CN115841857A - Method for predicting service life of internal fatigue failure of metal material - Google Patents
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Abstract
The invention discloses a method for predicting the service life of internal fatigue failure of a metal material, which comprises the following steps: 1. obtaining a stress-life fitting formula of the metal material under the condition of loading a constant load; 2. obtaining an initial Gibbs free energy variable equation; 3. acquiring plastic strain energy density under the condition of periodic load loading; 4. correcting the surface energy of the crack in the initial Gibbs free energy variable equation; 5. estimating the crack initiation life; 6. and verifying the obtained crack initiation life precision. According to the invention, a relationship based on Gibbs free energy change and energy evolution when an internal crack is initiated is established, then the plastic strain energy density under a cyclic loading condition is calculated by combining a crystal plastic finite element, and further an initial Gibbs free energy change equation is corrected based on energy efficiency factor evaluation, a mesoscopic internal fatigue crack initiation life prediction model is established, the fatigue life of a metal material is predicted and verified, and the design requirements of mechanical structure environment-high performance-long life are met.
Description
Technical Field
The invention belongs to the technical field of fatigue failure of metal materials, and particularly relates to a life prediction method for internal fatigue failure of a metal material.
Background
With the progress of science and technology, the mechanical structures of aerospace, automobiles, nuclear energy and the like face the requirements of light weight, environmental adaptability and long service life, and the mechanical structures are directly related to the service performance, service life and safety and reliability of mechanical mechanisms. For a mechanical structure, a structural material of the mechanical structure is influenced by factors such as a complex environment in the service process, and then high-cycle environment-fatigue coupling damage occurs, so that the development requirements of high performance, high durability and low maintenance cost of the mechanical structure are greatly restricted, and breakthrough progress in the aspects of material selection, failure diagnosis, service life prediction and the like of the structure is urgently needed. In addition, the traditional mechanical structure is established on the strength criterion of 'safety factor of 2' or 'static design and dynamic calibration', and the requirement of long-life prediction of the mechanical structure and materials under a complex service environment cannot be met. Therefore, on the premise of defining the fatigue coupling damage mode, rule and mechanism of the metal structure and the material, a metal material environment-fatigue damage evolution equation needs to be disclosed, analyzed and constructed based on the multidisciplinary theory and method, and a high fatigue life fatigue coupling damage assessment method based on a failure mechanism is formed, so that the design requirements of mechanical structure environment-high performance-long life can be met.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a method for predicting the internal fatigue failure life of a metal material aiming at the defects in the prior art, wherein a relationship based on Gibbs free energy change and energy evolution when an internal crack is initiated is established, then the plastic strain energy density under a cyclic loading condition is calculated by combining a crystal plastic finite element, an initial Gibbs free energy variable equation is corrected based on energy efficiency factor evaluation, a mesoscopic internal fatigue crack initiation life prediction model is established, the fatigue life of the metal material is estimated and verified, a high fatigue life fatigue coupling damage evaluation method based on a failure mechanism is formed, and the design requirements of mechanical structure environment-high performance-long life are met.
In order to solve the technical problems, the invention adopts the technical scheme that: a life prediction method for internal fatigue failure of a metal material is characterized by comprising the following steps: the method comprises 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 Is 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, and taking the unit with the highest plastic strain energy density value as the critical value of crack initiationA cell having a plastic strain energy density of a critical cell of
And->
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 which leads to the initiation of a crack is pick>
And W eq Has a relation of->
Step 403, crack length
Absolute value of sum Berger's 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 second step can be converted into the energy evolution equation in the third step and the fourth step by combining formulas in the third step and the fourth step
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 as much, then->
Step six, verifying the obtained crack initiation life precision: the method comprises the steps of establishing a coordinate system by taking the test fatigue life as an abscissa and the estimated crack initiation life as an ordinate, marking the ratio of the estimated 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 estimated 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 estimated crack initiation life as the internal fatigue failure life of the metal material.
The method for predicting the service life of the internal fatigue failure of the metal material is characterized by comprising the following steps: 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.
The method for predicting the service life of the internal fatigue failure of the metal material is characterized by comprising the following steps: in the second step, W is 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.
The method for predicting the service life of the internal fatigue failure of the metal material is characterized by comprising the following steps: 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 belt.
The method for predicting the service life of the internal fatigue failure of the metal material is characterized by comprising the following steps: in step two, rootObtaining the virtual crack length according to the relationship between the dislocation pile-up width and the virtual crack length
The method has the advantages that the relationship based on Gibbs free energy change and energy evolution when internal cracks are initiated is established, then the plastic strain energy density under the cyclic loading condition is calculated by combining with the crystal plastic finite element, the initial Gibbs free energy variable equation is corrected based on energy efficiency factor evaluation, a microscopic 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 assessment method based on the failure mechanism is formed, and the design requirements of mechanical structure environment-high performance-long life are met.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a graph of maximum plastic strain energy density and cycle number of a metallic material SLM-IN718 according to the present invention when the slip is (111) [ -110] IN simulation analysis.
FIG. 2 is a graph showing the relationship between the maximum plastic strain energy density and the number of cycles of the metal material SLM-IN718 according to the present invention when the slip is (111) [0-11] IN simulation analysis.
FIG. 3 is a comparison graph of predicted fatigue life and experimental fatigue life of the metal material SLM-IN718 of the present invention IN simulation analysis.
FIG. 4 is a block flow diagram of the method of the present invention.
Detailed Description
A method for predicting the life of an internal fatigue failure of a metallic material as shown in fig. 1 to 4, the method comprising the steps of:
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 the constant load fatigue test of the metal material through linear fittingStress-life curve under load loading condition and fitting formula lg sigma a ＝AlgN f + B; wherein σ a Magnitude of stress, N, for loading 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 partial external work stored in lattice defects of the metal material as an 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->
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 which leads to the initiation of a crack is +>
And W eq Has a relation of->
Step 403, crack length
Absolute value of sum Berger's vector b and number of dislocations n c The relationship between is
Combining the step 401 with 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 second step can be converted into the energy evolution equation in the third step and the fourth step by combining formulas in the third step and the fourth step
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 as much, 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.
According to the method, a relationship based on Gibbs free energy change and energy evolution when an internal crack is initiated is established, then the plastic strain energy density under a cyclic loading condition is calculated by combining a crystal plastic finite element, an initial Gibbs free energy change equation is corrected based on energy efficiency factor evaluation, a microscopic internal fatigue crack initiation life prediction model is established, the fatigue life of a metal material is predicted and verified, a high fatigue life fatigue coupling damage evaluation method based on a failure mechanism is formed, and the design requirements of mechanical structure environment-high performance-long life are met.
And in the stress-life curve in the step one, a coordinate system is established by taking the fatigue life of the test as an abscissa and the stress amplitude as an ordinate.
In practical use, the process of fatigue fracture of the metal material under the action of periodic load can be regarded as the process of forming a new surface of the material, and the fatigue load relates to repeated loading and unloading processes; while Mura and Nakasone think that dislocation dipoles formed by reverse slip in the unloading process are accumulated continuously along with the continuous application of the load, so that an energy evolution equation in the second step can be obtained.
In the third step, the material parameters are fitted based on the selected constitutive equation, and when the consistency of the calculated value of the stress-strain relation and the measured value is good, the group of material parameters can be used for subsequent calculation of plastic strain energy density. By modifying the load spectrum, cyclic load is applied to the model, and the plastic strain energy density of the crystal grains under the cyclic load is an important parameter in the calculation result of the plastic finite element of the crystal, and the parameter is used for predicting the crack initiation life. The single crystal grain has a specific crystal grain orientation, so in the simulation calculation process, the unit with the highest plastic strain energy density value can be regarded as the critical position for crack initiation, and the maximum plastic strain energy density value tends to be stable after a certain cycle. When the maximum plastic strain energy density value is stable, the calculation results of the model obtained in different cyclic load cycles are similar, so that the calculation results at the moment can be used for subsequent analysis and research, and corresponding delta tau and delta gamma can be extracted from the calculation results p To calculate the plastic strain energy density.
As shown in FIGS. 1 and 2, the maximum plastic strain energy density of different slip systems at a certain position in the first 25 cycles is related to the cycle, and it can be seen that as shown in FIG. 1, the maximum plastic strain energy density of the slip system with the slip direction of the slip plane (111) [ -110] is increased with the increase of the cycle, while as shown in FIG. 2, the maximum plastic strain energy density of the slip system with the slip direction of the slip plane (111) [ -0, -1,1] is decreased with the increase of the cycle, and both are stable when the load number is greater than 15 cycles. IN order to reduce the calculation cost when performing the ultrahigh cycle fatigue characteristic simulation analysis of the metal material SLM-IN718, the stress and strain states at the time of the maximum plastic strain energy density stabilization are used as references, and the whole ultrahigh cycle fatigue cycle number is not calculated, so the calculation result of the 20 th cycle is used as the basis IN the subsequent analysis.
In the fourth step, the slip band is a band formed by 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, and the slip bands are often formed by grouping fine lines which are called slip lines and observed under a microscope. Slip bands are an important characteristic of plastic deformation of crystals.
And step five, starting from the initial moment of crack initiation, indicating that an energy limit for judging whether the crack is initiated exists when the Gibbs free energy change delta G is positive. When the dislocation dipole intrinsic energy and the crack initiation energy are in an equilibrium state, the free energy is maximum at this time. Then along with the continuous application of cyclic load, the crack free energy is gradually reduced, and the dislocation dipole structure is unstable when the crack completely grows. The moment of maximum gibbs free energy is therefore taken as the moment of completion of crack initiation. In short, the crack initiation G grows as the crack grows and reaches a critical value at that time. In the fifth step, according to the metal material in the mechanical structure, the energy efficiency factor of the metal material is obtained
Wherein σ max The maximum load value in the applied load, E is the modulus of elasticity;
it should be noted that, as shown IN FIG. 3, R is the predicted fatigue life and the experimental fatigue life of the SLM-IN718 metal materialForce ratio, i.e. the ratio of the minimum stress value and the maximum stress value; the 3-fold line is the standard of the checking precision in the fatigue life test, the coordinate system is that the test fatigue life is used as an abscissa x, the estimated crack initiation life is used as an ordinate y, the dotted line in the figure is the limit when y = x, and the two solid lines are respectively the line when y =3x,
Lines of time.
In this example, in step two, 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 grain size, v is the Poisson ratio, k is the critical shear stress of slip start, N is the cycle of applying the cyclic load, and ζ is a constant.
In this embodiment, in the second step, according to the theory of Fine and Bhat, W is d Is W d ＝2c vir N delta; where δ is the energy stored by the virtual crack after the end of each cycle.
In this embodiment, δ is a characteristic curve of the restoring force under the action of the periodic load
In the formula, f is an energy efficiency factor, and h is the width of the slip band.
In this embodiment, 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
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and all simple modifications, changes and equivalent structural changes made to the above embodiment according to the technical spirit of the present invention still fall 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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