High-throughput peridynamic numerical simulation method for damage and fracture analysis of in-service equipment

Abstract

This paper discloses a high-throughput peridynamic numerical simulation method for damage and fracture analysis of in-service equipment. This method uses a neural network for auxiliary solution to improve model solution efficiency. By combining basic peridynamic theory, high-throughput computational methods, and data-driven models, this research establishes a computational model for peridynamic damage and fracture analysis of in-service equipment in nuclear reactor systems. This method develops a high-throughput peridynamic damage and fracture solution method, acquires massive amounts of data, and establishes a neural network-based data-driven model. This method can significantly improve the efficiency of solving elastic-plastic peridynamic models for pressure vessels.

Description

Technical Field

[0001] The present invention relates to the fields of mechanics, deep learning and model simulation technology, and in particular to a high-throughput peridynamic numerical simulation method for damage and fracture analysis of in-service equipment. Background Art

[0002] The structural integrity of the reactor pressure vessel (RPV), a critical component of nuclear power plants, is crucial to its safe operation. However, during long-term service, pressure vessels often face harsh environments such as high temperature, high pressure, and high radiation exposure. These factors can degrade the material's mechanical properties and potentially induce defects such as cracks. Over time, the initiation, propagation, and confluence of cracks can lead to equipment failure, threatening the safe operation of the system.

[0003] Traditional crack analysis methods primarily rely on the finite element method (FEM), which can achieve relatively accurate results for single crack problems. However, when faced with complex situations involving multiple cracks and multiple operating conditions, the FEM's meshing and boundary condition processing become extremely complex, resulting in low computational efficiency and difficulty meeting the needs of real-time monitoring and assessment. Therefore, a numerical simulation method that can efficiently simulate the damage and fracture behavior of in-service equipment is urgently needed.

[0004] Peridynamics (PD), a meshless numerical method, effectively overcomes the limitations of traditional finite element methods for large deformation and crack propagation problems. Using a nonlocal interaction model, it describes the interaction between any two points within a material, naturally addressing crack initiation, propagation, and convergence. Combining high-throughput simulation techniques with machine learning models, it enables rapid prediction and offline assessment of the fracture behavior of multiple cracks in in-service equipment. Summary of the Invention

[0005] Purpose of the invention: The purpose of the present invention is to address the deficiencies in the prior art and to provide a high-throughput peridynamic numerical simulation method for damage and fracture analysis of in-service equipment.

[0006] Technical solution: A high-throughput peridynamic numerical simulation method for damage and fracture analysis of in-service equipment of the present invention comprises the following steps:

[0007] Step 1: Discretize the geometric model of the in-service equipment, define the interaction radius, construct the near field of each material point, and define the physical and mechanical properties parameters of the material;

[0008] Step 2: Determine the initial temperature field, stress field, boundary conditions, total calculation time t, and problem-solving time step Δt based on the actual working conditions of the equipment. There are a total of t / Δt time steps.

[0009] Step 3: Calculate the temperature change ΔT in the model at the current time step based on the distribution of the temperature field in the model at the previous time step, and then use the explicit difference method to calculate the distribution of the temperature field in the model at the current time step;

[0010] Step 4: Based on the obtained temperature field of the current time step, the stress field of the previous time step, and the boundary conditions, the internal force of the pressure vessel RPV at the current moment is calculated by introducing the thermo-elasto-plastic constitutive relationship of the pressure vessel RPV metal material 16MnD5 steel. Then, the implicit static method is used to calculate the displacement. After meeting the convergence criterion, the displacement of the current time step and the geometric configuration of the in-service equipment are obtained, and then the simulation data is obtained.

[0011] Here, the internal force of the pressure vessel RPV at the current moment is obtained by calculating the sum of the bond force density of each material point;

[0012] If the current calculation time does not reach the total calculation time t, return to step 3 to calculate the temperature field of the next time step; if the current calculation time reaches the total calculation time t, return to step 1; after reaching the specified number of samples, execute step 5;

[0013] Step 5: Based on the simulation data obtained in step 4, a fully connected neural network (FCNN) is trained to establish a rapid prediction model for equipment damage and fracture behavior. Then, the real-time monitoring data of the in-service equipment is analyzed to obtain the corresponding input data, which is then transmitted to the trained rapid prediction model to achieve offline prediction of the equipment status.

[0014] The present invention uses a fully connected neural network structure and data processing flow to train a rapid prediction model that can quickly predict the damage state of the equipment, with significantly improved accuracy and efficiency. In addition, the rapid prediction model combines real-time monitoring data of in-service equipment to achieve offline prediction and dynamic updates, enhancing the timeliness and applicability of the prediction results. In the present invention, the input data can include the five-dimensional vectors of the length of the first crack, the length of the second crack, the angle between the two cracks, the inner wall temperature, and the inner wall pressure; the final predicted output data can include the J integral of the first crack, the J integral of the second crack, the maximum opening displacement of the first crack, the maximum opening displacement of the second crack, the average radial displacement of the two-dimensional ring, the average radial strain of the two-dimensional ring, the average crack tip damage of the first crack, the average crack tip damage of the second crack, and the rate of change of the inner wall circumference.

[0015] In step 1 above, a large number of simulation models with different crack distributions and working conditions are generated through an automated crack generation program. Batch processing technology and high-performance computing resources are used to perform parallel calculations on all simulation models to obtain damage and fracture behavior data under different working conditions.

[0016] Furthermore, in step 3, the temperature field is solved using the enhanced peridynamic differential operator (E-PDDO);

[0017] The local heat conduction equation of peridynamics is expressed as follows:

[0018]

[0019] In the above formula, As an enhanced peridynamic differential operator, the basic solution of the heat conduction equation is introduced compared with the original peridynamic differential operator (PDDO); for material points x and x'∈Ω, the position vectors of the two particles are x and x' respectively, and the relative position between the two particles is ξ=x'-x, H x is the interaction domain of material point x; N is the total number of material points;

[0020] In M-dimensional space, the N-order Taylor series expansion of the function f(x') = f(x + ξ) is:

[0021]

[0022] Among them, n1, n2, ···, n M For the variable x k (k=1,…,M) differential order, n i =0,…,N; R(N,x) is the residual term;

[0023] The enhanced peridynamic function is constructed by introducing the fundamental solution of the heat conduction equation and the orthogonal basis:

[0024]

[0025] Among them, p i Represents the variable x k The differential order of p i ,q i =0,…,N; is the weight function of the Hermite polynomial is x k The qth component i In step 3, the enhanced peridynamic differential operator (E-PDDO) is used to solve the temperature field, which has higher accuracy and convergence.

[0026] Furthermore, the step 3 uses the explicit difference method to calculate the distribution of the temperature field in the current time step model, that is, the step-by-step integration method is used to complete the calculation of the heat conduction process. When the explicit forward difference format is used, the temperature from step n to step n+1 is:

[0027]

[0028] Txt n+1 ) is x in tn+ 1 The temperature at the moment, ΔT refers to the temperature change, through The temperature change in a short period of time is calculated, that is, the temperature change ΔT is obtained by multiplying the time by the temperature change rate.

[0029] Furthermore, the detailed process in step 4 is as follows:

[0030] First, solve the peridynamic equations of motion as follows:

[0031]

[0032] Where r is the density of the material, is the acceleration, u and u′ are the accelerations of the material point x i and the material point x in its near field j displacement, b is the external body force density, dV x′ is the material point x j The volume element of H x is the material point x i Near field range;

[0033] Based on the elastic-plastic linear hardening elastic-plastic model, calculate the material point x in the PD thermo-elastoplastic model i and material point x j The bond density f ji , the formula is as follows:

[0034]

[0035] Where c ji is a material point x j For material point x i The microelastic modulus constant, Represents the material point x i and the material point x in its near field j The critical elongation of the bond formed between the two electrodes when it enters the yield stage, s ji Represents the material point x i and the material point x in its near field j The elongation of the bond formed between When the inertia effect is not considered and the temperature effect is considered, the equilibrium equation is as follows:

[0036]

[0037] In the above formula, is the material point x i and other material points x in its near field j The displacement vector u pis the displacement vector between the material point x and other material points x' in its near field, η ji is the material point x i and the material point x in its near field j The relative displacement between the two points can be obtained by obtaining the displacement vector of each material point.

[0038] Next, the elastic-plastic linear hardening elastic-plastic model equation is solved and the displacement increment δu is solved using the Newton-Raphson iteration method. p , then:

[0039]

[0040] Where dL is the residual, is the tangent stiffness matrix;

[0041] Then, the tangent stiffness matrix of each material point is assembled into the overall stiffness matrix [K] using the “matching” method. 2N×2N , and then the incremental motion equation is written in matrix form as follows:

[0042] [K] 2N×2N [dU] 2N×1 =-[L * +b * ] 2N×1 (9)

[0043] Where N is the total number of material points, the vector matrix δU contains all unknown displacement increments, and K is the overall stiffness matrix; the vector L * +b * A known unbalanced force density is specified;

[0044] The constraint equations are imposed by the Lagrange multiplier method. Finally, the algebraic equations for δU and λ are solved.

[0045]

[0046] Since the global stiffness matrix [K] 2N×2N It is a sparse matrix whose matrix dimension depends on the refinement of the geometric model. The stiffness matrix [K] 2N×2N The assembly of the matrix will consume a lot of time and occupy a large amount of computer memory; therefore, the present invention uses a matrix compressed sparse row (CSR) scheme to directly store the stiffness coefficients, and uses a large sparse linear equation solver (such as Intel direct solver PARDISO or Intel iterative solver GMRES) to efficiently solve the above algebraic equations.

[0047] Furthermore, in step 4, a scalar state function μ is introduced to characterize whether the bond is broken or not:

[0048]

[0049] Where s0 is the critical elongation of the bond;

[0050] The local damage of a material point is defined as the weighted ratio of the number of broken bonds to the total number of initial bonds within the near field of the material point, expressed as:

[0051]

[0052] In the formula, the damage value changes from 0 to 1. When , the material point is completely damaged and does not interact with any material point, and the damage value , indicating that all interactions are well preserved.

[0053] Furthermore, in step 5, by optimizing the neural network structure and data processing flow, the trained deep learning model can quickly predict the damage status of the equipment, with significantly improved accuracy and efficiency. This model, combined with real-time monitoring data from the equipment, enables offline prediction and dynamic updates, enhancing the timeliness and applicability of the prediction results.

[0054] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0055] (1) This invention significantly improves the efficiency of damage and fracture behavior analysis for in-service equipment such as pressure vessels by introducing high-throughput computing and machine learning models. Compared with traditional finite element methods, the peridynamic method of this invention does not require meshing and can automatically adapt to crack initiation, propagation, and intersection, simplifying the analysis process for complex structures.

[0056] (2) The present invention uses an enhanced peridynamic differential operator to perform temperature field analysis, which improves the calculation accuracy. In particular, under complex temperature boundary conditions, it can accurately calculate the transient heat conduction problems of in-service equipment and more accurately predict the damage development of equipment.

[0057] (3) The present invention trains a deep learning model based on a large amount of simulation data, realizes real-time monitoring and offline prediction of equipment status, effectively improves the timeliness of equipment status assessment, and avoids the lag of traditional methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 is a flow chart of the overall method of the present invention;

[0059] Figure 2 It is the plane strain model of the RPV cylinder section in the embodiment of the present invention.

[0060] Figure 3 These are the temperature boundary conditions and pressure boundary conditions under the start-up conditions of the pressure vessel in the embodiment of the present invention.

[0061] Figure 4 This is a cloud diagram showing the damage, radial displacement, and circumferential displacement distribution of an RPV cylinder section with multiple cracks in an embodiment of the present invention.

[0062] Figure 5 1 is a diagram of a neural network structure in an embodiment of the present invention.

[0063] Figure 6 3 is a comparison chart of the neural network predicted value and the true value in an embodiment of the present invention. DETAILED DESCRIPTION

[0064] The technical solution of the present invention is described in detail below, but the protection scope of the present invention is not limited to the embodiments.

[0065] like Figure 1 As shown, the high-throughput peridynamic numerical simulation method for damage and fracture analysis of in-service equipment of the present invention comprises the following steps:

[0066] Step 1: Discretize the geometric model of the in-service equipment, define the interaction radius, construct the near field of each material point, and define the physical and mechanical properties parameters of the material;

[0067] Step 2: Determine the initial temperature field, stress field, boundary conditions, total calculation time t, and problem-solving time step Δt based on the actual working conditions of the equipment; (a total of t / Δt time steps)

[0068] Step 3: Calculate the temperature change ΔT in the model at the current time step based on the distribution of the temperature field in the model at the previous time step, and then use the explicit difference method to calculate the distribution of the temperature field in the model at the current time step;

[0069] Step 4: Based on the obtained temperature field of the current time step, the stress field of the previous time step, and the boundary conditions, the internal force of the pressure vessel RPV at the current moment is calculated by introducing the thermo-elasto-plastic constitutive relationship of the pressure vessel RPV metal material 16MnD5 steel. Then, the implicit static method is used to calculate the displacement. After meeting the convergence criterion, the displacement of the current time step and the geometric configuration of the in-service equipment are obtained, and then the simulation data is obtained.

[0070] Here, the internal force of the pressure vessel RPV at the current moment is obtained by calculating the sum of the bond force density of each material point;

[0071] If the current calculation time does not reach the total calculation time t, return to step 3 to calculate the temperature field of the next time step; if the current calculation time reaches the total calculation time t, return to step 1; after reaching the specified number of samples, execute step 5;

[0072] Step 5: Based on the simulation data obtained in step 4, a fully connected neural network (FCNN) is trained to establish a rapid prediction model for equipment damage and fracture behavior.

[0073] Then, the real-time monitoring data of the in-service equipment is analyzed to obtain the corresponding input data, and the input data is transmitted to the trained fast prediction model to realize offline prediction of the equipment status.

[0074] In step 3 of this embodiment, the temperature field is solved using the enhanced peridynamic differential operator (E-PDDO);

[0075] The local heat conduction equation of peridynamics is expressed as follows:

[0076]

[0077] In the above formula, is an enhanced peridynamic differential operator; for material points x and x'∈Ω, the position vectors of the two particles are x and x' respectively, and the relative position between the two particles is ξ=x'-x, H x is the interaction domain of the material point x;

[0078] In M-dimensional space, the N-order Taylor series expansion of the function f(x') = f(x + ξ) is:

[0079]

[0080] Among them, n1, n2, ···, n M For the variable x k (k=1,…,M) differential order, n i =0,…,N; R(N,x) is the residual term;

[0081] The enhanced peridynamic function is constructed by introducing the fundamental solution of the heat conduction equation and the orthogonal basis:

[0082]

[0083] Among them, p i Represents the variable x k The differential order of p i ,q i =0,…,N; is the weight function of the Hermite polynomial is x k The qth component i Hermitian polynomials.

[0084] The derivation process of the above-mentioned peridynamic local heat conduction equation (28) in this embodiment is as follows:

[0085] The classic local heat conduction equation is obtained through Fourier's law as follows:

[0086]

[0087] An enhanced peridynamic differential operator is used to replace the local spatial derivative to construct a generalized bond-type peridynamic nonlocal heat conduction model. Based on the nonlocal integral expression of the second-order local differential, the integral expression of the second-order temperature derivative of a material point with a complete symmetric near-field domain in a three-dimensional problem is obtained. Substituting the integral of the temperature derivative into the local heat conduction equation, the following peridynamic heat conduction equation for the three-dimensional problem is obtained:

[0088]

[0089] When the material point is located in the boundary area, the near field of the material point is incomplete and asymmetric. According to the differential operator formula of peridynamics, the integral expression of the second derivative of the temperature in the three-dimensional problem can be obtained as follows:

[0090]

[0091] Where, is the enhanced peridynamic function; then substituting the integral of the temperature derivative into the local heat conduction equation, the following peridynamic heat conduction equation is obtained:

[0092]

[0093] Where tr represents the trace of the matrix.

[0094] In step 3 of this embodiment, the explicit difference method is then used to calculate the distribution of the temperature field in the current time step model, that is, the stepwise integration method is used to complete the calculation of the heat conduction process. When the explicit forward difference format is used, the temperature from step n to step n+1 is:

[0095]

[0096] Txt n+1 ) is x in tn+ 1 The temperature at the moment, ΔT refers to the temperature change, through The temperature change in a short period of time is calculated, that is, the temperature change ΔT is obtained by multiplying the time by the temperature change rate.

[0097] The detailed process of step 4 of this embodiment is as follows:

[0098] First, solve the peridynamic equations of motion as follows:

[0099]

[0100] Where r is the density of the material, is the acceleration, u and u′ are the accelerations of the material point x i and the material point x in its near field j displacement, b is the external body force density, dV x′ is the material point x j The volume element of H x is the material point x i Near field range;

[0101] Based on the elastic-plastic linear hardening elastic-plastic model, calculate the material point x in the PD thermo-elastoplastic model i and material point x j The bond density f ji , the formula is as follows:

[0102]

[0103] Where c ji is a material point x j For material point x i The microelastic modulus constant, Represents the material point x i and the material point x in its near field j The critical elongation of the bond formed between the two electrodes when it enters the yield stage, s ji Represents the material point x i and the material point x in its near field j When the inertia effect is not considered and the temperature effect is considered, the equilibrium equation is as follows:

[0104]

[0105] In the above formula, is the material point x i and other material points x in its near field j The displacement vector u p is the displacement vector between the material point x and other material points x' in its near field, η ji is the material point x i and the material point x in its near field j The relative displacement between the two points can be obtained by obtaining the displacement vector of each material point.

[0106] Next, the elastic-plastic linear hardening elastic-plastic model equation is solved and the displacement increment δu is solved using the Newton-Raphson iteration method. p , then:

[0107]

[0108] Where dL is the residual, is the tangent stiffness matrix / Jacobian matrix;

[0109] Then, the tangent stiffness matrix of each material point is assembled into the overall stiffness matrix [K] using the “matching” method. 2N×2N , and then the incremental motion equation is written in matrix form as follows:

[0110] [K] 2N×2N [dU] 2N×1 =-[L * +b * ] 2N×1 (9)

[0111] Where N is the total number of material points, the vector matrix δU contains all unknown displacement increments, and K is the overall stiffness matrix; the vector L * +b * A known unbalanced force density is specified. To apply the force boundary conditions, the external forces are applied via the body force densities at several layer points and added to the right-hand side vector. In addition, the incremental displacement condition is expressed as:

[0112] [G][dU]+[dU * ]=0

[0113] Where, the known matrix G contains the coefficients of the constraint equations related to the unknown vector δU, and the vector δU * Contains the imposed displacement increment; then the constraint equations are imposed by the Lagrange multiplier method, and finally, the algebraic equations for δU and λ are solved.

[0114]

[0115] In step 4, the embodiment introduces a scalar state function μ to characterize whether the bond is broken or not:

[0116]

[0117] Where s0 is the critical elongation of the bond;

[0118] The local damage of a material point includes the weighted ratio of the number of broken bonds to the total number of initial bonds within the near field of the material point, which can be expressed as:

[0119]

[0120] In the formula, the damage value changes from 0 to 1. When the material point is completely damaged and does not interact with any material point, the damage value , indicating that all interactions are well preserved.

[0121] Example

[0122] Take the thermomechanical coupling analysis simulation of the heating process of the plane strain model of the RPV cylinder section (16MnD5 steel material) with multiple radial cracks under the start-up condition based on the technical solution of the present invention as an example (e.g. Figure 2 As shown), the accuracy and effectiveness of the high-throughput peridynamics numerical simulation method proposed in the present invention are further described in detail in combination with the technical solution and the accompanying drawings.

[0123] Step 1: Discretize the plane strain model of the RPV cylinder segment (e.g. Figure 2 As shown in the figure), define the interaction radius, construct the near field of each material point, and define the physical and mechanical properties parameters of the material.

[0124] Step 2: Determine the initial temperature field, stress field, boundary conditions, total calculation time t = 50,000 s, and problem-solving time step Δt = 2.5 s based on the actual working conditions of the equipment.

[0125] Step 3: Calculate the temperature change ΔT in the current time step model based on the distribution of the temperature field in the previous time step model, and use the explicit difference method to calculate the distribution of the temperature field in the current time step model.

[0126] Step 4: Based on the temperature field of the current time step, the stress field of the previous time step, and the boundary conditions, the thermoelastic-plastic constitutive relationship of the RPV metal material, 16MnD5 steel, is used to calculate the internal forces of the RPV at the current time step. The displacement is calculated using the implicit static method. Once the convergence criterion is met, the displacement for the current time step and the RPV geometry are obtained. Return to Step 3 to calculate the temperature field for the next time step. When the calculation duration reaches 50,000 seconds, return to Step 1. Once the specified number of samples is reached, proceed to Step 5.

[0127] Step 5: Based on the simulation data, train the deep learning model and establish a rapid prediction model for equipment damage and fracture behavior; by analyzing the real-time monitoring data of the equipment, use the trained machine learning model to achieve offline prediction of the equipment status.

[0128] Experimental Example: Analysis of Damage and Fracture Behavior of a Pressure Vessel with Multiple Radial Cracks under Startup Conditions

[0129] In step 1, the plane strain geometry of the RPV is as follows Figure 2 As shown in the figure, the lengths of crack 1 and crack 2, as well as their relative positions, are randomly generated. The model is discretized uniformly in the radial direction, with Δx = 0.00625 m and an interaction radius δ = 3.015 Δx. Material parameters for 16MnD5 steel: elastic modulus 191 GPa, Poisson's ratio v = 0.25, density ρ = 7769 kg / m 3 , yield stress σ y =377MPa, thermal conductivity k T=39.246 J / (s·m·℃), specific heat capacity c v =565.32J / (kg·℃), thermal expansion coefficient α=1.34×10 -5 .

[0130] In this embodiment, the temperature boundary conditions of the pressure vessel under the startup condition change as follows: Figure 3 As shown in (a) in FIG, the pressure boundary conditions under the start-up condition of the pressure vessel in this embodiment are as follows: Figure 3 As shown in (b), after obtaining the calculated RPV geometry model with multiple cracks and load information, the damage and fracture behavior of the RPV is analyzed by iterating through steps 3 and 4. Finally, the J-integral of the RPV's preset crack, the maximum crack opening displacement, the average radial displacement of the RPV, and the rate of change of the RPV's inner wall circumference are obtained under given temperature and pressure input conditions.

[0131] In this example, the RPV cylinder section with multiple cracks is damaged as follows Figure 4 As shown in (a), the radial displacement of this embodiment is as follows Figure 4 As shown in (b), the circumferential displacement distribution cloud diagram of this embodiment is as follows Figure 4 As shown in (c) in .

[0132] This embodiment repeatedly loops through steps 1 to 4 to acquire massive amounts of data and establish a data-driven model based on a neural network. The resulting massive amounts of data include input data and output data. The input data includes a five-dimensional vector of the length of the first crack, the length of the second crack, the angle between the two cracks, the inner wall temperature, and the inner wall pressure. The output data includes the J-integral of the first crack, the J-integral of the second crack, the maximum opening displacement of the first crack, the maximum opening displacement of the second crack, the average radial displacement of the two-dimensional annulus, the average radial strain of the two-dimensional annulus, the average crack tip damage of the first crack, the average crack tip damage of the second crack, and the rate of change of the inner wall circumference.

[0133] For each output data, a separate fully connected neural network (FCNN) is constructed and trained uniformly, such as Figure 5 The trained FCNN model is used to predict the test set of this example and compared with the peridynamic results to demonstrate the accuracy and practicality of the FCNN model. In the current working condition, the average radial strain of the two-dimensional ring, the average crack tip damage of the first crack, and the average crack tip damage of the second crack have almost no change. The mean square error between the true value and the predicted value is 2.069×10 -22 , 3.101×10 -22 , 2.991×10 -8 It can be seen that for these three outputs, the prediction effect of FCNN is very good; for the other 6 outputs, the FCNN prediction value is compared with the true value. Figure 6As shown in the figure, the overall goodness of fit is above 0.99.

[0134] in, Figure 6 (a) is a comparison chart of the J-integral predicted value and the actual value of the first crack. Figure 6 (b) is a comparison chart of the J-integral predicted value and the actual value of the second crack. Figure 6 (c) is a comparison chart of the predicted value and the actual value of the maximum opening displacement of the first crack. Figure 6 (d) is a comparison chart of the predicted value and the actual value of the maximum opening displacement of the second crack. Figure 6 (e) is a comparison chart of the predicted and true values ​​of the average radial displacement of the two-dimensional ring. Figure 6 (f) is a comparison chart of the predicted value and the actual value of the inner wall circumference change rate.

[0135] Using the trained model to predict the 1,401 test data points takes only 4 seconds, while peridynamic calculations for the same 1,401 data points take about 7 hours. FCNN significantly reduces computational efficiency.

Claims

1. A high-throughput peridynamic numerical simulation method for damage and fracture analysis of in-service equipment, characterized by: The following steps are involved: Step 1: Discretize the geometric model of the in-service equipment, define the interaction radius, and construct the near field of each material point; Step 2: Determine the initial temperature field, stress field, boundary conditions, total calculation time t, and problem-solving time step Δt based on the actual working conditions of the equipment; Step 3: Calculate the temperature change ΔT in the model at the current time step based on the distribution of the temperature field in the model at the previous time step, and then use the explicit difference method to calculate the distribution of the temperature field in the model at the current time step; Step 4: Based on the obtained temperature field of the current time step, the stress field of the previous time step, and the boundary conditions, the internal force of the pressure vessel RPV at the current moment is calculated by introducing the thermo-elasto-plastic constitutive relationship of the pressure vessel metal material. Then, the displacement is calculated using the implicit static method. After the convergence criterion is met, the displacement of the current time step and the geometric configuration of the in-service equipment are obtained, and then the simulation data is obtained. Here, the internal force of the pressure vessel RPV at the current moment is obtained by calculating the sum of the bond force density of each material point; If the current calculation time does not reach the total calculation time t, return to step 3 to calculate the temperature field of the next time step; if the current calculation time reaches the total calculation time t, return to step 1; after reaching the specified number of samples, execute step 5; Step 5: Based on the simulation data obtained in step 4, a fully connected neural network is trained to establish a rapid prediction model for equipment damage and fracture behavior; Then, the real-time monitoring data of the in-service equipment is analyzed to obtain the corresponding input data, and the input data is transmitted to the trained fast prediction model to realize the offline prediction of the equipment status; wherein, in step 3, the enhanced peridynamic differential operator (E-PDDO) is used to solve the temperature field; The local heat conduction equation of peridynamics is expressed as follows: In the above formula, is an enhanced peridynamic differential operator; for material points x and x'∈Ω, the position vectors of the two particles are x and x' respectively, and the relative position between the two particles is ξ=x'-x, H x is the interaction domain of the material point x; In M-dimensional space, the N-order Taylor series expansion of the function f(x') = f(x + ξ) is: Among them, n1, n2, ···, n M For the variable x k The differential order, n i =0,…,N; R(N,x) is the residual term; k=1,…,M; N is the total number of material points; The enhanced peridynamic function is constructed by introducing the fundamental solution of the heat conduction equation and the orthogonal basis: Among them, p i Represents the variable x k The differential order of p i ,q i =0,…,N; is the weight function of the Hermite polynomial is x k The qth component i Hermitian polynomials.

2. The high-throughput peridynamic numerical simulation method for damage and fracture analysis of in-service equipment according to claim 1 is characterized in that: In step 3, the temperature field distribution in the current time step model is calculated using the explicit difference method, that is, the heat conduction process calculation is completed using the step-by-step integration method. When the explicit forward difference format is used, the temperature from step n to step n+1 is: Txt n+1 ) is x at t n+1 The temperature at the moment, ΔT refers to the temperature change, through The temperature change in a short period of time is calculated, that is, the temperature change ΔT is obtained by multiplying the time by the temperature change rate.

3. The high-throughput peridynamic numerical simulation method for damage and fracture analysis of in-service equipment according to claim 1 is characterized in that: The detailed process in step 4 is: First, solve the peridynamic equations of motion as follows: Where ρ is the material density, is the acceleration, u and u′ are the accelerations of the material point x i and the material point x in its near field j displacement, b is the external body force density, dV x′ is the material point x j The volume element of H x is the material point x i Near field range; Based on the elastic-plastic linear hardening elastic-plastic model, calculate the material point x in the PD thermo-elastoplastic model i and material point x j The bond density f ji , the formula is as follows: Where c ji is a material point x j For material point x i The microelastic modulus constant, Represents the material point x i and the material point x in its near field j The critical elongation of the bond formed between the two components when it enters the yield stage; s ji Represents the material point x i and the material point x in its near field j When the inertia effect is not considered and the temperature effect is considered, the equilibrium equation is as follows: In the above formula, is the material point x i and other material points x in its near field j The displacement vector u p is the displacement vector between the material point x and other material points x' in its near field, η ji is the material point x i and the material point x in its near field j The relative displacement between Next, the elastic-plastic linear hardening elastic-plastic model equation is solved and the displacement increment δu is solved using the Newton-Raphson iteration method. p , then: Where dL is the residual, is the tangent stiffness matrix; Then, the tangent stiffness matrices of individual material points are assembled into the overall stiffness matrix [K] using the matching method. 2N×2N , and then the incremental motion equation is written in matrix form as follows: [K] 2N×2N [δU] 2N×1 =-[L * +b * ] 2N×1 (9) Where N is the total number of material points, the vector matrix δU contains all unknown displacement increments, and K is the overall stiffness matrix; the vector L * +b * Specify known unbalanced force density; The constraint equations are imposed by the Lagrange multiplier method. Finally, the algebraic equations for δU and λ are solved.

4. The high-throughput peridynamic numerical simulation method for damage and fracture analysis of in-service equipment according to claim 1 or 3, characterized in that: In step 4, a scalar state function μ is introduced to characterize whether the bond is broken or not: Where s0 is the critical elongation of the bond; The local damage of a material point includes the weighted ratio of the number of broken bonds to the total number of initial bonds within the near field of the material point, which can be expressed as: In the formula, the damage value changes from 0 to 1. When , the material point is completely damaged and does not interact with any material point, and the damage value , indicating that all interactions are well preserved.

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