Formula 20:

[0100] Wherein, L, as shown in Formula 21 below, is a Lagrangian function that includes the thermal energy and thermal potential energy of the substance.

[0101] Formula 21:

[0102] in The heat generated per unit mass of object, where ρ is density, is given by substituting Equation 19 into Equation 21 and expanding at x to obtain Equation 22:

[0103] Formula 22:

[0104] in, and The following formula, 23, is given by combining Equation 19 above with the chain rule:

[0105] Formula 23:

[0106] in, The Frechet derivative of thermal energy Z with respect to the scalar temperature state Q is given by the chain rule, as shown in Equation 24 below:

[0107] Formula 24:

[0108] in, The component form of the Frechet derivative is shown in Equation 25 below:

[0109] Formula 25:

[0110] Among them, K pi ξ is the component notation form of the shape tensor. p This is the component notation form for a relative position vector.

[0111] Unconventional ground-based near-field dynamics can also conveniently apply the classical Fourier law of heat conduction. The heat flux density is introduced into the unconventional state-based peri-field dynamics solution framework, which is combined with the specific form of heat generation per unit mass of an object. Finally, Equation 22 above simplifies to the integral-differential form of the transient heat conduction equation, as shown in Equation 26 below:

[0112] Formula 26:

[0113] in, H <ξ> and H ′<-ξ> represents the near-field dynamic heat flux scalar state, as shown in Equation 27 below:

[0114] Formula 27:

[0115] The momentum conservation equation and transient heat conduction equation represented by Equations 15 and 16 above are the basic format of CA-PC-PD proposed in this invention, and can be solved using numerical methods such as meshless methods.

[0116] It is understood that the specific implementation steps of the CA-PC-PD calculation cycle diagram proposed in this invention are as follows.

[0117] Step 1: Discretize the structure using an appropriate size of material points, assign corresponding material properties to the material points, including physical and mechanical properties, and determine the set of each material point and its neighborhood points based on the position coordinates of the discretized material points and the specified near-field dynamic neighborhood radius δ, and establish the interaction relationship between the material points.

[0118] Step 2: Define the total computation time t for the thermo-coupling problem TC Transient heat conduction problem with time step Δt T The time interval Δt for solving mechanical problems d The number of steps in the dynamic relaxation method is n. max ;

[0119] Step 3: Calculate the thermal flow state of the structure based on the temperature field, and update the temperature by explicit time history integration using the forward Euler method. When the time meets the solution interval of the mechanical problem, proceed to step 4.

[0120] Step 4: Based on the temperature field calculation results, the internal forces of the structure are calculated by introducing the classical plastic and creep constitutive relations. The displacement of the material point is calculated by using the dynamic relaxation method. After satisfying the convergence criterion, the displacement solution, velocity solution and stress solution in this time interval are obtained. Then, return to step 3 to calculate the next time interval.

[0121] Understandably, in step 1, to more accurately fit the smooth surface of the complex structure of the nuclear reactor pressure vessel, quadrilateral meshing is performed using commercial FEM software. The centroid of each element serves as the coordinates of the material point, and the volume of each element serves as the volume of the material point. The system to be solved is discretized in space into N material points, x j There are k material points in the neighborhood of .

[0122] In step 3, the discretized material point x i On the Nth T The transient heat conduction equation for the step is shown in Equation 28 below:

[0123] Formula 28:

[0124] Where ρ(x) i c(x) represents the density of point i; i Let be the specific heat capacity of substance point i; x is the time derivative of the temperature of substance point i at time t; i The position vector of the discretized material point i in the reference configuration is used to calculate the relevant variables of material point i; t = N T Δt T Let N be the current calculation time, where N is the time of calculation. T =1,2,3… represents the time steps, Δt T Calculate the time increment for the heat conduction problem; H <ξij > represents the thermal flow state of matter point i acting on matter point j, as defined in near-field dynamics. ij =x i -x j Let x be the material point i to matter point x j The relative position vector between them, x j The position vector of the discretized material point j in the reference configuration is used to identify the material point j; H <ξ ji > is the thermal flow state of matter point j acting on matter point i, as defined in peri-field dynamics; Let s be the volume element of a material point j discretized in the reference configuration; b (x i Let ) be the volumetric heat source of substance point i, where the subscript b indicates that it acts directly on the substance point; k is the heat source of substance point x. i The number of other material points in the neighborhood is determined using the forward Euler method.

[0125] In step 3, in order to suppress the inherent zero-energy modes in the near-field dynamics of the unconventional state basis, this invention proposes a bond-based temperature gradient correction method, defining the correction of the temperature scalar state as shown in Equation 29 below:

[0126] Formula 29:

[0127] in, Q It is a temperature scalar state; ξ represents the nonlocal temperature gradient; ξ is the relative position vector between material points in the reference configuration. z Q The non-uniform part of the temperature scalar state;

[0128] Adding the non-uniform part of the temperature scalar state to the heat flux scalar state yields the following formula 30:

[0129] Formula 30:

[0130] in, The corrected heat flow state; ω <ξ> is the influence function, used to describe the degree of interaction between material points; z Q q represents the non-uniform part of the temperature scalar state; k is the material thermal conductivity matrix, K is the shape tensor, and q is the heat flux density.

[0131] In step 3, Equation 28 is solved using the forward Euler method. The specific integration process is given in pseudocode form.

[0132] (1) Initialize the variables, let N T =0;

[0133] (2) Let N T =N T +1, start the loop;

[0134] (2.1) Cycle through all material points, using temperature according to the peri-field dynamics method. Calculate the nonlocal temperature gradient Heat flux density q;

[0135] (2.2) Cycle through all material points and calculate the scalar state of heat flux according to formulas 30 and 28. and temperature-time derivative

[0136] (2.3) Cycle through all material points and calculate.

[0137] (3) When N T Δt T ≥N d Δt d When the loop ends, the loop terminates.

[0138] In step 3, when considering the ablation behavior under high temperature, the materialpoint deletion technique (MPDT) is used to update the remaining geometric model and load boundaries. The geometric model update is performed through a scalar function. The ablation damage state of material points is determined as shown in Formula 31 below:

[0139] Formula 31:

[0140] When the temperature of a substance exceeds its melting point T m Subsequently, it is assumed that the material point was ablated. At this point, the state of the bonds with x and its neighborhood x′ in the near-field dynamics is... μ T <ξ> can be given by the following formula 32:

[0141] Formula 32:

[0142] Corresponding influence function ω <ξ> is updated to Formula 33:

[0143] Formula 33: ω <ξ>= μ T <ξ> ω <ξ>

[0144] Subsequently, thermal loads were applied to the new load boundary to simulate dynamic ablation.

[0145] In step 4, the substance point x i On the Nth d The discrete format of the momentum conservation equation for the step is shown in Equation 34 below.

[0146] Formula 34:

[0147] The equation is solved using the dynamic relaxation method, where t is no longer considered a real physical quantity. The equation then transforms into the following formula 35.

[0148] Formula 35:

[0149] Where Λ is a virtual density diagonal matrix. It is adaptive damping, where X and U are the position and displacement vectors of all points, respectively, and f is the internal force vector composed of all points on the right-hand side of equation 34 above. Equation 35 above is solved using the central difference method. The maximum iteration step value n is set during the solution process. max The displacement and velocity of the next iteration are given by the following formula 36.

[0150] Formula 36:

[0151] Where f n U is the internal force vector at the nth iteration. n Let n be the displacement vector at the nth iteration. Let be the velocity vector at the midpoint of the nth iteration. n is the nth step in the iterative process of the dynamic relaxation method. The initial iteration can be set as follows: It is the adaptive damping coefficient in each iteration, where f 0 The initial internal force vector is given by the following formula 37.

[0152] Formula 37:

[0153] In this invention, the value of the virtual density diagonal matrix is ​​Λ. ii =1, corresponding to the critical step size of the dynamic relaxation method. Where E is the elastic modulus of the material.

[0154] In step 4, the zero-energy modes inherent in near-field dynamics only exist when solving for deformation gradients in the plane. Therefore, this invention proposes a bond-based deformation gradient correction method for axisymmetric planes, defining the correction of the deformation vector state as shown in Equation 38 below:

[0155] Formula 38:

[0156] Adding the non-uniform part of the deformation vector state to the force vector state yields the following formula 39.

[0157] Formula 39:

[0158] in, The corrected force state; ω <ξ> is the influence function; P in Pi is the in-plane PKI stress; K is the shape tensor; β<ξ> is the vector representing the direction; Pi is the in-plane PKI stress. out For out-of-plane PKI stress; is an intermediate variable for nonlocal displacement, where C is a circular neighborhood of a point x with radius δ. in The material elastic tensor C is the portion remaining in the out-of-plane direction after removing the portion from the plane. z Y This refers to the non-uniform portion of the deformation vector state.

[0159] In step 4, the specific integration process of the dynamic relaxation method is given in pseudocode form.

[0160] (1) Initialize the iteration variables, let n = 0;

[0161] (2) Let n = n + 1, and start the loop;

[0162] (2.1) Loop through all material points and, according to the peri-field dynamics method, use displacement u n Calculate the nonlocal deformation gradient and Stress σ is calculated using elastoplastic constitutive integrals;

[0163] (2.2) Cycle through all material points and calculate the force vector state according to Formula 39. And internal force f;

[0164] (2.3) Calculate the adaptive damping according to formulas 37 and 36. and

[0165] (2.4) Update the displacement according to formula 36 U n+1 ;

[0166] (3) When When the loop ends, the loop terminates.

[0167] In step 4, the present invention considers a constitutive model that couples J2 elastoplastic and time-hardening creep damage, and proposes a simple radial return algorithm to update stress, plastic strain and creep strain.

[0168] Under the assumption of small deformation, the PK1 stress is replaced by the Cauchy stress. Considering the sequential coupling of displacement and temperature, the two equations to be solved are coupled through thermal strain, as shown in Equation 40 below:

[0169] Formula 40: P≈σ=C:(ε-ε p -ε cr -ε T )

[0170] Where P is the PK1 stress; σ is the Cauchy stress; ε p For plastic strain; ε cr For creep strain; ε T ε is the thermal strain; ε is the total strain, calculated through the deformation gradient, as shown in Equation 41 below:

[0171] Formula 41:

[0172] in This represents the nonlocal form of the structural deformation gradient in axisymmetric mode; I is the unit tensor.

[0173] Thermal strain ε T The calculation is based on temperature and the coefficient of thermal expansion, as shown in Formula 42 below:

[0174] Formula 42: ε T =αTI

[0175] Where α is the coefficient of thermal expansion;

[0176] Plastic strain ε p With creep strain ε cr The constitutive model is obtained through a constitutive integration algorithm. The constitutive model considering the coupled J2 elastoplastic and time-hardening creep damage is shown in Table 1.

[0177] Table 1 Elastic-Plastic-Creep-Damage Coupling Model

[0178]

[0179] Where c1, c2, and c3 are the parameters of the creep constitutive model. and These are the plastic multiplier and the creep multiplier, respectively. and Let σ represent the plastic and creep intrinsic variables, respectively, where K is the hardening modulus of the bilinear plasticity model, and σ is the hardening modulus. m For volumetric stress, Let ε be the equivalent stress, and s be the deviatoric stress tensor. f For uniaxial fracture creep strain, For the equivalent creep strain of multiaxial fracture, two values ​​determine the evolution of material integrity w in the third stage of creep.

[0180] After calculating the total strain ε according to formula 41, constitutive integration is performed. The plastic strain, creep strain, and stress updates are shown in Table 2 using the constitutive integration algorithm proposed in this invention.

[0181] Table 2 Constitutive Integrals of Elastic-Plastic-Creep Coupling

[0182]

[0183] After obtaining accurate plastic strain, creep strain, and stress variables, the material integrity w, which characterizes the third stage of creep, is updated according to the following formula 43.

[0184] Formula 43:

[0185] in Let N be the current time step. d +1 corresponds to the material integrity at the actual creep moment. For the previous time step N d Corresponding to the material integrity at the actual creep moment; Δγ cr Let N be the current time step. d Corresponding to the creep multiplier increment at the actual creep moment; ε f c1 represents the uniaxial fracture creep strain; c2 represents the creep constitutive model parameter. Let N be the current time step. d +1 corresponds to the volumetric stress at the actual creep moment; Let N be the current time step. d +1 corresponds to the equivalent stress at the actual creep moment; N d This is the mechanical time step, and also the creep time step.

[0186] In step 4, the overall damage variable D of the material is first defined based on the equivalent plastic strain and equivalent creep strain of the material points. This damage variable is used to characterize the degree of nonlinear deformation of the material. When material failure is determined, cracks begin to initiate and propagate. Figure 4 As shown, this invention proposes a corresponding CPC-FM based on the near-field dynamics model, which uses a scalar function to determine the fracture state of material points, as shown in Equation 44 below:

[0187] Formula 44:

[0188] The damage variable D is defined as a relatively conservative linear superposition form, as shown in Equation 45 below:

[0189] Formula 45:

[0190] in and These represent the critical equivalent plastic strain and the critical equivalent creep strain. When the total damage variable D at a material point exceeds 1, the material point is considered completely destroyed and a crack initiates at that point. At this time, the bond state between x and x′ in the near-field dynamics is... μ d <ξ> can be given by the following formula 46.

[0191] Formula 46:

[0192] Corresponding influence function ω <ξ> is updated to the following formula 47.

[0193] Formula 47: ω <ξ>= μ d <ξ> μ T <ξ> ω <ξ>

[0194] in μ T <ξ> represents the ablation state of the bond with x and its neighborhood x′ in the near-field dynamics. μ T <ξ>.

[0195] In addition, a scalar function φ(x) needs to be introduced. i To describe the matter point x, use ,t) i The degree of failure is specifically shown in Formula 48 below:

[0196] Formula 48:

[0197] The performance of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. The following embodiments are used to illustrate the present invention, but are not intended to limit the scope of the invention.

[0198] To make the objectives, technical solutions, and specific implementation effects of this invention clearer, four specific embodiments are described below in conjunction with the accompanying drawings. Figure 5 To be continued Figure 15 The accuracy and effectiveness of the CA-PC-PD and CPC-FM proposed in this invention are further explained in detail. First, three examples of thick-walled cylinders verify that the proposed method can effectively and accurately capture the elasto-plastic-creep coupling response and the third stage of creep in metallic materials when solving axisymmetric thermo-coupled problems. Then, a nuclear reactor pressure vessel example demonstrates that the proposed CA-PC-PD and CPC-FM can effectively simulate the ablation-elasto-plastic-creep fracture behavior of pressure vessels under complex thermal loads during severe accidents.

[0199] Example 1: Thermo-coupling elastoplastic analysis of a thick-walled cylinder

[0200] This embodiment is a standard numerical example that considers the elastoplastic problem of a thick-walled cylinder with axisymmetric characteristics under the influence of an internal and external temperature difference. Its geometric dimensions and thermal and mechanical boundary conditions are as follows: Figure 5 As shown. Inner diameter 1000mm, outer diameter 3000mm, height 6000mm. The internal and external temperature difference is 700℃. The outer wall is radially constrained, with a fixed constraint in the lower right corner. The physical properties of the thick-walled cylindrical material are density ρ = 1t / mm³. 3 Specific heat capacity c = 1.0 J / (t·℃), thermal conductivity k T =200W / (mm·℃), coefficient of thermal expansion α=2e-6. Mechanical properties include Young's modulus E=200e3 MPa, Poisson's ratio v=0.3, and initial yield stress. The plastic hardening modulus H = 100e3 MPa. The solution is obtained by discretizing the material into 30,000 material points. To ensure consistency of integration points between the two methods, FEM uses 7,500 elements for the solution. Figure 6 The calculation results using the CA-PC-PD method and FEM method proposed in this invention are presented. It can be seen that the temperature distribution, displacement distribution, equivalent stress, and equivalent plastic strain are all in good agreement. Figure 7 The paper also presents a comparison of temperature distribution along the path and a comparison of radial displacement and equivalent stress distribution. The curve results show that the CA-PC-PD numerical results are basically consistent with those of FEM. This embodiment effectively demonstrates the accuracy of the CA-PC-PD proposed in solving the elastoplastic problem of metals under high temperature, and verifies the correctness of the program.

[0201] Example 2: Elastic-plastic-creep coupling analysis of thick-walled cylinders

[0202] As shown in the figure, consider a thick-walled cylinder under tension. Its basic geometric information and load information are as follows: Figure 8 As shown. The material's elastic modulus E = 200e³ MPa, Poisson's ratio v = 0.3. The plastic parameter is the initial yield stress. The hardening modulus is K = 200e3 MPa. This example considers time-hardening creep constitutive parameters of c1 = 5e-23, c2 = 7, and c3 = 0. Two types of loads are considered: the first is a uniformly distributed load, with tension on both sides of the structure, and the load magnitude is q = 0.02 MPa / s; the second is a displacement load with a magnitude of u. y =5e-6mm / s. For both load conditions, the calculation time is taken as 10000s, and the load step is taken as N. d =100. The calculation results for both cases are as follows: Figure 9As shown, the equivalent creep strain-time curve, equivalent plastic strain-time curve, and equivalent stress-time curve for point A were plotted. Figure 9 It can be seen that the calculation results using the near-field dynamics model agree well with the ANSYS calculation results. At 5000 s, a small amount of creep deformation has already occurred before the material reaches yield. Subsequent loading causes a combined increase in creep and plastic strain, with the plastic strain exhibiting a linear distribution. When displacement loading is used, the material is in the elastic stage for the first 5000 s, with stress showing a linear relationship with time and a small amount of creep deformation. When entering the yield stage, the equivalent stress does not increase linearly but decreases with increasing time, while the plastic strain also shows a non-linear relationship with time. It is worth noting that if only elastic properties are considered, the deformation, stress, and strain produced by 200 MPa and 0.05 mm are consistent. Therefore, this embodiment effectively demonstrates that the CA-PC-PD proposed in this invention can consider the plastic-creep coupling effect during the material deformation process under different loads.

[0203] Example 3: Third-stage analysis of creep in thick-walled cylinders

[0204] Basic geometric information and load information, such as Figure 8 As shown in Tables 3 to 5, the creep parameters of the materials are taken from 16MnD5 steel commonly used in nuclear pressure vessels. The critical failure creep strain is selected based on the experimental curve. The remaining elastic parameters are only used as basic values. The creep behavior at four different temperatures (600℃, 800℃, 1000℃, and 1200℃) is considered, and the compared values ​​are derived from experimental data. Figure 10 Equivalent creep strain curves at four different stress levels and with experimental results are presented, showing good agreement. This embodiment effectively demonstrates that the CA-PC-PD proposed in this invention can effectively simulate the third stage of creep.

[0205] Table 3 Physical property parameters of 16MnD5 steel

[0206]

[0207] Table 4. Elastic modulus, Poisson's ratio, yield strength, and tensile strength of 16MnD5 steel

[0208]

[0209] Table 5 Constitutive parameters of three-stage creep damage in 16MnD5 steel

[0210]

[0211] Example 4: Ablation-elastoplastic analysis of the lower head of a spherical pressure vessel

[0212] The final embodiment considers an irregularly shaped spherical pressure vessel lower head structure. The internal thermal load is the heat flux density that varies with the lower head angle. For example... Figure 11 The spherical lower head shown has an inner diameter of 2200 mm, a wall thickness of 168 mm for the lower head section, and the same wall thickness for the cylindrical section. The transition section between the cylindrical section and the lower head is 716 mm high. The material is 16MnD5 steel. Different magnitudes of internal pressure are applied to the inner wall surface simultaneously. The stress-strain distribution of the pressure vessel's lower head is analyzed at the start of the load holding period and after 72 hours. The critical equivalent plastic strain is determined. With critical equivalent creep strain Take values ​​of 0.11 and 0.15 respectively. Figure 12 The residual geometric models and temperature distribution contour maps after ablation are presented using CA-PC-PD and FEM calculations, respectively. Figure 13 The equivalent stress, equivalent plastic strain, and equivalent creep strain distribution cloud maps calculated using CA-PC-PD are presented before and after 72 hours of load holding under internal pressure of 0–5 MPa. Figure 14 The total displacement and overall damage variable distribution cloud maps are given after 72 hours. When the internal pressure further increases to 7.75 MPa, the pressure vessel first fractures due to plastic strain on the outer wall, which further causes the creep of the inner wall to increase rapidly, and the cracks extend from the outer wall to the inner wall. Figure 15 The distribution contour maps of various variables and the three-dimensional view of the fracture are presented at two time points, 39h and 40h, under an internal pressure of 7.75MPa.

[0213] In summary, we first verified through three thick-walled cylindrical examples that the CA-PC-PD and CPC-FM proposed in this invention can accurately simulate the thermo-mechanical coupling behavior, elasto-plastic-creep coupling behavior, and third-stage creep behavior of axisymmetric structures under high temperature. Subsequently, through the ablation fracture analysis of the lower head structure of a spherical pressure vessel, we demonstrated that the CA-PC-PD proposed in this invention can effectively simulate ablation and fracture behavior under complex thermal loads, while simultaneously verifying that CPC-FM can accurately capture the elasto-plastic-creep coupling fracture phenomenon after pressure vessel ablation. Therefore, the CA-PC-PD and CPC-FM proposed in this invention are highly promising numerical algorithms and models.

[0214] The embodiments of the present invention are given for illustrative and descriptive purposes only, and are not intended to be exhaustive or to limit the invention to the forms disclosed. Many modifications and variations will be apparent to those skilled in the art. The embodiments were chosen and described to better illustrate the principles and practical application of the invention, and to enable those skilled in the art to understand the invention and design various embodiments with various modifications suitable for a particular purpose.

[0215] To address the aforementioned technical problems, embodiments of the present invention also provide a computer device. Please refer to [link / reference needed]. Figure 6 , Figure 16 This is a basic structural block diagram of the computer device in this embodiment.

[0216] like Figure 16 The diagram shows the internal structure of a computer device. The computer device includes a processor, non-volatile storage medium, memory, and a network interface connected via a system bus. The non-volatile storage medium stores the operating system, database, and computer-readable instructions. The database may store control information sequences. When the computer-readable instructions are executed by the processor, they enable the processor to implement a data relationship reconstruction method. The processor provides computing and control capabilities, supporting the operation of the entire computer device. The memory stores computer-readable instructions, which, when executed by the processor, enable the processor to implement a data relationship reconstruction method. The network interface of the computer device is used for communication with a terminal. Those skilled in the art will understand that… Figure 16 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0217] The memory stores the program code and various types of data required to execute the above modules. The network interface is used for data transmission between the user terminal and the server. In this embodiment, the memory stores the program code and data required to execute all sub-modules in the data relationship reconstruction device, and the server can call the server's program code and data to execute the functions of all sub-modules.

[0218] The present invention also provides a storage medium storing computer-readable instructions, which, when executed by one or more processors, cause the one or more processors to perform the steps of the data relationship reconstruction method of any of the above embodiments.

[0219] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. This computer program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. The aforementioned storage medium can be a non-volatile storage medium such as a magnetic disk, optical disk, or read-only memory (ROM), or random access memory (RAM).

[0220] Those skilled in the art will understand that the steps, measures, and solutions in the various operations, methods, and processes discussed in this application can be alternated, modified, combined, or deleted. Furthermore, other steps, measures, and solutions in the various operations, methods, and processes discussed in this application can also be alternated, modified, rearranged, decomposed, combined, or deleted. Furthermore, steps, measures, and solutions in the prior art that are similar to those disclosed in this application can also be alternated, modified, rearranged, decomposed, combined, or deleted.

[0221] The above description is only a partial embodiment of this application. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of this application, and these improvements and modifications should also be considered within the scope of protection of this application.

Claims

1. A near-field dynamic-thermal coupling method for fracture analysis of pressure vessel structures, characterized in that, include: Step 1: Discretize the structure of the pressure vessel using a preset material point size, and set corresponding material properties for the material points. Based on the position coordinates of the discretized material points and the specified near-field dynamic neighborhood radius, determine the set of points in each material point and its neighborhood, and establish the interaction relationship between the material points. The material properties include physical properties and mechanical properties. Step 2: Define the total computation time for the thermo-coupling problem, the time step for the transient heat conduction problem, the time interval for solving the mechanics problem, and the number of steps for the dynamic relaxation method; Step 3: Calculate the thermal flow state of the structure based on the temperature field, and update the temperature by explicit time history integration using the forward Euler method. When the time meets the time interval for solving the mechanical problem, proceed to step 4. Step 4: Based on the temperature field calculation results, the internal forces of the structure are calculated by introducing the classical plastic and creep constitutive relations. The displacement of the material point is calculated by using the dynamic relaxation method. After satisfying the convergence criterion, the displacement solution and velocity solution within this time interval are obtained. Then, return to step 3 to calculate the next time interval.

2. The method according to claim 1, characterized in that, In step 1, in order to more accurately fit the smooth surface of the complex structure of the nuclear reactor pressure vessel, quadrilateral meshing is performed using commercial FEM software. The centroid of the cell is used as the coordinate of the material point, and the volume of the cell is used as the volume of the material point.

3. The method according to claim 1, characterized in that, In step 3, the discretized material point x i On the Nth T The transient heat conduction equation for step is: Where ρ(x) i c(x) represents the density of point i; i Let be the specific heat capacity of substance point i; x is the time derivative of the temperature of substance point i at time t; i The position vector of the discretized material point i in the reference configuration is used to calculate the relevant variables of material point i; t = N T Δt T Let N be the current calculation time, where N is the time of calculation. T =1,2,3… represents the time steps, Δt T Calculate the time increment for the heat conduction problem; H <ξ ij > represents the thermal flow state of matter point i acting on matter point j, as defined in near-field dynamics. oj =x i -x j Let x be the material point i to matter point x j The relative position vector between them, x j The position vector of the discretized material point j in the reference configuration is used to identify the material point j; H <ξ ji > is the thermal flow state of matter point j acting on matter point i, as defined in peri-field dynamics; Let s be the volume element of a material point j discretized in the reference configuration; b (x i Let ) be the volumetric heat source of substance point i, where the subscript b indicates that it acts directly on the substance point; k is the heat source of substance point x. i The number of other material points in the neighborhood is determined using the forward Euler method. When N T Δt T ≥N d Δt d When to enter the Nth d Solving the mechanical problem of step, where N d =1,2,3… are the loop variables, Δt d Calculate the time increment for a mechanics problem; Discretized material point x i On the Nth T The momentum conservation equation for the step is: Where, ü(x i ,t) is the second derivative of the displacement of material point i at time t; t=nΔt is the calculation time in the dynamic relaxation method, where n=1,2,3… is the spurious time step in the dynamic relaxation method, and Δt is the calculation time increment in the dynamic relaxation method; T <ξ ij > is the force state of matter point i acting on matter point j, as defined in near-field dynamics; T <ξ ji > is the force state of matter point j acting on matter point i, as defined in peridynamics; b(x i Let ,t) represent the body force at material point i, where the subscript b represents the force acting directly on the material point. Dynamic relaxation is used to solve this problem.

4. The method according to claim 1, characterized in that, In step 4, a radial return algorithm is used to update stress, plastic strain, and creep strain; Under the assumption of small deformation, the PK1 stress is replaced by the Cauchy stress. Considering the sequential coupling of displacement and temperature, the two equations to be solved are coupled through thermal strain. P≈v=C:(e-e p -v cr -e T ); Where P is the PK1 stress; σ is the Cauchy stress; ε p For plastic strain; ε cr For creep strain; ε T Thermal strain; For the total strain, where, This represents the nonlocal form of the structural deformation gradient in axisymmetric mode; I is the unit tensor. Thermal strain ε T ε is calculated from temperature and the coefficient of thermal expansion. T =αTI, where α is the coefficient of thermal expansion; Plastic strain ε p With creep strain ε cr Obtained through constitutive integration algorithm; After calculating the total strain ε, constitutive integration is performed, and the plastic strain ε is obtained using the constitutive integration algorithm. p Creep strain ε cr And the stress σ is updated, wherein the damage variable w, which characterizes the third stage of creep, is updated iteratively according to the following expression; in Let N be the current time step. d +1 corresponds to the material integrity at the actual creep moment, w Nd For the previous time step N d Corresponding to the material integrity at the actual creep moment; Δγ cr Let N be the current time step. d Corresponding to the creep multiplier increment at the actual creep moment; ε f c1 represents the uniaxial fracture creep strain; c2 represents the creep constitutive model parameter. Let N be the current time step. d +1 corresponds to the volumetric stress at the actual creep moment; Let N be the current time step. d +1 corresponds to the equivalent stress at the actual creep moment; N d This is the mechanical time step, and also the creep time step.

5. The method according to claim 1, characterized in that, In step 4, the overall damage variable D of the material is defined based on the equivalent plastic strain and equivalent creep strain of the material points. This damage variable is used to characterize the degree of nonlinear deformation of the material. When material failure is determined, cracks begin to initiate and propagate. Based on the near-field dynamics model, a corresponding CPC-FM is proposed, which uses a scalar function to determine the fracture state of the material points. Where x is the position vector of a material point, used to identify any material point; the damage variable D is defined as a linear superposition. in and The critical equivalent plastic strain and critical equivalent creep strain are defined as follows: when the total damage variable D of a material point exceeds 1, it is considered that the material point is completely destroyed and a crack is initiated at that point.

6. The method according to claim 1, characterized in that, In step 4, the solution process for the mechanics problem is given in pseudocode form, including: loop variable N d =0; S1: Let N d =N d +1; S2: Entering the solution of the heat conduction problem, loop variable N T =0; S21: Let N T =N T +1, use the forward Euler method to solve the transient heat conduction equation to obtain the temperature field response T; S22: According to scalar functions Determine the ablation state of material points and update the geometric model using MPDT; S23: If N T Δt T ≥N d Δt d If the condition is met, proceed to step S3; otherwise, return to step S21 and continue the loop. S3: Loop variable n = 0; S31: Let n = n+1, and use the dynamic relaxation method to solve the momentum conservation equation discretization scheme to obtain the displacement field response u based on the temperature field information; S32: Determine the damage state of material points based on CPC-FM and update crack propagation; S3: If Proceed to step S4; otherwise, return to step S31 and continue the loop, where n is the loop variable; n max The threshold value is the loop variable; N is the total number of material points discretized on the reference configuration; |u(x i | represents the magnitude of the displacement vector of material point i, and u represents the displacement field response; |u old (x i | represents the magnitude of the displacement vector of substance point i in the previous cycle step n, x i The position vector of the discretized material point i in the reference configuration is used to identify the material point i; u old is the displacement field response in the previous iteration step n; ∈ is a small quantity used to determine whether the calculation has converged; S4: Output the calculation file for post-processing.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

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