CN115841857A - Method for predicting service life of internal fatigue failure of metal material - Google Patents

Abstract

The invention discloses a life prediction method for internal fatigue failure of metal materials, comprising: 1. Obtaining the stress-life fitting formula of the metal material under the condition of constant load; 2. Obtaining the initial Gibbs free energy change equation; 3. Obtain the plastic strain energy density under cyclic loading conditions; 4. Correct the crack surface energy in the initial Gibbs free energy change equation; 5. Estimate the crack initiation life; 6. Verify the accuracy of the obtained crack initiation life. The present invention establishes the relationship between Gibbs free energy change and internal crack initiation energy evolution, and then calculates the plastic strain energy density under cyclic loading conditions in combination with crystal plastic finite elements, and then evaluates the initial Gibbs free energy based on the energy efficiency factor. The variable equation is corrected, and the mesoscopic internal fatigue crack initiation life prediction model is established to predict and verify the fatigue life of metal materials, which meets the design requirements of mechanical structure environment-high performance-long life.

Description

A life prediction method for internal fatigue failure of metal materials

Technical Field

The invention belongs to the technical field of fatigue failure of metal materials, and in particular relates to a life prediction method for internal fatigue failure of metal materials.

Background Art

With the advancement of science and technology, mechanical structures in aerospace, automobiles, nuclear energy, etc. are facing the needs of "lightweight", "environmental adaptability" and "long life", which are directly related to the service performance, service life and safety and reliability of mechanical mechanisms. For mechanical structures, their structural materials will be affected by factors such as complex environment during service, and then high-cycle environmental-fatigue coupling damage will occur, which greatly restricts the development needs of high performance-high durability-low maintenance cost of mechanical structures. It is urgent to make breakthroughs in material selection, failure diagnosis and life prediction of structures. In addition, traditional mechanical structures are based on the strength criteria of "safety factor of 2" or "static design, dynamic calibration", which is far from meeting the requirements of long life prediction of mechanical structures and materials under complex service environments. Therefore, it is necessary to reveal, analyze and construct the environmental-fatigue damage evolution equation of metal materials based on multidisciplinary theories and methods, and form a high fatigue life fatigue coupling damage assessment method based on failure mechanism, so as to meet the requirements of mechanical structure environment-high performance-long life design.

Summary of the invention

The technical problem to be solved by the present invention is to provide a life prediction method for internal fatigue failure of metal materials in response to the deficiencies in the above-mentioned prior art. The method establishes a relationship between the Gibbs free energy change and the energy evolution during internal crack initiation, and then combines the crystal plasticity finite element to calculate the plastic strain energy density under cyclic loading conditions. The initial Gibbs free energy change equation is corrected based on the energy efficiency factor evaluation, and a microscopic internal fatigue crack initiation life prediction model is established. The fatigue life of the metal material is estimated and verified, forming a high fatigue life fatigue coupled damage assessment method based on the failure mechanism, which meets the mechanical structure environment-high performance-long life design requirements.

In order to solve the above technical problems, the technical solution adopted by the present invention is: a life prediction method for internal fatigue failure of metal materials, characterized in that the method comprises the following steps:

Step 1, obtain the stress-life fitting formula of the metal material under the condition of constant load: according to the fatigue test standard of metal materials, a 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 lgσ _a =AlgN _f +B of the metal material under the condition of constant load are obtained through linear fitting; wherein, σ _a is the loaded stress amplitude, N _f is the test fatigue life corresponding to the loaded stress amplitude, and A and B are fitting parameters;

Step 2, obtaining the initial Gibbs free energy change equation: Combining the Gibbs free energy theory and the theories of Mura and Nakasone, 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= _-We - _Wd + _2cvirγs ; wherein ΔG is the Gibbs free energy change, _We is the elastic energy released by the material when the crack opens, _Wd is the part of the external work stored in the lattice defects of the metal material by the internal energy, _cvir is 1/2 of the virtual crack length value, and _γs is the crack surface energy;

且

其中，Δτ为局部剪切应力变化范围，Δγ_p为对应位置的塑性剪切应变变化范围；Step 3: Obtain the plastic strain energy density under periodic load conditions: Use finite element software to establish a polycrystalline representative volume element model, use Lagrangian solid elements to discretize the polycrystalline representative volume element model, apply periodic loads to the discretized polycrystalline representative volume element model, and use the unit with the highest plastic strain energy density value as the critical unit for crack initiation. The plastic strain energy density of the critical unit is

and

Among them, Δτ is the variation range of local shear stress, and Δγ _p is the variation range of plastic shear strain at the corresponding position;

Step 4: Correct the crack surface energy in the initial Gibbs free energy equation. The process is as follows:

其中，b为伯氏矢量，W_eq为单一滑移带内部位错偶极子存储的应变能，d为晶粒尺寸，h为滑移带宽度，μ为剪切模量；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

Where, b is the Burgers vector, W _eq is the strain energy stored in 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;

则导致裂纹萌生的最低表面能

与W_eq之间的关系式为

Step 402: When the crack initiation is complete, according to the Murakami theory, the crack characteristic length is

The minimum surface energy that leads to crack initiation is

The relationship between W _eq is

和伯氏矢量绝对值b与位错数量n_c之间的关系为

结合步骤401和步骤402，得到位错数量n_c的表达式为

进而得到裂纹表面能γ_s的表达式为

Step 403: Crack length

The relationship between the absolute value of the Burgers vector b and the number of dislocations n _c is

Combining step 401 and step 402, the expression of the number of dislocations n _c is obtained as follows:

Then the expression of crack surface energy _γs is obtained as

Step 5: Estimate crack initiation life: According to the metal material in the mechanical structure, the energy efficiency factor f of the metal material remains constant. Combining the formulas in steps 3 and 4, the energy evolution equation in step 2 can be transformed into

Taking partial derivative of this formula we get

时，吉布斯自由能变ΔG最大，则When the energy stored in the dislocation dipole is in equilibrium with the crack initiation energy, that is,

When , the Gibbs free energy change ΔG is the largest, then

则此时的N为裂纹萌生寿命N_i；get

Then N at this time is the crack initiation life _Ni ;

的两倍，则

In addition, Δτ·Δγ _p is the plastic strain energy density of the critical element

twice of

Step 6. Verify the accuracy of the obtained crack initiation life: Use 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 and the test fatigue life when the metal material in the mechanical structure fails internally in the coordinate system, and the ratio of the estimated crack initiation life and the test fatigue life when the metal material in the mechanical structure fails internally is within the 3-fold line boundary, and the estimated crack initiation life is obtained as the internal fatigue failure life of the metal material.

其中，d为晶粒尺寸，ν为泊松比，k为滑移启动的临界剪切应力，N为循环载荷施加周次，ζ为常数。The above-mentioned life prediction method for internal fatigue failure of a metal material is characterized in that: in step 2, 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 dislocation dipoles, then W _e is

Where d is the grain size, ν is the Poisson's ratio, k is the critical shear stress for slip initiation, N is the number of cycles of cyclic load application, and ζ is a constant.

The above-mentioned life prediction method for internal fatigue failure of metal materials is characterized in that: in step 2, according to the theory of Fine and Bhat, W _d is W _d = 2c _vir Nδ; wherein δ is the energy stored in the virtual crack after each cycle ends.

式中，f为能效因子，h为滑移带宽度。The above-mentioned life prediction method for internal fatigue failure of a metal material is characterized in that: according to the characteristic curve of the restoring force under the action of periodic load, δ is

Where f is the energy efficiency factor and h is the slip band width.

The above-mentioned life prediction method for internal fatigue failure of a metal material is characterized in that: in step 2, the virtual crack length is obtained according to the relationship between the dislocation accumulation width and the virtual crack length.

The beneficial effects of the present invention are as follows: by establishing a relationship between Gibbs free energy change and energy evolution during internal crack initiation, and then combining the crystal plasticity finite element to calculate the plastic strain energy density under cyclic loading conditions, the initial Gibbs free energy change equation is corrected based on the energy efficiency factor evaluation, and a microscopic internal fatigue crack initiation life prediction model is established. The fatigue life of metal materials is estimated and verified, forming a high fatigue life fatigue coupled damage assessment method based on failure mechanism, which meets the mechanical structure environment-high performance-long life design requirements.

The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graph showing the relationship between the maximum plastic strain energy density and the number of cycles when the slip system is (111)[-110] in the simulation analysis of the metal material SLM-IN718 of the present invention.

FIG. 2 is a graph showing the relationship between the maximum plastic strain energy density and the number of cycles when the slip system is (111) [0-11] in the simulation analysis of the metal material SLM-IN718 of the present invention.

FIG3 is a comparison diagram of the estimated fatigue life and the experimental fatigue life of the metal material SLM-IN718 of the present invention in the simulation analysis.

FIG4 is a flowchart of the method of the present invention.

DETAILED DESCRIPTION

A life prediction method for internal fatigue failure of a metal material as shown in FIGS. 1 to 4 comprises the following steps:

Step 1, obtain the stress-life fitting formula of the metal material under the condition of constant load: according to the fatigue test standard of metal materials, a 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 lgσ _a =AlgN _f +B of the metal material under the condition of constant load are obtained through linear fitting; wherein, σ _a is the loaded stress amplitude, N _f is the test fatigue life corresponding to the loaded stress amplitude, and A and B are fitting parameters;

Step 2, obtaining the initial Gibbs free energy change equation: Combining the Gibbs free energy theory and the theories of Mura and Nakasone, 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= _-We - _Wd + _2cvirγs ; wherein ΔG is the Gibbs free energy change, _We is the elastic energy released by the material when the crack opens, _Wd is the part of the external work stored in the lattice defects of the metal material by the internal energy, _cvir is 1/2 of the virtual crack length value, and _γs is the crack surface energy;

且

其中，Δτ为局部剪切应力变化范围，Δγ_p为对应位置的塑性剪切应变变化范围；Step 3: Obtain the plastic strain energy density under periodic load conditions: Use finite element software to establish a polycrystalline representative volume element model, use Lagrangian solid elements to discretize the polycrystalline representative volume element model, apply periodic loads to the discretized polycrystalline representative volume element model, and use the unit with the highest plastic strain energy density value as the critical unit for crack initiation. The plastic strain energy density of the critical unit is

and

Among them, Δτ is the variation range of local shear stress, and Δγ _p is the variation range of plastic shear strain at the corresponding position;

Step 4: Correct the crack surface energy in the initial Gibbs free energy equation. The process is as follows:

其中，b为伯氏矢量，W_eq为单一滑移带内部位错偶极子存储的应变能，d为晶粒尺寸，h为滑移带宽度，μ为剪切模量；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

Where, b is the Burgers vector, W _eq is the strain energy stored in 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;

则导致裂纹萌生的最低表面能

与W_eq之间的关系式为

Step 402: When the crack initiation is complete, according to the Murakami theory, the crack characteristic length is

The minimum surface energy that leads to crack initiation is

The relationship between W _eq is

和伯氏矢量绝对值b与位错数量n_c之间的关系为

结合步骤401和步骤402，得到位错数量n_c的表达式为

进而得到裂纹表面能γ_s的表达式为

Step 403: Crack length

The relationship between the absolute value of the Burgers vector b and the number of dislocations n _c is

Combining step 401 and step 402, the expression of the number of dislocations n _c is obtained as follows:

Then the expression of crack surface energy _γs is obtained as

Step 5: Estimate crack initiation life: According to the metal material in the mechanical structure, the energy efficiency factor f of the metal material remains constant. Combining the formulas in steps 3 and 4, the energy evolution equation in step 2 can be transformed into

Taking partial derivative of this formula we get

时，吉布斯自由能变ΔG最大，则When the energy stored in the dislocation dipole is in equilibrium with the crack initiation energy, that is,

When , the Gibbs free energy change ΔG is the largest, then

则此时的N为裂纹萌生寿命N_i；get

Then N at this time is the crack initiation life _Ni ;

的两倍，则

In addition, Δτ·Δγ _p is the plastic strain energy density of the critical element

twice of

Step 6. Verify the accuracy of the obtained crack initiation life: Use 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 and the test fatigue life when the metal material in the mechanical structure fails internally in the coordinate system, and the ratio of the estimated crack initiation life and the test fatigue life when the metal material in the mechanical structure fails internally is within the 3-fold line boundary, and the estimated crack initiation life is obtained as the internal fatigue failure life of the metal material.

The present invention establishes a relationship between Gibbs free energy change and the energy evolution during internal crack initiation, and then combines the crystal plasticity finite element to calculate the plastic strain energy density under cyclic loading conditions, and then corrects the initial Gibbs free energy change equation based on energy efficiency factor evaluation, establishes a micro-internal fatigue crack initiation life prediction model, estimates and verifies the fatigue life of metal materials, and forms a high fatigue life fatigue coupled damage assessment method based on failure mechanism, which meets the mechanical structure environment-high performance-long life design requirements.

In the stress-life curve in step 1, the coordinate system is established with the test fatigue life as the horizontal axis and the stress amplitude as the vertical axis.

In actual use, the process of fatigue fracture of metal materials under periodic loads can be regarded as the process of forming a new surface of the material, and the fatigue load involves repeated loading and unloading processes; Mura and Nakasone believe that the dislocation dipoles formed by reverse slip during the unloading process will continue to accumulate as the load continues to be applied, so the energy evolution equation in step two can be obtained.

In step three, the material parameters are fitted based on the selected constitutive equation. When the calculated value of the stress-strain relationship is consistent with the measured value, it indicates that this set of material parameters can be used for subsequent plastic strain energy density calculation. By modifying the load spectrum and applying cyclic loads to the model, the plastic strain energy density of the grain under cyclic loads is a very important parameter in the crystal plastic finite element calculation results. This parameter has been used to predict the crack initiation life. A single grain has a specific grain orientation. Therefore, in the simulation calculation process, the unit 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 stabilize after a certain number of cycles. When the maximum plastic strain energy density value is stable, the calculation results obtained by the model in different cyclic load cycles are similar, so the calculation results at this moment can be used for subsequent analysis and research. Therefore, the corresponding Δτ and Δγ _p can be extracted from the calculation results to calculate the plastic strain energy density.

As shown in Figures 1 and 2, the maximum plastic strain energy density values of different slip systems at a certain position in the first 25 cycles vary with the number of cycles. It can be seen that, as shown in Figure 1, the maximum plastic strain energy density on the slip system with the slip direction [-110] of the slip plane (111) increases with the increase of the number of cycles, while as shown in Figure 2, the maximum plastic strain energy density on the slip system with the slip direction [0, -1, 1] of the slip plane (111) decreases with the increase of the number of cycles. Both tend to be stable when the load number is greater than 15 cycles. In the simulation analysis of the ultra-high cycle fatigue characteristics of the metal 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 week are used as the basis in the subsequent analysis.

In step 4, the slip band is a band composed of a group of parallel slip lines. When the crystal slips under the action of shear stress, microscopic steps are formed on the surface of the crystal. When observed under a microscope, they are some thin lines, called slip lines. Slip lines often appear in groups to form slip bands. Slip bands are an important feature of plastic deformation of crystals.

其中，σ_max为施加载荷中的最大载荷值，E为弹性模量；In step five, starting from the initial moment of crack initiation, the Gibbs free energy change ΔG becomes positive, indicating that there is an energy limit for determining whether the crack has initiated. When the energy contained in the dislocation dipole and the crack initiation energy are in equilibrium, the free energy is maximum. Then, as the cyclic load continues to be applied, the crack free energy gradually decreases, and the dislocation dipole structure becomes unstable when the crack is fully initiated. Therefore, the moment of maximum Gibbs free energy is taken as the moment when crack initiation is completed. In short, the G of crack initiation increases with the growth of the crack, and reaches a critical value at that time. In step five, based on the metal material in the mechanical structure, the energy efficiency factor of the metal material is obtained.

Wherein, σ _max is the maximum load value in the applied load, and E is the elastic modulus;

时的线条。It should be noted that, as shown in FIG3 , in the comparison diagram of the estimated fatigue life and the experimental fatigue life of metal material SLM-IN718, R is the stress ratio, that is, the ratio of the minimum stress value to the maximum stress value; the 3-fold line is the standard for verifying the accuracy in the fatigue life test, and the coordinate system is based on the experimental fatigue life as the horizontal coordinate x and the estimated crack initiation life as the vertical coordinate y. The dotted line in the figure is the limit when y=x, and the two solid lines are the lines when y=3x,

The lines of time.

其中，d为晶粒尺寸，ν为泊松比，k为滑移启动的临界剪切应力，N为循环载荷施加周次，ζ为常数。In this embodiment, in step 2, the elastic energy _We released by the material when the crack opens includes the energy contained in the dislocation itself and the energy contained in the interaction between dislocation dipoles, so _We is

Where d is the grain size, ν is the Poisson's ratio, k is the critical shear stress for slip initiation, N is the number of cycles of cyclic load application, and ζ is a constant.

In this embodiment, in step 2, 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 after each cycle.

式中，f为能效因子，h为滑移带宽度。In this embodiment, according to the characteristic curve of the restoring force under periodic load, δ is

Where f is the energy efficiency factor and h is the slip band width.

In this embodiment, in step 2, the virtual crack length is obtained based on the relationship between the dislocation accumulation width and the virtual crack length.

The above description is only a preferred embodiment of the present invention and does not limit the present invention in any way. Any simple modification, change and equivalent structural change made to the above embodiment based on the technical essence of the present invention still falls within the protection scope of the technical solution of the present invention.

Claims (5)

1. A method for predicting the service life of internal fatigue failure of a metal material is characterized by comprising the following steps:

step one, obtaining a stress-life fitting formula of a metal material under a constant load loading condition: according to the fatigue test standard of the metal material, performing a constant load fatigue test under the condition of periodic load loading, drawing the obtained test data in a coordinate system, and obtaining a stress-life curve and a fitting formula lg sigma of the metal material under the condition of constant load loading through linear fitting _a ＝AlgN _f + B; wherein σ _a Magnitude of stress for load, N _f The test fatigue life corresponding to the loaded stress amplitude is shown, and A and B are fitting parameters;

step two, obtaining an initial Gibbs free energy variable equation: combining Gibbs free energy theory and Mura and Nakasone theory to obtain an energy evolution equation of delta G = -W in the internal crack initiation process under the condition of applying periodic load to the metal material _e -W _d +2c _vir γ _s (ii) a Wherein Δ G is Gibbs free energy change, W _e The elastic energy released by the material when the crack opens, W _d A part of external work stored in lattice defects of the metal material as internal energy, c _vir Is 1/2, gamma of the virtual crack length value _s Is the crack surface energy;

step three, obtaining the plastic strain energy density under the condition of periodic load loading: establishing a polycrystal representative volume element model by using finite element software, dispersing the polycrystal representative volume element model by adopting Lagrange entity units, applying periodic load to the dispersed polycrystal representative volume element model, taking the unit with the highest plastic strain energy density value as a critical unit for crack initiation, and then setting the plastic strain energy density of the critical unit as

And is

Wherein, delta tau is the variation range of local shear stress, delta gamma _p The plastic shear strain variation range of the corresponding position;

step four, correcting the surface energy of the crack in the initial Gibbs free energy variable equation, wherein the process is as follows:

step 401, assuming that all dislocation dipoles in the slip band of the metal material can affect crack initiation, the number n of dislocation dipoles in a single slip band _eq And is and

wherein b is a Boehringer vector, W _eq Strain energy stored by dislocation dipoles inside a single slip band, d is the size of a crystal grain, h is the width of the slip band, and mu is shear modulus;

step 402, when the crack initiation is finished, according to the Murakami theory, the crack characteristic length is

The lowest surface energy leading to crack initiation

And W _eq The relation between is

Step 403, crack length

Absolute value of the sum-Boehringer vector b and number of dislocations n _c The relationship between is

Combining the step 401 and the step 402 to obtain the dislocation number n _c Is expressed as

Thereby obtaining the surface energy gamma of the cracks _s Is expressed as

And fifthly, estimating the crack initiation life: according to the metal material in the mechanical structure, the energy efficiency factor f of the metal material is kept constant, and the energy evolution equation in the step two can be converted into the energy evolution equation in the step three and the energy evolution equation in the step four by combining the formulas in the step three and the step four

The formula is calculated to obtain the deviation

When the energy stored by the dislocation dipole is in equilibrium with the crack initiation energy, i.e.

When the change of Gibbs free energy is maximum, the

To obtain

N at this time is the crack initiation life N _i ；

In addition, Δ τ Δ γ _p Is the plastic strain energy density of the critical unit

Twice of, then

Step six, verifying the obtained crack initiation life precision: the method comprises the steps of taking the test fatigue life as an abscissa and the predicted crack initiation life as an ordinate, establishing a coordinate system, marking the ratio of the predicted crack initiation life to the test fatigue life when the metal material in the mechanical structure is subjected to internal failure in the coordinate system, and locating the ratio of the predicted crack initiation life to the test fatigue life when the metal material in the mechanical structure is subjected to internal failure in a 3-fold line boundary to obtain the predicted crack initiation life as the internal fatigue failure life of the metal material.

2. The method for predicting the service life of the internal fatigue failure of the metal material according to claim 1, wherein: in the second step, the elastic energy W released by the material when the crack opens _e Including the energy contained in the dislocations themselves and the energy contained in the interactions between the dislocation dipoles, W _e Is composed of

Wherein d is the crystal grain size, v is the Poisson ratio, k is the critical shear stress of slip start, N is the cycle of applying cyclic load, and zeta is a constant.

3. The method for predicting the service life of the internal fatigue failure of the metal material as recited in claim 1, wherein: in the second step, W can be known according to the theory of Fine and Bhat _d Is W _d ＝2c _vir N delta; where δ is the energy stored by the virtual crack after the end of each cycle.

4. The method for predicting the life of the internal fatigue failure of the metal material according to claim 3, wherein: according to the characteristic curve of the restoring force under the action of the periodic load, delta is

In the formula, f is an energy efficiency factor, and h is the width of the slip band.

5. The method for predicting the service life of the internal fatigue failure of the metal material as recited in claim 1, wherein: in the second step, the virtual crack length is obtained according to the relationship between the dislocation pile-up width and the virtual crack length

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