A thickness-sensitive TMF life prediction method for nickel-based single crystal alloys with different phase angles

Abstract

This invention relates to a method for predicting the life of a nickel-based single-crystal alloy with different phase angles that is sensitive to wall thickness. The steps are as follows: (1) Conduct creep tests on standard parts with different wall thicknesses and establish a time-related damage model that reflects the thin-wall effect caused by high-temperature tension; (2) Conduct low-cycle fatigue tests on standard parts with different wall thicknesses and establish a cycle-related damage model that reflects the thin-wall effect; (3) Based on step (2), conduct creep-fatigue tests on standard parts with different wall thicknesses containing only compression load and establish a time-related damage model that reflects the thin-wall effect caused by high-temperature compression; (4) Introduce an effective temperature to measure the temperature change in the TMF and combine it with the nonlinear damage accumulation theory to characterize the TMF damage; (5) Consider the influence of the temperature gradient in the TMF and establish a TMF damage model that reflects the thin-wall effect and the influence of the temperature gradient to realize the prediction of the life of TMF with different phase angles for standard parts with different wall thicknesses.

Description

Technical Field

[0001] This invention relates to a thickness-sensitive method for predicting the TMF lifetime of nickel-based single-crystal alloys at different phase angles. It is mainly used for predicting the TMF lifetime of nickel-based single-crystal alloys, laying the foundation for the lifetime design and evaluation of nickel-based single-crystal alloy components (such as nickel-based single-crystal turbine blades). It belongs to the fields of high-temperature mechanical property prediction of materials and aero-engine technology. Background Technology

[0002] Turbine blades are a crucial component of aero-engines, exhibiting both structural and load complexity. Their lifespan and reliability significantly impact engine safety. Compared to traditional equiaxed superalloys and directionally solidified superalloys, nickel-based single-crystal alloys greatly enhance their high-temperature performance by eliminating grain boundaries, which are prone to failure at high temperatures, and are widely used in the manufacture of advanced aero-engine turbine blades. Because turbine blades must withstand alternating centrifugal and thermal loads from engine start-up, shutdown, and irregular maneuvers during service, TMF (Transient Turbine Fissure) failure is inevitable. Studies have shown that TMF is one of the main failure modes in the turbine blade body. Furthermore, to improve cooling efficiency and reduce weight, turbine blades have evolved from traditional solid structures to hollow, thin-walled structures with complex internal cavities, resulting in significant dimensional differences compared to traditional standard specimens. Existing research indicates that nickel-based single-crystal alloys exhibit a significant thin-wall effect. Even under identical chemical composition, crystal orientation, microstructure, and testing environment conditions, specimen size still significantly influences the mechanical properties of nickel-based single-crystal alloys. This thin-wall effect makes it difficult for theoretical models based on traditional standard specimen test results to accurately assess the mechanical properties of real turbine blades. Therefore, the effect of thin-walled effect needs to be fully considered in the TMF lifetime prediction of nickel-based single-crystal alloys.

[0003] Currently, lifetime prediction methods reflecting the thin-wall effect can be divided into two categories:

[0004] (1) First type of method: The high temperature fracture process of the specimen is closely related to the formation of the surface oxide layer. The formation of the oxide layer will reduce the effective bearing area of ​​the specimen and increase the effective stress. Surface oxidation usually has a greater impact on thinner specimens. By quantifying the influence of surface oxidation on standard specimens with different wall thicknesses, establishing the relationship between effective stress and wall thickness, and bringing the effective stress into the traditional life model, the life prediction of standard specimens with different wall thicknesses can be realized (Zhang Li, Yu Huichen, Guo Guangping, et al.

[001] Creep performance and fracture behavior of thin-walled specimens of oriented DD6 single crystal alloy [J]. Journal of Aerospace Power, 2019, 34: 122-129).

[0005] (2) The second type of method: directly establish a life model or damage model related to wall thickness, so as to realize the life prediction of standard parts with different wall thicknesses (Han Jianfeng. Study on size effect and rafting of nickel-based single crystal alloy creep specimens [D]. Northwestern Polytechnical University, 2011).

[0006] Currently, lifetime prediction methods reflecting the thin-wall effect mainly target creep loads. Creep damage is generally considered time-dependent, while TMF damage includes not only time-dependent damage but also cycle-dependent damage. The interaction of different types of damage is the main cause of TMF failure, and the damage accumulation differs at different phase angles. Therefore, existing creep lifetime prediction methods reflecting the thin-wall effect are insufficient for predicting the TMF lifetime of nickel-based single-crystal alloys at different phase angles.

[0007] This invention focuses on the IP-TMF and OP-TMF of nickel-based single-crystal alloys, quantifying the impact of thin-wall effect on the lifespan of IP-TMF and OP-TMF of nickel-based single-crystal alloys. Combining the nonlinear damage accumulation theory, a new method for predicting the lifespan of TMFs with different phase angles in nickel-based single-crystal alloys with wall thickness sensitivity is established, which can accurately predict the lifespan of IP-TMF and OP-TMF of standard nickel-based single-crystal alloy parts with different wall thicknesses. Summary of the Invention

[0008] The technical solution of this invention is a method for predicting the lifetime of TMF (Transient Metal Flesh) at different phase angles in nickel-based single-crystal alloys with wall thickness sensitivity. This method can accurately predict the IP-TMF and OP-TMF lifetimes of standard nickel-based single-crystal alloy parts with different wall thicknesses. The specific implementation steps are as follows:

[0009] The first step is to conduct high-temperature creep tests on standard nickel-based single-crystal alloy parts with different wall thicknesses using a high-temperature creep testing machine. The test temperature is usually higher than 700℃. Based on the creep life test results, a time-related damage model reflecting the thin-wall effect caused by high-temperature tensile stress is established.

[0010] The time-related damage model for high-temperature tensile stress, which reflects the thin-wall effect, divides the entire standard part into two parts during the establishment process: region 1, which is the material surface, and region 2, which is the material interior. The thickness of region 1 is determined by the standard part with the smallest wall thickness, and the thickness of region 2 is the difference between the total thickness of the standard part and the thickness of region 1.

[0011] For region 2, when the nickel-based single-crystal alloy is oriented along

[001] or

[011] , the time-related damage D caused by high-temperature stretching, reflecting the thin-wall effect, is... t-2 Represented as:

[0012]

[0013] Among them, D t The total damage to the entire specimen. The maximum Schmid stress on the octahedral slip surface is given by , where m, A, and R are temperature-dependent material constants, and t is time. The material constants m, A, and R are obtained by fitting the creep test lifetime of standard

[001] and

[011] oriented nickel-based single-crystal alloys with the largest wall thickness. For

[111] oriented nickel-based single-crystal alloys, the above formula also applies, but the maximum Schmid stress on the octahedral slip surface in the model is different. It should be replaced with the maximum Schmid stress on the hexahedral slip surface. The material constants m, A, and R need to be fitted to obtain the creep test life of the

[111] oriented nickel-based single crystal alloy standard part with the largest wall thickness.

[0014] For region 1, when the nickel-based single-crystal alloy is oriented along

[001] or

[011] , the time-related damage D caused by high-temperature stretching, reflecting the thin-wall effect, is... t-1 Represented as:

[0015]

[0016] Where v is a temperature-dependent material constant. The material constant v is obtained by fitting the creep test life of standard

[001] and

[011] oriented nickel-based single crystal alloys with the smallest wall thickness. For

[111] oriented nickel-based single crystal alloys, the above formula also applies, but the maximum Schmid stress on the octahedral slip surface in the model is different. It should be replaced with the maximum Schmid stress on the hexahedral slip surface. The material constant v was obtained by fitting the creep test life of the

[111] oriented nickel-based single crystal alloy standard with the smallest wall thickness.

[0017] The specimen fails when the total damage to the entire standard part reaches the critical damage level. The damage process of a standard part with thin-wall effect corresponds to two cases:

[0018] (1) Case 1: The cumulative damage in both Region 1 and Region 2 has not reached 1.

[0019] In this case, the total damage rate of the entire standard part is the area average of the damage rates in region 1 and region 2, that is:

[0020]

[0021] Among them, D t-1 D t-2 D t Let S1 represent the damage in region 1, the damage in region 2, and the total damage of the entire standard part, respectively. Let S1, S2, and S be the areas of region 1, region 2, and the total area of ​​the entire standard part, respectively. In this case, the total damage D of the entire standard part is... t The first derivative with respect to time can be further expressed as:

[0022]

[0023] (2) Case 2: The cumulative damage in region 1 reaches 1, while the cumulative damage in region 2 does not reach 1.

[0024] In this case, the damage process of the entire standard part consists of two stages: In the first stage, the total damage rate of the entire standard part is the average area of ​​the damage rates of region 1 and region 2; In the second stage, the total damage rate of the entire standard part is equal to the product of the damage rate of region 2 and the area ratio S2 / S of region 2, that is:

[0025]

[0026] Among them, D t-I This is the total damage to the entire standard part in the first stage, D. t-II This represents the total damage to the entire standard part in the second stage. In this case, the first derivative of the total damage to the entire standard part with respect to time can be further expressed as:

[0027]

[0028] The second step involves conducting low-cycle fatigue tests on standard nickel-based single-crystal alloy parts with different wall thicknesses using a high-temperature fatigue testing machine. Based on the results of the low-cycle fatigue life tests, a cycle-related damage model reflecting the thin-wall effect is established.

[0029] The cyclically related damage model reflecting the thin-wall effect is related to the relative surface area. Taking the cyclically related damage of the standard part with the largest wall thickness as the benchmark, when the nickel-based single crystal alloy is oriented along

[001] or

[011] , the cyclically related damage D reflecting the thin-wall effect is... N Represented as:

[0030]

[0031] in, Let be the maximum Schmid stress amplitude on the octahedral slip surface, and b, M, β, and γ be temperature-dependent material constants. This refers to the relative surface area of ​​a standard part with a specific wall thickness. Where is the relative surface area of ​​the standard part with the largest wall thickness, and N is the number of cycles. The temperature-dependent material constants b, M, and β are obtained by fitting the low-cycle fatigue test life of the

[001] and

[011] oriented nickel-based single-crystal alloy standard parts with the largest wall thickness. The temperature-dependent material constant γ is obtained by fitting the low-cycle fatigue test life of the

[001] and

[011] oriented nickel-based single-crystal alloy standard parts with different wall thicknesses. For the

[111] oriented nickel-based single-crystal alloy, the above formula is also applicable, but the maximum Schmid stress amplitude of the octahedral slip surface in the model is different. It should be replaced with the maximum Schmid stress amplitude of the hexahedral slip surface. Temperature-dependent material constants b, M, and β were obtained by fitting the low-cycle fatigue test life of the

[111] -oriented nickel-based single-crystal alloy standard with the largest wall thickness. Temperature-dependent material constant γ was obtained by fitting the low-cycle fatigue test life of

[111] -oriented nickel-based single-crystal alloy standard with different wall thicknesses.

[0032] The third step involves establishing a cyclically related damage model that reflects the thin-wall effect. For nickel-based single-crystal alloy standard parts with different wall thicknesses, creep-fatigue tests with only compression load are conducted. The test temperature is usually higher than 700℃. Based on the test results, a time-related damage model that reflects the thin-wall effect caused by high-temperature compression is established.

[0033] The time-dependent damage model reflecting the thin-wall effect caused by high-temperature compression is related to the relative surface area. When the nickel-based single-crystal alloy is oriented along

[001] or

[011] , the time-dependent damage reflecting the thin-wall effect caused by high-temperature compression is... Represented as:

[0034]

[0035] in, p is a temperature-dependent material constant. For creep-fatigue with only compressive load, when the nickel-based single-crystal alloy is oriented along

[001] or

[011] , its damage D c-f The following results were obtained by coupling a cyclically correlated damage model reflecting the thin-wall effect and a time-correlated damage model caused by high-temperature compression reflecting the thin-wall effect:

[0036]

[0037] Integrating the time-dependent damage over a loop, the first derivative of the total damage with respect to the number of loops is expressed as:

[0038]

[0039] Where Δt0 is the time when time-dependent damage caused by high-temperature compression occurs in one cycle. Under isothermal loading, time-dependent damage caused by high-temperature compression occurs within the compression hold time, i.e., Δt0 is the compression hold time.

[0040] Based on the material constants obtained in the cyclically related damage model reflecting the thin-wall effect, the material constants in the time-related damage model reflecting the high-temperature compression of the thin-wall effect are... The material constant ρ was obtained by fitting the creep-fatigue test life of standard

[001] and

[011] oriented nickel-based single-crystal alloys with the largest wall thickness under compression-controlled conditions. The material constant ρ was also obtained by fitting the creep-fatigue test life of standard

[001] and

[011] oriented nickel-based single-crystal alloys with different wall thicknesses under compression-controlled conditions. For

[111] oriented nickel-based single-crystal alloys, the above formula also applies, but the maximum Schmid stress on the octahedral slip surface... Maximum Schmid stress amplitude on octahedral slip surface It should be replaced with the maximum Schmid stress on the hexahedral slip surface. Maximum Schmid stress amplitude on hexahedral slip surface Material constants The material constant p was obtained by fitting the creep-fatigue test life of the

[111] oriented nickel-based single crystal alloy standard with the largest wall thickness under compression load.

[0041] The fourth step involves using effective temperature to measure the temperature changes during the TMF test, combining the nonlinear damage accumulation theory to characterize the TMF damage, and characterizing the IP-TMF damage by coupling the time-related damage model caused by high-temperature stretching that reflects the thin-wall effect and the cyclic-related damage model that reflects the thin-wall effect. Similarly, the OP-TMF damage is characterized by coupling the time-related damage model caused by high-temperature compression that reflects the thin-wall effect and the cyclic-related damage model that reflects the thin-wall effect.

[0042] Effective temperature T eff Represented as:

[0043]

[0044] Where Q is the apparent activation energy, R' = 8.314 J / (mol·K) is the gas constant, T(t) is the temperature-time function, t1 and t2 are the time to first reach the activation temperature and the time to reach the activation temperature again in each temperature cycle, respectively, and Δt = t2 - t1 represents the time range above the activation temperature in each temperature cycle.

[0045] The specific characterization methods for IP-TMF damage and OP-TMF damage are as follows:

[0046] 1) IP-TMF damage

[0047] Considering the thin-wall effect, the IP-TMF damage D with a stress ratio of -1 IP-TMF Cyclic related damage D reflecting thin-wall effect N and time-related damage D caused by high-temperature stretching reflecting the thin-wall effect t Relevant, namely:

[0048] dD IP-TMF =dD N +dD t

[0049] Time-related damage D due to high-temperature stretching reflecting the thin-wall effect t Since there are two scenarios, IP-TMF damage reflecting the thin-wall effect also includes two scenarios:

[0050] (1) Case 1: The cumulative damage in both Region 1 and Region 2 has not reached 1.

[0051] In this case, the IP-TMF damage reflects the thin-wall effect. IP-TMF Represented as:

[0052]

[0053] Integrating the time-dependent damage caused by high-temperature stretching, which reflects the thin-wall effect, over a cycle, the first derivative of the IP-TMF damage with respect to the number of cycles is expressed as:

[0054]

[0055] in, The maximum Schmid stress-time function of the octahedral slip surface; Δt1 represents the tensile stage of the cyclic load. The above formula applies to

[001] -oriented or

[011] -oriented nickel-based single-crystal alloys. For

[111] -oriented nickel-based single-crystal alloys, the form of the above formula also applies, but the amplitude of the maximum Schmid stress on the octahedral slip surface in the model will be different. Maximum Schmid stress-time function of octahedral slip surface It should be replaced with the maximum Schmid stress amplitude of the hexahedral slip surface. Maximum Schmid stress-time function of hexahedral slip surface

[0056] (2) Case 2: The cumulative damage in region 1 reaches 1, while the cumulative damage in region 2 does not reach 1.

[0057] In this case, the first and second stages of IP-TMF damage reflect the thin-wall effect. IP-TMF-I and D IP-TMF-II Represented as:

[0058]

[0059] Integrating the time-dependent damage caused by high-temperature stretching, which reflects the thin-wall effect, over a cycle, the first derivative of the IP-TMF damage with respect to the number of cycles can be expressed as:

[0060]

[0061] The above formula applies to nickel-based single-crystal alloys with

[001] or

[011] orientation. For

[111] -oriented nickel-based single-crystal alloys, the above formula also applies, but the maximum Schmid stress amplitude on the octahedral slip surface in the model will be different. Maximum Schmid stress-time function of octahedral slip surface It should be replaced with the maximum Schmid stress amplitude of the hexahedral slip surface. Maximum Schmid stress-time function of hexahedral slip surface

[0062] 2) OP-TMF damage

[0063] Considering the thin-wall effect, the OP-TMF damage D with a stress ratio of -1 OP-TMF Cyclic related damage D reflecting thin-wall effect N and time-related damage caused by high-temperature compression reflecting the thin-wall effect Relevant, namely:

[0064]

[0065] In this case, OP-TMF damage reflects the thin-wall effect. OP-TMF Represented as:

[0066]

[0067] Integrating the time-dependent damage caused by high-temperature compression, which reflects the thin-wall effect, over a single cycle, the first derivative of the OP-TMF damage with respect to the cycle number is expressed as:

[0068]

[0069] Where Δt2 is the time when time-dependent damage caused by high-temperature compression occurs in one cycle; under OP-TMF load with a stress ratio of -1, time-dependent damage caused by high-temperature compression occurs in the compression stage of the cyclic load, that is, Δt2 is the compression stage of the cyclic load. The above formula is for

[001] oriented or

[011] oriented nickel-based single crystal alloys. For

[111] oriented nickel-based single crystal alloys, the above formula is also applicable, but the maximum Schmid stress amplitude of the octahedral slip surface in the model is different. Maximum Schmid stress-time function of octahedral slip surface It should be replaced with the maximum Schmid stress amplitude of the hexahedral slip surface. Maximum Schmid stress-time function of hexahedral slip surface

[0070] The fifth step, based on the fourth step, further uses the wall thickness-related function θ to describe the influence of the temperature gradient, and establishes IP-TMF and OP-TMF damage models that reflect the thin wall effect and the influence of the temperature gradient, so as to realize the IP-TMF and OP-TMF life prediction of standard parts with different wall thicknesses.

[0071] The wall thickness-related function θ is defined as:

[0072]

[0073] Where δ is the wall thickness of the standard part. These are material constants that are temperature-dependent.

[0074] At this point, the specific characterization methods for IP-TMF damage and OP-TMF damage are as follows:

[0075] 1) IP-TMF damage

[0076] Considering the effect of temperature gradient, the IP-TMF damage D with a stress ratio of -1 IP-TMF It can be represented as:

[0077] dD IP-TMF =(dD) N +dD t )θ

[0078] Due to the time-related damage D caused by the high-temperature stretching in the first step, which reflects the thin-wall effect. t Since there are two scenarios, IP-TMF damage reflecting temperature gradient and thin-wall effect also includes two scenarios:

[0079] (1) Case 1: The cumulative damage in both Region 1 and Region 2 has not reached 1.

[0080] In this case, the IP-TMF damage reflects the thin-wall effect. IP-TMF Represented as:

[0081]

[0082] When D IP-TMF When N=0, D IP-TMF =D cri (Critical damage) N = N IP-TMF (IP-TMF lifetime of

[001] and

[011] oriented nickel-based single crystal alloys), then:

[0083]

[0084] The above formula applies to nickel-based single-crystal alloys with

[001] or

[011] orientation. For

[111] -oriented nickel-based single-crystal alloys, the above formula also applies, but the maximum Schmid stress amplitude on the octahedral slip surface in the model will be different. Maximum Schmid stress-time function of octahedral slip surface It should be replaced with the maximum Schmid stress amplitude of the hexahedral slip surface. Maximum Schmid stress-time function of hexahedral slip surface

[0085] (2) Case 2: The cumulative damage in region 1 reaches 1, while the cumulative damage in region 2 does not reach 1.

[0086] In this case, the first and second stages of IP-TMF damage reflect the thin-wall effect. IP-TMF-I and D IP-TMF-II Represented as:

[0087]

[0088] When the accumulated damage in region 1 reaches 1 at time N', the total damage of the entire specimen is D', i.e., D IP-TMF =D' when N=N', further, when D IP-TMF =D cri (Critical damage) N = N IP-TMF (IP-TMF lifetime of

[001] and

[011] oriented nickel-based single crystal alloys), from the above formula, we can obtain:

[0089]

[0090] The above formula applies to nickel-based single-crystal alloys with

[001] or

[011] orientation. For

[111] -oriented nickel-based single-crystal alloys, the above formula also applies, but the maximum Schmid stress amplitude on the octahedral slip surface in the model will be different. Maximum Schmid stress-time function of octahedral slip surface It should be replaced with the maximum Schmid stress amplitude of the hexahedral slip surface. Maximum Schmid stress-time function of hexahedral slip surface

[0091] 2) OP-TMF damage

[0092] Considering the effect of temperature gradient, the OP-TMF damage D with a stress ratio of -1 OP-TMF It can be represented as:

[0093]

[0094] In this case, OP-TMF damage reflects temperature gradient and thin-wall effect. OP-TMF It can be represented as:

[0095]

[0096] When D OP-TMF When N=0, D OP-TMF =D cri (Critical damage) N = N OP-TMF (The lifetime of OP-TMF for

[001] and

[011] oriented nickel-based single crystal alloys) is then:

[0097]

[0098] The above formula applies to nickel-based single-crystal alloys with

[001] or

[011] orientation. For

[111] -oriented nickel-based single-crystal alloys, the above formula also applies, but the maximum Schmid stress amplitude on the octahedral slip surface in the model will be different. Maximum Schmid stress-time function of octahedral slip surface It should be replaced with the maximum Schmid stress amplitude of the hexahedral slip surface. Maximum Schmid stress-time function of hexahedral slip surface

[0099] The advantages of this invention compared to existing technologies are as follows: current thickness-sensitive lifetime prediction methods mainly target creep loads and are difficult to predict the TMF lifetime of nickel-based single-crystal alloys at different phase angles. This invention proposes a thickness-sensitive TMF lifetime prediction method for nickel-based single-crystal alloys at different phase angles, which can accurately predict the IP-TMF and OP-TMF lifetimes of standard nickel-based single-crystal alloy parts with different wall thicknesses. Attached Figure Description

[0100] Figure 1 The following is the implementation process of the method of the present invention;

[0101] Figure 2 This is a schematic diagram showing the division of standard parts areas;

[0102] Figure 3 The creep life prediction results for DD6 standard parts of nickel-based single crystal alloy with different wall thicknesses and

[001] orientation at 760℃;

[0103] Figure 4 The creep life prediction results are as follows for DD6 standard parts of nickel-based single crystal alloy with different wall thicknesses and

[001] orientation at 980℃;

[0104] Figure 5 The prediction law between creep life and specimen wall thickness of standard DD6 nickel-based single crystal alloy with different wall thicknesses and

[001] orientation at 760℃ is used to show the relationship between creep life and specimen wall thickness.

[0105] Figure 6 The prediction law between creep life and specimen wall thickness of standard DD6 nickel-based single crystal alloy with different wall thicknesses and

[001] orientation at 980℃ is used to show the relationship between creep life and specimen wall thickness.

[0106] Figure 7 This diagram illustrates the impact of surface crack initiation on standard parts with different wall thicknesses. In the diagram, dots represent initiating cracks, the lightest colored rings represent the area affected by cracks on the outer surface, and the darkest colored rings represent the area affected by cracks on the inner surface.

[0107] Figure 8 Prediction results of low-cycle fatigue life for standard nickel-based single-crystal alloy DD6 with different orientations and wall thicknesses

[001] ;

[0108] Figure 9

[001] Prediction of the relationship between low-cycle fatigue life and specimen wall thickness of DD6 standard nickel-based single crystal alloy with different orientations;

[0109] Figure 10 The standard part of the

[001] oriented nickel-based single crystal alloy DD6 only contains the creep-fatigue life prediction results under compression load;

[0110] Figure 11 This is a schematic diagram of TMF damage coupling under different phase angles with a stress ratio of -1.

[0111] Figure 12

[001] TMF lifetime prediction results for DD6 standard nickel-based single crystal alloys with different orientations and wall thicknesses;

[0112] Figure 13 The prediction law between the TMF lifetime and the wall thickness of the DD6 standard nickel-based single crystal alloy with different orientations

[001] . Detailed Implementation

[0113] The technical solution of the thickness-sensitive TMF lifetime prediction method for nickel-based single-crystal alloys at different phase angles proposed in this invention will be further explained below with reference to the accompanying drawings and examples. The preliminary research material in this example is

[001] oriented nickel-based single-crystal alloy DD6.

[0114] like Figure 1 As shown, the specific implementation process of this invention is as follows:

[0115] The first step is to conduct high-temperature creep tests on standard nickel-based single-crystal alloy parts with different wall thicknesses using a high-temperature creep testing machine. The test temperature is usually higher than 700℃. Based on the creep life test results, a time-related damage model reflecting the thin-wall effect caused by high-temperature tensile stress is established.

[0116] Due to factors such as surface oxidation, the surface and internal damage behaviors of nickel-based single-crystal alloys under isothermal constant loading follow different evolutionary patterns. The thin-wall effect of nickel-based single-crystal alloys under isothermal constant loading may be caused by the difference in damage behavior between the material's surface and internal components (i.e., the surface and internal damage behaviors follow different evolutionary patterns). Therefore, in establishing a time-dependent damage model reflecting the thin-wall effect caused by high-temperature tensile stress, according to... Figure 2 The diagram shows the entire standard part divided into two parts: Region 1 (material surface) and Region 2 (material interior). The thickness of Region 1 is determined by the standard part with the smallest wall thickness, and the thickness of Region 2 is the difference between the total thickness of the standard part and the thickness of Region 1. Figure 2 As shown, when the minimum wall thickness of the standard part is δ, for standard parts with wall thicknesses of δ, 2δ, and 4δ, the thicknesses of region 1 are δ, δ, and δ, respectively, and the thicknesses of region 2 are 0, δ, and 3δ, respectively.

[0117] For region 2, when the nickel-based single-crystal alloy is oriented along

[001] or

[011] , the time-related damage D caused by high-temperature stretching, reflecting the thin-wall effect, is... t-2 It can be represented as:

[0118]

[0119] Among them, D t The total damage to the entire specimen. The maximum Schmid stress on the octahedral slip surface is given by , where m, A, and R are temperature-dependent material constants, and t is time. The material constants m, A, and R are obtained by fitting the creep test lifetime of standard

[001] and

[011] oriented nickel-based single-crystal alloys with the largest wall thickness. For

[111] oriented nickel-based single-crystal alloys, the above formula also applies, but the maximum Schmid stress on the octahedral slip surface in the model is different. It should be replaced with the maximum Schmid stress on the hexahedral slip surface. The material constants m, A, and R need to be fitted to obtain the creep test life of the

[111] oriented nickel-based single crystal alloy standard part with the largest wall thickness.

[0120] For region 1, when the nickel-based single-crystal alloy is oriented along

[001] or

[011] , the time-related damage D caused by high-temperature stretching, reflecting the thin-wall effect, is... t-1 It can be represented as:

[0121]

[0122] Where v is a temperature-dependent material constant. The material constant v is obtained by fitting the creep test life of standard

[001] and

[011] oriented nickel-based single crystal alloys with the smallest wall thickness. For

[111] oriented nickel-based single crystal alloys, the above formula also applies, but the maximum Schmid stress on the octahedral slip surface in the model is different. It should be replaced with the maximum Schmid stress on the hexahedral slip surface. The material constant v was obtained by fitting the creep test life of the

[111] oriented nickel-based single crystal alloy standard with the smallest wall thickness.

[0123] The specimen fails when the total damage to the entire standard part reaches the critical damage level. The damage process of a standard part with thin-wall effect corresponds to two cases:

[0124] (1) Case 1: The cumulative damage in both Region 1 and Region 2 has not reached 1.

[0125] In this case, the total damage rate of the entire standard part is the area average of the damage rates in region 1 and region 2, that is:

[0126]

[0127] Among them, D t-1 D t-2 D t Let S1 represent the damage in region 1, the damage in region 2, and the total damage of the entire standard part, respectively. Let S1, S2, and S be the areas of region 1, region 2, and the total area of ​​the entire standard part, respectively. In this case, the total damage D of the entire standard part is... t The first derivative with respect to time can be further expressed as:

[0128]

[0129] When D t =0 when t=0, D t =D cri (Critical damage) t = t creep (The creep life of

[001] and

[011] oriented nickel-based single crystal alloys), the integral formula (4) yields:

[0130]

[0131] Among them, D cri The critical damage is the total damage to the entire standard part (when the total damage to the entire standard part reaches the critical damage, the standard part will fracture). Typically, fracture will occur when the actual stress the material bears reaches its ultimate tensile strength. At this point, the critical damage is D. cri The relationship with macroscopic stress σ is as follows:

[0132]

[0133] Where, σ b The ultimate tensile strength. Based on formula (6), the critical damage D cri It can be represented as:

[0134]

[0135] (2) Case 2: The cumulative damage in region 1 reaches 1, while the cumulative damage in region 2 does not reach 1.

[0136] In this case, the damage process of the entire standard part consists of two stages: In the first stage, the total damage rate of the entire standard part is the average area of ​​the damage rates of region 1 and region 2; In the second stage, the total damage rate of the entire standard part is equal to the product of the damage rate of region 2 and the area ratio S2 / S of region 2, that is:

[0137]

[0138] Among them, D t-I This is the total damage to the entire standard part in the first stage, D. t-II This represents the total damage to the entire standard part in the second stage. From formula (8), the first derivative of the total damage to the entire standard part with respect to time in this case can be further expressed as:

[0139]

[0140] When the accumulated damage in region 1 reaches 1 at time t', the total damage of the entire standard part is D', i.e., D t =D' when t=t', further, when D t =D cri When t = t creep (The creep life of

[001] and

[011] oriented nickel-based single crystal alloys) can be obtained from formula (9):

[0141]

[0142] Based on formulas (5) and (10), the creep life of DD6 standard parts of nickel-based single crystal alloy with different wall thicknesses and

[001] orientation is predicted. The predicted creep life of DD6 standard parts of nickel-based single crystal alloy with different wall thicknesses and

[001] orientation at 760℃ is as follows: Figure 3 As shown, the predicted creep life of standard parts with wall thicknesses of 0.3mm, 0.6mm, 1.2mm, and 2.5mm are basically within the twice the dispersion band of the experimental results; the predicted creep life of standard parts of nickel-based single crystal alloy DD6 with different wall thicknesses and

[001] orientation at 980℃ is as follows. Figure 4As shown, the predicted creep life of standard parts with wall thicknesses of 0.3mm, 0.6mm, 1.2mm, and 2.5mm are basically within the twice dispersion band of the experimental results; the predicted relationship between creep life and specimen wall thickness of

[001] nickel-based single crystal alloy DD6 standard parts with different orientations at 760℃ is as follows. Figure 5 As shown, the predicted creep life of standard parts with wall thicknesses of 0.3mm, 0.6mm, 1.2mm, and 2.5mm is in good agreement with the experimental results; the predicted creep life of

[001] oriented nickel-based single crystal alloy DD6 standard parts with different wall thicknesses is as follows: Figure 6 As shown, the predicted creep life of standard parts with wall thicknesses of 0.3mm, 0.6mm, 1.2mm, and 2.5mm is in good agreement with the experimental results.

[0143] The second step involves conducting low-cycle fatigue tests on standard nickel-based single-crystal alloy parts with different wall thicknesses using a high-temperature fatigue testing machine. Based on the results of the low-cycle fatigue life tests, a cycle-related damage model reflecting the thin-wall effect is established.

[0144] Under isothermal cyclic loading, cracks in standard specimens of different wall thicknesses all initiate on the specimen surface and then propagate into the specimen. The specimen fails when the total damage reaches the critical damage threshold. For a specific test section, the crack initiation probability per unit perimeter and the influence area of ​​the crack initiation site are usually consistent. The effect of surface crack initiation on standard specimens of different wall thicknesses can be analyzed using... Figure 7 Indicated. By Figure 7 It can be seen that for a specific test section, the larger the relative perimeter (the ratio of the perimeter of the test section to the area), the greater the impact of surface crack initiation on the entire standard part. Similarly, for test sections of standard parts with different wall thicknesses, the larger the relative surface area (the ratio of the surface area of ​​the test section to the volume), the greater the impact of surface crack initiation on the entire standard part, and the more prone the standard part is to failure. Generally, the probability of crack initiation per unit area and the influence area of ​​the crack source are consistent. The damage of standard parts with different wall thicknesses under low cyclic fatigue load is related to the relative surface area. Taking the cyclic-related damage of the standard part with the largest wall thickness as the benchmark, when the nickel-based single crystal alloy is oriented along

[001] or

[011] , the cyclic-related damage D reflecting the thin-wall effect is... N It can be represented as:

[0145]

[0146] in, Let be the maximum Schmid stress amplitude on the octahedral slip surface, and b, M, β, and γ be temperature-dependent material constants. This refers to the relative surface area of ​​a standard part with a specific wall thickness. Let N be the relative surface area of ​​the standard part with the largest wall thickness, and N be the number of cycles. The temperature-dependent material constants b, M, and β are obtained by fitting the low-cycle fatigue test life of the

[001] and

[011] oriented nickel-based single-crystal alloy standard parts with the largest wall thickness. The temperature-dependent material constant γ can be obtained by fitting the low-cycle fatigue test life of

[001] and

[011] oriented nickel-based single-crystal alloy standard parts with different wall thicknesses. For

[111] oriented nickel-based single-crystal alloys, the above formula is also applicable, but the maximum Schmid stress amplitude of the octahedral slip surface in the model is different. It should be replaced with the maximum Schmid stress amplitude of the hexahedral slip surface. Temperature-dependent material constants b, M, and β were obtained by fitting the low-cycle fatigue test life of the

[111] -oriented nickel-based single-crystal alloy standard with the largest wall thickness. Temperature-dependent material constant γ was obtained by fitting the low-cycle fatigue test life of

[111] -oriented nickel-based single-crystal alloy standard with different wall thicknesses.

[0147] When D N When N=0, D N =D cri (D cri The calculation method is shown in formula (7) when N = N LCF (Low cyclic fatigue life of

[001] and

[011] oriented nickel-based single crystal alloys), the integral formula (11) yields:

[0148]

[0149] Based on formula (12), the low-cycle fatigue life of DD6 standard parts of nickel-based single crystal alloy with different orientations and wall thicknesses is predicted. The prediction results of the low-cycle fatigue life of DD6 standard parts of nickel-based single crystal alloy with different orientations and wall thicknesses are as follows: Figure 8 As shown, the predicted low-cycle fatigue life of standard parts with wall thicknesses of 1.0 mm, 1.5 mm, and 4.5 mm are basically within the twice the dispersion band of the experimental results;

[001] The prediction law between the low-cycle fatigue life of standard parts of nickel-based single crystal alloy DD6 with different orientations and wall thicknesses and the test piece wall thickness is as follows Figure 9 As shown, the predicted relationship between the low-cycle fatigue life of standard parts with wall thicknesses of 1.0 mm, 1.5 mm, and 4.5 mm and the wall thickness of the test specimens is in good agreement with the experimental results.

[0150] The third step involves establishing a cyclically related damage model that reflects the thin-wall effect. For nickel-based single-crystal alloy standard parts with different wall thicknesses, creep-fatigue tests with only compression load are conducted. The test temperature is usually higher than 700℃. Based on the test results, a time-related damage model that reflects the thin-wall effect caused by high-temperature compression is established.

[0151] The time-dependent damage model reflecting the thin-wall effect caused by high-temperature compression is related to the relative surface area. When the nickel-based single-crystal alloy is oriented along

[001] or

[011] , the time-dependent damage reflecting the thin-wall effect caused by high-temperature compression is... It can be represented as:

[0152]

[0153] in, p is a temperature-dependent material constant; for creep-fatigue with only compressive stress, when the nickel-based single crystal alloy is oriented along

[001] or

[011] , its damage D c-f The following results were obtained by coupling a cyclically correlated damage model reflecting the thin-wall effect and a time-correlated damage model caused by high-temperature compression reflecting the thin-wall effect:

[0154]

[0155] Integrating the time-dependent damage over a loop, the first derivative of the total damage with respect to the number of loops can be expressed as:

[0156]

[0157] Where Δt0 is the time when time-dependent damage caused by high-temperature compression occurs in one cycle. Under isothermal loading, time-dependent damage caused by high-temperature compression occurs within the compression hold time, i.e., Δt0 is the compression hold time.

[0158] Based on the material constants obtained in the cyclically related damage model reflecting the thin-wall effect, the material constants in the time-related damage model reflecting the high-temperature compression of the thin-wall effect are... The material constant ρ was obtained by fitting the creep-fatigue test life of standard

[001] and

[011] oriented nickel-based single-crystal alloys with the largest wall thickness under compression-controlled conditions. The material constant ρ was also obtained by fitting the creep-fatigue test life of standard

[001] and

[011] oriented nickel-based single-crystal alloys with different wall thicknesses under compression-controlled conditions. For

[111] oriented nickel-based single-crystal alloys, the above formula also applies, but the maximum Schmid stress on the octahedral slip surface... Maximum Schmid stress amplitude on octahedral slip surface It should be replaced with the maximum Schmid stress on the hexahedral slip surface. Maximum Schmid stress amplitude on hexahedral slip surface Material constants The material constant p was obtained by fitting the creep-fatigue test life of the

[111] oriented nickel-based single crystal alloy standard with the largest wall thickness under compression load.

[0159] When D c-f When N=0, D c-f =D cri (D cri The calculation method is shown in formula (7). (If

[001] and

[011] oriented nickel-based single-crystal alloys only contain creep-fatigue life under compression), then:

[0160]

[0161] Based on formula (16), the creep-fatigue life of the

[001] -oriented nickel-based single crystal alloy DD6 standard part with only compressive stress is predicted. The prediction results of the

[001] -oriented nickel-based single crystal alloy DD6 life at 760℃ and 980℃ are as follows: Figure 10 As shown, the lifetime prediction results are basically within twice the dispersion band of the experimental results.

[0162] The fourth step involves using effective temperature to measure the temperature changes during the TMF test, combining the nonlinear damage accumulation theory to characterize the TMF damage, and characterizing the IP-TMF damage by coupling the time-related damage model caused by high-temperature stretching that reflects the thin-wall effect and the cyclic-related damage model that reflects the thin-wall effect. Similarly, the OP-TMF damage is characterized by coupling the time-related damage model caused by high-temperature compression that reflects the thin-wall effect and the cyclic-related damage model that reflects the thin-wall effect.

[0163] Unlike isothermal fatigue, temperature changes during TMF (Transient Temperature Flow). To quantify this temperature change, an effective temperature T is introduced. eff The effective temperature T measures the temperature change during TMF testing. eff It can be represented as:

[0164]

[0165] Where Q is the apparent activation energy, R' = 8.314 J / (mol·K) is the gas constant, T(t) is the temperature-time function, t1 and t2 are the times when the activation temperature is first reached and re-reached in each temperature cycle, respectively, and Δt = t2 - t1 represents the time range above the activation temperature in each temperature cycle. For nickel-based single-crystal alloys, the minimum activation temperature is approximately 800℃, and the apparent activation energy Q is approximately 160.0 kJ / mol.

[0166] Under TMF loading, both cyclic-dependent damage and time-dependent damage exist simultaneously, and these two types are coupled and mutually reinforcing. Typically, time-dependent damage (including oxidation and creep damage) has a smaller impact at low temperatures; the TMF lifetime is mainly affected by cyclic-dependent damage and time-dependent damage at high temperatures. A schematic diagram of TMF damage coupling at different phase angles with a stress ratio of -1 is shown below. Figure 11 As shown, when the phase angle is 0° (corresponding to IP-TMF), the interaction between the high-temperature environment and the tensile stage of cyclic loading is significant. At this point, the dominant damage consists of cyclic-related damage and time-dependent damage caused by high-temperature tension. The TMF damage at 0° phase angle can be characterized by coupling the cyclic-related damage reflecting the thin-wall effect with the time-dependent damage caused by high-temperature tension, which also reflects the thin-wall effect. As the phase angle increases, the proportion of the interaction between the high-temperature environment and the tensile stage of cyclic loading gradually decreases, while the proportion of the interaction with the compression stage of cyclic loading gradually increases. At this point, the dominant damage consists of cyclic-related damage, time-dependent damage caused by high-temperature tension, and damage caused by high-temperature compression. The time-dependent damage can be characterized by coupling the cyclically dependent damage reflecting the thin-wall effect, the time-dependent damage caused by high-temperature tension reflecting the thin-wall effect, and the time-dependent damage caused by high-temperature compression reflecting the thin-wall effect. When the phase angle is 180° (corresponding to OP-TMF), the interaction between the high-temperature environment and the compression stage of the cyclic load results in cyclically dependent damage and time-dependent damage caused by high-temperature compression as the dominant damage. The TMF damage at a phase angle of 180° can be characterized by coupling the cyclically dependent damage reflecting the thin-wall effect and the time-dependent damage caused by high-temperature compression reflecting the thin-wall effect.

[0167] The specific characterization methods for IP-TMF damage and OP-TMF damage are as follows:

[0168] 1) IP-TMF damage

[0169] Considering the thin-wall effect, the IP-TMF damage D with a stress ratio of -1 IP-TMF Cyclic related damage D reflecting thin-wall effect N and time-related damage D caused by high-temperature stretching reflecting the thin-wall effect t Relevant, namely:

[0170] dD IP-TMF =dD N +dD t (18)

[0171] Time-related damage D due to high-temperature stretching reflecting the thin-wall effect t Since there are two scenarios, IP-TMF damage reflecting the thin-wall effect also includes two scenarios:

[0172] (1) Case 1: The cumulative damage in both Region 1 and Region 2 has not reached 1.

[0173] Combining formulas (4), (11), and (18), it can be seen that the IP-TMF damage D reflecting the thin-wall effect in this case is... IP-TMF It can be represented as:

[0174]

[0175] Integrating the time-dependent damage caused by high-temperature stretching, which reflects the thin-wall effect, over a cycle, the first derivative of the IP-TMF damage with respect to the number of cycles can be expressed as:

[0176]

[0177] in, The maximum Schmid stress-time function of the octahedral slip surface is given by Δt1, where Δt1 represents the tensile stage of the cyclic load. This equation applies to

[001] -oriented or

[011] -oriented nickel-based single-crystal alloys. For

[111] -oriented nickel-based single-crystal alloys, the form of the equation also applies, but the amplitude of the maximum Schmid stress on the octahedral slip surface in the model will be different. Maximum Schmid stress-time function of octahedral slip surface It should be replaced with the maximum Schmid stress amplitude of the hexahedral slip surface. Maximum Schmid stress-time function of hexahedral slip surface

[0178] (2) Case 2: The cumulative damage in region 1 reaches 1, while the cumulative damage in region 2 does not reach 1.

[0179] Combining formulas (9), (11), and (18), it can be seen that, under this condition, the first and second stages of IP-TMF damage reflect the thin-wall effect. IP-TMF-I and D IP-TMF-II Represented as:

[0180]

[0181] Integrating the time-dependent damage caused by high-temperature stretching, which reflects the thin-wall effect, over a cycle, the first derivative of the IP-TMF damage with respect to the number of cycles can be expressed as:

[0182]

[0183] The above formula applies to nickel-based single-crystal alloys with

[001] or

[011] orientation. For

[111] -oriented nickel-based single-crystal alloys, the above formula also applies, but the maximum Schmid stress amplitude on the octahedral slip surface in the model will be different. Maximum Schmid stress-time function of octahedral slip surface It should be replaced with the maximum Schmid stress amplitude of the hexahedral slip surface. Maximum Schmid stress-time function of hexahedral slip surface

[0184] 2) OP-TMF damage

[0185] Considering the thin-wall effect, the OP-TMF damage D with a stress ratio of -1 OP-TMF Cyclic related damage D reflecting thin-wall effect N and time-related damage caused by high-temperature compression reflecting the thin-wall effect Relevant, namely:

[0186]

[0187] Combining formulas (11) and (13), it can be seen that the OP-TMF damage D reflecting the thin-wall effect in this case is... OP-TMF It can be represented as:

[0188]

[0189] Integrating the time-dependent damage caused by high-temperature compression, which reflects the thin-wall effect, over a cycle, the first derivative of the OP-TMF damage with respect to the cycle number can be expressed as:

[0190]

[0191] Where Δt2 is the time when time-dependent damage caused by high-temperature compression occurs in one cycle; under OP-TMF load with a stress ratio of -1, time-dependent damage caused by high-temperature compression occurs in the compression stage of the cyclic load, that is, Δt2 is the compression stage of the cyclic load. The above formula is for

[001] oriented or

[011] oriented nickel-based single crystal alloys. For

[111] oriented nickel-based single crystal alloys, the above formula is also applicable, but the maximum Schmid stress amplitude of the octahedral slip surface in the model is different. Maximum Schmid stress-time function of octahedral slip surface It should be replaced with the maximum Schmid stress amplitude of the hexahedral slip surface. Maximum Schmid stress-time function of hexahedral slip surface

[0192] The fifth step, based on the fourth step, further uses the wall thickness-related function θ to describe the influence of the temperature gradient, and establishes IP-TMF and OP-TMF damage models that reflect the thin wall effect and the influence of the temperature gradient, so as to realize the life prediction of IP-TMF and OP-TMF of standard parts with different wall thicknesses.

[0193] Currently, temperature loads in TMF (Total Temperature Magnetic) testing are primarily applied through two methods: electromagnetic induction heating and radiative heating. During electromagnetic induction heating, an alternating current flows through the conductor, and the current distribution within the conductor is non-uniform, with higher current density closer to the surface (skin effect). This leads to temperature inconsistencies between the surface and interior of thicker specimens during electromagnetic induction heating. Similarly, radiative heating acts directly on the outer surface of the specimen, while the internal temperature rise is achieved through heat conduction. This also results in temperature inconsistencies between the surface and interior of thicker specimens. In isothermal tests, the surface and interior temperatures gradually converge over time due to heat conduction. However, in variable-temperature tests, the temperature inconsistency between the surface and interior of the specimen cannot be avoided and can only be mitigated by reducing the test frequency or the specimen wall thickness.

[0194] During the cooling process in TMF testing, the cooling airflow acts directly on the outer surface of the specimen, while the internal temperature decreases through heat conduction. For specimens with large wall thicknesses, the internal temperature may remain high even when the outer surface temperature drops to the load spectrum trough. This higher internal temperature not only results in lower internal mechanical properties of the material but also leads to tensile stress on the outer surface caused by a large temperature gradient. Similarly, the inconsistency between the internal and surface temperatures of the specimen during cooling is unavoidable and can only be mitigated by reducing the test frequency or the specimen wall thickness.

[0195] In fact, TMF testing typically uses thin-walled round tubes, but solid parts and structural components are also used. Real turbine blades are heated by high-temperature combustion gases during service, and this heating method also leads to a temperature difference between the surface and interior of the thicker parts of the turbine blade; during cooling, the interior temperature of the thicker parts of the turbine blade will also be higher than the surface temperature. Therefore, the existence of this temperature gradient is consistent with the actual situation of real turbine blades during service.

[0196] Considering the effect of the temperature gradient alone, when the wall thickness decreases to a certain extent, the temperature gradient becomes insignificant, and the TMF lifetime no longer decreases. The effect of the temperature gradient is described using a wall thickness-dependent function θ, defined as:

[0197]

[0198] Where δ is the wall thickness of the standard part. These are material constants that are temperature-dependent.

[0199] At this point, the specific characterization methods for IP-TMF damage and OP-TMF damage are as follows:

[0200] 1) IP-TMF damage

[0201] Considering the effect of temperature gradient, the IP-TMF damage with a stress ratio of -1 can be expressed as:

[0202] dD IP-TMF =(dD) N +dD t )θ (27)

[0203] Due to the time-related damage D caused by the high-temperature stretching in the first step, which reflects the thin-wall effect. t Since there are two scenarios, IP-TMF damage reflecting temperature gradient and thin-wall effect also includes two scenarios:

[0204] (1) Case 1: The cumulative damage in both Region 1 and Region 2 has not reached 1.

[0205] Combining formulas (20) and (27), it can be seen that the IP-TMF damage D reflects the temperature gradient and thin-wall effect under this condition. IP-TMF It can be represented as:

[0206]

[0207] When D IP-TMF When N=0, D IP-TMF =D cri (D cri The calculation method is shown in formula (7) when N = N IP-TMF (IP-TMF lifetime of

[001] and

[011] oriented nickel-based single crystal alloys), then:

[0208]

[0209] The above formula applies to nickel-based single-crystal alloys with

[001] or

[011] orientation. For

[111] -oriented nickel-based single-crystal alloys, the above formula also applies, but the maximum Schmid stress amplitude on the octahedral slip surface in the model will be different. Maximum Schmid stress-time function of octahedral slip surface It should be replaced with the maximum Schmid stress amplitude of the hexahedral slip surface. Maximum Schmid stress-time function of hexahedral slip surface

[0210] (2) Case 2: The cumulative damage in region 1 reaches 1, while the cumulative damage in region 2 does not reach 1.

[0211] Combining formulas (22) and (27), it can be seen that, under this condition, the first and second stages of IP-TMF damage reflect the thin-wall effect. IP-TMF-I and D IP-TMF-II Represented as:

[0212]

[0213] When the accumulated damage in region 1 reaches 1 at time N', the total damage of the entire specimen is D', i.e., D IP-TMF =D' when N=N', further, when D IP-TMF =D cri (D cri The calculation method is shown in formula (7) when N = N IP-TMF (IP-TMF lifetime of

[001] and

[011] oriented nickel-based single crystal alloys), can be obtained from formula (30):

[0214]

[0215] The above formula applies to nickel-based single-crystal alloys with

[001] or

[011] orientation. For

[111] -oriented nickel-based single-crystal alloys, the above formula also applies, but the maximum Schmid stress amplitude on the octahedral slip surface in the model will be different. Maximum Schmid stress-time function of octahedral slip surface It should be replaced with the maximum Schmid stress amplitude of the hexahedral slip surface. Maximum Schmid stress-time function of hexahedral slip surface

[0216] 2) OP-TMF damage

[0217] Considering the effect of temperature gradient, the OP-TMF damage D with a stress ratio of -1 OP-TMF It can be represented as:

[0218] dD OP-TMF =(dD) N +dD t )θ (32)

[0219] Combining formulas (25) and (32), it can be seen that the OP-TMF damage D reflects the temperature gradient and thin-wall effect under this condition. OP-TMF It can be represented as:

[0220]

[0221] When D OP-TMF When N=0, D OP-TMF =D cri (D cri The calculation method is shown in formula (7) when N = N OP-TMF (The lifetime of OP-TMF for

[001] and

[011] oriented nickel-based single crystal alloys) is then:

[0222]

[0223] The above formula applies to nickel-based single-crystal alloys with

[001] or

[011] orientation. For

[111] -oriented nickel-based single-crystal alloys, the above formula also applies, but the maximum Schmid stress amplitude on the octahedral slip surface in the model will be different. Maximum Schmid stress-time function of octahedral slip surface It should be replaced with the maximum Schmid stress amplitude of the hexahedral slip surface. Maximum Schmid stress-time function of hexahedral slip surface

[0224] Based on formulas (29), (31), and (34), the TMF lifetime of DD6 standard nickel-based single-crystal alloys with different orientations and wall thicknesses is predicted. The predicted TMF lifetime results for DD6 standard nickel-based single-crystal alloys with different orientations and wall thicknesses are as follows: Figure 12 As shown, the predicted lifespan of standard parts with wall thicknesses of 1.0 mm, 1.5 mm, 2.0 mm, and 4.5 mm is basically within the twice dispersion band of the experimental results;

[001] The prediction law between the TMF lifespan of nickel-based single-crystal alloy DD6 standard parts with different orientations and wall thicknesses and the test piece wall thickness is as follows Figure 13 As shown, the predicted TMF life of standard parts with wall thicknesses of 1.0 mm, 1.5 mm, 2.0 mm, and 4.5 mm is in good agreement with the experimental results.

[0225] The above embodiments are provided merely for the purpose of describing the present invention and are not intended to limit the scope of the invention. The scope of the invention is defined by the appended claims. Various equivalent substitutions and modifications made without departing from the spirit and principles of the invention should be covered within the scope of the invention.

Claims

1. A method for predicting the lifetime of a nickel-based single-crystal alloy at different phase angles that is sensitive to wall thickness, characterized in that, The steps include the following: Step (1): High-temperature creep tests were conducted on standard nickel-based single-crystal alloy parts with different wall thicknesses using a high-temperature creep testing machine. Based on the creep life test results, a time-related damage model reflecting the thin-wall effect caused by high-temperature tensile stress was established. Step (2): Low-cycle fatigue tests of nickel-based single-crystal alloy standard parts with different wall thicknesses were carried out using a high-temperature fatigue testing machine. Based on the results of the low-cycle fatigue life test, a cycle-related damage model reflecting the thin-wall effect was established. Step (3): Based on step (2), creep-fatigue tests with only compression load are carried out on nickel-based single crystal alloy standard parts with different wall thicknesses. The time-related damage model caused by high-temperature compression that reflects the thin-wall effect is established in combination with the test results. Step (4): The effective temperature is used to measure the temperature change in the thermomechanical fatigue test. The thermomechanical fatigue is abbreviated as TMF. The TMF damage is characterized by combining the nonlinear damage accumulation theory. The same phase thermomechanical fatigue damage is characterized by coupling the time-related damage model caused by high temperature tension that reflects the thin wall effect and the cyclic-related damage model that reflects the thin wall effect. The same phase thermomechanical fatigue is abbreviated as IP-TMF. The opposite phase thermomechanical fatigue damage is characterized by coupling the time-related damage model caused by high temperature compression that reflects the thin wall effect and the cyclic-related damage model that reflects the thin wall effect. The opposite phase thermomechanical fatigue is abbreviated as OP-TMF. Step (5): Based on step (4), a wall thickness-related function is further applied. The influence of temperature gradient is described, and IP-TMF and OP-TMF damage models reflecting the thin-wall effect and the influence of temperature gradient are established to achieve IP-TMF and OP-TMF life prediction of standard parts with different wall thicknesses. In step (5), Defined as: in, For standard part wall thickness, These are material constants that are temperature-dependent.

2. The method for predicting the lifetime of a thickness-sensitive nickel-based single-crystal alloy at different phase angles according to claim 1, characterized in that: In step (1), the time-related damage model reflecting the thin-wall effect caused by high-temperature stretching divides the entire standard part into two parts: region 1, which is the material surface, and region 2, which is the material interior. The thickness of region 1 is determined by the standard part with the smallest wall thickness, and the thickness of region 2 is the difference between the total thickness of the standard part and the thickness of region 1. For region 2, when the nickel-based single-crystal alloy is oriented along [001] or [011], the time-related damage caused by high-temperature stretching, reflecting the thin-wall effect, is observed. Represented as: in, The total damage to the entire specimen. The maximum Schmid stress on the octahedral slip surface is given by , where m, A, and R are temperature-dependent material constants, and t is time. The material constants m, A, and R are obtained by fitting the creep test life of standard [001] and [011] oriented nickel-based single-crystal alloys with the largest wall thickness. For [111] oriented nickel-based single-crystal alloys, the above formula also applies, but the maximum Schmid stress on the octahedral slip surface in the model is... It should be replaced with the maximum Schmid stress on the hexahedral slip surface. The material constants m, A, and R need to be fitted to obtain the creep test life of the [111] oriented nickel-based single crystal alloy standard parts with the largest wall thickness; For region 1, when the nickel-based single-crystal alloy is oriented along [001] or [011], the time-related damage caused by high-temperature stretching, reflecting the thin-wall effect, is as follows: Represented as: Where v is a temperature-dependent material constant, which is obtained by fitting the creep test life of standard [001] and [011] oriented nickel-based single crystal alloys with the smallest wall thickness. For [111] oriented nickel-based single crystal alloys, the above formula is also applicable, but the maximum Schmid stress on the octahedral slip surface in the model is different. It should be replaced with the maximum Schmid stress on the hexahedral slip surface. The material constant v was obtained by fitting the creep test life of the [111] oriented nickel-based single crystal alloy standard with the smallest wall thickness; The specimen fails when the total damage to the entire standard part reaches the critical damage level. The damage process of a standard part with thin-wall effect corresponds to two cases: (1) Case 1: The cumulative damage in both Region 1 and Region 2 has not reached 1. In this case, the total damage rate of the entire standard part is the area average of the damage rates in region 1 and region 2, that is: in, , D t Let S1 represent the damage in region 1, the damage in region 2, and the total damage of the entire standard part, respectively. Let S1, S2, and S be the areas of region 1, region 2, and the total area of ​​the entire standard part, respectively. In this case, the total damage D of the entire standard part is... t The first derivative with respect to time can be further expressed as: (2) Case 2: The cumulative damage in region 1 reaches 1, while the cumulative damage in region 2 does not reach 1. In this case, the damage process of the entire standard part consists of two stages: In the first stage, the total damage rate of the entire standard part is the average area of ​​the damage rates of region 1 and region 2; In the second stage, the total damage rate of the entire standard part is equal to the product of the damage rate of region 2 and the area ratio S2 / S of region 2, that is: Among them, D t-I This is the total damage to the entire standard part in the first stage, D. t-II This represents the total damage to the entire standard part in the second stage. In this case, the first derivative of the total damage to the entire standard part with respect to time can be further expressed as: 。 3. The method for predicting the lifetime of a thickness-sensitive nickel-based single-crystal alloy at different phase angles according to claim 1, characterized in that: In step (2), the cyclic-related damage model reflecting the thin-wall effect is related to the relative surface area. Taking the cyclic-related damage of the standard part with the largest wall thickness as the benchmark, when the nickel-based single crystal alloy is oriented along [001] or [011], the cyclic-related damage reflecting the thin-wall effect is... Represented as: in, For the maximum Schmid stress amplitude of the octahedral slip surface, b, M, β, These are temperature-dependent material constants. This refers to the relative surface area of ​​a standard part with a specific wall thickness. The relative surface area of ​​the standard part with the largest wall thickness is given by N, where N is the number of cycles. The temperature-dependent material constants b, M, and β are obtained by fitting the low-cycle fatigue test life of the [001] and [011] oriented nickel-based single-crystal alloy standard parts with the largest wall thickness. The low-cycle fatigue life of [001] and [011] oriented nickel-based single-crystal alloy standard parts with different wall thicknesses was obtained by fitting the low-cycle fatigue test life. For [111] oriented nickel-based single-crystal alloy, the above formula is also applicable, but the maximum Schmid stress amplitude of the octahedral slip surface in the model is different. It should be replaced with the maximum Schmid stress amplitude of the hexahedral slip surface. The temperature-dependent material constants b, M, and β were obtained by fitting the low-cycle fatigue test life of the [111]-oriented nickel-based single-crystal alloy standard part with the largest wall thickness. The lifespan was obtained by fitting low-cycle fatigue tests of standard [111]-oriented nickel-based single-crystal alloy parts with different wall thicknesses.

4. The method for predicting the lifetime of a thickness-sensitive nickel-based single-crystal alloy at different phase angles according to claim 1, characterized in that: In step (3), the time-dependent damage model reflecting the thin-wall effect caused by high-temperature compression is related to the relative surface area. When the nickel-based single crystal alloy is oriented along [001] or [011], the time-dependent damage reflecting the thin-wall effect caused by high-temperature compression is... Represented as: in, , , p is a temperature-dependent material constant. For creep-fatigue with only compressive stress, when the nickel-based single crystal alloy is oriented along [001] or [011], its damage D c-f This is represented by coupling a cyclically related damage model reflecting the thin-wall effect and a time-related damage model caused by high-temperature compression reflecting the thin-wall effect: Integrating the time-dependent damage over a loop, the first derivative of the total damage with respect to the number of loops is expressed as: in, Let be the time it takes for time-dependent damage caused by high-temperature compression to occur within one cycle. Under isothermal loading, the time-dependent damage caused by high-temperature compression occurs within the compression hold time, i.e. To reduce the load holding time; Based on the material constants obtained in the cyclically related damage model reflecting the thin-wall effect, the material constants in the time-related damage model reflecting the high-temperature compression of the thin-wall effect are... , , The material constant ρ was obtained by fitting the creep-fatigue test life of standard [001] and [011] oriented nickel-based single crystal alloys with the largest wall thickness under compression-controlled conditions. The material constant ρ was also obtained by fitting the creep-fatigue test life of standard [001] and [011] oriented nickel-based single crystal alloys with different wall thicknesses under compression-controlled conditions. For [111] oriented nickel-based single crystal alloys, the above formula also applies, but the maximum Schmid stress on the octahedral slip surface is different. Maximum Schmid stress amplitude on octahedral slip surface It should be replaced with the maximum Schmid stress on the hexahedral slip surface. Maximum Schmid stress amplitude on the hexahedral slip surface Material constants , , The material constant p was obtained by fitting the creep-fatigue test life of the [111] oriented nickel-based single crystal alloy standard with the largest wall thickness under compression load.

5. The method for predicting the lifetime of a thickness-sensitive nickel-based single-crystal alloy at different phase angles according to claim 1, characterized in that: In step (4), the effective temperature T is used. eff The effective temperature T measures the temperature change during TMF testing. eff Represented as: Where Q is the apparent activation energy. =8.314 J / (mol·K) is the gas constant, T(t) is the temperature-time function, t1 and t2 are the time to first reach the activation temperature and the time to reach the activation temperature again in each temperature cycle, respectively, and Δt=t2-t1 represents the time range above the activation temperature in each temperature cycle.

6. The method for predicting the lifetime of a thickness-sensitive nickel-based single-crystal alloy at different phase angles according to claim 1, characterized in that: In step (4), the specific characterization methods for IP-TMF damage and OP-TMF damage are as follows: 1) IP-TMF damage Considering the thin-wall effect, IP-TMF damage with a stress ratio of -1 Cyclic related damage reflecting thin-wall effect Time-related damage caused by high-temperature stretching, reflecting the thin-wall effect Relevant, namely: Time-related damage due to high-temperature stretching, reflecting the thin-wall effect Since there are two scenarios, IP-TMF damage reflecting the thin-wall effect also includes two scenarios: Scenario 1: The cumulative damage in both Region 1 and Region 2 has not reached 1. IP-TMF damage reflecting the thin-wall effect in this case Represented as: Integrating the time-dependent damage caused by high-temperature stretching, which reflects the thin-wall effect, over a cycle, the first derivative of the IP-TMF damage with respect to the number of cycles is expressed as: in, The maximum Schmid stress-time function of the octahedral slip surface; For the tensile stage of cyclic loading, the above formula applies to [001]-oriented or [011]-oriented nickel-based single-crystal alloys. For [111]-oriented nickel-based single-crystal alloys, the form of the above formula also applies, but the maximum Schmid stress amplitude on the octahedral slip surface in the model will be different. Maximum Schmid stress-time function of octahedral slip surface It should be replaced with the maximum Schmid stress amplitude of the hexahedral slip surface. Maximum Schmid stress-time function of hexahedral slip surface ; Scenario 2: The cumulative damage in region 1 reaches 1, while the cumulative damage in region 2 does not reach 1. In this case, the first and second stages of IP-TMF damage reflect the thin-wall effect. and Represented as: Integrating the time-dependent damage caused by high-temperature stretching, which reflects the thin-wall effect, over a cycle, the first derivative of the IP-TMF damage with respect to the number of cycles can be expressed as: The above formula applies to nickel-based single-crystal alloys with [001] or [011] orientation. For [111]-oriented nickel-based single-crystal alloys, the above formula also applies, but the maximum Schmid stress amplitude on the octahedral slip surface in the model will be different. Maximum Schmid stress-time function of octahedral slip surface It should be replaced with the maximum Schmid stress amplitude of the hexahedral slip surface. Maximum Schmid stress-time function of hexahedral slip surface ; 2) OP-TMF damage Considering the thin-wall effect, OP-TMF damage with a stress ratio of -1 Cyclic related damage reflecting thin-wall effect and time-related damage caused by high-temperature compression reflecting the thin-wall effect Relevant, namely: OP-TMF damage reflecting the thin-wall effect in this case Represented as: Integrating the time-dependent damage caused by high-temperature compression, which reflects the thin-wall effect, over a single cycle, the first derivative of the OP-TMF damage with respect to the cycle number is expressed as: in, The time-dependent damage caused by high-temperature compression occurs during one cycle. Under an OP-TMF load with a stress ratio of -1, the time-dependent damage caused by high-temperature compression occurs during the compression phase of the cyclic load, i.e. For the compression phase of cyclic loading, the above formula applies to [001]-oriented or [011]-oriented nickel-based single-crystal alloys. For [111]-oriented nickel-based single-crystal alloys, the form of the above formula also applies, but the maximum Schmid stress amplitude on the octahedral slip surface in the model will be different. Maximum Schmid stress-time function of octahedral slip surface It should be replaced with the maximum Schmid stress amplitude of the hexahedral slip surface. Maximum Schmid stress-time function of hexahedral slip surface .

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