Notched part fatigue life prediction method based on energy gradient

Abstract

The invention discloses a notched part fatigue life prediction method based on energy gradient. The notched part fatigue life prediction method comprises the steps of determining a critical plane based on an energy method; determining a size effect influence factor based on the energy gradient and the notch geometric parameters; and determining damage parameters. According to the method, the concept of strain energy gradient factors is proposed to describe complex non-uniform energy distribution around the notch, and the influence of stress and strain changes on the fatigue life is well reflected; quantifying different contributions of shear and normal strain energy to damage by using an energy ratio on a critical surface; and introducing a size effect factor to quantify the influence of the size effect on the fatigue life of the notched test piece by combining an energy gradient factor and a notched size parameter.

Description

Technical Field

[0001] The invention relates to a multi-axis fatigue life prediction technology, and in particular to a notched component fatigue life prediction method based on energy gradient. Background Art

[0002] At present, new progress has been made in the study of fatigue strength of notched parts under multiaxial loads, and the life prediction models developed are mostly the coupling of several commonly used methods. Some people reviewed and compared the critical plane method, local stress / strain method, critical distance theory, stress gradient method and weighted control parameter method, providing a reference for future notch fatigue analysis. So far, the stress gradient method mainly uses the relative stress gradient method and the normalized stress gradient method to characterize the notch effect under multiaxial load. Some people use the normalization idea to propose the definition of stress gradient influencing factor, associate the fatigue life of notched and smooth specimens, and establish a fatigue life prediction model for notched parts considering the average stress effect. Based on the relative stress gradient, some people introduce a weight function in the critical distance theory to consider the contribution of different positions in the effective damage zone to fatigue damage, and propose a low-cycle fatigue life prediction model for predicting TA19 notched specimens. Some people have re-explained the critical distance based on their original work, which is more suitable for fatigue life analysis of notched parts. On this basis, some people use the critical distance theory and critical plane method to estimate the fatigue life of notched parts under variable amplitude load conditions. The novelty is that many theoretical works in the past are integrated in a formal way. Some people have analyzed and compared the influence of different coupling sequences of critical distance theory and critical surface method on the fatigue life prediction accuracy of notched parts.

[0003] In addition, another important effect that appears in pairs with the notch effect is the size effect. Some people simulated the non-uniform stress field of notched parts, described in detail the notch support effect based on the stress gradient effect, and then characterized the size effect. Finally, an estimation model was established with the help of local probability method. On this basis, some people used a similar method to propose a fatigue life estimation model framework for notched parts considering the size effect. In particular, a new effective stress was used to describe the non-uniform stress distribution state at the notch. In recent years, more and more attention has been focused on statistical size and size effects, because both have a major impact on fatigue life. Some people simultaneously considered statistical and geometric size effects, established the weakest link model under low-cycle fatigue life conditions, and used the Bayesian inference method to correct the model parameters to improve the accuracy of the model. Similarly, some people used the stress field intensity method to perform fatigue analysis of notched parts, developed a new weight function considering the crack initiation effect, discussed the relationship between the effective radius of the fatigue damage area and the fatigue life, and finally established an estimation model considering statistical and geometric size effects.

[0004] A large number of experiments have shown that during non-proportional cyclic loading, the principal strain axis will rotate, and the material will show non-proportional additional strengthening that will not appear in uniaxial and any proportional loading process, resulting in a reduction in fatigue life. Therefore, in the process of fatigue strength analysis, it is particularly important to study non-proportional additional strengthening. Some people regard the two factors that affect the reduction of life under non-proportional loading, namely the rotation of the principal strain axis and the additional hardening of the material, as two independent factors affecting multi-axial fatigue damage, and propose a new non-proportional influence parameter to characterize the comprehensive influence. Some people have summarized some important non-proportional effects and given a new non-proportional description. Based on the π-plane projection path of the loading path, a new multi-axial fatigue damage parameter is finally proposed. Some people have proposed a refined equivalent deformation criterion in the process of non-proportional loading fatigue analysis. This criterion takes into account non-proportional additional cyclic hardening and strain amplitude, and uses Ti-6Al-4V specimens for multi-axial loading tests to verify the accuracy of the proposed criterion. In this regard, some people have proposed a new refined equivalent deformation criterion for fatigue life of engineering components, which is applicable to two different metals with different non-proportional sensitivities. Some people have conducted multiaxial low-cycle fatigue tests on commercial pure titanium under stress control conditions. The results show that the non-proportional strengthening coefficient of the material is independent of the control model, and that under this load, the critical plane is consistent with the maximum principal stress plane observed under an optical microscope.

[0005] Most fatigue analyses of notched parts only consider the effect of stress gradient on fatigue life, and most multiaxial fatigue damage parameters are simple combinations of stress and strain. In fact, it is incomplete to use stress or strain alone to describe the effect of notch effect on fatigue strength. In this regard, energy-based damage parameters can be used for low-cycle and high-cycle fatigue life prediction because they integrate stress and strain components, and the irreversible deformation that usually causes fatigue damage will eventually react through energy accumulation. Fatigue life prediction models based on energy methods, including plasticity and total strain energy density, have been widely used in fatigue life prediction under different materials and loading conditions. Some people have conducted fracture tests on nickel-based single crystal high-temperature alloys, using shear strain and strain energy damage parameters to simulate crack propagation orientations. The results show that the results obtained by strain energy parameters are more consistent with the test results, and the important conclusion that the fracture surface and slip surface coincide is obtained. Similarly, some people use stress, strain and strain energy parameters to analyze the fatigue life of isotropic metal materials, and select 12 sets of fatigue test data to estimate and compare damage parameters. The results show that strain energy parameters have the best correlation coefficient fitting characteristics. It can be seen that compared with strain and stress parameters, energy parameters have obvious prediction advantages. Based on the critical surface method, an improved strain energy density model was established. In particular, the procedures for normal and shear strain energy density were determined. The results show that the new model can be well applied to most materials and loading paths. Some people use inherent dissipation as a damage factor for multiaxial fatigue analysis and establish a dedicated fatigue life model based on energy dissipation. Experimental verification shows that the new model has a good prediction effect for any loading path of proportional and non-proportional loading. Based on this study, some people compared the critical surface method with the dissipated energy method and established a new energy model. Finally, it was found that the developed energy model has a better prediction effect. Some people evaluate fatigue damage by considering the different rates of dissipated energy under shear and tensile strains, and propose a multiaxial fatigue life prediction model based on energy dissipation.

[0006] However, if only the influence of stress or strain is considered, the impact of notch effect on fatigue life cannot be fully characterized.

[0007] Classical model based on energy and critical surface method:

[0008] Someone first proposed the concept of the energy method, and believed that the continuous accumulation of plastic energy would lead to irreversible fatigue damage, and that it was the main cause of fatigue damage. On this basis, some people pointed out that regardless of uniaxial or multiaxial loading, the plastic energy absorbed by the material in each cycle is equal. Someone proposed the theory of total strain energy, pointing out that there is a certain relationship between fatigue life and total strain energy. In recent years, many scholars have considered the unique advantages of the critical surface and energy methods, combined the two, and selected the strain energy on the critical surface as the damage parameter. Specific calculation parameters are as follows: Figure 1 shown.

[0009] Liu Model

[0010] Someone proposed a damage parameter based on virtual strain energy, which consists of two parts: elastic and plastic virtual strain energy. In addition, according to two typical failure modes, namely the tensile-dominated and shear-dominated models, the critical surface is defined as the plane where the maximum normal or shear strain energy is located, that is, the maximum damage plane is selected as the critical surface, which improves the problem that the original energy method is not combined with the critical surface.

[0011] Assuming that fatigue failure occurs on the plane of maximum strain energy, for the tensile-dominated failure model, the maximum damage plane, i.e., the plane with the largest normal strain energy density, is selected as the critical plane. The sum of the normal and shear strain energy densities is defined as the damage parameter, and the model can be expressed as:

[0012]

[0013] Where: f ′ and ε f ′ is the fatigue strength and fatigue ductility coefficient respectively; b and c are the fatigue strength and fatigue ductility index respectively; E is the elastic modulus of the material; Δτ and Δγ are the shear stress and shear strain ranges on the critical surface respectively; Δσ n and Δε n are the normal strain and normal stress ranges on the critical surface, respectively.

[0014] For the shear-dominated failure model, the maximum damage plane, i.e., the plane with the largest shear strain energy density, is selected as the critical plane, and its model is expressed as:

[0015]

[0016] CCB Model

[0017] Some people use energy-based damage parameters similar to the CXH model, using maximum stress instead of stress amplitude to consider the influence of average stress. In addition, the critical plane is defined as the maximum damage plane, and combined with the Manson-Coffin equation, the following fatigue life prediction model is proposed:

[0018]

[0019] Where: max and τ max represent the maximum normal and shear stresses on the critical surface respectively; ε a and γ a are the normal and shear strain amplitudes on the critical surface, respectively. Summary of the invention

[0020] The main purpose of the present invention is to provide a fatigue life prediction method for notched parts based on energy gradient, propose the concept of energy gradient factor by adopting normalization idea, and use the energy weight index on the critical surface to characterize the contribution of shear and normal strain energy to fatigue damage.

[0021] The technical solution adopted by the present invention is: a method for predicting fatigue life of notched parts based on energy gradient, comprising:

[0022] Determine critical surfaces based on energy;

[0023] Determine the size effect influencing factor based on energy gradient and notch geometry parameters;

[0024] Determine the damage parameters.

[0025] Further, determining the critical surface based on energy includes:

[0026] Determine the critical surface by searching for the slip plane at the dangerous point;

[0027] Assume that the critical plane has two rotational degrees of freedom Its initial position is in the yz plane, with the counterclockwise direction as the positive direction; the angles of rotation around the z-axis and y-axis are θ and In order to obtain the stress and strain of any plane at the dangerous point, the coordinate transformation method is used;

[0028] The stress tensor σ and strain tensor ε in the basic coordinate system xyz are:

[0029]

[0030] The coordinate transformation matrix is:

[0031]

[0032] Therefore, through the coordinate rotation matrix transformation, the stress tensor and strain tensor of any plane passing through the dangerous point in the new coordinate system x′y′z′ can be expressed as follows:

[0033] σ ij ′=Μ T σ ij Μ

[0034] εij ′=Μ T ε ij M (6)

[0035] Determine the critical surface:

[0036] The plastic strain energy on any plane at the critical point of the notch can be expressed as Function:

[0037]

[0038] make(·) a =[(·) 11 -(·) 22 ] / 2, (·) m =[(·) 11 +(·) 22 ] / 2, represents stress or strain, so the above formula is expressed as:

[0039]

[0040] By finding the stationary point of equation (8), we can obtain At the extreme point θ, Through specific calculation and analysis, the position of the critical surface is finally determined as:

[0041]

[0042] By extracting the stress and strain at the dangerous point at the root of the notch with the help of finite element software, the position of the critical surface can be deduced. Furthermore, the determination of the size effect influencing factor based on the energy gradient and the notch geometric parameters includes: using n w Characterize the size effect, the expression is:

[0043]

[0044] Furthermore, the determining of the damage parameter includes:

[0045] Determine the modified equivalent strain energy calculation method:

[0046]

[0047] Where: a0 and b0 are material constants;

[0048] The fatigue life prediction model that comprehensively considers non-proportional additional strengthening, size effect and energy gradient is proposed as follows:

[0049]

[0050] The corrected relationship between strain energy and fatigue life is expressed by a power function:

[0051] W′=a(N f ) b (25)

[0052] Where b and c are fatigue strength and fatigue ductility index, respectively.

[0053] Advantages of the present invention:

[0054] The present invention analyzes fatigue life problems based on the energy criterion combined with the critical surface method, which can overcome the defect that energy is a scalar and has clear physical meaning. Because from the energy point of view, the uneven distribution of the energy field on the crack initiation surface is the direct factor that directly affects the crack initiation behavior. The present invention proposes the concept of strain energy gradient factor to describe the complex non-uniform energy distribution around the notch, which better reflects the influence of stress and strain changes on fatigue life; uses the energy ratio on the critical surface to quantify the different contributions of shear and normal strain energy to damage; combines the energy gradient factor and the notch size parameter, and introduces the size effect factor to quantify the influence of the size effect on the fatigue life of the notch specimen. In summary, studying the energy gradient of the crack initiation surface is of great significance for accurately evaluating the fatigue performance of notch specimens.

[0055] A stress correction factor considering material properties and phase difference is introduced, and a direct damage parameter based on equivalent strain energy is determined, which better reflects the influence of non-proportional additional strengthening effect on fatigue life. Combining the energy method and critical surface method, a robust fatigue life model of notched parts under multiaxial loading is developed.

[0056] The proposed model is verified and compared with the other two models using the test data of three materials: GH4169, En8 and C40. The prediction results of the proposed model are all within the 2-fold dispersion band, which is better than the other models.

[0057] In addition to the above-described purposes, features and advantages, the present invention has other purposes, features and advantages. The present invention will be further described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] The drawings constituting a part of this application are used to provide a further understanding of the present invention. The illustrative embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0059] Figure 1 is a schematic diagram of cyclic strain energy density;

[0060] Figure 2 A flow chart for determining a critical surface of the present invention;

[0061] Figure 3 A schematic diagram of determining a critical surface by means of finite element software according to the present invention;

[0062] Figure 4 A schematic diagram of the stress distribution state near the notch of the notch member of the present invention;

[0063] Figure 5 This is a schematic diagram of energy distribution of the notch member of the present invention;

[0064] Figure 6 is a normalized curve diagram of strain energy density distribution on a cross section of the present invention;

[0065] Figure 7 It is a normalized curve diagram of strain energy density distribution on the critical surface of the present invention;

[0066] Figure 8 is an energy-based fracture mechanism diagram of the present invention;

[0067] Fig. 9 The energy weight index α and fatigue life N of the present invention are f Relationship diagram;

[0068] Fig.10 It is a schematic diagram of the gap parameter of the present invention;

[0069] Fig.11 A relationship diagram between the size influence index and the lifespan of the present invention;

[0070] Fig.12 is a fatigue life prediction flow chart of the present invention;

[0071] Fig.13 It is a schematic diagram of proportional and non-proportional loading stress-strain cycle curves of the present invention;

[0072] Fig.14 is the prediction result of the model proposed in the present invention;

[0073] Fig.15 These are the prediction results of the comparative models ((a) Liu model and (b) CCB model) used in the present invention. DETAILED DESCRIPTION

[0074] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0075] Determine the critical surface based on the energy method:

[0076] The critical surface method has attracted wide attention because it can well explain the experimental phenomenon of crack initiation and expansion on a specific plane. Generally, the definition of the critical surface is different for different damage parameters. The present invention defines the plane with the maximum total strain energy density of stress and strain components as the critical surface. Accurately determining the position of the critical surface is the key to this type of method. Generally, for different structures and loading methods, the definition of the selected critical surface is different, but a similar process can be used to search for the exact position of the critical surface. The following briefly introduces the general process of determining the critical surface.

[0077] (1) Perform finite element analysis on the component to be analyzed according to the load requirements on the component;

[0078] (2) Based on the results of finite element analysis, the stress-strain distribution state is obtained, the location of the dangerous point is determined, and the data there is extracted;

[0079] (3) Analyze and search for the exact position of the critical surface through coordinate transformation;

[0080] (4) While performing the coordinate transformation, the damage parameter elements corresponding to the selected critical surface are calculated. Finally, the proposed prediction model is used to calculate the predicted life.

[0081] Specifically, the flowchart of determining the critical surface of the present invention is as follows Figure 2 shown.

[0082] The invention determines the critical surface by means of strain energy density, and simultaneously considers the influence of stress and strain on the fatigue crack position, and proposes a simple theoretical method for determining the critical surface.

[0083] Critical plane coordinate transformation:

[0084] In fact, finding the critical surface is the process of determining the crack initiation and extension direction, and the stress and strain on the surface must be determined first, so it has certain physical significance. The present invention determines the critical surface by searching the slip plane at the dangerous point.

[0085] Assume that the critical plane has two rotational degrees of freedom Its initial position is in the yz plane, with the counterclockwise direction as the positive direction; the angles of rotation around the z-axis and y-axis are θ and In order to obtain the stress and strain of any plane at the dangerous point, the coordinate transformation method is used;

[0086] The stress tensor σ and strain tensor ε in the basic coordinate system xyz are:

[0087]

[0088] The coordinate transformation matrix is:

[0089]

[0090] Therefore, through the coordinate rotation matrix transformation, the stress tensor and strain tensor of any plane passing through the dangerous point in the new coordinate system x′y′z′ can be expressed as follows:

[0091] σ ij ′=Μ T σ ij Μ

[0092] ε ij ′=Μ T ε ij M (6)

[0093] Determine the critical surface:

[0094] The plastic strain energy on any plane at the critical point of the notch can be expressed as Function:

[0095]

[0096] To simplify the process, let (·) a =[(·) 11 -(·) 22 ] / 2, (·) m =[(·) 11 +(·) 22 ] / 2, represents stress or strain, so the above formula can be expressed as:

[0097]

[0098] By finding the stationary point of equation (8), we can obtain At the extreme point θ,

[0099] Through specific calculation and analysis, the position of the critical surface is finally determined as:

[0100]

[0101] By extracting the stress and strain at the critical point of the notch root with the help of finite element software, the position of the critical surface can be deduced. On the critical surface, a path AB is defined, and the stress and strain are extracted along the path, such as Figure 3 shown.

[0102] Notch Effect:

[0103] Energy gradient influencing factors:

[0104] The present invention proposes the concept of energy gradient influencing factor. At present, when fatigue life analysis of notched parts is performed, finite element analysis is mostly used, and the usual practice is to substitute the stress and strain of the dangerous point at the notch of the component during the stable cycle into the fatigue life prediction model for solution. However, a large number of test results show that when the notch is sharp, the fatigue analysis prediction results directly using the stress and strain data of the dangerous part at the root of the notch are always conservative.

[0105] As we all know, for notched parts, the stress drops faster near the notch root. For parts farther away from the notch root, that is, parts with lower stress gradients, they can withstand higher peak stress amplitudes within a given cyclic load, so they have longer fatigue life when subjected to the same load. This phenomenon is called the notch (support) effect. A schematic diagram of energy distribution near the notch can also be drawn, such as Figure 4 shown.

[0106] However, it must be pointed out that if only the influence of stress or strain is considered, the influence of notch effect on fatigue life cannot be fully characterized. Considering that strain energy is closely related to stress and strain, in order to fully reflect the influence of stress and strain changes in actual structures, the present invention provides a definition of strain energy gradient. Figure 5 To explore the law of energy near the notch, under multiaxial loading, the strain energy and distance on the notch bisector of the notch specimen passing the dangerous point are normalized. The normalized strain energy curve of the specified path on the cross section passing the dangerous point is as follows: Figure 6 As shown. Figure 6 In, W max is the maximum strain energy at the root of the notch, W(x) is the energy at different positions on the notch bisector, x is the distance between the specified distance (point D on the notch bisector and the dangerous point C at the root of the notch), and r is the curvature radius of the notch root. Then, the ratio of the strain energy at any position on the notch bisector to the maximum strain energy is calculated, that is, W(x) / W max , and calculate the ratio of the specified distance x to the notch radius r, that is, x / r, to establish the coordinate system W(x) / W max -x / r. After analysis, when the normalized distance of the notch root is less than 0.5, the normalized energy on the notch bisector of the samples with different notch forms is almost the same, so the energy gradient influencing factor proposed in the present invention is defined as follows:

[0107]

[0108] Where: A 0.5 It is the area enclosed by the normalized energy distribution curve on the notch bisector and the coordinate axis in the interval 0≤x / r≤0.5.

[0109] The following explains why this definition is used. On the one hand, when the energy is evenly distributed, that is, there is no stress concentration phenomenon, the energy gradient influence factor is 1. Because in this case, A in the above definition 0.5 is the area of ​​the rectangle, that is, A 0.5 =0.5×1=0.5, in fact, there is no influence of energy gradient; on the other hand, using integration to solve the area and then study the energy gradient can reduce the error caused by the derivative of the energy distribution function at the root of the notch.

[0110] Obviously, the above method gives the definition of the energy gradient influencing factor of the cross section at the notch from the energy perspective. However, after a large number of studies, it was found that the uneven energy distribution on the crack initiation surface is the direct factor affecting fatigue damage and life. Therefore, the present invention will focus on the study of the non-uniform energy distribution on the crack initiation surface (critical surface). First, determine the critical surface according to the method in Section 3. Then, extract and analyze the stress and strain state on the critical surface, calculate the equivalent strain energy, and use an exponential function to fit the non-uniform energy distribution. According to the definition method of the cross section of the notch root above, the energy gradient influencing factor on the critical surface is further given as:

[0111]

[0112] Where: A′ 0.5 is the area enclosed by the normalized curve of strain energy distribution on the critical surface and the coordinate axis in the interval 0≤x / r≤0.5. The normalized curve of energy distribution on the critical surface is shown in Figure 7 .

[0113] Energy gradient influence index:

[0114] In order to better characterize the influence of energy gradient on fatigue life, an energy gradient influence index is proposed. Some people have proposed a stress-related factor, which highlights the influence of normal stress on fatigue damage accumulation. It is well known that fatigue crack formation is a complex process, and its formation is the result of the combined action of normal stress and shear stress. Some people consider introducing a parameter, namely the stress ratio on the critical surface, as shown in formula (11). The introduction of this parameter can reflect this dynamic effect to measure the synergistic effect of different stress components on crack formation.

[0115]

[0116] Where: τ a is the shear stress amplitude on the critical surface; σ n,max is the maximum normal stress on the critical surface.

[0117] Obviously, the stress ratio on the critical surface is defined as the ratio of the maximum normal stress and shear stress amplitude on the critical surface. Drawing on the idea of ​​the above method, the present invention considers the strain energy caused by the normal stress and the shear stress respectively, such as Figure 8 As shown in the figure, it is believed that shear strain energy is the main driving force for crack initiation and expansion, while the strain energy caused by normal stress is conducive to crack expansion. Therefore, a definition of the energy ratio on the critical surface is proposed, as shown in the following formula:

[0118]

[0119] Where: Wσ ,max is the maximum normal strain energy on the critical surface, and is the shear strain energy amplitude on the critical surface.

[0120] It is worth mentioning that the influence index in formula (12) actually represents the different contributions of shear and normal strain energy to the crack propagation process, and can be considered as an energy weight index.

[0121] Analyze the test data of various materials, and the energy weight index α and fatigue life N f The relationship can be expressed as:

[0122] α=A(2N f ) B (13)

[0123] By α and N f The relationship between the energy gradient influence index and fatigue life can be fitted to obtain the constants A and B in formula (15). Fig. 9 shown.

[0124] Depend on Fig. 9 It can be seen that α and N f There is an obvious linear relationship between them.

[0125] Size Effect:

[0126] Notches have an important influence on the stress-raising effect of components subjected to cyclic loads, which poses a huge challenge to the integrity and service reliability assessment of actual mechanical structures. In addition, another important effect that appears in pairs with the notch effect is the size effect. In the fatigue life prediction of complex structures, the comprehensive consideration of the role of notch effect and size effect is more in line with engineering practice, and is more conducive to accurately grasping the design life of components, thereby helping to achieve the optimization and improvement of design schemes. For the case of structural integrity assessment, the model combining notch effect and size effect usually makes analogy analysis possible, which can avoid duplication of work and reduce the cost of large-scale or full-scale testing. For structures undergoing fatigue analysis, size effects can be divided into four categories: a) statistical size effect, which is attributed to the higher probability of defects in larger components; b) geometric size effect, which is caused by the diverse stress distribution caused by different notch geometries and parameters; c) production size effect, which is caused by manufacturing technology; d) surface size effect, which is caused by surface treatment process. In recent years, more and more attention has been focused on statistical size and geometric size effects, because both have a major impact on fatigue life. So far, various methods have been developed to consider size effects, including the weakest link theory, high stress volume model, generalized local model, etc. In particular, some people use relative stress gradient to describe the notch effect. The factor form based on relative stress gradient can be written as formula (6). Similarly, there is formula (7):

[0127]

[0128] Where: S g is the distance of the slip band in the failed particle, A and K χ is a constant fitted by the experimental data.

[0129] χ* is the relative stress gradient.

[0130] From the above description, it can be seen that the present invention characterizes the influence of notch effect on fatigue life based on energy gradient. Considering that the notch effect and size effect are usually closely related in the fatigue analysis of multi-axis notched parts, the present invention proposes to characterize the size effect by using energy gradient factor and notch geometric size. A size effect influencing factor is proposed:

[0131]

[0132] Where: R is the radius of the specimen (radius of the smooth part), t is the depth of the notch. Fig.10 shown.

[0133] From the above formula (16), it can be seen that for the same material, if is a fixed value, then we can use Y w ' to reflect the influence of size effect. For different materials, it can be used and Y w ′ reflects the size effect of different depths. It is worth pointing out that Y w ′Studying the size effect can avoid considering too many notch parameters, such as Fig.11 As shown, this method can simplify the calculation process.

[0134] In order to better characterize the contribution of size effect to fatigue damage in actual loading process, the size effect index m is proposed. Through the analysis of material test data, it is found that there is the following relationship between m and test life, as shown in the following table. Fig.11 shown.

[0135] m=A(2N f ) B (17)

[0136] Where: A and B are constants, which can be obtained by fitting the experimental data.

[0137] Finally, the present invention uses n w ′ represents the size effect, and the expression is:

[0138]

[0139] Determine the damage parameters:

[0140] Calculation of equivalent strain energy:

[0141] In recent years, the energy method has been favored by many scholars because it can better predict multiaxial fatigue life under certain circumstances. In addition, in order to make up for the key problem that the energy method is a scalar, combining the critical surface method and the energy method is an important trend in multiaxial fatigue research methods to explain the direction of crack initiation and propagation and thus improve the accuracy of fatigue life prediction.

[0142] Based on the energy gradient, the present invention proposes a damage parameter that takes several influencing factors into consideration and provides a general flow chart of such a method, such as Fig.12 .

[0143] For fatigue specimens under tension and torsion loading, the equivalent stress and equivalent strain are given based on the von Mises criterion as follows:

[0144]

[0145] Taking advantage of the fact that equivalent stress and equivalent strain can simplify the complex state at the fatigue point, a method for calculating equivalent strain energy is proposed:

[0146]

[0147] Among them: Δσ and Δε are the normal stress and strain ranges respectively; Δτ and Δγ are the shear stress and shear strain ranges respectively.

[0148] Many studies have shown that most metal materials exhibit significantly different fatigue behaviors under non-proportional loads than under proportional loads. For most materials, when in a low-cycle fatigue state, non-proportional loads will present higher stress values ​​compared to proportional loads with the same strain range, which is called additional non-proportional strengthening. In the fatigue analysis process, if the crack initiation and propagation directions of the structure are simulated and the fatigue life is estimated, it is also necessary to consider the effect of non-proportional additional strengthening on fatigue strength. On the one hand, during the non-proportional loading process, a non-proportional additional strengthening phenomenon will occur that will not occur in uniaxial and any proportional loading, such as Fig.13 As shown. Moreover, under certain conditions, non-proportional loading will produce the greatest non-proportional strengthening phenomenon. For other non-proportional loading paths, their stress-strain cycle curves are distributed between the proportional loading and non-proportional loading curves. On this basis, many scholars have concluded through experiments or theoretical analysis that under certain conditions, as the phase angle increases, the degree of non-proportional additional strengthening increases.

[0149] The present invention considers additional strengthening to propose a modified stress factor, and finally determines a direct damage parameter based on strain energy. Similarly, some people have also proposed a solution to deal with the non-proportional strengthening phenomenon. Considering the above factors, the present invention introduces a stress correction factor to correct the equivalent stress of formula (22) as follows:

[0150]

[0151] Where: n,max is the maximum normal stress on the critical surface; σ y is the yield strength; is the phase angle influencing factor. It should be emphasized that the present invention is aimed at symmetrical loading with constant amplitude, so the maximum normal stress, average normal stress and normal stress amplitude are converted to each other, so σ n,max The effect of mean stress can be described. The ratio It can characterize the additional strengthening effect caused by non-proportional loads when the material is subjected to cyclic loading. In addition, when non-proportional additional strengthening occurs, if the maximum normal stress σ n,max The larger the value, the more serious fatigue damage and shorter fatigue life will be. u increases with the increase of phase angle. For proportional loading, u = 1, which is consistent with the general rule. In summary, formula (22) considers the influence of non-proportional additional strengthening effect from three factors: material properties, loading load and phase angle.

[0152] Therefore, a modified calculation method of equivalent strain energy can be proposed:

[0153]

[0154] Where: a0 and b0 are material constants.

[0155] Determine the damage parameters:

[0156] In view of the above results, the modified formula (23) is used to calculate the damage parameters, and the fatigue life prediction model that comprehensively considers non-proportional additional strengthening, size effect and energy gradient is proposed:

[0157]

[0158] The corrected relationship between strain energy and fatigue life can be expressed by a power function:

[0159] W′=a(N f ) b (25)

[0160] Where b and c are fatigue strength and fatigue ductility index, respectively.

[0161] At present, most of the damage parameters based on the critical surface method are a combination of stress and strain, and many of them do not consider the influencing factors such as mean stress and non-proportional additional strengthening. Some people believe that a good multiaxial damage parameter should include the following characteristics: (1) It can be used in a variety of load conditions, whether it is uniaxial or multiaxial, proportional loading or non-proportional loading; (2) It can be used for low-cycle and high-cycle fatigue; (3) The damage parameter includes the mean stress effect; (4) It can characterize the properties of the material and the non-proportional additional strengthening effect; (5) It is consistent with continuous damage mechanics in terms of physical properties; (6) It does not require any additional material coefficients; (7) It depends on the loading path; (8) It can characterize the fatigue damage mechanism. In summary, since this model basically meets the conditions of a good fatigue life prediction model, this model has a good advantage in prediction compared with other models. In order to well demonstrate the accuracy and feasibility of the model, experimental data are selected to verify the results.

[0162] Results verification and discussion:

[0163] Test materials and geometric parameters:

[0164] In order to evaluate and verify the proposed damage parameters based on energy and critical surface, the present invention selects three materials, GH4169, En8 and C40, to carry out tensile and torsion tests on notched specimens. The basic mechanical and fatigue properties of the materials are shown in Table 1.

[0165] Table 1 Basic mechanical and fatigue properties of materials

[0166]

[0167] Note: υ is Poisson’s ratio, σ is y is the yield stress.

[0168] Model Validation and Comparison:

[0169] Two models based on critical surface and energy method (Liu model and CCB model) are introduced and compared with the proposed model. Fig.14 and Fig.15 shown.

[0170] Fig.15 It can be seen that the two selected models have different prediction capabilities for the three materials GH4169, En8 and C40. The prediction accuracy of the Liu model and the CCB model for different materials varies greatly, but the prediction results of the two models for GH4169 are within the 3 times tolerance band. It should be pointed out that Fig.15 It shows that the CCB model has an overly conservative prediction result for GH4169, and the Liu model has a good life prediction ability for GH4169. It is worth pointing out that for En8, the degree of stress concentration will affect the dispersion of the model prediction results. In other words, for En8, when r = 1.5mm and 3mm, that is, when the stress concentration is large, the discreteness of the prediction results is large; when r = 6mm, that is, when the stress concentration is small, the discreteness of the prediction results is small. The reason for this result can be attributed to the fact that En8 is a shear-dominated material rather than a tensile-dominated material. In particular, most of the prediction results of the Liu model are within the 3-fold tolerance band, so it has a relatively ideal prediction effect for all three materials. Its advantage can be explained by the fact that the Liu model defines different critical surfaces and shear or tensile models based on the differences in failure forms of different materials. In addition, the selection of the maximum damage surface as the critical surface may also be the reason for its improved accuracy. Most of the prediction results of the CCB model are smaller than the test results. This may be explained by the fact that, for the CCB model, the maximum values ​​of the normal stress, shear stress components and the total strain energy are selected, so the effect of strain energy on fatigue damage is overestimated, which leads to conservative life prediction results.

[0171] from Fig.14 It can be seen that the prediction results of the proposed model are all within the 2-fold dispersion band, which is better than the prediction results of the other two models. The better prediction ability of the proposed model can be explained in the following aspects. First, the proposed damage parameter comprehensively considers the size effect and the non-proportional additional strengthening effect. In addition, whether the average stress effect is considered is also an important factor in life prediction. The factor that may be critical is that the strain energy gradient effect can fully reflect the influence of stress and strain gradient in the actual structure. The proposed model does not have any additional material coefficients, so it is more convenient for practical engineering applications and provides theoretical guidance for low-cycle fatigue life prediction.

[0172] In summary, compared with the other two models based on the energy method and critical surface, this model has better low-cycle fatigue life prediction capabilities. In addition to the advantages described above, this model has two advantages. On the one hand, it is relatively simple to calculate the damage parameters. Based on equivalent stress and strain, the elastic and plastic strain energies are calculated uniformly. Even under non-proportional loading, there is no need for a complex incremental plasticity model to estimate the damage parameters; on the other hand, the general weight coefficient is usually calculated by fitting uniaxial fatigue data. The weight index proposed in the present invention draws on the idea of ​​stress ratio and introduces energy ratio to quantify the influence of shear energy component on fatigue process. The calculation process is simple. In addition, the prediction ability of this model under variable amplitude loading conditions needs to be further verified.

[0173] For fatigue analysis of notched parts, some people point out that effective damage parameters should consider several key factors that affect the damage mechanism, such as cyclic plasticity parameters, stress or strain parameters, non-proportional load parameters and average stress parameters. From this perspective, the damage parameters proposed in the present invention also have outstanding advantages.

[0174] The present invention adopts the normalization concept to propose the concept of energy gradient factor, and uses the energy weight index on the critical surface to characterize the contribution of shear and normal strain energy to fatigue damage. In addition, based on the energy gradient and notch geometry, the influence of size effect on fatigue life is considered. Considering the influence of material properties and phase difference, a new equivalent strain energy method that directly considers average stress and non-proportional additional strengthening is proposed.

[0175] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for predicting fatigue life of notched parts based on energy gradient, characterized in that: include: Determine critical surfaces based on energy; Determine the size effect influencing factor based on energy gradient and notch geometry parameters; Determine the damage parameters.

2. The energy gradient-based notched component fatigue life prediction method according to claim 1, characterized in that: Determining the critical surface based on energy includes: Determine the critical surface by searching for the slip plane at the dangerous point; Assume that the critical plane has two rotational degrees of freedom Its initial position is in the yz plane, with the counterclockwise direction as the positive direction; the angles of rotation around the z-axis and y-axis are θ and In order to obtain the stress and strain of any plane at the dangerous point, the coordinate transformation method is used; The stress tensor σ and strain tensor ε in the basic coordinate system xyz are: The coordinate transformation matrix is: Therefore, through the coordinate rotation matrix transformation, the stress tensor and strain tensor of any plane passing through the dangerous point in the new coordinate system x′y′z′ can be expressed as follows: s ij ′=M T s ij M e ij ′=M T e ij M (6) Determine the critical surface: The plastic strain energy density on any plane at the critical point of the notched part can be expressed as Function: make(·) a =[(·) 11 -(·) 22 ] / 2, (·) m =[(·) 11 +(·) 22 ] / 2, · represents stress or strain, so the above formula is expressed as: By finding the stationary point of equation (8), we can obtain At the extreme point θ, Through specific calculation and analysis, the position of the critical surface is finally determined as: By using finite element software to extract the stress and strain at the dangerous point at the root of the notch, the position of the critical surface can be deduced.

3. The method for predicting fatigue life of notched parts based on energy gradient according to claim 1 is characterized in that: The size effect influencing factors determined based on the energy gradient and the notch geometric parameters include: Use n w Characterize the size effect, the expression is:

4. The method for predicting fatigue life of notched parts based on energy gradient according to claim 1, characterized in that: Determining the damage parameter comprises: Determine the modified equivalent strain energy calculation method: Where: a0 and b0 are material constants; The fatigue life prediction model that comprehensively considers non-proportional additional strengthening, size effect and energy gradient is proposed as follows: The corrected relationship between strain energy and fatigue life is expressed by a power function: W′=a(N f ) b (25) Where b and c are fatigue strength and fatigue ductility index, respectively.

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