Two-stage fatigue crack life prediction method for titanium alloy based on finite element analysis

Abstract

A two-stage full life prediction method for titanium alloy fatigue crack based on finite element analysis, a damage mechanics model is established for the titanium alloy structure to be tested, and the fatigue crack initiation stage simulation is carried out, the fatigue crack initiation life and the initial crack position are obtained; the fatigue crack propagation rate model is established based on fracture mechanics, and the propagation stage simulation is carried out at the initial crack position through the extended finite element method, and the fatigue crack propagation life is obtained; the fatigue crack full life of the titanium alloy structure to be tested is obtained by fusing the simulation results of the two stages. The present application is based on damage mechanics and fracture mechanics, by considering the propagation characteristics of short fatigue cracks in the early failure stage, a bridge between the fatigue crack initiation finite element simulation and the macro crack propagation finite element simulation is built, the effective evaluation of the full life of the titanium alloy complex structure under complex load is realized, and the whole process of the fatigue crack from initiation to continuous expansion is intuitively shown.

Description

Technical Field

[0001] This invention relates to a technology in the field of titanium alloy processing, specifically a two-stage full-life prediction method for fatigue crack initiation and propagation in titanium alloys based on finite element analysis. Background Technology

[0002] Structural fatigue life is divided into crack initiation life and crack propagation life. Fatigue crack initiation life refers to the life before a crack reaches a certain "engineering-inspectable length," while fatigue crack propagation life refers to the life when the crack extends from that "engineering-inspectable length" to a certain failure length. When the target cycle life of a structure is long, both crack initiation life and propagation life are non-negligible, requiring the selection of appropriate methods for life prediction based on the fatigue crack initiation and propagation mechanisms. Current technologies can only simulate a single fatigue crack initiation or propagation process using the finite element method. Furthermore, the fatigue life formula established through extrapolation has high requirements for the type of load and is difficult to intuitively describe the evolution of material fatigue damage and the process of macroscopic crack propagation. Summary of the Invention

[0003] This invention addresses the problem that existing full-life prediction technologies suffer from numerous material parameters in their microstructural models and complex calibration processes, making it difficult to effectively assess the fatigue crack life of complex titanium alloy structural components under complex loads in practical engineering. It proposes a two-stage full-life prediction method for titanium alloy fatigue cracks based on finite element analysis. Based on damage mechanics and fracture mechanics, and considering the propagation characteristics of short fatigue cracks in the early stages of failure, this method bridges the gap between finite element simulation of fatigue crack initiation and finite element simulation of macroscopic crack propagation. This enables effective assessment of the fatigue crack life of complex titanium alloy structural components under complex loads and visually demonstrates the entire process from fatigue crack initiation to continuous propagation. It also provides quantitative guidance for determining the safety inspection time and cycle for titanium alloy engineering structural components.

[0004] This invention is achieved through the following technical solution:

[0005] This invention relates to a two-stage full-life prediction method for fatigue cracks in titanium alloys based on finite element analysis. A damage mechanics model is established for the titanium alloy structural component under test, and the fatigue crack initiation stage is simulated to obtain the fatigue crack initiation life and initial crack location. A fatigue crack propagation rate model is established based on fracture mechanics, and the propagation stage is simulated at the initial crack location using the extended finite element method to obtain the fatigue crack propagation life. The full fatigue crack life of the titanium alloy structural component under test is obtained by fusing the two-stage simulation results.

[0006] The damage mechanics model includes: the elastic stress-strain constitutive equation and the damage evolution equation for coupled damage, specifically: Cauchy stress. Rate of change of damage variables Where: ε ij Let D be the infinitesimal strain tensor and D be the damage variable. This represents the positive principal strain tensor component. λ represents the negative principal strain tensor component, and λ and μ are the Lamé constants of the material. and These are the effective Lamé constants of the material under tension and compression conditions, respectively: h1,h2,α (n) ,β (n) Here, n represents the non-negative material parameter, and n is the number of terms in the series; Kronecker notation. Let A,m be the rate of change of the damage variable, and let A,m be a non-negative material parameter.

[0007] The aforementioned simulation of the fatigue crack initiation stage refers to: establishing a finite element model based on the actual engineering problem, simulating the fatigue crack initiation process based on the damage mechanics model, and recording the number of load cycles at this point as the fatigue crack initiation life N when the damaged element meets the fatigue crack initiation conditions. initiation Specifically, the ABAQUS user subroutine VUMAT is written in Fortran to define the stress-strain constitutive relation of the material under elastic and coupled isotropic damage conditions. It calculates the damage increment over a time interval based on the damage evolution equation. The effective Lamé constant of the material is corrected based on the current damage variables, the strain and stress distributions are updated for the next time step, and the damage increment for the next time interval is recalculated, repeating this process continuously.

[0008] As the number of cycles increases, the fatigue damage of the element continuously increases. When the accumulated damage of the element reaches the damage threshold, the element is considered to have completely failed and is removed. The fatigue crack initiation life N is defined as the life before a certain "engineering-detectable crack" appears in the structure. ini When the length of the cumulatively failed element reaches the initial fatigue crack length, fatigue crack initiation is considered to have occurred on this structural component, and the calculation is stopped. When the calculation stops, the number of load cycles at this point is recorded as the fatigue crack initiation life N. ini And record the location of the completely failed unit when fatigue cracks initiate.

[0009] The fatigue crack initiation life is typically around 0.3 mm.

[0010] The fatigue crack propagation rate model described above is used to describe the relationship between the fatigue crack propagation rate and the stress intensity factor at the crack tip, specifically: Where: da / dN is the fatigue crack propagation rate, ΔK is the stress intensity factor, and ΔK th K is the crack propagation threshold value. cFor fracture toughness, C and m are non-negative material parameters. When ΔK approaches ΔK... th At that time, under the influence of the exponent m, the rapid growth characteristic of the fatigue crack propagation rate in the early stage can be reflected; when ΔK approaches K c When da / dN approaches infinity, it reflects the rapid propagation of fatigue cracks, thus describing the entire fatigue crack propagation process.

[0011] The aforementioned simulation of the propagation stage at the initial crack location using the extended finite element method refers to: using the ABAQUS user subroutine UMIXMODEFATIGUE written in Fortran to update the crack propagation rate variable by measuring the maximum and minimum energy release rates at the crack tip within one cycle, thereby controlling the fatigue crack propagation rate; and using a certain threshold for the total fatigue crack length as the criterion for complete fatigue failure of the specimen, i.e., stopping the calculation when the fatigue crack length reaches this threshold and recording the number of load cycles at this point as the fatigue crack propagation life N. propagation .

[0012] This invention relates to a system for implementing the above-mentioned method, comprising: a fatigue crack initiation life prediction unit and a fatigue crack propagation life prediction unit, wherein: the fatigue crack initiation life prediction unit calculates the damage evolution process of the material under cyclic loading conditions based on a suitable damage mechanics model, obtaining the initial fatigue crack characteristics and the fatigue crack initiation life; the fatigue crack propagation life prediction unit calculates the continuous propagation process of the crack under cyclic loading conditions based on the initial fatigue crack characteristics and a suitable fatigue crack propagation rate control equation, obtaining the fatigue crack propagation life. Through the combined action of the two units, fatigue life prediction is achieved.

[0013] Technical effect

[0014] This invention, based on the non-negligible nature of the two stages of fatigue crack initiation and propagation under high-cycle cyclic loading, combines traditional and extended finite element methods, and, based on damage mechanics and fracture mechanics theories, proposes a full-life simulation method for fatigue crack initiation-propagation in titanium alloys using finite element analysis. Based on engineering practice and theoretical foundations, it rationally addresses the delineation between the two processes of fatigue crack initiation and propagation, and proposes a method to connect the prediction of fatigue crack initiation and fatigue crack propagation.

[0015] Compared with existing technologies, this invention is applicable to the full life prediction of fatigue cracks in complex titanium alloy structures under various complex load conditions. It has a wide range of applications, realizes the prediction of the entire fatigue failure process, and intuitively describes the fatigue damage evolution and macroscopic crack propagation process of titanium alloy materials, as well as the joint simulation of fatigue crack "initiation-propagation" life from damage mechanics to fracture mechanics. It combines the computational advantages of the two theoretical methods, reduces the amount of numerical simulation calculations and lowers the cost of fatigue testing, provides data support for the fatigue resistance design of structures, and has important practical engineering significance. Attached Figure Description

[0016] Figure 1 This is a flowchart of the method of the present invention;

[0017] Figure 2 This is a schematic diagram of the finite element model of the TC4 titanium alloy component under vibration conditions in the embodiment.

[0018] Figure 3 This is a schematic diagram illustrating the connection between fatigue crack initiation simulation and fatigue crack propagation simulation in this embodiment. Detailed Implementation

[0019] like Figure 1 As shown in this embodiment, a two-stage full-life fatigue crack prediction method for titanium alloys based on finite element analysis is used to predict the full-life fatigue crack of TC4 titanium alloy under vibration loading conditions. The method includes the following steps:

[0020] S1: Establish a finite element model based on the actual engineering problem, and simulate the fatigue crack initiation process based on the damage mechanics model. When the damaged element meets the fatigue crack initiation condition, record the number of load cycles at this time as the fatigue crack initiation life N. initiation Specifically, it includes:

[0021] S11: As Figure 2 As shown, a geometric model of the TC4 titanium alloy specimen was established. The actual vibration loading process was simulated by applying a fixed boundary condition to one end of the specimen and a periodic displacement boundary condition to the other end.

[0022] S12: Considering the relatively small amplitude of the vibration load and the fact that the specimen is in an elastic state, an elastic damage constitutive model is used to calculate the vibration fatigue damage evolution process. Specifically, this involves the elastic stress-strain constitutive equation for coupled damage, i.e., Cauchy stress. Where: ε ij Let D be the infinitesimal strain tensor and D be the damage variable. This represents the positive principal strain tensor component. λ represents the negative principal strain tensor component, and λ and μ are the Lamé constants of the material. and These are the effective Lamé constants of the material under tension and compression conditions, respectively: h1,h2,α (n) ,β (n) Here, n represents the non-negative material parameter, and n is the number of terms in the series; Kronecker notation.

[0023] The fatigue damage evolution equation is:

[0024] in: Let Am be the rate of change of the damage variable, and Am be a non-negative material parameter. For engineering problems, the number of series terms n is usually taken as 2.

[0025] S13: Write the ABAQUS user subroutine VUMAT using Fortran to define the stress-strain constitutive relation of the material under elastic and coupled isotropic damage conditions, and calculate the damage increment over a time interval based on the damage evolution equation. This is based on the effective Lamé constant of the material under the current damage variable D. and The process involves making corrections, updating the strain and stress distribution for the next time step, and recalculating the damage increment for the next time interval, repeating this process. When the accumulated damage of an element reaches a damage threshold, the element is considered to have completely failed and is deleted. In this embodiment, the vibration fatigue crack shape of the structure is a 1 / 4 ellipse. Therefore, when the length of the element that has accumulated failure along the surface of the structure reaches 0.3 mm (the initial fatigue crack length), the fatigue crack on this structural component is considered to have initiated, and the calculation stops.

[0026] The aforementioned correction is specifically implemented as follows:

[0027]

[0028] S14: When the calculation stops, record the vibration fatigue crack initiation life N of the TC4 titanium alloy specimen. ini And record the location of the element that completely fails when fatigue cracks initiate.

[0029] S2: Using the location of the failed damage element in step S1 as the initial fatigue crack location, simulate the fatigue crack propagation process based on fracture mechanics and the extended finite element method. When the crack propagation satisfies the condition for complete fatigue failure of the specimen, record the number of load cycles at this point as the fatigue crack propagation life N. propagation Specifically, it includes:

[0030] S21: As Figure 3As shown, in step S14, an initial crack (1 / 4 ellipse) is inserted at the completely failed unit. The length of the initial crack is the same as the total length of the accumulated failed units, and the normal of the initial crack surface is parallel to the direction of the maximum tensile stress.

[0031] S22: Considering the characteristics of crack propagation rate and crack tip stress intensity factor in the early and late stages of vibration fatigue crack propagation, the governing equation for fatigue crack propagation rate is constructed: Where: da / dN is the fatigue crack propagation rate, ΔK is the stress intensity factor, and ΔK th K is the crack propagation threshold value. c denoted as fracture toughness, and C and m as material parameters.

[0032] S23: An ABAQUS user subroutine UMIXMODEFATIGUE, written in Fortran, updates the crack propagation rate variable by measuring the maximum and minimum values ​​of three energy release rates at the crack tip within one cycle, thus controlling the fatigue crack propagation rate. When the total fatigue crack length reaches a certain threshold, the sample is considered to have completely failed due to fatigue, and the calculation stops.

[0033] S24: When the calculation stops, record the vibration fatigue crack propagation life N of the TC4 titanium alloy specimen. propagation .

[0034] S3: The fatigue crack initiation life N calculated in steps S1 and S2. initiation and extended lifetime N propagation The prediction of the entire life cycle N of vibration fatigue crack in TC4 titanium alloy from "initiation-propagation" was obtained. total =N initiation +N propagation .

[0035] Based on specific fatigue life prediction calculations, taking TC4 titanium alloy specimens under vibration maximum stress amplitudes of 373 MPa and 400 MPa as examples, the two-stage fatigue crack life and total fatigue life of TC4 titanium alloy were predicted, as shown in Table 1. The initiation of fatigue cracks in TC4 titanium alloy was defined as the point at which the specimen could not achieve stable resonance, and the termination of fatigue crack propagation was defined as the point at which the specimen could not achieve stable resonance. The two-stage fatigue crack life and total fatigue life of TC4 titanium alloy under vibration maximum stress amplitudes of 373 MPa and 400 MPa were obtained, as shown in Table 1.

[0036] The predicted fatigue crack life of TC4 titanium alloy under vibration was compared with the experimentally observed life, and the specific data are shown in Table 1. It can be seen that the prediction results of the fatigue crack life prediction method based on the present invention are relatively accurate. The maximum relative error between the predicted value and the experimental value of the vibration fatigue life under the two stress amplitudes is 11.4%, while the minimum relative error is only 1.4%.

[0037] Table 1. Simulation Analysis Results and Experimental Results of Vibration Fatigue Crack Full Life Cycle in TC4 Titanium Alloy

[0038]

[0039] Compared with existing technologies, this method is the first to achieve full-life prediction of vibration fatigue in titanium alloys through finite element simulation, and the accuracy of this finite element simulation method has been demonstrated by experimental data. By combining the traditional finite element method and the extended finite element method, this method overcomes the shortcomings of single methods in fatigue life prediction by quantifying the material property degradation process and crack propagation process, thereby improving the overall computational efficiency and reducing the difficulty of mesh generation at the crack tip.

[0040] The above-described specific implementations can be partially adjusted by those skilled in the art in different ways without departing from the principles and purpose of the present invention. The scope of protection of the present invention is defined by the claims and is not limited to the above-described specific implementations. All implementation schemes within the scope of the claims are bound by the present invention.

Claims

1. A two-stage life prediction method for fatigue crack of titanium alloy based on finite element analysis, characterized in that, A damage mechanics model was established for the titanium alloy structural component under test, and the fatigue crack initiation stage was simulated to obtain the fatigue crack initiation life and the initial crack location. A fatigue crack propagation rate model was established based on fracture mechanics, and the extended finite element method was used to simulate the propagation stage at the initial crack location to obtain the fatigue crack propagation life. The fatigue crack life of the titanium alloy structural component under test is obtained by integrating the two-stage simulation results. The damage mechanics model includes: the elastic stress-strain constitutive equation for coupled damage and the damage evolution equation; The fatigue crack initiation stage simulation refers to: establishing a finite element model according to an actual engineering problem, simulating a fatigue crack initiation process based on a damage mechanics model, and recording a load cycle number at this time as a fatigue crack initiation life when a damage element meets a fatigue crack initiation condition ; The damage mechanics model specifically includes: Cauchy stress Rate of change of damage variables in: Let D be the infinitesimal strain tensor and D be the damage variable. , This represents the positive principal strain tensor component. This represents the negative principal strain tensor component. and Let Lame constant be the material. and These are the effective Lamé constants of the material under tension and compression conditions, respectively: Here, n represents the non-negative material parameter, and n is the number of terms in the series; Kronecker notation. ; The rate of change of the damage variable, These are non-negative material parameters; The simulation of the fatigue crack initiation stage is specifically as follows: The ABAQUS user subroutine VUMAT is written in Fortran language to define the stress-strain constitutive relationship of the material under elastic and coupled isotropic damage state. The damage increment within the interval is periodically calculated according to the damage evolution equation. Based on the current damage variables, the effective Lamé constant of the material is corrected, the strain and stress distribution at the next moment are updated, and the damage increment in the next time interval is recalculated. This process is repeated. When the accumulated damage of a unit reaches the damage threshold, the unit is considered to have completely failed and is removed. The lifespan before the appearance of a certain "engineering-detectable crack" in the structure is taken as the fatigue crack initiation life. When the length of the cumulatively failed element reaches the initial fatigue crack length, fatigue crack initiation is considered to have occurred on this structural component, and the calculation is stopped. When the calculation stops, the number of load cycles at this point is recorded as the fatigue crack initiation life. And record the location of the completely failed unit when fatigue cracks initiate.

2. The two-stage full-life fatigue crack prediction method for titanium alloys according to claim 1, characterized in that, The fatigue crack propagation rate model described above is used to describe the relationship between the fatigue crack propagation rate and the stress intensity factor at the crack tip, specifically: ,in: This represents the fatigue crack propagation rate. Stress intensity factor This is the crack propagation threshold value. For fracture toughness, C and m are non-negative material parameters. Approaching At that time, under the influence of the exponent m, the rapid growth characteristic of the fatigue crack propagation rate in the early stage can be reflected; when Approaching hour, Approaching infinity reflects the rapid propagation of fatigue cracks, thus describing the entire fatigue crack propagation process.

3. The two-stage full-life fatigue crack prediction method for titanium alloys according to claim 1, characterized in that, The aforementioned simulation of the propagation stage at the initial crack location using the extended finite element method refers to: using the ABAQUS user subroutine UMIXMODEFATIGUE written in Fortran to update the crack propagation rate variable by measuring the maximum and minimum energy release rates at the crack tip within one cycle, thereby controlling the fatigue crack propagation rate; and using a certain threshold for the total fatigue crack length as the criterion for complete fatigue failure of the specimen, i.e., stopping the calculation when the fatigue crack length reaches this threshold and recording the number of load cycles at this point as the fatigue crack propagation life. .

4. The two-stage full-life prediction method for fatigue cracks in titanium alloys according to any one of claims 1-3, characterized in that, specifically... include: S1: Establish a finite element model based on the actual engineering problem, and simulate the fatigue crack initiation process based on the damage mechanics model; When the damaged element meets the fatigue crack initiation condition, the number of load cycles at this time is recorded as the fatigue crack initiation life. Specifically, it includes: S11: Establish a geometric model of the TC4 titanium alloy specimen. Simulate the actual vibration loading process by applying a fixed boundary condition to one end of the specimen and a periodic displacement boundary condition to the other end. S12: Considering the relatively small amplitude of the vibration load and the fact that the specimen is in an elastic state, an elastic damage constitutive model is used to calculate the vibration fatigue damage evolution process. Specifically, this involves the elastic stress-strain constitutive equation for coupled damage, i.e., Cauchy stress. in: Let D be the infinitesimal strain tensor and D be the damage variable. , This represents the positive principal strain tensor component. This represents the negative principal strain tensor component. and Let Lame constant be the material. and These are the effective Lamé constants of the material under tension and compression conditions, respectively: Here, n represents the non-negative material parameter, and n is the number of terms in the series; Kronecker notation. The fatigue damage evolution equation is: in: The rate of change of the damage variable, These are non-negative material parameters; S13: Write the ABAQUS user subroutine VUMAT using Fortran to define the stress-strain constitutive relation of the material under elastic and coupled isotropic damage conditions, calculate the damage increment over a time interval based on the damage evolution equation, and apply the effective Lamé constant of the material based on the current damage variable D. and The process involves making corrections, updating the strain and stress distribution for the next time step, and recalculating the damage increment for the next time interval. This process is repeated until the accumulated damage of an element reaches the damage threshold. In this case, the element is considered to have completely failed and is deleted. The aforementioned correction is specifically implemented as follows: S14: When the calculation stops, record the vibration fatigue crack initiation life of the TC4 titanium alloy specimen. And record the location of the element that completely fails when fatigue cracks initiate; S2: Using the location of the failed damage element in step S1 as the initial fatigue crack location, simulate the fatigue crack propagation process based on fracture mechanics and the extended finite element method; when the crack propagation meets the condition for complete fatigue failure of the specimen, record the number of load cycles at this time as the fatigue crack propagation life. Specifically, it includes: S21: An initial crack is inserted at the completely failed unit in step S14. The length of the initial crack is the same as the total length of the accumulated failed units, and the normal of the initial crack surface is parallel to the direction of the maximum tensile stress. S22: Considering the characteristics of crack propagation rate and crack tip stress intensity factor in the early and late stages of vibration fatigue crack propagation, the governing equation for fatigue crack propagation rate is constructed: ,in: This represents the fatigue crack propagation rate. Stress intensity factor This is the crack propagation threshold value. C represents fracture toughness, and m represents material parameters. S23: The ABAQUS user subroutine UMIXMODEFATIGUE, written in Fortran, updates the crack propagation rate variable by the maximum and minimum values ​​of the three energy release rates at the crack tip within one cycle, thereby controlling the fatigue crack propagation rate; when the total fatigue crack length reaches a certain threshold, the sample is considered to have completely failed due to fatigue, and the calculation is stopped. S24: When the calculation stops, record the vibration fatigue crack propagation life of the TC4 titanium alloy specimen. ; S3: Fatigue crack initiation life calculated in steps S1 and S2. and extended lifespan The whole life prediction of vibration fatigue crack initiation-propagation in TC4 titanium alloy was obtained. .

5. A system for implementing the two-stage full-life fatigue crack prediction method for titanium alloys according to any one of claims 1-4, characterized in that, include: The fatigue crack initiation life prediction unit and the fatigue crack propagation life prediction unit are as follows: The fatigue crack initiation life prediction unit calculates the damage evolution process of the material under cyclic loading conditions based on a suitable damage mechanics model, and obtains the initial fatigue crack characteristics and fatigue crack initiation life. The fatigue crack propagation life element calculates the process of crack propagation under cyclic loading conditions based on the initial fatigue crack characteristics and a suitable fatigue crack propagation rate control equation, thus obtaining the fatigue crack propagation life. Through the combined action of the two elements, fatigue life prediction is achieved.

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