Limited data-based nickel-based single crystal alloy low-cycle fatigue life prediction method

Abstract

A nickel-based single crystal alloy low-cycle fatigue life prediction method based on limited data relates to the field of aero-engines, and comprises the following steps: establishing a unified stress-strain prediction model based on limited material data; obtaining a cyclic tensile stress-strain relation curve by using a unified stress-strain prediction model, and taking the curve as preposed data of fatigue life calculation under different crystal orientations without considering time and frequency factors, so as to establish a fatigue data set under each crystal orientation; taking a fatigue data set as a fitting basis, and establishing an anisotropic cross-temperature macroscopic aesthetic fatigue life model by introducing a new variable; a prediction empirical formula for a fatigue creep coupling factor is provided based on a linear cumulative damage method by introducing a time factor and considering the influence of endurance strength and creep strength; and predicting the low-cycle fatigue life of the nickel-based single crystal alloy according to the prediction empirical formula. The method greatly reduces the cost of predicting the low-cycle fatigue life, is convenient and flexible to apply, and has a cross-temperature prediction capability.

Description

Technical Field

[0001] The present invention relates to the technical field of aero-engines, and in particular to a method for predicting the low-cycle fatigue life of a nickel-based single crystal alloy based on limited data. Background Art

[0002] As the temperature before the turbine increases year by year, the fatigue problem of the turbine becomes more and more prominent. Fatigue is a failure phenomenon that occurs when metal materials are subjected to alternating loads. In the aviation field, fatigue damage is one of the main causes of failure of mechanical parts. According to the number of stress cycles experienced during fatigue failure, fatigue can be divided into low-cycle fatigue and high-cycle fatigue. Low-cycle fatigue refers to a fatigue phenomenon in which a material has fewer failure cycles under alternating loads and generally fails within 10^2-10^5 cycles. It has the characteristics of high stress level and large material deformation, which will have a greater impact on mechanical parts. The present invention focuses on the field of low-cycle fatigue.

[0003] To cope with high-temperature stresses, nickel-based single-crystal alloys, known for their superior performance, have gained widespread application in turbine blades. Compared to conventional materials, one of the most notable characteristics of nickel-based single-crystal alloys is the orthotropic anisotropy resulting from their face-centered cubic crystal configuration. For orthotropic materials, their macroscopic mechanical properties vary with crystal orientation, posing new challenges in predicting the low-cycle fatigue life of nickel-based single-crystal alloys.

[0004] Currently, the following methods are commonly used to predict the high-temperature low-cycle fatigue life of nickel-based single crystal alloys:

[0005] (1) Based on the microscopic plasticity theory of materials, a crystal slip fatigue life model is established by studying the plastic slip laws of specific slip systems of materials. This method studies nickel-based single crystal alloys based on the crystal slip theory and can obtain a more accurate microscopic model. However, the deformation mechanism of single crystals has its own complexity, such as the activation of the slip system and the evolution of the slip law. There are many influencing factors, large computational consumption, and high cost. Therefore, there are still relatively large limitations in engineering applications.

[0006] (2) The macroscopic phenomenological fatigue life model of isotropic materials was expanded and applied to nickel-based single crystal alloys. This method is easy to use and has good accuracy at a fixed temperature. It has been widely recognized in the engineering field. However, this method requires a large amount of macroscopic phenomenological experimental data as support. A large number of experiments at different temperatures are required to obtain basic data such as cyclic tensile stress-strain curves. The entire process is long, costly, and requires a large investment. Although the Masing hypothesis provides a simple estimation method for cyclic stress-strain curves to a certain extent, it is not completely applicable to nickel-based single crystal alloys. Even in material handbooks edited by professional organizations, only cyclic stress-strain curves at two fixed temperatures and fixed orientations are usually given at 760°C and 980°C. Turbine blades are in a complex high-temperature environment with obvious temperature non-uniformity. Using a single fixed-temperature cyclic stress-strain curve to predict the life of turbine blades across temperatures will result in large errors. Summary of the Invention

[0007] In order to solve the problems of existing high-temperature low-cycle fatigue life prediction methods for nickel-based single crystal alloys, such as high prediction cost, limitation by limited and highly dispersed experimental data, limitations in actual engineering applications, and lack of cross-temperature prediction capabilities, the present invention provides a low-cycle fatigue life prediction method for nickel-based single crystal alloys based on limited data.

[0008] The technical solutions adopted by the present invention to solve the technical problems are as follows:

[0009] The present invention provides a method for predicting the low-cycle fatigue life of a nickel-based single crystal alloy based on limited data, comprising the following steps:

[0010] Step S1: establishing a unified stress-strain prediction model based on limited material data obtained from average tensile stress-strain experiments or material handbooks;

[0011] Step S2: Using a unified stress-strain prediction model, a cyclic tensile stress-strain relationship curve is obtained, which is used as the pre-data for fatigue life calculation in different crystal directions without considering time and frequency factors. This is used to establish a fatigue data set for each crystal direction; using the fatigue data set as the fitting basis, an anisotropic cross-temperature macro-phenomenological fatigue life model is established by introducing new variables;

[0012] Step S3: By introducing the time factor and considering the influence of the endurance strength and creep strength, a prediction empirical formula for the fatigue-creep coupling factor is proposed based on the linear cumulative damage method; the low-cycle fatigue life of the nickel-based single crystal alloy is predicted based on the prediction empirical formula.

[0013] Furthermore, the limited material data include elastic modulus, yield strength, tensile strength and elongation.

[0014] Furthermore, the Ramberg-Osgood equation is modified to establish a unified stress-strain prediction model as follows:

[0015]

[0016] Where:

[0017]

[0018] Where Δε is the total strain, σ is the equivalent stress, E is the elastic modulus, σ s is the yield strength, n is the equivalent strain hardening exponent, K is the equivalent strength coefficient, c1 is the differentiation constant, and T is the Rankine temperature.

[0019] Furthermore, when the discrimination constant c1 is 0.5-1.5, the unified stress-strain prediction model determines the yield strength σ corresponding to the material at different temperatures and different crystal orientations. s To invert the corresponding average tensile stress-strain relationship; when the distinction constant c1 is 0.1-0.3, the unified stress-strain prediction model determines the yield strength σ corresponding to the material at different temperatures and different crystal orientations s To invert the corresponding cyclic tensile stress-strain relationship.

[0020] Furthermore, in step S2, the cyclic tensile stress-strain relationship curve of a single crystal is first calculated: first, a cyclic tensile stress-strain experiment at different temperatures is performed using a unified stress-strain prediction model to determine the yield strength σ of the material at different crystal directions. s and elastic modulus E and establish a cyclic tensile stress-strain model; then, the equivalent stress σ is obtained by finite element calculation or theoretical deduction, and the total strain Δε is calculated using the cyclic tensile stress-strain model; finally, the downward cyclic tensile stress-strain relationship curve of a single crystal is inverted based on the total strain Δε.

[0021] Furthermore, in step S2, based on the cyclic tensile stress-strain relationship curve of a single crystal downward, combined with the Mason-Coffin formula with Morrow strain correction and the general slope method, the fatigue life N of different crystal downwards at a constant temperature without considering time and frequency factors is calculated using the total strain Δε. T,＜hkl＞ ; The mathematical expression of this process is:

[0022]

[0023] Where:

[0024] b=-0.12

[0025] c=-0.6

[0026] σ′f =1.75σ b

[0027] ε' f =0.5δ -0.6

[0028] Among them, σ m is the mean stress, σ' f is the fatigue strength coefficient, b is the fatigue strength index, ε' f is the fatigue ductility coefficient, c is the fatigue ductility index, <hkl> is the crystal orientation, δ is the material elongation; different fatigue life N T,＜hkl＞ Create a single grain-down fatigue data set.

[0029] Furthermore, in step S2, the fatigue data sets of each single crystal are summarized to establish an anisotropic cross-temperature macroscopic phenomenological fatigue life model:

[0030]

[0031] Where:

[0032] f(A <hkl >=1-DA <hkl>< / hkl>

[0033] Among them, N f0 is the low cycle fatigue life, b1~b7 are constants to be fitted, σ b is the tensile strength, N f is the lifespan, f(A ＜hkl＞ ) is the crystal orientation function, B is a constant, μ ＜001＞ 、E ＜001＞ , G ＜001＞ Crystal <001> Oriented Poisson's ratio, elastic modulus, and shear modulus.

[0034] Furthermore, the calculation formula of the linear cumulative damage method is:

[0035]

[0036] Where D is the damage factor; N f0 、N f are the low cycle fatigue life before and after correction respectively; B is the fatigue creep coupling factor, which is used to measure the coupling effect between creep and fatigue life; t f , t i are the creep life before and after correction respectively.

[0037] Furthermore, the fitting empirical formula of the fatigue-creep coupling factor B is:

[0038]

[0039] When the equivalent stress σ is lower than the yield strength σ s When B is negative, fatigue-creep coupling plays a positive role in promoting the low-cycle fatigue life, and the conservative low-cycle fatigue life estimate near the yield stage is corrected; when the equivalent stress σ is higher than the yield strength σ s When B is positive, fatigue-creep coupling has a reverse inhibitory effect on the low-cycle fatigue life, and the low-cycle fatigue life estimation that is too radical in the high plasticity stage is corrected, and the low-cycle fatigue life is further reduced.

[0040] Furthermore, the Larson-Miller formula is expressed as a comprehensive equation of creep thermal strength parameters to calculate the creep life t before correction. f , and its calculation formula is:

[0041]

[0042] Where:

[0043]

[0044] x=lgσ

[0045] Where θ is the Celsius temperature; T is the Rankine temperature; σ is the equivalent stress; c1 to c5 are material constants; and x is the logarithm of the equivalent stress.

[0046] The beneficial effects of the present invention are:

[0047] The present invention provides a method for predicting the low-cycle fatigue life of nickel-based single crystal alloys based on limited data. Compared with the existing technology, the method has the advantages of low prediction cost, convenient application, and cross-temperature prediction capability. Specifically,

[0048] (1) The present invention proposes a unified stress-strain prediction model, which only requires low-cost and easy-to-carry average tensile stress-strain experiments to obtain the elastic modulus E and yield strength σ of the material in different crystal directions. s , tensile strength σ b , elongation δ, and the four basic material parameters can be obtained by consulting the material manual without experimental conditions, so as to predict the cyclic tensile stress-strain model required for fatigue calculation. The prediction model can replace the cyclic tensile stress-strain experiment with high experimental cost and long cycle, and then the cyclic tensile stress-strain curve can be established, which greatly reduces the cost of predicting low-cycle fatigue life.

[0049] (2) This paper proposes a cross-temperature macro-phenomenological fatigue life model that takes into account anisotropy. Compared with the traditional macro-phenomenological fatigue life model, the advantages of this model are as follows:

[0050] 1) The model introduces a new variable σ b , δ, which makes the model more compatible with the Mason-Coffin formula. The fatigue data set obtained with the unified stress-strain prediction model as the pre-data shows a higher correlation coefficient with the macro-phenomenological fatigue life model in the fitting, which is conducive to reducing errors. At the same time, the model introduces a new variable T, which enables the model to have the ability of cross-temperature prediction, no longer sticking to the specific temperature points in the material manual, and is more flexible in engineering applications.

[0051] 2) The present invention proposes a new idea of replacing experimental data with a prediction data set, so that all the fitting data required to establish the model can be obtained by a unified stress-strain prediction model and a relatively simple and easy-to-operate mathematical fitting method. The amount of fitting data set can be freely expanded from the perspectives of crystal orientation, stress-strain range, and cross-temperature region according to actual needs, breaking through the problem that traditional macroscopic phenomenological fatigue life models are limited by limited and highly dispersed experimental data during the establishment process.

[0052] (3) The present invention proposes an empirical formula for predicting the fatigue-creep coupling factor. In traditional methods, the fatigue-creep coupling factor usually depends on experimental data. The proposal of this empirical formula for predicting the fatigue-creep coupling factor further reduces the cost of low-cycle fatigue life prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 This is a flow chart of a method for predicting the low-cycle fatigue life of nickel-based single crystal alloys based on limited data provided by the present invention. DETAILED DESCRIPTION

[0054] The present invention is further described in detail below with reference to the accompanying drawings.

[0055] Based on the thermal fatigue research method of "expanding the macroscopic phenomenological fatigue life model of isotropic materials and constructing an orientation function to consider the anisotropy and nonlinear effects of the material", this paper proposes a low-cycle fatigue life prediction method for nickel-based single crystal alloys based on limited data.

[0056] like Figure 1 As shown, the present invention provides a method for predicting the low-cycle fatigue life of nickel-based single crystal alloys based on limited data, and its specific implementation process is as follows:

[0057] (1) Establish a unified stress-strain prediction model;

[0058] Currently, the existing stress-strain models mainly include the average tensile stress-strain model and the cyclic tensile stress-strain model.

[0059] Among them, the average tensile stress-strain focuses on the ultimate bearing capacity of the material. In the experiment, the elastic modulus E and yield strength σ of a single specimen can usually be obtained by monotonically loading a single specimen until the material fails. s , tensile strength σ b , elongation δ and other basic material parameters. The experimental cost is low, and only a few specimens are needed to obtain the above basic material parameters at different temperatures and establish the average tensile stress-strain model. In the absence of experimental conditions, the above material data can usually be found in the material manual.

[0060] Among them, cyclic tensile stress-strain focuses on the fatigue life of the material (crack initiation and propagation). By observing the cyclic hardening and softening phenomena of the specimen through periodic cyclic loading, parameters such as the specimen's strength coefficient and strain hardening exponent can be obtained, and a cyclic tensile stress-strain model can be established. This experimental cycle is long and the cost is high. Material manuals usually only provide cyclic tensile stress-strain models at a few typical temperatures. When the temperature deviates significantly from the typical temperature, continuing to apply the cyclic tensile stress-strain model at the typical temperature will lead to large fatigue life calculation errors.

[0061] To solve the above problems, the present invention proposes a unified stress-strain prediction model. The present invention is based on the limited material data (i.e. elastic modulus E, yield strength σ s , tensile strength σ b , elongation δ) and establish a unified stress-strain prediction model, which greatly reduces the experimental cost.

[0062] Specifically, the present invention modifies the Ramberg-Osgood equation to construct the following unified stress-strain prediction model:

[0063]

[0064] Where:

[0065]

[0066] Where Δε is the total strain, σ is the equivalent stress, E is the elastic modulus, σ s is the yield strength, n is the equivalent strain hardening exponent, when applied to nickel-based single crystal alloys, n is approximately in the range of 0.15-0.20, K is the equivalent strength coefficient, c1 is the differentiation constant, and T is the Rankine temperature.

[0067] When the discrimination constant c1 is 0.5-1.5, the unified stress-strain prediction model only needs to determine the yield strength σ corresponding to different crystal directions at each temperature. s, the average tensile stress-strain relationship of each material at different crystal orientations at different temperatures can be inverted; when the discrimination constant c1 is 0.1-0.3, the unified stress-strain prediction model only needs to determine the yield strength σ of the material at different crystal orientations at different temperatures. s , we can invert the cyclic tensile stress-strain relationship corresponding to each material at different crystal orientations at different temperatures.

[0068] It can be seen from this that the unified stress-strain prediction model only requires a few material samples with different crystal orientations to conduct average tensile stress-strain experiments at different temperatures to determine the yield strength σ of the material in different crystal orientations. s The average tensile stress-strain model and the cyclic tensile stress-strain model can be established based on the elastic modulus E and applied to subsequent low-cycle fatigue life calculations. If experimental conditions are unavailable, the above basic material parameters can be obtained by consulting a material manual. The average tensile stress-strain model and the cyclic tensile stress-strain model can then be inverted using the unified stress-strain prediction model. Compared to traditional methods that rely entirely on experiments, this method significantly reduces costs.

[0069] (2) Establish an anisotropic cross-temperature macroscopic phenomenological fatigue life model;

[0070] On the premise of step (1), the constructed unified stress-strain prediction model is used to obtain a cyclic tensile stress-strain relationship curve, which is used as the prerequisite data for fatigue life calculation in different crystal directions without considering time and frequency factors. A fatigue data set for each crystal direction is thus established. Using the fatigue data set as the fitting basis, new variables are introduced into the traditional macroscopic phenomenological fatigue life model, and then an anisotropic cross-temperature macroscopic phenomenological fatigue life model is established.

[0071] The specific implementation process is as follows:

[0072] S2.1: Calculate the downward cyclic tensile stress-strain curve for a single crystal;

[0073] First, the unified stress-strain prediction model obtained in step (1) is used to perform cyclic tensile stress-strain experiments at different temperatures to determine the yield strength σ of the material in different crystal directions. s The cyclic tensile stress-strain model is established based on the elastic modulus E. Finite element calculations or theoretical deduction are then used to determine the equivalent stress σ, which is then used to calculate the total strain Δε using the cyclic tensile stress-strain model. Finally, the cyclic tensile stress-strain curve for a single crystal is inverted based on the total strain Δε.

[0074] S2.2: Create a single grain-down fatigue data set;

[0075] Based on step S2.1, the fatigue life N at a constant temperature without considering time and frequency factors in different crystal directions is obtained by combining the Mason-Coffin formula with Morrow strain correction and the general slope method. T,＜hkl＞ The mathematical expression of this process is as follows:

[0076]

[0077] Where:

[0078] b=-0.12

[0079] c=-0.6

[0080] σ′ f =1.75σ b

[0081] ε' f =0.5δ -0.6

[0082] Where Δε is the total strain, σ m is the average stress, which is determined by the actual working conditions, σ' f is the fatigue strength coefficient, b is the fatigue strength index, ε' f is the fatigue ductility coefficient, c is the fatigue ductility index, N T,＜hkl＞ is the fatigue life in different crystal directions without considering time and frequency factors, <hkl> is the crystal orientation, and δ is the material elongation.

[0083] Different fatigue lives N can be calculated using different total strains Δε T,＜hkl＞ , a single crystal downward fatigue data set can be established according to actual needs. For example, the material manual usually controls the strain of low cycle fatigue test at 0.12%, so the yield strength σ s The corresponding total strain Δε is used as the starting point of the fatigue data set strain, 0.12% is used as the end point of the fatigue data set strain, and 0.005% is used as the strain gradient to establish a single crystal downward fatigue data set.

[0084] S2.3: Establish an anisotropic macroscopic phenomenological fatigue life model across temperature;

[0085] The fatigue data sets of different crystal orientations are aggregated to replace the data of traditional low-cycle fatigue experiments, and a cross-temperature macro-phenomenological fatigue life model is established as follows:

[0086]

[0087] Where:

[0088] f(A <hkl>< / hkl> )=1-DA <hkl>< / hkl>

[0089]

[0090] Among them, N f0 is the low cycle fatigue life, b1~b7 are constants to be fitted, σ b is the tensile strength, N f is the lifespan, f(A ＜hkl＞ ) is the crystal orientation function, D is a constant, μ ＜001＞ 、E ＜001＞ , G ＜001＞ Crystal <001> The Poisson's ratio, elastic modulus and shear modulus of orientation can be obtained from the crystal <001> The average tensile stress-strain experiment of the orientation is obtained; if there are no experimental conditions, the material manual can be consulted, but some nickel-based single crystal alloys do not have complete elastic constants related to each orientation. For example, the second-generation nickel-based single crystal alloy DD6 lacks crystal orientation information in the material manual. <001> Shear modulus G under orientation ＜001＞ , can be approximated by the following formula:

[0091]

[0092] S′ 12 =S 12 +SJ

[0093]

[0094] S=S 11 -S 12 -0.5S 44

[0095]

[0096] Among them, S is the flexibility coefficient, J is the calculation intermediate variable, and hkl is the directional constant in any orientation, such as <001> Orientation, h = 0, k = 0, l = 1, S 11 、S 12 、S 44 All are IC21 alloy <001> Flexibility coefficient under orientation, E ＜hkl＞ , G ＜hkl＞ 、μ ＜hkl＞ Any orientation <hkl>Elastic modulus, shear modulus and Poisson's ratio, S' 11 , S′ 12 、S' 44 All orientations are arbitrary <hkl>The flexibility coefficient on the surface, θ is an arbitrary orientation <hkl>and <001> The angle of orientation, q is the angle of orientation at any orientation. <100> - <010> The azimuth angle on the orientation, where the included angle and the azimuth angle can be calculated with the help of the face-centered cubic structure of the nickel-based single crystal alloy. It is only necessary to consult the material manual to obtain any E on any orientation of the nickel-based single crystal alloy DD6. ＜hkl＞ , G ＜hkl＞ 、μ ＜hkl＞ , we can solve the above equations to get the shear modulus G ＜001＞ , this idea can also be extended to other nickel-based single crystal alloys.

[0097] Among them, b1~b7 are constants to be fitted. Substitute the fatigue data sets of different crystal directions into the cross-temperature macro-phenomenological fatigue life model and fit the model using the multivariate linear regression method to obtain the constants b1~b7. For example, the second-generation nickel-based single crystal alloy DD6, nickel-based single crystal alloy DD6 is heated at 760-980℃. <001> <011> <111> Substituting the fatigue data set of three crystal orientations and a stress amplitude ratio of -1 into the equation, the multivariate linear regression method is used to fit the formula, and the corresponding cross-temperature macroscopic phenomenological fatigue life model is obtained:

[0098]

[0099] (3) Low cycle fatigue life prediction;

[0100] Based on step (2), the present invention introduces the time factor, considers the effects of endurance and creep strength, and proposes an empirical formula for predicting the fatigue-creep coupling factor based on the mature linear cumulative damage method. In traditional methods, this coupling factor usually relies on experimental data. The empirical formula for predicting the fatigue-creep coupling factor proposed in the present invention further reduces the cost of low-cycle fatigue life prediction.

[0101] It's important to note that the Mason-Coffin formula doesn't consider the effects of time and frequency on low-cycle fatigue life. This is because the Mason-Coffin formula is an empirical formula derived at room temperature and doesn't account for the effects of creep strength on the material itself. However, in actual operating conditions, turbine guide vanes typically need to operate at high temperatures for a certain period of time. Due to the influence of creep strength, turbine guide vanes will continue to undergo slow and continuous plastic deformation over time, significantly affecting the low-cycle fatigue life of the structure.

[0102] To further improve the calculation accuracy, this paper introduces considerations of endurance strength and creep strength based on the linear cumulative damage theory:

[0103]

[0104] Where D is the damage factor. When D=1, it is considered that the turbine guide blade structure is damaged. N f0 、N f are the low-cycle fatigue life before and after correction respectively; B is the fatigue-creep coupling factor, i.e., the interaction term, which is used to measure the coupling effect between creep and fatigue life; t f , t i are the creep life before and after correction respectively.

[0105] To calculate the creep life before correction t f The present invention introduces the Larson-Miller formula and expresses it as a comprehensive equation of creep thermal strength parameters. The mathematical expression of this process is as follows:

[0106]

[0107] Where:

[0108]

[0109] x=lgσ

[0110] Where θ is the Celsius temperature; T is the Rankine temperature; σ is the equivalent stress; c1 to c5 are material constants that can be obtained by fitting the creep strength or rupture strength data; and x is the logarithm of the equivalent stress.

[0111] In existing research, the interaction term B is usually derived from experiments and requires long-term fatigue-creep coupling experiments to determine, which is costly. To solve this problem, the present invention provides an empirical fitting formula for the interaction term B:

[0112]

[0113] When the equivalent stress σ is lower than the yield strength σ s When the interaction term B is negative, the fatigue-creep coupling plays a positive role in promoting the low-cycle fatigue life, and the conservative low-cycle fatigue life estimate near the yield stage is corrected; when the equivalent stress σ is higher than the yield strength σ s When , the interaction term B is positive. At this time, the fatigue-creep coupling has a reverse inhibitory effect on the low-cycle fatigue life, corrects the aggressive low-cycle fatigue life estimation in the high plasticity stage, and further reduces the low-cycle fatigue life.

[0114] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.< / hkl> < / hkl> < / hkl>

Claims

1. A method for predicting low-cycle fatigue life of nickel-based single crystal alloys based on limited data, characterized in that: The following steps are involved: Step S1: establishing a unified stress-strain prediction model based on limited material data obtained from average tensile stress-strain experiments or material handbooks; Step S2: Using a unified stress-strain prediction model, a cyclic tensile stress-strain relationship curve is obtained, which is used as the pre-data for fatigue life calculation in different crystal directions without considering time and frequency factors. This is used to establish a fatigue data set for each crystal direction; using the fatigue data set as the fitting basis, an anisotropic cross-temperature macro-phenomenological fatigue life model is established by introducing new variables; Step S3: By introducing the time factor and considering the influence of the endurance strength and creep strength, a prediction empirical formula for the fatigue-creep coupling factor is proposed based on the linear cumulative damage method; the low-cycle fatigue life of the nickel-based single crystal alloy is predicted based on the prediction empirical formula.

2. The method for predicting low cycle fatigue life of nickel-based single crystal alloy based on limited data according to claim 1, characterized in that: The limited material data include elastic modulus, yield strength, tensile strength and elongation.

3. The method for predicting low cycle fatigue life of nickel-based single crystal alloy based on limited data according to claim 1, characterized in that: The Ramberg-Osgood equation is modified to establish a unified stress-strain prediction model as follows: Where: Where Δε is the total strain, σ is the equivalent stress, E is the elastic modulus, σ s is the yield strength, n is the equivalent strain hardening exponent, K is the equivalent strength coefficient, c1 is the differentiation constant, and T is the Rankine temperature.

4. The method for predicting low cycle fatigue life of nickel-based single crystal alloy based on limited data according to claim 3, characterized in that: When the discrimination constant c1 is 0.5-1.5, the unified stress-strain prediction model determines the yield strength σ corresponding to the material at different temperatures and different crystal orientations. s To invert the corresponding average tensile stress-strain relationship; when the distinction constant c1 is 0.1-0.3, the unified stress-strain prediction model determines the yield strength σ corresponding to the material at different temperatures and different crystal orientations s To invert the corresponding cyclic tensile stress-strain relationship.

5. The method for predicting low cycle fatigue life of nickel-based single crystal alloy based on limited data according to claim 1, characterized in that: In step S2, the cyclic tensile stress-strain relationship curve of a single crystal is first calculated: first, the cyclic tensile stress-strain experiment at different temperatures is performed using the unified stress-strain prediction model to determine the yield strength σ of the material at different crystal directions. s and elastic modulus E and establish a cyclic tensile stress-strain model; then, the equivalent stress σ is obtained by finite element calculation or theoretical deduction, and the total strain Δε is calculated using the cyclic tensile stress-strain model; finally, the downward cyclic tensile stress-strain relationship curve of a single crystal is inverted based on the total strain Δε.

6. The method for predicting low cycle fatigue life of nickel-based single crystal alloy based on limited data according to claim 5, characterized in that: In step S2, based on the cyclic tensile stress-strain relationship curve of a single crystal downward, combined with the Mason-Coffin formula with Morrow strain correction and the general slope method, the fatigue life N at a constant temperature of different crystal downwards without considering time and frequency factors is calculated using the total strain Δε. T,＜hkl＞ ; The mathematical expression of this process is: Where: b＝-0.12 c＝-0.6 in f =1.75σ b e' f =0.5d -0.6 Among them, σ m is the mean stress, σ' f is the fatigue strength coefficient, b is the fatigue strength index, ε' f is the fatigue ductility coefficient, c is the fatigue ductility index, <hkl> is the crystal orientation, δ is the material elongation; different fatigue life N T,＜hkl＞ Create a single grain-down fatigue data set.

7. The method for predicting low cycle fatigue life of nickel-based single crystal alloy based on limited data according to claim 6, characterized in that: In step S2, the fatigue data sets of each single crystal are summarized to establish an anisotropic cross-temperature macroscopic phenomenological fatigue life model: Where: f(A ＜hkl＞ )=1-AND <hkl>< / hkl> Among them, N f0 is the low cycle fatigue life, b1~b7 are constants to be fitted, σ b is the tensile strength, N f is the lifespan, f(A ＜hkl＞ ) is the crystal orientation function, B is a constant, μ ＜001＞ 、E ＜001＞ , G ＜001＞ Crystal <001> Oriented Poisson's ratio, elastic modulus, and shear modulus.

8. The method for predicting low cycle fatigue life of nickel-based single crystal alloy based on limited data according to claim 1, characterized in that: The calculation formula of the linear cumulative damage method is: Where D is the damage factor; N f0 、N f are the low cycle fatigue life before and after correction respectively; B is the fatigue creep coupling factor, which is used to measure the coupling effect between creep and fatigue life; t f , t i are the creep life before and after correction respectively.

9. The method for predicting low cycle fatigue life of nickel-based single crystal alloy based on limited data according to claim 8, characterized in that: The fitting empirical formula of the fatigue creep coupling factor B is: When the equivalent stress σ is lower than the yield strength σ s When B is negative, fatigue-creep coupling plays a positive role in promoting the low-cycle fatigue life, and the conservative low-cycle fatigue life estimate near the yield stage is corrected; when the equivalent stress σ is higher than the yield strength σ s When B is positive, fatigue-creep coupling has a reverse inhibitory effect on the low-cycle fatigue life, and the low-cycle fatigue life estimation that is too radical in the high plasticity stage is corrected, and the low-cycle fatigue life is further reduced.

10. The method for predicting low cycle fatigue life of nickel-based single crystal alloy based on limited data according to claim 8, characterized in that: The Larson-Miller formula is expressed as a comprehensive equation of creep thermal strength parameters to calculate the creep life t before correction. f , and its calculation formula is: Where: x=lgσ Where θ is the Celsius temperature; T is the Rankine temperature; σ is the equivalent stress; c1 to c5 are material constants; and x is the logarithm of the equivalent stress.

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