Fatigue life prediction method for welded joints considering residual stress evolution

Abstract

This invention provides a method for predicting the fatigue life of welded joints considering the evolution of residual stress, belonging to the field of fatigue life prediction technology. Specific steps include: establishing a finite element model of the joint; simulating the welding process to obtain the initial residual stress distribution; selecting high-stress regions as dominant regions; calculating the stress sensitivity index of the dominant region and setting a negatively correlated cyclic load interval; dividing the loading stage according to the interval and extracting stress-strain data for each stage; iteratively updating the stress field based on the residual stress relaxation factor to obtain the residual stress evolution history; combining the load spectrum and material fatigue parameters, calculating and accumulating the damage at each stage using a damage accumulation model; and outputting the total number of cycles as the predicted life when the accumulated damage reaches a critical value, thus achieving a more scientific and accurate prediction of the fatigue life of welded joints.

Description

Technical Field

[0001] This invention relates to the field of fatigue life prediction technology, specifically to a method for predicting the fatigue life of welded joints that takes into account the evolution of residual stress. Background Technology

[0002] Welded joints are a common connection type in various engineering structures, and their performance directly affects the safety and lifespan of the entire structure. Under actual working conditions, welded joints are subjected to cyclic loads, which easily lead to the initiation and propagation of fatigue cracks in stress concentration areas, ultimately resulting in fatigue failure. During the welding process, local high-temperature heating and rapid cooling will form complex and large residual stresses inside the joint. These residual stresses, superimposed with the applied working load, act together on the material, which not only significantly changes the cyclic characteristics of fatigue loads, but also continues to evolve due to plastic deformation during cyclic loading, thus affecting the crack initiation life and propagation rate. Therefore, to accurately predict the fatigue life of welded joints, it is necessary to scientifically consider the existence of residual stresses and their evolution behavior during service.

[0003] In the prior art, a fatigue life prediction method for welded joints considering residual stress evolution, disclosed in CN111860993A, proposes the idea of ​​introducing steady-state residual stress as an average stress correction term into the fatigue life prediction model of the base material. However, this method mainly relies on obtaining the maximum steady-state tensile residual stress value through finite element simulation and assuming that the residual stress tends to stabilize after a few cycles, and then superimposing it as a fixed correction amount into subsequent life calculations. This method fails to accurately describe the dynamic and non-uniform evolution process of residual stress throughout the fatigue loading process, especially ignoring the differences in residual stress relaxation rate and evolution path caused by stress gradient and local plastic accumulation differences in different regions. In addition, this method does not establish an adaptive correlation between residual stress evolution and cyclic load intervals, nor does it dynamically segment and update the fatigue damage calculation process according to the sensitivity of stress evolution. This may lead to insufficient characterization of the damage accumulation process, especially the early damage in high stress gradient regions, thus affecting the accuracy of life prediction and engineering applicability.

[0004] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting the fatigue life of welded joints that takes into account the evolution of residual stress, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: The fatigue life prediction method for welded joints considering residual stress evolution includes the following steps: A finite element model is established based on the geometry of the welded joint, and its process parameters are applied as thermal load boundary conditions to the weld area of ​​the finite element model. The initial residual stress distribution of the welded joint when it cools to room temperature is simulated and analyzed to screen out the dominant region. Based on the stress gradient distribution and average level of the initial residual stress in the dominant region, a stress sensitivity index characterizing the sensitivity of the dominant region to stress evolution is calculated, and a cyclic load interval negatively correlated with the stress sensitivity index is set. The cyclic load application stages are divided according to the cyclic load interval, and then the cyclic load is applied to the finite element model in stages. After each stage, the stress and strain data of the dominant region are extracted. The initial residual stress distribution is calibrated as the initial stress field of the first stage. Based on the stress and strain data of the current stage, the residual stress relaxation factor is determined. The initial stress field of the current stage is updated by finite element iteration using the residual stress relaxation factor to obtain the residual stress distribution at the end of the current stage. This is then used as the initial stress field of the next stage. The calculations of each stage are completed in sequence to obtain the evolution data of the residual stress. Based on the evolution data of residual stress, the working load spectrum of the welded joint, and fatigue performance parameters, the fatigue damage amount at each stage is extracted and accumulated through a damage accumulation model. When the accumulated damage amount reaches a preset critical value, the corresponding total number of cycles is output as the predicted fatigue life of the welded joint.

[0007] Furthermore, the process parameters include welding heat input, welding speed, welding sequence and direction, and the number and arrangement of weld layers; The fatigue performance parameters include cyclic hardening parameters or cyclic softening parameters characterizing the low-cycle fatigue behavior of the material, and fatigue strength coefficient and fatigue strength index characterizing the high-cycle fatigue behavior; wherein, the cyclic hardening parameters or cyclic softening parameters are obtained through uniaxial strain-controlled fatigue tests of the material, and the fatigue strength coefficient and fatigue strength index are obtained through stress-controlled fatigue tests of the material. The working load spectrum includes load amplitude, load ratio and load frequency, wherein the load amplitude includes the maximum nominal stress and the minimum nominal stress.

[0008] Furthermore, a finite element model was constructed based on the geometry of the welded joint. Eight-node hexahedral elements were used to mesh the model, with the geometric center of each element designated as a node. A denser mesh was applied to the weld and heat-affected zone, while a sparser mesh was used for the base metal region. Process parameters were converted into corresponding moving heat source heat flux density, heating time, and the heat source's path along the weld, which were then applied as transient thermal load boundary conditions to the corresponding mesh elements in the weld region of the finite element model. Subsequently, a thermo-structural coupling analysis method was used to simulate the entire process from welding heating to natural cooling to room temperature. By solving the heat conduction equation and the thermo-elastic-plastic constitutive relation, the stress components at each node of the model were extracted when cooled to room temperature. The residual equivalent stress value is calculated to obtain the residual equivalent stress distribution when the model is cooled to room temperature, and this is used as the initial residual stress distribution. An equivalent stress threshold is set, which is determined based on the yield strength of the material used in the welded joint. The residual equivalent stress values ​​of all nodes in the model are traversed, and nodes with residual equivalent stress values ​​exceeding the set threshold are designated as stress concentration nodes. The mesh elements where the stress concentration nodes are located are designated as stress concentration elements. All stress concentration elements are clustered to form multiple discontinuous regions. Each region is designated as a potential concentration area, thus forming a set of potential concentration areas. The potential concentration area with the highest average residual equivalent stress value is selected from the set and marked as the dominant region. The average residual equivalent stress value of all nodes within the potential concentration area is taken as the average residual equivalent stress value of the potential concentration area.

[0009] Furthermore, within the defined dominant region, the residual equivalent stress value at each element node is extracted, and the average residual equivalent stress value within the dominant region is calculated as the average level of the initial residual stress within that region. ; For any unit node within the dominant region Based on its node coordinates The residual equivalent stress values ​​of adjacent elements are used to calculate the stress gradient vector components at the element node coordinates using the central difference method. ;in, For the index of the unit nodes within the dominant region; Then the stress gradient modulus at the node coordinates of this element for: The arithmetic mean of the stress gradient modulus at all element node coordinates within the dominant region is used as the stress gradient modulus to quantify the stress gradient distribution characteristics of that region. ; Based on the stress gradient distribution and the average level of initial residual stress in the dominant region, the stress sensitivity index, which characterizes the sensitivity of this region to stress evolution, is calculated using the following formula: In the formula, It is the stress sensitivity index; For reference stress; The preset feature length.

[0010] Furthermore, determine the allowable range of values ​​for the cyclic load interval. ,in The preset minimum cyclic load interval, The preset maximum cyclic load interval; the cyclic load interval is set according to the following formula. : in, and These are the lower and upper reference values ​​for the pre-set stress sensitivity index.

[0011] Furthermore, based on the maximum and minimum nominal stresses in the working load spectrum, cyclic surface force loads that vary with the load frequency are applied to the surface in the finite element model corresponding to the actual working force of the welded joint, according to the load ratio and load frequency, to simulate the actual working load; wherein, the load ratio refers to the ratio of the minimum nominal stress to the maximum nominal stress; Each cyclic load application process is defined as an independent stage, and the interval between two adjacent cyclic load applications is the cyclic load interval. The initial residual stress distribution is used as the initial stress field of the first stage. Within each stage, the same number of cyclic loads are continuously applied to the finite element model to simulate the fatigue loading process of that stage. After the last cyclic load of the stage is completed, the load application is immediately paused. The stress tensor components and plastic strain tensor components of each element node in the dominant region at this moment are extracted from the finite element solver. Based on the stress tensor components, the residual equivalent stress value of each node is calculated according to the Von Mises criterion. Based on the plastic strain tensor components, the equivalent plastic strain of each node is calculated according to the equivalent plastic strain formula. The calculated residual equivalent stress value and equivalent plastic strain of each node are recorded as the stress-strain data of each node in that stage.

[0012] Furthermore, for any stage Based on the stress-strain data of the dominant region, the equivalent plastic strain increment and equivalent stress relaxation amount of the dominant region at this stage are calculated. In the formula, and The first The equivalent plastic strain increment and equivalent stress relaxation amount at each stage; , The first The arithmetic mean of the equivalent plastic strain of all element nodes in the dominant region at the beginning and end of each stage; and The first The arithmetic mean of the residual equivalent stress values ​​of all unit nodes in the dominant region at the beginning and end of each stage; For the index of stages, ; Calculate the first according to the following formula. Residual stress relaxation factor at each stage : in, The yield strength of the material; Based on residual stress relaxation factor , for the The initial stress field of each stage is updated: the stress tensor components of each element node in the dominant region at the beginning of that stage are updated. Multiply by the reduction factor This yields the updated stress tensor components of the node at the end of this phase. ;in, This represents the stress tensor of the element node at the beginning of the m-th stage, corresponding to the coordinate axis. The amount, The subscript index of the component is used to represent the specific component of the stress tensor; This update operation is synchronously applied to all cell nodes in the dominant region, thereby obtaining the first... The overall residual stress distribution at the end of each stage is then used as the initial stress field for the next stage, and the above calculation process is repeated until all stages are completed, thus obtaining the evolution data of residual stress throughout the entire fatigue loading process.

[0013] Furthermore, based on the residual stress distribution evolution data, for each stage, the residual equivalent stress value of each unit node in the dominant region at the end of that stage is obtained. Combined with the load amplitude in the working load spectrum, the stress cycle characteristics of each unit node in that stage are calculated. The stress cycle characteristics include the maximum cyclic stress, the minimum cyclic stress, and the average cyclic stress. The maximum cyclic stress is obtained by adding the current residual equivalent stress value of the node to the maximum nominal stress value; the minimum cyclic stress is obtained by adding the current residual equivalent stress value of the node to the minimum nominal stress value; and the average cyclic stress is obtained by taking the arithmetic mean of the calculated maximum cyclic stress and the minimum cyclic stress. The calculated stress cycle characteristics are combined with the fatigue performance parameters, and the fatigue damage of each node element in this stage is calculated using a preset damage accumulation model. The damage of all node elements in the dominant region in this stage is summed to obtain the overall damage of this stage. The damage of each stage is accumulated in the order of stages to obtain the cumulative damage. When the cumulative damage reaches a preset critical value, the total number of cycles loaded at this time is output as the predicted fatigue life of the welded joint.

[0014] Compared with the prior art, the beneficial effects of the present invention are: First, based on the initial residual stress distribution, this invention identifies the dominant region from the potential high-stress areas by threshold screening and comparison with the average value, in order to focus on the key parts most likely to fail due to fatigue. Then, by combining the stress gradient distribution and average stress level of the dominant region, a stress sensitivity index is constructed, and the cyclic load interval is dynamically set accordingly: the higher the stress sensitivity index, the more sensitive the stress state of the region is to external loads and plastic deformation, and the more intense the evolution of residual stress. Therefore, a smaller load interval is used for data sampling to ensure sufficient data in the rapid evolution stage, while the interval is appropriately increased in the slow evolution stage to improve computational efficiency. Furthermore, after each divided loading stage, the residual stress relaxation factor is calculated based on the extracted stress-strain data, and this factor is used to update the initial stress field of the current stage using finite element iteration, thereby obtaining the updated residual stress distribution at the end of the stage, which is then used as the initial stress field for the next stage. Through this iterative process, the present invention can completely and continuously simulate the dynamic evolution trajectory of residual stress throughout the entire fatigue loading process, rather than just obtaining a static steady-state value. Based on the evolution data and combined with the damage accumulation model, the life prediction is performed, making the simulation of the damage process more accurate. This effectively overcomes the bias caused by the simplified handling of the residual stress evolution process in the prior art, thereby achieving a more scientific and accurate prediction of the fatigue life of welded joints. Attached Figure Description

[0015] Figure 1This is a schematic diagram of the overall method flow of the present invention; Figure 2 A dual Y-axis image showing the region-average residual stress, reference stress, and stress sensitivity index; Figure 3 A dual Y-axis image of the regional stress gradient modulus, the preset characteristic length, and the stress sensitivity index; Figure 4 A 3D scatter plot of the regional stress gradient modulus, a preset characteristic length, and a stress sensitivity index. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0017] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0018] Example: Please see Figures 1-4 The present invention provides a technical solution: The fatigue life prediction method for welded joints considering residual stress evolution includes the following steps: Step 1: Establish a finite element model based on the geometry of the welded joint, and apply its process parameters as thermal load boundary conditions to the weld area of ​​the finite element model. Simulate and analyze the initial residual stress distribution when the welded joint cools to room temperature, and screen out the dominant region. In this embodiment, the process parameters include welding heat input, welding speed, welding sequence and direction, and the number and arrangement of weld layers; The fatigue performance parameters include cyclic hardening parameters or cyclic softening parameters characterizing the low-cycle fatigue behavior of the material, and fatigue strength coefficient and fatigue strength index characterizing the high-cycle fatigue behavior of the material; wherein, the cyclic hardening parameters or cyclic softening parameters are obtained through uniaxial strain-controlled fatigue tests of the material, and the fatigue strength coefficient and fatigue strength index are obtained through stress-controlled fatigue tests of the material. In fatigue mechanics, materials under cyclic loading may exhibit two different behaviors: cyclic hardening, which means that under constant strain amplitude cyclic loading, the stress amplitude increases with the number of cycles; and cyclic softening, which means that under constant strain amplitude cyclic loading, the stress amplitude decreases with the number of cycles. Moreover, for a given material, it is impossible for both cyclic hardening and cyclic softening to occur simultaneously; it can only be one of these behaviors.

[0019] The working load spectrum includes load amplitude, load ratio and load frequency, wherein the load amplitude includes the maximum nominal stress and the minimum nominal stress.

[0020] A finite element model was constructed based on the geometry of the welded joint. Eight-node hexahedral elements were used to mesh the model, with the geometric center of each element designated as a node. A denser mesh was applied to the weld and heat-affected zone, while a sparser mesh was used for the base metal region. Process parameters were converted into corresponding moving heat source heat flux density, heating time, and the heat source's path along the weld, which were then applied as transient thermal load boundary conditions to the corresponding mesh elements in the weld region of the finite element model. Subsequently, a thermo-structural coupling analysis method was used to simulate the entire process from welding heating to natural cooling to room temperature. By solving the heat conduction equation and the thermo-elastic-plastic constitutive relation, the stress components at each node of the model were extracted and calculated when cooled to room temperature. The residual equivalent stress value is used to obtain the residual equivalent stress distribution when the model is cooled to room temperature, and this is used as the initial residual stress distribution. An equivalent stress threshold is set, which is determined based on the yield strength of the material used in the welded joint. The residual equivalent stress values ​​of all nodes in the model are traversed, and nodes with residual equivalent stress values ​​exceeding the set threshold are designated as stress concentration nodes. The mesh elements where the stress concentration nodes are located are designated as stress concentration elements. All stress concentration elements are clustered to form multiple discontinuous regions. Each region is designated as a potential concentration area, thus forming a set of potential concentration areas. The potential concentration area with the highest average residual equivalent stress value is selected from the set and marked as the dominant region. The average residual equivalent stress value of all nodes within the potential concentration area is taken as the average residual equivalent stress value of the potential concentration area.

[0021] In step 1, by acquiring the process parameters, fatigue performance parameters, and working load spectrum of the weld joint, and establishing a finite element model based on the joint geometry, the process parameters are applied as thermal load boundary conditions to the weld area to simulate the welding heating and natural cooling process, thereby obtaining the initial residual stress distribution when cooled to room temperature. Based on this, by setting an equivalent stress threshold based on the material yield strength, stress concentration nodes are screened through all nodes of the model, and the mesh elements containing these nodes are clustered to form multiple potential concentration areas. Finally, the area with the highest average residual equivalent stress value is selected and labeled as the dominant area. Step 1, through finite element simulation, can accurately reproduce the thermal stress during the welding process. - By analyzing structural coupling behavior, an initial residual stress field consistent with physical reality is obtained, providing reliable basic data for subsequent fatigue analysis. Secondly, through threshold filtering and cluster analysis, the key regions most likely to experience fatigue failure are automatically identified and focused on as dominant regions from the global model, avoiding redundant calculations across the entire model and significantly improving the computational efficiency of subsequent evolution simulation and damage analysis. Simultaneously, the dominant region is identified based on the clear criterion of the highest average residual equivalent stress value, ensuring that the region of interest has the highest initial stress level, consistent with the physical law that fatigue failure often begins in high-stress areas. This lays a solid foundation for the accuracy and relevance of the entire life prediction method.

[0022] Step 2: Based on the stress gradient distribution and average level of the initial residual stress in the dominant region, calculate the stress sensitivity index, which characterizes the sensitivity of the dominant region to stress evolution, and set the cyclic load interval that is negatively correlated with the stress sensitivity index. In this embodiment, within the calibrated dominant region, the residual equivalent stress value at each element node is extracted, and the average residual equivalent stress value within the dominant region is calculated as the average level of the initial residual stress within that region. ; For any unit node within the dominant region Based on its node coordinates The residual equivalent stress values ​​of adjacent elements are used to calculate the stress gradient vector components at the element node coordinates using the central difference method. ;in, For the index of the unit nodes within the dominant region; Among them, calculation The formula used is as follows: In the formula, , They are respectively with the unit node exist The residual equivalent stress at two adjacent element nodes in the direction For adjacent unit nodes in Distance in direction; Similarly, , The calculation formula is as follows: In the formula, , They are respectively with the unit node exist The residual equivalent stress at two adjacent element nodes in the direction For adjacent unit nodes in Distance in direction; , They are respectively with the unit node exist The residual equivalent stress at two adjacent element nodes in the direction For adjacent unit nodes in Distance in direction; Then the stress gradient modulus at the node coordinates of this element for: The arithmetic mean of the stress gradient modulus at all element node coordinates within the dominant region is used as the stress gradient modulus to quantify the stress gradient distribution characteristics of that region. ; Using the central difference method, based on the nodal coordinates and the residual equivalent stress values ​​of adjacent elements, the partial derivatives of the stress at the nodal point in the three coordinate directions are solved. Then, the square root of the sum of their squares is calculated to obtain the stress gradient modulus at that nodal location, which characterizes the degree of spatial variation of stress at that point. Furthermore, the arithmetic mean of the stress gradient moduli at all element nodes within the dominant region is taken to obtain the regional stress gradient modulus. As a characteristic parameter for quantifying the non-uniformity of stress distribution in the entire dominant region, the larger the value, the more non-uniform the stress distribution in the region and the more significant the local stress concentration phenomenon.

[0023] Based on the stress gradient distribution and the average level of initial residual stress in the dominant region, the stress sensitivity index, which characterizes the sensitivity of this region to stress evolution, is calculated using the following formula: In the formula, It is the stress sensitivity index; For reference stress; The preset feature length; For this formula, the stress sensitivity index This value is used to characterize the sensitivity of the dominant region of a welded joint to the evolution of residual stress under cyclic loading. A higher value indicates a more severe response of the residual stress in that region to external loads and local plastic deformation, a faster evolution rate, and the potential for significant relaxation in the early stages of fatigue loading; conversely, a lower value indicates a more severe response. The smaller the value, the more stable the residual stress state in the region, the more gradual the evolution process, and the contribution to fatigue damage is mainly due to the initial stress. In the formula, This reflects the initial stress level in the region. Higher stress levels indicate the material is closer to its yield limit, making it more susceptible to localized plastic flow under external cyclic loading, thus accelerating residual stress relaxation. Stress gradient modulus It characterizes the degree of drastic change in stress in space. The larger the gradient, the more uneven the stress distribution. The deformation incoordination between high-stress areas and low-stress areas will induce additional plastic strain and promote stress redistribution. This represents the effective range of the stress gradient effect in the region. The larger the value, the wider the influence area of ​​the high gradient region and the larger the range of plastic accumulation. The three factors together determine the driving force and scale of residual stress evolution. This formula combines the stress level with the stress gradient effect in a product form, the first term... The normalized stress level reflects how close the initial stress is to the material's reference stress; the second term The normalized stress gradient effect reflects the contribution of stress non-uniformity and its range of action to the evolution. The multiplication of the two factors takes into account both the influence of stress amplitude on plastic initiation and the amplification effect of stress distribution pattern on the evolution process. This conforms to the basic law of stress-driven plastic deformation and stress relaxation caused by the accumulation of plastic deformation in elastoplastic mechanics, and can comprehensively reflect the residual stress evolution potential of the dominant region.

[0024] Table 1: Statistics of Stress Sensitivity Index It should be noted that the regional average residual stress, reference stress, regional stress gradient modulus, preset characteristic length, and stress sensitivity index mentioned in Table 1 correspond to the following respectively: , , , and ; according to Figures 2-4 Based on the analysis of the 15 sets of data in Table 1, it can be seen that the stress sensitivity index... Average residual stress in the dominant region Stress gradient modulus and preset feature length The combined effects of these factors reflect the sensitivity of the region to the evolution of residual stress under cyclic loading. Figure 2 The image shows a dual Y-axis plot of the ratio of regional average residual stress to reference stress versus the stress sensitivity index, based on the data in Table 1. It illustrates the relationship between the ratio of average residual stress to reference stress and the stress sensitivity index. As can be seen from the figure, with... Compared to The increase, The upward trend indicates that regions with high residual stress levels are more sensitive to external loads, and the residual stress is more likely to evolve and relax. Figure 3 This is a dual Y-axis image plotted based on the data in Table 1, showing the product of the regional stress gradient modulus and the preset characteristic length with the stress sensitivity index. It presents the regional stress gradient modulus. With the preset feature length The correlation between the product of stress gradient and stress sensitivity index shows that the greater the stress gradient and the longer the characteristic length, the higher the stress sensitivity index value, which means that the uneven distribution of stress exacerbates the local plastic accumulation, thereby accelerating the evolution of residual stress. Figure 4 The three-dimensional scatter plot further comprehensively demonstrates... and right The combined effect of these two factors verifies their sensitivity to stress indices. Synergistic effect; In summary, the stress sensitivity index It can effectively quantify the residual stress evolution potential of the dominant region, providing a basis for subsequent dynamic division of cyclic load intervals and refined simulation of the residual stress evolution process.

[0025] Determine the allowable range of values ​​for the cyclic load interval. ,in The preset minimum cyclic load interval, The preset maximum cyclic load interval; the cyclic load interval is set according to the following formula. : in, and These are the preset lower and upper reference values ​​for the stress sensitivity index, respectively. Cyclic load interval This is used to characterize the time interval between two consecutive applications of cyclic loading to the welded joint and data acquisition during fatigue life prediction. Data acquisition includes stress-strain data extraction and stress field updating. The smaller the value, the shorter the time interval between two adjacent data acquisitions, and the higher the sensitivity to data acquisition. Such high-frequency acquisition can more accurately track the rapid evolution of residual stress and ensure that key changes are not missed in areas with high stress sensitivity index. Conversely, the larger the value, the lower the acquisition frequency, which is suitable for areas with slow evolution.

[0026] Stress sensitivity index This reflects the severity of the response of the residual stress in the dominant region to external loads. A larger value indicates a more rapid evolution of residual stress and a more significant relaxation in the region. This suggests that a substantial stress redistribution may occur in the early stages of fatigue loading, thus requiring a smaller cyclic loading interval. Dense sampling is performed to ensure accurate capture of key changes during evolution; conversely, insufficient sampling... The smaller the value, the more stable the residual stress state and the slower its evolution; therefore, it can be appropriately increased. To improve computational efficiency; The calculation formula uses linear interpolation to calculate the stress sensitivity index. Mapped to a preset cyclic load interval range inside, when Take the minimum value hour, Take the maximum value ;when Take the maximum value hour, Take the minimum value The intermediate values ​​are then linearly interpolated proportionally. This design ensures that... Follow The monotonically decreasing negative correlation will... By limiting the intervals within a reasonable range, the loss of evolutionary information due to excessively large intervals or the waste of computing resources due to excessively small intervals are avoided, thus achieving a balance between computational accuracy and efficiency.

[0027] In step 2, based on the identified dominant region, the average residual stress is calculated by extracting the residual equivalent stress values ​​of each element node. The stress gradient vector components at the nodes are solved using the central difference method, thereby obtaining the stress gradient modulus of each node. Then, the arithmetic mean of these values ​​is taken as the regional stress gradient modulus to quantify the non-uniformity of stress distribution throughout the dominant region. Based on this, comprehensive and and preset feature length Constructing a stress sensitivity index and based on With cyclic load interval The negative correlation is dynamically set by using a linear interpolation formula to determine the dominant region. The beneficial effects of this step are: firstly, the stress sensitivity index... By comprehensively considering the initial stress level and stress gradient effect, the sensitivity of the dominant region to the evolution of residual stress under cyclic loading can be quantified. A larger value indicates a more drastic evolution, providing a quantitative basis for subsequent adaptive segmentation; secondly, according to Dynamic settings This implements an adaptive computing strategy that increases sampling density as evolution becomes more drastic, i.e., using smaller sampling density in highly sensitive regions. To precisely capture the rapid evolution of residual stress, a larger [scale / size] is used in low-sensitivity regions. This improves computational efficiency, thereby effectively balancing computational costs while ensuring prediction accuracy.

[0028] Step 3: Divide the cyclic load application into stages according to the cyclic load interval, and then apply the cyclic load to the finite element model in stages. After each stage, extract the stress and strain data of the dominant region; wherein, the initial residual stress distribution is calibrated as the initial stress field of the first stage. In this embodiment, based on the maximum and minimum nominal stresses in the working load spectrum, a cyclic surface force load that varies with the load frequency is applied to the surface in the finite element model corresponding to the actual working force of the welded joint, according to the load ratio and load frequency, to simulate the actual working load; wherein, the load ratio refers to the ratio of the minimum nominal stress to the maximum nominal stress; Each cyclic load application process is defined as an independent stage, and the interval between two adjacent cyclic load applications is the cyclic load interval. The initial residual stress distribution is used as the initial stress field of the first stage. Within each stage, the same number of cyclic loads are continuously applied to the finite element model to simulate the fatigue loading process of that stage. After the last cyclic load of the stage is completed, the load application is immediately paused. The stress tensor components and plastic strain tensor components of each element node in the dominant region at this moment are extracted from the finite element solver. Based on the stress tensor components, the residual equivalent stress value of each node is calculated according to the Von Mises criterion. Based on the plastic strain tensor components, the equivalent plastic strain of each node is calculated according to the equivalent plastic strain formula. The calculated residual equivalent stress value and equivalent plastic strain of each node are recorded as the stress-strain data of each node in that stage.

[0029] By using the initial residual stress distribution as the initial stress field for the first stage and continuously applying cyclic loads to the finite element model according to dynamically set cyclic load intervals, numerical simulation of the fatigue process within each loading stage was achieved. Immediately after the end of each stage, the stress tensor components and plastic strain tensor components of all element nodes in the dominant region were extracted, and the residual equivalent stress value was calculated based on the Von Mises criterion, and the equivalent plastic strain was calculated according to the equivalent plastic strain formula, thereby obtaining the stress and strain data of each node at the end of the stage. This process not only provides raw data for subsequent calculation of the equivalent plastic strain increment and equivalent stress relaxation, but more importantly, by extracting stress and strain information stage by stage, the stress and plastic strain state of the dominant region under cyclic loading can be captured in real time, laying the foundation for the iterative update of the stress field based on the residual stress relaxation factor, and ensuring the continuity and accuracy of the residual stress evolution simulation.

[0030] Step 4: Determine the residual stress relaxation factor based on the stress and strain data of the current stage, use the residual stress relaxation factor to perform finite element iterative update on the initial stress field of the current stage, obtain the residual stress distribution at the end of the current stage, and use it as the initial stress field of the next stage. Complete the calculation of each stage in sequence to obtain the evolution data of residual stress. In this embodiment, for any stage Based on the stress-strain data of the dominant region, the equivalent plastic strain increment and equivalent stress relaxation amount of the dominant region at this stage are calculated. In the formula, and The first The equivalent plastic strain increment and equivalent stress relaxation amount at each stage; , The first The arithmetic mean of the equivalent plastic strain of all element nodes in the dominant region at the beginning and end of each stage; and The first The arithmetic mean of the residual equivalent stress values ​​of all unit nodes in the dominant region at the beginning and end of each stage; For the index of stages, ; For any stage Equivalent plastic strain increment Defined as the difference between the arithmetic mean of the equivalent plastic strain of all element nodes in the dominant region at the end of this stage and at the beginning, it is used to characterize the degree of cumulative plastic deformation in the dominant region during this stage; equivalent stress relaxation. Defined as the difference between the arithmetic mean of the equivalent stress at all element nodes in the dominant region at the beginning and end of the stage, it is used to characterize the attenuation of residual stress in the stage; together, they reflect the residual stress relaxation behavior in the dominant region caused by cyclic plastic deformation in each loading stage.

[0031] Calculate the first according to the following formula. Residual stress relaxation factor at each stage : in, The yield strength of the material; In the formula for calculating the residual stress relaxation factor, Used to characterize the in Within each loading stage, the degree of residual stress relaxation in the dominant region caused by cyclic plastic deformation is as follows: the larger the value, the greater the stress reduction caused by a unit increase in plastic strain, indicating that the residual stress relaxation is more significant in this stage; conversely, the smaller the value, the more limited the attenuation of residual stress is, and the stress state is relatively stable, even if plastic deformation occurs. Equivalent stress relaxation This reflects the actual decrease in residual stress during this stage; the larger the value, the more directly it leads to... Increase; equivalent plastic strain increment This characterizes the degree of plastic accumulation within this stage. Under the same conditions, the larger the increment of plastic strain, the more diluted the stress relaxation effect corresponding to unit strain. The yield strength of the material tends to decrease. As a normalization benchmark, it reflects the material's ability to resist plastic deformation. The higher the yield strength, the greater the plastic strain required to achieve the same stress relaxation. The smaller; This formula represents the equivalent stress relaxation. With material yield strength and equivalent plastic strain increment The product of these factors is related, and its physical basis lies in the fact that the relaxation of residual stress is essentially a process of plastic deformation releasing elastic strain energy. The stress reduction should be proportional to the increase in plastic strain, and the proportionality coefficient is constrained by the material's yield strength. The stress relaxation effect was normalized, making It becomes a dimensionless parameter, which can uniformly measure the relaxation strength under different stress levels and different degrees of plastic strain, and conforms to the basic principles of stress-strain relationship in plasticity mechanics.

[0032] Based on residual stress relaxation factor , for the The initial stress field of each stage is updated: the stress tensor components of each element node in the dominant region at the beginning of that stage are updated. Multiply by the reduction factor This yields the updated stress tensor components of the node at the end of this phase. ;in, This represents the stress tensor of the element node at the beginning of the m-th stage, corresponding to the coordinate axis. The amount, The subscript index of the component is used to represent the specific component of the stress tensor; This update operation is synchronously applied to all cell nodes in the dominant region, thereby obtaining the first... The overall residual stress distribution at the end of each stage is then used as the initial stress field for the next stage, and the above calculation process is repeated until all stages are completed, thus obtaining the evolution data of residual stress throughout the entire fatigue loading process.

[0033] Step 5: Based on the evolution data of residual stress, the working load spectrum of the welded joint and fatigue performance parameters, the fatigue damage amount of each stage is extracted and accumulated through the damage accumulation model. When the accumulated damage amount reaches the preset critical value, the corresponding total number of cycles is output as the predicted fatigue life of the welded joint. In this embodiment, based on the residual stress distribution evolution data, for each stage, the residual equivalent stress value of each unit node in the dominant region at the end of that stage is obtained. Combined with the load amplitude in the working load spectrum, the stress cycle characteristics of each unit node in that stage are calculated. The stress cycle characteristics include the maximum cycle stress, the minimum cycle stress, and the average cycle stress. The maximum cycle stress is obtained by adding the current residual equivalent stress value of the node to the maximum nominal stress value; the minimum cycle stress is obtained by adding the current residual equivalent stress value of the node to the minimum nominal stress value; and the average cycle stress is obtained by taking the arithmetic mean of the calculated maximum cycle stress and the minimum cycle stress. The calculated stress cycle characteristics, combined with the fatigue performance parameters, are used to calculate the fatigue damage of each node element at each stage using a preset damage accumulation model. The damage of all node elements in the dominant region at each stage is summed to obtain the overall damage for that stage. The damage of each stage is accumulated sequentially to obtain the cumulative damage. When the cumulative damage reaches a preset critical value, the total number of cycles loaded at that time is output as the predicted fatigue life of the welded joint. The damage accumulation model is based on the Miner criterion of linear damage accumulation, which assumes that the fatigue damage of the material at each stress level is proportional to the corresponding number of cycles, and that the damage can be linearly superimposed. Fatigue failure occurs when the total damage reaches 1.

[0034] In step 5, based on the residual stress evolution data obtained in step 4, for each loading stage, the residual equivalent stress value of each unit node in the dominant region at the end of the stage is obtained, and combined with the load amplitude in the working load spectrum, the stress cycle characteristics of each node in the stage are calculated; then, these stress cycle characteristics and material fatigue performance parameters are substituted into the preset damage accumulation model to calculate the fatigue damage of each node unit in the stage, and the damage of all node units in the dominant region is summed to obtain the overall damage of the stage. Finally, the damage of each stage is accumulated in the order of stages, and when the accumulated damage reaches the preset critical value, the corresponding total number of cycles is output as the predicted fatigue life of the welded joint. By superimposing the progressively updated residual stress with the working load, the dynamic influence of residual stress evolution on local stress cycle characteristics is realistically reflected, ensuring that the damage calculation at each stage is based on the current actual stress state, thus avoiding the errors caused by using constant residual stress for damage assessment. Secondly, a damage accumulation model is used to sum and accumulate the damage of all node elements in the dominant region, achieving a refined tracking of the entire fatigue damage evolution process. When the accumulated damage reaches a critical value, the life is output, which conforms to the physical nature of fatigue failure. Finally, step 5 organically combines the residual stress evolution data with fatigue damage theory, providing more scientific and accurate fatigue life prediction results for welded joints, effectively overcoming the prediction bias caused by ignoring the dynamic evolution of residual stress or simplifying the damage accumulation process in existing technologies.

[0035] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0036] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0037] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0038] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for predicting the fatigue life of welded joints considering the evolution of residual stress, characterized in that, include: A finite element model is established based on the geometry of the welded joint, and its process parameters are applied as thermal load boundary conditions to the weld area of ​​the finite element model. The initial residual stress distribution of the welded joint when it cools to room temperature is simulated and analyzed to screen out the dominant region. Based on the stress gradient distribution and average level of the initial residual stress in the dominant region, a stress sensitivity index characterizing the sensitivity of the dominant region to stress evolution is calculated, and a cyclic load interval negatively correlated with the stress sensitivity index is set. The cyclic load application stages are divided according to the cyclic load interval, and then the cyclic load is applied to the finite element model in stages. After each stage, the stress and strain data of the dominant region are extracted. The initial residual stress distribution is calibrated as the initial stress field of the first stage. Based on the stress and strain data of the current stage, the residual stress relaxation factor is determined. The initial stress field of the current stage is updated by finite element iteration using the residual stress relaxation factor to obtain the residual stress distribution at the end of the current stage. This is then used as the initial stress field of the next stage. The calculations of each stage are completed in sequence to obtain the evolution data of the residual stress. Based on the evolution data of residual stress, the working load spectrum of the welded joint, and fatigue performance parameters, the fatigue damage at each stage is extracted and accumulated using a damage accumulation model. When the accumulated damage reaches a preset critical value, the corresponding total number of cycles is output as the predicted fatigue life of the welded joint. Within the defined dominant region, the residual equivalent stress value at each element node is extracted, and the average residual equivalent stress value within the dominant region is calculated as the average level of the initial residual stress within that region. ; For any unit node within the dominant region Based on its node coordinates The residual equivalent stress values ​​of adjacent elements are used to calculate the stress gradient vector components at the element node coordinates using the central difference method. ;in, For the index of the unit nodes within the dominant region; Then the stress gradient modulus at the node coordinates of this element for: The arithmetic mean of the stress gradient modulus at all element node coordinates within the dominant region is used as the stress gradient modulus to quantify the stress gradient distribution characteristics of that region. ; Based on the stress gradient distribution and the average level of initial residual stress in the dominant region, the stress sensitivity index, which characterizes the sensitivity of this region to stress evolution, is calculated using the following formula: In the formula, It is the stress sensitivity index; For reference stress; The preset feature length; Determine the allowable range of values ​​for the cyclic load interval. ,in The preset minimum cyclic load interval, The preset maximum cyclic load interval; the cyclic load interval is set according to the following formula. : in, and These are the lower and upper reference values ​​for the pre-set stress sensitivity index.

2. The fatigue life prediction method for welded joints considering residual stress evolution according to claim 1, characterized in that: The process parameters include welding heat input, welding speed, welding sequence and direction, and the number and arrangement of weld layers; The fatigue performance parameters include cyclic hardening parameters or cyclic softening parameters characterizing the low-cycle fatigue behavior of the material, and fatigue strength coefficient and fatigue strength index characterizing the high-cycle fatigue behavior of the material; wherein, the cyclic hardening parameters or cyclic softening parameters are obtained through uniaxial strain-controlled fatigue tests of the material, and the fatigue strength coefficient and fatigue strength index are obtained through stress-controlled fatigue tests of the material. The working load spectrum includes load amplitude, load ratio and load frequency, wherein the load amplitude includes the maximum nominal stress and the minimum nominal stress.

3. The fatigue life prediction method for welded joints considering residual stress evolution according to claim 2, characterized in that: A finite element model was constructed based on the geometry of the welded joint. Eight-node hexahedral elements were used to mesh the finite element model, with the geometric center of each element serving as a node. The weld and heat-affected zone were meshed with a finer mesh, while the base material region was meshed with a sparse mesh. The process parameters were converted into the corresponding heat flux density of the moving heat source, heating time, and the movement path of the heat source along the weld, which were applied as transient thermal load boundary conditions to the corresponding mesh elements of the weld region in the finite element model. Subsequently, a thermo-structural coupling analysis method was used to simulate the entire process from welding heating to natural cooling to room temperature. By solving the heat conduction equation and the thermo-elastic-plastic constitutive relation, the stress components of each node of the model were extracted when cooled to room temperature, and the residual equivalent stress value was calculated. This yielded the residual equivalent stress distribution of the model when cooled to room temperature, which was then used as the initial residual stress distribution. An equivalent stress threshold is set, which is determined based on the yield strength of the material used in the welded joint. The residual equivalent stress values ​​of all nodes in the model are traversed. Nodes with residual equivalent stress values ​​exceeding the equivalent stress threshold are designated as stress concentration nodes, and the mesh elements where the stress concentration nodes are located are designated as stress concentration elements. All stress concentration elements are clustered to form multiple discontinuous regions. Each region is designated as a potential concentration area, thus forming a set of potential concentration areas. The potential concentration area with the highest average residual equivalent stress value is selected from the set and marked as the dominant region. The average residual equivalent stress value of all nodes within the potential concentration area is taken as the average residual equivalent stress value of the potential concentration area.

4. The fatigue life prediction method for welded joints considering residual stress evolution according to claim 3, characterized in that: Based on the maximum and minimum nominal stresses in the working load spectrum, cyclic surface force loads that vary with the load frequency are applied to the surface in the finite element model corresponding to the actual working force of the welded joint, according to the load ratio and load frequency, to simulate the actual working load; wherein, the load ratio refers to the ratio of the minimum nominal stress to the maximum nominal stress; Each cyclic load application process is defined as an independent stage, and the interval between two adjacent cyclic load applications is the cyclic load interval. The initial residual stress distribution is used as the initial stress field of the first stage. Within each stage, the same number of cyclic loads are continuously applied to the finite element model to simulate the fatigue loading process of that stage. After the last cyclic load of the stage is completed, the load application is immediately paused. The stress tensor components and plastic strain tensor components of each element node in the dominant region at this moment are extracted from the finite element solver. Based on the stress tensor components, the residual equivalent stress value of each node is calculated according to the Von Mises criterion. Based on the plastic strain tensor components, the equivalent plastic strain of each node is calculated according to the equivalent plastic strain formula. The calculated residual equivalent stress value and equivalent plastic strain of each node are recorded as the stress-strain data of each node in that stage.

5. The fatigue life prediction method for welded joints considering residual stress evolution according to claim 4, characterized in that: For any stage Based on the stress-strain data of the dominant region, the equivalent plastic strain increment and equivalent stress relaxation amount of the dominant region at this stage are calculated. In the formula, and The first The equivalent plastic strain increment and equivalent stress relaxation amount at each stage; , The first The arithmetic mean of the equivalent plastic strain of all element nodes in the dominant region at the beginning and end of each stage; and The first The arithmetic mean of the residual equivalent stress values ​​of all unit nodes in the dominant region at the beginning and end of each stage; For the index of stages, ; Calculate the first according to the following formula. Residual stress relaxation factor at each stage : in, The yield strength of the material; Based on residual stress relaxation factor , for the The initial stress field of each stage is updated: the stress tensor components of each element node in the dominant region at the beginning of that stage are updated. Multiply by the reduction factor This yields the updated stress tensor components of the node at the end of this phase. ;in, This represents the stress tensor of the element node at the beginning of the m-th stage, corresponding to the coordinate axis. The amount, The subscript index of the component is used to represent the specific component of the stress tensor; This update operation is synchronously applied to all cell nodes in the dominant region, thereby obtaining the first... The overall residual stress distribution at the end of each stage is then used as the initial stress field for the next stage, and the above calculation process is repeated until all stages are completed, thus obtaining the evolution data of residual stress throughout the entire fatigue loading process.

6. The fatigue life prediction method for welded joints considering residual stress evolution according to claim 5, characterized in that: Based on the residual stress distribution evolution data, for each stage, the residual equivalent stress value of each unit node in the dominant region at the end of that stage is obtained. Combined with the load amplitude in the working load spectrum, the stress cycle characteristics of each unit node in that stage are calculated. The stress cycle characteristics include the maximum cyclic stress, the minimum cyclic stress, and the average cyclic stress. The maximum cyclic stress is obtained by adding the current residual equivalent stress value of the node to the maximum nominal stress value; the minimum cyclic stress is obtained by adding the current residual equivalent stress value of the node to the minimum nominal stress value; and the average cyclic stress is obtained by taking the arithmetic mean of the calculated maximum cyclic stress and the minimum cyclic stress. The calculated stress cycle characteristics are combined with the fatigue performance parameters, and the fatigue damage of each node element in this stage is calculated using a preset damage accumulation model. The damage of all node elements in the dominant region in this stage is summed to obtain the overall damage of this stage. The damage of each stage is accumulated in the order of stages to obtain the cumulative damage. When the cumulative damage reaches a preset critical value, the total number of cycles loaded at this time is output as the predicted fatigue life of the welded joint.

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