Titanium / aluminum alloy fatigue life prediction method considering material crack tip plastic zone

Abstract

The invention discloses a titanium / aluminum alloy fatigue life prediction method considering a material crack tip plastic zone, and belongs to the technical field of material and structure fatigue life evaluation. The method comprises the following steps: acquiring a material parameter and a load; the crack tip plastic zone energy dissipation model is corrected, and the fatigue crack initiation life is calculated; determining a calculation starting point based on an equivalent initial defect size method, and calculating the crack propagation life by using an NASGRO equation; and finally summing to obtain the total life. According to the method, the defects that a traditional empirical model is insufficient in physical property and an existing physical model ignores plastic dissipation and is difficult to link short crack propagation are overcome, and full-period and high-precision life prediction from microcosmic initiation to macroscopic fracture is achieved through physical criteria and an equivalent method.

Description

Technical Field

[0001] This invention belongs to the field of material fatigue performance analysis and structural life prediction technology, and specifically relates to a material fatigue life prediction method based on physical mechanisms. This method achieves accurate simulation of the entire fatigue process by accurately predicting the fatigue crack initiation life and the multi-stage crack propagation life respectively. Background Technology

[0002] Fatigue is the primary cause of structural failure under alternating loads. Traditional fatigue life prediction methods heavily rely on empirical or semi-empirical models such as the SN curve. While widely used, these methods have significant limitations: they treat the fatigue process as a "black box," failing to explicitly differentiate between the two distinct physical mechanisms of crack initiation and crack propagation. In high-cycle and ultra-high-cycle fatigue, crack initiation accounts for the majority of the total lifespan, and empirical models cannot accurately capture the microscopic physical processes of this stage, resulting in highly variable and inaccurate predictions.

[0003] In terms of theoretical models, Tanaka and Mura proposed a classic crack initiation model based on the dislocation dipole accumulation theory, establishing for the first time a quantitative relationship between lifetime and microscopic parameters such as grain size. However, this original model did not fully consider the local plastic deformation and energy dissipation at the crack nucleation site, leading to predictions that often deviate from experimental data. During crack propagation, short cracks (with sizes comparable to grain size) exhibit different propagation behaviors than long cracks, such as propagation below the long crack threshold and a higher propagation rate, making it difficult to directly apply the traditional Paris formula or NASGRO equation. The equivalent initial defect size method, by inferring an equivalent initial defect, makes the total lifetime predicted by the long crack propagation model consistent with experiments, but it is often disconnected from crack initiation models, lacking a unified, full-cycle prediction framework from microscopic nucleation to macroscopic fracture.

[0004] Therefore, there is a significant gap in the existing technology: there is a lack of a fatigue crack initiation life prediction model that can take into account local plastic deformation and its energy dissipation, and a method that can accurately predict the entire fatigue life of materials. Summary of the Invention

[0005] To address the shortcomings of the prior art, the present invention aims to provide a material fatigue life prediction method with a clear physical mechanism, high prediction accuracy, and strong engineering applicability.

[0006] To achieve the objectives of this invention, the following technical solution is adopted:

[0007] A method for predicting the fatigue life of materials considering the plastic zone at the crack tip, applicable to high-cycle and ultra-high-cycle fatigue state prediction, includes the following steps:

[0008] Parameter acquisition: Obtain the mechanical parameters of the material to be predicted, including basic mechanical parameters, fracture mechanics parameters and microstructure parameters;

[0009] Construction of fatigue crack initiation life prediction model: Based on dislocation pile-up theory, the energy dissipation mechanism generated by the plastic zone at the crack tip is introduced; the shielding effect of the plastic zone size on the stress field at the crack tip is quantified by the banded yield model, and the plastic dissipation energy is calculated and the fracture surface energy of the material is corrected. A fatigue crack initiation life prediction model including plastic zone correction term is established, and fatigue crack initiation life is calculated.

[0010] Construction of fatigue crack propagation life prediction model: The equivalent initial defect size method is adopted to back-calculate the equivalent initial crack size based on the long crack propagation law, so as to eliminate the influence of microstructure sensitivity in the short crack propagation stage; the crack propagation rate equation is used to construct a crack propagation life prediction model from the equivalent initial crack size to the critical fracture size, and the crack propagation life is calculated.

[0011] Fatigue life calculation: The fatigue crack initiation life and fatigue crack propagation life are added together to obtain the predicted total fatigue life of the material under the alternating stress.

[0012] Furthermore, fundamental mechanical parameters include yield strength. Elastic modulus E, Poisson's ratio Fracture mechanics parameters include fatigue crack propagation threshold. fracture toughness Microstructure parameters include grain size. .

[0013] Furthermore, a fatigue crack initiation life prediction model is constructed, including the following steps:

[0014] Using the Dugdale-Barenblatt model, the size of the plastic zone at the crack tip is calculated based on the stress intensity factor and yield strength:

[0015] ;

[0016] in, For the dimensions of the plastic zone, This is the crack propagation threshold value. For fracture toughness, Yield strength;

[0017] The intrinsic fracture surface energy is calculated, and a correction coefficient related to the stress intensity factor threshold and grain size is introduced to characterize the constraint effect of the microstructure on the energy dissipation in the plastic region, thus obtaining the corrected effective fracture energy:

[0018] ;

[0019] in, To correct the range of stress intensity factor, Where E is the crack length and E is the elastic modulus. This is the crack propagation threshold value. Yield strength;

[0020] Substituting the modified effective fracture energy into the Tanaka-Mura model framework, we obtain the fatigue crack initiation life, where the fatigue crack initiation life is directly proportional to the modified effective fracture energy and inversely proportional to the square of the applied stress range.

[0021] ;

[0022] in, Taylor factor, For the fitting parameters, For stress amplitude, For dislocation frictional stress, Lifespan for crack initiation.

[0023] Furthermore, a fatigue crack propagation life prediction model is constructed, including the following steps:

[0024] Determine the equivalent initial defect size: Assume that the extended life of the material at the fatigue limit stress level tends to infinity. Using the geometric correction factor, the equivalent initial crack size is derived in reverse through the fatigue limit stress and stress intensity factor threshold value.

[0025] ;

[0026] in, The fatigue limit, For geometric correction factor, This is the threshold value for crack propagation;

[0027] Determining the critical crack size: Based on linear elastic fracture mechanics, the critical crack size at which the crack becomes unstable and fractures is determined by the fracture toughness of the material and the maximum applied stress.

[0028] ;

[0029] in, For maximum stress, For fracture toughness;

[0030] Calculation of crack propagation life: The NASGRO equation, which takes into account the crack closure effect, is used as the crack propagation rate model. The crack length is numerically integrated from the equivalent initial crack size to the critical crack size to calculate the crack propagation life. The NASGRO equation comprehensively considers the rapid propagation effect caused by stress ratio and fracture toughness, as well as the low-speed propagation effect near the threshold value.

[0031] ;

[0032] in, The equivalent initial crack size is, The critical crack size. C is the maximum stress intensity factor. , , These are the fitting parameters.

[0033] Compared with the prior art, the beneficial effects of the present invention are:

[0034] 1. Strong predictive physicality and significantly improved accuracy: By introducing a plastic zone energy correction term based on fracture mechanics, the initiation model more realistically reflects the dominant role of local micro-plastic deformation under low stress and high cycle fatigue, fundamentally improving the prediction bias of traditional physical models in the near fatigue limit region, thus achieving a significant improvement in prediction accuracy over the entire lifespan, especially in the long lifespan region.

[0035] 2. A natural transition across damage scales is achieved: The inherent properties of materials are creatively used as the physical criterion for the end of the initiation stage, and the equivalent initial defect size a0 is determined based on this. This design establishes a clear, reasonable, and physically-based transition bridge between the accumulation of physical damage at the microscale and the engineering-calculable crack propagation at the macroscale, solving the long-standing problem of the disconnect between the "initiation" and "propagation" models.

[0036] 3. A complete prediction chain covering the entire life cycle has been formed: This invention constructs an integrated framework of "a nucleation model with physical mechanism correction" + "a NASGRO extended model based on EIFS". This framework is logically rigorous and the steps are clear. For the first time, it systematically realizes continuous and quantitative prediction of the entire life cycle from the beginning of nanoscale / microscale dislocation motion, through microcrack nucleation and short crack propagation, to macroscopic long crack instability and fracture.

[0037] 4. Excellent engineering applicability and practicality: All input parameters required by this invention can be reliably obtained through internationally or nationally standardized material testing and microscopic analysis, without the need for difficult-to-obtain mesoscopic parameters. Examples demonstrate that this method exhibits excellent predictive ability for different material systems, including aluminum alloys (such as 6082) and titanium-aluminum intermetallic compounds (such as TNM-TiAl), proving its broad applicability. Attached Figure Description

[0038] Figure 1 This is a flowchart illustrating the overall process of the method of the present invention.

[0039] Figure 2 This is a schematic diagram showing the fitting of experimental SN data and classic SN curves for 6082 aluminum alloy in Example 1.

[0040] Figure 3 A schematic diagram illustrating the principle of correcting the plastic zone at the crack tip.

[0041] Figure 4 This is a comparison chart of the fatigue crack initiation life curve of 6082 aluminum alloy predicted based on the modified model of the present invention and experimental data in Example 1.

[0042] Figure 5 This is a schematic diagram illustrating the core principle of the equivalent initial defect size method.

[0043] Figure 6 This is a comparison chart of the experimental data on the fatigue crack propagation rate of 6082 aluminum alloy in Example 1 and the curve fitted using the NASGRO equation.

[0044] Figure 7 This is a comparison and verification diagram of the fatigue life SN curve of 6082 aluminum alloy predicted by the method of the present invention and the experimental data in Example 1.

[0045] Figure 8 This is a comparison and verification diagram of the SN curve of the TNM-TiAl alloy fatigue life predicted by the method of the present invention and the experimental data in Example 2. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the described embodiments are only for explaining the invention and are not intended to limit the invention.

[0047] like Figure 1 As shown, the implementation of the method of the present invention begins with the complete acquisition of the parameters of the target material or component and the clear definition of the service load (step S1). Subsequently, the process executes two core calculation threads in parallel: thread one calculates the fatigue crack initiation life based on the "initiation model modified by the plastic zone". (Step S2); Thread 2 calculates the crack propagation life N based on the "extended model based on EIFS and NASGRO equations". p (Step S3). Finally, the results from the two threads are combined to synthesize the total lifetime. The model is then validated by comparing it with independent experimental data (step S4).

[0048] Example 1:

[0049] This embodiment uses 6082 aluminum alloy sheet, which is widely used in the aerospace field, as an example to demonstrate the specific implementation process of the present invention.

[0050] Step S1: Parameter Acquisition

[0051] The necessary parameter set for 6082 aluminum alloy was obtained by performing national standard material tests and consulting publicly available reliable literature:

[0052] Microstructure parameters: The average grain size was obtained statistically using the cross-section method through metallographic sample preparation and image analysis software. .

[0053] Basic mechanical property parameters: Tensile tests were conducted at room temperature according to GB / T 228.1 to obtain: Yield strength. =300MPa, elastic modulus E Poisson's ratio =0.3.

[0054] Fracture mechanical properties parameters:

[0055] Fatigue crack propagation threshold = fracture toughness K IC = The fatigue crack propagation rate was obtained by using compact tensile (CT) specimens according to the GB / T 6398 standard.

[0056] For the experimentally measured da / dN-ΔK data points, nonlinear regression fitting was performed using the NASGRO equation form to obtain the material constants: , , , .

[0057] Fatigue limit: From Figure 2 The SN data shown, obtained through group fatigue testing, is defined at 10 9 The stress amplitude at which the material does not fail under multiple cycles is the fatigue limit, which is 103.8 MPa.

[0058] Load conditions: Set the stress range to be evaluated, for example... =200MPa (corresponding stress ratio R=-1).

[0059] Step S2: Calculate fatigue crack initiation life .

[0060] Model Formula: The original Tanaka-Mura model views crack initiation as a process where dislocation dipoles accumulate within the slip band, eventually leading to microcrack nucleation. Its energy balance primarily considers the surface energy required to form the new crack surface. However, in real materials, especially ductile materials, a plastic zone forms at the crack tip during the early nucleation and early micro-propagation stages. Plastic deformation in this region consumes additional energy, which is neglected in the original model. To quantitatively describe this effect, the Dugdale-Barenblatt model is introduced. Based on this model, the size of the plastic zone at the crack tip can be approximated as:

[0061]

[0062] in, For the dimensions of the plastic zone, This is the crack propagation threshold value. For fracture toughness, It represents the yield strength.

[0063] The effective stress intensity factor range after considering the plastic zone correction can be expressed as:

[0064]

[0065] According to fracture mechanics, the energy required for crack propagation per unit area (i.e., the energy release rate) Alternatively, the fracture energy may be proportional to the square of the stress intensity factor. Therefore, the effective fracture energy after introducing the plastic zone correction... for:

[0066]

[0067] in, To correct the range of stress intensity factor, Where E is the crack length and E is the elastic modulus. This is the crack propagation threshold value. The term within square brackets represents the yield strength. This is the core energy correction term for the plastic zone at the crack tip. This term explicitly includes the energy correction term derived from the yield strength. and crack length The contribution of plastic dissipation determined by it.

[0068] The modified fracture energy is substituted into the energy balance framework of the original Tanaka-Mura model to replace the original surface energy term. Simultaneously, the Taylor factor is used... The range of shear stress on the micro-slip surface With macroscopic normal stress range Connect them and introduce a fitting parameter. To improve the model's adaptability to experimental data, the revised expression for fatigue crack initiation life was derived as follows:

[0069]

[0070] in, Taylor factor, For the fitting parameters, For stress amplitude, For dislocation frictional stress, Lifespan for crack initiation.

[0071] Parameter determination: Taylor factor The average orientation factor for polycrystalline materials is used; a typical value is taken in this example. =2. Dislocation frictional stress related terms. In engineering, this can be approximated as the fatigue limit of the material. The exponential fitting parameters in the model... The model was determined by fitting it to a set of crack initiation test data, and in this example, the following results were obtained. =0.22.

[0072] Physical criterion setting: Based on the core idea of ​​this invention, the initiation stage is defined as ending when a microcrack propagates to the point of crossing the first grain boundary. Therefore, in the model calculation, the crack length is taken as... .

[0073] Calculation process: Substitute all the above parameters into the model. For a given... Since all the right-hand side of the model equation consists of known constants, a constant value can be calculated. The lifespan of the germination stage can then be calculated using the following formula: For a series of different Repeat this calculation to obtain the germination lifespan. Predicted curves as stress changes. (Example) Figure 4 As shown, the predicted curve is in high agreement with the experimental data points.

[0074] Step S3: Calculate crack propagation life

[0075] Determine the equivalent initial crack size :

[0076] For standard CT specimens, the geometric correction factor This can be determined by consulting a manual or through finite element calculations; in this example, it is simplified to... .

[0077] Substitute into the calculation formula: The calculation yields: ≈35.8×10 −6m = 35.8 μm. This value is slightly larger than the grain size. Physically, it represents the equivalent starting point after the germination process ends and the process enters the stable expansion phase, such as... Figure 5 As shown in the principle.

[0078] Determine the critical crack size :

[0079] For load =200MPa (R=-1), maximum stress =100MPa, substitute into the calculation formula: The calculation yields: ≈0.00127m=1.27mm.

[0080] Numerical integration based on the NASGRO equation :

[0081] The NASGRO equation is expressed as follows:

[0082]

[0083] in, The effective stress intensity factor range can be calculated using a closed-loop model; The range of stress intensity factors; This is the maximum stress intensity factor.

[0084] Extended lifespan By integrating the reciprocal of the above equation, we obtain:

[0085]

[0086] in, The equivalent initial crack size is, The critical crack size. C is the maximum stress intensity factor. , , These are the fitting parameters.

[0087] Write an integration program using numerical computation software (such as MATLAB or Python). The program needs to consider the load ratio. Calculate using empirical formulas such as Newman's. and .

[0088] Set the minimum score to The upper limit is The integral value is calculated using numerical integration methods such as adaptive Simpson or Runge-Kutta, and this value is the integral value in the given condition. Crack propagation life below .

[0089] Figure 6 This demonstrates the application of the NASGRO equations to the material in this example. Excellent fit of experimental data is a prerequisite for ensuring the accuracy of integration.

[0090] Step S4: Calculate and verify the fatigue life.

[0091] For each stress level Perform arithmetic addition:

[0092] The calculated series of data points are plotted as the SN curve predicted by the method of this invention. This predicted curve, along with the full-life fatigue test data of 6082 aluminum alloy obtained from published literature using the standard rise-fall method or the group method, is then plotted together on [a graph / plot]. Figure 7 The comparison results show that the SN curve predicted by the method of this invention accurately penetrates the central region of the experimental data distribution band, within 10... 4 Up to 10 9 The method demonstrated excellent prediction accuracy over a wide range of cycles, fully verifying the reliability, effectiveness, and high precision of the method for aluminum alloy material systems.

[0093] Example 2:

[0094] To fully demonstrate the universality and cross-material applicability of the method of this invention, it was applied to TNM-TiAl intermetallic compounds with significantly different microstructures and properties. This material is a candidate material for advanced high-pressure turbine blades in aero-engines, and its fatigue assessment is crucial.

[0095] Parameter acquisition:

[0096] Key parameter sets for TNM-TiAl alloys were obtained through published research papers and supplementary experiments:

[0097] Average grain size .

[0098] Basic mechanical properties: yield strength Elastic modulus E Poisson's ratio .

[0099] Fracture mechanical properties: fatigue crack propagation threshold fracture toughness .

[0100] Fatigue limit: defined at 10°C based on its SN curve characteristics. 7 The fatigue limit for each cycle is 400 MPa.

[0101] NASGRO equation parameters: through the alloy A new set of values ​​was obtained by fitting the experimental curve.

[0102] Calculation and verification:

[0103] Initiation life calculation: Substitute the parameters of the TNM-TiAl alloy into the same initiation model formula described in step S2. Similarly, take the first critical size. The fitting parameter α value corresponding to the material is determined by fitting.

[0104] Extended life calculation: Strictly follow the procedure described in step S3 and use the same calculation formula to calculate the lifespan of the material. , And obtained through numerical integration .

[0105] Fatigue life calculation and verification: calculation .like Figure 8 The schematic diagram shows a comparison between the predicted SN curve and independent fatigue test data of the TNM-TiAl alloy. Quantitative analysis indicates that the predicted curve and the experimental data agree well, with a goodness of fit ( ). The accuracy can reach over 0.97. This result strongly demonstrates that the core method framework proposed in this invention—namely, describing the initiation mechanism uniformly through plastic region correction and bridging the extension stage through EIFS—has strong adaptability and high-precision prediction capabilities for different types of materials (from aluminum alloys to titanium-aluminum intermetallic compounds).

[0106] The fatigue life prediction method provided by this invention has clear steps, and all required input parameters can be obtained through mature industrial standard tests, exhibiting good operability and repeatability. The prediction results can be directly used for initial design material selection, process optimization, safe life determination, maintenance cycle formulation, and service reliability assessment of engineering structures.

[0107] The above embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of the patent. Any simple modifications, equivalent substitutions, and improvements made based on the technical solutions of the present invention without departing from the spirit and technical essence disclosed herein should be included within the protection scope of the claims of the present invention.

Claims

1. A method for predicting the fatigue life of a titanium / aluminum alloy considering the plastic zone at the crack tip, characterized by, The application relates to a method for predicting the fatigue life of a material, and belongs to the technical field of fatigue life prediction. Parameter acquisition: the mechanical parameters of a material to be predicted are acquired, wherein the mechanical parameters include basic mechanical parameters, fracture mechanics parameters and microstructure parameters; Fatigue crack initiation life prediction model construction: based on the dislocation pile-up theory, an energy dissipation mechanism generated in a plastic zone of a crack tip is introduced; a strip yield model is used to quantize a shielding effect of the plastic zone size on the stress field of the crack tip, so that plastic dissipation energy is calculated, the fracture surface energy of the material is modified, a fatigue crack initiation life prediction model containing a plastic zone correction term is established, and the fatigue crack initiation life is calculated; Fatigue crack propagation life prediction model construction: an equivalent initial defect size method is adopted, an equivalent initial crack size is deduced based on long crack propagation rules, so that the influence of microstructure sensitivity in the short crack propagation stage is eliminated; a crack propagation rate equation is used to construct a crack propagation life prediction model from the equivalent initial crack size to a critical fracture size, so that the crack propagation life is calculated; Fatigue total life calculation: the fatigue crack initiation life and the fatigue crack propagation life are added, so that the predicted total fatigue life of the material under the alternating stress is obtained.

2. The method of claim 1, wherein, The predicted material is a titanium alloy or an aluminum alloy.

3. The method of claim 1, wherein, Basic mechanical parameters include yield strength , elastic modulus , and Poisson's ratio ; fracture mechanics parameters include fatigue crack growth threshold and fracture toughness ; and microstructural parameters include grain size .

4. The method of claim 1, wherein, The fatigue crack initiation life prediction model is constructed and comprises the following steps: A Dugdale-Barenblatt model is used to calculate the plastic zone size of the crack tip according to the stress intensity factor and the yield strength; The intrinsic fracture surface energy is calculated, a correction coefficient related to the stress intensity factor threshold value and the grain size is introduced, and the correction coefficient is used to represent the constraint effect of the microstructure on the plastic zone energy dissipation, so that the effective fracture energy after correction is obtained; The effective fracture energy after correction is substituted into a Tanaka-Mura model framework, so that the fatigue crack initiation life is obtained, wherein the fatigue crack initiation life is proportional to the effective fracture energy after correction and inversely proportional to the square of the applied stress range.

5. The method of claim 1, wherein, The fatigue crack propagation life prediction model is constructed and comprises the following steps: Equivalent initial defect size determination: the propagation life of the material under the fatigue limit stress level tends to infinity, a geometric correction factor is used, and the fatigue limit stress and the stress intensity factor threshold value are reversely deduced to obtain the equivalent initial crack size; Critical crack size determination: according to linear elastic fracture mechanics, the critical crack size when the crack is unstably fractured is determined according to the fracture toughness of the material and the maximum applied stress; Propagation life calculation: the NASGRO equation considering the crack closure effect is used as a crack propagation rate model, the crack length is numerically integrated from the equivalent initial crack size to the critical crack size, and the crack propagation life is calculated.

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