A method for predicting multi-axial low cycle fatigue of cast stainless steel

Abstract

The application particularly relates to a cast stainless steel multiaxial low-cycle fatigue prediction method, which comprises the following steps: measuring or calculating the axial strain amplitude and the corresponding axial stress, the shear strain amplitude and the corresponding shear stress, and the phase difference between the axial strain amplitude and the shear strain amplitude of a cast stainless steel concerned part; calculating the equivalent axial strain amplitude and the equivalent shear strain amplitude of the cast stainless steel concerned part after correction and containing the influence of thermal aging; and substituting the equivalent axial strain amplitude and the equivalent shear strain amplitude of the cast stainless steel concerned part after correction and containing the influence of thermal aging and the phase difference therebetween into a cast stainless steel multiaxial low-cycle fatigue prediction model containing the influence of thermal aging to calculate the multiaxial low-cycle fatigue life and the fatigue crack direction of the cast stainless steel after thermal aging. The cast stainless steel multiaxial low-cycle fatigue prediction method can accurately predict the fatigue life of the cast stainless steel under multiaxial low-cycle fatigue loading and the direction of fatigue crack initiation and initial propagation.

Description

Technical Field

[0001] This invention relates to the field of multiaxial low-cycle fatigue prediction technology for cast stainless steel after hot aging, and in particular to a method for predicting multiaxial low-cycle fatigue in cast stainless steel. Background Technology

[0002] Since the early 1970s, cast austenitic stainless steel has been used to manufacture many important safety-related components in the primary loop of light water reactors. Due to its good ductility, high notch toughness, corrosion resistance, and formability, it has been selected for manufacturing a number of light water reactor components, such as pump casings, elbows, pipes, fittings, and valve housings. However, it was determined as early as the early 1980s that these materials would undergo thermal aging and embrittlement at operating temperatures of around 300°C in pressurized water reactors. This is mainly a result of the evolution of the ferrite phase microstructure in cast austenitic stainless steel. The amplitude-modulated decomposition of ferrite and the precipitation of the G phase are the main causes of the degradation of the mechanical properties of components made from cast austenitic stainless steel, leading to increased hardness, increased tensile strength, and decreased toughness, thus affecting the long-term safe and reliable operation of the pressure boundary components in the primary loop.

[0003] The loads experienced by actual nuclear power plant components are far more complex than those tested in laboratories that establish specifications and standards. A significant source of fatigue loads in actual components is pressure and thermal transients, which may include thermal delamination, peeling, or impact. Thermal transients and pressure loads, coupled with complex component geometries and material discontinuities, typically induce multiaxial or non-proportional stress distributions in actual nuclear power plant components. The impact of these more complex stress distributions on the fatigue life of nuclear power plant components differs significantly from fatigue life predictions based on data from uniaxially loaded specimens in the laboratory. However, when performing fatigue assessments of nuclear power plants according to most specifications and standards, strain calculations based on three-dimensional stress states are required, which are then converted into effective one-dimensional stress ranges for designing fatigue profiles. The supporting evidence and validation effects of these methods are limited, necessitating the development of multiaxial fatigue prediction models that consider complex stress states.

[0004] To manage the aging and predict the lifespan of cast stainless steel components for nuclear power plants operating in high-temperature environments, it is necessary to consider both the reduction in toughness caused by thermal aging and the multiaxial fatigue stress distribution characteristics that more closely approximate the actual service load conditions. Currently, there is little research on multiaxial fatigue of cast stainless steel after thermal aging, and existing multiaxial fatigue assessment methods are inadequate. It is necessary to better consider the characteristics of multiaxial fatigue loads and how to correctly assess the multiaxial low-cycle fatigue life of cast stainless steel after thermal aging. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting multiaxial low-cycle fatigue of cast stainless steel, including the effects of thermal aging. Based on the performance parameters of uniaxial low-cycle fatigue and torsional low-cycle fatigue of cast stainless steel and their normalized thermal aging parameters, this method can accurately predict the fatigue life of cast stainless steel after thermal aging during long-term service in a high-temperature environment under multiaxial low-cycle fatigue loading, as well as the direction of fatigue crack initiation and initial propagation.

[0006] To achieve the above objectives, the present invention provides a method for predicting multiaxial low-cycle fatigue in cast stainless steel, comprising the following steps:

[0007] S101. Perform strain measurement or finite element calculation on the key areas of the cast stainless steel to obtain the axial strain amplitude ε of the key areas of the cast stainless steel. x，a Shear strain amplitude γ xy，a Axial strain amplitude ε x，a The corresponding axial stress σ x，a Shear strain amplitude γ xy，a The corresponding shear stress τ xy，a Axial strain amplitude ε x，a With shear strain amplitude γ xy，a phase difference δ xy ;

[0008] S102, Axial strain amplitude ε in the key areas of cast stainless steel x，a The corresponding axial stress σ x，a Exceeding the tensile yield strength or shear strain amplitude γ xy，a The corresponding shear stress τ xy，a When the shear yield strength is exceeded, the axial strain amplitude ε of the relevant part of the cast stainless steel is... x，a and shear strain amplitude γ xy，a Corrections were made separately, and the equivalent axial strain amplitude ε of the cast stainless steel in the areas of interest after correction, including the effects of thermal aging, was calculated. x，ae and equivalent shear strain amplitude γ xy，ae ;

[0009] S103, The equivalent axial strain amplitude ε of the cast stainless steel in the affected area after correction, including the effect of heat aging. x，ae and equivalent shear strain amplitude γ xy，ae And the axial strain amplitude ε of the key parts of cast stainless steel x，a With shear strain amplitude γ xy，a Phase difference δ between xy Substitute the multiaxial low-cycle fatigue prediction model of cast stainless steel that includes the effects of thermal aging into the model to calculate the multiaxial low-cycle fatigue life N and fatigue crack direction of cast stainless steel after thermal aging.

[0010] Furthermore, in S101, if the axial strain amplitude ε of the cast stainless steel at the point of interest...x，a The corresponding axial stress σ x，a Exceeding the tensile yield strength or shear strain amplitude γ xy，a The corresponding shear stress τ xy，a When the shear yield strength is exceeded, it indicates that the cast stainless steel exhibits plastic strain, which is a form of multiaxial low-cycle fatigue. Therefore, a prediction model for multiaxial low-cycle fatigue of cast stainless steel is applicable. If the axial strain amplitude ε of the area of ​​interest in the cast stainless steel is... x，a The corresponding axial stress σ x，a The tensile yield strength was not exceeded and the shear strain amplitude γ xy，a The corresponding shear stress τ xy，a If the shear yield strength is not exceeded, it indicates that the cast stainless steel is undergoing medium-to-high cycle fatigue, and the multiaxial low-cycle fatigue prediction model for cast stainless steel is not applicable.

[0011] Furthermore, in S102, the equivalent axial strain amplitude ε of the cast stainless steel in the area of ​​concern, after correction and including the effects of thermal aging, is calculated according to the following formula. x，ae and equivalent shear strain amplitude γ xy，ae :

[0012] ε x，ae =ε x，a (1+k ε Pδ) (1)

[0013] γ xy，ae =γ xy，a (1+k γ Pδ) (2)

[0014] Where, k ε k is the sensitivity coefficient for hot aging-uniaxial low-cycle fatigue of cast stainless steel. ε >0 indicates a decrease in uniaxial fatigue life after hot aging of cast stainless steel, k ε <0 indicates that the uniaxial fatigue life of cast stainless steel increases after hot aging, k ε =0 indicates that the uniaxial fatigue life of cast stainless steel remains unchanged after hot aging; k γ For the sensitivity coefficient of hot aging-torsional low-cycle fatigue in cast stainless steel, k γ >0 indicates that the torsional fatigue life of cast stainless steel decreases after hot aging, k γ <0 indicates that the torsional fatigue life of cast stainless steel increases after hot aging, k γ =0 indicates that the torsional fatigue life of cast stainless steel does not change after hot aging; Pδ is the normalized hot aging parameter of cast stainless steel, P is the Arrhenius hot aging parameter of cast stainless steel; δ is the ferrite content of cast stainless steel.

[0015] Furthermore, the sensitivity coefficient k of hot aging-uniaxial low-cycle fatigue in cast stainless steel is... εThe uniaxial low-cycle strain amplitude-fatigue life curve ε of cast stainless steel in the initial state of hot aging was obtained. x，a =ε(N) and uniaxial strain amplitude-fatigue life data points of cast stainless steel after hot aging. x，ai -N i The difference between them is used to determine this.

[0016] Furthermore, the uniaxial low-cycle strain amplitude-fatigue life curve ε of cast stainless steel in the initial state of hot aging. x，a =ε(N) is the Manson-Coffin equation:

[0017]

[0018] Where, ε x，a σ′ represents the axial strain amplitude of the cast stainless steel, N represents the fatigue life of the cast stainless steel, and σ′ represents the axial strain amplitude. f Let ε' be the uniaxial fatigue strength coefficient of cast stainless steel, b be the uniaxial fatigue strength exponent of cast stainless steel, E be the elastic modulus of cast stainless steel, and ε′ be the elastic modulus of cast stainless steel. f denoted as , where is the uniaxial fatigue strength ductility coefficient of cast stainless steel, and c is the uniaxial fatigue strength ductility index of cast stainless steel.

[0019] Furthermore, the uniaxial strain amplitude-fatigue life data points ε of cast stainless steel after hot aging. x，ai -N i For the uniaxial strain amplitude-fatigue life data points at time node t after hot aging of cast stainless steel:

[0020] ε x，ai -N i (4)

[0021] Among them, the time node t after hot aging of cast stainless steel is selected as the longest hot aging time of cast stainless steel, and the number of uniaxial strain amplitude-fatigue life data points at the time node t after hot aging of cast stainless steel is one or more uniaxial strain amplitude-fatigue life data at the time node t after hot aging of cast stainless steel, i = 1, 2, 3, ...

[0022] Furthermore, the sensitivity coefficient k of hot aging-torsional low-cycle fatigue in cast stainless steel is... γ The torsional low-cycle shear strain amplitude-fatigue life curve γ of cast stainless steel in the initial state of hot aging. xy，a =γ(N) and the data points of torsional low-cycle shear strain amplitude-fatigue life of cast stainless steel after hot aging γ xy，ai -N i The difference between them is used to determine this.

[0023] Furthermore, the torsional low-cycle shear strain amplitude-fatigue life curve γ of cast stainless steel in the initial state of hot aging. xy，a =γ(N) is:

[0024]

[0025] Where, γ xy，a τ′ represents the shear strain amplitude of cast stainless steel. f b is the torsional fatigue strength coefficient of cast stainless steel. γ γ′ is the torsional fatigue strength index of cast stainless steel, G is the shear modulus of cast stainless steel, and γ′ is the torsional fatigue strength index of cast stainless steel. f c is the ductility coefficient of torsional fatigue strength of cast stainless steel. γ This is the ductility index for torsional fatigue strength of cast stainless steel.

[0026] Furthermore, the torsional low-cycle shear strain amplitude-fatigue life data points γ of cast stainless steel after hot aging. xy，ai -N i For the shear strain amplitude-fatigue life data points at time node t after hot aging of stainless steel:

[0027] γ xy，ai -N i (6)

[0028] Among them, the time node i after hot aging of cast stainless steel is selected as the longest hot aging time of cast stainless steel, and the number of shear strain amplitude-fatigue life data points at time node i after hot aging of cast stainless steel is one or more shear strain amplitude-fatigue life data at time node t after hot aging of cast stainless steel, i = 1, 2, 3, ...

[0029] Furthermore, the Arrhenius thermal aging parameter P of cast stainless steel is calculated according to the following formula:

[0030]

[0031] Where T is the thermal aging temperature of cast stainless steel, in °C; and Q is the activation energy value of cast stainless steel, in kJ / mole.

[0032] Furthermore, in S103, the multiaxial low-cycle fatigue prediction model for cast stainless steel, which incorporates the effects of thermal aging, uses the equivalent axial strain amplitude ε of the relevant area in the cast stainless steel. x，ae and equivalent shear strain amplitude γ xy，ae The nonlinear combination value reaches its maximum value during fatigue loading as the critical surface. Then, the low-cycle fatigue damage weight coefficient values ​​of normal strain and shear strain are obtained by using uniaxial fatigue and torsional fatigue as boundary conditions respectively.

[0033] The multiaxial low-cycle fatigue prediction model for cast stainless steel that incorporates the effects of thermal aging is as follows:

[0034]

[0035] in:

[0036]

[0037]

[0038]

[0039]

[0040] Where λ is the strain ratio of the cast stainless steel, λ = γ xy，ae / ε x，ae , (1+υ)≤λ≤2; υ is the Poisson's ratio of cast stainless steel; γ is the angle in the direction of the critical surface of cast stainless steel; ae For equivalent shear strain damage on the critical surface of cast stainless steel, ε under symmetrical fatigue loading x，ae =ε x，a γ xy，ae =γ xy，a ;γ a ε n，a These represent the shear strain and normal strain on the critical surface of cast stainless steel, respectively.

[0041] When the left side of the multiaxial low-cycle fatigue prediction model for stainless steel equals the right side, the multiaxial low-cycle fatigue life (fatigue N) predicted by the multiaxial low-cycle fatigue prediction model for cast stainless steel after hot aging increases by 1; the multiaxial low-cycle fatigue life (fatigue N) predicted by the multiaxial low-cycle fatigue prediction model for cast stainless steel after hot aging is between 1 and 10. 4 cycle;

[0042] Start inputting the equivalent axial strain amplitude ε of the cast stainless steel area of ​​concern, including the effects of thermal aging. x，ae and equivalent shear strain amplitude γ xy，ae And the axial strain amplitude ε of the key parts of cast stainless steel x，a With shear strain amplitude γ xv，a Phase difference δ between xy Subsequently, the fatigue life (N) of multiaxial low-cycle fatigue life after hot aging of cast stainless steel gradually increased from 1 to 10. 4 At the same time, the angle in the direction of the critical surface of the cast stainless steel As the temperature gradually increases from -90° to +90°, when the left side of the stainless steel multiaxial low-cycle fatigue prediction model equals the right side, and the right side value reaches its maximum value, the multiaxial low-cycle fatigue life N of the cast stainless steel after hot aging and the critical surface direction of the cast stainless steel are output. This refers to the multiaxial low-cycle fatigue life, fatigue N, and fatigue crack direction of cast stainless steel after thermal aging, as predicted by the multiaxial low-cycle fatigue prediction model.

[0043] Beneficial technical effects of the present invention:

[0044] The multiaxial low-cycle fatigue prediction model for cast stainless steel of this invention uses the nonlinear combination of the equivalent axial strain amplitude and the equivalent shear strain amplitude on the plane of interest reaching its maximum value during fatigue loading as the critical surface. Uniaxial fatigue and torsional fatigue are used as boundary conditions to obtain the low-cycle fatigue damage weight coefficients for normal strain and shear strain, respectively. The model considers the influence of the independent periodic changes of these two strain components over time on the multiaxial low-cycle fatigue behavior. Considering the influence of thermal aging, normalized thermal aging parameters are introduced to correct the strain amplitudes of axial strain fatigue and shear strain fatigue, respectively. The model considers the effects of different thermal aging times, temperatures, ferrite content, and chemical compositions on the thermal aging and multiaxial low-cycle fatigue of cast stainless steel, thus having a wide range of applications. It can accurately predict the fatigue life of cast stainless steel after long-life service thermal aging under multiaxial low-cycle fatigue loading in high-temperature environments, as well as the direction of fatigue crack initiation and initial propagation. Attached Figure Description

[0045] Figure 1 This is an analysis flowchart of an embodiment of the multiaxial low-cycle fatigue prediction model for cast stainless steel of the present invention.

[0046] Figure 2 This is a flowchart illustrating the calculation process of an embodiment of the multiaxial low-cycle fatigue prediction model for cast stainless steel according to the present invention. Detailed Implementation

[0047] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains; the terminology used herein in the specification is for the purpose of describing particular embodiments only and is not intended to limit the application; the terms “comprising” and “equivalent to”, and any variations thereof, in the specification, claims, and foregoing description of the drawings are intended to cover non-exclusive inclusion.

[0048] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0049] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings and specific embodiments.

[0050] See Figure 1-2This embodiment provides a method for predicting multiaxial low-cycle fatigue in cast stainless steel, including the following steps:

[0051] S101. Perform strain measurement or finite element calculation on the key areas of the cast stainless steel to obtain the axial strain amplitude ε of the key areas of the cast stainless steel. x，a Shear strain amplitude γ xy，a Axial strain amplitude ε x，a The corresponding axial stress σ x，a Shear strain amplitude γ xy，a The corresponding shear stress τ xy，a Axial strain amplitude ε x，a With shear strain amplitude γ xy，a phase difference δ xy ;

[0052] S102, Axial strain amplitude ε in the key areas of cast stainless steel x，a The corresponding axial stress σ x，a Exceeding the tensile yield strength or shear strain amplitude γ xy，a The corresponding shear stress τ xy，a When the shear yield strength is exceeded, the axial strain amplitude ε of the relevant part of the cast stainless steel is... x，a and shear strain amplitude γ xy，a Corrections were made separately, and the equivalent axial strain amplitude ε of the cast stainless steel in the areas of interest after correction, including the effects of thermal aging, was calculated. x，ae and equivalent shear strain amplitude γ xy，ae ;

[0053] S103, The equivalent axial strain amplitude ε of the cast stainless steel in the affected area after correction, including the effect of heat aging. x，ae and equivalent shear strain amplitude γ xy，ae And the axial strain amplitude ε of the key parts of cast stainless steel x，a With shear strain amplitude γ xy，a Phase difference δ between xy Substitute the multiaxial low-cycle fatigue prediction model of cast stainless steel that includes the effects of thermal aging into the model to calculate the multiaxial low-cycle fatigue life N and fatigue crack direction φ of cast stainless steel after thermal aging.

[0054] Furthermore, in S101, if the axial strain amplitude ε of the cast stainless steel at the point of interest... x，a The corresponding axial stress σ x，a Exceeding the tensile yield strength or shear strain amplitude γ xy，a The corresponding shear stress τ xy，a When the shear yield strength is exceeded, it indicates that the cast stainless steel exhibits plastic strain, which is a form of multiaxial low-cycle fatigue. Therefore, a multiaxial low-cycle fatigue prediction model for cast stainless steel is applicable. If the axial strain amplitude ε of the area of ​​interest in the cast stainless steel is... x，a The corresponding axial stress σx，a The tensile yield strength was not exceeded and the shear strain amplitude γ xy，a The corresponding shear stress τ xy，a If the shear yield strength is not exceeded, it indicates that the cast stainless steel is undergoing medium-to-high cycle fatigue, and the multiaxial low-cycle fatigue prediction model for cast stainless steel is not applicable.

[0055] Furthermore, in S102, the equivalent axial strain amplitude ε of the cast stainless steel in the area of ​​concern, after correction and including the effects of thermal aging, is calculated according to the following formula. x，ae and equivalent shear strain amplitude γ xy，ae :

[0056] ε x，ae =ε x，a (1+k ε Pδ) (1)

[0057] γ xy，ae =γ xy，a (1+k γ Pδ) (2)

[0058] Where, k ε k is the sensitivity coefficient for hot aging-uniaxial low-cycle fatigue of cast stainless steel. ε >0 indicates a decrease in uniaxial fatigue life after hot aging of cast stainless steel, k ε <0 indicates that the uniaxial fatigue life of cast stainless steel increases after hot aging, k ε =0 indicates that the uniaxial fatigue life of cast stainless steel remains unchanged after hot aging; k γ For the sensitivity coefficient of hot aging-torsional low-cycle fatigue in cast stainless steel, k γ >0 indicates that the torsional fatigue life of cast stainless steel decreases after hot aging, k γ <0 indicates that the torsional fatigue life of cast stainless steel increases after hot aging, k γ =0 indicates that the torsional fatigue life of cast stainless steel does not change after hot aging; Pδ is the normalized hot aging parameter of cast stainless steel, P is the Arrhenius hot aging parameter of cast stainless steel, and δ is the ferrite content (%) of cast stainless steel.

[0059] Furthermore, the sensitivity coefficient k of hot aging-uniaxial low-cycle fatigue in cast stainless steel is... ε The uniaxial low-cycle strain amplitude-fatigue life curve ε of cast stainless steel in the initial state of hot aging was obtained. x，a =ε(N) and uniaxial strain amplitude-fatigue life data points of cast stainless steel after hot aging. x，ai -N i The difference between them is used to determine this.

[0060] Furthermore, the uniaxial low-cycle strain amplitude-fatigue life curve ε of cast stainless steel in the initial state of hot aging. x，a=ε(N) is the Manson-Coffin equation:

[0061]

[0062] Where, ε x，a σ′ represents the axial strain amplitude of the cast stainless steel, N represents the fatigue life of the cast stainless steel, and σ′ represents the axial strain amplitude. f Let ε' be the uniaxial fatigue strength coefficient of cast stainless steel, b be the uniaxial fatigue strength exponent of cast stainless steel, E be the elastic modulus of cast stainless steel, and ε′ be the elastic modulus of cast stainless steel. f denoted as , where is the uniaxial fatigue strength ductility coefficient of cast stainless steel, and c is the uniaxial fatigue strength ductility index of cast stainless steel.

[0063] Furthermore, the uniaxial strain amplitude-fatigue life data points ε of cast stainless steel after hot aging. x，ai -N i For the uniaxial strain amplitude-fatigue life data points at time node t after hot aging of cast stainless steel:

[0064] ε x，ai -N i (4)

[0065] Among them, the time node t after hot aging of cast stainless steel is selected as the longest hot aging time of cast stainless steel, and the number of uniaxial strain amplitude-fatigue life data points at the time node t after hot aging of cast stainless steel is one or more uniaxial strain amplitude-fatigue life data at the time node t after hot aging of cast stainless steel, i = 1, 2, 3, ...

[0066] Furthermore, the sensitivity coefficient k of hot aging-torsional low-cycle fatigue in cast stainless steel is... γ The torsional low-cycle shear strain amplitude-fatigue life curve γ of cast stainless steel in the initial state of hot aging. xy，a =γ(N) and the data points of torsional low-cycle shear strain amplitude-fatigue life of cast stainless steel after hot aging γ xy，ai -N i The difference between them is used to determine this.

[0067] Furthermore, the torsional low-cycle shear strain amplitude-fatigue life curve γ of cast stainless steel in the initial state of hot aging. xy，a =γ(N) is:

[0068]

[0069] Where, γ xy，a τ′ represents the shear strain amplitude of cast stainless steel. f b is the torsional fatigue strength coefficient of cast stainless steel. γ γ′ is the torsional fatigue strength index of cast stainless steel, G is the shear modulus of cast stainless steel, and γ′ is the torsional fatigue strength index of cast stainless steel. fc is the ductility coefficient of torsional fatigue strength of cast stainless steel. γ This is the ductility index for torsional fatigue strength of cast stainless steel.

[0070] Furthermore, the torsional low-cycle shear strain amplitude-fatigue life data points γ of cast stainless steel after hot aging. xy，ai -N i For the shear strain amplitude-fatigue life data points at time node t after hot aging of stainless steel:

[0071] γ xy，ai -N i (6)

[0072] Among them, the time node t after hot aging of cast stainless steel is selected as the longest hot aging time of cast stainless steel, and the number of shear strain amplitude-fatigue life data points at the time node t after hot aging of cast stainless steel is one or more shear strain amplitude-fatigue life data at the time node t after hot aging of cast stainless steel, i = 1, 2, 3, ...

[0073] Furthermore, the Arrhenius thermal aging parameter P of cast stainless steel is calculated according to the following formula:

[0074]

[0075] Where T is the thermal aging temperature of cast stainless steel, in °C; and Q is the activation energy value of cast stainless steel, in kJ / mole.

[0076] Furthermore, in S103, the multiaxial low-cycle fatigue prediction model for cast stainless steel, which incorporates the effects of thermal aging, uses the equivalent axial strain amplitude ε of the relevant area in the cast stainless steel. x，ae and equivalent shear strain amplitude γ xy，ae The nonlinear combination value reaches its maximum value during fatigue loading as the critical surface. Then, the low-cycle fatigue damage weight coefficient values ​​of normal strain and shear strain are obtained by using uniaxial fatigue and torsional fatigue as boundary conditions respectively.

[0077] The multiaxial low-cycle fatigue prediction model for cast stainless steel that incorporates the effects of thermal aging is as follows:

[0078]

[0079] in:

[0080]

[0081]

[0082]

[0083]

[0084] Where λ is the strain ratio of the cast stainless steel, λ = γ xy，ae / ε x，ae , (1+υ)≤λ≤2; υ is the Poisson's ratio of cast stainless steel; γ is the angle in the direction of the critical surface of cast stainless steel; ae For equivalent shear strain damage on the critical surface of cast stainless steel, ε under symmetrical fatigue loading x，ae =ε x，a γ xy，ae =γ xy，a ;γ a ε n，a These represent the shear strain and normal strain on the critical surface of cast stainless steel, respectively.

[0085] When the left side of the multiaxial low-cycle fatigue prediction model for stainless steel equals the right side, the multiaxial low-cycle fatigue life (fatigue N) predicted by the multiaxial low-cycle fatigue prediction model for cast stainless steel after hot aging increases by 1; the multiaxial low-cycle fatigue life (fatigue N) predicted by the multiaxial low-cycle fatigue prediction model for cast stainless steel after hot aging is between 1 and 10. 4 cycle;

[0086] Start inputting the equivalent axial strain amplitude ε of the cast stainless steel area of ​​concern, including the effects of thermal aging. x，ae and equivalent shear strain amplitude γ xy，ae And the axial strain amplitude ε of the key parts of cast stainless steel x，a With shear strain amplitude γ xy，a Phase difference δ between xy Subsequently, the fatigue life (N) of multiaxial low-cycle fatigue life after hot aging of cast stainless steel gradually increased from 1 to 10. 4 At the same time, the angle in the direction of the critical surface of the cast stainless steel As the temperature gradually increases from -90° to +90°, when the left side of the stainless steel multiaxial low-cycle fatigue prediction model equals the right side, and the right side value reaches its maximum value, the multiaxial low-cycle fatigue life N of the cast stainless steel after hot aging and the critical surface direction of the cast stainless steel are output. This refers to the multiaxial low-cycle fatigue life, fatigue N, and fatigue crack direction of cast stainless steel after thermal aging, as predicted by the multiaxial low-cycle fatigue prediction model.

[0087] The multiaxial low-cycle fatigue prediction model for cast stainless steel of the present invention is based on the performance parameters of uniaxial low-cycle fatigue and torsional low-cycle fatigue of cast stainless steel and their normalized thermal aging parameters. It can accurately predict the fatigue life of cast stainless steel after long-life service thermal aging under multiaxial low-cycle fatigue loading, as well as the direction of fatigue crack initiation and initial propagation.

[0088] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method for predicting multiaxial low-cycle fatigue in cast stainless steel, characterized in that, Includes the following steps: S101. Perform strain measurement or finite element calculation on the key areas of the cast stainless steel to obtain the axial strain amplitude of the key areas of the cast stainless steel. Shear strain amplitude Axial strain amplitude Corresponding axial stress Shear strain amplitude Corresponding shear stress Axial strain amplitude With shear strain amplitude phase difference ; S102, Axial strain amplitude in key areas of cast stainless steel Corresponding axial stress Exceeding the tensile yield strength or shear strain amplitude Corresponding shear stress When the shear yield strength is exceeded, the axial strain amplitude of the relevant parts of the cast stainless steel is... and shear strain amplitude Corrections were made separately, and the equivalent axial strain amplitude of the cast stainless steel in the areas of interest, including the effects of thermal aging, was calculated. and equivalent shear strain amplitude ; S103, The equivalent axial strain amplitude of the cast stainless steel in the affected area after correction, including the effect of heat aging. and equivalent shear strain amplitude and axial strain amplitude With shear strain amplitude phase difference Substituting the multiaxial low-cycle fatigue prediction model of cast stainless steel that includes the effects of thermal aging, the multiaxial low-cycle fatigue life of cast stainless steel after thermal aging is calculated. and the direction of fatigue cracks; In S103, the multiaxial low-cycle fatigue prediction model for cast stainless steel is as follows: ； in: ； ； ； ； in, This refers to the strain ratio for cast stainless steel. , ; Poisson's ratio for cast stainless steel; The angle of the critical surface direction of cast stainless steel; For equivalent shear strain damage on the critical surface of cast stainless steel, under symmetrical fatigue loading , ; , These represent the shear strain and normal strain on the critical surface of cast stainless steel, respectively. When the left side of the multiaxial low-cycle fatigue prediction model for stainless steel equals the right side, the multiaxial low-cycle fatigue life predicted by the multiaxial low-cycle fatigue prediction model for cast stainless steel after thermal aging is... Increase by 1; Start inputting the equivalent axial strain amplitude of the cast stainless steel area of ​​concern, including the effects of thermal aging. and equivalent shear strain amplitude And the axial strain amplitude of the relevant parts of cast stainless steel With shear strain amplitude phase difference between Then, when the condition that the left side of the stainless steel multiaxial low-cycle fatigue prediction model equals the right side and the right side value reaches its maximum value is met, the multiaxial low-cycle fatigue life of the cast stainless steel after hot aging is output. and the direction of the critical surface of cast stainless steel This refers to the multiaxial low-cycle fatigue life predicted by the multiaxial low-cycle fatigue prediction model for cast stainless steel after thermal aging. And the direction of fatigue cracks.

2. The method for predicting multiaxial low-cycle fatigue of cast stainless steel according to claim 1, characterized in that: In S102, the equivalent axial strain amplitude of the cast stainless steel in the area of ​​concern, after correction and including the effects of thermal aging, is calculated according to the following formula. and equivalent shear strain amplitude : ； ； in, The sensitivity coefficient of hot aging-uniaxial low-cycle fatigue in cast stainless steel. >0 indicates that the uniaxial fatigue life of cast stainless steel decreases after hot aging. <0 indicates that the uniaxial fatigue life of cast stainless steel increases after hot aging. =0 indicates that the uniaxial fatigue life of cast stainless steel remains unchanged after hot aging. For the sensitivity coefficient of hot aging-torsional low-cycle fatigue in cast stainless steel, A value >0 indicates that the torsional fatigue life of cast stainless steel decreases after hot aging. <0 indicates that the torsional fatigue life of cast stainless steel increases after hot aging. =0 indicates that the torsional fatigue life of cast stainless steel remains unchanged after hot aging. Normalized thermal aging parameters for cast stainless steel. The Arrhenius thermal aging parameters for cast stainless steel. The ferrite content (%) of cast stainless steel.

3. The method for predicting multiaxial low-cycle fatigue of cast stainless steel according to claim 2, characterized in that: Hot aging of cast stainless steel - uniaxial low-cycle fatigue sensitivity coefficient Uniaxial low-cyclic strain amplitude-fatigue life curves of cast stainless steel in the initial state of hot aging. Uniaxial strain amplitude-fatigue life data points of cast stainless steel after hot aging The difference between them is used to determine this.

4. The method for predicting multiaxial low-cycle fatigue of cast stainless steel according to claim 3, characterized in that: Uniaxial low-cycle strain amplitude-fatigue life curve of cast stainless steel in the initial state of hot aging For the Manson-Coffin equation: ； in, This refers to the axial strain amplitude of cast stainless steel. To improve the fatigue life of cast stainless steel. This refers to the uniaxial fatigue strength coefficient of cast stainless steel. The uniaxial fatigue strength index is for cast stainless steel. The elastic modulus of cast stainless steel. This is the uniaxial fatigue strength ductility coefficient of cast stainless steel. This is the uniaxial fatigue strength ductility index for cast stainless steel.

5. The method for predicting multiaxial low-cycle fatigue of cast stainless steel according to claim 3, characterized in that: Uniaxial strain amplitude-fatigue life data points of cast stainless steel after hot aging Time points after hot aging of cast stainless steel Uniaxial strain amplitude - fatigue life data points: ； Among them, the time nodes after hot aging of cast stainless steel Select the longest hot aging time for cast stainless steel, and the time nodes after hot aging of cast stainless steel. The number of uniaxial strain amplitude-fatigue life data points is the time node after hot aging of cast stainless steel. Single or multiple uniaxial strain amplitude-fatigue life data at time. =1,2,3,…… 6. The method for predicting multiaxial low-cycle fatigue of cast stainless steel according to claim 2, characterized in that: The sensitivity coefficient of cast stainless steel to thermal aging and torsional low-cycle fatigue The torsional low-cycle shear strain amplitude-fatigue life curve of cast stainless steel in the initial state of hot aging. Data points on torsional low-cycle shear strain amplitude and fatigue life of cast stainless steel after hot aging The difference between them is used to determine this.

7. The method for predicting multiaxial low-cycle fatigue of cast stainless steel according to claim 6, characterized in that: Torsional low-cycle shear strain amplitude-fatigue life curve of cast stainless steel in the initial state of hot aging for: ； in, This represents the shear strain amplitude of cast stainless steel. This represents the torsional fatigue strength coefficient of cast stainless steel. This refers to the torsional fatigue strength index of cast stainless steel. The shear modulus of cast stainless steel. This refers to the ductility coefficient of torsional fatigue strength in cast stainless steel. This is the ductility index for torsional fatigue strength of cast stainless steel.

8. The method for predicting multiaxial low-cycle fatigue of cast stainless steel according to claim 6, characterized in that: Data points on torsional low-cycle shear strain amplitude and fatigue life of cast stainless steel after hot aging Time points after thermal aging of stainless steel Shear strain amplitude - fatigue life data points: ； Among them, the time nodes after hot aging of cast stainless steel Select the longest hot aging time for cast stainless steel, and the time nodes after hot aging of cast stainless steel. The number of shear strain amplitude-fatigue life data points is the time node after hot aging of cast stainless steel. Single or multiple shear strain amplitude-fatigue life data at time, =1,2,3,…… 9. The method for predicting multiaxial low-cycle fatigue of cast stainless steel according to claim 2, characterized in that: Arrhenius thermal aging parameters of cast stainless steel Calculate using the following formula: ； in, The temperature for the thermal aging of cast stainless steel is expressed in °C. The activation energy value for cast stainless steel is expressed in kJ / mole.

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