Axial-symmetry near-field kinetic analysis method for elastic-plastic creep fracture of pressure vessel

Abstract

The invention belongs to the technical field of computational mechanics, and particularly relates to an axisymmetric near-field kinetic analysis method for elastic-plastic creep fracture of a pressure vessel. The method comprises the following steps: 1, constructing a thermal-mechanical coupling model for a pressure vessel, and obtaining a momentum conservation equation integral-differential form under an axisymmetric near-field dynamics model framework and a transient heat conduction equation of an axisymmetric heat conduction problem under the near-field dynamics framework; 2, dispersing the structure of the pressure vessel by adopting a material point size of 5mm, and endowing the material point with a corresponding physical performance parameter; 3, solving a heat conduction problem of the pressure vessel; and 4, taking the most dangerous temperature within the safety check time as the creep temperature, and solving the creep fracture problem of the pressure vessel under the action of internal pressure. According to the method, the complexity of traditional fracture mechanical damage characterization is reduced, and the fracture prediction capability of the near-field dynamic model is effectively improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of computational mechanics, and in particular relates to an axisymmetric peridynamic analysis method for elastic-plastic creep fracture of a pressure vessel. Background Art

[0002] The reactor pressure vessel (RPV), a critical structure in nuclear power facilities, is essential for maintaining safe system operation. Research has shown that in the event of a severe accident, when core melt is trapped in the lower head of the pressure vessel, a high heat flux boundary directly impacts the inner wall of the pressure vessel. This inevitably causes ablation of the inner wall, thinning it and compromising its structural integrity. The thermal stresses generated by high temperatures can exceed the yield limit of the structure, causing irreversible deformation. Furthermore, metal materials inevitably undergo creep behavior under high temperatures, significantly impacting the strength, stiffness, service life, and structural integrity of the component, ultimately leading to structural damage and fracture. Due to this thermal-mechanical coupling and the presence of nonlinear creep fracture, the safety analysis of pressure vessels under severe accidents remains a significant challenge.

[0003] Experimental investigation of fracture and the deformation mechanisms of materials during this process is not only difficult and costly, but also requires a significant amount of time when faced with high-temperature creep tests. With the development of computers, numerical simulation methods have provided a viable solution for detailed investigation of the creep response and fracture behavior of structures subjected to prolonged high temperatures. By selecting appropriate constitutive and fracture models, the fracture behavior of pressure vessels can be quickly and accurately predicted. In engineering thermomechanical coupling and nonlinear analysis, numerical calculation methods such as the finite element method (FEM) based on the continuum mechanics model are the most widely used, and commercial FEM-based software is already largely mature. Despite this, FEM still faces many difficulties in characterizing crack propagation when simultaneously addressing fracture. These difficulties, coupled with the discontinuity of the crack surface, further complicate structural integrity analysis, severely interfering with normal damage evolution and crack propagation calculations.

[0004] Peridynamics (PD), as a nonlocal model, demonstrates advantages over FEM in addressing discontinuities and other problems. Its core concept is to replace spatial differential equations with integral equations, resolving the difficulty of continuum-based mechanics models in being differentiable across cracks.

[0005] In addition, pressure vessels have a high degree of axisymmetry and are often simplified into axisymmetric models in engineering to reduce the scale of calculations and alleviate the difficulties brought about by three-dimensional numerical calculations. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a coupled axisymmetric plastic-creep peridynamics for RPVfracture (CPC-PD-RPV-F) analysis method for pressure vessel elastic-plastic creep fracture, which can solve some problems existing in the prior art: the use of an unconventional state-based peridynamic model overcomes the shortcomings of the Poisson's ratio limitation in the bond basis and the need to introduce complex assumptions to describe the nonlinear mechanical response of the material; the use of a coupled radial return mapping algorithm to solve the elastic-plastic creep coupled constitutive integral avoids the numerical divergence problem caused by solving the nonlinear equation system; the use of an elastic-plastic-creep coupled fracture model combines rate-dependent and rate-independent nonlinear responses, reduces the complexity of traditional fracture mechanics damage characterization, and effectively improves the fracture prediction capability of the peridynamic model.

[0007] The technical solution adopted in the present invention is:

[0008] A method for analyzing the elastic-plastic creep fracture of a pressure vessel using axisymmetric peridynamics is disclosed, comprising the following steps: Step 1: constructing a thermomechanical coupling model for the pressure vessel to obtain the integral-differential form of the momentum conservation equation within the axisymmetric peridynamics model framework and the transient heat conduction equation for the axisymmetric heat conduction problem within the peridynamics framework; Step 2: discretizing the pressure vessel structure using a material point size of 5 mm and assigning corresponding physical performance parameters to the material points; Step 3: solving the heat conduction problem for the pressure vessel; Step 4: setting the most dangerous temperature within the safety check time as the creep temperature, and solving the creep fracture problem of the pressure vessel under the action of internal pressure.

[0009] Obtaining the integral-differential form of the momentum conservation equation in the axisymmetric peridynamic model framework:

[0010] Based on the axisymmetric peridynamics framework and combined with the characteristics of axisymmetric problems, the corresponding reference configuration and current configuration of the peridynamic model in the axisymmetric plane are given, where x is the position vector of the material point in the reference configuration, y is the position vector of the material point in the current configuration, and u is the displacement vector of the material point. T is the force vector state, Y is the deformation vector state, is a circular neighborhood of material point x with a radius of δ, x' is an arbitrary point in the neighborhood, ξ = x'-x is the relative position vector in the reference configuration, η = u'-u is the relative displacement between material points x and x',

[0011] Among them, the integral-differential form of the momentum conservation equation in the framework of the peridynamic model is,

[0012]

[0013] Where b is the body force, ü is the acceleration, ρ is the material density, V x' is the volume of point x' in the neighborhood of material point x, T <ξ> and T '<-ξ> is the peridynamic force vector state and is written under the axisymmetric condition,

[0014]

[0015] Where (*)' represents the corresponding variable of point x', P is the PK1 stress, is the correction factor after considering axisymmetry, ω is the influence function between two material points, K is the shape tensor of the material point, P in With P out is the component of PK1 stress inside and outside the symmetry plane, and the specific expression is:

[0016]

[0017] It is derived from the nonlocal form of the deformation gradient in the peridynamic model Calculation, where the interior of the plane is divided into,

[0018]

[0019] Out-of-plane deformation gradient Non-local form of writing in is a nonlocal displacement vector, written as

[0020] The transient heat conduction equation of the axisymmetric heat conduction problem in the peridynamics framework is:

[0021]

[0022] Where c is the specific heat capacity, is the temperature velocity, s b is the heat source density, H <ξ> and H '<-ξ> is the heat flux scalar state related to the heat flux density in the peridynamics framework, written as,

[0023]

[0024] Since the temperature in the axisymmetric problem is not transferred out of the plane, the nonlocal form of the temperature gradient in the axisymmetric mode is in Q =T(x',t)-T(x,t) is the temperature scalar state defined in the peridynamics framework.

[0025] The equations (1) and (5) are solved by a meshless method.

[0026] The physical performance parameters include temperature, specific heat capacity, thermal expansion coefficient, thermal conductivity, and density.

[0027] In step 2, the pressure vessel structure is divided into quadrilateral mesh units using FEM commercial software. The centroid of the unit is used as the material point coordinate, and the volume of the unit is used as the material point volume. The discretized pressure vessel system to be solved is spatially discretized into N material points, x j There are q material points in the neighborhood of .

[0028] The step 3 comprises the following steps:

[0029] Input the geometric model and the parameters required for calculation;

[0030] Discretize the geometric domain into a material point model, given the accident variables t0, s b ,u0,b;

[0031] Loop variable N T =N T +1;

[0032] Given the total problem solving time t TC , input the boundary conditions of the heat conduction problem, and use the forward Euler method to solve the discrete material point x i In the Nth T The transient heat conduction equation of the step,

[0033]

[0034] where t = N T Δt T ,N T =1,2,3…, when N T Δt T <t TC Resolve when N T Δt T ≥t TC Go to step 4.

[0035] In step 3, the material point temperature is determined. When the material point temperature exceeds the metal melting point T m After that, delete the material point and change the corresponding influence function of the interaction relationship between the two material points ω <ξ> is updated to 0.

[0036] The step 4 comprises the following steps:

[0037] The temperature field at the highest temperature moment is selected as the load;

[0038] Loop variable t = t + Δt cr , N d =N d +1;

[0039] Otherwise, k=0, and the variable k=k+1 of the cyclic dynamic relaxation method is used to solve the position response;

[0040] Solving for deformation gradients

[0041] A radial return algorithm is used to update stress, plastic strain, and creep strain;

[0042] Determine the fracture state of the material point and update the influence function;

[0043] If k ≥ k max and Otherwise, return and continue the loop;

[0044] If t≥t TC , ending the solution of the elastic-plastic creep problem.

[0045] In step 4, the material point x i In the Nth d The discrete format of the momentum conservation equation is:

[0046]

[0047] The equation is solved using the dynamic relaxation method, where t is no longer a real physical quantity.

[0048] In step 4, considering the constitutive model of coupling J2 elastic-plastic and Wen-Tu creep under the assumption of small deformation, the yield surface equation and evolution equation of the two nonlinear constitutive models are written as,

[0049]

[0050] and

[0051]

[0052] in is the initial yield stress of the material, is the equivalent stress, α p is the plastic internal variable, K is the hardening modulus, s is the deviatoric stress tensor, c1, c2 and c3 are the creep constitutive model parameters, and W is the damage variable simulating the third stage of creep, which satisfies the following damage evolution law,

[0053]

[0054] in is the damage rate, is the equivalent creep rate, σ m is the volume stress, ε f is the uniaxial fracture creep strain, is the multiaxial fracture equivalent creep strain.

[0055] In step 4, the temperature sequence coupling form is introduced, and the specific stress update format is written as,

[0056] P≈σ=C∶(ε-ε p -ε cr -ε T ) (12)

[0057] where ε, ε p , ε cr With ε T are the total strain tensor, plastic strain tensor, creep strain tensor and temperature strain of the material point respectively. The total strain tensor ε is calculated by the nonlocal deformation gradient.

[0058]

[0059] Thermal strain tensor ε T Calculated by temperature and thermal expansion coefficient,

[0060] ε T =αTI (14).

[0061] In step 4, the plastic strain tensor ε p and creep strain tensor ε cr The stress, plastic strain and creep strain are updated by the radial return algorithm. The coupling effect of the J2 elastic-plastic constitutive model and the Wen-Tu creep constitutive model is considered, and the high-temperature coupled constitutive model of the metal material is characterized in the form of rate. The specific integration algorithm is given by the following process.

[0062] S1 determines the current time t=t+Δt cr , solve the displacement according to the previous dynamic relaxation step and update the nonlocal deformation gradient

[0063] S2 initializes the iteration variable n=0;

[0064] S3 updates the total strain ε through equations (10) and (11) n+1,t Temperature strain

[0065] S4 Calculation of test stress Test hydrostatic pressure Deviatoric stress tensor Equivalent test stress and yield surface

[0066] S5 sets n=n+1 and starts the loop;

[0067] S5-1 Solving nonlinear equations Update creep multiplier

[0068] S5-2 Determine if R≤1×10 -8 , if satisfied, end the iteration and enter S6, otherwise continue the loop;

[0069] S6 Calculates equivalent stress Judge f n+1,t ≤1×10 -8 If satisfied, go to S8, otherwise, initialize the iteration variable n=0 and go to S7;

[0070] S7 sets n=n+1 and starts the loop;

[0071] S7-1 solves nonlinear equations

[0072] S7-2 Update Plasticity Multiplier

[0073] S7-3 Determine if R≤1×10 -8 , if satisfied, end the iteration and enter S9, otherwise continue the loop;

[0074] S8 updated equivalent stress hydrostatic pressure deviatoric stress tensor Equivalent creep strain Creep strain tensor and the stress tensor

[0075] S9 updated equivalent stress hydrostatic pressure deviatoric stress tensor Equivalent creep strain Creep strain tensor Equivalent plastic strain Plastic strain tensor and the stress tensor

[0076] S10 Update damage variables Go to the next dynamic relaxation step.

[0077] In step 4, the equivalent plastic strain and equivalent creep strain are defined according to the linear superposition principle, and the overall damage variable of the material is defined. and is the critical equivalent plastic strain and the critical equivalent creep strain. The damage variable is used to characterize the nonlinear deformation degree of the material. When the material is judged to have failed, the crack begins to initiate and expand. A scalar function is used to determine the fracture state of the material point.

[0078]

[0079] When the total damage variable D of a material point exceeds 1, the material point is considered to be completely destroyed and a crack is initiated at the point; at this time, the state of the bond with x and its neighborhood x' in the peridynamics is μ d <ξ> can be given by the following formula,

[0080]

[0081] The corresponding influence function ω <ξ>Updated to μ d <ξ> ω <ξ>,

[0082] In addition, a scalar function φ(x i ,t) to describe the material point x i The degree of failure,

[0083]

[0084] Step 1 is shown in pseudo code:

[0085] Establish a discrete material point model, construct a neighborhood, define the interaction radius, and define the material physical properties including density ρ, thermal conductivity k T , thermal expansion coefficient α, specific heat capacity c parameters, mechanical properties including 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.

[0086] Step 2 is shown in pseudocode form: Determine the total calculation time t of the problem TC , time step Δt for transient heat conduction problem T , creep problem solving time interval Δt cr , dynamic relaxation method step number k max , apply loads and initialize variables such as temperature, velocity, and displacement;

[0087] Step 3 is shown in pseudo code: Enter the heat conduction problem solution, set the loop variable NT =0;

[0088] S3-1 Let N T =N T +1, use the forward Euler method to solve equation (7) to obtain the temperature field response T;

[0089] S3-2 judges the state of material point ablation. When the temperature exceeds the melting point T m Then delete the material points and update the geometric model and temperature boundary conditions;

[0090] S3-3 if N T Δt T ≥t TC , end the solution of the heat conduction problem;

[0091] Step 4 is shown in pseudo code form: Enter the elastic-plastic creep problem solution, set the loop variable N d = 0, let the temperature field at the moment of highest temperature in the heat conduction process be applied to the structure;

[0092] S4-1 Let t = t + Δt cr , N d =N d +1;

[0093] S4-2 loop variable k=0;

[0094] S4-2-1 Let k = k + 1, and solve equation (8) using the dynamic relaxation method based on the temperature field information;

[0095] S4-2-2 Solving non-local deformation gradients

[0096] S4-2-3 uses the radial return algorithm proposed in the present invention to update stress, plastic strain and creep strain;

[0097] S4-2-4 Determine the fracture state of the material point according to equations (17) and (18) and update the influence function ω <ξ> and φ(x,t);

[0098] S4-2-5if Otherwise, return to step S4-2-1 and continue the loop;

[0099] S4-2 if t≥t TC , end the solution of the elastic-plastic creep problem, otherwise return to S4-1;

[0100] S5 outputs the calculation file for post-processing.

[0101] Compared with the prior art, the embodiments of the present invention have the following beneficial effects:

[0102] (1) The present invention provides an axisymmetric peridynamic analysis method for elastic-plastic creep fracture of pressure vessels, CPC-PD-RPV-F, which provides a high-precision numerical simulation method for the elastic-plastic creep coupling analysis of pressure vessel structures composed of metal materials. By coupling the temperature field and the displacement field in a sequential coupling manner, the present invention can effectively simulate the metal elastic-plastic and creep behaviors of pressure vessel structures under high temperature.

[0103] (2) The present invention provides an axisymmetric peridynamic analysis method for elastic-plastic creep fracture of pressure vessels, CPC-PD-RPV-F, which provides a simple constitutive integration algorithm for the elastic-plastic-creep coupled constitutive analysis of metal materials under high-temperature loads. The two-dimensional nonlinear equation group consisting of the metal J_2 elastic-plastic constitutive coupling and the Wen-Tu constitutive coupling including the third stage of creep is reduced in dimensionality and converted into a nonlinear equation to be solved, which effectively improves the convergence of the nonlinear equation group when solving iteratively. At the same time, an elastic-plastic creep-damage sequential decoupling solution process is established, which reduces the numerical difficulty of solving the coupled damage.

[0104] (3) The present invention provides an axisymmetric peridynamic analysis method for elastic-plastic creep fracture of pressure vessels, CPC-PD-RPV-F. Within the peridynamic framework, an effective peridynamic fracture model for simulating the structure under the elastic-plastic-creep coupling effect is established by linearly superimposing the critical equivalent plastic strain and the critical equivalent variable strain. This enables the present invention to effectively predict the high-temperature creep fracture phenomenon of pressure vessels under severe accidents.

[0105] (4) The present invention provides an axisymmetric peridynamic analysis method for elastic-plastic creep fracture in pressure vessels, which expands the application of peridynamic models in the field of solid mechanics and thermomechanical coupling. By establishing a fast constitutive integration algorithm for elastic-plastic creep coupling, the elastic-plastic creep coupling response and crack propagation behavior of pressure vessel structures caused by high temperatures during ablation can be accurately simulated. This provides an effective approach for structural safety analysis of nuclear reactor pressure vessels. BRIEF DESCRIPTION OF THE DRAWINGS

[0106] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0107] Figure 1 The initial configuration and current configuration of the axisymmetric peridynamics adopted in the present invention;

[0108] Figure 2Schematic diagram of the geometric model and heat flow boundary load of a spherical nuclear reactor pressure vessel according to an embodiment of the present invention;

[0109] Figure 3 1 is an operational flow chart of the axisymmetric peridynamic analysis method for elastic-plastic creep rupture (CPC-PD-RPV-F) of the present invention;

[0110] Figure 4 The CPC-PD-RPV-F of the present invention is used to simulate and compare the high-temperature creep curve of the 16MnD5 steel material in Example 1;

[0111] Figure 5 Schematic diagram of the elastic-plastic creep coupled fracture model of the present invention;

[0112] Figure 6 The temperature distribution diagrams before and after ablation obtained using CPC-PD-RPV-F and FEM respectively in Example 1 of the present invention;

[0113] Figure 7 The equivalent stress, equivalent plastic strain, and equivalent creep strain distribution diagrams at 72 hours under different internal pressures obtained using CPC-PD-RPV-F in Example 1 of the present invention are as follows;

[0114] Figure 8 The displacement and overall damage distribution diagrams at 72 hours under different internal pressures obtained using CPC-PD-RPV-F in Example 1 of the present invention;

[0115] Figure 9 This is the elastic-plastic-creep rupture phenomenon under the action of 7.75 MPa internal pressure simulated by CPC-PD-RPV-F in Example 1 of the present invention. DETAILED DESCRIPTION

[0116] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0117] In the description of the present invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings and are intended solely to facilitate and simplify the description of the present invention. They are not intended to indicate or imply that the devices or components referred to must have, be constructed, or operate in a specific orientation, and therefore should not be construed as limitations on the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0118] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" should be understood in a broad sense. For example, they may refer to fixed, detachable, or integral connections; mechanical or electrical connections; direct or indirect connections through an intermediate medium; and internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on the specific circumstances.

[0119] The present invention provides an axisymmetric peridynamic analysis method for elastic-plastic creep fracture of a pressure vessel, comprising the following steps:

[0120] Step 1: Construct a thermomechanical coupling model for the pressure vessel to obtain the integral-differential form of the momentum conservation equation in the axisymmetric peridynamics model framework and the transient heat conduction equation for the axisymmetric heat conduction problem in the peridynamics framework.

[0121] Based on the axisymmetric peridynamics framework and combined with the characteristics of axisymmetric problems, Figure 1 The corresponding reference configuration and current configuration of the peridynamic model in the axisymmetric plane are given, where x is the position vector of the material point in the reference configuration, y is the position vector of the material point in the current configuration, and u is the displacement vector of the material point. T is the force vector state, Y is the deformation vector state, is a circular neighborhood of material point x with a radius of δ, x' is an arbitrary point in the neighborhood, ξ = x'-x is the relative position vector in the reference configuration, η = u'-u is the relative displacement between material points x and x',

[0122] Among them, the integral-differential form of the momentum conservation equation in the framework of the peridynamic model is,

[0123]

[0124] Where b is physical strength, is the acceleration, ρ is the material density, V x' is the volume of point x' in the neighborhood of material point x,T <ξ> and T '<-ξ> is the peridynamic force vector state and is written under the axisymmetric condition,

[0125]

[0126] Where (*)' represents the corresponding variable of point x', P is the PK1 stress, is the correction factor after considering axisymmetry, ω is the influence function between two material points, K is the shape tensor of the material point, P in With P out is the component of PK1 stress inside and outside the symmetry plane, and the specific expression is:

[0127]

[0128] It is derived from the nonlocal form of the deformation gradient in the peridynamic model Calculation, where the interior of the plane is divided into,

[0129]

[0130] Out-of-plane deformation gradient Non-local form of writing in is a nonlocal displacement vector, written as

[0131] In addition, the transient heat conduction equation for the axisymmetric heat conduction problem in the peridynamics framework is written as:

[0132]

[0133] Where c is the specific heat capacity, is the temperature velocity, s b is the heat source density, H <ξ> and H '<-ξ> is the heat flux scalar state related to the heat flux density in the peridynamics framework, written as,

[0134]

[0135] Since the temperature in the axisymmetric problem is not transferred out of the plane, the nonlocal form of the temperature gradient in the axisymmetric mode is in Q =T(x',t)-T(x,t) is the temperature scalar state defined in the peridynamics framework.

[0136] The momentum conservation equation and transient heat conduction equation represented by equations (1) and (5) are the basic format of the CPC-PD-RPV-F proposed in this invention and are solved using numerical methods such as the meshless method.

[0137] Step 2: Place the pressure vessel structure ( Figure 2 ) The material points are discretized with an average size of about 5 mm, totaling 24,320 material points, and the corresponding physical performance parameters are assigned to the material points (Table 1).

[0138] Table 1 Physical properties of 16MnD5 steel

[0139]

[0140]

[0141] In step 2, in order to more accurately fit the smooth surface of the complex structure of the nuclear reactor pressure vessel, the pressure vessel structure is divided into quadrilateral mesh units using FEM commercial software. The centroid of the unit is used as the material point coordinate, and the volume of the unit is used as the material point volume. The discretized pressure vessel system to be solved is spatially discretized into N material points, x j There are q material points in the neighborhood of ;

[0142] Step 3: Follow Figure 3 The solution process shown is used to solve the heat conduction problem of the pressure vessel.

[0143] In step 3, given the total problem solving time t TC = 259200s, input the boundary conditions of the heat conduction problem ( Figure 2 ), the forward Euler method is used to solve the discrete material point x i In the Nth T The transient heat conduction equation of the step,

[0144]

[0145] Where t = N T Δt T ,N T =1,2,3…, when N T Δt T ≥t TC The solution ends when

[0146] In step 3, the material point temperature is determined. When the material point temperature exceeds the metal melting point T m =1327℃, delete the material point and change the corresponding influence function of the interaction between the two material points ω <ξ> is updated to 0;

[0147] Step 4: Let the most dangerous temperature within the safety check time be the creep temperature, according to Figure 3 The solution process shown solves the creep rupture problem of a pressure vessel under internal pressure and defines the creep problem solution time increment Δt cr =3600s, number of steps of dynamic relaxation method k max =20000, and the mechanical property parameters of the material are given (Table 2).

[0148] Table 2 Elastic modulus, Poisson's ratio, yield strength, and tensile strength of 16MnD5 steel

[0149]

[0150]

[0151] In step 4, the material point x i In the Nth d The discrete format of the momentum conservation equation is:

[0152]

[0153] The equation is solved using the dynamic relaxation method, where t is no longer a real physical quantity.

[0154] In step 4, the present invention considers the constitutive model of coupling J2 elastic-plasticity and Wen-Tu creep under the assumption of small deformation, and the yield surface equation and evolution equation of the two nonlinear constitutive models are written as:

[0155]

[0156] and

[0157]

[0158] in is the initial yield stress of the material, is the equivalent stress, α p is the plastic internal variable, K is the hardening modulus, s is the deviatoric stress tensor, c1, c2 and c3 are the creep constitutive model parameters, and W is the damage variable simulating the third stage of creep, which satisfies the following damage evolution law,

[0159]

[0160] in is the damage rate, is the equivalent creep rate, σ m is the volume stress, ε f is the uniaxial fracture creep strain, is the equivalent creep strain of multiaxial fracture. The creep damage constitutive parameters of the material are shown in Table 3. The uniaxial creep curve fitting and verification of the corresponding temperature are shown in Table 3. Figure 4 As shown,

[0161] Table 3 Three-stage creep damage constitutive parameters of 16MnD5 steel

[0162]

[0163] In step 4, the temperature sequence coupling form is introduced, and the specific stress update format is written as,

[0164] P≈σ=C∶(ε-ε p -ε cr -ε T ) (12)

[0165] where ε, ε p , ε cr With ε T are the total strain tensor, plastic strain tensor, creep strain tensor and temperature strain of the material point respectively. The total strain tensor ε is calculated by the nonlocal deformation gradient.

[0166]

[0167] Thermal strain tensor ε T Calculated by temperature and thermal expansion coefficient,

[0168] ε T =αTI (14)

[0169] In step 4, the plastic strain tensor ε p and the creep strain tensor ε cr A simple radial return algorithm is used to update stress, plastic strain, and creep strain. Considering the coupling effect of the J2 elastic-plastic constitutive model and the Wen-Tu creep constitutive model, the high-temperature coupled constitutive model of metal materials is characterized in the form of rate. The specific integration algorithm is given by the following process.

[0170] S1 determines the current time t=t+Δt cr , solve the displacement according to the previous dynamic relaxation step and update the nonlocal deformation gradient

[0171] S2 initializes the iteration variable n=0;

[0172] S3 updates the total strain ε through equations (10) and (11) n+1,t Temperature strain

[0173] S4 Calculation of test stress Test hydrostatic pressure Deviatoric stress tensor Equivalent test stress and yield surface

[0174] S5 sets n=n+1 and starts the loop;

[0175] S5-1 Solving nonlinear equations Update creep multiplier

[0176] S5-2 Determine if R≤1×10 -8 , if satisfied, end the iteration and enter S6, otherwise continue the loop;

[0177] S6 Calculates equivalent stress Judge f n+1,t ≤1×10 -8 If satisfied, go to S8, otherwise, initialize the iteration variable n=0 and go to S7;

[0178] S7 sets n=n+1 and starts the loop;

[0179] S7-1 solves nonlinear equations

[0180] S7-2 Update Plasticity Multiplier

[0181] S7-3 Determine if R≤1×10 -8 , if satisfied, end the iteration and enter S9, otherwise continue the loop;

[0182] S8 updated equivalent stress hydrostatic pressure deviatoric stress tensor Equivalent creep strain Creep strain tensor and the stress tensor

[0183] S9 updated equivalent stress hydrostatic pressure deviatoric stress tensor Equivalent creep strain Creep strain tensor Equivalent plastic strain Plastic strain tensor and the stress tensor

[0184] S10 Update damage variables Enter the next dynamic relaxation step,

[0185] In step 4, firstly, the equivalent plastic strain and equivalent creep strain are defined according to the linear superposition principle to define the overall damage variable of the material. and is the critical equivalent plastic strain and the critical equivalent creep strain. The damage variable is used to characterize the nonlinear deformation degree of the material. When the material is judged to have failed, the crack begins to initiate and expand ( Figure 5 ), a scalar function is used to determine the fracture state of the material point,

[0186]

[0187] When the total damage variable D of a material point exceeds 1, the material point is considered to be completely destroyed and a crack is initiated at that point. μ d <ξ> can be given by the following formula,

[0188]

[0189] The corresponding influence function ω <ξ>Updated to μ d <ξ> ω <ξ>,

[0190] In addition, a scalar function φ(x i ,t) to describe the material point x i The degree of failure,

[0191]

[0192] In summary, combined with Figure 3 The specific implementation process of CPC-PD-RPV-F proposed in the present invention will be shown in the following pseudo code form:

[0193] S1 establishes a discrete material point model, constructs a neighborhood, defines the interaction radius, defines the material physical properties (density ρ, thermal conductivity k T , thermal expansion coefficient α, specific heat capacity c) parameters, 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;

[0194] S2 determines the total computation time t of the problem TC , time step Δt for transient heat conduction problemT , creep problem solving time interval Δt cr , dynamic relaxation method step number k max , apply loads and initialize variables such as temperature, velocity, and displacement;

[0195] S3 enters the heat conduction problem solution and sets the loop variable N T =0;

[0196] S3-1 Let N T =N T +1, use the forward Euler method to solve equation (7) to obtain the temperature field response T;

[0197] S3-2 judges the state of material point ablation. When the temperature exceeds the melting point T m Then delete the material points and update the geometric model and temperature boundary conditions;

[0198] S3-3 if N T Δt T ≥t TC , end the solution of the heat conduction problem;

[0199] S4 enters the elastic-plastic creep problem solution and sets the loop variable N d = 0, let the temperature field at the highest temperature during the heat conduction process be applied to the structure;

[0200] S4-1 Let t = t + Δt cr , N d =N d +1;

[0201] S4-2 loop variable k=0;

[0202] S4-2-1 Let k = k + 1, and solve equation (8) using the dynamic relaxation method based on the temperature field information;

[0203] S4-2-2 Solving non-local deformation gradients

[0204] S4-2-3 uses the radial return algorithm proposed in the present invention to update stress, plastic strain and creep strain;

[0205] S4-2-4 Determine the fracture state of the material point according to equations (17) and (18) and update the influence function ω <ξ> and φ(x,t);

[0206] S4-2-5if Otherwise, return to step S4-2-1 and continue the loop;

[0207] S4-2 if t≥t TC , end the solution of the elastic-plastic creep problem, otherwise return to S4-1;

[0208] S5 outputs the calculation file for post-processing.

[0209] Based on the above steps, Figure 6 The residual geometric model and temperature distribution cloud map after ablation calculated by CPC-PD-RPV-F and FEM are given respectively. Figure 7 The distribution cloud diagrams of equivalent stress, equivalent plastic strain and equivalent creep strain before and after 72h of loading under internal pressure of 0-5MPa calculated by CPC-PD-RPV-F are given. Figure 8 The total displacement and overall damage variable distribution cloud diagram after 72 hours is given. When the internal pressure further increases to 7.75MPa, the pressure vessel first breaks due to plastic strain on the outer wall, which further causes the inner wall to creep rapidly, and the cracks extend from the outer wall to the inner wall. Figure 9 The distribution cloud diagrams of various variables and the three-dimensional view of the fracture are given at 39h and 40h under the action of 7.75MPa internal pressure.

[0210] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above and that the invention can be embodied in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered in all respects as illustrative and non-restrictive, and the scope of the invention is defined by the appended claims, not the foregoing description, and all variations within the meaning and range of equivalents of the claims are intended to be included therein. Any reference sign in a claim should not be construed as limiting the claim to which it relates.

[0211] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A method for analyzing the axisymmetric peridynamics of elastic-plastic creep fracture of pressure vessels, characterized by: The steps include: Step 1: Construct a thermal-mechanical coupling model for the pressure vessel to obtain the integral-differential form of the momentum conservation equation in the framework of the axisymmetric peridynamic model and the transient heat conduction equation of the axisymmetric heat conduction problem in the framework of the peridynamic model; Step 2: Discretize the pressure vessel structure with a material point size of 5 mm and assign corresponding physical performance parameters to the material points; Step 3: Solve the heat conduction problem of the pressure vessel; Step 4: Set the most dangerous temperature within the safety verification time as the creep temperature, and solve the creep rupture problem of the pressure vessel under the action of internal pressure.

2. The axisymmetric peridynamic analysis method for elastic-plastic creep fracture of pressure vessels according to claim 1, characterized in that: Obtaining the integral-differential form of the momentum conservation equation in the axisymmetric peridynamic model framework: Based on the axisymmetric peridynamics framework and combined with the characteristics of axisymmetric problems, the corresponding reference configuration and current configuration of the peridynamic model in the axisymmetric plane are given, where x is the position vector of the material point in the reference configuration, y is the position vector of the material point in the current configuration, and u is the displacement vector of the material point. T is the force vector state, Y is the deformation vector state, is a circular neighborhood of the material point x with a radius of δ, x′ is any point in the neighborhood, ξ=x ′ -x is the relative position vector in the reference configuration, η=u ′ -u is the relative displacement between material points x and x′, Among them, the integral-differential form of the momentum conservation equation in the framework of the peridynamic model is, Where b is physical strength, is the acceleration, ρ is the material density, V x′ is the volume of point x′ in the neighborhood of material point x, T <ξ> and T ′ <-ξ> is the peridynamic force vector state and is written under axisymmetric conditions as, Among them (★) ′ Representative point x ′ The corresponding variable, P is the PK1 stress, is the correction factor after considering axisymmetry, ω is the influence function between two material points, K is the shape tensor of the material point, P in With P out is the component of PK1 stress inside and outside the symmetry plane, and the specific expression is: It is derived from the nonlocal form of the deformation gradient in the peridynamic model Calculation, where the interior of the plane is divided into, Out-of-plane deformation gradient Non-local form of writing in is a nonlocal displacement vector, written as 3. The axisymmetric peridynamic analysis method for elastic-plastic creep fracture of pressure vessels according to claim 2, characterized in that The transient heat conduction equation of the axisymmetric heat conduction problem in the peridynamics framework is: Where c is the specific heat capacity, is the temperature velocity, s b is the heat source density, H <ξ> and H ′ <-ξ> is the heat flux scalar state related to the heat flux density in the peridynamic framework and is written as, Since the temperature in the axisymmetric problem is not transferred out of the plane, the nonlocal form of the temperature gradient in the axisymmetric mode is in Q =T(x ′ ,t)-T(x,t) is the temperature scalar state defined in the peridynamics framework.

4. The axisymmetric peridynamic analysis method for elastic-plastic creep fracture of pressure vessels according to claim 3, characterized in that: The equations (1) and (5) are solved by a meshless method.

5. The axisymmetric peridynamic analysis method for elastic-plastic creep fracture of pressure vessels according to claim 4, characterized in that: The physical performance parameters include temperature, specific heat capacity, thermal expansion coefficient, thermal conductivity, and density.

6. The axisymmetric peridynamic analysis method for elastic-plastic creep fracture of pressure vessels according to claim 5, characterized in that: In step 2, the pressure vessel structure is divided into quadrilateral mesh units using FEM commercial software. The centroid of the unit is used as the material point coordinate, and the volume of the unit is used as the material point volume. The discretized pressure vessel system to be solved is spatially discretized into N material points, x j There are q material points in the neighborhood of .

7. The axisymmetric peridynamic analysis method for elastic-plastic creep fracture of pressure vessels according to claim 6, characterized in that: The step 3 comprises the following steps: Input the geometric model and the parameters required for calculation; Discretize the geometric domain into a material point model, given the accident variables t0, s b ,u0,b; Loop variable N T =N T +1; Given the total problem solving time t TC , input the boundary conditions of the heat conduction problem, and use the forward Euler method to solve the discrete material point x i In the Nth T The transient heat conduction equation of the step, where t = N T Δt T ,N T =1,2,3…, when N T Δt T <t TC Resolve when N T Δt T ≥t TC Go to step 4.

8. The axisymmetric peridynamic analysis method for elastic-plastic creep fracture of pressure vessels according to claim 7, characterized in that: In step 3, the material point temperature is determined. When the material point temperature exceeds the metal melting point T m After that, delete the material point and change the corresponding influence function of the interaction relationship between the two material points ω <ξ> is updated to 0.

9. The axisymmetric peridynamic analysis method for elastic-plastic creep fracture of pressure vessels according to claim 7, characterized in that: The step 4 comprises the following steps: The temperature field at the highest temperature moment is selected as the load; Loop variable t = t + Δt cr , N d =N d +1; Otherwise, k=0, and the variable k=k+1 of the cyclic dynamic relaxation method is used to solve the position response; Solving for deformation gradients A radial return algorithm is used to update stress, plastic strain, and creep strain; Determine the fracture state of the material point and update the influence function; If k ≥ k max and Otherwise, return and continue the loop; If t≥t TC , ending the solution of the elastic-plastic creep problem.

10. The axisymmetric peridynamic analysis method for elastic-plastic creep fracture of pressure vessels according to claim 9, characterized in that: In step 4, the material point x i In the Nth d The discrete format of the momentum conservation equation is: The equation is solved using the dynamic relaxation method, where t is no longer a real physical quantity.

11. The axisymmetric peridynamic analysis method for elastic-plastic creep fracture of pressure vessels according to claim 10, characterized in that: In step 4, considering the constitutive model of coupling J2 elastic-plastic and Wen-Tu creep under the assumption of small deformation, the yield surface equation and evolution equation of the two nonlinear constitutive models are written as, and in is the initial yield stress of the material, is the equivalent stress, α p is the plastic internal variable, K is the hardening modulus, s is the deviatoric stress tensor, c1, c2 and c3 are the creep constitutive model parameters, and W is the damage variable simulating the third stage of creep, which satisfies the following damage evolution law, in is the damage rate, is the equivalent creep rate, σ m is the volume stress, ε f is the uniaxial fracture creep strain, is the multiaxial fracture equivalent creep strain.

12. The axisymmetric peridynamic analysis method for elastic-plastic creep fracture of pressure vessels according to claim 11, characterized in that: In step 4, the temperature sequence coupling form is introduced, and the specific stress update format is written as, P≈σ=C∶(e-e) p -e cr -e T ) (12) where ε, ε p , ε cr With ε T are the total strain tensor, plastic strain tensor, creep strain tensor and temperature strain of the material point respectively. The total strain tensor ε is calculated by the nonlocal deformation gradient. Thermal strain tensor ε T Calculated by temperature and thermal expansion coefficient, e T = αTI (14).

13. The axisymmetric peridynamic analysis method for elastic-plastic creep fracture of pressure vessels according to claim 12, characterized in that: In step 4, the plastic strain tensor ε p and the creep strain tensor ε cr The stress, plastic strain and creep strain are updated by the radial return algorithm. The coupling effect of the J2 elastic-plastic constitutive model and the Wen-Tu creep constitutive model is considered, and the high-temperature coupled constitutive model of the metal material is characterized in the form of rate. The specific integration algorithm is given by the following process. S1 determines the current time t=t+Δt cr , solve the displacement according to the previous dynamic relaxation step and update the nonlocal deformation gradient S2 initializes the iteration variable n=0; S3 updates the total strain ε through equations (10) and (11) n+1,t Temperature strain S4 Calculation of test stress Test hydrostatic pressure Deviatoric stress tensor Equivalent test stress and yield surface S5 sets n=n+1 and starts the loop; S5-1 Solving nonlinear equations Update creep multiplier S5-2 Determine if R≤1×10 -8 , if satisfied, end the iteration and enter S6, otherwise continue the loop; S6 Calculates equivalent stress Judge f n+1,t ≤1×10 -8 If satisfied, go to S8, otherwise, initialize the iteration variable n=0 and go to S7; S7 sets n=n+1 and starts the loop; S7-1 solves nonlinear equations S7-2 Update Plasticity Multiplier S7-3 Determine if R≤1×10 -8 , if satisfied, end the iteration and enter S9, otherwise continue the loop; S8 updated equivalent stress hydrostatic pressure deviatoric stress tensor Equivalent creep strain Creep strain tensor and the stress tensor S9 updated equivalent stress hydrostatic pressure deviatoric stress tensor Equivalent creep strain Creep strain tensor Equivalent plastic strain Plastic strain tensor and the stress tensor S10 Update damage variables Go to the next dynamic relaxation step.

14. The axisymmetric peridynamic analysis method for elastic-plastic creep fracture of pressure vessels according to claim 13, characterized in that: In step 4, the equivalent plastic strain and equivalent creep strain are defined according to the linear superposition principle, and the overall damage variable of the material is defined. and is the critical equivalent plastic strain and the critical equivalent creep strain. The damage variable is used to characterize the nonlinear deformation degree of the material. When the material is judged to have failed, the crack begins to initiate and expand. A scalar function is used to determine the fracture state of the material point. 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 initiates at the point; at this time, the peridynamics is related to x and its neighborhood x ′ The state of the key μ d <ξ> can be given by the following formula, The corresponding influence function ω <ξ>Updated to μ d <ξ> ω <ξ>, In addition, a scalar function φ(x i ,t) to describe the material point x i The degree of failure, 15. The axisymmetric peridynamic analysis method for elastic-plastic creep fracture of pressure vessels according to claim 14, characterized in that: Step 1 is shown in pseudo code: Establish a discrete material point model, construct a neighborhood, define the interaction radius, and define the material physical properties including density ρ, thermal conductivity k T , thermal expansion coefficient α, specific heat capacity c parameters, mechanical properties including 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.

16. The axisymmetric peridynamic analysis method for elastic-plastic creep fracture of pressure vessels according to claim 15, characterized in that: Step 2 is shown in pseudocode form: Determine the total calculation time t of the problem TC , time step Δt for transient heat conduction problem T , creep problem solving time interval Δt cr , dynamic relaxation method step number k max , apply loads and initialize variables such as temperature, velocity, and displacement.

17. The axisymmetric peridynamic analysis method for elastic-plastic creep fracture of a pressure vessel according to claim 16, characterized in that: Step 3 is shown in pseudo code: Enter the heat conduction problem solution, set the loop variable N T =0; S3-1 Let N T =N T +1, use the forward Euler method to solve equation (7) to obtain the temperature field response T; S3-2 judges the state of material point ablation. When the temperature exceeds the melting point T m Then delete the material points and update the geometric model and temperature boundary conditions; S3-3 if N T Δt T ≥t TC , ending the solution to the heat conduction problem.

18. The axisymmetric peridynamic analysis method for elastic-plastic creep fracture of pressure vessels according to claim 17, characterized in that: Step 4 is shown in pseudo code form: Enter the elastic-plastic creep problem solution, set the loop variable N d = 0, let the temperature field at the moment of highest temperature in the heat conduction process be applied to the structure; S4-1 Let t = t + Δt cr , N d = N d + 1; S4-2 loop variable k=0; S4-2-1 Let k = k + 1, and solve equation (8) using the dynamic relaxation method based on the temperature field information; S4-2-2 Solving non-local deformation gradients S4-2-3 uses the radial return algorithm proposed in the present invention to update stress, plastic strain and creep strain; S4-2-4 Determine the fracture state of the material point according to equations (17) and (18) and update the influence function ω <ξ> and φ(x,t); S4-2-5 if k≥k max & no Then return to step S4-2-1 and continue the cycle; S4-2 if t≥t TC , end the solution of the elastic-plastic creep problem, otherwise return to S4-1; S5 outputs the calculation file for post-processing.

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