Method for Establishing Quantitative Analysis Model of Plate-Form Vibration Fatigue Stress Fracture of Nickel-Based Single Crystal Superalloy and Application of the Model

Abstract

The present invention provides a method for establishing a quantitative analysis model of the plate-shaped vibration fatigue stress fracture of a nickel-based single crystal superalloy, comprising the following steps: using the size of the plastic zone at the crack tip as the quantitative information of the vibration fatigue fracture of the nickel-based single crystal superalloy, and establishing a model with the vibration fatigue stress; according to the distribution region of the plastic zone at the crack tip, dividing the crack tip into a crack tip initiation zone and a crack tip propagation zone; establishing an analysis model one of the vibration fatigue stress and the size of the crack tip initiation zone of the nickel-based single crystal superalloy; establishing an analysis model two of the vibration fatigue stress and the size of the crack tip propagation zone of the nickel-based single crystal superalloy. The above model establishment method provided by this application establishes a model based on the particularity of the vibration fatigue crack of the nickel-based single crystal superalloy, and the fatigue stress fracture information can be analyzed by using this model.

Description

Technical Field

[0001] The present invention relates to the technical field of nickel-based high-temperature alloy vibration fatigue research, and in particular to a method for establishing a plate-shaped vibration fatigue stress fracture quantitative analysis model of a nickel-based single crystal high-temperature alloy and application of the model. Background Art

[0002] The quantitative analysis technology of fatigue fracture is an analysis method that uses the fatigue fracture characteristics formed on the component after fracture to reversely analyze and infer the stress and life experienced by the component. This analysis technology has been successfully applied in polycrystalline materials such as steel and Al, providing strong support for failure analysis and troubleshooting in engineering practice.

[0003] Ni-based single crystal high temperature alloy adopts directional solidification process to eliminate grain boundaries, reduce grain boundary strengthening elements that reduce melting point, increase the initial melting temperature of alloy, and its high temperature strength is greatly improved compared with equiaxed crystal and directional columnar crystal; it is now widely used in the manufacture of turbine hot end components of advanced aircraft engines. In the working environment, the hot end components of aircraft engine turbines are inevitably subjected to vibration loads, and fatigue fractures due to resonance often occur.

[0004] Nickel-based single crystal superalloys are different from conventional steel and aluminum materials and have their own unique cracking characteristics. Studies have shown that at 980°C and below, fatigue cracks in Ni-based single crystal superalloys mainly start in the octahedral slip system, with the main slip plane (fracture plane) being the (111) plane, which forms a certain angle with the load application direction

[001] , presenting a type I, II, and III composite crack. Therefore, the common type I crack shape factor expression for this type of composite crack is no longer applicable.

[0005] In view of the special plate-shaped vibration fatigue cracking characteristics of Ni-based single crystal high-temperature alloys, it is of great significance to select a fracture quantitative analysis method that can characterize the vibration fatigue cracking characteristics of single crystal alloys. Summary of the invention

[0006] The technical problem solved by the present invention is to provide a method for establishing a quantitative analysis model of plate-shaped vibration fatigue stress fracture of a nickel-based single crystal high-temperature alloy. The model established by the model establishment method can analyze the fracture information of vibration fatigue stress of the nickel-based single crystal high-temperature alloy.

[0007] In view of this, the present application provides a method for establishing a plate vibration fatigue stress fracture quantitative analysis model of a nickel-based single crystal high-temperature alloy, comprising the following steps:

[0008] The size of the plastic zone at the crack tip is used as the quantitative information of the vibration fatigue fracture of nickel-based single crystal high-temperature alloy and the vibration fatigue stress model is established;

[0009] According to the distribution area of the plastic zone at the crack tip, the crack tip area is divided into a crack tip initiation area and a crack tip propagation area;

[0010] Establish an analysis model I for the vibration fatigue stress and the size of the crack tip initiation area of a nickel-based single-crystal superalloy;

[0011] Establish an analysis model II for the vibration fatigue stress and the size of the crack tip propagation area of a nickel-based single-crystal superalloy;

[0012]

[0013] Among them, in model I, σ is the vibration fatigue stress, r p is the size of the crack tip initiation area, Y 复合 is the shape factor of the type-I, type-II, and type-III composite inclined crack, a is the crack length, σ ys is the yield strength;

[0014] In model II, σ is the vibration fatigue stress, r p is the size of the crack tip initiation area, Y 复合 is the shape factor of the type-I, type-II, and type-III composite inclined crack, a is the crack length, σ ys is the yield strength, and υ is the Poisson's ratio.

[0015] Preferably, the shape factor Y 复合 = 0.74×Y Ⅰ ; where, Y Ⅰ is the type-I crack shape factor.

[0016] Preferably, the type-I crack shape factor is related to the working section crack and the 1 / 4 elliptical corner crack, and the shape factors under bending and tension of the nickel-based single-crystal superalloy. The calculation formula is as follows:

[0017]

[0018] Among them, in the expression of F, a is the semi-minor axis of the 1 / 4 elliptical corner crack, b is the semi-major axis of the 1 / 4 elliptical corner crack, w is the plate width, t is the thickness, and θ is the angle between the main crack and the semi-major axis, and the measured values are adopted;

[0019] F is the crack correction factor, σ is the vibration fatigue stress, and a is the crack length;

[0020] The units of a, b, and W are unified as mm;

[0021] E(k) is the complete elliptic integral of the second kind, and is expressed by the following formula:

[0022]

[0023] For If within the range, F and H can be calculated using empirical formulas based on finite element results;

[0024]

[0025] H = H1 + (H2 - H1)sin p θ;

[0026] For the parameters in the above formula, the following calculation formulas are used for calculation:

[0027]

[0028] f(w) = 1 - 0.2λ + 9.4λ 2 -19.4λ 3 +27λ 4 ;

[0029]

[0030]

[0031] Preferably, the nickel-based single crystal superalloy is a first-generation nickel-based single crystal superalloy or a second-generation nickel-based single crystal superalloy.

[0032] This application also provides the application of the model established by the described establishment method in the quantitative analysis of the vibration fatigue stress fracture surface of nickel-based single crystal superalloy plates.

[0033] Preferably, the quantitative analysis of the vibration fatigue stress fracture surface is specifically:

[0034] Obtain the fracture surface information of the vibration fatigue stress according to analysis model one and / or the described analysis model two.

[0035] Preferably, the fracture surface information is the stress of crack initiation and / or crack propagation of the vibration fatigue fracture surface of the nickel-based superalloy.

[0036] Preferably, the nickel-based single crystal superalloy is a first-generation nickel-based single crystal superalloy or a second-generation nickel-based single crystal superalloy.

[0037] The present application provides a method for establishing a quantitative analysis model of the plate-shaped vibration fatigue stress fracture of a nickel-based single-crystal superalloy. Taking the size of the plastic zone at the crack tip as the quantitative information of the vibration fatigue fracture of the nickel-based single-crystal superalloy, a model is established with the vibration fatigue stress. On this basis, according to the distribution area of the plastic zone at the crack tip, the crack development process is divided into a crack initiation zone and a crack propagation zone. Then, an analysis model one of the vibration fatigue stress of the nickel-based single-crystal superalloy and the size of the crack tip initiation zone is established, and an analysis model two of the plate-shaped vibration fatigue stress of the nickel-based single-crystal superalloy and the size of the crack tip propagation zone is established. In the above model establishment method, the present application establishes a model with the size of the plastic zone at the crack tip and the vibration fatigue stress. On this basis, according to the different distribution areas of the plastic zone at the crack tip, model one and model two are respectively established. Using model one and model two, when the crack size and other sizes are known, the relevant information of the vibration fatigue stress fracture can be accurately analyzed. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Schematic diagram of the plastic deformation zone at the crack tip of the present invention;

[0039] Figure 2 Shape of the plastic zone at the crack tip of type I under the Tresca yield criterion;

[0040] Figure 3 Schematic diagram of the model of the shape factor of the plate-shaped vibration fatigue specimen "quarter-elliptical corner crack, subjected to bending and tension";

[0041] Figure 4 Schematic diagram of the actual vibration fatigue cracking and composite crack of DD6 nickel-based single-crystal sheet;

[0042] Figure 5 Curve graph of the application characteristics of the load spectrum with a stress ratio R = -1;

[0043] Figure 6 KAM diagram of plastic deformation and curve graph of original data processing for different numbers;

[0044] Figure 7 Photographs of the fracture morphology of the quarter-elliptical corner crack of the fracture for different samples. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0045] In order to further understand the present invention, the preferred implementation embodiments of the present invention will be described below in conjunction with the embodiments. However, it should be understood that these descriptions are only for further explaining the features and advantages of the present invention, rather than limiting the claims of the present invention.

[0046] In view of the unique fatigue fracture characteristics of nickel-based single-crystal superalloys, the present application provides a method for establishing a quantitative analysis model of the plate-shaped vibration fatigue stress fracture of nickel-based single-crystal superalloys, and also provides the application of the model established by this method in the quantitative analysis of the vibration fatigue stress fracture of nickel-based single-crystal superalloys; this method is based on the fatigue stress of nickel-based single-crystal superalloys being represented by the stress field parameter K at the crack tip and using the size of the plastic zone at the crack tip as the quantitative information of the fracture. Based on this, models for different vibration fatigue stress fracture types are determined. According to this model, when the vibration fatigue-related parameters are known, the quantitative information of the fracture can be accurately analyzed. Specifically, the embodiments of the present invention disclose a method for establishing a quantitative analysis model of the plate-shaped vibration fatigue stress fracture of nickel-based single-crystal superalloys, including the following steps:

[0047] Establish a model with the size of the plastic zone at the crack tip as the quantitative information of the vibration fatigue fracture of nickel-based single-crystal superalloys and the vibration fatigue stress;

[0048] According to the distribution area of the plastic zone at the crack tip, the crack tip is divided into a crack tip initiation zone and a crack tip propagation zone;

[0049] Establish analysis model one for the vibration fatigue stress of nickel-based single-crystal superalloys and the size of the crack tip initiation zone;

[0050] Establish analysis model two for the vibration fatigue stress of nickel-based single-crystal superalloys and the size of the crack tip propagation zone;

[0051]

[0052] Among them, in model one, σ is the vibration fatigue stress, r p is the size of the crack tip initiation zone, Y 复合 is the shape factor of the type I, type II, and type III composite inclined cracks, a is the crack length, σ ys is the yield strength;

[0053] In model two, σ is the vibration fatigue stress, r p is the size of the crack tip propagation zone, Y 复合 is the shape factor of the type I, type II, and type III composite inclined cracks, a is the crack length, σ ys is the yield strength, and υ is the Poisson's ratio.

[0054] In the present application, the specific process of the method for establishing a quantitative analysis model of the plate-shaped vibration fatigue stress fracture of nickel-based single-crystal superalloys is as follows:

[0055] In the vibration fatigue fracture of nickel-based single-crystal superalloy plates, according to the crack development process, it can be divided into the initiation zone stress fracture and the propagation zone stress fracture.

[0056] First, analyze the relationship between the size of the plastic zone at the crack tip and stress: For the inverse fatigue stress calculation based on fracture surface quantification, it is necessary to establish a connection between the fatigue stress and the fracture surface quantification information. The fatigue stress can be represented by the stress field parameter K at the crack tip. During the crack propagation process, a plastic zone appears at the crack tip. As Figure 1 shown, the size of the plastic zone at the crack tip is positively correlated with K. Therefore, the size of the plastic zone at the crack tip can be used to establish a connection between the fracture surface quantification information and the fatigue stress. At different crack lengths, K is calculated based on the size of the plastic zone. According to formula (1), the fatigue stress can be further calculated from the inversely derived K, and the fatigue stress of the vibration fatigue stress fracture surface can be obtained;

[0057]

[0058] where Y is the crack shape factor and a is the crack length.

[0059] Once the relationship between the size of the plastic zone at the crack tip and the fatigue stress is preliminarily determined, a plastic zone model at the crack tip is established based on the Tresca yield criterion; the Tresca yield criterion is also known as the shear stress yield criterion. The criterion states that under complex stress loading conditions, yielding occurs when the maximum shear stress is equal to the material's shear yield stress; under single-load tension conditions, the size of the plastic zone at the crack tip is given by the following formula:

[0060]

[0061] where r p is the size of the plastic zone at the crack tip, K is the stress intensity factor at the crack tip, θ is the angle between the measurement position and the x-axis of the crack tip, as Figure 2 shown, σ ys is the yield strength, υ is the Poisson's ratio, a parameter related to temperature, and π is a constant.

[0062] For the angle γ value of the measurement position of the length of the plastic zone directly below the fracture surface, then and during cyclic loading, due to the existence of a reverse plastic zone during the unloading process, its plastic zone size can be given by the following formula:

[0063]

[0064] Nickel-based superalloys are face-centered cubic crystals, and their crack opening modes exhibit typical crystallographic plane characteristics, that is, fracture occurs along fixed primary slip planes, and the final fracture surface forms a crystallographic plane, which is quite different from the fracture characteristics of polycrystalline materials such as steel and Al. Plate-shaped specimens are commonly used specimen forms for vibration fatigue. For polycrystalline alloys, the cracking direction (fracture surface direction) is perpendicular to the plate length direction, while for nickel-based single-crystal superalloys, the crack propagates along a fixed slip plane, forming a certain angle with the plate length direction, that is, exhibiting the characteristics of type I, II, and III composite cracks, as Figure 4 shown.

[0065] For the crack shape factor of type I cracking (plate shape): The crack shape factor is generally related to the load type, stress distribution, specimen shape, cracking location, and crack orientation, etc. For the plate-shaped vibration fatigue specimen, according to the cracking characteristics, the crack in its working section refers to the shape factor of the plate-shaped specimen "1 / 4 elliptical corner crack, subjected to bending and tension", as Figure 3 shown, the stress intensity factor at the crack front is shown in the following formula:

[0066]

[0067] In the formula, a is the semi-minor axis of the 1 / 4 elliptical corner crack, b is the semi-major axis of the 1 / 4 elliptical corner crack, w is the plate width, t is the thickness, θ is the angle between the main crack and the semi-major axis, and the measured value is adopted. The units of a, b, and W are unified as mm. E(k) is the complete elliptic integral of the second kind and is expressed by the following formula:

[0068]

[0069] For within the range, there is an empirical formula, and F and H can be calculated by the empirical formula based on the finite element results;

[0070]

[0071] H = H1 + (H2 - H1)sin p θ (9);

[0072] The required parameters in the formula are calculated using formulas 2.1 - 10 to 2.1 - 19

[0073]

[0074] f(w) = 1 - 0.2λ + 9.4λ 2 - 19.4λ 3 + 27λ 4 (16);

[0075]

[0076]

[0077] According to the cracking characteristics of the plate-shaped vibration fatigue of nickel-based single crystal alloy, the crack forms a certain angle with the load application direction and is a composite inclined crack of types I, II, and III, as Figure 4 shown. β is the angle between the crack plane (111 plane) and the plate length (

[001] direction), which is calculated according to the crystallographic plane angle. The β angle is 35.3° (90° - 54.7° = 35.3°). Then the composite crack shape factor is calculated according to the following formula:

[0078]

[0079] In formula (22), Y 复合 is the shape factor of type I, II, and III composite cracks, and the β angle is the angle between the normal direction of the main slip plane ((111) plane) of the Ni-based single crystal and the stress application direction (001) direction), which is calculated using formula (26); in formula (25), The coefficient 1.25 is an empirical value. The coefficient is calculated using the empirical formula 1 / (1-2ν), where ν is the parameter Poisson's ratio.

[0080] Nickel-based high-temperature alloy is a face-centered cubic crystal. Its slip cracking is based on the crystal plastic slip theory, and the β angle is calculated using formula (26).

[0081]

[0082] Wherein, the

[111] direction is the normal direction of the main slip plane (111) of the Ni-based single crystal alloy, and the

[001] direction is the stress application direction, which is also the growth direction of the single crystal alloy.

[0083] Combined with the calculation results of the type I crack shape factor (Equation 21), the final composite crack shape factors of I, II, and III are obtained as shown in Expression (27);

[0084] Y 复合 =0.74×Y Ι (27).

[0085] After the above analysis, we can get the quantitative analysis model of vibration fatigue initiation stress fracture: vibration fatigue crack initiates on the surface, which belongs to the plane stress state. According to formula (2), the plastic zone r of the crack tip is p The relationship between stress intensity factor K and stress σ, crack length a (Formula 1) and the expression of composite crack shape factor are used to obtain the crack tip plastic zone r p The expression between and stress σ (28, 29):

[0086]

[0087] Extended stress fracture quantitative analysis model: The fracture quantitative analysis model of the crack tip plastic zone is similar to the initiation stress model, because the crack adopts the plane strain state formula inside, see formula (30);

[0088]

[0089] In nickel-based single-crystal superalloys, there is an oxide layer on the fracture surface of some alloys. The oxide layer will affect the size of the plastic zone at the crack tip, so it is necessary to correct the size of the plastic zone at the crack tip. For the propagation zone, the correction formula is as shown in the following formula:

[0090] H x = H0 * 0.58 (32);

[0091] r p = r p原 - (H o * (1 - 0.58)) (33);

[0092] Among them, H0 is the original thickness of the oxide layer, and H x is the corrected thickness of the oxide layer;

[0093] r p is the size of the plastic zone at the crack tip after correction, and r p原 is the original size of the plastic zone at the crack tip.

[0094] Similarly, for the initiation zone, the correction formula is as shown in the following formula:

[0095] H x = H0 * 0.58 (34);

[0096] r p = r p原 - (H o * (1 - 0.58)) (35);

[0097] Among them, H0 is the original thickness of the oxide layer, and H x is the corrected thickness of the oxide layer;

[0098] r p is the size of the plastic zone at the crack tip after correction, and r p原 is the original size of the plastic zone at the crack tip.

[0099] Furthermore, the present application also provides the application of the model established by the above model establishment method in the quantitative analysis of the vibration fatigue stress fracture of nickel-based single-crystal superalloy plates.

[0100] In the present application, the quantitative analysis of the vibration fatigue stress fracture is specifically as follows:

[0101] The fracture information of the vibration fatigue stress is obtained according to Analysis Model 1 and / or Analysis Model 2; the fracture information can specifically know the stress at which the crack of the vibration fatigue stress initiates or the stress at which the crack propagates.

[0102] To further understand the present invention, the following will provide a detailed description of a method for establishing a model of the vibration fatigue stress fracture surface of a nickel-based single-crystal superalloy and the application of the model in conjunction with embodiments. The protection scope of the present invention is not limited by the following embodiments.

[0103] Embodiment

[0104] 1) Quantitative analysis of the initiation and propagation stress fracture surface of the plate-shaped vibration fatigue of nickel-based single-crystal superalloys

[0105] Under cyclic loading, the maximum plastic zone size at the crack tip generated by different stress ratios is different. In this embodiment, a plate-shaped vibration fatigue test under the condition of stress ratio R = -1 was carried out. Research shows that when the maximum stress intensity factor K max is constant, the fatigue crack propagation rate under constant amplitude tension and compression loading (stress ratio R < 0) is significantly higher than that under constant amplitude tension and tension loading (R > 0). The compression load part of the tension-compression cyclic load has a promoting effect on the fatigue crack propagation rate. This is because, in the case of R < 0, due to the existence of the reverse compression load, a relatively large reverse plastic zone will be generated, and the crack tip experiences relatively severe blunting damage, accelerating the crack propagation speed. The application characteristics of the load spectrum with R = -1 are as Figure 5 shown. Therefore, the plastic zone at the crack tip is the result of the combined action of tension and compression loads. The size r p of the plastic zone at the crack tip is related to the stress range (Δσ) under the condition of stress R < 0; that is, the calculation formulas for the initiation and propagation stresses are as shown below:

[0106]

[0107] 2) Fracture surface characteristics of the vibration fatigue plate-shaped specimen

[0108] A plate-shaped vibration fatigue test of DD6

[001] orientation was carried out, and the plate-shaped vibration fatigue fracture surface was obtained. The test conditions are shown in Table 1, where the position numbers of different fracture surfaces are 023-2-8, 023-2-9, and 023-2-12 respectively;

[0109] Table 1 Data table of the overall test situation

[0110] Number Temperature / °C Stress ratio <![CDATA[Maximum stress σ max / MPa]]> Number of cycles 023-2-8 850 -1 300 7027920 023-2-9 850 -1 350 1037021 023-2-12 850 -1 310 9383331

[0111] 3) Characterization of the composite crack shape factor

[0112] According to the vibration fatigue fracture surface characteristics, the crack propagation size was depicted on the cross-section to obtain the parameters required in the model of the 1 / 4 elliptical corner crack, and then the composite crack shape factor was calculated according to formula XX.

[0113] Table 2 Data table of the calculation results of the crack shape factor

[0114] Specimen number a / mm b / mm t / mm w / mm θ / ° Y composite 023-2-8 2.34 7.20 3.00 12.00 45 1.06 023-2-9 1.06 6.00 2.36 10.00 90 1.05 023-2-12 1.70 7.50 2.76 12.50 30 1.19

[0115] 4) Quantitative analysis of stress-induced fracture surface

[0116] (a) Characterization and analysis of the size of the plastic zone at the crack tip

[0117] The KAM map reflects the degree of plastic deformation uniformity. Higher values indicate a greater degree of plastic deformation or a higher defect density. Analyze the original KAM (local orientation) data from the fracture surface to the matrix. Smooth the KAM data, take the first derivative, and then the second derivative in sequence, as Figure 6 shown Figure 6 The three figures in are the KAM maps and the processed curve graphs of the original data of the specimens numbered 023-2-8, 023-2-9, and 023-2-12 respectively; obtain the change rate of KAM from the fracture surface to the matrix, take the size of the point where the second derivative is first 0 from the fracture edge, and thus calculate the plastic zone at the crack tip. The results are shown in Table 3;

[0118] Table 3 Observation positions and calculation of plastic zone size

[0119] Specimen number Crack length a / mm Plastic zone size / μm 023-2-8 0.05 4.63 023-2-9 0.07 7.11 023-2-12 0.06 8.08

[0120] (b) Analysis of the influence of the size of the fracture surface oxide layer on the size of the plastic zone

[0121] According to the energy spectrum analysis results, the main component of the fracture surface oxide layer is NiO. Compared with the nickel matrix, during the formation of NiO, the volume expands. Therefore, its thickness needs to be corrected. According to the molar masses and densities of NiO and Ni, the calculated molar volume ratio correction coefficient is 0.58. The correction formula for the influence of the oxide layer on the plastic zone size is shown in (33). The correction coefficients are shown in Table 4, and the results after oxide layer correction are shown in Table 5. The size of the plastic zone after correction is the final stress calculation size, as shown in Table 6;

[0122] H x = H0 * 0.58 Oxide layer correction (32);

[0123] In the formula, H o is the original thickness of the oxide layer, and H x is the corrected thickness of the oxide layer

[0124] r p = r p原 - (H o * (1 - 0.58)) Plastic zone correction (33);

[0125] In the formula, r p is the size of the plastic zone after correction, and r p原 is the original size

[0126] Table 4 Data Sheet for Calculating Correction Coefficient

[0127]

[0128] Table 5 Data Sheet for Observation Positions and Oxide Layer Correction Results

[0129]

[0130] Table 6 Data Sheet for Observation Positions and Calculation of Plastic Zone Size

[0131] Specimen number Crack length a / mm Plastic zone size / μm Modified plastic zone size / μm 023-2-8 0.05 4.63 3.97 023-2-9 0.07 7.11 7.11 023-2-12 0.06 8.08 7.45

[0132] (c) Calculation of Initiation Stress and Error Analysis

[0133] Calculate the compound crack shape factor Y through Equation (27) 复合 ; Substitute the obtained plastic zone size r p and crack length a into Equation (36), σ ys = 978 MPa, and the reverse calculation results of the vibration fatigue initiation stress range Δσ are shown in

[0134] Table 7

[0135]

[0136] Table 7 Initiation Y 复合 Data Sheet of Calculation Results

[0137] Specimen number Crack length a / mm H <![CDATA[F Ι > E(k) <![CDATA[Y 复合 > 023-2-8 0.05 0.34 4.72 1.11 1.06 023-2-9 0.07 0.52 2.83 1.04 1.05 023-2-12 0.06 0.54 3.17 1.06 1.19

[0138] Remark: The calculation data in Table 7 are obtained by Excel calculation. The calculation results adopt the actual values, and only 2 decimal places are shown in the table

[0139] Table 8 Data Sheet of Initiation Stress Calculation Results and Errors

[0140]

[0141] Remark: The calculation data in Table 8 are obtained by Excel calculation. The calculation results adopt the actual values, and only 2 decimal places are shown in the table

[0142] 4) Quantitative Analysis of Vibration Fatigue Propagation Stress Fracture

[0143] (a) Test Conditions

[0144] Conducted plate vibration fatigue tests under the conditions of 850 °C and R = -1. The life result range is between 10 5 ~ 10 7 , and the specific test information is shown in Table 9

[0145] Table 9 Data Sheet of Conditions for Conducting Plate Shape Vibration Fatigue Test

[0146]

[0147] (b) Measurement and Correction of Plastic Zone Size at Crack Tip

[0148] In order to quantitatively analyze and determine the plastic zone size at the crack tip, the original data of the local orientation (KAM) from the fracture surface to the matrix are processed: the data are successively smoothed, the first derivative is calculated, and the second derivative is calculated. The test results are shown in Table 10;

[0149] Table 10 Data Sheet of Observation Positions and Calculation of Plastic Zone Size

[0150]

[0151] (c) Correction of Plastic Zone Size

[0152] According to the change of Euler angles from the fracture surface to the matrix, the outermost layer of the fracture is the grain layer. According to the energy spectrum analysis results, its main component is NiO, and compared with the nickel matrix, the volume expands during the formation of NiO. Therefore, it is necessary to correct the thickness of the oxide layer. The correction method and formula are shown in 32 and 33, and the results are shown in Table 11;

[0153] H x = H0 * 0.58 Oxide Layer Correction (32)

[0154] In the formula, H o is the original thickness of the oxide layer, and H x is the corrected thickness of the oxide layer

[0155] r p = r p原 - (H o * (1 - 0.58)) Plastic Zone Correction (33)

[0156] In the formula, H o is the thickness of the oxide layer, r p is the size of the corrected plastic zone, and r p原 is the original size

[0157] Table 11 Data Sheet of Oxide Layer Measurement and Correction Values

[0158]

[0159] (d) Calculation of Expansion Stress Based on Plastic Zone Size at Crack Tip

[0160] Under the condition that the stress ratio R = -1, the plastic zone size r at the crack tip pIt is related to the stress range (Δσ) under conditions, as shown in Equation 37; in the formula for the plastic zone at the crack tip, the Poisson's ratio υ is a temperature-dependent constant. For the DD6 single crystal at 850 °C, the Poisson's ratio υ = 0.383, and the yield strength σ ys = 978 Mpa; the composite crack shape factor Y 复合 Expression 27;

[0161]

[0162] Characterize the obtained different crack lengths a and the size r of the plastic zone at the crack tip at this a p , and perform quantitative fracture surface back-calculation. The results are shown in Table 12, Figure 7 which are the fracture surface morphology photos of the 1 / 4 elliptical corner cracks of different specimens;

[0163] Table 12 Data table of vibration fatigue propagation stress calculation and error

[0164]

[0165] As can be seen from Table 12, compared with the stress applied in the test, the calculation errors of the stress calculated by using the model in this embodiment are all within 1.3 times.

[0166] The description of the above embodiments is only used to help understand the method of the present invention and its core idea. It should be noted that for those of ordinary skill in the art of this technology, without departing from the principle of the present invention, several improvements and modifications can still be made to the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

[0167] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but will be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for establishing a plate-shaped vibration fatigue stress fracture quantitative analysis model of a nickel-based single crystal high-temperature alloy, comprising the following steps: The size of the plastic zone at the crack tip is used as the quantitative information of the vibration fatigue fracture of nickel-based single crystal high-temperature alloy and the vibration fatigue stress model is established; According to the distribution area of ​​the crack tip plastic zone, the crack tip is divided into a crack tip initiation zone and a crack tip extension zone; Establish an analytical model for the vibration fatigue stress and crack tip initiation zone size of nickel-based single crystal high-temperature alloys; Establish the analytical model II of vibration fatigue stress and crack tip extension zone size of nickel-based single crystal high temperature alloy; In model 1, σ is the vibration fatigue stress, r p is the size of the crack tip initiation zone, Y 复合 is the shape factor of type I, type II, and type III composite oblique cracks, a is the crack length, σ ys is the yield strength; In model 2, σ is the vibration fatigue stress, r p is the size of the crack tip initiation zone, Y 复合 is the shape factor of type I, type II, and type III composite oblique cracks, a is the crack length, σ ys is the yield strength, υ is the Poisson’s ratio; The shape factor Y 复合 =0.74×Y Ⅰ ; Among them, Y Ⅰ is the I crack shape factor; the I crack shape factor is related to the working section crack and the 1 / 4 elliptical angle crack, bending and tensile shape factor of the nickel-based single crystal high-temperature alloy, and the calculation formula is as follows: Where E(k) is the complete elliptic integral of the second kind; F Ⅰ is the crack correction factor I, and H can be calculated using an empirical formula based on finite element results.

2. The establishment method according to claim 1, characterized in that: The calculation formula of the I crack shape factor is as follows: Among them, in the expression of F, a is the semi-minor axis of the 1 / 4 elliptical angle crack, b is the semi-major axis of the 1 / 4 elliptical angle crack, w is the plate width, t is the thickness, and θ is the angle between the main crack and the semi-major axis, which is the measured value; F is the crack correction factor, σ is the vibration fatigue stress, and a is the crack length; The units of a, b, and W are all in mm; E(k) is the complete elliptic integral of the second kind and is expressed as follows: right If the range is within the range, F and H can be calculated using empirical formulas based on finite element results; H=H1+(H2-H1)sin p I; The parameters in the above formula are calculated using the following formula: f(w)=1-0.2λ+9.4λ 2 -19.4m 3 +27min 4 ; 3. The establishment method according to any one of claims 1 to 2, characterized in that: The nickel-based single crystal high temperature alloy is a first-generation nickel-based single crystal high temperature alloy or a second-generation nickel-based single crystal high temperature alloy.

4. Application of the model established by the establishment method described in any one of claims 1 to 2 in the quantitative analysis of vibration fatigue stress fracture of nickel-based single crystal high-temperature alloy plate.

5. The use according to claim 4, characterized in that: The vibration fatigue stress fracture quantitative analysis is specifically as follows: The fracture information of vibration fatigue stress is obtained according to the analysis model 1 and / or the analysis model 2.

6. The use according to claim 5, characterized in that: The fracture information is the stress of crack initiation and / or crack propagation of the vibration fatigue fracture of the nickel-based high-temperature alloy.

7. The use according to claim 4, characterized in that: The nickel-based single crystal high temperature alloy is a first-generation nickel-based single crystal high temperature alloy or a second-generation nickel-based single crystal high temperature alloy.

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