A method for constructing a crack tip stress field correction model based on a CJP model

Abstract

The present application relates to the technical field of fatigue crack propagation crack tip stress field model, and provides a kind of construction method of crack tip stress field correction model based on CJP model.The present application considers the influence of dislocation slip accumulation and crack tip blunting on crack propagation, uses dislocation field to modify existing CJP model, and introduces plastic flow factor ρ to modify the displacement of the crack surface of fatigue crack, so that the obtained crack tip stress field correction model can more accurately describe the experimental plastic zone when keeping the description effect of CJP model on larger plastic zone, so as to better describe the plasticity-induced closure phenomenon appearing in the process of fatigue crack propagation;At the same time, the modified stress intensity factor obtained based on the crack tip stress field correction model is also more accurate.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of fatigue crack propagation crack tip stress field model, in particular to a construction method of a crack tip stress field correction model based on a CJP model. BACKGROUND

[0002] Fatigue crack is one of the important reasons for the failure of metal materials. According to the different stress forms of the crack, the crack is divided into opening type (referred to as I type), sliding type (referred to as II type) and tearing type (referred to as III type), wherein the I type crack belongs to the main crack propagation behavior.

[0003] At present, on the basis of linear elastic fracture mechanics, a large number of studies on crack tip field have been carried out, and the stress intensity factor K is used to characterize the crack propagation driving force, so as to reveal the crack propagation law. In 1963, Paris proposed the famous Paris crack propagation rate formula through a large number of experiments, and the model corresponding to the formula is one of the models widely used in the early stage of crack research field. However, due to the influence of the plastic zone around the crack tip and the crack surface, plastic induced crack closure phenomenon may occur in the process of fatigue crack propagation, and then the local strain field of crack propagation under the global elastic stress field becomes very complex, and the actual stress intensity factor range is lower than the nominal value. Therefore, in 2007, three scholars, Christopher, James and Patterson, considered the influence of elastic-plastic compatible stress and plastic induced crack closure, and proposed a new crack tip stress field model, namely CJP model. The model equivalent to the shielding effect of crack tip plastic zone and wake zone on crack propagation as several forces, and introduces a correction term on the basis of the traditional Williams model. In addition to defining the stress intensity factor K I (in the CJP model, K F ) with the same meaning as the traditional model, the shear stress intensity factor K S characterizing the elastic-plastic interface and the stress intensity factor K R caused by Poisson effect to hinder crack propagation are also defined, so as to more accurately explain the plastic induced crack closure phenomenon in the process of crack propagation by the CJP model.

[0004] The crack tip stress diagram of the CJP model is shown in Figure 1 , wherein the smooth curve encloses the crack tip plastic zone and wake zone. When the crack opens, the plastic zone expands in the y direction and shrinks in the x direction; the wake zone shrinks in the x direction, and the shear force F S is obtained according to the displacement compatibility; the force F Ax and F Ay corresponding to the crack tip stress field generated by the external loadwhich drives the crack propagation, characterized by the stress intensity factor. When the crack is closed, the force F Px and F Py ; the wake region is stretched in the x-direction, which generates an opposing shear force F S , while the wake region is inflated in the y-direction, which generates a compressive contact force F C , F C and F P are considered as permanent plastic deformation to generate the force that hinders crack propagation, resulting in a plastic shielding effect.

[0005] At the same time, during the crack propagation, dislocation, blunting, hardening, crack branching, etc. are also important factors affecting the propagation rate, and it is particularly necessary to quantify and separate various factors affecting fatigue crack propagation. In 1969, Dundurs proposed the crack dislocation effect, and obtained the displacement field and stress field through the stress function Φ. Atkinson and Kanninen used dislocation slip theory to simulate the plastic behavior of the crack, and revealed the hardening phenomenon of dislocation movement. Hills et al. obtained the super dislocation strength and position according to the force balance and singular cancellation equation of super dislocation, and established a relatively simple mathematical model to predict the crack propagation rate. Pommier proposed that under the action of external load, especially super load, the material will harden, resulting in crack tip blunting, which changes the crack tip field. In 2010, Pommier and Hamam simulated the crack by using edge dislocation, and used dislocation dipole to characterize the plastic zone at the crack tip, and explained the blunting, dislocation slip and accumulation and plastic behavior in the crack propagation process.

[0006] As can be seen, fatigue crack propagation is affected by many factors, but both the traditional Williams model and the existing CJP model consider only a single factor. SUMMARY

[0007] The purpose of the present application is to provide a construction method of a crack tip stress field correction model based on a CJP model, which modifies the existing CJP model by using dislocation field, and introduces a plastic flow factor ρ to correct the displacement of the crack surface, so as to overcome the problems existing in the existing CJP model.

[0008] The purpose of the present application is achieved by the following technical solutions:

[0009] A construction method of a crack tip stress field correction model based on a CJP model, comprising the following steps:

[0010] Step S1. Establish a preliminary CJP model;

[0011] wherein the stress field of the CJP model under type I loading is represented as:

[0012]

[0013]

[0014]

[0015] where A, B, C, F are four parameters defined by CJP model to describe the stress field near the crack tip; r is the distance to the crack tip, and θ is the polar angle to the crack surface;

[0016] Correspondingly, the displacement field of CJP model under mode I loading is expressed as:

[0017]

[0018] where G is the shear modulus, and G = E / [2(1+υ)], E is the Young's modulus, and υ is the Poisson's ratio; u is the horizontal displacement; v is the vertical displacement; k = (3-υ) / (1+υ) under the plane stress state, and k = 3-4υ under the plane strain state;

[0019] Step S2. The crack edge dislocation based on Bueckner theory, the mode I crack propagation has a dislocation intensity of b y burgers vector, and the corresponding dislocation field stress function is:

[0020]

[0021] The dislocation intensity is defined as ρ, and then b y = ρ;

[0022] At this time, the expression of the dislocation displacement field u ⊥ is:

[0023]

[0024]

[0025] where ρ is the plastic flow factor caused by the dislocation field;

[0026] Step S3. According to the small deformation assumption satisfied by the dislocation motion, the dislocation stress field is calculated from formula (6) and formula (7), and is expressed as:

[0027]

[0028]

[0029]

[0030] Step S4. Superimposing formula (6) and formula (7) with formula (4) respectively to obtain the real displacement field of the crack tip neighborhood of the crack tip stress field correction model, expressed as:

[0031]

[0032]

[0033]

[0034] Meanwhile, superimposing formula (8), formula (9) and formula (10) with formula (1), formula (2) and formula (3) respectively to obtain the real stress field of the crack tip neighborhood of the crack tip stress field correction model, expressed as:

[0035]

[0036]

[0037]

[0038] Optionally, the method further comprises the step of:

[0039] Step S5. According to the stress intensity factor correction principle of the CJP model, the stress intensity factor of the crack tip stress field correction model is corrected to obtain a new stress intensity factor, expressed as:

[0040]

[0041]

[0042]

[0043] K ρ *=ρ (19)。

[0044] The technical scheme of the embodiment of the application has at least the following advantages and beneficial effects:

[0045] The application considers the influence of dislocation slip accumulation and crack tip blunting on crack propagation, uses dislocation field to correct the existing CJP model, and introduces a plastic flow factor ρ to correct the displacement of the crack surface of the fatigue crack, so that the obtained crack tip stress field correction model can not only keep the description effect of the CJP model when the plastic zone is large, but also can more accurately describe the experimental plastic zone when the plastic zone is small, so as to better describe the plastic-induced closure phenomenon in the fatigue crack propagation process; meanwhile, the corrected stress intensity factor obtained based on the crack tip stress field correction model is also more accurate. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 A schematic diagram of stress on a crack tip of an existing CJP model is provided for an embodiment of the present application.

[0047] Figure 2 A schematic diagram of edge dislocation of a crack based on Bueckner theorem is provided for an embodiment of the present application.

[0048] Figure 3 A schematic diagram of edge dislocation and dislocation dipole thereof is provided for an embodiment of the present application.

[0049] Figure 4 A schematic diagram of size structure of a DENT sample in a fatigue crack propagation experiment is provided for an embodiment of the present application.

[0050] Figure 5 A horizontal displacement cloud chart in a fatigue crack propagation experiment is provided for an embodiment of the present application.

[0051] Figure 6 A vertical displacement cloud chart in a fatigue crack propagation experiment is provided for an embodiment of the present application.

[0052] Figure 7 A schematic diagram of a plastic zone of a crack tip with a pixel interval of 9 in a fatigue crack propagation experiment is provided for an embodiment of the present application.

[0053] Figure 8 A schematic diagram of a plastic zone of a crack tip with a pixel interval of 1 in a fatigue crack propagation experiment is provided for an embodiment of the present application.

[0054] Figure 9 A schematic diagram of fitting of an elastic zone of a crack tip parameter in a fatigue crack propagation experiment is provided for an embodiment of the present application.

[0055] Figure 10 A comparison diagram of plastic zone sizes of a stress field correction model and a CJP model of a crack tip when a crack length is 13.67 mm is provided for an embodiment of the present application.

[0056] Figure 11 A comparison diagram of plastic zone sizes of a stress field correction model and a CJP model of a crack tip when a crack length is 14.23 mm is provided for an embodiment of the present application.

[0057] Figure 12 A comparison diagram of plastic zone sizes of a stress field correction model and a CJP model of a crack tip when a crack length is 14.76 mm is provided for an embodiment of the present application.

[0058] Figure 13 A comparison diagram of plastic zone sizes of a stress field correction model and a CJP model of a crack tip when a crack length is 15.1 mm is provided for an embodiment of the present application.

[0059] Figure 14A plastic zone size comparison chart of the crack tip stress field correction model and the CJP model when the crack length is 15.59 mm is provided for the embodiment of the present application;

[0060] Figure 15 A plastic zone size comparison chart of the crack tip stress field correction model and the CJP model when the crack length is 15.98 mm is provided for the embodiment of the present application;

[0061] Figure 16 A plastic zone size comparison chart of the crack tip stress field correction model and the CJP model when the crack length is 16.42 mm is provided for the embodiment of the present application;

[0062] Figure 17 A plastic zone size comparison chart of the crack tip stress field correction model and the CJP model when the crack length is 16.91 mm is provided for the embodiment of the present application;

[0063] Figure 18 A plastic zone size comparison chart of the crack tip stress field correction model and the CJP model when the crack length is 17.35 mm is provided for the embodiment of the present application;

[0064] Figure 19 A plastic zone size comparison chart of the crack tip stress field correction model and the CJP model when the crack length is 17.65 mm is provided for the embodiment of the present application;

[0065] Figure 20 A relative error and experimental plastic zone area relationship diagram of the crack tip stress field correction model and the CJP model is provided for the embodiment of the present application;

[0066] Figure 21 A experimental plastic zone area and stress intensity factor K CJP,max and relationship diagram is provided for the embodiment of the present application;

[0067] Figure 22 A stress intensity factor K CJP and K CJP * trend chart with external load change is provided for the embodiment of the present application;

[0068] Figure 23 A stress intensity factor K S trend chart with external load change is provided for the embodiment of the present application;

[0069] Figure 24 A plastic flow factor p trend chart with external load cycle change is provided for the embodiment of the present application;

[0070] Figure 25 A stress intensity factor range ΔK CJPand ΔK CJP * and ΔK I trend chart of change with ΔK

[0071] Figure 26 range of stress intensity factor ΔK CJP , ΔK CJP * and ΔK I trend chart of change with crack length. DETAILED DESCRIPTION

[0072] Embodiment

[0073] Considering that the existing CJP model for describing fatigue crack propagation does not consider the influence of dislocation slip accumulation and passivation on crack propagation, and thus the effect is poor when the CJP model is used to describe the related crack propagation problem. Therefore, the embodiment provides a construction method of a crack tip stress field correction model based on the CJP model, so as to correct the existing CJP model through the dislocation field, and thus make up for the deficiency of the existing CJP model. The construction method of the crack tip stress field correction model includes the following steps:

[0074] Step S1. Establish a preliminary CJP model. In combination with the existing CJP model crack tip stress diagram shown in FIG. 1, the stress field of the CJP model under I-type loading is represented as: Figure 1

[0075]

[0076]

[0077]

[0078] In the formula, A, B, C, and F are four parameters for defining the crack tip stress field of the CJP model; r is the distance to the crack tip, and θ is the polar angle with the crack surface;

[0079] Correspondingly, the displacement field of the CJP model under I-type loading is represented as:

[0080]

[0081] In the formula, G is the shear modulus, and G=E / [2(1+υ)], E is the Young's modulus, and υ is the Poisson's ratio; u is the horizontal displacement; v is the vertical displacement; under the plane stress state, k=(3-υ) / (1+υ), and under the plane strain state, k=3-4υ.

[0082] ​Unlike the traditional Williams model, the CJP model characterizes the shielding and elastic-plastic compatibility in the plastic zone, so as to better describe the crack propagation problem related to plasticity-induced crack closure. For the existing CJP model, the stress intensity factor K F driving the crack opening is generated by the external load F , and the definition of the traditional mode I crack propagation stress intensity factor K I is the same. At the same time, due to the existence of the plastic wake, the Poisson's ratio is different, and the elastic-plastic compatibility stress is generated in the wake zone, resulting in the generation of the shear stress intensity factor K S along the side of the crack. In addition, due to the contact of the crack surface and the elastic-plastic compatibility stress, a stress intensity factor K R parallel to the crack and preventing crack propagation is generated. At this time, the expressions of the three stress intensity factors of the CJP model are as follows:

[0083]

[0084]

[0085]

[0086] T = -C; wherein T is the T stress.

[0087] Step S2. When the structure is deformed under the action of external force, dislocation movement will occur in the material. When the dislocation encounters a grain boundary obstacle to form a dislocation pile-up, the material will exhibit hardening behavior. The accumulated dislocations form a large disturbance at the grain boundary, such as voids and micro-cracks, which become the starting point of fatigue or fracture. At this time, combined with the crack edge dislocation diagram based on Bueckner's theorem shown in FIG. 1, in a continuous elastic body, cutting is performed along x = ±a, y = 0, and opposite traction forces are applied to the two opposite surfaces of the elastic body. Some material is inserted at the gap formed to simulate crack surface separation, and finally the system is connected to form a new continuous object, and the inserted material will form an edge dislocation, also known as a climbing dislocation. Figure 2

[0088] Based on the crack edge dislocation of Bueckner's theorem, the dislocation strength is equal to the opening gap, which is called the burgers (b x ,b y ) vector. Since mode I crack propagation is only subjected to opening force perpendicular to the crack, there is no shear force acting on it, so b x = 0. At this time, mode I crack propagation has a burgers vector with a dislocation strength of b y , and the corresponding dislocation field stress function is:

[0089] ​

[0090] At the same time, the dislocation intensity is defined as an unknown number p, then b y = p.

[0091] Combining Figure 3 the edge dislocation and its dislocation dipole figure shown in Fig. Figure 3 (a) The plastic effect at the crack tip is represented by two dislocation dipoles on the glide plane. To ensure the volume constancy during plastic deformation, the sum of the Burgers vectors of the two dislocations in each dipole is equal to zero, and the dislocation dipole produces an internal stress to shield the far-field load, which corresponds to the plastic shielding effect in the CJP model. Figure 3 (b) The insertion of dislocations ① and ③ is a stress source along the crack line, which causes the singularity of the stress field at the crack tip. Figure 3 (c) The single edge dislocation located at the crack tip represents the dislocation behavior of the I-type crack, and its dislocation intensity is equal to the vector sum of dislocations ① and ③ but with opposite signs to restore the non-traction state along the crack surface and eliminate the crack tip singularity, which will produce a dislocation displacement field u ⊥ .

[0092] At this time, the expression of the dislocation displacement field u ⊥ is:

[0093]

[0094]

[0095] In the above formula, the unknown number p defined above is the plastic flow factor caused by the dislocation field, which can also be represented as the crack tip blunting amount.

[0096] Under the action of external load, the actual displacement field u(x) is composed of three parts: the elastic displacement K I ∞ u e (x) caused by the far-field load, the displacement K I sh u e (x) caused by the internal stress of the crack tip plastic effect, and the geometrically necessary dislocation ρu⊥(x), therefore, the actual displacement field u(x) can also be represented as:

[0097]

[0098] In the above formula, K I sh is equivalent to the stress intensity factor in the CJP model considering the influence of the plastic zone; In the sense of K F , K R , KS The same. This embodiment uses dislocation field correction CJP model, and then characterizes the dislocation motion and crack tip blunting behavior when plastic effect exists.

[0099] Step S3. According to the dislocation motion satisfying the small deformation assumption, the dislocation stress field can be calculated by using the geometric equation in elasticity mechanics and combining the generalized Hooke's law, expressed as formula (6) and formula (7):

[0100]

[0101]

[0102]

[0103] Step S4. According to the two displacement field forms being in the elastic region and satisfying the small deformation assumption, based on Bueckner theorem, formula (6) and formula (7) are superimposed with formula (4) respectively, to obtain the real displacement field of the crack tip neighborhood of the crack tip stress field correction model, expressed as formula (8), formula (9) and formula (10):

[0104]

[0105]

[0106]

[0107] At the same time, formula (8), formula (9) and formula (10) are superimposed with formula (1), formula (2) and formula (3) respectively, to obtain the real stress field of the crack tip neighborhood of the crack tip stress field correction model, expressed as formula (11), formula (12) and formula (13):

[0108]

[0109]

[0110]

[0111] Thus, the fatigue crack tip stress field correction model based on CJP model is obtained.

[0112] Step S5. At the same time, considering that the influence of dislocation does not change the nature of the stress intensity factor of CJP model, the expression containing plastic flow factor p term is related to r. Therefore, according to the stress intensity factor correction principle of CJP model, the stress intensity factor of the above obtained crack tip stress field correction model is corrected to obtain a new stress intensity factor, expressed as formula (14):

[0113]

[0114]

[0115]

[0116] K ρ *=ρ (19).

[0117] The following section will conduct fatigue crack propagation experiments using specific specimens and explain how to solve for the new stress intensity factor K in the modified crack tip stress field model. F * K R * K S * and K ρ * The method is to intuitively demonstrate the effect of using the crack tip stress field correction model provided in this embodiment, as well as the differences between the crack tip stress field correction model and the existing CJP model.

[0118] Specifically, the samples were made of U71MnG rail steel, and their chemical composition and mechanical properties are shown in Tables 1 and 2. The samples were machined using wire cutting. Figure 4 The 1mm thick double-notched tensile (DENT) specimen was subjected to fatigue crack propagation testing on an ElectroPuls E3000 dynamic testing machine. During the test, the maximum load was 2400N, the stress ratio R was 0.1, a sinusoidal loading method was used, and the test frequency was 10Hz. Simultaneously, based on digital image correlation (DIC) technology, full-field data (i.e., crack tip displacement field data at different crack lengths) was acquired using a Dantec Q-400 3D digital image correlation system. Before the test, the first surface (the side used for DIC data acquisition) was polished and then sprayed with randomly distributed black and white speckles. The opposite surface was simply polished to facilitate tracking the crack tip position under high magnification. The DIC imaging field of view was 1624 pixels × 1202 pixels, with each pixel corresponding to an actual size of 0.0114mm.

[0119] Table 1. Mass fraction of chemical composition of U71MnG rail steel

[0120]

[0121] Table 2 Mechanical Properties of U71MnG Rail Steel

[0122]

[0123] In this embodiment, the plastic zone has a certain relationship with the stress intensity factor, which is an important parameter for describing the crack propagation rate and can be used as a comparison parameter for optimization effect. Therefore, on the basis of obtaining full-field data through fatigue crack propagation experiments, the displacement cloud map is obtained using the open source software ncorr, the displacement field data is obtained, the strain field is obtained using the two-dimensional Savitaky-Golay full-field strain solving method, and then the stress field is obtained, and the size and shape of the experimental plastic zone are obtained by substituting the Von Mises yield criterion. Among them, the transverse displacement cloud map and the longitudinal displacement cloud map are shown in Figure 5 and Figure 6 .

[0124] At the same time, considering that there is noise interference in obtaining the original displacement field data using the DIC technology, the speckle at the crack boundary will be destroyed when performing speckle analysis at a certain step and fitting area, and the displacement field data is missing, which leads to errors in the area of the plastic zone. Therefore, the BP neural network is used to fit the displacement field data in this embodiment, the gradient descent method is adopted, the best weight vector and threshold vector of the fitting sample are searched using the back propagation algorithm according to the loss function, and then the full-field displacement field is calculated. Combined with the crack tip plastic zone diagram with a pixel interval of 9 as shown in Figure 7 , the displacement field is fitted by the BP neural network to obtain an encrypted and smooth continuous displacement field, and then the size and shape of the plastic zone with a pixel interval of 1 are obtained, as shown in Figure 8 , so that the plastic zone is more consistent with the experimental plastic.

[0125] Secondly, considering that the solution of the stress intensity factor parameter has a strong sensitivity to the crack tip position and the size of the calculation area, it is crucial to obtain the accurate crack tip position and fitting area outer diameter. Therefore, the L-M nonlinear iteration method is adopted in this embodiment, the crack tip position is taken as an unknown quantity for calculation, and the relatively accurate crack tip position and parameters are obtained. Combined with the crack tip parameter fitting elastic zone diagram as shown in Figure 9 , when the crack length is 17.35 mm, the plastic field area is removed with the plastic zone boundary as the inner diameter, the fitting outer diameter is selected as 1.856 mm, which is about 0.1 times the crack length, which meets the accuracy requirement, and the four parameters A, B, C and F of the crack tip field defined in the CJP model and the plastic flow factor p introduced in the crack tip stress field correction model provided in this embodiment are solved by the L-M nonlinear iteration method, and then the corresponding stress intensity factors K F * , K R * , K S * and K ρ * are calculated and obtained.

[0126] The displacement field data at the maximum load of 2400 N is obtained by using the DIC technology, and the experimental plastic zone is obtained. The parameters A, B, C, F and p are calculated by using the elastic field data, and the theoretical plastic zone is obtained by back calculation. The shapes and sizes of the theoretical plastic zones of the CJP model and the crack tip stress field correction model are compared with the experimental plastic zone, and the results are shown in FIG. 1, wherein the CJP curve in the figure corresponds to the CJP model, and the crack tip stress field correction model curve corresponds to the crack tip stress field correction model. Figures 10-19 * When the plastic zone is large in the later stage of crack propagation, the theoretical plastic zone of the crack tip stress field correction model provided in the embodiment and the existing CJP model is basically the same as the experimental plastic zone, which proves that the crack tip stress field correction model has the description effect of the CJP model when the plastic zone is large. However, when the plastic zone is small in the early stage of crack propagation, the description effect of the crack tip stress field correction model provided in the embodiment is better, and the existing CJP model is quite different. From the comparison of the plastic zones, it can be seen that the crack tip stress field correction model has better effect in each stage of crack propagation, which makes up for the deficiency of the CJP model when the plastic zone is small in the early stage of crack propagation, and provides a more accurate basis for describing crack propagation in the plastic zone.

[0127] At the same time, based on the fact that the plastic zone area is an important parameter for describing the crack propagation rate, the plastic zone with a pixel interval of 1 is obtained by using the BP neural network, and a rectangular area with a fixed area of l x w mm 2 with a pixel interval of 1 is used. The area A e of the plastic zone is obtained by using the correlation between the points and the area in the rectangular area and the points and the area of the plastic zone = l x w x n / m mm 2 , wherein n and m are the number of pixel points of the plastic zone and the rectangle respectively, and the relative error e of the theoretical plastic zone and the experimental plastic zone is = (A p -A e ) / A e (%). At this time, the experimental plastic zone area under each crack length and its relative error are shown in Table 3.

[0128] Table 3 Plastic zone area and its relative error of experiment and theory

[0129]

[0130] ​As can be seen from Table 3, when the crack length is greater than 16.42 mm, the crack tip stress field correction model provided by the embodiment and the existing CJP model have better description effect, and the difference is small. The crack tip stress field correction model maintains the advantage of the CJP model in the wide range of elastic approximation of the crack tip field. However, when the plastic zone is small, the crack tip stress field correction model shows better description effect, especially in the early stage of crack propagation. Since the dislocation field corrects the displacement near the crack surface, it is different from the plastic effect corrected crack surface displacement. When the plastic zone is small, the dislocation accumulation phenomenon is not obvious, and the plastic effect of the crack tip is small. Therefore, by taking dislocation slip as the main part and introducing the blunting parameter, the crack tip stress field correction model shows better description effect.

[0131] Secondly, in combination with Figure 20 , it can be seen from the schematic diagram of the relative error of the crack tip stress field correction model and the CJP model and the experimental plastic zone area that the relative error of the crack tip stress field correction model almost changes within ±10%, while the relative error of the CJP model is larger when the plastic zone is small, and the maximum is about 37.8%. In combination with Figure 21 , it can be seen from the relationship diagram of the experimental plastic zone area and the stress intensity factor K CJP,max , wherein K CJP,max is the stress intensity factor corresponding to the CJP model, and K CJP = K F -K R , and correspondingly, is the stress intensity factor corresponding to the crack tip stress field correction model. The experimental plastic zone area and the stress intensity factor are almost linearly related, which can be expressed as a direct parameter for driving crack propagation. When the plastic zone is small, the crack tip stress field correction model has obvious stability and accuracy, and the curve is smoother, proving that the crack tip stress field correction model is better when the plastic zone is small.

[0132] At the same time, in combination with Figure 22 , the trend diagram of the stress intensity factor K CJP,max and under the change of external load when the crack length is 17.65 mm, under the same crack length, the stress intensity factors corresponding to the crack tip stress field correction model and the CJP model are almost the same. Under the same load, the stress intensity factor is larger during unloading than during loading. During the unloading process, the plastic zone has a reverse plastic behavior to form a cyclic plastic zone, and there is residual stress in the plastic zone. The larger the plastic zone, the greater the residual stress, and the stronger the resistance to external load, resulting in a larger stress intensity factor during unloading. At the same time, by comparing the difference between the stress intensity factors before and after correction under different loads, K CJPThe change is small, indicating that the dislocation correction is independent of the plasticity correction of the CJP model, and the dislocation correction is correct, and the plasticity-induced closure and elastic-plastic compatible stress are independent influencing factors. However, the dislocation field has a greater impact on K S , and K S is formed due to the shear stress intensity factor generated by the elastic-plastic compatible stress in the plastic wake zone, which points to the crack tip when the crack is closed and deviates from the crack tip when the crack is opened. Dislocation slip occurs when dislocations move towards the crack tip under external load. Once the dislocation occurs, it is difficult to reverse, and the two forms exist independently, making K S form a change trend diagram as shown in Figure 23 .

[0133] In addition, in combination with the change trend diagram of the plastic flow factor p shown in Figure 24 , the plastic flow factor p increases with the increase of the external load, and under the same load, the plastic flow factor p is larger when the crack length is 17.65mm than when it is 17.35mm, indicating that the plastic flow factor p increases with the increase of the stress intensity factor, and also indicating that the crack tip blunting is more serious. At the same time, Figure 25 shows the stress intensity factor range ΔK CJP of the CJP model and the stress intensity factor range ΔK CJP of the crack tip stress field correction model. * With the change of the traditional stress intensity factor range ΔK I , the crack tip stress field correction model and the CJP model have the same change trend, but when ΔK I is small, the crack tip stress field correction model shows better stability and accuracy. Secondly, Figure 26 shows the change trend diagram of the stress intensity factor with the change of the crack length. In the initial stage of crack propagation, ΔK CJP obtained by the CJP model is larger than ΔK I , reflecting the influence of the shielding effect of additional stress in the CJP model, i.e. the influence of the coordinated stress induced by the tail contact and elastic-plastic boundary behind the crack tip, and the stress intensity factor range ΔK CJP * of the crack tip stress field correction model shows better stability and accuracy. When the crack length exceeds 17.35mm, it is lower than the traditional stress intensity factor, and when the plastic zone is large, the residual stress will reduce the stress intensity factor generated by the external load, and reduce the crack propagation rate.

[0134] It can be seen that, by considering the influence of dislocation slip accumulation and crack tip blunting on crack propagation, the dislocation field is used to modify the existing CJP model, and the plastic flow factor p is introduced to modify the displacement of the crack surface of the fatigue crack, so that the obtained crack tip stress field correction model can not only keep the description effect of the CJP model when the plastic zone is large, but also can more accurately describe the experimental plastic zone when the plastic zone is small, so as to better describe the plastic-induced closure phenomenon appearing in the fatigue crack propagation process; at the same time, the modified stress intensity factor obtained based on the crack tip stress field correction model is also more accurate.

[0135] The above only is the preferred embodiment of the present application, and is not used to limit the present application, for the person skilled in the art, the present application can have various changes and changes. Any modification, equivalent replacement, improvement, etc. within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A method for constructing a modified crack tip stress field model based on the CJP model, characterized in that, Includes the following steps: Step S1. Establish a preliminary CJP model; The stress field of the CJP model under type I loading is expressed as follows: In the formula, A, B, C, and F are four parameters defining the stress field at the crack tip in the CJP model; r is the distance to the crack tip, and θ is the polar angle with the crack surface. Correspondingly, the displacement field of the CJP model under type I loading is expressed as: In the formula, G is the shear modulus, and G=E / [2(1+υ)], E is Young's modulus, υ is Poisson's ratio; u is horizontal displacement; v is vertical displacement; under plane stress, k=(3-υ) / (1+υ), under plane strain, k=3-4υ; Step S2. Based on Bueckner's theorem, dislocations at the crack edge, type I crack propagation has a dislocation strength of b. y The Burgers vector, and the corresponding dislocation field stress function are: If we define the dislocation strength as ρ, then we have b y =ρ; At this time, the dislocation displacement field u ⊥ The expression is: In the formula, ρ is the plastic flow factor caused by the dislocation field; Step S3. Based on the assumption that dislocation motion satisfies small deformation, the dislocation stress field is calculated using equations (6) and (7), and expressed as: Step S4. Superimpose equations (6) and (7) with equation (4) respectively to obtain the true displacement field in the crack tip neighborhood of the crack tip stress field correction model, expressed as: Simultaneously, equations (8), (9), and (10) are superimposed with equations (1), (2), and (3) respectively to obtain the true stress field in the crack tip neighborhood of the crack tip stress field correction model, expressed as:

2. The method for constructing the crack tip stress field correction model based on the CJP model according to claim 1, characterized in that, It also includes the following steps: Step S5. Based on the stress intensity factor correction principle of the CJP model, the stress intensity factor of the crack tip stress field correction model is corrected to obtain a new stress intensity factor, expressed as: K ρ * =p (19).

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