A method for rapid prediction of thermal-mechanical fatigue life of metal materials based on hysteretic energy density

Abstract

The present application relates to the field of material science and engineering application technology, specifically to a kind of metal material thermal mechanical fatigue life fast prediction method based on hysteresis energy density.First, hysteresis curve is used to calculate hysteresis energy density, then the quantitative relationship between shape coefficient, stress variation range and plastic strain range between low cycle fatigue and thermal mechanical fatigue is used, to achieve the purpose of predicting thermal mechanical fatigue hysteresis energy density under the same mechanical strain amplitude by low cycle fatigue, finally, energy accumulation damage model is used to predict thermal mechanical fatigue life.The method carries out two groups of experiments for low cycle fatigue and thermal mechanical fatigue respectively, realizes the prediction of thermal mechanical fatigue life under different mechanical strain amplitudes by low cycle fatigue, establishes the correlation between low cycle fatigue and thermal mechanical fatigue by using the similarity between them in the process of cyclic loading, effectively reduces the experimental amount required for thermal mechanical fatigue life evaluation, and is applied to the thermal mechanical fatigue life prediction of high-temperature alloy and vermicular cast iron and other metal materials.

Description

Technical Field

[0001] This invention relates to the field of materials science and engineering application technology, specifically to a rapid prediction method for the thermomechanical fatigue life of metallic materials based on hysteresis energy density. Background Technology

[0002] Low-cycle fatigue and thermomechanical fatigue are both common failure modes of engineering components during service. The key difference lies in the fact that thermomechanical fatigue requires additional temperature cycling at specific intervals on top of load cycling. In actual testing, ensuring the accuracy of temperature cycling necessitates reducing the loading frequency and introducing highly sensitive temperature control elements into the testing platform, which significantly increases time and economic costs. Therefore, utilizing isothermal low-cycle fatigue data to rapidly assess and predict the thermomechanical fatigue life of materials has great application potential.

[0003] Currently, classic fatigue life prediction models can be divided into two categories: the traditional Basquin model and the Coffin-Manson model. These models assume that the fatigue life of a material is mainly related to the stress or strain amplitude it bears. However, since the strength and plasticity of metallic materials are usually inversely related, these models are not comprehensive in evaluating the fatigue performance of different materials. Due to these issues, researchers have proposed energy accumulation damage models that simultaneously consider strength and plasticity, thus providing a comprehensive assessment of fatigue damage occurring during cyclic loading. However, how to establish a correlation between low-cycle fatigue and thermomechanical fatigue through energy accumulation damage models to achieve rapid prediction of thermomechanical fatigue life requires further research. Summary of the Invention

[0004] To address the high testing costs associated with thermomechanical fatigue performance evaluation, this invention aims to provide a rapid prediction method for the thermomechanical fatigue life of metallic materials based on hysteresis energy density. By obtaining common influencing parameters between low-cycle fatigue and thermomechanical fatigue, the method can predict thermomechanical fatigue life using low-cycle fatigue. This method comprehensively considers the influence of stress and plastic deformation on material fatigue damage, effectively reducing the time and economic costs of traditional thermomechanical fatigue life testing while also providing optimization directions for the fatigue resistance design of metallic materials.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A rapid prediction method for the thermomechanical fatigue life of metallic materials based on hysteresis energy density, the method specifically includes the following steps:

[0007] (1) Select two different mechanical strain amplitudes to perform strain-controlled thermomechanical fatigue and isothermal low-cycle fatigue performance tests on the metal material at the peak temperature of thermomechanical fatigue, and obtain the corresponding hysteresis curves and fatigue life values.

[0008] (2) Select the mid-life hysteresis curve to obtain the corresponding stress variation range and plastic strain range, and obtain the hysteresis energy density and shape factor data by calculating the area of ​​the hysteresis curve.

[0009] (3) The mid-lifetime hysteresis energy density W s With fatigue life N f Linear fitting is performed in a double logarithmic coordinate system to obtain the corresponding fitting parameters;

[0010] (4) Using the low-cycle fatigue and thermomechanical fatigue plastic strain range Δε obtained in step (2) p Perform linear fitting to obtain the corresponding fitting parameters m and n;

[0011] (5) Using the low-cycle fatigue plastic strain range Δε obtained in step (2) p The stress variation range Δσ, shape factor k, and fitting parameters m and n obtained in step (4) are used to calculate the thermomechanical fatigue hysteresis energy density under the same mechanical strain amplitude.

[0012] (6) Substitute the thermomechanical fatigue hysteresis energy density obtained in step (5) into step (3) to calculate the corresponding thermomechanical fatigue life.

[0013] In the rapid prediction method for thermomechanical fatigue life of metallic materials based on hysteresis energy density, step (1) involves strain-controlled thermomechanical fatigue, which includes low-cycle fatigue and thermomechanical fatigue. The selected mechanical strain amplitude is not lower than the yield strain of the material under the corresponding experimental conditions.

[0014] In the rapid prediction method for thermomechanical fatigue life of metallic materials based on hysteresis energy density, in step (2), the area of ​​the hysteresis curve is not 0, the stress variation range is the difference between the maximum stress and the minimum stress, the plastic strain range is the distance between the intersection of the hysteresis loop and the strain axis when the stress is 0, and the shape factor is the ratio of the hysteresis energy density to the product of the stress variation range and the plastic strain range.

[0015] In the aforementioned rapid prediction method for thermomechanical fatigue life of metallic materials based on hysteresis energy density, step (3) uses W0 and β as linear fitting parameters in a double logarithmic coordinate system, with the following expression:

[0016] W s =W0·N f -1 / β

[0017] In the formula, W sRepresents hysteresis energy density (MJ / m 3 W0 represents intrinsic fatigue toughness (MJ / m). 3 ), β represents the fatigue damage conversion index (dimensionless parameter), N f Represents fatigue life (weeks).

[0018] In the aforementioned rapid prediction method for thermomechanical fatigue life of metallic materials based on hysteresis energy density, step (4) shows a linear relationship between the plastic strain range of low-cycle fatigue and thermomechanical fatigue, expressed as follows:

[0019] Δε p-TMF =mΔε p-LCF +n

[0020] In the formula, Δε p-TMF Represents the range of thermomechanical fatigue plastic strain (%), Δε p-LCF denoted by , representing the range of low-cycle fatigue plastic strain (%), where m and n are fitting constants.

[0021] In the rapid prediction method for thermomechanical fatigue life of metallic materials based on hysteresis energy density, in step (5), the shape factor k and stress variation range Δσ of the same metallic material are basically the same in high temperature low cycle fatigue (the experimental temperature is the peak temperature of thermomechanical fatigue) and thermomechanical fatigue process, and equivalent substitution is performed.

[0022] In the aforementioned rapid prediction method for thermomechanical fatigue life of metallic materials based on hysteresis energy density, step (6) refers to the thermomechanical fatigue hysteresis energy density W. s-TMF The calculation formula is as follows:

[0023] W s-TMF =k LCF ·Δσ LCF ·(mΔε p-LCF +n)

[0024] In the formula, W s-TMF Thermomechanical fatigue hysteresis energy density (MJ / m 3 ), Δε p-LCF For the low-cycle fatigue plastic strain range (%), k LCF The shape factor Δσ represents low-cycle fatigue. LCF The parameter k represents the stress variation range during low-cycle fatigue. LCF and Δσ LCF The parameters m and n are determined by linear fitting of the plastic strain ranges obtained from thermomechanical fatigue and low-cycle fatigue tests, based on the hysteresis curves obtained from low-cycle fatigue tests.

[0025] The design concept of this invention is:

[0026] Traditional fatigue life prediction models typically apply only to a single loading mode and fail to establish a correlation between fatigue performance under different loading modes. This invention leverages the similarity between low-cycle fatigue and thermomechanical fatigue during cyclic loading to clarify the interconversion relationships of relevant parameters in the life prediction model. Finally, by combining this with an energy accumulation damage model, a correlation is established between low-cycle fatigue and thermomechanical fatigue life. This method requires only two sets of experiments each for low-cycle fatigue and thermomechanical fatigue to predict thermomechanical fatigue life under different mechanical strain amplitudes using low-cycle fatigue.

[0027] The advantages and beneficial effects of this invention are as follows:

[0028] 1. This invention utilizes the similarity between low-cycle fatigue and thermomechanical fatigue during cyclic loading to accurately identify three sets of interconversion parameters, and establishes the relationship between low-cycle fatigue and thermomechanical fatigue by combining the energy accumulation damage model.

[0029] 2. The fatigue life prediction parameters of this invention can be obtained through low-cycle fatigue testing, which effectively reduces the amount of experiments required for thermomechanical fatigue performance evaluation and greatly reduces testing costs.

[0030] 3. The model of this invention has high accuracy and universality, and is applicable to the prediction of thermomechanical fatigue life of metallic materials under different types and test environments under strain control. Attached Figure Description

[0031] Figure 1 This is a flowchart of a method for predicting the fatigue life of materials.

[0032] Figure 2 This is a schematic diagram of the relevant model parameters in a hysteresis loop. In the figure, the horizontal axis ε represents strain, and the vertical axis σ represents stress.

[0033] Figure 3 The linear relationship between thermomechanical fatigue hysteresis energy and fatigue life of laser-selected melt-formed high-temperature alloy materials is shown on a double logarithmic coordinate system. In the figure, the horizontal axis, Number of cycles to failure, represents the fatigue life (N). f The ordinate represents the hysteretic energy density (MJ / m³). 3 TMF-OP is an anti-phase thermomechanical fatigue test.

[0034] Figure 4 The equivalent transformation relationship of the shape factor k in low-cycle fatigue and thermomechanical fatigue of laser-selected melt-formed high-temperature alloy materials is shown in the figure. Δε p The vertical axis represents the range of plastic strain, and Δσ represents the range of stress variation; the vertical axis represents the hysteretic energy density (MJ / m²). 3 ).

[0035] Figure 5 For laser-selected high-temperature alloy materials, the range of low-cycle fatigue stress variation gradually approaches the range of thermomechanical fatigue stress variation with increasing experimental temperature. In the figure, the horizontal axis Δε... m / 2 represents the mechanical strain amplitude (%), Δσ LCF For the range of low-cycle fatigue stress variation, Δσ TMF This represents the range of thermomechanical fatigue stress variation.

[0036] Figure 6 The linear relationship between the plastic strain range in low-cycle fatigue and thermomechanical fatigue of laser-selected melt-formed high-temperature alloy materials is shown in the figure. The horizontal axis represents Δε. p-TMF The thermomechanical fatigue plastic strain range (%) is represented by the vertical axis Δε. p-LCF The range of low-cycle fatigue plastic strain (%).

[0037] Figure 7 This figure shows the results of low-cycle fatigue prediction of thermomechanical fatigue life for melt-formed high-temperature alloy materials using laser selection. The horizontal axis is N. f The vertical axis represents the actual fatigue life (Exp), and the horizontal axis N represents the actual fatigue life. f This represents the predicted fatigue life (Cal).

[0038] Figure 8 The figure shows the linear relationship between thermomechanical fatigue hysteresis energy and fatigue life of vermicular graphite cast iron on a double logarithmic coordinate system. In the figure, the horizontal axis, Number of cycles to failure, represents fatigue life (N). f The ordinate represents the hysteretic energy density (MJ / m³). 3 ).

[0039] Figure 9 This represents the equivalent transformation relationship of the shape factor k in low-cycle fatigue and thermomechanical fatigue of vermicular graphite cast iron. In the figure, Δε... p The vertical axis represents the range of plastic strain, and Δσ represents the range of stress variation; the vertical axis represents the hysteretic energy density (MJ / m²). 3 ).

[0040] Figure 10 This figure shows the equivalent transformation relationship between the low-cycle fatigue stress variation range and the thermomechanical fatigue stress variation range of vermicular graphite cast iron. The horizontal axis Δε... m / 2 represents the mechanical strain amplitude, Δσ LCF For the range of low-cycle fatigue stress variation, Δσ TMF This represents the range of thermomechanical fatigue stress variation.

[0041] Figure 11This represents the linear relationship between the plastic strain range in low-cycle fatigue and thermomechanical fatigue of vermicular graphite cast iron. In the figure, the horizontal axis represents Δε. p-TMF The ordinate represents the range of plastic strain during thermomechanical fatigue, Δε. p-LCF This refers to the range of plastic strain during low-cycle fatigue.

[0042] Figure 12 The results of predicting thermomechanical fatigue life of vermicular graphite cast iron material using low-cycle fatigue are shown in the figure. The horizontal axis is N. f The vertical axis represents the actual fatigue life (Exp), and the horizontal axis N represents the actual fatigue life. f This represents the predicted fatigue life (Cal). Detailed Implementation

[0043] In the specific implementation process, the present invention first uses the hysteresis curve to calculate the hysteresis energy density, then uses the equivalent relationship of the shape factor and the equivalent transformation relationship between the stress variation range and the plastic strain range in low-cycle fatigue and thermomechanical fatigue, so as to achieve the purpose of predicting the hysteresis energy density of thermomechanical fatigue through low-cycle fatigue, and finally combines the linear relationship between hysteresis energy density and fatigue life under double logarithmic coordinates to predict thermomechanical fatigue life.

[0044] like Figure 1 As shown, this invention proposes a rapid prediction method for the thermomechanical fatigue life of metallic materials based on hysteresis energy density. The specific steps are as follows:

[0045] Step (1): Analyze the service conditions of the components and determine the mechanical strain range, service temperature, strain rate and other parameters of the components during service.

[0046] Step (2): Select a metallic material and perform strain-controlled isothermal low-cycle fatigue and thermomechanical fatigue performance tests under two mechanical strain amplitudes to obtain mid-life hysteresis loop data. Among them, the isothermal low-cycle fatigue test temperature is the peak temperature of the thermomechanical fatigue test, and mid-life means half of the fatigue life.

[0047] Step (3): Using the obtained hysteresis curve, calculate the stress variation range and plastic strain range, and obtain the hysteresis energy density and shape factor by calculating the area of ​​the hysteresis curve. The stress variation range and plastic strain range are as follows: Figure 2 As shown.

[0048] Step (4): The hysteresis energy density and fatigue life of thermomechanical fatigue are linearly fitted in a double logarithmic coordinate system according to formula (1) to obtain the linear fitting parameters W0 and β.

[0049] W s =W0·N f -1 / β (1)

[0050] In the formula, Ws Represents hysteresis energy density (MJ / m 3 W0 represents intrinsic fatigue toughness (MJ / m). 3 ), β represents the fatigue damage conversion index (dimensionless parameter), N f Represents fatigue life (weeks).

[0051] Step (5): The hysteresis energy density is linearly fitted with the stress variation range and the plastic strain range according to formula (2) to obtain the shape factor k.

[0052] W s =k·Δσ·Δε p (2)

[0053] In the formula, W s Represents hysteresis energy density (MJ / m 3 ), Δε p Δσ represents the range of plastic strain, and Δσ represents the range of stress variation.

[0054] Step (6): Linearly fit the plastic strain ranges of low-cycle fatigue and thermomechanical fatigue according to formula (3):

[0055] Δε p-TMF =mΔε p-LCF +n (3)

[0056] In the formula, Δε p-TMF Represents the range of plastic strain during thermomechanical fatigue; Δε p-LCF This represents the range of plastic strain during low-cycle fatigue. m and n are fitting constants.

[0057] Step (7): The thermomechanical fatigue hysteresis energy density W s-TMF Calculate according to formula (4):

[0058] W s-TMF =k LCF ·Δσ LCF ·(mΔε p-LCF +n) (4)

[0059] In the formula, W s-TMF Thermomechanical fatigue hysteresis energy density (MJ / m 3 ), Δε p-LCF For the low-cycle fatigue plastic strain range (%), k LCF The shape factor Δσ represents low-cycle fatigue. LCF The stress variation range (MPa) representing low-cycle fatigue, parameter k LCF and Δσ LCF The parameters m and n are determined by linear fitting of the plastic strain ranges obtained from thermomechanical fatigue and low-cycle fatigue tests, based on the hysteresis curves obtained from low-cycle fatigue tests.

[0060] Step (8): Obtain the thermomechanical fatigue hysteresis energy W in step (7). s-TMF Substitute the data into formula (1) to calculate the thermomechanical fatigue life.

[0061] The present invention will now be further described in conjunction with embodiments and accompanying drawings.

[0062] Example 1:

[0063] like Figure 1 As shown, this embodiment predicts the reverse-phase thermomechanical fatigue life of high-temperature alloy materials, including the following steps:

[0064] Step 1: High-temperature alloy material (GH4169) was prepared using laser selective melting forming technology. According to the service conditions, isothermal low-cycle fatigue was carried out at 650℃, and the mechanical strain amplitude was selected as 0.4%, 0.6%, and 0.8%. Thermomechanical fatigue test was carried out at a temperature of 350-650℃, with the phase selected as anti-phase (OP), and the mechanical strain amplitude was selected as 0.4%, 0.6%, and 0.8%.

[0065] Step two: After the test, obtain the mid-life hysteresis loop data, based on... Figure 2 Calculate the hysteresis energy density under different mechanical strain amplitudes, establish a linear relationship between hysteresis energy density and fatigue life on a double logarithmic coordinate system, and obtain the linear fitting parameters W0 and β (e.g., ...). Figure 3 (As shown). For the current experimental conditions, in the anti-phase thermomechanical fatigue test, W0 = 12460.9, β = 0.8.

[0066] Step 3: Utilize the linear relationship between hysteresis energy density and the product of stress variation range and plastic strain range (e.g., ... Figure 4 As shown in the figure, the shape factor k is obtained. For the current experimental conditions, k≈0.82 for isothermal low-cycle fatigue and thermomechanical fatigue.

[0067] Step four, replace the stress variation range of thermomechanical fatigue with the equivalent stress variation range of low-cycle fatigue at the peak temperature (e.g., Figure 5 (As shown).

[0068] Step 5: Perform a linear fit between the plastic strain range of low-cycle fatigue and the plastic strain range of thermomechanical fatigue, such as... Figure 6 As shown, the corresponding fitting parameters m and n were obtained, where m = 1.53 and n = -0.13.

[0069] Step six: Based on the experimental parameters obtained in steps two, three, four, and five, the thermomechanical fatigue life of the material can be predicted through low-cycle fatigue testing. For example... Figure 7As shown, the relationship between the predicted thermomechanical fatigue life and the experimental results verifies the accuracy of the prediction results.

[0070] Example 2:

[0071] like Figure 1 As shown, this embodiment predicts the reverse-phase thermomechanical fatigue life of vermicular graphite cast iron (RuT450), including the following steps:

[0072] Step 1: Based on the service conditions, isothermal low-cycle fatigue is conducted at 400℃, with mechanical strain amplitudes of 0.15%, 0.2%, and 0.25% selected; thermomechanical fatigue tests are conducted at temperatures between 100 and 400℃, with the phase selected as anti-phase (OP), and mechanical strain amplitudes of 0.15%, 0.2%, and 0.25% selected.

[0073] Step two: After the test, obtain the mid-life hysteresis loop data, based on... Figure 2 Calculate the hysteresis energy density under different mechanical strain amplitudes, establish a linear relationship between hysteresis energy density and fatigue life on a double logarithmic coordinate system, and obtain the linear fitting parameters W0 and β (e.g., ...). Figure 8 (As shown). Under the current experimental conditions, the antiphase thermomechanical fatigue W0 = 22.5, β = 1.38.

[0074] Step 3: Utilize the linear relationship between hysteresis energy density and the product of stress variation range and plastic strain range (e.g., ... Figure 9 As shown), the shape factor k is obtained; for the current experimental conditions, k≈0.78 for isothermal low-cycle fatigue and thermomechanical fatigue.

[0075] Step four: The stress variation range of thermomechanical fatigue is equivalently replaced by the stress variation range of low-cycle fatigue at the corresponding peak temperature, such as... Figure 10 As shown.

[0076] Step 5: Perform a linear fit between the plastic strain range of low-cycle fatigue and the plastic strain range of thermomechanical fatigue, such as... Figure 11 As shown, the corresponding fitting parameters m and n were obtained, where m = 0.79 and n = -0.0075.

[0077] Step six: Based on the experimental parameters obtained in steps two, three, four, and five, the thermomechanical fatigue life of the material can be predicted through low-cycle fatigue testing. For example... Figure 12 As shown, the relationship between the predicted thermomechanical fatigue life and the experimental results verifies the accuracy of the prediction results.

[0078] The results show that the method of the present invention establishes a correlation between low-cycle fatigue and thermomechanical fatigue during cyclic loading by utilizing the similarity between the two. It can quickly predict the thermomechanical fatigue life of the corresponding material through low-cycle fatigue, effectively reducing the amount of experiments required for thermomechanical fatigue life prediction, greatly reducing the cost of predicting and evaluating the thermomechanical fatigue performance of metallic materials, and has high accuracy. It can be widely applied to the strain-controlled thermomechanical fatigue life prediction of high-temperature alloys and heat-resistant metal materials such as turbine disks, turbine blades, internal combustion engine cylinder heads and pistons.

[0079] The above embodiments and comparative examples are merely illustrative of the principles and performance of the present invention and are not exhaustive. People can obtain other embodiments based on these embodiments without creative effort, and these embodiments all fall within the protection scope of the present invention.

Claims

1. A method for rapid prediction of thermomechanical fatigue life of metallic materials based on hysteresis energy density, characterized in that, First, the hysteresis energy density is calculated using the hysteresis curve. Then, the equivalent relationship of the shape factor and the equivalent transformation relationship between stress variation range and plastic strain range in low-cycle fatigue and thermomechanical fatigue are used to predict the hysteresis energy density of thermomechanical fatigue through low-cycle fatigue. Finally, the thermomechanical fatigue life is predicted by combining the linear relationship between hysteresis energy density and fatigue life in a double logarithmic coordinate system. The specific steps of this method are as follows: (1) Select two different mechanical strain amplitudes to perform strain-controlled thermomechanical fatigue and isothermal low-cycle fatigue performance tests on the metal material at the corresponding peak temperature of thermomechanical fatigue, and obtain the corresponding hysteresis curves and fatigue life values. (2) Select the mid-life hysteresis curve to obtain the corresponding stress variation range and plastic strain range, and obtain the hysteresis energy density and shape factor data by calculating the area of ​​the hysteresis curve; In step (2), the area of ​​the hysteresis curve is not 0, the stress variation range is the difference between the maximum stress and the minimum stress, the plastic strain range is the distance between the intersection of the hysteresis loop and the strain axis when the stress is 0, and the shape factor is the ratio of the hysteresis energy density to the product of the stress variation range and the plastic strain range. (3) The mid-lifetime hysteresis energy density W s With fatigue life N f Linear fitting is performed in a double logarithmic coordinate system to obtain the corresponding fitting parameters; In step (3), the linear fitting parameters under double logarithmic coordinates are W0 and β, respectively, and their expressions are: In the formula, W s W represents hysteresis energy density, W0 represents intrinsic fatigue toughness, β represents fatigue damage conversion index, and N represents hysteresis energy density. f Represents fatigue life; (4) Using the low-cycle fatigue and thermomechanical fatigue plastic strain range obtained in step (2) Perform linear fitting to obtain the corresponding fitting parameters m and n; In step (4), the plastic strain range of low-cycle fatigue and thermomechanical fatigue is linearly related, and its expression is: In the formula, Δε p-TMF Represents the range of plastic strain during thermomechanical fatigue, Δε p-LCF This represents the range of plastic strain during low-cycle fatigue, where m and n are fitting parameters. (5) Using the low-cycle fatigue plastic strain range obtained in step (2) Stress variation range The shape factor k and the fitting parameters m and n obtained in step (4) are used to calculate the thermomechanical fatigue hysteresis energy density under the same mechanical strain amplitude. In step (5), the shape factor k and stress variation range are obtained for the same metallic material during high-temperature low-cycle fatigue and thermomechanical fatigue. Consistent, equivalent substitution is performed; among them, the experimental temperature of high temperature low cycle fatigue is the peak temperature of thermomechanical fatigue; (6) Substitute the thermomechanical fatigue hysteresis energy density obtained in step (5) into step (3) to calculate the corresponding thermomechanical fatigue life.

2. The method for rapid prediction of thermomechanical fatigue life of metallic materials based on hysteresis energy density according to claim 1, characterized in that, In step (1), strain-controlled thermomechanical fatigue includes low-cycle fatigue and thermomechanical fatigue, and the selected mechanical strain amplitude is not lower than the yield strain of the material under the corresponding experimental conditions.

3. The method for rapid prediction of thermomechanical fatigue life of metallic materials based on hysteresis energy density according to claim 1, characterized in that, In step (6), the thermomechanical fatigue hysteresis energy density W s-TMF The calculation formula is as follows: In the formula, W s-TMF Let Δε be the thermomechanical fatigue hysteresis energy density. p-LCF For the low-cycle fatigue plastic strain range, k LCF The shape factor Δσ represents low-cycle fatigue. LCF The parameter k represents the stress variation range during low-cycle fatigue. LCF and Δσ LCF The parameters m and n are determined by linear fitting of the plastic strain ranges obtained from thermomechanical fatigue and low-cycle fatigue tests, based on the hysteresis curves obtained from low-cycle fatigue tests.

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