Numerical simulation method of damage in nickel-based superalloys based on viscoplastic M-integral

Abstract

The present invention discloses a method for numerically simulating damage of nickel-based high-temperature alloy materials based on the viscoplastic M-integral, comprising the following steps: constructing a geometric model of a nickel-based high-temperature alloy containing defects, determining geometric parameters and material parameters; setting an equivalent integration domain for the viscoplastic M-integral, applying boundary conditions and load conditions, obtaining stress fields, displacement fields, strain fields, and strain energy density, and calculating the viscoplastic M-integral value using the equivalent domain integration method. Since the physical meaning of the M-integral represents the energy release rate of the self-similar expansion of defects, it is related to the damage and failure of the material and has the advantages of being path-independent and not requiring consideration of specific information about complex defects within the material. The present invention can calculate a geometric model of a nickel-based high-temperature alloy containing complex defects, such as multiple cracks and multiple pores, and calibrate the damage degree thereof using the viscoplastic M-integral value. This method is of great significance for the material damage evolution analysis and structural integrity evaluation of nickel-based high-temperature alloys.

Description

Technical Field

[0001] The present invention relates to a defect damage evaluation method for a nickel-based high-temperature alloy material, and in particular to a damage numerical simulation method for a nickel-based high-temperature alloy material based on viscoplastic M-integral. Background Art

[0002] Superalloys, also known as heat-resistant alloys, possess excellent mechanical properties, such as high room-temperature and high-temperature strength, good oxidation and hot corrosion resistance, and excellent structural stability. They are widely used in aviation, aerospace, gas turbines, and other industrial sectors. High-temperature nickel-based alloys, as a representative example of new superalloy materials, are used in hot-end components such as turbine blades and combustion chambers in aircraft engines due to their excellent comprehensive material properties, including high-temperature resistance, corrosion resistance, creep resistance, as well as good fatigue performance and fracture toughness. These blades and turbine disks are subjected to high temperatures, varying centrifugal forces, and thermal stresses during service, which can cause fatigue, creep, and damage in the material. In severe cases, these components can even fail. Therefore, studying the material damage caused by defects in nickel-based alloys is beneficial for understanding the mechanisms of defect damage and failure, ensuring the integrity of high-temperature structural components.

[0003] Currently, damage assessment methods for nickel-based superalloys generally analyze the material's phase structure, which is significantly affected by factors such as processing technology, temperature, and load. Different defect types also require differentiation, making it difficult to uniformly assess and calibrate the damage caused by various defects to nickel-based superalloys, resulting in inaccurate results. Therefore, an evaluation method is desired that can address at least one of the shortcomings of existing solutions. Summary of the Invention

[0004] The purpose of this invention is to propose a numerical simulation method for damage of nickel-based high-temperature alloy materials based on viscoplastic M-integral to uniformly describe the damage levels of viscoplastic nickel-based high-temperature alloy materials such as cracks, voids, dislocations, creep, and plasticity, realize the damage calibration of original defects, and thus determine the degree of defect damage.

[0005] In order to achieve the above purpose, the technical solution adopted by the present invention is:

[0006] The numerical simulation method of nickel-based superalloy material damage based on viscoplastic M-integral includes the following steps:

[0007] 1) Construct a numerical simulation model of defective nickel-based superalloy and determine the model geometric parameters and material parameters;

[0008] 2) Setting the integration region for the viscoplastic M-integral, applying boundary conditions and load conditions, performing calculations based on the geometric and material parameters in step 1), obtaining the stress field, displacement field, strain field, and strain energy density, and calculating the viscoplastic M-integral value using the equivalent domain integration method;

[0009] 3) Based on the geometric parameters of the numerical simulation model in 1), numerical simulation models with different defect forms are established, and the viscoplastic M integral value corresponding to each model is obtained;

[0010] 4) Based on the order of the viscoplastic M integral values corresponding to each model obtained in 3), the damage degree of the viscoplastic nickel-based high-temperature alloy is evaluated.

[0011] A further improvement of the present invention is that, in step 1), a geometric model of the defective nickel-based alloy material is constructed, and the material property is defined as a viscoplastic material.

[0012] A further improvement of the present invention is that the specific implementation method of step 2) includes:

[0013] The viscoplastic M-integral considering the time effect is derived from the hardening and steady-state creep behavior of uniaxial elastic-viscoplastic materials and the definition of M-integral:

[0014]

[0015] Where i, j, k = 1, 2, b ij (t)=ψ E δ ij -σ jk u k,i represents the Eshelby energy-momentum tensor in viscoplastic materials; represents the change in strain energy density caused by plastic isotropic hardening; represents the change in strain energy density caused by viscous dissipation.

[0016] A further improvement of the present invention is that the viscoplastic M-integral is converted into a regional integral form through an equivalent regional integration method, a far-field closed integral path C surrounding the defect in the material is selected, and the viscoplastic M-integral of the defect-containing material is calculated along the closed integral path C.

[0017] A further improvement of the present invention is to write a Python software script to perform numerical calculations on the viscoplastic material M-integral to obtain the viscoplastic M-integral value.

[0018] A further improvement of the present invention is that, in step 3), the nickel-based high-temperature alloy material containing different defect forms is modeled, multiple numerical simulation models containing different defects are constructed, and the stress field, displacement field, strain field and strain energy density of each model are obtained, and then the corresponding viscoplastic M integral value is calculated.

[0019] A further improvement of the present invention is that, in step 3), the different defect forms include cracks, holes and inclusions.

[0020] A further improvement of the present invention is that, in step 4), the damage degree evaluation standard is calibrated by the value of the viscoplastic M integral, and a larger viscoplastic M integral value represents a greater damage degree, and vice versa.

[0021] Compared with the prior art, the present invention has at least the following beneficial technical effects:

[0022] The present invention provides a method for numerically simulating damage of nickel-based high-temperature alloy materials based on viscoplastic M-integral. The M-integral is calculated along the contour surrounding all defects rather than a single crack tip. It has special advantages in quantifying the degree of damage of viscoplastic materials such as nickel-based alloys. By using the time-dependent M-integral as a damage parameter to characterize the damage evolution of the material, the material damage problems caused by cracks, voids, dislocations, creep, plasticity, etc. in the viscoplastic nickel-based alloy material are uniformly described using the M-integral. A far-field closed integral path C surrounding all defects is selected in the material, and then the M-integral value M of the defect is calculated. VP , M VP The damage assessment method of the present invention has the advantages of unified standards, high computational efficiency, and greater accuracy for defect classification, and is of great significance for the assessment and analysis of material damage and structural integrity of nickel-based high-temperature alloy components.

[0023] In summary, this paper proposes a numerical damage simulation method for nickel-based superalloys based on the viscoplastic M-integral to assess damage evolution in nickel-based superalloys. For nickel-based superalloys with defect damage, the corresponding M-integral value is calculated to determine the degree of damage and assess the damage grade. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 Schematic diagram of the regional integration method for calculating M integral.

[0025] Figure 2 This is a flow chart for the numerical calculation of the viscoplastic M integral of the present invention.

[0026] Figure 3 Finite element model of a cracked viscoplastic nickel-based alloy plate for calculating the M integral value.

[0027] Figure 4 Creep deformation represented by the M integral value: (a) total loading process; (b) Step I; (c) Step II. DETAILED DESCRIPTION

[0028] The exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art. It should be noted that, unless there is a conflict, the embodiments of the present disclosure and the features described in the embodiments can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0029] (1) Explain the definition of the viscoplastic M integral:

[0030] For viscoplastic nickel-based superalloy materials, it is believed that the material strain comes from the contributions of elasticity, plasticity and viscosity.

[0031] ε=ε el +ε pl +ε cr

[0032] Where ε is the total strain tensor, ε el , ε pl and ε cr Corresponding to the elastic, plastic and viscous strain tensors respectively. Considering the hardening and steady-state creep behavior of uniaxial viscoplastic materials, the following relationship is obtained:

[0033]

[0034] Where σ is the stress tensor, E is the Young's modulus, N is the hardening exponent, and n is i is the creep index, B i is the material parameter, where B0 is usually expressed as yield stress σ Y express Combining the above, we have That is, the power law hardening law; That is Norton's creep law.

[0035] Correspondingly, the strain energy density expression considering elasticity, plasticity and viscosity can be written as:

[0036]

[0037] Substituting it into the term to be integrated in the definition of M integral, we can get:

[0038]

[0039] Finally, the form of the viscoplastic M integral is obtained:

[0040]

[0041] Among them, b ij (t)=ψ E δ ij -σ jk u k,i represents the Eshelby energy-momentum tensor in viscoplastic materials; represents the change in strain energy density caused by plastic isotropic hardening; represents the change in strain energy density caused by viscous dissipation.

[0042] (2) For numerical implementation, the rate-dependent viscoplastic M integral obtained in step 1 is converted into a regional integral and numerically solved. The specific implementation method is:

[0043] like Figure 1 As shown, two integral paths enclosing all defects are defined as Γ0(BCDB) and Γ(EFGE), with the annular domain between them as A(BEFGEBCDB). Next, a transition function q is introduced. q can be any smooth function passing through domain A, and its value is insensitive to the final result of the numerical solution. On the inner boundary Γ0, q = 1; on the outer boundary Γ, q = 0. Processing the M integral yields:

[0044]

[0045] Introducing Green's formula and processing the above formula, we have:

[0046] M(t)=-∫ BDCBEFGEB M j n j qds=-∫∫ A (M j,j q+M j q ,j )dA

[0047] Since there is no singularity in A, the condition is satisfied Substituting the above formula into the expression of viscoplastic M integral, we can obtain:

[0048]

[0049] in,

[0050]

[0051]

[0052]

[0053] The function q is related to the unit coordinates and shape functions:

[0054]

[0055] Among them, N i It is a shape function that only depends on the coordinate points x and y of the element. is the unit node value.

[0056] (r, s) is the position coordinate of the Gaussian point, and the global coordinates are converted to local coordinates:

[0057] dA=dxdy=|J|drds

[0058] Applying the Gaussian integral to each element yields:

[0059]

[0060]

[0061]

[0062] in, For each unit M i (t) value. and By superposition, we can get the M of each unit. e Repeat the above steps for each cell in region A, M e The sum of the corresponding integral values of the selected integral profile is the value of the viscoplastic M integral M VP .

[0063]

[0064]

[0065] Where n is the number of elements in the integration domain. According to the above process, a Python script is written based on the ABAQUS software platform to realize the numerical calculation of the M-integral of the viscoplastic material, as shown in the following example: Figure 2 shown.

[0066] (3) Example

[0067] In this example, the effectiveness of the M-integral as a damage parameter in assessing damage in viscoplastic materials when creep deformation is considered is numerically investigated. The model is a nickel-based superalloy (LSHR) plate with a single central crack. The material parameters are shown in Table 1. The plate is subjected to a uniformly distributed tensile load σ, as shown in Figure 3 The dimensions of the 2D plate are 45 × 45 mm, and the length of the central crack is 3 mm. The mesh consists of fully integrated four-node plane strain elements (CPE4).

[0068] Table 1 Material parameters of nickel-based high-temperature alloy

[0069]

[0070]

[0071] Creep deformation is simulated by subjecting the plate to a constant load for a sufficiently long time. Figure 4 As shown in Figure 1, two analysis steps are set in the finite element analysis. In Step I, the load increases monotonically, with a peak value of 500 MPa and a loading time of 50 s; in Step II, the load is maintained at 500 MPa and the loading time is 10,000 s. Figure 4 Figures (b) and (c) show the evolution of the M-integral over two analysis steps. In Step I (b), the M-integral value rapidly increases to 8976 N. In Step II (c), the M-integral value slowly increases over time, from 8976 N to 40360 N, consistent with steady-state creep. These results demonstrate that the M-integral can characterize the accumulation of material damage caused by creep deformation, a relatively slow process. The M-integral value can be used to assess the amount of creep deformation under different loads.

[0072] Although the present invention has been described in detail above using general descriptions and specific embodiments, it will be apparent to those skilled in the art that modifications and improvements may be made based on the present invention. Therefore, such modifications and improvements, which do not depart from the spirit of the present invention, are intended to be within the scope of protection claimed herein.

Claims

1. A numerical simulation method for damage of nickel-based superalloy materials based on viscoplastic M integral, characterized by: The following steps are involved: 1) Construct a numerical simulation model of defective nickel-based superalloy and determine the model geometric parameters and material parameters; 2) Setting the integration region for the viscoplastic M-integral, applying boundary conditions and load conditions, performing calculations based on the geometric parameters and material parameters in step 1), obtaining the stress field, displacement field, strain field, and strain energy density, and calculating the viscoplastic M-integral value using the equivalent domain integration method; the specific implementation method includes: The viscoplastic M-integral considering the time effect is derived from the hardening and steady-state creep behavior of uniaxial elastic-viscoplastic materials and the definition of M-integral: Where i, j, k = 1, 2, b ij (t)=ψ E δ ij -σ jk u k,i represents the Eshelby energy-momentum tensor in viscoplastic materials; represents the change in strain energy density caused by plastic isotropic hardening; represents the change in strain energy density caused by viscous dissipation; 3) Based on the geometric parameters of the numerical simulation model in 1), numerical simulation models with different defect forms are established, and the viscoplastic M integral value corresponding to each model is obtained; 4) Based on the order of the viscoplastic M integral values corresponding to each model obtained in 3), the damage degree of the viscoplastic nickel-based high-temperature alloy is evaluated.

2. The method for numerical simulation of nickel-based high-temperature alloy material damage based on viscoplastic M-integral according to claim 1, characterized in that: In step 1), a geometric model of a nickel-based alloy material containing defects is constructed, and the material properties are defined as a viscoplastic material.

3. The method for numerical simulation of nickel-based high-temperature alloy material damage based on viscoplastic M-integral according to claim 1, characterized in that: The viscoplastic M-integral is converted into a regional integral through the equivalent regional integration method. The far-field closed integration path C surrounding the defect in the material is selected, and the viscoplastic M-integral of the defective material is calculated along the closed integration path C.

4. The method for numerical simulation of nickel-based high-temperature alloy material damage based on viscoplastic M-integral according to claim 3, characterized in that: A Python software script was written to perform numerical calculations on the M-integral of viscoplastic materials and obtain the viscoplastic M-integral value.

5. The method for numerical simulation of nickel-based high-temperature alloy material damage based on viscoplastic M-integral according to claim 1, characterized in that: In step 3), the nickel-based high-temperature alloy material containing different defect forms is modeled, and multiple numerical simulation models containing different defects are constructed. The stress field, displacement field, strain field and strain energy density of each model are obtained, and then the corresponding viscoplastic M integral value is calculated.

6. The method for numerical simulation of nickel-based high-temperature alloy material damage based on viscoplastic M-integral according to claim 1, characterized in that: In step 3), different defect forms include cracks, holes and inclusions.

7. The method for numerical simulation of nickel-based high-temperature alloy material damage based on viscoplastic M-integral according to claim 1, characterized in that: In step 4), the damage degree evaluation standard is calibrated by the value of the viscoplastic M integral. A larger viscoplastic M integral value represents a greater damage degree, and vice versa.

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