A method and system for evaluating the hydrogen-induced fatigue life of bolts based on the Bayesian method

Abstract

The present application discloses a method and system for evaluating the hydrogen-induced fatigue life of bolts based on the Bayesian method, which relates to the field of fatigue life evaluation. The method includes obtaining a fatigue constitutive model of the bolt at the material level; determining a basic fatigue characteristic curve according to the fatigue constitutive model of the bolt at the material level and material experimental data, and using the finite element analysis method to perform stress analysis on the actual structure of the bolt to determine the stress concentration coefficient; correcting the fatigue constitutive model at the material level according to the stress concentration coefficient and the hydrogen embrittlement correction function to obtain a corrected fatigue constitutive model; determining a non-linear cumulative damage model according to the corrected fatigue constitutive model by using the non-linear cumulative damage theory; optimizing the non-linear cumulative damage model by using the Bayesian statistical method according to the material experimental data. The present application can improve the accuracy and reliability of bolt fatigue life prediction.

Description

Technical Field

[0001] This application relates to the field of fatigue life assessment, and particularly to a method and system for evaluating the hydrogen-induced fatigue life of bolts based on the Bayesian method. Background Art

[0002] High-strength bolts used in ocean engineering and other extreme environments are often subjected to the combined action of corrosion, mechanical loads, and environmental hydrogen. These factors can easily cause hydrogen embrittlement, which significantly reduces the fatigue life of the bolts. Hydrogen embrittlement (HE) refers to the phenomenon that hydrogen atoms penetrate into the interior of metal materials, causing a sharp reduction in the plasticity and toughness of the materials, especially having a profound impact on the fatigue behavior of high-strength bolts. Hydrogen embrittlement has a significant impact on the fatigue performance of materials, mainly manifested as follows: 1. Reducing fatigue strength and fatigue life: The presence of hydrogen reduces the fatigue limit and fatigue strength coefficient of materials; 2. Accelerating the initiation and propagation of fatigue cracks: Hydrogen atoms accumulate in stress concentration regions (such as crack tips), promoting the formation and propagation of cracks. The mechanism of hydrogen embrittlement mainly includes the following aspects: The aggregation of hydrogen atoms inside the material weakens the atomic bonding force, reduces the bonding strength of the fracture surface, and leads to cleavage-type fracture. This mechanism is particularly significant in high-strength steels. The presence of hydrogen reduces the resistance to dislocation movement, promotes dislocation slip, leads to the concentration of local plastic deformation, and accelerates the accumulation of fatigue damage. Under the combined action of tensile stress and corrosive environment, hydrogen penetrates into the material, triggering stress corrosion cracking and accelerating the propagation of fatigue cracks.

[0003] Currently, the methods for evaluating the fatigue life of bolts in the marine environment mainly include experimental methods and numerical simulation methods based on traditional S-N curves. However, traditional fatigue life prediction methods often ignore the complex action mechanism of hydrogen embrittlement effects. Especially in the case of the coupling of stress concentration effects and hydrogen content, there is a large deviation between the evaluation results and the actual service conditions; in the case of limited experimental data or high test costs, traditional methods cannot make full use of limited information to statistically correct model parameters. This makes the model respond poorly to complex coupling effects, and the prediction results lack sufficient robustness and credibility; moreover, traditional fatigue life prediction methods often default that material parameters, environmental factors, and load characteristics are determined values, lacking an effective description of parameter uncertainty and randomness. When there is insufficient data or large fluctuations in engineering practice, existing methods are difficult to make reasonable statistical inferences about model parameters, thus affecting the reliability of fatigue life prediction.

[0004] In the prior art, fatigue damage models usually adopt the linear cumulative damage theory, such as the Miner linear cumulative damage rule. Although this method is easy to apply in practical engineering, it is difficult to effectively reflect the non-linear fatigue damage accumulation process of materials under complex stress levels. Under the service conditions of high-strength bolts, the interaction between the stress concentration effect and the hydrogen embrittlement effect has an important impact on the fatigue life. The stress concentration area is the potential starting point of fatigue failure, and the penetration of hydrogen atoms further exacerbates the crack initiation and propagation in these areas.

[0005] The prior art often relies on existing experimental data or empirical formulas, but has limited ability to dynamically incorporate new experimental data and on-site measurement results. It is difficult to achieve effective integration between existing experience (prior knowledge) and new observed data, resulting in poor adaptability of the model under complex working conditions and difficulty in updating prediction results in a timely manner.

[0006] Therefore, there is an urgent need for an advanced evaluation method that can simultaneously consider the stress concentration effect, the influence of hydrogen content, and the non-linear fatigue damage accumulation characteristics. Summary of the Invention

[0007] The purpose of this application is to provide a bolt hydrogen-induced fatigue life evaluation method and system based on the Bayesian method, which can improve the accuracy and reliability of bolt fatigue life prediction.

[0008] To achieve the above purpose, this application provides the following solutions:

[0009] This application provides a bolt hydrogen-induced fatigue life evaluation method based on the Bayesian method. The bolt hydrogen-induced fatigue life evaluation method based on the Bayesian method includes:

[0010] Obtain the fatigue constitutive model based on the material level of the bolt; the fatigue constitutive model based on the material level is used to characterize the relationship between stress, strain, and fatigue life of the bolt under cyclic loading;

[0011] According to the fatigue constitutive model based on the material level of the bolt and the material experimental data, determine the basic fatigue characteristic curve, and use the finite element analysis method to perform stress analysis on the actual structure of the bolt to determine the stress concentration coefficient; the basic fatigue characteristic curve includes: stress-life curve and strain-life curve;

[0012] Modify the fatigue constitutive model based on the material level according to the stress concentration coefficient and the hydrogen embrittlement correction function to obtain the modified fatigue constitutive model;

[0013] According to the modified fatigue constitutive model, use the non-linear cumulative damage theory to determine the non-linear cumulative damage model;

[0014] Optimize the non-linear cumulative damage model using the Bayesian statistical method according to the material experimental data.

[0015] Optionally, obtaining the fatigue constitutive model of the bolt at the material level specifically includes:

[0016] Using the formula to determine the fatigue constitutive model of the bolt at the material level;

[0017] Wherein, is the fatigue strength coefficient, used to reflect the fatigue resistance strength of the bolt; is the fatigue life; is the fatigue strength index; is the fatigue ductility coefficient, used to reflect the anti-plastic fatigue performance; is the fatigue ductility index; is the total strain amplitude, including the elastic strain amplitude and the plastic strain amplitude; is the elastic modulus; is the local maximum stress.

[0018] Optionally, according to the fatigue constitutive model of the bolt at the material level and the material experimental data, determining the basic fatigue characteristic curve, and using the finite element analysis method to perform stress analysis on the actual structure of the bolt to determine the stress concentration coefficient, specifically including:

[0019] Using the formula to determine the stress concentration coefficient ;

[0020] Wherein, is the theoretical stress concentration coefficient, is the plastic influence coefficient.

[0021] Optionally, using the formula to determine the local maximum stress ;

[0022] Wherein, is the nominal stress, , is the external load, is the stress-bearing cross-sectional area of the bolt.

[0023] Optionally, modifying the fatigue constitutive model at the material level according to the stress concentration coefficient and the hydrogen embrittlement correction function to obtain the modified fatigue constitutive model, specifically including:

[0024] Using the formula to determine the modified fatigue constitutive model;

[0025] Wherein, is the hydrogen embrittlement correction function of the fatigue strength coefficient, is the hydrogen content in the bolt, is the hydrogen embrittlement correction function of the fatigue ductility coefficient, is the hydrogen embrittlement correction function of the fatigue strength exponent, is the hydrogen embrittlement correction function of the fatigue ductility exponent, is the hydrogen embrittlement correction function of the reduction of area, is the hydrogen embrittlement correction function of the elongation after fracture.

[0026] Optionally, the hydrogen embrittlement correction function specifically includes:

[0027] Using the formula to determine the hydrogen embrittlement correction function of the fatigue strength coefficient;

[0028] Using the formula to determine the hydrogen embrittlement correction function of the fatigue ductility coefficient;

[0029] Using the formula and the formula to determine the hydrogen embrittlement correction function of the fatigue strength exponent and the hydrogen embrittlement correction function of the fatigue ductility exponent;

[0030] Using the formula to determine the hydrogen embrittlement correction function of the reduction of area;

[0031] Using the formula to determine the hydrogen embrittlement correction function of the elongation after fracture;

[0032] where, is the fatigue strength coefficient under the condition of no hydrogen charging, 、 are the correction parameters of the fatigue strength coefficient, is the fatigue ductility coefficient under the condition of no hydrogen charging, 、 are the correction parameters of the fatigue ductility coefficient, is the fatigue strength exponent under the condition of no hydrogen charging, is the fatigue ductility exponent under the condition of no hydrogen charging, 、 are the correction parameters of the fatigue strength exponent, 、 are the correction parameters of the fatigue ductility exponent, is the reduction of area under the condition of no hydrogen charging, is the elongation after fracture under the condition of no hydrogen charging, 、 are the correction parameters of the reduction of area, 、 are the correction parameters of the elongation after fracture.

[0033] Optionally, according to the corrected fatigue constitutive model, the nonlinear cumulative damage theory is adopted to determine the nonlinear cumulative damage model, specifically including:

[0034] According to the corrected fatigue constitutive model, the Newton-Raphson numerical iteration method is used to determine the fatigue life;

[0035] According to the fatigue life, a nonlinear cumulative damage model is constructed by using the nonlinear cumulative damage theory; the nonlinear cumulative damage model is used to characterize the cumulative damage value of the bolt;

[0036] The fatigue life of the bolt is evaluated according to the cumulative damage value of the bolt.

[0037] Optionally, according to the fatigue life, a nonlinear cumulative damage model is constructed by using the nonlinear cumulative damage theory, specifically including:

[0038] Using the formula To determine the nonlinear cumulative damage model;

[0039] Among them, Is the cumulative damage value, Is the total number of different stress levels, Is the The number of cycles at the Is the The fatigue life at the Is the hydrogen embrittlement correction function of the reduction of area, Is the hydrogen embrittlement correction function of the elongation after fracture, Is the reduction of area under the condition of no hydrogen charging, Is the elongation after fracture under the condition of no hydrogen charging, 、 、 Are correction parameters.

[0040] Optionally, the fatigue life of the bolt is evaluated according to the cumulative damage value of the bolt, specifically including:

[0041] When the cumulative damage value The bolt has not reached the fatigue failure condition and continues to serve;

[0042] When the cumulative damage value The bolt reaches the fatigue failure condition and the life is exhausted;

[0043] When the cumulative damage value The bolt exceeds the fatigue failure condition and measures are taken.

[0044] In a second aspect, the present application provides a bolt hydrogen-induced fatigue life evaluation system based on the Bayesian method. The bolt hydrogen-induced fatigue life evaluation system based on the Bayesian method includes:

[0045] A fatigue constitutive model acquisition module for obtaining a fatigue constitutive model of a bolt at the material level; the fatigue constitutive model at the material level is used to characterize the relationship between stress, strain and fatigue life of the bolt under cyclic loading;

[0046] A stress concentration factor determination module for determining a basic fatigue characteristic curve according to the fatigue constitutive model of the bolt at the material level and material experimental data, and performing stress analysis on the actual structure of the bolt by using the finite element analysis method to determine the stress concentration factor; the basic fatigue characteristic curve includes: a stress-life curve and a strain-life curve;

[0047] A fatigue constitutive model correction module for correcting the fatigue constitutive model at the material level according to the stress concentration factor and the hydrogen embrittlement correction function to obtain a corrected fatigue constitutive model;

[0048] A non-linear cumulative damage model determination module for determining a non-linear cumulative damage model according to the corrected fatigue constitutive model by using the non-linear cumulative damage theory;

[0049] A non-linear cumulative damage model optimization module for optimizing the non-linear cumulative damage model by using the Bayesian statistical method according to the material experimental data.

[0050] According to the specific embodiments provided in the present application, the present application has the following technical effects:

[0051] The present application provides a bolt hydrogen-induced fatigue life assessment method and system based on the Bayesian method. Based on the fatigue constitutive model of the bolt at the material level and the geometric characteristics of the bolt, the stress concentration factor is determined; the fatigue constitutive model at the material level is corrected according to the stress concentration factor and the hydrogen embrittlement correction function to correct the stress state of the bolt under different service conditions. The non-linear cumulative damage theory is used to systematically describe the cumulative process of fatigue damage, especially the influence on the fatigue life of the bolt when the hydrogen content gradually increases, and a non-linear cumulative damage model is determined. In combination with the stress concentration effect and the non-linear cumulative damage theory, the fatigue life of the bolt in a complex service environment can be predicted more accurately; through the Bayesian statistical method, the experimental data is combined with the non-linear cumulative damage model, and the randomness and uncertainty of the material parameters are quantified, so as to realize more accurate fatigue life prediction. The present application effectively combines the hydrogen embrittlement effect, the stress concentration effect and the non-linear cumulative damage theory, and can more accurately predict the fatigue life of the bolt in a complex environment. Description of the Drawings

[0052] To more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0053] Figure 1 Schematic flow chart of a bolt hydrogen-induced fatigue life assessment method based on the Bayesian method in an embodiment of the present application;

[0054] Figure 2 Schematic diagram of the relationship between the fatigue life and the local maximum stress of high-strength bolts under different hydrogen content conditions;

[0055] Figure 3 Graph of the relationship between the correction parameter and the hydrogen content;

[0056] Figure 4 Graph of the relationship between the reduction of area and the elongation after fracture with the hydrogen content;

[0057] Figure 5 Graph of the prior and posterior distributions of parameters in the Bayesian statistical method. Detailed implementation manners

[0058] The following will clearly and completely describe the technical solutions in the embodiments of the present application in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all of the embodiments. Based on the embodiments of the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present application.

[0059] To make the above objects, features, and advantages of the present application more obvious and understandable, the present application will be further described in detail below in conjunction with the drawings and specific implementation manners.

[0060] In an exemplary embodiment, as Figure 1 shown, a bolt hydrogen-induced fatigue life assessment method based on the Bayesian method is provided, and this method includes the following steps 201 to step 208. Among them,

[0061] S101, obtain the fatigue constitutive model based on the material level of the bolt; the fatigue constitutive model based on the material level is used to characterize the relationship between stress, strain, and fatigue life of the bolt under cyclic loading;

[0062] The stress-life model is mainly used to describe the fatigue behavior of materials in high-cycle fatigue (usually with a life greater than cycles). Basquin proposed the classical stress-life (S-N) relationship, and its expression is:

[0063] ;

[0064] Among them, is the stress amplitude, i.e., the amplitude of the cyclic stress; is the fatigue strength coefficient, reflecting the fatigue strength of the material; is the fatigue life, i.e., the number of cycles experienced by the material before failure under a given stress amplitude; is the fatigue strength exponent, reflecting the slope of the S-N curve, usually negative.

[0065] Through linear regression in logarithmic coordinates, the values of and can be determined:

[0066] ;

[0067] The strain-life model can better describe the performance of materials in the low-cycle fatigue region, especially when plastic deformation is significant. The strain-life model is mainly used to describe the fatigue behavior of materials in low-cycle fatigue (usually with a life less than cycles). Coffin-Manson proposed the strain-life relationship, and its expression is:

[0068] ;

[0069] Among them, includes the elastic strain amplitude and the plastic strain amplitude ; ;

[0070] The energy-life model is based on the energy dissipation of materials during cyclic loading and is a commonly used model for low-cycle and high-cycle fatigue. That is:

[0071] Using the formula to determine the fatigue constitutive model of bolts based on the material level; the fatigue constitutive model is the Smith-Watson-Topper parameter model (Smith-Watson-Topper, SWT); the SWT model combines the contributions of elastic and plastic strain energies and can better describe the medium-high cycle fatigue behavior, especially suitable for the case of the existence of mean stress or stress asymmetry.

[0072] Among them, is the fatigue ductility exponent, usually negative; is the total strain amplitude; is the elastic modulus; is the local maximum stress.

[0073] S102. Determine the basic fatigue characteristic curve according to the fatigue constitutive model based on the material level of the bolt and the material experimental data, and use the finite element analysis method to perform stress analysis on the actual structure of the bolt to determine the stress concentration coefficient. The basic fatigue characteristic curve includes: stress-life curve and strain-life curve.

[0074] S102 specifically includes:

[0075] Use the formula to determine the stress concentration coefficient ;

[0076] where is the theoretical stress concentration coefficient, obtained through thread geometric parameters or finite element analysis, is the plastic influence coefficient. For bolts made of high-strength steel, take .

[0077] where is the nominal stress, , is the external load, that is, the axial force acting on the bolt, is the stress area of the bolt, usually taking the cross-sectional area of the bolt rod.

[0078] Suppose the geometric parameters of a certain bolt are the nominal diameter of the thread and the root diameter of the thread ;

[0079] where the formula is used to determine the theoretical stress concentration coefficient;

[0080] Calculate the actual stress concentration coefficient : ; At this time, is 0.95.

[0081] Use the formula to determine the local maximum stress ;

[0082] S103. Modify the fatigue constitutive model based on the material level according to the stress concentration coefficient and the hydrogen embrittlement correction function to obtain the modified fatigue constitutive model.

[0083] The increase in hydrogen content will cause the fatigue strength coefficient , fatigue ductility coefficient , fatigue strength index and fatigue ductility index of the material to change. These changes reflect the negative impact of hydrogen embrittlement on the fatigue performance of the material. Specifically, the fatigue strength coefficient : The increase in hydrogen content leads to Decreases, indicating a weakened anti-fatigue ability of the material under high-cycle fatigue; fatigue ductility coefficient : The increase in hydrogen content leads to Decreases, reflecting a reduced ability of the material to resist plastic deformation; fatigue strength coefficient and fatigue ductility coefficient : The increase in hydrogen content will cause and The absolute values of increase, indicating an increased sensitivity of stress and strain to fatigue life.

[0084] As Figure 2 shown, by numerically calculating the fatigue life of bolts with hydrogen contents of 4 ppm, 8 ppm, and 12 ppm under different external loads, fatigue life curves were obtained. The results show that as the hydrogen content increases, the fatigue life of the bolts decreases significantly. For example, when the hydrogen content increases from 4 ppm to 12 ppm, the fatigue life is reduced by more than an order of magnitude, indicating that the hydrogen embrittlement effect has a serious impact on the fatigue performance of bolts, especially at high hydrogen contents, where the attenuation of fatigue life is particularly obvious. Figure 2 Intuitively demonstrates the significant effect of hydrogen on the fatigue behavior of materials.

[0085] To introduce the hydrogen embrittlement effect into the fatigue constitutive model, a hydrogen embrittlement correction function affected by hydrogen needs to be established:

[0086] Using the formula to determine the hydrogen embrittlement correction function of the fatigue strength coefficient; the hydrogen embrittlement correction function of the fatigue strength coefficient reflects the saturation effect of hydrogen content on the fatigue strength coefficient. As Figure 3 shown, as the hydrogen content increases, gradually approaches 1, indicating that the decrease in the fatigue strength coefficient tends to saturate.

[0087] Using the formula to determine the hydrogen embrittlement correction function of the fatigue ductility coefficient; as Figure 3 shown, the hydrogen embrittlement correction function of the fatigue ductility coefficient describes the exponential decay effect of hydrogen content on the fatigue ductility coefficient, reflecting the influence of hydrogen on the material's ability to resist plastic fatigue deformation.

[0088] Using and the formula to determine the hydrogen embrittlement correction function of the fatigue strength coefficient and the hydrogen embrittlement correction function of the fatigue ductility coefficient; as Figure 3 shown, the hydrogen embrittlement correction function of the fatigue strength coefficient and the hydrogen embrittlement correction function of the fatigue ductility coefficient are logarithmic correction functions. The logarithmic correction function can describe the non-linear influence of hydrogen content on the fatigue strength coefficient and the fatigue ductility coefficient, especially in the low hydrogen content range, is approximately linear, and as the hydrogen content increases, the growth rate slows down;

[0089] On the basis of fitting the correction parameters of the existing fatigue strength coefficient, fatigue ductility coefficient, fatigue strength index, and fatigue ductility index, the fitting of the correction parameters for the reduction of area and the elongation after fracture is newly added, as shown in part (a) of Figure 4 and part (b) of Figure 4 ;

[0090] Using the nonlinear least squares method, such as the Newton-Raphson method or the Levenberg-Marquardt algorithm, minimize the error between the theoretical value and the experimental value to solve the correction parameter ;

[0091] Evaluate the fitting accuracy of the correction function by calculating statistical indicators such as the coefficient of determination and the mean square error (MSE). Use an independent validation dataset to ensure the applicability and accuracy of the correction parameters.

[0092] Taking the correction of the fatigue strength coefficient as an example:

[0093] For each hydrogen content , there is:

[0094] ;

[0095] Let:

[0096] ;

[0097] Substitute the data of and into it, and use the nonlinear regression method to fit and obtain and . The fitting processes of other correction parameters are similar. Through independent systems of equations, determine , , , , , respectively.

[0098] To ensure that the corrected fatigue constants accurately reflect the hydrogen embrittlement effect, it is necessary to verify through additional experimental data. Specific methods include: selecting hydrogen content and fatigue life data that were not involved in the fitting, substituting them into the correction function to calculate the theoretical value, comparing with the experimental value, and evaluating the prediction ability of the model. Calculate the deviation between the predicted value and the experimental value, and evaluate the prediction accuracy of the model (such as mean square error, mean absolute error, etc.). Judge the reliability and applicable range of the correction function through statistical indicators, and adjust the form of the correction function or refit the parameters if necessary.

[0099] To further accurately describe the influence of hydrogen embrittlement effect on the fatigue performance of materials, the reduction of area ( ), and the elongation after fracture ( ) are introduced as direct correction factors, and the specific correction functions are as follows:

[0100] ;

[0101] ;

[0102] Among them, and are the reduction of area and elongation after fracture under the condition of no hydrogen charging respectively is the correction parameter to be determined by fitting experimental data. These correction functions reflect the direct influence of hydrogen content on the plastic deformation ability and reduction of area of materials. By establishing the hydrogen influence correction function, the model can quantitatively describe the influence of hydrogen content on the fatigue performance of materials;

[0103] Among them, is the fatigue strength coefficient under the condition of no hydrogen charging, , are the correction parameters of the fatigue strength coefficient, is the fatigue ductility coefficient under the condition of no hydrogen charging, , are the correction parameters of the fatigue ductility coefficient, is the fatigue strength exponent under the condition of no hydrogen charging, is the fatigue ductility exponent under the condition of no hydrogen charging, , are the correction parameters of the fatigue strength exponent, , are the correction parameters of the fatigue ductility exponent, is the reduction of area under the condition of no hydrogen charging, is the elongation after fracture under the condition of no hydrogen charging, , are the correction parameters of the reduction of area, , are the correction parameters of the elongation after fracture.

[0104] Among them, is the hydrogen embrittlement correction function of the fatigue strength coefficient, is the hydrogen content in the bolt, is the hydrogen embrittlement correction function of the fatigue ductility coefficient, is the hydrogen embrittlement correction function of the fatigue strength exponent, is the hydrogen embrittlement correction function of the fatigue ductility exponent, is the hydrogen embrittlement correction function of the reduction of area, is the hydrogen embrittlement correction function of the elongation after fracture.

[0105] Furthermore, use the formula to determine the corrected fatigue constitutive model;

[0106] The corrected fatigue constitutive model is a non - linear equation about and can be solved by numerical methods. The specific steps are as follows:

[0107] Initial guess: Set as the estimated value of the initial fatigue life.

[0108] Iterative calculation: Use the Newton - Raphson method or other suitable numerical iterative methods to update the value of :

[0109] ;

[0110] where is the difference between the left - hand side and the right - hand side of the equation: ;

[0111] is the derivative of with respect to :

[0112] ;

[0113] Convergence judgment: When (the set tolerance), stop the iteration and take as the final fatigue life.

[0114] Assume that all parameters are known, and solve according to the above method:

[0115] Set parameters , , , ; Modify parameters , ; Hydrogen content ; External load , cross - sectional area ; Elastic modulus .

[0116] Calculate the corrected fatigue constant

[0117] ;

[0118] ;

[0119] Calculate , similarly. Finally, calculate the stress concentration factor and obtain and the strain amplitude . Finally, establish and solve the nonlinear equation, and iteratively obtain .

[0120] S104. According to the modified fatigue constitutive model, adopt the nonlinear cumulative damage theory to determine the nonlinear cumulative damage model;

[0121] Fatigue damage is the process in which the internal structure of a material gradually deteriorates under cyclic loading and finally leads to fracture. The cumulative damage model is used to quantify this deterioration process to predict the fatigue life of the material or component. The classical Miner's rule assumes that the damage accumulates linearly at each stress level, while the nonlinear cumulative damage model takes into account the nonlinear characteristics of damage accumulation at different stress levels.

[0122] Expression of the linear Miner's rule:

[0123] ;

[0124] where is the total cumulative damage; is the actual number of cycles at the th stress level; is the fatigue life at the th stress level.

[0125] Expression of the nonlinear cumulative damage model:

[0126] ;

[0127] where is the nonlinear cumulative damage index, usually ;

[0128] Other symbols are the same as those in Miner's rule.

[0129] The nonlinear cumulative damage model is based on the following assumptions and theoretical bases:

[0130] The nonlinearity of damage accumulation, that is, the damage accumulation rate is different at different stress levels, and the damage accumulation rate is faster at high stress levels. Consideration of interaction effects, that is, the cycles at different stress levels may affect each other, resulting in the complexity of damage accumulation. The influence of material and environmental factors, such as the accelerating effect of hydrogen embrittlement on damage accumulation.

[0131] The key to the nonlinear cumulative damage model lies in determining the nonlinear index as well as the correction parameter and the correction parameter . These parameters are usually obtained by fitting experimental data.

[0132] Among them, The value reflects the non - linear degree of damage accumulation and is determined through the following steps: Conduct fatigue tests at different stress levels to obtain and . Use the least - squares method or other optimization algorithms to fit the experimental data to determine . The correction parameter and the correction parameter are used to reflect the influence of hydrogen embrittlement effect on cumulative damage. The corresponding determination steps include: Obtain the reduction of area and the elongation after fracture at different hydrogen contents . Through the non - linear regression method, fit the experimental data to determine the values of and . Use an independent validation data set to evaluate the accuracy and applicability of the correction parameters.

[0133] Applying the non - linear cumulative damage model for fatigue life prediction generally includes the following steps:

[0134] Adopt the rain - flow counting method to convert the actual bolt loading load time series into a stress - time curve, identify the closed stress cycles, and count each stress amplitude and the corresponding number of cycles . For each stress amplitude , perform the following calculations:

[0135] Calculate the strain amplitude :

[0136] ;

[0137] Apply the modified SWT model to establish an equation about :

[0138] ;

[0139] Numerically solve the fatigue life :

[0140] Adopt the Newton - Raphson numerical iteration method to solve the above non - linear equation to obtain . Use the non - linear cumulative damage model to calculate the total cumulative damage :

[0141] ;

[0142] Among them, is the total number of different stress levels; is the number of cycles at the th stress level; is the fatigue life at the th stress level; , is the reduction of area and elongation after fracture at the hydrogen content; , is the reduction of area and elongation after fracture under the condition of no hydrogen charging; , , are correction parameters.

[0143] Assume that there are stress levels in the load spectrum. The local maximum stress of each stress level: , , , . The corresponding number of cycles: , , , . Material parameters: , , , , . Hydrogen embrittlement correction parameters: , , , , , . Nonlinear index: .

[0144] For each stress level , calculate the strain amplitude:

[0145] ;

[0146] Apply the modified SWT model to establish an equation about :

[0147] ;

[0148] Numerically solve the fatigue life By numerical methods such as the Newton-Raphson method, solve the above equation to obtain .

[0149] Calculate the total cumulative damage:

[0150] ;

[0151] According to the cumulative damage value judge whether the component reaches or exceeds the fatigue failure condition.

[0152] When the cumulative damage value is reached, the bolt has not reached the fatigue failure condition and continues to be in service;

[0153] When the cumulative damage value is reached, the bolt reaches the fatigue failure condition and its life is exhausted;

[0154] When the cumulative damage value is exceeded, the bolt exceeds the fatigue failure condition and measures are taken.

[0155] S105. According to the material experiment data, the Bayesian statistical method is used to optimize the non-linear cumulative damage model.

[0156] The Bayesian statistical method is based on Bayes' theorem. By combining prior information and observed data, the understanding of parameters is updated. Its core idea is to use the known information (prior distribution) and the newly obtained data (likelihood function) to infer the posterior distribution of parameters.

[0157] As Figure 5 shown, the Bayesian method shows high flexibility in dealing with uncertainty and small amounts of data, especially effective in complex material systems. This figure visualizes the sampling trajectories of model parameters (such as α1, β1, γ1) and the posterior probability density function, comparing the parameter uncertainty ranges before and after Bayesian inference. The results show that the model significantly reduces the estimation uncertainty of parameters by combining observed data, improving the reliability of fatigue life prediction. Figure 5 The comparison between the prior and posterior in

[0158] clearly demonstrates the influence of data on the estimation of model parameters in the Bayesian framework, making the prediction results more robust and accurate, reflecting the advantages of the Bayesian method in dealing with complex material fatigue problems.

[0159] The expression of Bayes' theorem is as follows:

[0160] ;

[0161] where is the posterior distribution, representing the distribution of parameter under the observed data data. is the likelihood function, representing the probability of the observed data data appearing under the parameter . is the prior distribution, representing the knowledge of the parameters before observing the data. is the marginal likelihood, which serves as a normalization constant to ensure that the probability density of the posterior distribution integrates to 1.

[0162] The prior distribution reflects the knowledge or belief about the parameters before observing the data. The prior distribution can be set based on historical data, theoretical analysis, or engineering experience. The likelihood function is based on the probability of the observed data given the parameters. It reflects the degree of match between the model and the observed data. The posterior distribution combines the prior information and the observed data to provide an updated understanding of the parameters under the condition of the observed data. In the prediction of the fatigue life of high-strength bolts, the accurate estimation and uncertainty quantification of the model parameters are crucial for the accuracy and reliability of the prediction. Bayesian statistical methods provide a systematic theoretical framework for this process.

[0163] Prior distribution of the fatigue strength coefficient :

[0164] ;

[0165] where is the mean value of the fatigue strength coefficient; is the variance of the fatigue strength coefficient. Prior distribution of the fatigue ductility coefficient :

[0166] ;

[0167] where is the mean value of the fatigue ductility coefficient; is the variance of the fatigue ductility coefficient. Prior distribution of the correction parameter , :

[0168] ;

[0169] ;

[0170] where represents a uniform distribution; and are the value ranges of the parameters, set based on physical meaning and engineering experience.

[0171] Prior distribution of the non-linear cumulative damage index :

[0172] ;

[0173] where​ is the mean value of the non - linear cumulative damage index; is the variance of the non - linear cumulative damage index.

[0174] The rationality test of the prior distribution needs to ensure that the prior distribution reflects reasonable physical meanings and the parameter value ranges are within the actual possible ranges. The rationality of the prior distribution can be verified through sensitivity analysis and expert evaluation. The likelihood function reflects the probability of the observed data data occurring given the parameter . In this study, it is assumed that there is an error between the observed value and the model predicted value of the fatigue life, and the error follows a normal distribution.

[0175] Error model: ;

[0176] Take the logarithm: ;

[0177] Among them, ;

[0178] Expression of the likelihood function: ;

[0179] Among them, is the number of observed data; is the variance of the observation error, which is usually estimated from experimental data or included as a parameter to be estimated in the model.

[0180] The determination of the error variance can be estimated according to the precision of experimental measurement, or can be included as a parameter to be estimated in the Bayesian analysis. Since the posterior distribution usually cannot be analytically expressed, the Markov Chain MonteCarlo (MCMC) method is used for numerical solution. The basic steps of using the No - U - Turn Sampler for solution

[0181] Initialize the parameter : Select an initial parameter value as close as possible to the mean of the prior distribution.

[0182] The iterative sampling process of the NUTS method is:

[0183] Prior distribution setting: ;

[0184] Likelihood function: Assume that the observation error follows a log - normal distribution, and the likelihood function is:

[0185] ;

[0186] Among them, The fatigue life predicted by the model depends on the parameters .

[0187] NUTS combines the advantages of Hamiltonian Monte Carlo (HMC) by introducing potential energy and kinetic energy to construct a Hamiltonian system:

[0188] ;

[0189] where are model parameters. is an auxiliary momentum variable, usually following a normal distribution , is the mass matrix, usually set to the identity matrix.

[0190] HMC simulates the trajectory in the parameter space through Hamiltonian dynamics to achieve efficient parameter exploration. However, traditional HMC requires manual adjustment of the step size and the number of leap steps , which is difficult in high-dimensional and complex models. NUTS automatically avoids U-turn paths by adaptively adjusting the step size and the number of leap steps, improving the sampling efficiency.

[0191] For each parameter introduce momentum , and the momentum follows a normal distribution:

[0192] ;

[0193] Specifically, constructing the Hamiltonian system includes:

[0194] 1. Define the potential energy and kinetic energy:

[0195] ;

[0196] ;

[0197] 2. The Hamiltonian is: ;

[0198] 3. Dynamic path construction: Using the gradient information, simulate the Hamiltonian dynamics through the Leapfrog method to generate candidate parameter paths. NUTS automatically determines the path length and avoids U-turns in the path.

[0199] 4. Sampling candidate parameters: Randomly select a new parameter sample from the constructed path .

[0200] 5. Accept or reject;

[0201] 6. Calculate the change in Hamiltonian: ;

[0202] 7. The acceptance probability is: ;

[0203] Generate a uniform random number , if , accept as the new sample, otherwise retain the current sample .

[0204] 8. Iterative update: Repeat the above steps to generate posterior distribution samples of the parameters.

[0205] The core of NUTS lies in effectively exploring the parameter space through Hamiltonian dynamics, avoiding inefficient random walks. The specific formulas include:

[0206] : ;

[0207] ;

[0208] ;

[0209] ; ; ;

[0210] Through the above steps, NUTS can efficiently sample from complex posterior distributions and generate high-quality parameter samples.

[0211] Ensuring that the sampling process has fully explored the posterior distribution and achieved convergence is a crucial step in MCMC sampling. Common methods for judging convergence include monitoring the autocorrelation of samples and calculating the Gelman-Rubin diagnostic index .

[0212] Autocorrelation measures the degree of dependence between samples. Low autocorrelation indicates a high degree of sample independence. High autocorrelation reduces the effective sample size and affects the accuracy of parameter estimation.

[0213] For parameter , the autocorrelation function is defined as:

[0214] ;

[0215] where is the lag order. By plotting the ACF graph, the autocorrelation of the sample can be visually judged.

[0216] Effective sample size The calculation formula is:

[0217] ;

[0218] where is the total sample size. The larger the ESS, the higher the sample independence.

[0219] The Gelman-Rubin diagnostic evaluates the convergence between and within chains by comparing the variances of multiple independent chains. Run multiple independent MCMC chains, and each chain generates samples. Calculate the sample mean and the sample variance for each chain. Calculate the overall mean and variance of all chains:

[0220] ;

[0221] Estimate the overall variance :

[0222] ;

[0223] Calculate the Gelman-Rubin index:

[0224] ;

[0225] If , it is considered that the chain has converged to the target posterior distribution.

[0226] After obtaining a sufficient number of posterior samples, statistical analysis of the parameters can be performed to quantify the uncertainty.

[0227] Posterior mean and variance:

[0228] ;

[0229] ;

[0230] where represents the th sample, is the total number of samples.

[0231] Using the percentile method, calculate the 95% confidence interval of the parameter:

[0232] ;

[0233] Among them, represents the value of the parameter at the quantile.

[0234] Calculate the correlation coefficient matrix between parameters, identify highly correlated parameters, and model simplification or parameter reconstruction may be required.

[0235] For each parameter sample , calculate the corresponding fatigue life prediction value . Through statistical analysis, obtain the posterior distribution, and then calculate its mean, variance, and confidence interval. Calculate the posterior distribution of each parameter and analyze its central tendency and dispersion degree. Among them the uncertainty distribution of can intuitively understand the failure probability at different life levels.

[0236] Known observed data: fatigue test samples, and the observed fatigue life of each sample is , among which . Model parameters: fatigue strength coefficient , fatigue ductility coefficient , correction parameter , , non-linear cumulative damage index , correction parameter , .

[0237] According to the material mechanical properties and engineering experience, set the prior distribution of each parameter:

[0238] ;

[0239] ;

[0240] ;

[0241] ;

[0242] ;

[0243] Assume that the observation error follows a normal distribution, and the likelihood function is:

[0244] ;

[0245] Use the Metropolis-Hastings algorithm for iterative sampling to generate posterior distribution samples of parameters .

[0246] Calculate the posterior mean:

[0247] ;

[0248] Calculate the posterior variance:

[0249] ;

[0250] Calculate the 95% confidence interval:

[0251] ;

[0252] For each parameter sample , calculate the corresponding fatigue life prediction value . Through statistical analysis, obtain the posterior distribution of, and then calculate its mean, variance, and confidence interval.

[0253] Show the posterior distribution of each parameter through the posterior distribution histogram of the parameters, and analyze its central tendency and dispersion degree. Calculate the probability density function (PDF) and cumulative distribution function (CDF) of the fatigue life to visualize the uncertainty distribution of, and intuitively understand the failure probability at different life levels.

[0254] Quantifying the uncertainty in the probabilistic prediction of fatigue life is crucial in fatigue life prediction. Through the posterior distribution, the probability of component failure at different numbers of cycles can be evaluated.

[0255] ;

[0256] Among them, represents the reliability of the component at the target life .

[0257] In reliability assessment, a target life can be set, and the reliability of the bolt at this life can be calculated:

[0258] ;

[0259] Among them,

[0260] ;

[0261] ;

[0262] By setting different reliability levels (such as 90%, 95%), determine the design life or replacement cycle of the bolt to ensure its safety during service.

[0263] This application is not only applicable to the fatigue life prediction of high-strength bolts, but also, by adjusting geometric parameters, material properties, and hydrogen content distribution, applicable to the fatigue assessment of other hydrogen-affected structural components (such as bolts for offshore platforms, pipe joints, and connecting bolts for wind turbine towers, etc.), thereby providing a theoretical basis for the design, maintenance, and safety management of related structures. By comprehensively applying Bayesian statistics, the nonlinear cumulative damage theory, and stress concentration analysis, this application can dynamically correct the local stress level and damage rate function. At the same time, the parameters are updated posteriorly using experimental data, coupling the hydrogen embrittlement effect and the stress concentration effect into consideration, and ultimately providing a reliable technical means for the accurate prediction and uncertainty quantification of the remaining fatigue life of bolts (or other hydrogen-sensitive structural components) in complex environments.

[0264] It can be seen that the technical effects of this application are as follows:

[0265] 1. Comprehensive uncertainty quantification and parameter update:

[0266] Using the Bayesian statistical method, the prior information is organically combined with limited and imperfect experimental data, and the uncertainty of parameters is quantitatively characterized by the posterior distribution. By sampling the posterior distribution through the Markov chain Monte Carlo (MCMC) method, the true distribution ranges of material properties, hydrogen content, and loading conditions can be explored more effectively in the parameter space. This not only improves the robustness of the model for parameter estimation under limited data conditions but also makes the predicted fatigue life results have a confidence interval, thus providing a more reliable reference for engineering decisions.

[0267] 2. Dynamically integrating prior and observed data to achieve model self-adaptability:

[0268] When new experimental data or on-site monitoring data (such as bolt strain, stress, and hydrogen content measurement results) appear, the Bayesian update mechanism can timely correct the posterior distribution and dynamically update the model parameters. In this way, the model can be continuously optimized with changes in the environment and working conditions, thus maintaining a high prediction accuracy and adaptability under complex and variable offshore service conditions.

[0269] 3. More comprehensively characterizing the multi-factor coupling effect:

[0270] Combining the Bayesian statistical method with the nonlinear cumulative damage theory and stress concentration analysis can comprehensively model the hydrogen embrittlement effect, stress concentration, and the nonlinear accumulation process of fatigue damage. Compared with the deterministic model that only relies on the traditional S-N curve, the method proposed in this application can better handle multiple uncertain factors and complex coupling effects, improving the accuracy and robustness of fatigue life prediction.

[0271] This application establishes a high-cycle fatigue life assessment model for high-strength bolts that comprehensively considers the effects of hydrogen embrittlement, stress concentration, nonlinear cumulative damage, and the conversion of fatigue performance from the material level to the component level. It is necessary to deeply understand and apply a variety of fatigue theories and related mechanical principles, including fatigue constitutive relations, hydrogen embrittlement effects, stress concentration effects, nonlinear cumulative damage theories, and methods for converting fatigue performance from the material level to the component level. Through systematic theoretical analysis and formula derivation, the theoretical framework of the model is constructed, laying a solid theoretical foundation for the subsequent establishment of the model and parameter solution.

[0272] The following specific examples illustrate respectively that this application constructs a comprehensive model by combining stress concentration effects, nonlinear cumulative damage theories, and Bayesian statistical methods to systematically predict the fatigue life of bolts in complex service environments, with high applicability and reliability;

[0273] Example 1: Calculation of stress concentration factor

[0274] In this example, first, for the geometric characteristics of the bolt, the finite element analysis (FEA) is used to calculate the stress concentration factor ( ). The geometric parameters of the bolt include the nominal thread diameter ( ), and the root diameter of the thread ( ). The theoretical stress concentration factor is obtained through finite element simulation, and its calculation formula is:

[0275] ;

[0276] The actual stress concentration factor is then adjusted by the correction factor , The value of is

[0277] ;

[0278] Through precise geometric modeling and load application, the local stress distribution of the bolt under complex load conditions is simulated, providing the necessary input parameters for the subsequent fatigue life assessment.

[0279] Example 2: Application of nonlinear cumulative damage theory

[0280] Based on the stress concentration analysis, this example uses the nonlinear cumulative damage theory to describe the fatigue damage accumulation process of the bolt. For the damage evolution of high-strength bolts under different hydrogen contents, the fatigue life is quantified using modified fatigue constants.

[0281] Fatigue strength coefficient ( ), and fatigue ductility coefficient ( ) are all non - linear functions of hydrogen content and are corrected using the following formulas respectively: ;

[0282] ;

[0283] ;

[0284] In addition, the fatigue strength index ( ) and the fatigue ductility index ( ) are also affected by hydrogen content, and their correction formulas are as follows:

[0285] ;

[0286] ;

[0287] By combining the above - corrected fatigue constants with the local maximum stress , the fatigue life performance of the bolt under different hydrogen contents and stress levels can be obtained.

[0288] Example 3: Calculation of Fatigue Life

[0289] Based on the corrected fatigue constants and stress levels, this example uses the Brentq root - finding numerical solution method to solve for the fatigue life ( ). The cumulative damage function of the cumulative damage theory is defined as follows:

[0290] ;

[0291] Among them, is the damage rate function, represents the time variation of the stress level, is the hydrogen content. The fatigue life satisfies the condition of cumulative damage and is obtained through the numerical solution method.

[0292] In the specific calculation, first calculate the local maximum stress through the stress concentration coefficient, and then combine the corrected fatigue strength coefficient and fatigue ductility coefficient to solve for the fatigue life using the following equation:

[0293] ;

[0294] The solution equation for the fatigue life is:

[0295] ;

[0296] Numerically solve the above equation using the Brentq root-finding method to obtain the fatigue life of the bolt under different conditions.

[0297] Example 4: Application of Bayesian statistical method

[0298] To improve the accuracy of fatigue life prediction, this example introduces the Bayesian statistical method to optimize the model parameters. By measuring the fatigue life experimental data of the bolt and combining prior information, a Bayesian statistical model is constructed to quantify the uncertainty of material parameters.

[0299] Specifically, the prior distribution is constructed based on previous experimental experience data, and the observed data comes from the fatigue experimental results under different hydrogen contents and stress levels. The Bayesian update process is implemented by the Markov chain Monte Carlo (MCMC) method to sample the posterior distribution and obtain the posterior estimate of the model parameters. The mathematical expression of the Bayesian update process is:

[0300] ;

[0301] where is the prior distribution, is the likelihood function. By sampling the posterior distribution using the MCMC method, the dynamic update of the model parameters is realized, thus significantly improving the accuracy of fatigue life prediction.

[0302] Example 5: Experimental verification and result visualization

[0303] To verify the effectiveness of the method of this application, a series of experiments were conducted. Under different hydrogen contents (4 ppm, 8 ppm, and 12 ppm) and different external loads (4000 N to 7000 N), the fatigue life of the bolt was measured, and the experimental results were compared with the model prediction values. The experimental results show that the model of this application can accurately capture the influence trend of hydrogen content on fatigue life. Especially under high hydrogen content conditions, the model prediction is highly consistent with the experimental measurement results.

[0304] To more intuitively display the prediction ability of this application, the fatigue life curves under different hydrogen contents as shown in Figure 2 and the relationship diagram between the corrected material parameters and hydrogen content as shown in Figure 3 were plotted. Figure 2 shows the relationship between the local maximum stress and the fatigue life. The results show that as the hydrogen content increases, the fatigue life of the bolt decreases significantly. Figure 3 shows the influence of hydrogen embrittlement effect on key parameters such as fatigue strength coefficient and fatigue ductility coefficient.

[0305] The embodiment of the present application provides a method capable of dynamically evaluating the fatigue life of bolts, especially considering the coupling effect of hydrogen embrittlement effect and stress concentration effect in a complex service environment. Through Bayesian statistics for parameter optimization of the model, the present application achieves a high-precision evaluation of fatigue life prediction, which is particularly applicable to the design, maintenance, and replacement of high-strength bolts in harsh environments such as ocean engineering, providing important technical support and scientific basis for the safety of engineering structures.

[0306] In this embodiment, the fatigue life of high-strength bolts under different hydrogen contents and local maximum stress conditions is calculated and analyzed. By applying the aforementioned modeling methods (including stress concentration analysis, nonlinear cumulative damage theory, Bayesian statistical parameter update) to the actual bolt working conditions, the fatigue life prediction results under different conditions are obtained. At the same time, the posterior distribution estimation of the model parameters is carried out through the Bayesian statistical method to quantify the uncertainty and improve the prediction credibility. The following gives the specific calculation process and results.

[0307] The fatigue life of the bolt is predicted under the conditions of hydrogen contents of 4.0 ppm, 8.0 ppm, and 12.0 ppm respectively. Through finite element analysis (FEA) and the aforementioned calculation method of the stress concentration coefficient the local maximum stress is obtained. On this basis, using the nonlinear cumulative damage model and the modified fatigue constitutive parameters (modified according to the hydrogen content), the fatigue life of the bolt is calculated.

[0308] When the hydrogen content H = 4.0 ppm, at a lower hydrogen content, the bolt life is relatively high. The specific calculation results are shown in Table 1 (local maximum stress / MPa, fatigue life / number of cycles);

[0309] Table 1

[0310]

[0311] When the hydrogen content H = 8.0 ppm, after the content increases, the bolt fatigue life decreases significantly, especially at high stress levels, as shown in Table 2:

[0312] Table 2

[0313]

[0314] When the hydrogen content H = 12.0 ppm, at a higher hydrogen content, the hydrogen-induced embrittlement effect is more significant, resulting in a further shortening of the fatigue life, as shown in Table 3:

[0315] Table 3

[0316]

[0317] As can be seen from the above results, with the increase of hydrogen content, the fatigue life of the bolt decreases significantly under the same stress level, which is consistent with the mechanism of hydrogen embrittlement effect, indicating that the method of this application is highly effective in quantifying hydrogen-induced fatigue life reduction.

[0318] Combining the above fatigue life prediction results with the experimental data, the posterior distributions of key parameters (such as and the standard deviation of the observation error ) are estimated by Bayesian statistical methods. After the MCMC sampling is completed, the following statistical results can be obtained, as shown in Table 4:

[0319] Table 4

[0320]

[0321] It can be seen from the parameter estimation results that the posterior distributions of the parameters alpha1, beta1, and gamma1 are relatively concentrated, and the Gelman-Rubin diagnostic index (r_hat) is close to 1, indicating that the MCMC chain has converged and the parameter estimation is stable and reliable. By extracting the posterior distribution, it can provide parameter uncertainty quantification for the model to predict the life under different working conditions in the future, making the prediction results have a confidence interval. This provides more robust and referenceable decision-making information for engineering practice.

[0322] In summary, through numerical calculation and Bayesian statistical analysis, this embodiment verifies the effectiveness and robustness of the method of this application in evaluating the fatigue life of high-strength bolts considering the effects of hydrogen embrittlement and stress concentration. The calculation results show that the increase of hydrogen content significantly reduces the fatigue life, and Bayesian statistical analysis provides a technical means for parameter estimation and quantification of prediction uncertainty, which helps to evaluate and make decisions on the bolt life more scientifically and reliably in practical engineering.

[0323] Based on the same inventive concept, the embodiment of this application also provides a Bayesian method-based bolt hydrogen-induced fatigue life evaluation system for implementing the above-mentioned Bayesian method-based bolt hydrogen-induced fatigue life evaluation method. The implementation solutions provided by this system to solve problems are similar to those recorded in the above method. Therefore, the specific limitations in one or more embodiments of the following Bayesian method-based bolt hydrogen-induced fatigue life evaluation system can refer to the limitations on the Bayesian method-based bolt hydrogen-induced fatigue life evaluation method in the above text, and will not be repeated here.

[0324] In an exemplary embodiment, a Bayesian method-based bolt hydrogen-induced fatigue life evaluation system is provided, including:

[0325] A fatigue constitutive model acquisition module for acquiring a fatigue constitutive model of the bolt at the material level; the fatigue constitutive model at the material level is used to characterize the relationship between stress, strain and fatigue life of the bolt under cyclic loading;

[0326] A stress concentration factor determination module for determining a basic fatigue characteristic curve according to the fatigue constitutive model of the bolt at the material level and material experimental data, and performing stress analysis on the actual structure of the bolt by using the finite element analysis method to determine the stress concentration factor; the basic fatigue characteristic curve includes: a stress-life curve and a strain-life curve;

[0327] A fatigue constitutive model correction module for correcting the fatigue constitutive model at the material level according to the stress concentration factor and the hydrogen embrittlement correction function to obtain a corrected fatigue constitutive model;

[0328] A non-linear cumulative damage model determination module for determining a non-linear cumulative damage model according to the corrected fatigue constitutive model by using the non-linear cumulative damage theory;

[0329] A non-linear cumulative damage model optimization module for optimizing the non-linear cumulative damage model by using the Bayesian statistical method according to the material experimental data.

[0330] In this application, all actions of acquiring signals, information or data are carried out on the premise of complying with the corresponding data protection regulations and policies of the country where it is located and obtaining the authorization given by the owner of the corresponding device.

[0331] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0332] In this article, specific examples are used to elaborate on the principle and implementation manner of this application. The description of the above embodiments is only used to help understand the method and its core idea of this application; at the same time, for those of ordinary skill in the art, according to the idea of this application, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to this application.

Claims

1. A method for evaluating hydrogen-induced fatigue life of bolts based on Bayesian method, characterized in that: The method for assessing hydrogen-induced fatigue life of bolts based on the Bayesian method includes: Obtaining a material-level fatigue constitutive model of the bolt; the material-level fatigue constitutive model is used to characterize the relationship between stress, strain and fatigue life of the bolt under cyclic load; According to the fatigue constitutive model of the bolt based on the material level and the material experimental data, the basic fatigue characteristic curve is determined, and the stress concentration factor is determined by performing stress analysis on the real structure of the bolt using the finite element analysis method; the basic fatigue characteristic curve includes: a stress-life curve and a strain-life curve; The fatigue constitutive model based on the material level is corrected according to the stress concentration factor and the hydrogen embrittlement correction function to obtain a corrected fatigue constitutive model; According to the modified fatigue constitutive model, the nonlinear cumulative damage model is determined by using the nonlinear cumulative damage theory; According to the material experimental data, the Bayesian statistical method is used to optimize the nonlinear cumulative damage model; The method of correcting the fatigue constitutive model based on the material level according to the stress concentration factor and the hydrogen embrittlement correction function to obtain the corrected fatigue constitutive model specifically includes: Using the formula Determine the modified fatigue constitutive model; in, is the hydrogen embrittlement correction function of the fatigue strength coefficient, is the hydrogen content in the bolt, is the hydrogen embrittlement correction function of the fatigue ductility coefficient, is the hydrogen embrittlement correction function of the fatigue strength index, is the hydrogen embrittlement correction function of the fatigue ductility index, is the hydrogen embrittlement correction function of the cross-sectional shrinkage rate, is the hydrogen embrittlement correction function of elongation after fracture, is the total strain amplitude, including elastic strain amplitude and plastic strain amplitude, is the local maximum stress, E is the elastic modulus, is the fatigue life; According to the modified fatigue constitutive model, the nonlinear cumulative damage theory is used to determine the nonlinear cumulative damage model, which includes: According to the modified fatigue constitutive model, the fatigue life is determined by using the Newton-Raphson numerical iteration method. According to fatigue life, a nonlinear cumulative damage model is constructed by adopting nonlinear cumulative damage theory; the nonlinear cumulative damage model is used to characterize the cumulative damage value of the bolt; The fatigue life of the bolt is evaluated based on the cumulative damage value of the bolt; According to the fatigue life, the nonlinear cumulative damage model is constructed using the nonlinear cumulative damage theory, including: Using the formula Determine the nonlinear cumulative damage model; in, is the cumulative damage value, is the total number of different stress levels, For the The number of cycles at each stress level, For the Fatigue life at each stress level, is the hydrogen embrittlement correction function of the cross-sectional shrinkage rate, is the hydrogen embrittlement correction function of elongation after fracture, is the cross-sectional shrinkage under the condition of no hydrogen filling, is the elongation after fracture under the condition of no hydrogen charging, , , To correct the parameters.

2. The method for evaluating hydrogen-induced fatigue life of bolts based on the Bayesian method according to claim 1, characterized in that: The method of obtaining the fatigue constitutive model of the bolt based on the material level specifically includes: Using the formula Determine the material level based fatigue constitutive model for the bolt; in, is the fatigue strength coefficient, which is used to reflect the fatigue strength of the bolt; is the fatigue strength index; is the fatigue ductility coefficient, which is used to reflect the anti-plastic fatigue performance; is the fatigue ductility index.

3. The method for evaluating hydrogen-induced fatigue life of bolts based on the Bayesian method according to claim 2, characterized in that: The method of determining the basic fatigue characteristic curve based on the fatigue constitutive model of the bolt based on the material level and the material experimental data, and performing stress analysis on the real structure of the bolt using the finite element analysis method to determine the stress concentration factor specifically includes: Using the formula Determining Stress Concentration Factors ; in, is the theoretical stress concentration factor, is the plasticity influence coefficient.

4. The method for evaluating hydrogen-induced fatigue life of bolts based on the Bayesian method according to claim 3, characterized in that: Using the formula Determining the local maximum stress ; in, is the nominal stress, , is the external load, is the load-bearing cross-sectional area of ​​the bolt.

5. The method for evaluating hydrogen-induced fatigue life of bolts based on the Bayesian method according to claim 1, characterized in that: The hydrogen embrittlement correction function specifically includes: Using the formula Determine the hydrogen embrittlement correction function for the fatigue strength coefficient; Using the formula Determine the hydrogen embrittlement correction function for fatigue ductility coefficient; use and formula Determine the hydrogen embrittlement correction function of the fatigue strength index and the hydrogen embrittlement correction function of the fatigue ductility index; Using the formula Determine the hydrogen embrittlement correction function for the reduction of area; Using the formula Determine the hydrogen embrittlement correction function for elongation after fracture; in, is the fatigue strength coefficient under the condition of no hydrogen charging, , is the correction parameter of fatigue strength coefficient, is the fatigue ductility coefficient under the condition of no hydrogen charging, , is the correction parameter of fatigue ductility coefficient, is the fatigue strength index under the condition of no hydrogen charging, is the fatigue ductility index under non-hydrogen charging conditions, , is the correction parameter of fatigue strength index, , is the correction parameter of fatigue ductility index, is the cross-sectional shrinkage under the condition of no hydrogen filling, is the elongation after fracture under the condition of no hydrogen charging, , is the correction parameter of the section shrinkage rate, , It is the correction parameter of elongation after fracture.

6. The method for evaluating hydrogen-induced fatigue life of bolts based on the Bayesian method according to claim 1, characterized in that: The fatigue life of the bolt is evaluated based on the cumulative damage value of the bolt, including: When the cumulative damage value When the bolts have not reached fatigue failure conditions, they continue to serve; When the cumulative damage value When the bolt reaches fatigue failure condition, its service life is exhausted; When the cumulative damage value When the bolt exceeds the fatigue failure condition, take measures.

7. A bolt hydrogen-induced fatigue life assessment system based on Bayesian method, used to implement the bolt hydrogen-induced fatigue life assessment method based on Bayesian method according to any one of claims 1 to 6, characterized in that: The bolt hydrogen-induced fatigue life assessment system based on the Bayesian method includes: A fatigue constitutive model acquisition module is used to acquire a fatigue constitutive model of the bolt based on the material level; the fatigue constitutive model based on the material level is used to characterize the relationship between stress, strain and fatigue life of the bolt under cyclic load; A stress concentration factor determination module is used to determine a basic fatigue characteristic curve according to a fatigue constitutive model of the bolt based on material level and material experimental data, and to perform stress analysis on the real structure of the bolt using a finite element analysis method to determine the stress concentration factor; the basic fatigue characteristic curve includes: a stress-life curve and a strain-life curve; A fatigue constitutive model correction module is used to correct the fatigue constitutive model based on the material level according to the stress concentration factor and the hydrogen embrittlement correction function to obtain a corrected fatigue constitutive model; A nonlinear cumulative damage model determination module is used to determine the nonlinear cumulative damage model based on the modified fatigue constitutive model and the nonlinear cumulative damage theory; The nonlinear cumulative damage model optimization module is used to optimize the nonlinear cumulative damage model based on material experimental data using the Bayesian statistical method.

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