A method for predicting the life of fatigue failure in a metal material

Abstract

The application discloses a kind of life prediction methods of fatigue failure inside metal material, comprising: one, obtaining the stress-life fitting formula of metal material under constant load condition;Two, obtain the initial gibbs free energy change equation;Three, obtain the plastic strain energy density under periodic load loading condition;Four, correct the crack surface energy in initial gibbs free energy change equation;Five, estimate crack initiation life;Six, verify the accuracy of the crack initiation life obtained.The application establishes the relationship based on gibbs free energy change and energy evolution when internal crack initiation, then combines the plastic strain energy density under cyclic loading condition calculated by crystal plastic finite element, and then corrects the initial gibbs free energy change equation based on energy efficiency factor evaluation, establishes the micro internal fatigue crack initiation life prediction model, estimates and verifies the fatigue life of metal material, meets the mechanical structure environment-high performance-long life design requirements.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of metal material fatigue failure, and particularly relates to a metal material internal fatigue failure life prediction method. BACKGROUND

[0002] With the progress of science and technology, mechanical structures such as aerospace, automobiles and nuclear energy are facing the needs of 'lightweight', 'environmental adaptability' and 'longevity', which are directly related to the service performance, service life and safety reliability of the mechanical structures. For the mechanical structures, the structural materials will be affected by complex environment and other factors during the service, and then high-cycle environmental-fatigue coupling damage occurs, which greatly restricts the development needs of high performance-high durability-low maintenance cost of the mechanical structures, and breakthroughs are urgently needed in the aspects of material selection, failure diagnosis and life prediction of the structures. In addition, the traditional mechanical structures are established on the strength criterion of'safety factor of 2' or'static design and dynamic calibration', which has been far unable to meet the requirements of long life prediction of the mechanical structures and materials under complex service environments. Therefore, on the premise of clarifying the fatigue coupling damage mode, law and mechanism of the metal structures and materials, based on the theories and methods of multiple disciplines, the environmental-fatigue damage evolution equation of the metal materials is revealed, analyzed and constructed, the high fatigue life fatigue coupling damage evaluation method based on the failure mechanism is formed, and the design requirements of environmental-high performance-long life of the mechanical structures are met. SUMMARY

[0003] The technical problem to be solved by the application is to provide a metal material internal fatigue failure life prediction method to solve the above problems in the prior art. The relationship between the Gibbs free energy change and the energy evolution of the internal crack initiation is established, then the plastic strain energy density under the cyclic loading condition is calculated by combining the crystal plastic finite element, the initial Gibbs free energy change equation is modified based on the energy efficiency factor evaluation, the mesoscopic internal fatigue crack initiation life prediction model is established, the fatigue life of the metal material is predicted and verified, the high fatigue life fatigue coupling damage evaluation method based on the failure mechanism is formed, and the design requirements of environmental-high performance-long life of the mechanical structures are met.

[0004] To solve the above technical problems, the technical scheme adopted by the application is that a metal material internal fatigue failure life prediction method is provided, characterized by comprising the following steps:

[0005] Step one, obtaining the stress-life fitting formula of the metal material under the constant load condition: according to the metal material fatigue test standard, the constant load fatigue test under the periodic load loading condition is carried out, the obtained test data is plotted in the coordinate system, and the stress-life curve and fitting formula of the metal material under the constant load loading condition are obtained by linear fitting, that is, lgσ a= AlgN f + B; wherein, σ a is the stress amplitude, N f is the fatigue life corresponding to the stress amplitude, and A and B are fitting parameters.

[0006] Step two, obtaining the initial Gibbs free energy change equation: combining the Gibbs free energy theory, Mura and Nakasone's theory, the energy evolution equation of the internal crack initiation process of the metal material under the condition of applying periodic load is obtained as ΔG = - W e -W d + 2c vir γ s ; wherein, ΔG is the Gibbs free energy change, W e is the elastic energy released by the material when the crack opens, W d is the internal energy stored in the lattice defects of the metal material, c vir is the value of 1 / 2 of the virtual crack length, γ s is the crack surface energy.

[0007] Step three, obtaining the plastic strain energy density under the condition of periodic load: a polycrystalline representative volume element model is established by using finite element software, the polycrystalline representative volume element model is discretized by using Lagrangian solid elements, and periodic load is applied to the discretized polycrystalline representative volume element model. The element with the highest plastic strain energy density value is taken as the critical element of crack initiation, and the plastic strain energy density of the critical element is and wherein, Δτ is the local shear stress variation range, and Δγ p is the plastic shear strain variation range of the corresponding position.

[0008] Step four, correcting the crack surface energy in the initial Gibbs free energy change equation, the process is as follows:

[0009] Step 401, assuming that all dislocation dipoles in the slip band of the metal material will affect crack initiation, the number of dislocation dipoles in a single slip band is n eq , and wherein, b is the Burgers vector, W eq is the strain energy stored by the dislocation dipole in the single slip band, d is the grain size, h is the slip band width, and μ is the shear modulus.

[0010] Step 402, when the crack initiation ends, according to the Murakami theory, the crack characteristic length is then the relationship between the lowest surface energy causing crack initiation and W eq is

[0011] Step 403, crack length and the relationship between the absolute value of the Burgers vector b and the dislocation number n is c The expression of the dislocation number n obtained by combining step 401 and step 402 is c The expression of the crack surface energy γ obtained by further obtaining the crack surface energy γ is s

[0012] Step five, estimate the crack initiation life: according to the mechanical structure of the metal material, the energy efficiency factor f of the metal material remains constant, and the energy evolution equation in step two can be converted into

[0013]

[0014] The partial derivative of the formula is

[0015]

[0016] When the energy stored by the dislocation dipole and the crack initiation energy are in equilibrium, that is, , the Gibbs free energy change ΔG is maximum, then

[0017]

[0018] N is the crack initiation life N i at this time.

[0019] In addition, Δτ·Δγ p is twice the plastic strain energy density of the critical unit , then

[0020] Step six, verify the accuracy of the obtained crack initiation life: take the test fatigue life as the horizontal coordinate and the estimated crack initiation life as the vertical coordinate to establish a coordinate system, and mark the ratio of the estimated crack initiation life to the test fatigue life when the metal material in the mechanical structure fails internally in the coordinate system. The ratio of the estimated crack initiation life to the test fatigue life when the metal material in the mechanical structure fails internally is within the 3 times line boundary, and the estimated crack initiation life is the internal fatigue failure life of the metal material.

[0021] The above-mentioned metal material internal fatigue failure life prediction method is characterized in that: in step two, the elastic energy W e released by the material when the crack opens includes the energy contained in the dislocation itself and the energy contained in the interaction between the dislocation dipoles, so W e ​​​​​Wherein, d is the grain size, v is the Poisson's ratio, k is the critical shear stress of slip initiation, N is the cycle number of cyclic loading, and ζ is a constant.

[0022] The life prediction method of internal fatigue failure of the metal material has the characteristics that, in step two, according to the theory of Fine and Bhat, W d is W d = 2c vir Nδ; wherein δ is the energy stored by the virtual crack at the end of each cycle.

[0023] The life prediction method of internal fatigue failure of the metal material has the characteristics that, according to the restoring force characteristic curve under the periodic load, δ is In the formula, f is the energy efficiency factor, and h is the slip band width.

[0024] The life prediction method of internal fatigue failure of the metal material has the characteristics that, in step two, according to the relationship between the dislocation accumulation width and the virtual crack length, the virtual crack length W

[0025] The beneficial effects of the present application are that by establishing the relationship between the Gibbs free energy change and the energy evolution when the internal crack is initiated, then combining the plastic strain energy density under the cyclic loading calculated by the crystal plastic finite element, and further modifying the initial Gibbs free energy change equation based on the energy efficiency factor, a mesoscopic internal fatigue crack initiation life prediction model is established to predict and verify the fatigue life of the metal material, a high fatigue life fatigue coupling damage evaluation method based on the failure mechanism is formed to meet the design requirements of mechanical structure environment-high performance-long life.

[0026] The technical solutions of the present application will be further described in detail below with the help of the drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 Fig. 4 is a relationship diagram of the maximum plastic strain energy density and the cycle number of the metal material SLM-IN718 in the simulation analysis of the present application when the slip system is (111) [-110].

[0028] Figure 2 Fig. 5 is a relationship diagram of the maximum plastic strain energy density and the cycle number of the metal material SLM-IN718 in the simulation analysis of the present application when the slip system is (111) [0-11].

[0029] Figure 3 Fig. 6 is a comparison diagram of the predicted fatigue life and the test fatigue life of the metal material SLM-IN718 in the simulation analysis of the present application.

[0030] Figure 4A flow chart of the method of the present application. DETAILED DESCRIPTION

[0031] As shown in the life prediction method of internal fatigue failure of a metal material, the method comprises the following steps: Figures 1 to 4

[0032] Step one, obtaining a stress-life fitting formula of the metal material under constant load conditions: according to the metal material fatigue test standard, performing a constant load fatigue test under periodic load conditions, plotting the obtained test data in a coordinate system, and obtaining a stress-life curve and a fitting formula of the metal material under constant load conditions by linear fitting, i.e., lgσ a = AlgN f +B; wherein, σ a is a stress amplitude, N f is a test fatigue life corresponding to the stress amplitude, and A and B are fitting parameters.

[0033] Step two, obtaining an initial Gibbs free energy change equation: combining the Gibbs free energy theory and the theories of Mura and Nakasone, an energy evolution equation of the internal crack initiation process of the metal material under the condition of applying periodic load is obtained, i.e., ΔG = -W e -W d + 2c vir γ s ; wherein, ΔG is the Gibbs free energy change, W e is the elastic energy released by the crack opening, W d is the internal energy stored in the lattice defects of the metal material, c vir is 1 / 2 of the virtual crack length value, and γ s is the crack surface energy.

[0034] Step three, obtaining the plastic strain energy density under periodic load conditions: a polycrystalline representative volume element model is established by using a finite element software, the polycrystalline representative volume element model is discretized by using Lagrangian solid elements, periodic load is applied to the discretized polycrystalline representative volume element model, and the element with the highest plastic strain energy density value is taken as the critical element of crack initiation, then the plastic strain energy density of the critical element is and wherein, Δτ is a local shear stress variation range, and Δγ p is a plastic shear strain variation range of the corresponding position.

[0035] Step four, correcting the crack surface energy in the initial Gibbs free energy change equation, the process is as follows:

[0036] ​Step 401, assuming that all dislocation dipoles in the metal material slip band affect crack initiation, the number of dislocation dipoles n in a single slip band eq , and Where b is the Burgers vector, W eq is the strain energy stored by dislocation dipoles in a single slip band, d is the grain size, h is the slip band width, and μ is the shear modulus.

[0037] Step 402, when crack initiation is complete, according to the Murakami theory, the crack characteristic length is The minimum surface energy that leads to crack initiation The relationship between W eq and b is

[0038] Step 403, the relationship between crack length and the absolute value of the Burgers vector b and the number of dislocations n c is Combining step 401 and step 402, the expression for the number of dislocations n c is Further, the expression for the crack surface energy γ s is

[0039] Step five, estimate the crack initiation life: according to the mechanical structure of the metal material, the energy efficiency factor f of the metal material remains constant, combining the formulas in steps three and four, the energy evolution equation in step two can be converted to

[0040]

[0041] Taking the partial derivative of the formula gives

[0042]

[0043] When the energy stored by the dislocation dipole and the crack initiation energy are in equilibrium, i.e. , the Gibbs free energy change ΔG is maximum, then

[0044]

[0045] Get N at this time is the crack initiation life N i ;

[0046] In addition, Δτ·Δγ p is twice the plastic strain energy density of the critical unit, then

[0047] Step six, verifying the accuracy of the obtained crack initiation life: taking the test fatigue life as the horizontal coordinate and the estimated crack initiation life as the vertical coordinate, a coordinate system is established, the ratio of the estimated crack initiation life to the test fatigue life when the metal material in the mechanical structure is internally failed is marked in the coordinate system, and the ratio of the estimated crack initiation life to the test fatigue life when the metal material in the mechanical structure is internally failed is located within 3 times the line boundary, so that the estimated crack initiation life is obtained as the internal fatigue failure life of the metal material.

[0048] The present application establishes the relationship between the Gibbs free energy change and the energy evolution when the internal crack is initiated, then combines the plastic strain energy density under the cyclic loading condition calculated by the crystal plastic finite element, and further modifies the initial Gibbs free energy change equation based on the energy efficiency factor evaluation, to establish the mesoscopic internal fatigue crack initiation life prediction model, estimate and verify the fatigue life of the metal material, form the high fatigue life fatigue coupling damage evaluation method based on the failure mechanism, and meet the mechanical structure environment-high performance-long life design requirements.

[0049] In the stress-life curve in step one, a coordinate system is established by taking the test fatigue life as the horizontal coordinate and the stress amplitude as the vertical coordinate.

[0050] In actual use, the fatigue fracture process of the metal material under the periodic load can be regarded as the process of forming a new surface of the material, and the fatigue load involves repeated loading and unloading processes; and Mura and Nakasone believe that the dislocation dipole formed by the reverse slip in the unloading process will continuously accumulate with the continuous application of the load, so the energy evolution equation in step two can be obtained.

[0051] In step three, based on the selected constitutive equation fitting material parameters, when the stress-strain relationship calculation value and the measured value are consistent, it indicates that the set of material parameters can be used for subsequent plastic strain energy density calculation. By modifying the load spectrum, the model is subjected to cyclic loading, and the plastic strain energy density of the grain under the cyclic loading is a very important parameter in the crystal plastic finite element calculation result, which has been used to predict the crack initiation life. A single grain has a specific grain orientation, so in the simulation calculation process, the element with the highest plastic strain energy density value can be regarded as the critical position of crack initiation, and the maximum plastic strain energy density value will tend to be stable after a certain cycle. When the maximum plastic strain energy density value is stable, the calculation results of the model in different cycle load cycles are similar, so the calculation results at this time can be used for subsequent analysis and research, so the corresponding Δτ and Δγ p to calculate the plastic strain energy density.

[0052] As Figure 1 and Figure 2As shown, the maximum plastic strain energy density of different slip systems at a certain location varies with the number of cycles within the first 25 cycles. It can be seen that, as... Figure 1 As shown, the maximum plastic strain energy density on the slip system along the slip direction [-110] of the slip surface (111) increases with the number of cycles, while as Figure 2 As shown, the maximum plastic strain energy density on the slip system of slip surface (111) in the slip direction [0, -1, 1] decreases with increasing cycle number, and both tend to stabilize when the load number is greater than 15 cycles. In the simulation analysis of the ultra-high cycle fatigue characteristics of metallic material SLM-IN718, in order to reduce the calculation cost, the stress and strain state when the maximum plastic strain energy density is stable is used as a reference, instead of calculating the entire ultra-high cycle fatigue cycle. Therefore, the calculation results of the 20th cycle are used as the basis in the subsequent analysis.

[0053] In step four, the slip band is a band composed of a set of parallel slip lines. When a crystal slips under shear stress, microscopic steps are formed on the crystal surface. Under a microscope, these appear as fine lines called slip lines. Slip lines often appear in groups, forming slip bands. Slip bands are an important characteristic of plastic deformation in crystals.

[0054] In step five, starting from the initial moment of crack initiation, a positive Gibbs free energy change ΔG indicates the existence of an energy threshold for determining whether a crack has initiated. The free energy is at its maximum when the energy contained in the dislocation dipole and the energy for crack initiation are in equilibrium. Subsequently, as the cyclic load continues to be applied, the crack free energy gradually decreases, and the dislocation dipole structure becomes unstable at the moment of complete crack initiation. Therefore, the moment of maximum Gibbs free energy is taken as the moment of complete crack initiation. In short, G for crack initiation increases with crack growth and reaches a critical value at that point. In step five, the energy efficiency factor of the metal material in the mechanical structure is obtained. Where, σ max E represents the maximum load value applied, and E is the elastic modulus.

[0055] It should be noted that, as Figure 3 As shown in the comparison graph of the estimated fatigue life and experimental fatigue life of SLM-IN718 for metallic materials, R represents the stress ratio, i.e., the ratio of the minimum stress value to the maximum stress value; the 3x line is the standard for verifying the accuracy in the fatigue life test. The coordinate system is with the experimental fatigue life as the horizontal axis (x) and the estimated crack initiation life as the vertical axis (y). The dashed line in the graph represents the boundary when y = x, and the two solid lines represent the boundary when y = 3x. The lines of time.

[0056] In this embodiment, in step two, the elastic energy W released by the material when the crack opens eW = W dislocation + W dislocation dipole e is where d is the grain size, v is the Poisson's ratio, k is the critical shear stress for slip initiation, N is the number of cycles of loading, and ζ is a constant.

[0057] In this embodiment, in step two, according to the theory of Fine and Bhat, W d is W d = 2c vir Nδ; where δ is the energy stored in the virtual crack at the end of each cycle.

[0058] In this embodiment, according to the restoring force characteristic curve under periodic loading, δ is where f is the energy efficiency factor and h is the slip band width.

[0059] In this embodiment, in step two, according to the relationship between the dislocation pile-up width and the virtual crack length, the virtual crack length L is obtained as

[0060] The above description is only the preferred embodiment of the present application, and does not limit the present application in any way. Any simple modification, change, and equivalent structural change made according to the technical essence of the present application to the above embodiments are still within the protection scope of the technical solution of the present application.

Claims

1. A method of life prediction of fatigue failure inside a metal material, characterized by, The method comprises the following steps: Step one, obtaining the stress-life fitting formula of the metal material under the condition of loading constant load: according to the metal material fatigue test standard, the constant load fatigue test under the condition of periodic load is carried out, the obtained test data is plotted in the coordinate system, and the stress-life curve and fitting formula of the metal material under the condition of loading constant load are obtained by linear fitting lgσ a = AlgN f +B; wherein, σ a is the stress amplitude of loading, N f is the test fatigue life corresponding to the stress amplitude of loading, and A and B are fitting parameters; Step two, obtain the initial Gibbs free energy change equation: combined with the Gibbs free energy theory, Mura and Nakasone's theory, the energy evolution equation of the internal crack initiation process of the metal material under the condition of applying periodic load is obtained as ΔG = -W e -W d + 2c vir γ s ; wherein, ΔG is the Gibbs free energy change, W e is the elastic energy released by the material when the crack is opened, W d is the internal energy stored in the lattice defects of the metal material, c vir is the value of 1 / 2 of the virtual crack length, γ s is the crack surface energy; Step three, obtaining the plastic strain energy density under the condition of periodic load: a polycrystalline representative volume element model is established by using a finite element software, the polycrystalline representative volume element model is discretized by using Lagrangian solid elements, periodic load is applied to the discretized polycrystalline representative volume element model, and the element with the highest plastic strain energy density value is taken as a critical element of crack initiation, and the plastic strain energy density of the critical element is and wherein Δτ is a local shear stress variation range, Δγ p is a plastic shear strain variation range of a corresponding position. Step four, correct the crack surface energy in the initial Gibbs free energy change equation, the process is as follows: Step 401, assuming that all dislocation dipoles in the metal material slip band will affect crack initiation, the number of dislocation dipoles n in a single slip band eq , and where b is the Burgers vector, W eq is the strain energy stored by the dislocation dipole inside a single slip band, d is the grain size, h is the slip band width, and μ is the shear modulus; Step 402, when the crack initiation ends, according to the Murakami theory, the crack characteristic length is The minimum surface energy leading to crack initiation is The relationship between W eq and W Step 403, crack length And the relationship between the absolute value of the Burgers vector b and the dislocation number n c Is Combined with step 401 and step 402, the expression of the dislocation number n c Is Further, the expression of the crack surface energy γ s Is Step five, estimate the crack initiation life: according to the mechanical structure of the metal material, the energy efficiency factor f of the metal material remains constant, combined with the formula in step three and step four, the energy evolution equation in step two can be transformed into The partial derivative of the formula is When the energy stored by the dislocation dipole is in equilibrium with the crack initiation energy, i.e. the Gibbs free energy change ΔG is maximum, then Obtained N is the crack initiation life N i ; Further, Δτ·Δγ p is twice the plastic strain energy density of the critical element ​ Step six, verify the accuracy of the obtained crack initiation life: take the test fatigue life as the horizontal coordinate and the estimated crack initiation life as the vertical coordinate to establish a coordinate system, mark the ratio of the estimated crack initiation life to the test fatigue life of the metal material in the mechanical structure when internal failure occurs in the coordinate system, and the ratio of the estimated crack initiation life to the test fatigue life of the metal material in the mechanical structure when internal failure occurs is within 3 times the line boundary, so that the estimated crack initiation life is the internal fatigue failure life of the metal material.

2. The method of life prediction of internal fatigue failure of a metal material according to claim 1, characterized in that: The elastic energy W released by the material when the crack opens in step two e including the energy contained in the dislocation itself and the energy contained in the interaction between dislocation dipoles, then W e is where d is the grain size, v is the Poisson's ratio, k is the critical shear stress for slip initiation, N is the number of cycles of applied load, and ζ is a constant.

3. The method of claim 1, wherein: In step two, according to the theories of Fine and Bhat, W d For W d =2c vir Nδ; where δ is the energy stored in the virtual crack after each cycle.

4. The method of life prediction of fatigue failure in a metal material according to claim 3, characterized in that: According to the restoring force characteristic curve under the periodic load, δ is In the formula, f is an energy efficiency factor, and h is a slip band width.

5. The method of claim 1, wherein: In step two, according to the relationship between the dislocation pile-up width and the virtual crack length, the virtual crack length is obtained

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