Fatigue life prediction method based on physical failure mechanism under liquid lead-bismuth environment

Abstract

The application relates to a fatigue life prediction method based on a physical failure mechanism under a liquid lead-bismuth environment, which comprises the following steps: establishing a representative volume element model and defining elements belonging to a slip band; defining a crystal plasticity constitutive equation; determining parameters in the crystal plasticity constitutive equation; calculating an average shear strain range of the slip band; carrying out a fracture toughness test to obtain a specific fracture energy; establishing a fatigue life prediction model based on the physical failure mechanism; carrying out a low-cycle fatigue test of a metal material under a high-temperature and high-oxygen liquid lead-bismuth environment to determine an oxide film thickness; and establishing a fatigue life prediction model under a high-oxygen-concentration liquid lead-bismuth environment to predict the fatigue life of the metal material under the high-oxygen-concentration liquid lead-bismuth environment. The low-cycle fatigue test for calibrating parameters of the crystal plasticity constitutive equation in the prediction temperature air and the fracture toughness test in the air and the liquid lead-bismuth environment can be carried out, so that the fatigue life under the liquid lead-bismuth environment can be predicted.

Description

Technical Field

[0001] This invention relates to the field of fatigue life prediction technology for metallic materials in a liquid lead-bismuth environment, and specifically to a fatigue life prediction method based on physical failure mechanisms in a liquid lead-bismuth environment. Background Technology

[0002] The lead-cooled fast reactor, one of the reactor types in Generation IV nuclear energy systems, employs a closed fuel cycle and possesses excellent nuclear waste transmutation and nuclear fuel breeding capabilities. Its coolant, liquid lead-bismuth eutectic (LBE), has superior neutron and thermal properties and does not react with water or air. Therefore, the lead-cooled fast reactor can well meet the target requirements of Generation IV nuclear energy systems and is internationally recognized as an important option for realizing nuclear energy development.

[0003] However, the incompatibility between structural materials and liquid lead-bismuth leads to embrittlement of the liquid metal, posing a significant challenge to the development of lead-cooled fast reactors. Temperature variations and pressure fluctuations during nuclear power plant operation subject components to cyclic loading, leading to low-cycle fatigue failure. In a liquid lead-bismuth environment, the fatigue life of structural materials is significantly reduced. Therefore, accurate prediction of the fatigue life of materials in a liquid lead-bismuth environment is crucial for ensuring safety and economic efficiency.

[0004] Currently, there are few methods for assessing the fatigue life of metals in liquid lead-bismuth environments, and most are based on empirical models that require fitting to a series of experimental data. Furthermore, fatigue life prediction models based on physical failure mechanisms do not describe the embrittlement phenomenon of liquid metals and may not be applicable to liquid lead-bismuth environments. In addition, there are currently no models describing the impact of oxide films formed on the surface of metal materials in high-oxygen-concentration liquid environments on fatigue life.

[0005] To address the above technical problems, this invention proposes a fatigue life prediction method based on physical failure mechanisms in a liquid lead-bismuth environment. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a fatigue life prediction method based on physical failure mechanism in liquid lead-bismuth environment. It only requires low-cycle fatigue test to calibrate the crystal plastic constitutive equation parameters in air at the prediction temperature and fracture toughness test in air and liquid lead-bismuth environment to predict the fatigue life in air and low oxygen concentration liquid lead-bismuth environment. Furthermore, by determining the oxide film thickness through a small number of low-cycle fatigue tests in high oxygen concentration liquid lead-bismuth environment, the fatigue life in high oxygen concentration liquid lead-bismuth environment can be predicted.

[0007] The technical problem solved by this invention is achieved through the following technical solution:

[0008] A fatigue life prediction method based on physical failure mechanism in a liquid lead-bismuth environment includes the following steps:

[0009] Step 1: Establish a representative volume element model, assign random orientation, and define elements belonging to the slip zone;

[0010] Step 2: Define the constitutive equation for crystal plasticity:

[0011] The crystal plastic constitutive equation of the material in the uniaxial symmetric cyclic low-cycle fatigue test is defined by the user subroutine UMAT, thereby describing the stress-strain relationship of the representative volume element model in step 1 under uniaxial symmetric cyclic loading.

[0012] Step 3: Determine the parameters in the crystal plastic constitutive equation using the cyclic stress amplitude curve or fatigue hysteresis loop from the experiment.

[0013] A symmetrical cyclic low-cycle fatigue test was conducted on the metallic material in an air environment at a predicted temperature to obtain the cyclic stress amplitude curve or fatigue hysteresis loop of the test.

[0014] By calling the UMAT subroutine in ABAQUS software, the crystal plastic constitutive equation is used to perform finite element calculations on the representative volume element model in step 1 above, obtaining the cyclic stress amplitude curve or fatigue hysteresis loop after finite element calculation; the parameters in the crystal plastic constitutive equation above are determined by the trial-and-error method, and the cyclic stress amplitude curve or fatigue hysteresis loop obtained by finite element calculation in air environment is compared with the curve obtained by experiment in air environment until the fitting degree of the cyclic stress amplitude curve or fatigue hysteresis loop obtained by finite element calculation converges with that of the cyclic stress amplitude curve or fatigue hysteresis loop obtained by experiment.

[0015] Step 4: Calculate the average shear strain range of the slip band based on the elements defined in Step 1.

[0016] Based on the representative volume element model in step 1 and the crystal plastic constitutive equation parameters determined in step 3, finite element calculations are performed under different strain amplitude conditions. The shear strain range of the slip band is calculated using Python code. Specifically, the shear strain range of the elements contained in the slip band is calculated and the average value is obtained to get the shear strain range of the slip band. The shear strain ranges of all slip bands are sorted, and the maximum value is taken for subsequent fatigue life prediction.

[0017] The average value of the shear strain range of the slip system in the slip band is calculated by crystal plastic finite element method and then applied to fatigue life prediction.

[0018] Step 5: Conduct fracture toughness tests in the corresponding environment to obtain the specific fracture energy.

[0019] Step 6: Establish a fatigue life prediction model based on physical failure mechanism. Based on the established model and the data from Step 4 and Step 5, predict the fatigue life of the metal material in air and low-oxygen liquid lead-bismuth environments.

[0020] Step 7: Conduct symmetrical cyclic low-cycle fatigue tests on the metallic material in a high-oxygen liquid lead-bismuth environment at the predicted temperature to determine the oxide film thickness;

[0021] Step 8: Establish a fatigue life prediction model for liquid lead-bismuth in a high oxygen concentration environment. Based on the established model and the data from steps 4 to 7, predict the fatigue life of metallic materials in a high oxygen concentration liquid lead-bismuth environment.

[0022] The fatigue life prediction model based on the physical failure mechanism is used to predict the fatigue life of metallic materials in a liquid lead-bismuth environment with different temperatures and oxygen concentrations.

[0023] Further, in step 1, a two-dimensional representative volume element model containing multiple grains is established using ABAQUS finite element software to describe the microstructure information of the metallic material. Each grain is assigned a random crystal orientation. The grains are rotated using a rotation matrix, and the intersection of the rotated slip surface and the plane of the finite element model is defined as a slip zone. Only the slip zone passing through the grain centroid is considered. The distance from the center of each element within the grain to the intersection line is calculated. If the distance is less than or equal to the size of an element, the element is determined to belong to the slip zone.

[0024] Furthermore, the crystal plastic constitutive equation used in step 2 is:

[0025] ,

[0026] ,

[0027] ,

[0028] ,

[0029] ,

[0030] ,

[0031] ,

[0032] ,

[0033] ,

[0034] in, For the first Plastic slip ratio of the slip system For reference strain rate, For the first Decomposed shear stress of slip system For the first Back stress of a slip system For the first Critical decomposed shear stress of a slip system It is a strain rate sensitive parameter. For stress tensor, and The first The slip direction vector and the normal vector of the slip surface of the slip system. For direct hardening parameters, The coefficient of recovery is the dynamic recovery factor. To control The monotonic terms that evolve under monotonic deformation For cyclical softening terms, For latent hardening modulus, For the first Plastic slip ratio of the slip system The latent hardening coefficient represents the latent hardening modulus. and self-hardening modulus The ratio, parameter , and These are the initial hardening modulus, the initial critical decomposed shear stress, and the saturation stress, respectively. The total cumulative shear strain across all slip systems. This refers to saturated softening, specifically the maximum reduction in the critical decomposition shear stress caused by the cyclic softening effect. and For the cyclic softening parameters, For cyclically accumulated plastic strain.

[0035] Furthermore, in step 5, fracture toughness tests are conducted on the metallic material in air and low-oxygen-concentration liquid lead-bismuth environments at the predicted temperature to obtain the fracture toughness of the metallic material in the corresponding environment. Then, the specific fracture energy is obtained according to the relationship that the specific fracture energy is half of the fracture toughness. The specific fracture energy is obtained from the fracture toughness test, and the specific fracture energy value is half of the fracture toughness value.

[0036] Furthermore, in step 6, a fatigue life prediction model is established based on the Tanaka-Mura model for air and low-oxygen-concentration liquid lead-bismuth environments:

[0037] ,

[0038] In the formula, Fatigue life in air or low-oxygen-concentration liquid lead-bismuth environments. Poisson's ratio, For the specific fracture energy, Shear modulus It is half the grain size. This represents the shear strain range of the slip system. Wherein, Poisson's ratio... shear modulus Half the grain size The shear strain range of the slip system is determined based on the inherent properties of the metallic material itself. Based on step 4, the specific fracture energy As determined in step 5;

[0039] The fatigue life of metals in low-oxygen-concentration liquid lead-bismuth and air environments follows the same pattern, and the fatigue life of metals in both environments can be predicted using the aforementioned fatigue life prediction model. Perform fatigue life prediction;

[0040] The parameters of the crystal plastic constitutive equation are calibrated through a symmetrical low-cycle fatigue test in an air environment in step 3. The shear strain range of the slip system in the slip band is determined in step 4. The specific fracture energy in the corresponding environment was determined by the fracture toughness tests in air and low-oxygen liquid lead-bismuth in step 5. Then, Poisson's ratio is determined by combining the inherent properties of the metallic material itself. shear modulus and half the grain size Substitute into the fatigue life prediction model The low-cycle fatigue life of metallic materials in air and low-oxygen-concentration liquid lead-bismuth environments is predicted.

[0041] Furthermore, in step 8, the extrusion height of the metal material on the surface under cyclic loading is:

[0042] ,

[0043] In the formula, This refers to the extrusion height of the metal material surface during cyclic loading. This refers to the shear strain range of the slip system. For the number of times the loop loads, The composite index, representing the degree of randomness in the slip process within the slip zone, ranges from 0.5 to 1. It is half the grain size. It is the slip irreversible factor. The universal constant is 2.78;

[0044] When the extrusion height of the metal material surface When the oxide film thickness equals that in step 7, the oxide film of the metal material is considered to be destroyed. The number of cycles required to destroy the oxide film is then determined. for:

[0045] ,

[0046] In the formula, The number of cycles required to break down the oxide film, For oxide film thickness, This refers to the shear strain range of the slip system. It is the slip irreversible factor. The universal constant is 2.78.

[0047] The relationship between the extrusion height during cyclic loading and the oxide film thickness in step 7 is used to determine whether the oxide film on the surface of the metal material is damaged in a high oxygen concentration liquid lead-bismuth environment. If the extrusion height on the surface of the metal material is equal to the oxide film thickness, then the oxide film on the surface of the metal material is considered to be damaged.

[0048] The fatigue life in a high-oxygen-concentration liquid lead-bismuth environment is the sum of the oxide film lifetime and the fatigue life in a low-oxygen-concentration liquid lead-bismuth environment under the same temperature and loading conditions.

[0049] ,

[0050] in, Fatigue life in a high-oxygen-concentration liquid lead-bismuth environment. Poisson's ratio, For the specific fracture energy, Shear modulus It is half the grain size. This refers to the shear strain range of the slip system. For oxide film thickness, The irreversible slip coefficient, The universal constant is 2.78. The composite index, which is based on the degree of randomness of the slip process in the slip zone, is between 0.5 and 1. By substituting the determined parameters into the above formula, the fatigue life of metallic materials in a high-oxygen-concentration liquid lead-bismuth environment can be predicted.

[0051] The fatigue life in a high-oxygen-concentration liquid lead-bismuth environment is the sum of the oxide film lifetime and the fatigue life in a low-oxygen-concentration liquid lead-bismuth environment under the same temperature and loading conditions.

[0052] The oxide film thickness was determined by symmetrical cycling low-cycle fatigue tests in a liquid lead-bismuth environment with a small amount of high oxygen concentration, using the formula... The oxide film lifetime was calculated and then added to the fatigue lifetime of the metal material in a low-oxygen-concentration liquid lead-bismuth environment under the same temperature and loading conditions to predict the low-cycle fatigue lifetime of the metal material in a high-oxygen-concentration liquid lead-bismuth environment.

[0053] The advantages and positive effects of this invention are as follows: This invention only requires conducting low-cycle fatigue tests to calibrate the parameters of the crystal plastic constitutive equation in air at the predicted temperature, as well as fracture toughness tests in air and liquid lead-bismuth environments, to predict the fatigue life in air and low-oxygen-concentration liquid lead-bismuth environments. Furthermore, by determining the thickness of the oxide film through a small number of low-cycle fatigue tests in high-oxygen-concentration liquid lead-bismuth environments, the fatigue life in high-oxygen-concentration liquid lead-bismuth environments can be predicted. This fills the gap in current methods for predicting the fatigue life of metals in liquid lead-bismuth environments, which lack fatigue life prediction models based on physical failure mechanisms. Attached Figure Description

[0054] Figure 1 This is a flowchart of the fatigue life prediction method based on physical failure mechanism in a liquid lead-bismuth environment according to the present invention.

[0055] Figure 2 This invention includes a two-dimensional representative volume element model diagram of multiple grains, boundary conditions, and a slip band defined in one of the grains;

[0056] Figure 3 The figure shows the fitting results of the test data and simulation results of the cyclic stress amplitude of T91 steel with strain amplitudes of 0.43%, 0.76%, and 1.03% in an air environment at 350℃ according to the present invention.

[0057] Figure 4 This is a fatigue life prediction diagram for T91 steel under air conditions at 350℃, as presented in this invention.

[0058] Figure 5 The fatigue life prediction diagram for T91 steel in a low oxygen concentration liquid lead-bismuth environment at 350℃ and 200℃ is shown in the present invention.

[0059] Figure 6 This is a fatigue life prediction diagram for T91 steel in a high oxygen concentration liquid lead-bismuth environment at 350℃, according to the present invention. Detailed Implementation

[0060] The present invention will be further described in detail below through specific embodiments. The following embodiments are merely descriptive and not limiting, and should not be used to limit the scope of protection of the present invention.

[0061] like Figure 1 As shown, the fatigue life prediction method based on physical failure mechanism in liquid lead-bismuth environment includes the above steps:

[0062] Step 1: Establish a representative volume element model, assign random orientations, and define elements belonging to slip bands. Using ABAQUS finite element software, establish a two-dimensional representative volume element model containing multiple grains to describe the microstructure of T91 steel. Each grain is assigned a random crystal orientation. Rotate the grains using a rotation matrix. The intersection of the rotated slip surface and the plane of the finite element model is defined as a slip band. Only slip bands passing through the grain centroid are considered. The distance from the center of each element within the grain to this intersection line is calculated. If this distance is less than or equal to the size of one element, that element is considered to belong to a slip band. The established representative volume element model, boundary conditions, and the slip band of one grain are shown below. Figure 2 As shown.

[0063] Step 2: Define the constitutive equation for crystal plasticity:

[0064] The crystal plastic constitutive equation for the material in a uniaxially symmetric cyclic low-cycle fatigue test is defined using the user subroutine UMAT. This equation describes the stress-strain relationship of the representative volume element model (metallic material) in step 1 under uniaxially symmetric cyclic loading. The crystal plastic constitutive equation used is as follows:

[0065] ,

[0066] ,

[0067] ,

[0068] ,

[0069] ,

[0070] ,

[0071] ,

[0072] ,

[0073] ,

[0074] in, For the first Plastic slip ratio of the slip system For reference strain rate, For the first Decomposed shear stress of slip system For the first Back stress of a slip system For the first Critical decomposed shear stress of a slip system It is a strain rate sensitive parameter. For stress tensor, and The first The slip direction vector and the normal vector of the slip surface of the slip system. For direct hardening parameters, The coefficient of recovery is the dynamic recovery factor. To control The monotonic terms that evolve under monotonic deformation For cyclical softening terms, For latent hardening modulus, For the first Plastic slip ratio of the slip system The latent hardening coefficient represents the latent hardening modulus. and self-hardening modulus The ratio, parameter , and These are the initial hardening modulus, the initial critical decomposed shear stress, and the saturation stress, respectively. The total cumulative shear strain across all slip systems. This refers to saturated softening, specifically the maximum reduction in critical decomposition shear stress caused by the cyclic softening effect. and For the cyclic softening parameters, For cyclically accumulated plastic strain.

[0075] Step 3: Determine the parameters in the crystal plastic constitutive equation using the cyclic stress amplitude curve or fatigue hysteresis loop from the experiment.

[0076] A symmetrical cyclic low-cycle fatigue test was conducted on the metallic material in an air environment at a predicted temperature to obtain the cyclic stress amplitude curve or fatigue hysteresis loop of the test.

[0077] By calling the UMAT subroutine in ABAQUS software, the crystal plastic constitutive equation is used to perform finite element calculations on the above representative volume element model to obtain the cyclic stress amplitude curve or fatigue hysteresis loop after finite element calculation. The parameters in the above crystal plastic constitutive equation are determined by the trial-and-error method. The cyclic stress amplitude curve or fatigue hysteresis loop obtained by finite element calculation in air environment is compared with the curve obtained by experiment in air environment until the fitting degree of the cyclic stress amplitude curve or fatigue hysteresis loop obtained by finite element calculation converges with that of the cyclic stress amplitude curve or fatigue hysteresis loop obtained by experiment.

[0078] Symmetrical cyclic low-cycle fatigue tests were conducted on T91 steel in an air environment at 350℃ with strain amplitudes of 0.43%, 0.76%, and 1.04%, and the cyclic stress amplitude curves of the test were obtained.

[0079] By calling the UMAT subroutine in ABAQUS software, the crystal plastic constitutive equation is used to perform finite element calculations on the above representative volume element model to obtain the cyclic stress amplitude curve after finite element calculation. The parameters in the above crystal plastic constitutive equation are determined by the trial-and-error method. The cyclic stress amplitude curve obtained by finite element calculation is compared with the cyclic stress amplitude curve obtained by the symmetrical cyclic low-cycle fatigue test of T91 steel in an air environment at 350℃ until the cyclic stress amplitude curve or fatigue hysteresis loop obtained by finite element calculation has a good fit with the cyclic stress amplitude curve or fatigue hysteresis loop obtained by the test. By fitting the cyclic stress amplitude curves of symmetrical cyclic low-cycle fatigue tests conducted on T91 steel at 350℃ in air with strain amplitudes of 0.43%, 0.76%, and 1.04% as described in the literature "Low cycle fatigue behavior of a modified 9Cr–1Mo ferritic–martensitic steel in lead–bismuth eutectic at 350℃–Effects of oxygen concentration in the liquid metal and strain rate", the parameters of the crystal plastic constitutive equation were determined as follows: strain rate sensitive parameter =100, reference strain rate =0.001, initial hardening modulus =95MPa, saturation stress =190MPa, initial critical decomposed shear stress =138MPa, direct hardening parameter =10000MPa, dynamic recovery coefficient =400, saturated softening =60MPa, cyclic softening parameter =0.6MPa, cyclic softening parameter =90MPa. The fitting results of the simulated cyclic stress amplitude curve and the experimental cyclic stress amplitude curve are as follows: Figure 3 As shown, the experimental data and simulation results are in good agreement.

[0080] Step 4: Calculate the average shear strain range of the slip band based on the elements defined in Step 1: Based on the representative volume element model from Step 1 and the crystal plastic constitutive equation parameters determined in Step 3, perform finite element calculations under different strain amplitude conditions. Calculate the shear strain range of the slip band using Python code. Specifically, calculate the shear strain range of the elements contained in the slip band and calculate the average value to obtain the shear strain range of the slip band. Sort all the shear strain ranges of the slip bands and take the maximum value for subsequent fatigue life prediction. The average value of the shear strain range of the slip system in the slip band is calculated using crystal plastic finite element analysis and then applied to fatigue life prediction.

[0081] Based on the representative volume element model from step 1 and the crystal plastic constitutive equation parameters determined in step 3, the above finite element calculations are performed under the condition that the strain amplitude range is 0.2%-1.2%. The shear strain range of the slip band of T91 steel is calculated using Python code. Specifically, the shear strain range of the elements contained in the slip band is calculated and the average value is obtained to get the shear strain range of the slip band. The shear strain ranges of all slip bands are sorted, and the maximum value is taken for subsequent fatigue life prediction.

[0082] Step 5: Conduct fracture toughness tests in the corresponding environment to obtain specific fracture energy: Conduct fracture toughness tests on the metallic material in air and low oxygen concentration liquid lead-bismuth environments at the predicted temperature to obtain the fracture toughness of the metallic material in the corresponding environment, and then obtain the specific fracture energy based on the relationship that the specific fracture energy is half of the fracture toughness; the specific fracture energy is obtained from the fracture toughness test, and the specific fracture energy value is half of the fracture toughness value.

[0083] Fracture toughness tests were conducted on T91 steel in three environments: 350℃ air, 350℃ low-oxygen liquid lead-bismuth, and 200℃ low-oxygen liquid lead-bismuth. The fracture toughness of T91 steel in these environments was obtained. The specific fracture energy was then calculated based on the relationship that the specific fracture energy is half the fracture toughness. According to the literature "Investigating liquid-metal embrittlement of T91 steel by fracturetoughness tests," the fracture toughness of T91 steel in the 350℃ air and 350℃ low-oxygen liquid lead-bismuth environments was 417 kJ / m² and 51.5 kJ / m², respectively. Therefore, the specific fracture energy, being half the fracture toughness, was 208.5 kJ / m² and 25.75 kJ / m², respectively. According to the literature "Influence of displacement rate and temperature on the severity of liquid metal embrittlement of T91 steel,"... According to the data from "inLBE", the fracture toughness of T91 steel in a low oxygen concentration liquid lead-bismuth environment at 200℃ is 212.75 kJ / m2, and the specific fracture energy is 106.375 kJ / m2.

[0084] Step 6: Establish a fatigue life prediction model based on physical failure mechanisms. Based on the established model and the data from Steps 4 and 5, predict the fatigue life of T91 steel in three environments: 350℃ air, 350℃ low-oxygen-concentration liquid lead-bismuth, and 200℃ low-oxygen-concentration liquid lead-bismuth.

[0085] Based on the Tanaka-Mura model, fatigue life prediction models were established for air and low-oxygen-concentration liquid lead-bismuth environments:

[0086] ,

[0087] In the formula, Fatigue life in air or low-oxygen-concentration liquid lead-bismuth environments. Poisson's ratio, For the specific fracture energy, Shear modulus It is half the grain size. This represents the shear strain range of the slip system. Among them, the Poisson's ratio of T91 steel... shear modulus Half the grain size The shear strain range of the slip system is determined based on the inherent properties of the metallic material itself. Based on the calculations in step 4, the specific fracture energy of T91 steel in air at 350℃, liquid lead-bismuth at 350℃ with low oxygen concentration, and liquid lead-bismuth at 200℃ with low oxygen concentration is calculated. From step 5, the values ​​are 208.5 kJ / m², 25.75 kJ / m², and 106.375 kJ / m², respectively. Substituting the known parameters into the above formula, the predicted lifetimes can be obtained under the following environments: 350℃ air, 350℃ low-oxygen liquid lead-bismuth, and 200℃ low-oxygen liquid lead-bismuth. To verify the proposed method, the predicted lifetimes under the following environments were tested: 350℃ air and low-oxygen liquid lead-bismuth environments in the literature "Low cycle fatigue behavior of a modified 9Cr–1Mo ferritic–martensitic steel in lead–bismuth eutectic at 350℃ – Effects of oxygen concentration in the liquid metal and strain rate" and the literature "Temperature dependence of liquid metal embrittlement susceptibility of a modified 9Cr–1Mo steel under low cycle fatigue in lead–bismuth eutectic at 350℃". The fatigue life of T91 steel in a low-oxygen liquid lead-bismuth environment at 200℃ was predicted according to the standard "160–450℃". The fatigue life prediction results in an air environment at 350℃ are as follows: Figure 4 As shown, the predicted results are almost all within the 2x dispersion band, and the predicted results are quite close to the experimental data. The fatigue life results for liquid lead-bismuth environments with low oxygen concentration at 350℃ and 200℃ are as follows: Figure 5 As shown, the prediction results are all within the 2x dispersion band, indicating good prediction performance.

[0088] The fatigue life of metals in low-oxygen-concentration liquid lead-bismuth and air environments follows the same pattern, and the fatigue life of metals in both environments can be predicted using the aforementioned fatigue life prediction model. Fatigue life prediction is performed. Due to the difference in specific fracture energy between air environment and low oxygen concentration liquid lead-bismuth environment, the fatigue life of metallic materials differs between air environment and low oxygen concentration liquid lead-bismuth environment.

[0089] The parameters of the crystal plastic constitutive equation are calibrated through a symmetrical low-cycle fatigue test in an air environment in step 3. The shear strain range of the slip system in the slip band is determined in step 4. The specific fracture energy in the corresponding environment was determined by the fracture toughness test in air and low-oxygen liquid lead-bismuth in step 5. Then, Poisson's ratio is determined by combining the inherent properties of the metallic material itself. shear modulus and half the grain size Substitute into the fatigue life prediction model The low-cycle fatigue life of metallic materials in air and low-oxygen-concentration liquid lead-bismuth environments is predicted.

[0090] Step 7: Conduct symmetrical cyclic low-cycle fatigue tests on the metallic material in a high-oxygen liquid lead-bismuth environment at the predicted temperature to determine the oxide film thickness;

[0091] Symmetrical cyclic low-cycle fatigue tests were conducted on T91 steel in a high-oxygen liquid lead-bismuth environment at 350℃ to determine the thickness of the oxide film. The oxide film thickness of T91 steel in the high-oxygen liquid lead-bismuth environment at 350℃ was approximately 3μm, according to the literature "The role of oxide films in preventing liquid metalembrittlement of T91 steel exposed to liquid lead-bismuth eutectic".

[0092] Step 8: Establish a fatigue life prediction model for liquid lead-bismuth in a high-oxygen-concentration environment. Based on the established model and the data from steps 4 to 7, predict the fatigue life of T91 steel in this environment. In a high-oxygen-concentration liquid lead-bismuth environment, the influence of the oxide film on fatigue life needs to be considered. The relationship between the extrusion height and oxide film thickness on the surface of T91 steel during cyclic loading is used to determine whether the oxide film is damaged. The extrusion height of T91 steel under cyclic loading is:

[0093] ,

[0094] In the formula, This refers to the extrusion height of the metal material surface during cyclic loading. The shear strain range of the slip system (determined according to step 4). For the number of times the loop loads, The composite index, representing the degree of randomness in the slip process within the slip zone, ranges from 0.5 to 1. It is half the grain size. It is the slip irreversible factor. The universal constant is 2.78;

[0095] When the extrusion height of the T91 steel surface When the oxide film thickness equals that in step 7, the oxide film of the T91 steel is considered to be destroyed. The number of cycles required to destroy the oxide film (oxide film lifetime) is then determined. for:

[0096] ,

[0097] In the formula, The number of cycles required to destroy the oxide film (oxide film lifetime). The thickness of the oxide film (determined according to step 7). The shear strain range of the slip system (determined according to step 4). It is the slip irreversible factor. The universal constant is 2.78.

[0098] The relationship between the extrusion height during cyclic loading and the oxide film thickness in step 7 is used to determine whether the oxide film on the surface of the metal material is damaged in a high oxygen concentration liquid lead-bismuth environment. If the extrusion height on the surface of the metal material is equal to the oxide film thickness, then the oxide film on the surface of the metal material is considered to be damaged.

[0099] The fatigue life in a high-oxygen-concentration liquid lead-bismuth environment is the sum of the oxide film lifetime and the fatigue life in a low-oxygen-concentration liquid lead-bismuth environment under the same temperature and loading conditions.

[0100] ,

[0101] in, Fatigue life in a high-oxygen-concentration liquid lead-bismuth environment. Poisson's ratio, The specific fracture energy (the specific fracture energy in a high-oxygen-concentration liquid lead-bismuth environment is the same as that in a low-oxygen-concentration liquid lead-bismuth environment). Shear modulus It is half the grain size. The shear strain range of the slip system (determined according to step 4). The thickness of the oxide film (determined according to step 7). The irreversible slip coefficient, The universal constant is 2.78. The composite index, representing the degree of randomness in the slip process within the slip zone, is taken to range from 0.5 to 1. Substituting the determined parameters into the above formula allows for the prediction of the fatigue life of metallic materials in a high-oxygen-concentration liquid lead-bismuth environment. The Poisson's ratio of T91 steel... =0.3, shear modulus =74231MPa, half the grain size =10μm, shear strain range of slip system Based on finite element calculations under the corresponding strain amplitude conditions in 4 conditions, the specific fracture energy in a 350℃ high-oxygen liquid lead-bismuth environment is obtained. Specific fracture energy compared to a 350°C low-oxygen liquid lead-bismuth environment Similarly, as can be seen from step 6, it is 25.75 kJ / m 2 Oxide film thickness As shown in step 7, the irreversible slip coefficient is 3 μm. =0.5, =2.78, composite index =0.5. Substituting the determined parameters into the above formula, the predicted life of T91 steel in a high-oxygen liquid lead-bismuth environment at 350℃ can be obtained. To verify the proposed method, the fatigue life of T91 steel in a high-oxygen liquid lead-bismuth environment at 350℃, as described in the literature "Low cycle fatigue behavior of a modified 9Cr–1Mo ferritic–martensitic steel in lead–bismuthutectic at 350℃–Effects of oxygen concentration in the liquid metal and strain rate", was predicted. The predicted fatigue life of T91 steel in a high-oxygen liquid lead-bismuth environment at 350℃ is as follows: Figure 6 As shown, the prediction results are almost all within the 2x dispersion band, indicating good prediction performance.

[0102] The fatigue life in a high-oxygen-concentration liquid lead-bismuth environment is the sum of the oxide film life and the fatigue life in a low-oxygen-concentration liquid lead-bismuth environment under the same temperature and loading conditions.

[0103] The oxide film thickness was determined by symmetrical cycling low-cycle fatigue tests in a liquid lead-bismuth environment with a small amount of high oxygen concentration, using the formula... The oxide film lifetime was calculated and then added to the fatigue lifetime of the metal material in a low-oxygen-concentration liquid lead-bismuth environment under the same temperature and loading conditions to predict the low-cycle fatigue lifetime of the metal material in a high-oxygen-concentration liquid lead-bismuth environment.

[0104] In a high-oxygen-concentration liquid lead-bismuth environment, the impact of the oxide film on fatigue life needs to be considered. The relationship between the extrusion height of the metal material surface and the oxide film thickness during cyclic loading is used to determine whether the oxide film is damaged. After the oxide film is damaged, the fatigue life in the high-oxygen-concentration liquid lead-bismuth environment is the same as that in the low-oxygen-concentration liquid lead-bismuth environment. Therefore, the fatigue life in the high-oxygen-concentration liquid lead-bismuth environment is the sum of the number of cycles required to damage the oxide film and the fatigue life in the low-oxygen-concentration liquid lead-bismuth environment under the same temperature and loading conditions.

[0105] The fatigue life prediction model based on the physical failure mechanism is used to predict the fatigue life of metallic materials in a liquid lead-bismuth environment with different temperatures and oxygen concentrations.

[0106] This invention only requires conducting low-cycle fatigue tests in air at the predicted temperature to calibrate the parameters of the crystal plastic constitutive equation, as well as fracture toughness tests in air and liquid lead-bismuth environments. This allows for the prediction of fatigue life in air and low-oxygen-concentration liquid lead-bismuth environments. Furthermore, by determining the oxide film thickness through a small number of low-cycle fatigue tests in high-oxygen-concentration liquid lead-bismuth environments, the fatigue life in high-oxygen-concentration liquid lead-bismuth environments can be predicted. This fills the gap in current methods for predicting the fatigue life of metals in liquid lead-bismuth environments, which lack fatigue life prediction models based on physical failure mechanisms.

[0107] Although embodiments and drawings of the present invention have been disclosed for illustrative purposes, those skilled in the art will understand that various substitutions, variations and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the scope of the present invention is not limited to the contents disclosed in the embodiments and drawings.

Claims

1. A fatigue life prediction method based on physical failure mechanism in a liquid lead-bismuth environment, characterized in that: Includes the following steps: Step 1: Establish a representative volume element model, assign random orientation, and define elements belonging to the slip zone; Step 2: Define the constitutive equation for crystal plasticity: The crystal plastic constitutive equation of the material in the uniaxial symmetric cyclic low-cycle fatigue test is defined by the user subroutine UMAT, thereby describing the stress-strain relationship of the representative volume element model in step 1 under uniaxial symmetric cyclic loading. Step 3: Determine the parameters in the crystal plastic constitutive equation using the cyclic stress amplitude curve or fatigue hysteresis loop from the experiment. A symmetrical cyclic low-cycle fatigue test was conducted on the metallic material in an air environment at a predicted temperature to obtain the cyclic stress amplitude curve or fatigue hysteresis loop of the test. By calling the UMAT subroutine in ABAQUS software, the crystal plastic constitutive equation is used to perform finite element calculations on the representative volume element model in step 1 above, obtaining the cyclic stress amplitude curve or fatigue hysteresis loop after finite element calculation; the parameters in the crystal plastic constitutive equation above are determined by the trial-and-error method, and the cyclic stress amplitude curve or fatigue hysteresis loop obtained by finite element calculation in air environment is compared with the curve obtained by experiment in air environment until the fitting degree of the cyclic stress amplitude curve or fatigue hysteresis loop obtained by finite element calculation converges with that of the cyclic stress amplitude curve or fatigue hysteresis loop obtained by experiment. Step 4: Calculate the average shear strain range of the slip band based on the elements defined in Step 1. Based on the representative volume element model in step 1 and the crystal plastic constitutive equation parameters determined in step 3, the shear strain range of the elements contained in the slip band is calculated and the average value is obtained to get the shear strain range of the slip band. The shear strain ranges of all slip bands are sorted and the maximum value is used for subsequent fatigue life prediction. Step 5: Conduct fracture toughness tests in the corresponding environment to obtain the specific fracture energy; Step 6: Establish a fatigue life prediction model based on physical failure mechanism. Based on the established model and the data from Step 4 and Step 5, predict the fatigue life of the metal material in air and low-oxygen liquid lead-bismuth environments. Step 7: Conduct symmetrical cyclic low-cycle fatigue tests on the metallic material in a high-oxygen liquid lead-bismuth environment at the predicted temperature to determine the oxide film thickness; Step 8: Establish a fatigue life prediction model for liquid lead-bismuth in a high oxygen concentration environment. Based on the established model and the data from steps 4 to 7, predict the fatigue life of metallic materials in a high oxygen concentration liquid lead-bismuth environment. , When the extrusion height of the metal material surface When the oxide film thickness equals that in step 7, the oxide film of the metal material is considered to be destroyed; the extrusion height of the metal material surface under cyclic loading is: ， in, Fatigue life in a high-oxygen-concentration liquid lead-bismuth environment. Poisson's ratio, For the specific fracture energy, Shear modulus It is half the grain size. This refers to the shear strain range of the slip system. For oxide film thickness, The irreversible slip coefficient, The universal constant is 2.

78. The composite index is based on the degree of randomness of the slip process in the slip zone, and its value ranges from 0.5 to 1. This refers to the extrusion height of the metal material surface during cyclic loading. This represents the number of times the loop will load.

2. The fatigue life prediction method based on physical failure mechanism in a liquid lead-bismuth environment according to claim 1, characterized in that: Step 1 involves establishing a two-dimensional representative volume element model containing multiple grains using ABAQUS finite element software to describe the microstructure information of the metallic material. Each grain is assigned a random crystal orientation. The grains are rotated using a rotation matrix, and the intersection of the rotated slip surface with the plane of the finite element model is defined as a slip zone. Only slip zones passing through the grain centroid are considered. The distance from the center of each element within the grain to this intersection line is then calculated. If this distance is less than or equal to the size of an element, then that element is identified as belonging to the slip zone.

3. The fatigue life prediction method based on physical failure mechanism in a liquid lead-bismuth environment according to claim 1, characterized in that: The crystal plastic constitutive equation used in step 2 is: ， ， ， ， ， ， ， ， ， in, For the first Plastic slip ratio of the slip system For reference strain rate, For the first Decomposed shear stress of slip system For the first Back stress of a slip system For the first Critical decomposed shear stress of a slip system It is a strain rate sensitive parameter. For stress tensor, and The first The slip direction vector and the normal vector of the slip surface of the slip system. For direct hardening parameters, The coefficient of recovery is the dynamic recovery factor. To control The monotonic terms that evolve under monotonic deformation For cyclical softening terms, For latent hardening modulus, For the first Plastic slip ratio of the slip system The latent hardening coefficient represents the latent hardening modulus. and self-hardening modulus The ratio, parameter , and These are the initial hardening modulus, the initial critical decomposed shear stress, and the saturation stress, respectively. The total cumulative shear strain across all slip systems. This refers to saturated softening, specifically the maximum reduction in critical decomposition shear stress caused by the cyclic softening effect. and For the cyclic softening parameters, For cyclically accumulated plastic strain.

4. The fatigue life prediction method based on physical failure mechanism in a liquid lead-bismuth environment according to claim 1, characterized in that: In step 5, fracture toughness tests are conducted on the metallic material in air and low oxygen concentration liquid lead-bismuth environments at the predicted temperature to obtain the fracture toughness of the metallic material in the corresponding environment. Then, the specific fracture energy is obtained according to the relationship that the specific fracture energy is half of the fracture toughness. The specific fracture energy is obtained from the fracture toughness test, and its value is half of the fracture toughness value.

5. The fatigue life prediction method based on physical failure mechanism in a liquid lead-bismuth environment according to claim 1, characterized in that: In step 6, a fatigue life prediction model is established based on the Tanaka-Mura model under air and low-oxygen-concentration liquid lead-bismuth environments: ， In the formula, Fatigue life in air or low-oxygen-concentration liquid lead-bismuth environments. Poisson's ratio, For the specific fracture energy, Shear modulus It is half the grain size. The range of shear strain in the slip system is given by where Poisson's ratio is given by . shear modulus Half the grain size The shear strain range of the slip system is determined based on the inherent properties of the metallic material itself. Based on step 4, the specific fracture energy As determined in step 5, the fatigue life of metals in low-oxygen-concentration liquid lead-bismuth and air environments follows the same pattern. The fatigue life of metals in both low-oxygen-concentration liquid lead-bismuth and air environments can be predicted using the aforementioned fatigue life prediction model. Perform fatigue life prediction; The parameters of the crystal plastic constitutive equation are calibrated through a symmetrical low-cycle fatigue test in an air environment in step 3. The shear strain range of the slip system in the slip band is determined in step 4. The specific fracture energy in the corresponding environment was determined by the fracture toughness tests in air and low-oxygen liquid lead-bismuth in step 5. Then, Poisson's ratio is determined by combining the inherent properties of the metallic material itself. shear modulus and half the grain size Substitute into the fatigue life prediction model The low-cycle fatigue life of metallic materials in air and low-oxygen-concentration liquid lead-bismuth environments is predicted.

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