A Crack Tip J-Integral Calculation Method for U-Notch Structure

Abstract

The present invention relates to a crack tip J-integral calculation method for a U-shaped notch structure, comprising: characterizing a defect structure to be measured, obtaining geometric features and defect size of the defect structure to be measured; constructing a finite element model of the defect structure to be measured according to the geometric features and defect size; obtaining the simulated crack tip J-integral under different ambient temperatures, different loads and different crack lengths based on the finite element model, and obtaining a plasticity coefficient based on the simulated crack tip J-integral; establishing a multi-factor coupled elastic-plastic J-integral calculation model based on the plasticity coefficient; calculating the crack tip J-integral of the defect structure to be measured based on the elastic-plastic J-integral calculation model, and obtaining the crack tip J-integral of the defect structure to be measured. The present invention provides a convenient and accurate evaluation of the crack tip fracture performance of ductile metal materials.

Description

Technical Field

[0001] The invention relates to the technical field of fracture performance evaluation of elastic-plastic materials, in particular to a crack tip J-integral calculation method of a U-shaped notch structure. Background Art

[0002] With the transformation of the energy and petrochemical industries and the rise of the new energy industry, higher requirements are placed on the reliability evaluation and safety of engineering materials. In order to adapt to the process and assembly requirements, geometric discontinuous structures (holes or notches) are often introduced in equipment processing, resulting in local high stress areas. Under the action of high-intensity alternating loads, fatigue damage accumulation will be accelerated, inducing crack initiation and expansion. Therefore, the crack propagation behavior at the notch is studied and a reasonable evaluation of the fracture performance is made. The purpose is to determine the safe use tolerance of service components and provide reasonable suggestions for subsequent maintenance.

[0003] As one of the important criteria for crack growth, stress intensity factor can be used to characterize the crack growth behavior of linear elastic materials. However, for metal materials with good toughness, significant plastic deformation often occurs before defects occur, especially in high-temperature working environments such as steam pipes, nuclear power reactors, and aerospace propulsion systems. There are more stringent requirements for the high-temperature performance of materials. At this time, the fracture analysis based on stress intensity factor is conservative. The elastic-plastic fracture mechanics parameters are used to more accurately characterize the fracture performance and determine a more appropriate safety margin. Common elastic-plastic variables that characterize crack growth behavior are CTOD and J integral. The J integral has a direct physical connection with the stress intensity factor under small-scale yielding, and is closely related to the loading parameters, which can more intuitively reflect the expansion ability of the crack tip.

[0004] The Fracture Design Manual published by the Electric Power Research Center (EPRI) of the United States proposed an engineering algorithm for solving the elastic-plastic J integral, which provides an effective means for the elastic-plastic fracture analysis and defect assessment of defective engineering structures.

[0005] However, the EPRI solution does not consider the impact of low loads on the J-integral full plastic solution, and the loads of actual components often fluctuate during service, which will cause the traditional EPRI solution based on the extreme load to have large errors and cannot be applied. Summary of the invention

[0006] The purpose of the present invention is to provide a crack tip J-integral calculation method for a U-shaped notch structure, which takes into account the influence of low load on the fully plastic solution of the J-integral, reflects the change process of the elastic-plastic J-integral under different load ratios, makes up for the problem that the traditional EPRI solution is not applicable to the defective structure under variable load conditions, enriches the existing fracture performance evaluation methods, and improves the accuracy and reliability of engineering practice applications.

[0007] To achieve the above object, the present invention provides the following solutions:

[0008] A crack tip J-integral calculation method for a U-shaped notch structure includes:

[0009] Characterize the defect structure to be measured, and obtain the geometric features and defect size of the defect structure to be measured;

[0010] Constructing a finite element model of the defect structure to be tested according to the geometric features and the defect size;

[0011] Based on the finite element model, obtaining the crack tip J integral of the finite element model under different ambient temperatures, different loads and different crack lengths, and obtaining the plasticity coefficient based on the crack tip J integral of the finite element model;

[0012] A multi-factor coupled elastic-plastic J-integral calculation model is established based on the plasticity coefficient;

[0013] Based on the elastic-plastic J-integral calculation model, the crack tip J-integral of the defect structure to be measured is calculated to obtain the crack tip J-integral of the defect structure to be measured.

[0014] Optionally, the defect size includes crack length, width and thickness at the notch root.

[0015] Optionally, a multi-factor coupled elastic-plastic J-integral calculation model is established including:

[0016] Performing a tensile test on a standard sample of the same material as the defective structure to be tested to obtain material properties of the defective structure to be tested, wherein the material properties include elastic modulus, Poisson's ratio, and yield strength;

[0017] Applying load to the finite element model to obtain a load ratio;

[0018] A multi-factor coupled elastic-plastic J-integral calculation model is established based on the plasticity coefficient, the material properties, the load ratio, and the crack length.

[0019] Optionally, obtaining the load ratio includes:

[0020] Applying a load to the finite element model using an arc length method to obtain a load-displacement curve;

[0021] According to the load-displacement curve, the limit load of the defective structure to be tested is obtained by using the double elastic slope criterion, and a first relationship model is constructed, wherein the first relationship model is a relationship model between the limit load and the defect size;

[0022] A target limit load is obtained according to the first relationship model, and the load ratio is obtained based on the target limit load.

[0023] Optionally, the first relationship model is:

[0024]

[0025] in, The coefficient expression that characterizes the change of the ultimate load with the defect size during crack propagation is: c = Wa, which is the depth of the remaining ligament at the U-shaped notch, a is the crack length, W is the width at the notch root, and σ 0 is the yield strength.

[0026] Optionally, establishing a multi-factor coupled elastic-plastic J-integral calculation model also includes:

[0027] According to the tensile test data, the Ramberg-Osgood power law relationship model is established;

[0028] Based on the Ramberg-Osgood power law relationship model, model parameters of the elastic-plastic J-integral calculation model are obtained, wherein the model parameters include a hardening coefficient and a hardening exponent.

[0029] Optionally, the multi-factor coupled elastic-plastic J-integral calculation model is:

[0030] J=J e +J p

[0031]

[0032]

[0033] Among them, J e and J p They respectively represent the contribution of elastic deformation and plastic deformation to the fracture performance at the crack tip. K is the stress intensity factor, and E' is the elastic modulus of the material under different stress distribution states. Under plane stress state, E' = E, and under plane strain state, μ is Poisson's ratio, α is the hardening coefficient of the material, n is the hardening index of the material, σ 0 is the yield stress, ε 0 is the yield strain, c = Wa, is the depth of the remaining ligament at the U-shaped notch, a is the crack length, W is the width at the root of the notch, is the plasticity coefficient, is the load ratio, P L is the limit load and P is the actual applied load.

[0034] Optionally, after obtaining the crack tip J-integral of the defect structure to be measured, the method includes: evaluating the crack tip J-integral effect of the defect structure to be measured.

[0035] Optionally, evaluating the crack tip J-integral effect of the defect structure to be tested includes:

[0036] Performing speckle preparation on the surface of the defect structure to be tested to obtain the processed defect structure to be tested;

[0037] Performing a fatigue crack growth test on the processed defective structure to be tested, and obtaining speckle deformation information of the crack tip of the processed defective structure to be tested by using digital image correlation technology;

[0038] Based on the speckle deformation information, acquiring a strain field at the crack tip;

[0039] The strain field is compared with the strain field obtained by calculating the J-integral of the crack tip of the defect structure to be measured, and the calculated J-integral of the crack tip of the defect structure to be measured is evaluated.

[0040] The beneficial effects of the present invention are:

[0041] (1) The present invention considers the influence of non-constant load on the plastic solution of J integral during crack propagation. Therefore, on the basis of the traditional EPRI solution to estimate J integral, the influence of different load ratios on the plastic coefficient is considered, the connection between the plastic coefficient and the defect size and load is established, the accuracy of J integral calculation is improved, and a more appropriate safety margin is determined.

[0042] (2) The crack tip J-integral calculation method of the U-notch structure improved based on the EPRI solution takes into account the influence of material, temperature, load and defect size on the calculation results, and can more intuitively reflect the degree of effect on the fracture performance of the crack tip.

[0043] (3) The accuracy of the EPRI improved solution was further verified by comparing the measurement results with the finite element calculation results using DIC technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. 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 paying creative labor.

[0045] Figure 1 A schematic diagram of the sample size and defect structure of an embodiment of the present invention;

[0046] Figure 2 Schematic diagram of the finite element model and the mesh distribution of the crack tip according to an embodiment of the present invention;

[0047] Figure 3 is a graph showing the relationship between the plasticity coefficient h and the load ratio under different crack lengths in an embodiment of the present invention;

[0048] Figure 4 Schematic diagram of the crack tip strain field of DIC measurement and finite element calculation under different crack lengths of an embodiment of the present invention, wherein (a) is a comparison of the strain field results near the crack tip when the crack length is 0.2 mm, (b) is a comparison of the strain field results near the crack tip when the crack length is 0.5 mm, (c) is a comparison of the strain field results near the crack tip when the crack length is 0.8 mm, (d) is a comparison of the strain field results near the crack tip when the crack length is 1 mm, (e) is a comparison of the strain field results near the crack tip when the crack length is 1.5 mm, and (f) is a comparison of the strain field results near the crack tip when the crack length is 2 mm;

[0049] Figure 5 A comparison diagram of crack front strain based on DIC and finite element solution according to an embodiment of the present invention;

[0050] Figure 6 The present invention is a flowchart of a crack tip J-integral calculation method of a U-shaped notch structure according to an embodiment of the present invention. DETAILED DESCRIPTION

[0051] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 creative work are within the scope of protection of the present invention.

[0052] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0053] This embodiment provides a method for calculating the J-integral of a crack tip of a U-shaped notch structure. Figure 6 As shown, including:

[0054] Characterize the defect structure to be detected, and obtain the geometric features and defect size of the defect structure to be detected;

[0055] Specifically, Figure 1 As shown, the size morphology of the cracked structure is characterized, and the crack defect size includes the crack length a, the width W at the root of the notch, and the thickness B.

[0056] Constructing a finite element model of the defect structure to be detected according to the geometric features and the defect size;

[0057] Based on the finite element model, obtaining the crack tip J integral of the finite element model under different ambient temperatures, different loads and different crack lengths, and obtaining the plasticity coefficient based on the crack tip J integral of the finite element model;

[0058] Specifically, different temperatures, loads and defect sizes are set through finite element calculation to obtain the elastic-plastic J integral of the crack tip of the U-shaped notch structure, and the plasticity coefficient h is obtained with reference to the EPRI fracture design manual. The size of the plasticity coefficient h depends on the defect size and the applied load, which reflects the bearing capacity of the plastic deformation at the crack tip.

[0059] Obtaining the plastic coefficient based on the crack tip elastic-plastic J integral includes: obtaining the plastic coefficient under different conditions according to the crack tip elastic-plastic J integral of the finite element model; fitting the plastic coefficient under different conditions to obtain a plastic coefficient calculation model; and calculating the plastic coefficient under actual conditions based on the plastic coefficient calculation model.

[0060] A multi-factor coupled elastic-plastic J-integral calculation model is established based on the plasticity coefficient;

[0061] Specifically, a tensile test is performed on a standard sample of the same material as the defect structure to be tested, and material properties are obtained according to the tensile test. The material properties include elastic modulus E, Poisson's ratio μ, yield strength σ 0 , and establish the Ramberg-Osgood relationship parameters.

[0062] The Ramberg-Osgood power law relationship model is shown below:

[0063]

[0064] Among them, σ and ε correspond to the stress and strain of the material at a certain moment; σ 0 , ε 0 is the yield strength and yield strain of the material; α is the hardening coefficient of the material; n is the hardening exponent of the material.

[0065] Set the specific loading method of the load, such as Figure 2 As shown in the figure, the U-shaped notch model with crack structure is loaded step by step by the arc length method to obtain the load-displacement curve, and the limit load P of the U-shaped notch crack plate is determined by the double elastic slope criterion. L , establish the limit load P L The relationship expression with defect size:

[0066]

[0067] in, is the coefficient expression that characterizes the change of ultimate load with defect size during crack propagation, c = Wa, is the depth of the remaining ligament at the U-shaped notch, σ 0 is the yield strength.

[0068] With reference to the EPRI fracture design manual, different from the traditional method which only considers the full plastic J-integral decomposition near the limit load, a multi-factor coupled elastic-plastic J-integral calculation formula is established.

[0069] J=J e +J p

[0070] J e and J p They respectively represent the contribution of elastic deformation and plastic deformation to the fracture performance at the crack tip, that is, performance indicators such as stress distribution at the crack tip, crack propagation direction, and fracture strength under tensile and compressive loads.

[0071]

[0072] Among them, K is the stress intensity factor, E' is the elastic modulus of the material under different stress distribution states, E'=E under plane stress state, and

[0073]

[0074] Among them, P L is the limit load, P is the actual applied load, and the plasticity coefficient It is strongly dependent on the applied load and is affected by the defect size. The load ratio is not considered in the traditional EPRI solution. The influence of the plasticity coefficient h will increase the error of the estimated solution under low loads, resulting in inaccurate evaluation of the fracture performance at the crack tip.

[0075] Based on the elastic-plastic J-integral calculation model, the crack tip J-integral of the defect structure to be measured is calculated to obtain the crack tip J-integral of the defect structure to be measured.

[0076] Taking the J integral of the crack tip of the defect structure to be tested includes:

[0077] The fatigue crack propagation test of U-notch specimen was carried out based on digital image correlation technology (DIC). The speckle preparation was performed on the specimen surface before the test. During the test, the speckle deformation information near the crack front was recorded and extracted by digital image correlation technology (DIC), and the strain field change at the crack front was measured.

[0078] The measured strain field at the crack front is compared with the results obtained by finite element calculation.

[0079] Example

[0080] In this embodiment, the defective component to be evaluated is a U-shaped notch sample, and its material is 316L stainless steel. Considering the good high temperature resistance of 316L, two groups of parameters at room temperature and 550°C are set for comparison.

[0081] Step S1: Characterize the size and morphology of the cracked structure (a = 1-6 mm, take a set of defect sizes every 0.5 mm, W = 9 mm, B = 3 mm). According to the tensile test data, determine the material properties of the defective structure to be evaluated, and establish the Ramberg-Osgood power law relationship model to obtain the hardening coefficient and hardening index of the material.

[0082] The Ramberg-Osgood power law relationship model is shown below:

[0083]

[0084] Among them, σ and ε correspond to the stress and strain of the material at a certain moment; σ 0 , ε 0 is the yield strength and yield strain of the material; α is the hardening coefficient of the material; n is the hardening index of the material. The material properties and RO relationship parameters at different temperatures are shown in Table 1.

[0085] Table 1

[0086]

[0087] Step S2: According to the geometric characteristics and defect size of the cracked structure, a finite element model of the U-shaped notch cracked structure is established, and the specific loading method of the load is set, such as Figure 2 As shown in the figure, the U-shaped notch model with crack structure is loaded step by step by the arc length method to obtain the load-displacement curve, and the limit load P of the U-shaped notch crack plate is determined by the double elastic slope criterion. L , establish the limit load P L The relationship expression with defect size:

[0088]

[0089] c and σ 0 The defect size and material constant are known, and the coefficient expression is obtained by the least square method. The fitting shows that:

[0090] At room temperature:

[0091]

[0092] 550℃:

[0093]

[0094] Where c = Wa, is the depth of the remaining ligament at the U-shaped notch, σ 0 is the yield strength, It is a coefficient expression that characterizes the change of ultimate load with defect size during crack propagation.

[0095] Step S3: Set different temperatures, loads and defect sizes through finite element calculation, based on the Ramberg-Osgood power law relationship model parameters and the limit load P L The elastic-plastic J integral obtained by finite element calculation is used to solve the plastic coefficient h, and the elastic-plastic J integral of the crack tip of the U-shaped notch structure is obtained, and then the corresponding plastic coefficient h is obtained. The size of the plastic coefficient h depends on the defect size and the applied load, which reflects the bearing capacity of the plastic deformation at the crack tip.

[0096] Right now:

[0097]

[0098] Among them, J p,FE The J integral obtained by finite element calculation. According to the different defect sizes and applied loads set by the finite element, the plasticity coefficient under different conditions is obtained. So as to fit it. Plasticity coefficient It is strongly dependent on the applied load and is affected by the defect size. Its evolutionary relationship with the two is as follows: Figure 3 As shown in Figure 2, the plasticity coefficient h gradually stabilizes as the load ratio increases. The average value of the stable segment near the limit load is selected for fitting to obtain h 0 , to characterize the crack growth process and defect size The changing relationship between them.

[0099] At room temperature:

[0100]

[0101] At 550°C:

[0102]

[0103] Figure 3 As the load ratio decreases, the plasticity coefficient h increases significantly, especially at low load ratios, where it far exceeds the stable section h 0 Therefore, it is necessary to characterize and The mapping relationship of is used to consider the influence of different load ratios, especially low load ratios, on the plasticity coefficient h. The contribution of low load ratios to the plasticity coefficient h needs to be derived. and The functional relationship between them.

[0104] At room temperature:

[0105]

[0106] At 550°C:

[0107]

[0108] Will and The plasticity coefficient obtained by multiplying The calculation function of The calculation function is the defect size and load ratio The common function of the fracture surface can more accurately characterize the fracture performance at the crack tip.

[0109] Step S4: Referring to the EPRI Fracture Design Manual, a multi-factor coupled elastic-plastic J-integral calculation formula is established, which is different from the traditional method that only considers the full plastic J-integral decomposition near the limit load.

[0110] J=J e +J p

[0111] J e and J p They respectively represent the contribution of elastic deformation and plastic deformation to the fracture performance at the crack tip, that is, performance indicators such as stress distribution at the crack tip, crack propagation direction, and fracture strength under tensile and compressive loads.

[0112]

[0113] Among them, K is the stress intensity factor, E' is the elastic modulus of the material under different stress distribution states, E'=E under plane stress state, and

[0114]

[0115] Among them, the plasticity coefficient The specific expression of has been given in step S3. According to the changes of defect size and applied load during the crack growth test, its actual size can be obtained, so as to obtain J during the test. pThe plasticity coefficient h of the elastic-plastic J integral calculation formula for multi-factor coupling is obtained by combining finite element calculation with comprehensive consideration of the influence of defect size and load ratio, which is a supplement to the EPRI fracture design manual.

[0116] Step S5: Based on the digital image correlation technology (DIC), the fatigue crack growth test of the U-notch specimen is carried out. Before the test, the speckle preparation is performed on the surface of the specimen. During the test, the speckle deformation information near the crack front is recorded and extracted by the digital image correlation technology (DIC), and the strain field change at the crack front is measured, such as Figure 4 As shown, (a) is the comparison of strain field results near the crack tip when the crack length is 0.2 mm, (b) is the comparison of strain field results near the crack tip when the crack length is 0.5 mm, (c) is the comparison of strain field results near the crack tip when the crack length is 0.8 mm, (d) is the comparison of strain field results near the crack tip when the crack length is 1 mm, (e) is the comparison of strain field results near the crack tip when the crack length is 1.5 mm, and (f) is the comparison of strain field results near the crack tip when the crack length is 2 mm.

[0117] Step S6: Compare the measured strain field at the crack front with the result obtained by finite element calculation. Figure 5 This shows that the calculation accuracy of the EPRI improved solution is higher and it can more reasonably characterize the propagation behavior of the crack tip.

[0118] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A crack tip J-integral calculation method for a U-shaped notch structure, characterized in that: include: Characterize the defect structure to be measured, and obtain the geometric features and defect size of the defect structure to be measured; Constructing a finite element model of the defect structure to be tested according to the geometric features and the defect size; Based on the finite element model, obtaining the crack tip J integral of the finite element model under different ambient temperatures, different loads and different crack lengths, and obtaining the plasticity coefficient based on the crack tip J integral of the finite element model; A multi-factor coupled elastic-plastic J-integral calculation model is established based on the plasticity coefficient; Based on the elastic-plastic J-integral calculation model, the crack tip J-integral of the defect structure to be measured is calculated to obtain the crack tip J-integral of the defect structure to be measured; The establishment of a multi-factor coupled elastic-plastic J-integral calculation model includes: Performing a tensile test on a standard sample of the same material as the defective structure to be tested to obtain material properties of the defective structure to be tested, wherein the material properties include elastic modulus, Poisson's ratio, and yield strength; Applying load to the finite element model to obtain a load ratio; Establishing a multi-factor coupled elastic-plastic J-integral calculation model based on the plasticity coefficient, the material properties, the load ratio, and the crack length; The elastic-plastic J-integral calculation model of multi-factor coupling is: J=J e +J p Among them, J e and J p They respectively represent the contribution of elastic deformation and plastic deformation to the fracture performance at the crack tip. K is the stress intensity factor, and E is the elastic modulus of the material under different stress distribution states. Under plane stress state, E′=E, and under plane strain state, μ is Poisson's ratio, α is the hardening coefficient of the material, n is the hardening index of the material, σ0 is the yield stress, ε0 is the yield strain, c=Wa, is the depth of the remaining ligament at the U-shaped notch, a is the crack length, W is the width at the root of the notch, is the plasticity coefficient, is the load ratio, P L is the limit load and P is the actual applied load.

2. The crack tip J-integral calculation method of the U-shaped notch structure according to claim 1 is characterized in that: The defect size includes crack length, width at the notch root and thickness.

3. The crack tip J-integral calculation method of the U-notch structure according to claim 1 is characterized in that: Obtaining the load ratio includes: Applying a load to the finite element model using an arc length method to obtain a load-displacement curve; According to the load-displacement curve, the limit load of the defective structure to be tested is obtained by using the double elastic slope criterion, and a first relationship model is constructed, wherein the first relationship model is a relationship model between the limit load and the defect size; A target limit load is obtained according to the first relationship model, and the load ratio is obtained based on the target limit load.

4. The crack tip J-integral calculation method of the U-shaped notch structure according to claim 3 is characterized in that: The first relational model is: in, To characterize the coefficient expression of the change of ultimate load with defect size during crack propagation, c = Wa, is the depth of the remaining ligament at the U-shaped notch, a is the crack length, W is the width at the notch root, and σ0 is the yield strength.

5. The crack tip J-integral calculation method of the U-notch structure according to claim 1 is characterized in that: The establishment of a multi-factor coupled elastic-plastic J-integral calculation model also includes: According to the tensile test data, the Ramberg-Osgood power law relationship model is established; Based on the Ramberg-Osgood power law relationship model, model parameters of the elastic-plastic J-integral calculation model are obtained, wherein the model parameters include a hardening coefficient and a hardening exponent.

6. The crack tip J-integral calculation method of the U-notch structure according to claim 1 is characterized in that: After obtaining the crack tip J integral of the defect structure to be measured, the method includes: evaluating the crack tip J integral effect of the defect structure to be measured.

7. The crack tip J-integral calculation method of the U-shaped notch structure according to claim 6 is characterized in that: The evaluation of the J-integral effect of the crack tip of the defect structure to be tested includes: Performing speckle preparation on the surface of the defect structure to be tested to obtain the processed defect structure to be tested; Performing a fatigue crack growth test on the processed defective structure to be tested, and obtaining speckle deformation information of the crack tip of the processed defective structure to be tested by using digital image correlation technology; Based on the speckle deformation information, acquiring a strain field at the crack tip; The strain field is compared with the strain field obtained by calculating the J-integral of the crack tip of the defect structure to be measured, and the calculated J-integral of the crack tip of the defect structure to be measured is evaluated.

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