Prediction method of high temperature creep life of nickel-based single crystal under the influence of orientation deviation

Abstract

The present invention proposes a method for predicting the high-temperature creep life of nickel-based single crystals under the influence of orientation deviation, which relates to the field of reliability technology. The method comprises: establishing a three-dimensional finite element round rod model based on the dimensions of a nickel-based single crystal creep specimen; establishing a constitutive equation for the nickel-based single crystal based on crystal plasticity theory, wherein the constitutive equation for the nickel-based single crystal includes a deformation equation that considers orientation deviation and a damage equation that considers orientation deviation; combining the three-dimensional finite element round rod model and the nickel-based single crystal constitutive equation to perform creep finite element simulation calculations on the round rod model; and establishing a creep time-strain curve and predicting the creep life based on the results of the creep finite element simulation calculations. The present invention can relatively accurately evaluate and predict the high-temperature creep life of nickel-based single crystal turbine blades used in actual industrial manufacturing.

Description

Technical Field

[0001] The present invention relates to the field of reliability technology, and in particular to a method for predicting the high-temperature creep life of a nickel-based single crystal under the influence of a small-angle orientation deviation from

[001] to

[011] . Background Art

[0002] Nickel-based single-crystal high-temperature alloys are widely used in hot zone components (turbine blades) of aero-engines and industrial gas turbines. They have excellent high-temperature tensile, creep, and fatigue properties, especially high-temperature creep resistance. Current nickel-based single-crystal high-temperature alloy turbine blades are almost all

[001] oriented. Industry experience shows that during the directional solidification of single-crystal castings, it is not always possible to make the interface heat flow direction consistent with the axial direction. The complex blade structure and casting limitations make it difficult to accurately control the temperature gradient and direction during the solidification process. The above factors inevitably lead to orientation deviation. In other words, it is very difficult to obtain precisely oriented nickel-based single-crystal high-temperature alloy blades.

[0003] Crystal orientation is an inherent property that plays a crucial role in ensuring the reliability and safety of nickel-based single-crystal superalloy turbine blades. Currently, the operating temperatures of aircraft engines are constantly increasing, and orientation deviation has a significant adverse effect on the creep performance of nickel-based single crystals in high-temperature environments. To fully realize the potential of single-crystal materials and ensure reliability throughout their design life, it is necessary to develop a creep life prediction model that considers the influence of orientation deviation for turbine blades in harsh high-temperature service environments.

[0004] In the existing technology, the research on the high-temperature creep life prediction method of nickel-based single crystals focuses on the ideal condition of precise orientation, ignoring the influence of the orientation deviation of nickel-based single crystals on the high-temperature creep life, resulting in inaccurate prediction of the high-temperature creep life prediction method of nickel-based single crystals, thereby increasing the use risk of turbine blades of aircraft engines and reducing the reliability of aircraft engines.

[0005] Therefore, it is necessary to design a high-temperature creep life prediction method for nickel-based single crystals that takes into account the small-angle (0°-10°) orientation deviation from

[001] to

[011] . Summary of the Invention

[0006] The purpose of the present invention is to overcome the prior art's neglect of the inevitable deviation between the actual orientation and the precise

[001] crystal orientation during the directional solidification preparation of nickel-based single crystals, and to provide a method for predicting the high-temperature creep life of nickel-based single crystals that takes into account the small-angle (0°-10°) orientation deviation from

[001] to

[011] . This method can more accurately evaluate and predict the high-temperature creep life of nickel-based single crystal turbine blades used in actual industrial manufacturing.

[0007] In order to achieve the above-mentioned object of the invention, the present invention adopts the following technical solutions:

[0008] The present invention provides a model and method for predicting the high-temperature creep life of nickel-based single crystals under the influence of small-angle orientation deviation from

[001] to

[011] , comprising:

[0009] The polar coordinates of the specimen Convert to orientation (u, v, w);

[0010] Establishing a three-dimensional finite element round rod model according to the size of the nickel-based single crystal creep specimen;

[0011] The constitutive equation of nickel-based single crystal is established based on crystal plasticity theory, including deformation equation and damage equation considering orientation deviation.

[0012] Combining the three-dimensional finite element round rod model and the nickel-based single crystal constitutive equation, a creep finite element simulation calculation of the round rod model is performed;

[0013] According to the results of the creep finite element simulation calculation, a creep time-strain curve is established and the creep life is predicted.

[0014] Furthermore, the coordinate transformation formula of the sample includes:

[0015] θ = arctanρ;

[0016] w=cos(2θ).

[0017] Furthermore, establishing a three-dimensional finite element circular rod model includes:

[0018] According to the size of the creep specimen, a round bar model is established in the "component" module of the finite element calculation software;

[0019] Hexahedral (C3D8) elements are used for meshing.

[0020] Furthermore, the crystal plasticity theory equations include:

[0021] τ (α) =σ:P (α)

[0022] Where σ(σ=σ ij ij,i,j=x,y,z) is the stress tensor under the crystal axis system, P (α) is the slip system α orientation factor of nickel-based single crystal material;

[0023]

[0024] m (α) is the slip direction of the slip system α of nickel-based single crystal material, n (α)is the unit normal vector of the slip plane in the slip system α of the nickel-based single crystal material;

[0025] The actual stress tensor σ considering the orientation deviation can be expressed as:

[0026] σ=T r σ applied

[0027] Among them, σ applied When the stress is applied only along the x-axis, the applied stress for uniaxial tensile creep can be expressed as σ applied =(σ xx ,0,0,0,0,0);

[0028] Furthermore, the transformation matrix T between the initial oxyz coordinate system and the updated OXYZ coordinate system is r include:

[0029]

[0030] Furthermore, the deformation equations established considering the orientation deviation include:

[0031]

[0032]

[0033]

[0034] Among them, ε c is the viscoplastic strain; α is the slip system of nickel-based single crystal material; is the creep shear strain rate of the slip system α of the nickel-based single crystal material; is the initial creep shear strain rate of the slip system α of the nickel-based single crystal material; is the equivalent shear stress of the slip system α of nickel-based single crystal material; is the thermal slip resistance of dislocation slip; R (α) isotropic hardening; X (α) is kinematic strengthening, also known as back stress; A is the creep parameter, T is the temperature, K is the Boltzmann constant; Q is the activation energy; P (α) is the slip system α orientation factor of the nickel-based single crystal material; and m (α) is the slip direction of the slip system α of nickel-based single crystal material, n (α) is the unit normal vector of the slip plane in the slip system α of the nickel-based single crystal material.

[0035] Furthermore, the constitutive equation involves two hardening mechanisms including:

[0036] Isotropic hardening R(α) and follow-up reinforcement X (α) (a form of back stress);

[0037] Isotropic hardening R (α) It can be expressed as:

[0038]

[0039] Where Λ is the correction factor for materials and operating environment, and its value is in the range of 0.238–2.15. [uvw] is the matrix channel width along the [uvw] direction;

[0040] Equivalent shear stress of slip system α It can be expressed as:

[0041]

[0042] in ω represents the damage, which changes from 0 (no damage) to 1 (failure). Considering the evolution of damage ω, σ is established. eff and the stress tensor σ.

[0043] Thermal slip resistance of dislocation slip It can be expressed as:

[0044]

[0045] Where μ(T) is the temperature-dependent average shear modulus, b is the norm of the Burgers vector, and ρ β is the isotropic state variable on the slip system β, the hardening matrix G αβ It can describe the average strength of the interaction between slip systems. Here, the active slip systems are considered to be octahedral slip systems and cubic slip systems.

[0046] Furthermore, the damage equation considering orientation deviation is established as follows:

[0047] ω=δω r +(1-δ)ω w ;

[0048]

[0049]

[0050]

[0051] Where ω is the damage of nickel-based single crystal material; δ is the weighting coefficient, which depends on the material properties and creep conditions; ω r is the damage equation for microstructural degradation; ω wDamage caused by micro holes and micro cracks; S () is the damage parameter; C damgage and r are the material factors of microstructural influence; is the initial damage rate, which depends on the initial porosity of the nickel-based single crystal; is the steady-state creep rate; x is the stress sensitivity coefficient; η is the creep parameter related to temperature; is the reference shear stress, representing the hardening law of the slip system.

[0052] Reference shear stress It can be expressed as:

[0053]

[0054] Among them, h αβ(＝β) and h αβ(≠β) are the self-hardening modulus and latent hardening modulus, respectively.

[0055] It can be seen from the above technical solution that the present invention has at least one of the following advantages and positive effects:

[0056] The present invention

[001] to

[011] discloses a model and method for predicting the high-temperature creep life of nickel-based single crystals under the influence of small-angle orientation deviation. The invention establishes a creep constitutive equation for nickel-based single crystal materials that takes orientation deviation into account based on crystal plasticity theory. Creep finite element simulation calculations are performed by associating a finite element round rod model with the nickel-based single crystal constitutive equation, thereby realizing the association between the creep mechanism of nickel-based single crystal alloys and orientation deviation. Based on the results of the creep finite element simulation calculations, a creep time-strain curve can be established and the creep life can be predicted. On the one hand, the damage portion of the creep constitutive equation of the present invention consists of material degradation and micropore damage. The excellent mechanical properties of nickel-based single crystals are attributed to their unique microstructure. Therefore, the invention can deepen the optimization design of nickel-based single crystal materials. On the other hand, the invention promotes and ensures the performance and reliability of nickel-based single crystal turbine blades. Compared with the prior art, the high-temperature creep life prediction method for nickel-based single crystals that takes orientation deviation into account has better accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0058] Figure 1 1. It is a schematic flow chart of a model and method for predicting the high-temperature creep life of nickel-based single crystals under the influence of a small-angle orientation deviation from

[001] to

[011] according to an embodiment of the present invention;

[0059] Figure 2 is a schematic diagram of a finite element circular rod model after meshing according to an embodiment of the present invention;

[0060] Figure 3 1 is a flow chart of a creep finite element simulation calculation of a round bar model according to an embodiment of the present invention;

[0061] Figure 4 It is a creep time-creep curve comparison diagram of the finite element simulation calculation results and the experimental results of the embodiment of the present invention. DETAILED DESCRIPTION

[0062] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0063] like Figure 1 As shown, an embodiment of the present invention provides a method for predicting the high-temperature creep life of nickel-based single crystals under the influence of small-angle orientation deviations from

[001] to

[011] , which is used to predict the high-temperature creep life of nickel-based single crystal turbine blades with orientation deviations in actual industrial manufacturing applications. The life prediction method includes:

[0064] S110, establish a finite element round rod model based on the size of the nickel-based single crystal creep specimen.

[0065] In specific implementation, the finite element round bar model can be established by the following method: establish a round bar model in the "component" module of the finite element calculation software; Figure 2 As shown, hexahedral elements (C3D8) are used for meshing. The finite element calculation software can be commercial finite element calculation software, and of course, other finite element calculation software can also be used.

[0066] It is understandable that when establishing a finite element rod model, boundary conditions and material parameters need to be set. When setting boundary conditions, a tensile creep load is applied to the top surface of the model; by setting displacement U2 = 0, the lower boundary is fixed in the y direction, and the boundaries in the x and z directions are allowed to shrink; by setting U R1 =U R3= 0 to constrain the boundary surface's rotation about the x- and z-axes to maintain concentricity during creep. When setting material parameters, you can associate them with the constitutive equation for nickel-based single crystals. For example, you can set the material parameters to a UMAT user-defined material and, in step 2, establish a UMAT subroutine based on the creep constitutive equation for nickel-based single crystals.

[0067] S120, based on crystal plasticity theory, establishes the constitutive equation of nickel-based single crystal considering crystal orientation.

[0068] In specific implementation, establishing the creep constitutive equation of nickel-based single crystal considering crystal orientation includes:

[0069] Based on the crystal plasticity theory, the deformation of the material is caused by the activation of the slip system, τ (α) is the shear stress of slip system α, which can be expressed as:

[0070] τ (α) =σ:P (α) ;

[0071] Where σ(σ=σ ij ij,i,j=x,y,z) is the stress tensor under the crystal axis system, P (α) is the slip system α orientation factor of nickel-based single crystal material; m (α) is the slip direction of the slip system α of nickel-based single crystal material, n (α) is the unit normal vector of the slip plane in the slip system α of the nickel-based single crystal material. The actual stress tensor σ considering the orientation deviation can be expressed as: σ = T r σ applied ; Among them, σ applied When the stress is applied only along the x-axis, the applied stress for uniaxial tensile creep can be expressed as σ applied =(σ xx ,0,0,0,0,0); Transformation matrix T r To consider the orientation deviation, the transformation relationship between the initial oxyz coordinate system and the updated OXYZ coordinate system can be expressed as:

[0072]

[0073] Where m and n are the direction cosines of the model coordinate axis OXY-axis in the crystal axis oxyz. l1 is the cosine of the OX axis in the

[001] direction (ox axis); l2 is the cosine of the OX axis in the

[010] direction (oy axis); and l3 is the cosine of the OX axis in the

[100] direction (oz axis). m1 is the cosine of the OY axis in the

[001] direction (ox axis); m2 is the cosine of the OY axis in the

[010] direction (oy axis); and m3 is the cosine of the OY axis in the

[100] direction (oz axis). n1 is the cosine of the OZ axis in the

[001] direction (ox axis); n2 is the cosine of the OZ axis in the

[010] direction (oy axis); and n3 is the cosine of the OZ axis in the

[100] direction (oz axis).

[0074] like Figure 3 As shown, the deformation equation of nickel-based single crystal material with orientation deviation during creep is obtained:

[0075] The macroscopic strain of nickel-based single crystal high-temperature alloy is divided into elastic part and viscoplastic part. The elastic strain follows Hooke's law and can be obtained from the knowledge of elastic mechanics. The viscoplastic strain ε c It is obtained by multiplying the shear strain of the slip system by the time integral sum of the orientation factor, that is:

[0076]

[0077] in, is the creep shear strain rate of different slip systems α of single crystal materials. Based on the continuum damage model, it is expressed by the thermally activated flow rule as follows: Among them, the initial creep shear strain rate Expressed as: A is the creep parameter, T is the temperature, K is the Boltzmann constant, and Q is the activation energy. The constitutive equation involves two hardening mechanisms: isotropic hardening R (α) and follow-up reinforcement X (α) (a form of back stress), where R (α) Sensitive to microstructure, expressed as: Where Λ is the correction factor for materials and operating environment, and its value is in the range of 0.238–2.15. [uvw] is the matrix channel width along the [uvw] direction. is the equivalent shear stress of the slip system α, which can be expressed as: Where ω represents the damage, which changes from 0 (no damage) to 1 (failure). Considering the evolution of damage ω, σ is established. eff and the stress tensor σ. That is, the damage ω changes the equivalent shear stress on the slip system Acts on deformation; is the thermal slip resistance of dislocation slip, expressed as: Where μ(T) is the temperature-dependent average shear modulus, b is the norm of the Burgers vector, and ρ β is the isotropic state variable on the slip system β, the hardening matrix G αβ It can describe the average strength of the interaction between slip systems. Here, the active slip systems are considered to be octahedral slip systems and cubic slip systems.

[0078] Based on the parabolic relationship between matrix channel width and creep time, a phenomenological formula for the evolution of γ matrix channel width under creep tensile stress is obtained, which is expressed as:

[0079]

[0080] Among them, W [uvw] is the current width of the matrix channel, W0 is the initial matrix channel width, and C is a parameter related to stress and temperature.

[0081] Taking into account the influence of orientation deviation, the above formula changes to:

[0082] Among them, C uvw Calculated from C and orientation deviation angle θ: C uvw =C·cosθ.

[0083] The temporal evolution of the dislocation density in the slip system α can be described by the energy storage recovery equation determined by the three-dimensional dislocation dynamics, which is used to describe the dislocation interaction affected by orientation and temperature and is expressed as:

[0084]

[0085] The first item in the brackets represents the dislocation accumulation rate, which depends on the dislocation mean free path L (α) , the mean free path represents the distance a dislocation segment travels before coming to rest. The second term γ c ρ () represents the dislocation annihilation due to dynamic recovery and depends on the actual dislocation density ρ () and characteristic length γ c , characteristic length γ c Represents the critical annihilation distance of dislocation. L (α) depends on dislocation interactions, stress, temperature, and material orientation and is expressed as: Among them, K uvw is the orientation correlation coefficient, expressed as: Among them, constants p0 = 0.117, k0 = 1.08, k = 0.291, na Indicates the number of activated sliding systems, in this embodiment K uvw =80.

[0086] The excellent high-temperature mechanical properties of nickel-based single-crystal alloys primarily stem from their two-phase microstructures of γ (matrix phase) and γ′ (strengthening phase), as well as their compositional design. The initial microstructure is formed by a high volume fraction of cubic γ′ precipitates uniformly coherently within the γ matrix phase. Under high temperature and stress, the γ′ phase grows in a fixed direction, forming a regular, plate-like or columnar rafted structure. This rafted structure, under the continuous action of stress and temperature, stabilizes for a period of time before breaking down. The regular rafted structure coarsens and fractures, a process known as derafting, which manifests itself as material damage on a macroscopic scale. This microstructural evolution of single-crystal materials accompanies the entire service life of the blade. As the material's microstructure evolves, the blade's material deteriorates, its macroscopic mechanical properties decline, and the material's creep life decreases.

[0087] Nickel-based single crystal alloys exhibit both solidification and homogeneous voids, as well as creep deformation voids generated during creep loading after material preparation and heat treatment. Initial porosity originates from solidification and homogeneous voids; creep deformation voids are generated during high-temperature creep testing and are highly dependent on the amount of plastic deformation. The nucleation, growth, and propagation of microvoids and microcracks can lead to increased damage in nickel-based single crystals, a degradation of macroscopic mechanical properties, and a reduction in creep life.

[0088] Prior art methods for predicting the high-temperature creep life of nickel-based single crystals are highly inaccurate in estimating material degradation and microvoid damage, which increases the risk of using single-crystal turbine blades in aircraft engines and reduces their reliability. This can also lead to material waste and increase engine maintenance costs. Therefore, it is crucial to develop a high-temperature creep life prediction method for nickel-based single crystals based on microstructural degradation and microvoid damage to improve the accuracy of creep life prediction for aircraft engine turbine blades and provide technical guidance for aircraft engine overhaul and blade replacement.

[0089] In the present invention, the increase in damage to nickel-based single crystals is attributed to two parts: one is the damage caused by the nucleation, growth and expansion of micropores; the other is the degradation of the microstructure caused by the coarsening of the precipitate phase under the influence of stress and temperature, and the weakening of the bonding force between the interface of the γ′ precipitate phase and the γ matrix phase, resulting in a decrease in the high-temperature creep performance of the nickel-based single crystal (the excellent high-temperature mechanical properties of nickel-based single crystals are mainly attributed to their unique microstructure).

[0090] like Figure 3 As shown in Figure 2, the creep damage equation of nickel-based single crystal is divided into two parts: the microstructure degradation damage equation and the micropore damage equation. Both parts are closely related to material deformation and parameters that affect damage, such as shear stress and slip rate. The creep damage equation is:

[0091] ω=δω r +(1-δ)ω w ;

[0092] Where δ is a weighting factor that depends on the material properties and creep conditions. The damage equation representing microstructural degradation is ω r , expressed as: Among them, S (α) is a damage parameter that cannot determine damage fracture but only accelerates the evolution of other damages. It is expressed as: Among them, C damgage and r are material factors affecting the microstructure; ω w Represents the damage caused by microvoids and microcracks, and its damage rate depends on the shear stress and slip rate, expressed as: in, is the initial damage rate, which depends on the initial porosity of the nickel-based single crystal. is the steady-state creep rate, x is the stress sensitivity coefficient, η is the creep parameter related to temperature, is the reference shear stress, representing the hardening law of the slip system, expressed as: Among them, h αβ(α＝β) and h αβ(α≠β) are the self-hardening modulus and latent hardening modulus, respectively.

[0093] S130, combining the finite element circular rod model and the nickel-based single crystal constitutive equation, performs creep finite element simulation calculations of the circular rod model.

[0094] S140, predicting creep life and establishing a creep time-creep strain curve based on the results of creep finite element simulation calculations.

[0095] like Figure 4 As shown in Figure 3, the creep life and time-strain curves predicted by the crystal plasticity finite element model are compared with the experimental data, verifying that the constitutive model supported by the proposed model parameters can well reflect the creep deformation behavior of nickel-based single crystals with small angle deviations in the

[001] -crystal orientation.

[0096] In the above embodiment, creep finite element simulation calculations were performed by associating a finite element round rod model with the creep constitutive equation of nickel-based single crystals. The effects of orientation deviation on stress distribution, dislocation motion, and damage evolution were clarified through the crystal plasticity theory based on microstructural evolution and continuum damage mechanics. Based on the results of the creep finite element simulation calculations, the creep life can be predicted and a creep time-strain curve can be established. This life prediction method can provide reference and guidance for the optimized design of nickel-based single crystal materials and the life prediction and damage judgment of nickel-based single crystal turbine cooling blades in actual industrial manufacturing and application, which can save a lot of economic and time costs.

[0097] In another embodiment, before step 1, the method further includes: using an X-ray Laue back reflection method to determine the specific crystal orientation of the

[001] -oriented nickel-based single crystal, wherein the creep specimen has an orientation deviation angle θ, and the coordinate position in the standard stereographic projection triangle is

[0098] According to the principle of stereoscopic projection, the polar coordinates of the sample are Converted to orientation (u, v, w), the formula is:

[0099] θ = arctanρ;

[0100] w=cos(2θ).

[0101] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the high-temperature creep life of nickel-based single crystals under the influence of small-angle orientation deviation, characterized in that: include: According to the size of nickel-based single crystal creep specimen, a round rod model was established in the finite element calculation software, and hexahedral elements were used for meshing. A constitutive equation of a nickel-based single crystal is established based on crystal plasticity theory, wherein the constitutive equation includes a deformation equation that takes orientation deviation into account and a damage equation that takes orientation deviation into account; Combining the three-dimensional finite element round rod model and the nickel-based single crystal constitutive equation, a creep finite element simulation calculation of the round rod model is performed; According to the results of the creep finite element simulation calculation, a creep time-strain curve is established and the creep life is predicted; Among them, the deformation equation considering orientation deviation is: ； ； ； in, is the viscoplastic strain; It is the slip system of nickel-based single crystal material; The slip system of nickel-based single crystal material Creep shear strain rate; The slip system of nickel-based single crystal material The initial creep shear strain rate; The slip system of nickel-based single crystal material The equivalent shear stress of is the thermal slip resistance of dislocation slip; It is isotropic hardening; is the kinematic strengthening, also known as the back stress; A is the creep parameter, T is the temperature, K is the Boltzmann constant; Q is the activation energy; The slip system of nickel-based single crystal material orientation factor; and , m (α) is the slip direction of the slip system α of nickel-based single crystal material, n (α) is the unit normal vector of the slip plane in the slip system α of the nickel-based single crystal material; Among them, the damage equation considering orientation deviation is: ； ； ； ； in, It is the damage of nickel-based single crystal material; is a weighting factor that depends on the material properties and creep conditions; is the damage equation for microstructural degradation; Damage caused by micro holes and micro cracks; is the damage parameter; and r is the material factor affected by the microstructure; is the initial damage rate, which depends on the initial porosity of the nickel-based single crystal; is the steady-state creep rate; x is the stress sensitivity coefficient; is the temperature-dependent creep parameter; is the reference shear stress, representing the hardening law of the slip system; The equations of the crystal plasticity theory include: ； Among them, σ ( ) is the stress tensor in the crystal axis system, is the slip system α orientation factor of nickel-based single crystal material; ； m (α) is the slip direction of the slip system α of nickel-based single crystal material, n (α) is the unit normal vector of the slip plane in the slip system α of the nickel-based single crystal material; Actual stress tensor considering orientation deviation σ , expressed as: ； in, σ applied When the stress is applied only along the x-axis, the applied stress for uniaxial tensile creep is expressed as .

2. The creep life prediction method according to claim 1, characterized in that: Before establishing the three-dimensional finite element round bar model, the polar coordinates of the specimen ( ρ, φ ) is converted into direction ( u,v,w ).

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