A method for modeling and simulating a butt welded joint based on shell elements

Abstract

The application discloses a butt welding joint modeling simulation method based on shell elements, comprising the following steps: based on microhardness testing, dividing a butt welding joint sample into a weld zone, a heat affected zone and a base material zone, and calibrating hardening model parameters for each zone; establishing a shell element model, assigning the hardening model parameters to corresponding shell elements, and correcting the flow stress of the shell elements in the weld zone by the excess height, wherein the correction coefficient K is the maximum load ratio of the reserved excess height sample and the milled excess height sample; defining a nonlinear damage accumulation fracture criterion for the shell elements, wherein the equivalent plastic failure strain is a function of the stress triaxiality; and introducing a grid dependency factor to correct the equivalent plastic failure strain. The application solves the problem of bearing capacity prediction distortion of the shell element model by microhardness partitioning and excess height correction, and realizes accurate prediction of the fracture behavior under a multi-stress state by the stress triaxiality related fracture criterion and grid regularization, and is suitable for large-scale engineering simulation such as vehicle collision.

Description

Technical Field

[0001] This invention relates to the field of finite element simulation technology for the mechanical properties of welded structures, and in particular to a modeling and simulation method for butt welded joints based on shell elements. Background Technology

[0002] With the automotive, rail transportation, and aerospace industries moving towards lightweighting, aluminum alloys, due to their excellent specific strength and formability, are widely used in key load-bearing components such as vehicle body structural parts and battery pack housings. Butt welds, as the primary form of connection in aluminum alloy structures, directly affect the safety and reliability of the overall structure. Accurately predicting the mechanical response and fracture behavior of butt welds is a core requirement for industrial structural simulation design.

[0003] In engineering applications, the internal microstructure and mechanical properties of butt-welded joints undergo significant changes after being subjected to welding thermal cycles. Material softening occurs in the weld zone and heat-affected zone, reducing the hardness of the joint area. Furthermore, the geometric characteristics of the weld reinforcement on the back side cause the local stiffness and load-bearing capacity of the joint to differ from that of the base material. These factors combined result in uncertainties in the deformation behavior and failure location of butt-welded joints during actual service, posing challenges for simulation prediction.

[0004] When existing shell element simulation methods are applied to butt welded joints, they face the following challenges: The material properties of different regions within the welded joint vary, and existing modeling methods struggle to accurately describe the combined effects of these performance differences on structural load-bearing and deformation processes. This leads to a systematic discrepancy between the simulation-predicted failure location and experimental observations, limiting the reliability of simulation methods in assessing structural safety. Furthermore, within the shell element modeling framework, the simulation predictions of the welded joint's load-bearing capacity do not match experimental results, and this discrepancy cannot be eliminated by adjusting the base material parameters. Additionally, the fracture strain of the same welded joint varies significantly under different stress states, such as simple shear, uniaxial tension, plane strain, and equal biaxial tension. Existing fracture models cannot uniformly describe this fracture behavior that varies with stress state, making it difficult to meet engineering requirements in terms of simulation accuracy. Summary of the Invention

[0005] In view of the above problems, a shell element-based modeling and simulation method for butt welded joints is proposed to overcome or at least partially solve these problems, including:

[0006] Based on microhardness testing, the butt weld joint sample is divided into weld zone, heat-affected zone and base material zone, and the hardening model parameters are calibrated for the weld zone, heat-affected zone and base material zone.

[0007] Based on the geometric dimensions of the weld zone, heat-affected zone, and base metal zone, a shell element model of the butt weld joint specimen is established. The shell element model contains shell elements corresponding to the weld zone, heat-affected zone, and base metal zone. The calibrated hardening model parameters are assigned to the corresponding shell elements, and the flow stress of the shell element corresponding to the weld zone is corrected for excess height to obtain the corrected shell element model. The correction coefficient K for excess height correction is the ratio of the maximum load of the specimen with excess height retained to that of the specimen with excess height removed.

[0008] A nonlinear damage accumulation fracture criterion is defined for the shell elements in the modified shell element model, wherein the equivalent plastic failure strain is a function of stress triaxiality.

[0009] The equivalent plastic failure strain is corrected by introducing a mesh-dependent factor.

[0010] Optionally, the Swift-Hockett-Sherby hardening model is used to calibrate the hardening model parameters for the weld zone, heat-affected zone, and base metal zone. The expression of the Swift-Hockett-Sherby hardening model is as follows:

[0011]

[0012] α represents the weights of the Swift model in the hybrid SHS model; ε p The plastic strain value after removing the elastic segment data; σ y The yield strength of the material; ε0, K, n, σ s N and p are model parameters.

[0013] Optionally, the failure increment ΔD is defined in the nonlinear damage accumulation fracture criterion, and the evolution equation of the failure increment ΔD is:

[0014]

[0015] In the formula: The equivalent plastic failure strain is a function of the stress triaxiality η. is the equivalent plastic strain increment; n is the material damage coefficient, used to define the degree of nonlinear damage to the material; This is an invalid value.

[0016] Optionally, calculating the correction coefficient K includes:

[0017] Two sets of butt weld joint specimens with the same material and process were prepared. The first set retained the original weld reinforcement, while the second set had the weld reinforcement milled off and ground flat to the same thickness as the base material. Quasi-static tensile tests were performed on the two sets of specimens. The average maximum load F1 of the first set of butt weld joint specimens and the average maximum load F2 of the second set of butt weld joint specimens were extracted. The correction coefficient K = F1 / F2.

[0018] Optionally, when correcting the excess height of the flow stress of the shell element corresponding to the weld zone, the correction coefficient K is applied as a multiplier to the flow stress of the weld zone material, so that the corrected flow stress is the original flow stress multiplied by the correction coefficient K, and then the corrected flow stress is extrapolated by large strain hardening.

[0019] Optionally, the nonlinear damage accumulation fracture criterion further defines an instability coefficient increment ΔF, the evolution equation of which is:

[0020]

[0021] In the formula: Let F be the equivalent instability plastic strain under different stress states, and let F be the variable representing the material softening behavior.

[0022] Optionally, when defining a nonlinear damage accumulation fracture criterion for the shell elements in the modified shell element model, the shell elements corresponding to the base material region are calibrated separately first, and then the calibrated base material region parameters are used as boundary conditions to calibrate the shell elements corresponding to the heat-affected zone and the weld zone in sequence.

[0023] Optionally, for the portion of the base material region in the butt weld joint specimen, a uniaxial tensile test simulation model with different mesh sizes is established. Based on the load-displacement curve, the mesh dependence factor value corresponding to each mesh size is obtained by inverse parameter calculation, and the relationship curve between the mesh dependence factor and the mesh size is obtained.

[0024] Optionally, the load-displacement curve is obtained in the following manner:

[0025] Butt weld joint specimens under different stress states were subjected to quasi-static tensile testing on a universal testing machine at a tensile speed of 4.2 mm / min. Digital image correlation technology was used to record the full-field strain during the deformation process of the specimens. Five experiments were conducted for each type of specimen. The experimental data were processed to obtain the load-displacement curves under each stress state.

[0026] Optionally, the butt weld joint specimens under different stress states are of six types: R5 notched tensile specimen, R20 notched tensile specimen, R4 tensile specimen with center hole, R7.5 tensile specimen with center hole, tensile-shear mixed specimen, and simple shear specimen.

[0027] This invention divides butt-welded joint samples into weld zone, heat-affected zone, and base metal zone based on microhardness testing, and calibrates the hardening model parameters for each zone. Microhardness, as a macroscopic mechanical characterization of the material's microstructure, objectively reflects the degree of change in the original microstructure of the base metal caused by the welding thermal cycle. The resulting zone division criterion is repeatable and quantitative, ensuring that the calibration of hardening model parameters for each zone is based on the true microstructure of the material. This accurately captures the performance gradient of different regions of the welded joint, eliminating the failure location prediction bias caused by inaccurate descriptions of performance differences in existing simulation methods.

[0028] This invention also corrects the flow stress of the shell element in the weld zone by introducing a correction coefficient K. The maximum load ratio between the retained high-height sample and the milled high-height sample is used as the basis for correction. The geometric enhancement effect of the high-height is equivalently transformed into the strength enhancement at the material constitutive level. This allows the shell element model to accurately reproduce the load-bearing characteristics of the high-height joint while maintaining the planar geometric properties. This solves the problem that the simulation results of the load-bearing capacity cannot match the experiment and cannot be eliminated by adjusting the base material parameters.

[0029] This invention also defines a nonlinear damage accumulation fracture criterion in which the equivalent plastic failure strain is a function of stress triaxiality. Stress triaxiality, as a key mechanical parameter characterizing the nucleation, growth, and aggregation processes of micropores within a material, controls the ductile exhaustion rate of the material under different loading paths. Introducing it into the fracture criterion enables a single model to uniformly describe the fracture behavior under different stress states, overcoming the limitation of existing fracture models that cannot adapt to fracture prediction under multiple stress states.

[0030] This invention also introduces a mesh-dependent factor to correct the equivalent plastic failure strain. Different mesh sizes result in varying energy dissipation when simulating strain localization. By establishing a mapping relationship between mesh size and failure strain, the numerical defects of insufficient energy dissipation in coarse mesh models are compensated, ensuring the consistency of fracture prediction results under different mesh sizes. This allows the method to obtain reliable prediction results with relatively coarse meshes in large-scale engineering simulations such as vehicle collisions, achieving a balance between computational accuracy and efficiency. Attached Figure Description

[0031] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description of the present invention will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 This is a flowchart of a shell element-based modeling and simulation method for butt welded joints provided in an embodiment of the present invention;

[0033] Figure 2 This is a microhardness distribution diagram of the Al6061-T6 welded joint in Embodiment 1 of the present invention;

[0034] Figure 3 This is a true stress-strain curve diagram of Al6061-T6 in the RD and TD directions in Embodiment 1 of the present invention;

[0035] Figure 4 This is a schematic diagram of the uniaxial tensile specimen provided in Embodiment 1 of the present invention;

[0036] Figure 5 This is a schematic diagram of the plastic extrapolation (SHS model) curves in different regions in Embodiment 1 of the present invention;

[0037] Figure 6 This is a schematic diagram of the load-displacement curve of the butt weld joint with or without excess height in Embodiment 1 of the present invention;

[0038] Figure 7 This is a schematic diagram of the plastic extrapolation (SHS model) curve of the Weld region of the Al6061-T6 welded joint after correction in Embodiment 1 of the present invention;

[0039] Figure 8 This is a schematic diagram of the welded joint sample in Embodiment 2 of the present invention;

[0040] Figure 9 This is a schematic diagram of the tensile load displacement curves of different Al6061-T6 specimens in Example 2 of the present invention;

[0041] Figure 10 This is a schematic diagram of the tensile load displacement curves of the Al6061-T6 welded joint under different stress states in Embodiment 2 of the present invention.

[0042] Figure 11 This is a flowchart of parameter optimization in Embodiment 2 of the present invention;

[0043] Figure 12 This is a schematic diagram of the GISSMO fracture model parameters of Al6061-T6 in the RD and TD directions in Embodiment 2 of the present invention;

[0044] Figure 13 This is a schematic diagram of the uniaxial tensile simulation model of the Al6061-T6 welded joint under different stress states in Embodiment 2 of the present invention;

[0045] Figure 14 This is a schematic diagram of the GISSMO fracture model parameters of the Al6061-T6 butt weld joint in Embodiment 2 of the present invention;

[0046] Figure 15This is a schematic diagram of the uniaxial stretching simulation model of Al6061-T6 with different mesh sizes in Embodiment 2 of the present invention;

[0047] Figure 16 This is a schematic diagram of the mesh dependence factor curves in the RD and TD directions of Al6061-T6 in Embodiment 2 of the present invention;

[0048] Figure 17 This is a schematic diagram showing the comparison between the load-displacement experimental results and simulation results of the four-point bending experiment based on the GISSMO model in Embodiment 2 of the present invention. Detailed Implementation

[0049] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0050] Reference Figure 1 This invention provides a method for modeling and simulating butt welded joints based on shell elements, which may specifically include:

[0051] Based on microhardness testing, the butt weld joint sample is divided into weld zone, heat-affected zone and base material zone, and the hardening model parameters are calibrated for the weld zone, heat-affected zone and base material zone.

[0052] Based on the geometric dimensions of the weld zone, heat-affected zone, and base metal zone, a shell element model of the butt weld joint specimen is established. The shell element model contains shell elements corresponding to the weld zone, heat-affected zone, and base metal zone. The calibrated hardening model parameters are assigned to the corresponding shell elements, and the flow stress of the shell element corresponding to the weld zone is corrected for excess height to obtain the corrected shell element model. The correction coefficient K for excess height correction is the ratio of the maximum load of the specimen with excess height retained to that of the specimen with excess height removed.

[0053] A nonlinear damage accumulation fracture criterion is defined for the shell elements in the modified shell element model, wherein the equivalent plastic failure strain is a function of stress triaxiality.

[0054] The equivalent plastic failure strain is corrected by introducing a mesh-dependent factor.

[0055] In practice, a butt weld joint sample can be obtained first. A hardness test sample is then cut perpendicular to the weld direction. The cut surface is ground and polished to ensure the surface roughness of the test section meets the requirements for microhardness testing. A microhardness tester is used to test the weld section. During testing, the indenter is pressed in perpendicular to the section, with a load of 0.5 kgf and a holding time of 10 seconds. The test path is perpendicular to the weld direction, starting at the weld center. Indentation tests are performed point by point at fixed intervals along both sides. The spacing between adjacent test points is determined based on the expected weld width. The spacing between test points is smaller in areas close to the weld center than in areas far from the weld center to capture the details of hardness changes in the weld zone and heat-affected zone. After recording the hardness values ​​point by point, a hardness distribution curve is plotted with the distance from the weld center as the x-axis and the hardness value as the y-axis.

[0056] Data processing is performed on the hardness distribution curve to determine the region boundaries. The hardness distribution curve is smoothed to remove signal noise caused by local microstructural inhomogeneities or testing errors during the indentation test. After smoothing, the first derivative of the hardness distribution curve, i.e., the rate of change of hardness value with distance, is calculated. Regions with an absolute value of the hardness change rate close to zero are identified as hardness stable regions, including the stable region with the lowest hardness at the weld center and the stable region with the highest hardness in the base metal region. Regions with an absolute value of the hardness change rate greater than zero are identified as hardness transition regions. The boundary between the hardness stable region at the weld center and the hardness transition region is the boundary between the weld region and the heat-affected zone (HAZ), and the boundary between the hardness transition region and the hardness stable region in the base metal region is the boundary between the HAZ and the base metal region.

[0057] To further pinpoint the boundary, 3 to 5 data points can be taken on each side of the initially determined boundary point and fitted with straight lines. The slope of the fitted line on the weld zone side is close to zero, while the slope of the fitted line on the heat-affected zone side is larger. The intersection of the fitted lines on both sides is calculated; this intersection point is the final boundary between the weld zone and the heat-affected zone on that side. The boundary between the heat-affected zone and the base metal zone is determined in the same way. In the hardness distribution curve, the range between the boundaries of the two heat-affected zones and the base metal zone includes both the weld zone and the two heat-affected zones; the range between the boundaries of the two weld zones and the heat-affected zone is the weld zone itself.

[0058] Hardening model parameters were calibrated for each region. Due to the limited width of the weld zone and heat-affected zone, it was impossible to directly cut standard tensile specimens containing only the weld zone or only the heat-affected zone from the butt weld joint specimens. Therefore, integral tensile specimens of the weld joint, including the weld zone, heat-affected zone, and base metal zone, were prepared. The tensile specimens were dog-bone shaped, with the weld located in the middle of the parallel segment of the specimen and perpendicular to the tensile direction. Random speckle patterns were prepared on the specimen surface. The speckles consisted of randomly distributed black and white microparticles. The size of the speckle particles needed to be clearly distinguishable in a single frame image of the digital image acquisition device, and the spacing between the particles needed to be sufficient for the relevant matching algorithm to distinguish adjacent particles. During speckle preparation, it was ensured that the speckles were firmly attached to the specimen surface, and that the speckles deformed synchronously with the specimen surface during tensile deformation without falling off.

[0059] Quasi-static uniaxial tensile tests were conducted on the integral tensile specimens of the welded joints. During the tensile test, speckle images of the specimen surface were continuously captured at a fixed frame rate using an image acquisition device to obtain a speckle image sequence of the entire tensile process. The undeformed initial image was used as the reference image, and the deformed images at each moment were used as the target images. Sub-regions centered on each pixel were selected in both the reference and target images. The gray-level distribution of the sub-regions was matched and calculated using a correlation function. The position in the target image that best matches the gray-level distribution of the reference sub-region was searched to determine the spatial coordinate changes of each pixel before and after deformation, thus obtaining the full-field displacement distribution of the specimen surface. Spatial differentiation was performed on the displacement field to obtain the strain field distribution.

[0060] In the strain field data obtained by digital image correlation technology, virtual extensometers are deployed in each region. Virtual extensometers in the weld zone are placed in the center of the weld; those in the heat-affected zone (HAZ) are placed within the HAZ of the hardness distribution curve; and those in the base metal zone are placed within the base metal zone of the hardness distribution curve. The gauge length of the virtual extensometers is determined based on the width of the corresponding region, ensuring that the virtual extensometers are completely within their respective areas. Each virtual extensometer records the average strain change in its region during the tensile process. Combined with the real-time load value output from the single tensile testing machine, load-strain data for each region is obtained. During the uniform plastic deformation stage, the load value is divided by the original cross-sectional area of ​​the specimen to obtain the engineering stress. The strain recorded by the virtual extensometers in each region is used as the engineering strain for that region. The true stress and true strain for each region are calculated, and these are obtained through engineering stress and engineering strain conversion.

[0061] Based on the obtained real stress-strain curves of each region, the hardening model parameters of each region are determined by fitting experimental data. The fitting process uses multiple sets of initial parameter values ​​for iterative calculation. Repeated experimental data of different welded joint specimens are used as the validation set. The parameter combination that minimizes the average deviation between the predicted curve and the validation set experimental curve is selected as the final calibration result to ensure that the hardening model can describe the plastic flow behavior of each region within a large strain range.

[0062] Based on the geometric dimensions of the weld zone, heat-affected zone (HAZ), and base metal zone, a shell element model of the butt-welded joint specimen was established in finite element software. The width of the weld zone was determined by the distance between the weld zone and the HAZ boundary in the hardness distribution curve, and the width of the HAZ was determined by the distance between the HAZ and the base metal boundary in the hardness distribution curve and the weld zone and the HAZ boundary. The shell element model was constructed based on the neutral plane of each region, with the neutral plane located at half the thickness of the specimen. The model distinguishes the weld zone, HAZ, and base metal zone by sets or groups of shell elements, and shared nodes are used at the boundaries between regions to ensure displacement continuity. The calibrated hardening model parameters were assigned to the corresponding shell elements of the weld zone, HAZ, and base metal zone in the form of material cards.

[0063] The shell elements corresponding to the weld zone undergo reinforcement correction. The weld reinforcement on the back side of the weld joint specimen causes the cross-sectional area of ​​the joint in the weld region to be larger than that in the base metal region. Under tensile load, the actual stress in the weld region is lower than the nominal stress calculated based on the base metal thickness. The geometry of the reinforcement alters the stress distribution in the weld region, creating a stress concentration effect at the weld-base metal interface. Simultaneously, it constrains the material in the weld region, suppressing plastic deformation, resulting in an overall enhanced load-bearing capacity of the joint. Within the shell element modeling framework, the shell elements are modeled based on neutral surfaces and have a constant thickness, making it impossible to geometrically describe the local thickening characteristics of the weld reinforcement.

[0064] The correction factor K is the ratio of the maximum load of the specimen with retained excess height to that of the specimen with milled excess height. This correction factor K is used to scale the flow stress of the shell element corresponding to the weld zone, making the corrected flow stress K times the original flow stress. After the flow stress correction, large strain hardening extrapolation is performed, extending the hardening curve, which originally only covered the uniform plastic deformation stage, to a larger strain range. This is because after the uniform plastic deformation stage in the tensile test data, local necking may have occurred in the specimen. However, due to the constraint effect caused by the excess height in the weld area, the equivalent plastic strain in the actual load-bearing process may exceed the strain range corresponding to the uniform elongation. The hardening curve based solely on the experimental data range cannot describe the material response in this stage; extrapolation is needed to obtain the flow stress within a large strain range. After excess height correction, the shell element model, while maintaining the neutral plane geometry, effectively reflects the enhancing effect of the weld excess height on the load-bearing capacity through the strength improvement at the material constitutive level.

[0065] A nonlinear damage accumulation fracture criterion is defined for the shell elements in the modified shell element model. This criterion describes the material's damage behavior by defining external variables. These external variables range from zero to a preset failure threshold of 1. The initial value of the external variables is zero, indicating that the material is in an undamaged state. As plastic deformation proceeds, the external variables are accumulated incrementally according to an accumulation rule. The increment value of each step depends on the current stress state, the equivalent plastic strain increment, and the accumulated external variable values.

[0066] Since damage is an irreversible process of gradual accumulation of micro-defects within a material, the accumulation rule of external variables reflects the nonlinear characteristics of damage: in the early stages of deformation, the micropores inside the material are in the nucleation stage, and the damage accumulation rate is relatively low; as deformation continues, the micropores enter the growth and coalescence stage, and the damage accumulation rate accelerates. The increase in the value of external variables has an amplifying effect on the incremental value of subsequent incremental steps. When the accumulation of external variables reaches the failure threshold, the shell element is determined to be failed and deleted from subsequent calculations.

[0067] The equivalent plastic failure strain is a function of stress triaxiality, which is the ratio of hydrostatic stress to equivalent stress, reflecting the relative proportion of volume change to shape change in a material under stress. Different stress states correspond to different values ​​of stress triaxiality: the stress triaxiality in uniaxial tension is approximately 1 / 3, in simple shear is approximately 0, and in iso-biaxial tension is approximately 2 / 3. At the microscale, stress triaxiality controls the rate of nucleation, growth, and aggregation of micropores within the material: under high stress triaxiality, the hydrostatic tensile stress component is large, promoting rapid growth of micropores, accelerating ductility depletion, and reducing the equivalent plastic failure strain; under low stress triaxiality or negative stress triaxiality, the hydrostatic tensile stress component is small or is compressive stress, inhibiting micropore growth, slowing ductility depletion, and increasing the equivalent plastic failure strain.

[0068] The equivalent plastic failure strain is defined as a function of stress triaxiality, so that the same nonlinear damage accumulation fracture criterion uses the equivalent plastic failure strain value corresponding to the stress state to determine failure under different load modes, thereby describing the fracture behavior of materials under different stress states such as simple shear, uniaxial tension, plane strain, and equal biaxial tension.

[0069] The functional relationship between equivalent plastic failure strain and stress triaxiality can be established as follows: Fracture tests are conducted on specimens with various geometries, each with a different stress triaxiality value at the fracture site, determined through finite element method (FEM) simulation. The surface strain field of each specimen is recorded using digital image correlation (DIC) technology from the onset of deformation to fracture. A reference region is selected near the fracture site, and the equivalent plastic strain variation with loading within this region is extracted. When a sudden load drop occurs in the load-displacement curve due to fracture, the equivalent plastic strain value reached in the reference region at that moment is determined as the equivalent plastic failure strain value corresponding to that stress triaxiality. This process is repeated for each stress triaxiality value to obtain multiple sets of data points on stress triaxiality and equivalent plastic failure strain. The functional relationship between equivalent plastic failure strain and stress triaxiality is then established through interpolation or fitting, ensuring that the corresponding equivalent plastic failure strain value can be obtained for any stress triaxiality value.

[0070] In one or more embodiments of the present invention, the hardening model parameters for the weld zone, heat-affected zone, and base metal zone are calibrated using the Swift-Hockett-Sherby hardening model, the expression of which is:

[0071]

[0072] α represents the weights of the Swift model in the hybrid SHS model; ε p The plastic strain value after removing the elastic segment data; σy The yield strength of the material; ε0, K, n, σ s N and p are model parameters.

[0073] When calibrating the above model parameters, the model was fitted based on the actual stress-strain curves obtained by combining digital image correlation technology with single-stretcher load data for each region. First, the elastic segment data was removed from the actual stress-strain curves. The elastic segment was determined through linear regression, with the slope of the initial linear segment of the stress-strain curve used as the elastic modulus. The endpoint of the elastic segment was determined by gradually increasing the number of data points and calculating the goodness of fit of the linear fit. After removing the elastic segment, the plastic strain ε was obtained. p The set of data points corresponding to the flow stress. Yield strength σ y The stress value corresponding to a plastic strain offset of 0.2% is taken from the actual stress-strain curve as the yield strength.

[0074] The hybrid Swift-Hockett-Sherby hardening model consists of a linear combination of two major terms. The first term is a power-law-based hardening term, describing the flow stress as it increases power-lawfully with increasing plastic strain. This term describes the continuous hardening behavior of the material during the uniform plastic deformation stage. The second term is a hardening term based on an exponentially approaching saturation relationship, describing the flow stress as it increases from the yield strength σ. y Initially, the flow stress approaches saturation exponentially with increasing plastic strain. At higher plastic strains, the flow stress gradually stabilizes, describing the decline in hardening capacity in the later stages of deformation due to microscopic mechanisms such as dislocation density saturation and dynamic recovery. The mixed weighting coefficient α controls the contribution ratio of the first and second major terms to the total flow stress. α ranges from 0 to 1; a larger α value indicates a greater contribution from the power-law hardening term, and a more significant sustained hardening trend in the later stages of deformation. Conversely, a smaller α value indicates a greater contribution from the exponentially approaching saturation hardening term, and a more significant hardening saturation trend in the later stages of deformation.

[0075] During the calibration process, the hybrid Swift-Hockett-Sherby hardening model has eight undetermined parameters. A step-by-step fitting strategy can be used to determine the values ​​of each parameter. Yield strength σ yData is directly read from the actual stress-strain curve and not used as a fitting variable. The initial value of the mixed weighting coefficient α is set to 0.5. Data points from the plastic segment of the actual stress-strain curve are substituted into the mixed model expression, and a nonlinear least squares optimization algorithm is used to iteratively adjust the values ​​of other model parameters to minimize the sum of squared residuals between the model-predicted flow stress values ​​and the experimentally obtained flow stress values. During the iteration process, physical rationality constraints are imposed on the parameters. These constraints are achieved by setting search boundaries for the parameters; when the trial values ​​of the parameters exceed the constraint boundaries during iteration, they are automatically pulled back within the boundary range.

[0076] In the above fitting process, the value of α is fixed at 0.5. After fitting, the obtained model parameter values ​​are fixed, and the mixed weight coefficient α is used as a single variable for code optimization. The value of α is changed in a preset step size within the interval 0 to 1. For each α value, the root mean square deviation between the model prediction curve and the experimental curve is calculated, and the curve of the root mean square deviation as a function of α is plotted. The α value that minimizes the root mean square deviation is selected as the final calibrated mixed weight coefficient. If the minimum root mean square deviation occurs near the endpoint of the α interval, the scanning range is expanded or a second scan is performed near that endpoint with a smaller step size to obtain the globally optimal α value. The above calibration process is performed on the weld zone, heat-affected zone, and base material zone respectively to obtain independent hardening model parameters for different regions. The calibrated hardening model parameters for each region are used to define the material properties of the corresponding regions in the shell element model.

[0077] In one or more embodiments of the present invention, the failure increment ΔD is defined in the nonlinear damage accumulation fracture criterion, and the evolution equation of the failure increment ΔD is:

[0078]

[0079] In the formula: The equivalent plastic failure strain is a function of the stress triaxiality η. is the equivalent plastic strain increment; n is the material damage coefficient, used to define the degree of nonlinear damage to the material; This is an invalid value.

[0080] The external variable D is used to describe the damage behavior of the material and is not coupled to the material's constitutive model. The value of external variable D ranges from 0 to 1, with an initial value of zero, indicating that the material is in an undamaged state and has not deformed. As the material deformation increases, the value of D continuously increases. When the accumulated value of external variable D reaches 1, it indicates that the material has failed at that point, and the shell element is deleted in the finite element simulation.

[0081] The material damage coefficient *n* controls the nonlinearity of damage accumulation. When *n* is greater than 1, the failure increment *ΔD* grows slowly in the early stages of damage. As the value of the external variable *D* increases, the growth rate of *ΔD* gradually accelerates, exhibiting characteristics of accelerated accumulation in the later stages of damage. When *n* is equal to 1, the failure increment *ΔD* is independent of the value of the external variable *D*, and damage accumulation shows a linear relationship. When *n* is less than 1, the failure increment *ΔD* grows rapidly in the early stages of damage. As the value of the external variable *D* increases, the growth rate of *ΔD* gradually slows down. For each region of the aluminum alloy butt weld joint, the material damage coefficient *n* is back-calibrated using experimental data, with the *n* values ​​for the weld zone, heat-affected zone, and base metal zone calibrated independently.

[0082] The equivalent plastic failure strain is a function of the stress triaxiality η, reflecting the equivalent plastic strain threshold corresponding to the ductility exhaustion of the material under different stress states. The stress triaxiality η is the ratio of hydrostatic stress to equivalent stress, characterizing the relative magnitude of the volume change component and the shape change component in the stress state of a material element. The value of the stress triaxiality η differs under different stress states. Under simple shear, the stress triaxiality η is approximately 0; under uniaxial tension, the stress triaxiality η is approximately 1 / 3; under plane strain tension, the stress triaxiality η is greater than that under uniaxial tension; and under equal biaxial tension, the stress triaxiality η is approximately 2 / 3. The equivalent plastic failure strain decreases with increasing stress triaxiality η. The physical mechanism is as follows: when stress triaxiality η is high, the hydrostatic tensile stress component is large, promoting the nucleation and growth of micropores inside the material, accelerating the rate of micropore aggregation and crack formation, accelerating the ductility depletion of the material, and decreasing the equivalent plastic failure strain. When stress triaxiality η is low or negative, the hydrostatic tensile stress component is small or compressive stress, inhibiting micropore growth, slowing down the ductility depletion of the material, and increasing the equivalent plastic failure strain. When calibrating the functional relationship between equivalent plastic failure strain and stress triaxiality η, after obtaining the equivalent plastic failure strain value corresponding to each stress state, multiple sets of stress triaxiality and equivalent plastic failure strain data points are interpolated to establish a functional relationship. This allows the equivalent plastic failure strain to be determined based on the current stress triaxiality η value of the shell element calculated at each increment step, using this functional relationship, and then the failure increment ΔD for that increment step can be calculated.

[0083] In each incremental step of the finite element simulation, the execution flow of the nonlinear damage accumulation fracture criterion is as follows: calculate the equivalent stress and hydrostatic stress of the shell element in the current incremental step to obtain the stress triaxiality η value; determine the equivalent plastic failure strain based on the stress triaxiality η value through a functional relationship; read the equivalent plastic strain increment of the current incremental step and the current external variable D value; substitute it into the failure increment evolution equation to calculate the failure increment ΔD; accumulate the failure increment ΔD to the external variable D value; determine whether the external variable D value reaches 1. If it reaches 1, mark the shell element as failed and delete it in subsequent calculations; if it does not reach 1, proceed to the next incremental step to continue the calculation.

[0084] In one or more embodiments of the present invention, calculating the correction coefficient K includes:

[0085] Two sets of butt weld joint specimens with the same material and process were prepared. The first set retained the original weld reinforcement, while the second set had the weld reinforcement milled off and ground flat to the same thickness as the base material. Quasi-static tensile tests were performed on the two sets of specimens. The average maximum load F1 of the first set of butt weld joint specimens and the average maximum load F2 of the second set of butt weld joint specimens were extracted. The correction coefficient K = F1 / F2.

[0086] Specifically, two sets of butt-welded joint specimens with identical materials and processes were prepared. The two sets of specimens were taken from adjacent positions of the same butt-welded joint plate to ensure consistency in welding process conditions, microstructure, and initial mechanical properties. The first set of specimens retained the original weld reinforcement without any processing, maintaining the original surface condition after welding. The second set of specimens had the weld reinforcement milled off along the back of the weld, with the milling direction parallel to the weld direction and the milling depth sufficient to completely remove the reinforcement. After milling, the surface was ground to achieve a surface roughness comparable to the original surface of the base material. During grinding, uniform force was applied in a single direction to minimize the influence of surface processing marks on the tensile test results. Except for the presence or absence of weld reinforcement, the two sets of specimens were identical in size, shape, and surface condition.

[0087] Two groups of specimens were subjected to quasi-static tensile tests under identical experimental conditions. These conditions included the same tensile speed, specimen clamping method, initial gauge length, and ambient temperature. The first group of specimens retained their excess height, while the second group had their excess height milled off. During the tensile tests, load and displacement values ​​were recorded in real time using a single tensile testing machine to obtain load-displacement curves for both groups of specimens. Each group of specimens underwent multiple repeated tests to evaluate the consistency and repeatability of the experimental data.

[0088] The maximum load value for each experiment was extracted from the experimental data of the first group of specimens, and the average maximum load F1 of the first group of specimens was calculated. F1 is the arithmetic mean of the maximum load values ​​borne by the specimens in each experiment of the first group of specimens, reflecting the load-bearing capacity level of the welded joint specimens with retained weld reinforcement. The maximum load value for each experiment was extracted from the experimental data of the second group of specimens, and the average maximum load F2 of the second group of specimens was calculated. F2 is the arithmetic mean of the maximum load values ​​borne by the specimens in each experiment of the second group of specimens, reflecting the load-bearing capacity level of the welded joint specimens after the weld reinforcement was removed. The correction factor K was calculated according to the formula K=F1 / F2. The physical meaning of the correction factor K is the enhancement factor of the weld reinforcement on the load-bearing capacity of the welded joint. A K value greater than 1 indicates that the load-bearing capacity of the specimens with retained weld reinforcement is higher than that of the specimens with removed weld reinforcement.

[0089] A correction factor K is applied to the material hardening curve of the shell element corresponding to the weld zone. The correction method involves scaling the flow stress of the weld zone material proportionally, so that the corrected flow stress value is K times the original flow stress value. After the flow stress correction, large strain hardening extrapolation is performed, extending the hardening curve to the large strain region beyond the range of uniform plastic deformation.

[0090] In one or more embodiments of the present invention, when correcting the excess height of the flow stress of the shell unit corresponding to the weld zone, the correction coefficient K is applied as a multiplier to the flow stress of the weld zone material, so that the corrected flow stress is the original flow stress multiplied by the correction coefficient K, and then the corrected flow stress is extrapolated by large strain hardening.

[0091] The correction factor K is determined by the ratio of the maximum load of the specimen with retained excess height to that of the specimen with milled excess height, and K is greater than 1. The correction factor K is applied as a multiplier to the flow stress value on the weld zone material hardening curve. Specifically, the flow stress value corresponding to each plastic strain value on the hardening curve is multiplied by the correction factor K to obtain the corrected flow stress value. This operation does not change the coordinate position of the plastic strain value, only the ordinate of the flow stress value. Under the same plastic strain, the corrected hardening curve shows an overall increase in flow stress value, and the curve shape maintains the proportional relationship with the original curve. The multiplicative effect of the correction factor K on the flow stress does not depend on the magnitude of the plastic strain value; that is, the value of K remains constant throughout the entire plastic strain range of the hardening curve.

[0092] Within the shell element modeling framework, the thickness of the shell elements is constant. The thickness of the shell elements in the weld zone is the same as that in the base material zone, both being the base material thickness. Geometrically, the shell element model does not reflect the local thickening characteristics of the weld reinforcement. Physically, the weld reinforcement increases the cross-sectional area of ​​the weld region and alters the stress distribution at the weld-base material interface, exerting a constraint effect on the weld region material. Using the correction factor K as a multiplier for the flow stress in the weld zone essentially transforms the geometric enhancement and constraint strengthening effects of the reinforcement into an equivalent increase in the constitutive strength of the weld region material. The corrected flow stress value in the weld zone is higher than the uncorrected flow stress value. In finite element calculations, the stress level borne by the shell elements in the weld zone under the same strain is increased, effectively achieving an enhanced load-bearing capacity of the joint with reinforcement.

[0093] When extrapolating the modified flow stress to large strain hardening, the modified hardening curve is extended from the plastic strain range covered by the experimental data to a larger plastic strain range. The experimental data comes from quasi-static uniaxial tensile tests. The actual stress-strain curve obtained from the experiment covers the plastic strain range of the uniform plastic deformation stage, and the maximum plastic strain is limited by the uniform elongation before the specimen necks.

[0094] During actual load-bearing, the constraint effect caused by the weld reinforcement inhibits local necking in the weld region. The equivalent plastic strain of the weld region material during load-bearing may exceed the plastic strain range corresponding to the uniform elongation of the base material. If only the hardening curve within the experimental data range is used for simulation calculations, the flow stress cannot be updated when the plastic strain of the shell element in the weld region exceeds the experimental data range, and the simulation cannot describe the material mechanical response at this stage. Large-strain hardening extrapolation extends the hardening curve to the region beyond the experimental data range, allowing the simulation to still obtain the corresponding flow stress value when the plastic strain in the weld region is large. The extrapolation method is based on the hardening trend of the modified hardening curve at the end of the experimental data, assuming that the flow stress continues to increase at the same or decreasing rate with increasing plastic strain until the required extrapolation range is reached. The extrapolated hardening curve and the experimental data segment of the modified hardening curve remain continuous at the connection point, and the flow stress value and hardening rate do not jump at the connection point. After the reinforcement height correction and large strain hardening extrapolation, the material hardening curve of the shell element in the weld zone is enhanced in both the flow stress amplitude and the plastic strain coverage. Under the premise of unchanged geometry, the shell element model reflects the enhancement effect of the weld reinforcement height on the load-bearing capacity through the correction at the material constitutive level.

[0095] In one or more embodiments of the present invention, the nonlinear damage accumulation fracture criterion further defines an instability coefficient increment ΔF, the evolution equation of which is:

[0096]

[0097] In the formula: Let F be the equivalent instability plastic strain under different stress states, and let F be the variable representing the material softening behavior.

[0098] F is a variable representing the softening behavior of the material. F is independent of the external variable D, and the two describe the instability stage and damage stage of the material failure process, respectively. The value of F ranges from zero to 1, with an initial value of zero, indicating that the material is in an undeformed state. When F equals 0, the material is undergoing plastic deformation but has not yet become unstable. As plastic deformation progresses, the instability coefficient increment ΔF is calculated in each increment step, and the instability coefficient increment ΔF is accumulated to the current F value, i.e., F = F + ΔF. When F accumulates to 1, it indicates that the material begins to neck, at which point F reaches a critical value, and the current value of the external variable D is recorded as the critical value D of the time variable. crit D crit Let F be the instantaneous value of the external variable D when F reaches 1.

[0099] After necking occurs, the material enters the softening stage. The stress of the shell element is calculated according to the softening formula. The element stress σ* after softening is calculated by the following formula:

[0100]

[0101] In the formula: σ∗ is the stress after softening; σ is the stress before softening; D crit is the critical value of variable D when F=1; m is the attenuation coefficient.

[0102] Before F reaches 1 (i.e., when F is less than 1), the material has not yet experienced necking, and the stress of the shell element is calculated according to the material hardening model without softening treatment. After F reaches 1, the external variable D continues to accumulate, and the value of the external variable D exceeds the critical value Dc. crit At this time (DD) crit ) / (1-D crit If the value is greater than zero, the softening coefficient [1-(DD)] is greater than zero. crit ) / (1-D crit )] m When the value is less than 1, the softened stress σ is lower than the unsoftened stress σ, and the shell element stress begins to decay. As the external variable D continues to increase, (DD... crit As the difference increases, the softening coefficient continues to decrease, and the softened stress σ continues to decline. When the external variable D reaches 1, (DD) crit ) / (1-D crit When the value is equal to 1, the softening coefficient is zero, the softened stress σ* drops to zero, the shell element is determined to be completely failed and deleted.

[0103] The attenuation coefficient *m* controls the rate of stress decay during the softening stage. A larger *m* value indicates slower stress decay and a longer process from necking to complete failure, exhibiting characteristics of ductile fracture. Conversely, a smaller *m* value indicates faster stress decay and a shorter process from necking to complete failure, exhibiting characteristics of brittle fracture. For each region of the aluminum alloy butt weld joint, the attenuation coefficient *m* was determined through experimental data calibration.

[0104] The equivalent instability plastic strain is a function of the stress triaxiality η. It reflects the equivalent plastic strain value corresponding to the point at which necking begins to occur in a material under different stress states. The difference between equivalent instability plastic strain and equivalent plastic failure strain lies in the following: equivalent instability plastic strain corresponds to the moment when the material reaches its peak load-bearing capacity and begins to exhibit strain localization; equivalent plastic failure strain corresponds to the moment when the material completely loses its load-bearing capacity and fractures. In physical processes, instability precedes failure; that is, for the same stress state, the value of the equivalent instability plastic strain is less than the value of the equivalent plastic failure strain.

[0105] In each incremental step of the finite element simulation, the collaborative workflow of F and the external variable D is as follows:

[0106] Calculate the equivalent stress and hydrostatic stress of the shell element in the current increment step to obtain the stress triaxiality η value; determine the equivalent plastic failure strain and equivalent instability plastic strain based on the stress triaxiality η value; read the equivalent plastic strain increment, the current external variable D value, and the current F value of the current increment step; determine whether F has reached 1. If F is less than 1, substitute them into the failure increment evolution equation to calculate the failure increment ΔD and the instability coefficient increment evolution equation to calculate the instability coefficient increment ΔF, respectively. Accumulate the failure increment ΔD to the external variable D and the instability coefficient increment ΔF to F; if F has reached 1, only calculate the failure increment ΔD and accumulate it to the external variable D, without updating F. At the same time, calculate the softened element stress σ* according to the softening formula to replace the original flow stress; determine whether the external variable D has reached 1. If it has reached 1, mark the shell element as completely failed and delete it in subsequent calculations. If it has not reached 1, proceed to the next increment step to continue calculation.

[0107] In one or more embodiments of the present invention, when defining a nonlinear damage accumulation fracture criterion for the shell elements in the modified shell element model, the shell elements corresponding to the base material region are calibrated separately first, and then the calibrated base material region parameters are used as boundary conditions to calibrate the shell elements corresponding to the heat-affected zone and the weld zone in sequence.

[0108] The base metal region was chosen as the primary calibration target because it has not undergone significant welding thermal cycling, its microstructure remains in its original state, and its microstructural features such as grain size, precipitate distribution, and dislocation density exhibit spatial uniformity and consistency. The mechanical properties of the base metal region are unaffected by fluctuations in welding process parameters, and its hardening and fracture behaviors are repeatable. The base metal region occupies a large proportion of the butt weld joint, allowing for the preparation of tensile and fracture specimens that meet standard dimensions. Experimental data acquisition is not limited by specimen size, resulting in high data consistency and reliability. Therefore, the calibration of the nonlinear damage accumulation fracture criterion parameters in the base metal region has high certainty and reliability, making it suitable as the starting point for calibration of all regions of the joint.

[0109] The calibration process for the parameters of the nonlinear damage accumulation fracture criterion in the parent material region includes the following steps: Various specimens with different geometries are prepared using the parent material. The stress triaxiality values ​​at the fracture location differ for each specimen, covering a range from simple shear to iso-biaxial tension. Load-displacement curves and strain evolution data at the fracture location are obtained for each specimen through quasi-static tensile testing and digital image correlation (DIP). Based on the equivalent plastic failure strain values ​​corresponding to each stress triaxiality obtained experimentally, a functional relationship between the equivalent plastic failure strain and stress triaxiality in the parent material region is established. A functional relationship between the equivalent instability plastic strain and stress triaxiality in the parent material region is also established. The material damage coefficient *n* in the parent material region is determined. The attenuation coefficient *m* in the parent material region is determined. After calibration, a complete set of nonlinear damage accumulation fracture criterion parameters is obtained for the parent material region, including the equivalent plastic failure strain function, the equivalent instability plastic strain function, the material damage coefficient *n*, and the attenuation coefficient *m*.

[0110] After the base metal region parameters are calibrated, the calibration results are used as the boundary conditions for the heat-affected zone (HAZ) calibration. The width of the HAZ in a butt weld joint is typically small, and due to the limited area size, it is impossible to cut a sufficient number of standard specimens from the HAZ for complete parameter calibration. The HAZ is located between the weld zone and the base metal region, and its microstructure exhibits a spatial gradient, with grain growth and microstructure evolution near the weld being greater than that near the base metal. The mechanical properties of the HAZ material change continuously within this narrow region. Directly performing comprehensive parameter calibration on the HAZ faces the dual challenges of difficult specimen preparation and parameter uncertainty.

[0111] The above problems are addressed using a boundary condition transfer strategy. When calibrating the nonlinear damage accumulation fracture criterion parameters of the heat-affected zone (HAZ), the material damage coefficient *n* and attenuation coefficient *m*, already calibrated in the base metal region, are used as the initial values ​​for the corresponding parameters of the HAZ. *n* and *m* are no longer optimized as free variables; only the equivalent plastic failure strain function and the equivalent instability plastic strain function are adjusted. The rationale for this strategy is that the base metal and the HAZ have the same chemical composition; the difference mainly stems from the microstructure evolution caused by the welding thermal cycle. The material damage coefficient *n* and attenuation coefficient *m* are relatively less sensitive to microstructure evolution, and the *n* and *m* values ​​in the base metal region can serve as reasonable initial estimates for the HAZ parameters. During HAZ calibration, welded joint specimens containing the HAZ are prepared. Fracture data of the HAZ under different stress states are obtained using digital image correlation (DIC) technology. The equivalent plastic failure strain function and the equivalent instability plastic strain function in the base metal region are used as initial values, and adjustments are made based on the experimental data of the HAZ to ensure that the load-displacement curve of the HAZ predicted by the model is consistent with the experimental curve.

[0112] After the parameters of the heat-affected zone (HAZ) are calibrated, the calibration results of the base metal region and the HAZ are used together as the boundary conditions for the weld zone calibration. The weld zone undergoes complete melting and resolidification, and its microstructure is as-cast, fundamentally different from the base metal region and the HAZ. The weld zone is typically narrow, also presenting challenges in specimen preparation. During weld zone calibration, the material damage coefficient *n* and attenuation coefficient *m* calibrated in the base metal region are used as the initial values ​​for the corresponding parameters of the weld zone; only the equivalent plastic failure strain function and the equivalent instability plastic strain function are adjusted. Experimental data for the weld zone are obtained from welded joint specimens containing the weld zone using digital image correlation (DICR) technology.

[0113] The technical benefits of the phased calibration strategy are reflected in the following aspects: First, processing the set of parameters to be calibrated in stages, with each stage's calibration degrees of freedom controlled within a small range, reduces the coupling effect between parameters when multiple parameters are simultaneously inversely calculated, thus improving the reliability of parameter calibration. Second, using the base material parameters as initial or fixed values ​​for subsequent calibration provides a reasonable search starting point for the calibration of the heat-affected zone and weld zone, ensuring the optimization process approaches the global optimum at its initial position in the parameter space, reducing the risk of getting trapped in local optima. Third, the calibration results for each region are built upon the parameter benchmarks of adjacent regions; the parameter differences between regions reflect the degree to which the welding thermal cycle alters the material's mechanical behavior in each region, and the spatial distribution of parameters possesses physical rationality and self-consistency.

[0114] In one or more embodiments of the present invention, for the portion corresponding to the base material region in the butt weld joint specimen, a uniaxial tensile test simulation model with different grid sizes is established. Based on the load-displacement curve, the grid dependence factor value corresponding to each grid size is obtained by inverse parameter calculation, and the relationship curve between the grid dependence factor and the grid size is obtained.

[0115] During modeling, the portion corresponding to the base material region adopts the geometry of a standard tensile specimen. The length and width of the parallel section of the specimen are determined based on the actual cutable dimensions of the base material region in the butt-welded joint specimen. Multiple finite element models are established, each using the same specimen geometry, material hardening model parameters, and boundary conditions; the only difference between the models is the mesh size. The mesh size covers a range from fine to coarse. Fine-mesh models can capture deformation details in strain localization regions, while coarse-mesh models can reduce computational costs to meet the needs of large-scale engineering simulations.

[0116] Uniaxial tensile simulations were performed on models with different mesh sizes. The same boundary conditions as in physical tensile experiments were applied: one end of the specimen was fixed, and a displacement load was applied to the other end, with the displacement direction parallel to the specimen length. Load-displacement curves for each model were output, where the load is the resultant force of the fixed-end constraint reaction, and the displacement is the displacement of the loaded end along the loading direction.

[0117] Using the load-displacement curves obtained from physical tensile experiments as a benchmark, the simulated load-displacement curves of models with different mesh sizes are compared and evaluated. The load-displacement curves from physical tensile experiments are obtained as follows: standard uniaxial tensile specimens are prepared using the base material, and quasi-static tensile experiments are conducted under the same boundary conditions as the simulation. The load and displacement values ​​during the experiment are recorded, and the experimental load-displacement curves are obtained after data processing.

[0118] For a model with a specific mesh size, an initial value for the mesh dependence factor is set. This factor is then incorporated into the equivalent plastic failure strain in the nonlinear damage accumulation fracture criterion, multiplying the equivalent plastic failure strain by the mesh dependence factor. A uniaxial tensile simulation of this mesh size model is performed to obtain the simulated load-displacement curves. The simulated curves are compared with the experimental curves, and the difference in load values ​​at the peak load and the difference in displacement values ​​at the fracture displacement are calculated. These two indicators—peak load and fracture displacement—are used as evaluation parameters.

[0119] If the deviations between the simulation curve and the experimental curve in peak load and fracture displacement do not exceed the preset deviation range, the current mesh dependency factor value is output as the mesh dependency factor value corresponding to that mesh size. If the deviation exceeds the preset range, the value of the mesh dependency factor is adjusted and the simulation calculation is repeated. When the mesh size increases, the coarse mesh model cannot capture the deformation gradient in the strain localization region, resulting in insufficient energy dissipation and an overestimation of the fracture displacement predicted by the simulation. In this case, the value of the mesh dependency factor is increased to reduce the equivalent plastic failure strain, causing the material to trigger failure earlier, thereby reducing the fracture displacement. When the mesh size decreases, the fine mesh model captures strain localization more accurately, and the fracture displacement predicted by the simulation is closer to the experimental result. In this case, the value of the mesh dependency factor approaches 1. The above adjustment and simulation process is repeated until the deviation between the simulation curve and the experimental curve meets the requirements. The mesh dependency factor value at this point is the final mesh dependency factor value corresponding to that mesh size.

[0120] The above parameter inverse calculation process is performed on models with different grid sizes to obtain the grid dependency factor values ​​corresponding to each grid size. After the parameter inverse calculation is completed, a coordinate system is established with the grid size as the abscissa and the grid dependency factor values ​​as the ordinate. Each grid size and its corresponding grid dependency factor value are plotted as data points on the coordinate system, and the relationship curve between the grid dependency factor and the grid size is obtained by curve fitting.

[0121] The relationship curve reflects the variation of the mesh dependence factor with mesh size: when the mesh size is small, the mesh dependence factor value is close to 1, and the equivalent plastic failure strain hardly needs adjustment; as the mesh size increases, the mesh dependence factor value gradually decreases, and the reduction in equivalent plastic failure strain increases to compensate for the insufficient energy dissipation of the coarse mesh model. In subsequent simulation calculations, based on the actual shell element mesh size used, the corresponding mesh dependence factor value is read from the relationship curve and applied to the nonlinear damage accumulation fracture criterion to adjust the equivalent plastic failure strain, so that models with different mesh sizes can obtain fracture prediction results consistent with experiments.

[0122] In one or more embodiments of the present invention, the load-displacement curve is obtained in the following manner:

[0123] Butt weld joint specimens under different stress states were subjected to quasi-static tensile testing on a universal testing machine at a tensile speed of 4.2 mm / min. Digital image correlation technology was used to record the full-field strain during the deformation process of the specimens. Five experiments were conducted for each type of specimen. The experimental data were processed to obtain the load-displacement curves under each stress state.

[0124] When obtaining load-displacement curves, quasi-static tensile tests were conducted using butt-welded joint specimens under different stress states. The specimens under different stress states have different geometric shapes, resulting in varying triaxial stress values ​​at the fracture location during loading. In specimen design, by changing the radius of the notch, the radius of the central hole, and the angle between the force direction and the weld, the specimens were subjected to different stress states during tensile testing, including shear, mixed tensile-shear, uniaxial tension, plane strain, and equal biaxial tension.

[0125] Butt-welded joint specimens under different stress states were clamped onto a universal testing machine. During clamping, ensure specimen alignment to avoid additional bending moments caused by eccentric loading. An MTSE45.105-ATBC universal testing machine can be used, equipped with load and displacement sensors to simultaneously record load and beam displacement values. The tensile speed was set to 4.2 mm / min, corresponding to an initial strain rate of 0.001 s. -1 During the tensile process, the testing machine collects load values ​​and beam displacement values ​​at a fixed frequency. The sampling frequency ensures that the number of data points collected before the specimen fractures is sufficient to describe the complete shape of the load-displacement curve.

[0126] During the tensile test, digital image correlation (DIR) technology was used to record the full-field strain on the specimen surface. Before the experiment, a random speckle pattern was prepared on the specimen surface, consisting of randomly distributed black and white microparticles. A sequence of speckle images was continuously captured at a fixed frame rate on the specimen surface from the start of loading to fracture. The frame rate was matched to the tensile speed to ensure that the deformation of the specimen surface between adjacent frames did not exceed the diameter of the speckle particles, thus guaranteeing the matching accuracy of the DIR algorithm. Five repeated experiments were conducted on butt-welded joint specimens under each different stress state to ensure the repeatability and reliability of the experimental data.

[0127] The experimental data were processed to obtain load-displacement curves under various stress states. Using digital image correlation (DIC) data processing software, two reference points were selected on the surface of the parallel section of the specimen as markers for the virtual extensometer. The line connecting the two reference points was parallel to the tensile direction. The reference points were located near the fracture site but unaffected by local necking, ensuring that the strain recorded by the virtual extensometer represented the macroscopic strain of the uniformly deformed section of the specimen. The distance change between the two reference points in each frame was extracted, and combined with the initial distance between the two reference points, the average strain within the gauge length of the virtual extensometer was calculated. The formula ε = ΔL / L was used to back-calculate the distance change ΔL between the two points during the tensile process, where ε is the average strain in the virtual extensometer region, and L is the length of the digital image correlation (DIC) extensometer.

[0128] The load values ​​synchronously recorded by the single-tension machine are combined with the relative displacement ΔL obtained by the reverse calculation to obtain the load-displacement curve for this experiment. Since there may be gap closure and mechanical adjustment between the specimen and the fixture during the initial loading stage, the initial segment of the load-displacement curve may exhibit nonlinear characteristics. Data processing is used to extend the linear segment of the load-displacement curve in reverse to the zero-load point, thereby correcting the initial displacement deviation. The above data processing is performed on five repeated experiments for each specimen to obtain five load-displacement curves. The arithmetic mean of the five curves is taken as the final load-displacement curve under this stress state to reduce the impact of random errors from a single experiment on subsequent calibration work. Experimental results showing obvious abnormal fracture locations (such as fracture occurring at the specimen clamping end rather than the designed fracture area) are discarded and not included in the average calculation.

[0129] In one or more embodiments of the present invention, the butt weld joint specimens under different stress states are six types of specimens, namely, R5 notched tensile specimen, R20 notched tensile specimen, center hole R4 tensile specimen, center hole R7.5 tensile specimen, tensile-shear mixed specimen, and simple shear specimen.

[0130] The purpose of designing six types of specimens is to generate different stress triaxiality values ​​at the fracture location, covering the stress triaxiality range from shear state to equal biaxial tensile state, and providing a data basis for calibrating the relationship between equivalent plastic failure strain and stress triaxiality function.

[0131] The R5 notched tensile specimen has symmetrical notches on both sides of the parallel section, with a notch radius of 5 mm. The presence of the notches causes stress concentration in the notch root region during tensioning. The material near the notch root is under triaxial tensile stress, and the triaxial stress value is higher than that under uniaxial tension. The smaller the notch radius, the higher the stress concentration and the greater the triaxial stress value at the notch root. The R5 notched tensile specimen is used to obtain the equivalent plastic failure strain value corresponding to moderately high stress triaxiality.

[0132] The R20 notched tensile specimen has symmetrical notches on both sides of the parallel section, with a notch radius of 20 mm. The notch radius is larger than that of the R5 notched tensile specimen, resulting in relatively lower stress concentration. The stress triaxiality value near the notch root is between that of the uniaxial tensile state and the R5 notched tensile state. The R20 notched tensile specimen is used in conjunction with the R5 notched tensile specimen to obtain data points in the transition range of stress triaxiality between the uniaxial tensile state and a higher stress triaxiality range.

[0133] The R4 tensile specimen with a center hole has a circular through-hole with a radius of 4 mm at the center of the parallel section. During the tensile test, the material near the hole edge experiences a superposition of circumferential and radial tensile stresses. The stress triaxiality value in the hole edge region depends on the ratio of the hole radius to the specimen width. The stress triaxiality value of the center-hole tensile specimen is lower than that of the notched tensile specimen but higher than that of the uniaxial tensile specimen, and is used to obtain the equivalent plastic failure strain value corresponding to moderate to low stress triaxiality.

[0134] A circular through-hole with a radius of 7.5 mm is drilled at the center of the parallel section of the R7.5 center-hole tensile specimen. The hole radius is larger than that of the R4 center-hole tensile specimen, resulting in a relatively lower stress concentration at the hole edge, and the stress triaxiality value in the hole edge region is closer to that under uniaxial tension. The R7.5 center-hole tensile specimen is used in conjunction with the R4 center-hole tensile specimen to obtain data points in the transition range of stress triaxiality between uniaxial tension and moderate stress triaxiality.

[0135] The tension-shear hybrid specimen has an asymmetric structure, with the force direction forming a certain angle with the weld direction, causing the fracture site to simultaneously bear tensile and shear stress components. The stress triaxiality value under the tension-shear hybrid stress state lies between that under pure shear and uniaxial tension, and is used to obtain the equivalent plastic failure strain value corresponding to the tension-shear hybrid stress state.

[0136] Simple shear specimens, by aligning the stress direction parallel to the weld direction or employing specific specimen geometry, ensure that the fracture site primarily bears shear stress, with a relatively small tensile stress component. The stress triaxiality value under simple shear conditions is close to zero, and this is used to obtain the equivalent plastic failure strain value corresponding to low-stress triaxiality.

[0137] All six types of specimens were prepared by cutting from the butt-welded joint plates, ensuring that the weld was located at a critical stress point during cutting. For the R5 notched and R20 notched tensile specimens, the notch was located at the center of the weld, causing fracture to occur within the weld zone. For the center-hole R4 and R7.5 tensile specimens, the center of the hole was located at the center of the weld, causing fracture at the hole edge to occur within the weld zone. For the tensile-shear mixed specimens and simple shear specimens, the relative position of the weld and the stress direction of the specimen was determined based on the stress characteristics of the specimen. The specific shape and critical dimensions of the six types of specimens, including the notch radius, center hole radius, parallel section width and length, transition section radius, and clamping end dimensions, were determined before specimen preparation based on the field of view of digital image correlation technology and the clamping requirements of the testing machine, ensuring that the fracture location of the specimen during tensile testing occurred within the field of view of digital image correlation technology and that the clamping end did not slip during tensile testing.

[0138] By conducting quasi-static tensile tests on six types of specimens, digital image correlation technology was used to record the full-field strain at the fracture location of each specimen. The equivalent plastic strain value at the fracture moment of each specimen was extracted. Combined with the stress triaxiality value of each specimen at the fracture location, six sets of data points on stress triaxiality and equivalent plastic failure strain were obtained, providing interpolation nodes for establishing the functional relationship between equivalent plastic failure strain and stress triaxiality.

[0139] This invention divides butt-welded joint samples into weld zone, heat-affected zone, and base metal zone based on microhardness testing, and calibrates the hardening model parameters for each zone. Microhardness, as a macroscopic mechanical characterization of the material's microstructure, objectively reflects the degree of change in the original microstructure of the base metal caused by the welding thermal cycle. The resulting zone division criterion is repeatable and quantitative, ensuring that the calibration of hardening model parameters for each zone is based on the true microstructure of the material. This accurately captures the performance gradient of different regions of the welded joint, eliminating the failure location prediction bias caused by inaccurate descriptions of performance differences in existing simulation methods.

[0140] This invention also corrects the flow stress of the shell element in the weld zone by introducing a correction coefficient K. The maximum load ratio between the retained high-height sample and the milled high-height sample is used as the basis for correction. The geometric enhancement effect of the high-height is equivalently transformed into the strength enhancement at the material constitutive level. This allows the shell element model to accurately reproduce the load-bearing characteristics of the high-height joint while maintaining the planar geometric properties. This solves the problem that the simulation results of the load-bearing capacity cannot match the experiment and cannot be eliminated by adjusting the base material parameters.

[0141] This invention also defines a nonlinear damage accumulation fracture criterion in which the equivalent plastic failure strain is a function of stress triaxiality. Stress triaxiality, as a key mechanical parameter characterizing the nucleation, growth, and aggregation processes of micropores within a material, controls the ductile exhaustion rate of the material under different loading paths. Introducing it into the fracture criterion enables a single model to uniformly describe the fracture behavior under different stress states, overcoming the limitation of existing fracture models that cannot adapt to fracture prediction under multiple stress states.

[0142] This invention also introduces a mesh-dependent factor to correct the equivalent plastic failure strain. Different mesh sizes result in varying energy dissipation when simulating strain localization. By establishing a mapping relationship between mesh size and failure strain, the numerical defects of insufficient energy dissipation in coarse mesh models are compensated, ensuring the consistency of fracture prediction results under different mesh sizes. This allows the method to obtain reliable prediction results with relatively coarse meshes in large-scale engineering simulations such as vehicle collisions, achieving a balance between computational accuracy and efficiency.

[0143] The above is the overall concept of the present invention. For ease of understanding, the present invention also provides the following embodiments:

[0144] Example 1

[0145] This embodiment uses Al6061-T6 aluminum alloy base material with a thickness of 2mm as the object, and uses TIG welding process to prepare butt weld joint samples. The base material includes parallel extrusion direction (RD) and perpendicular extrusion direction (TD).

[0146] S1. Delineation of welded joint areas and acquisition of material properties

[0147] Obtain a butt weld joint sample and cut a hardness test specimen perpendicular to the weld direction. The cut surface is ground and polished to ensure the surface roughness of the test section meets the requirements for microhardness testing. A Leco LM247AT microhardness tester is used to perform microhardness testing on the weld section, applying a load of 0.5 kgf for a holding time of 10 s. The test path is perpendicular to the weld direction, starting at the weld center, and indentation tests are performed at fixed intervals along both sides. The spacing between test points is smaller near the weld center than in areas farther away to capture details of hardness changes in the weld zone and heat-affected zone. After recording the hardness values ​​point by point, a hardness distribution curve is plotted with the distance from the weld center as the x-axis and the hardness value as the y-axis, as shown below. Figure 2 As shown.

[0148] The hardness distribution curve is smoothed to remove signal noise. The rate of change of hardness value with distance is then calculated. Regions with a rate of change close to zero are identified as stable hardness regions, while regions with a rate of change significantly greater than zero are identified as hardness transition regions. Multiple data points are taken on both sides of the initially determined boundary point, and straight lines are fitted to each. The intersection of the fitted lines on both sides is calculated as the region boundary. Based on the hardness distribution curve, in this embodiment, the welded joint is divided into five regions: the weld zone (Weld), approximately 6 mm wide; the parallel extrusion side heat-affected zone (HAZ-RD), approximately 9 mm wide; the perpendicular extrusion side heat-affected zone (HAZ-TD), approximately 9 mm wide; the base material parallel to the extrusion direction (RD); and the base material perpendicular to the extrusion direction (TD).

[0149] S2. Establishment and calibration of hardening models for each region

[0150] Sampling was performed according to GB / T 228.1-2010 standard. Integral tensile specimens of the weld joint, including the weld zone, heat-affected zone, and base metal zone, were prepared. The tensile specimens were dog-bone shaped, with the weld located in the middle of the parallel section of the specimen and perpendicular to the tensile direction. Uniaxial tensile specimens were prepared as follows: Figure 4 As shown, a random speckle pattern is prepared on the sample surface. The speckles are composed of randomly distributed black and white microparticles. During preparation, it is ensured that the speckles adhere firmly to the sample surface.

[0151] Quasi-static uniaxial tensile tests were conducted on the integral tensile specimens of the welded joints at a tensile speed of 4.2 mm / min and a strain rate of 0.001 s⁻¹. During the tensile process, digital image correlation (DIC) technology was used to record the full-field strain on the specimen surface, and a speckle image sequence was continuously captured at a fixed frame rate using an image acquisition device. From the strain field data obtained by DIC, virtual extensometers were placed in the weld zone, heat-affected zone, and base metal zone, respectively, with each virtual extensometer completely located within its corresponding area, recording the average strain change in its respective area during the tensile process. Combined with the real-time load values ​​output by the single tensile testing machine, load-strain data for each region were obtained, and the true stress-strain curves for each region were calculated. After data processing, the basic mechanical properties of Al6061-T6 aluminum alloy are shown in Table 1, including elastic modulus, tensile strength, yield strength, and anisotropy coefficient. The true stress-strain curves of the base metal in both directions are shown in Table 1. Figure 3 As shown.

[0152]

[0153] Table 1

[0154] The hybrid Swift-Hockett-Sherby hardening model was used to calibrate the hardening model parameters for each region. This model consists of a power-law-based hardening term and an exponentially approaching saturation hardening term, linearly combined with a hybrid weighting coefficient, which can take into account both the continuous hardening behavior of the material in the early stage of deformation and the hardening saturation trend in the later stage of deformation. The calibration was carried out in stages: the yield strength was directly read from the actual stress-strain curve; the initial value of the hybrid weighting coefficient was initially set to 0.5, and the remaining parameters were fitted by nonlinear least squares method; after the fitting was completed, the obtained parameters were fixed, and the hybrid weighting coefficient was optimized by scanning the code, and the hybrid weighting coefficient value that minimized the deviation between the model prediction and the experiment was selected as the final result. The above calibration process was performed on the weld zone, heat-affected zone, and base metal zone respectively. The calibration results of the hardening model parameters of Al6061-T6 base metal are shown in Table 2. For the performance degradation areas in the welded joint, tensile tests were conducted on standard welded joint specimens, referencing quasi-static uniaxial tensile tests on the base material. Strain data for different areas were extracted based on hardness zoning and digital image correlation techniques. Ignoring excess height, the base material thickness was used for data processing to obtain the nominal stress of the welded specimen. A hybrid Swift-Hockett-Sherby hardening model was used for extrapolation, and the plastic extrapolation curves for each area are shown below. Figure 5 As shown.

[0155]

[0156] Table 2

[0157] S3. Shell element model establishment and weld reinforcement correction

[0158] Based on the geometric dimensions of each region, shell element models of the butt-welded tensile specimens were established in finite element software. The mesh size of the shell elements corresponding to the weld zone was set to 0.5 mm, and the mesh size of the shell elements corresponding to the base material zone was set to 2 mm, with the mesh size transitioning uniformly from the weld zone to the base material zone. The thickness of the shell elements in each region was assigned the base material value, i.e., 2 mm. The calibrated hardening model parameters were assigned to the corresponding shell elements of each region in the form of material cards.

[0159] The excess height of the shell element corresponding to the weld zone was corrected. Two sets of butt-welded joint specimens with identical material and process were prepared. The first set retained the original weld excess height, while the second set had the weld excess height milled off along the back of the weld and ground smooth to the same thickness as the base material. The two sets of specimens were identical in size, shape, and surface condition except for the presence or absence of weld excess height. Quasi-static tensile tests were performed on both sets of specimens under the same experimental conditions. The average maximum load F1 of the first set of specimens and the average maximum load F2 of the second set of specimens were extracted, and the correction factor K = F1 / F2 was used. The load-displacement curves of the welded joint specimens with and without excess height are shown below. Figure 6 As shown.

[0160] A correction factor K is applied as a multiplier to the flow stress of the weld zone material, making the corrected flow stress K times the original flow stress. Then, a large strain hardening extrapolation is performed on the corrected flow stress. The extrapolated hardening curve of the corrected weld zone is shown below. Figure 7 As shown.

[0161] Example 2

[0162] Based on the shell element model and calibrated hardening model parameters established in Example 1, this embodiment further calibrates the nonlinear damage accumulation fracture criterion and introduces a mesh dependence factor for regularization. Finally, the model is verified through a four-point bending experiment of a U-shaped tube welded component.

[0163] S1. Fracture Limit Testing and Data Processing under Different Stress States

[0164] To determine the fracture limit of 6061 aluminum alloy base material under different stress states, this embodiment designed six butt weld joint specimens under different stress states for quasi-static tensile tests. The six specimens are: R5 notched tensile specimen, R20 notched tensile specimen, R4 tensile specimen with center hole, R7.5 tensile specimen with center hole, mixed tensile-shear specimen, and simple shear specimen. For Al6061-T6 butt weld joints, the specimen design is the same as that of the base material, ensuring the weld is located in the center of the specimen during cutting. The specimens for each weld joint are as follows... Figure 8 As shown, Figure 8(a) is a tensile-shear mixed specimen, (b) is a simple shear specimen, (c) is an R5 notched specimen, (d) is an R20 notched specimen, (e) is a specimen with a center hole of R7.5, and (f) is a specimen with a center hole of R4.

[0165] Random speckle patterns were prepared on the specimen surface and ensured to adhere firmly. The specimens were clamped on an MTS E45.105-ATBC universal testing machine and subjected to quasi-static tensile testing at a tensile speed of 4.2 mm / min. The full-field strain during the specimen deformation process was recorded using digital image correlation technology. Each specimen was tested five times.

[0166] The experimental data were processed to obtain load-displacement curves under various stress states. Strain data between any two points was extracted using digital image correlation technology, and the relative displacement was calculated using the formula ε=ΔL / L. Combined with the load values ​​obtained from a single tensile test, the relative load-displacement curve between the two points was obtained. Softening phenomena were observed in all experimental groups before fracture, indicating that the fracture mode of Al6061-T6 is ductile fracture. The tensile load-displacement curves of different specimens from the Al6061-T6 base material are shown below. Figure 9 As shown, the tensile load-displacement curves of the Al6061-T6 welded joint under different stress states are as follows: Figure 10 As shown; where, Figure 9 In the sample, (a) is a uniaxial tensile specimen; (b) is a specimen with a center hole R4; (c) is a specimen with a center hole R7.5; (d) is a specimen with an R5 notch; (e) is a simple shear specimen; (f) is a specimen with an R20 notch; and (g) is a tensile-shear mixed specimen. Figure 10 In the sample, (a) is a uniaxial tensile specimen; (b) is an R5 notched specimen; (c) is an R20 notched specimen; (d) is a center hole R4 specimen; (e) is a center hole R7.5 specimen; (f) is a tensile-shear mixed specimen; and (g) is a simple shear specimen.

[0167] S2. Calibration of the nonlinear damage accumulation fracture criterion

[0168] This embodiment uses the GISSMO failure model to describe the nonlinear damage accumulation and fracture behavior of each region. The GISSMO fracture criterion defines the material failure behavior through nonlinear damage accumulation, defining an external variable D that is not coupled with the constitutive model to describe the material's damage behavior. When the value of the external variable D of an element reaches 1 in the simulation, that element is deleted from the simulation. In addition to characterizing the fracture behavior of materials under different stress states, the GISSMO model also considers the instability of materials during fracture, and the softening behavior of the material is defined by the variable F.

[0169] Finite element models for various working conditions were established in LS-Prepost software, using 0.5mm shell elements. The material card used was MAT24_PIECEWISE_LINEAR_PLASTICITY in conjunction with MAT_ADD_DAMAGE_GISSMO. According to the GISSMO fracture criterion, the parameters required for input into the model include equivalent fracture plastic strain, equivalent instability plastic strain, attenuation coefficient m, and damage coefficient n. These parameters were determined using inverse finite element analysis.

[0170] The GISSMO model was calibrated using LS-OPT software. The load-displacement curves under seven different working conditions, including dog bone specimens, were used as optimization targets. The mean square error method was selected to calculate the error between the target curve and the optimized curve. In LS-OPT, it is necessary to specify the optimization interval and initial values ​​for the parameters to be optimized. Choosing appropriate initial values ​​can reduce parameter optimization time and prevent optimization from getting trapped in local optima. When using LS-OPT for multi-condition, multi-objective optimization, the large number of optimization parameters can lead to situations where the overall optimization is acceptable but individual curves are poorly optimized. Therefore, the working conditions were divided according to stress triaxiality, and the optimization was re-performed in intervals until the optimization requirements were met under all working conditions.

[0171] First, the material damage coefficient n and attenuation coefficient m were iteratively calibrated separately for the dog bone specimens. The nonlinear damage accumulation fracture criterion parameters for Al6061-T6 in the parallel and perpendicular extrusion directions are shown in Table 3 of the instruction manual. The optimization process is as follows: Figure 11 As shown. The relationship between the equivalent plastic failure strain and the stress triaxiality function obtained from model iterative optimization is as follows. Figure 12 As shown.

[0172]

[0173] Table 3

[0174] The shell element of the welded joint uses the GISSMO model, and its region division is based on hardness test results, divided into the weld zone, the heat-affected zone on the parallel extrusion side, the heat-affected zone on the perpendicular extrusion side, the base material in the parallel extrusion direction, and the base material in the perpendicular extrusion direction. Finite element models of the welded joint under different stress states are shown below. Figure 13 As shown. The equivalent plastic failure strain and stress triaxiality function relationship of the Al6061-T6 butt weld joint obtained by model iterative optimization is as follows. Figure 14 As shown.

[0175] S3, Mesh Regularization

[0176] Mesh generation affects the results of finite element simulations. In simulations of whole-vehicle collisions and automotive part forming, to balance simulation accuracy and efficiency, the GISSMO failure criterion introduces a mesh dependency factor to account for the size effect, ensuring consistent simulation results for different mesh sizes under the same stress state. Uniaxial tensile test simulation models with various mesh sizes are established for standard dog bone specimens of the parent material, such as... Figure 15 As shown, using the experimental load-displacement curve as a benchmark, the corresponding mesh dependence factor values ​​are obtained through inverse parameter calculation, ensuring that models with different mesh sizes can obtain load-displacement curves consistent with the experiments. The mesh dependence factor curves of Al6061-T6 in the parallel and perpendicular extrusion directions are shown below. Figure 16 As shown.

[0177] S4, Model Validation

[0178] To verify the accuracy of the GISSMO failure model for the Al6061-T6 butt weld joint and to avoid direct impact of the punches on the weld, a U-shaped tube weldment was designed for a four-point bending test. During the four-point bending test, four bending loads were applied to the U-shaped tube weldment, causing a pure bending segment between the loading points, simulating the bending stress experienced by the weldment during impact. The specimen was considered to have failed when significant cracks appeared or deformation increased sharply. The U-shaped tube was placed on a four-point bending test fixture with a support roller spacing of 120 mm, an upper punch spacing of 40 mm, and a punch diameter of 9 mm relative to the support rollers. The punch pressing speed during the test was 5 mm / min.

[0179] A finite element model of the U-shaped tube under the same experimental conditions was established to simulate the four-point bending test results. The deformation behavior of the U-shaped tube was described using the material model and failure model specified earlier. The support roller and punch roller were set as rigid bodies. The mesh size of the U-shaped tube in the simulation model was set to 5 mm, and the mesh was refined to 3 mm for the weld area with large deformation.

[0180] Figure 17 The experiment and simulation load-displacement comparison under four-point bending conditions are shown. The GISSMO model can accurately predict the deformation behavior of welded parts, and the prediction results are in good agreement with the material deformation behavior.

[0181] The above provides a detailed description of the shell element-based modeling and simulation method for butt welded joints. Specific examples are used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, those skilled in the art will recognize that there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A method of modeling and simulating a butt welded joint based on shell elements, characterized by, The method includes: Based on microhardness testing, the butt weld joint sample is divided into weld zone, heat-affected zone and base material zone, and the hardening model parameters are calibrated for the weld zone, heat-affected zone and base material zone. Based on the geometric dimensions of the weld zone, heat-affected zone, and base metal zone, a shell element model of the butt weld joint specimen is established. The shell element model contains shell elements corresponding to the weld zone, heat-affected zone, and base metal zone. The calibrated hardening model parameters are assigned to the corresponding shell elements, and the flow stress of the shell element corresponding to the weld zone is corrected for excess height to obtain the corrected shell element model. The correction coefficient K for excess height correction is the ratio of the maximum load of the specimen with excess height retained to that of the specimen with excess height removed. A nonlinear damage accumulation fracture criterion is defined for the shell elements in the modified shell element model, wherein the equivalent plastic failure strain is a function of stress triaxiality. The equivalent plastic failure strain is corrected by introducing a mesh-dependent factor.

2. The method according to claim 1, characterized in that, The hardening model parameters for the weld zone, heat-affected zone, and base metal zone were calibrated using the Swift-Hockett-Sherby hardening model, the expression of which is: ； where a is the weight of the Swift model in the mixed SHS model; ε p is the plastic strain value after removing the elastic segment data; σ y is the yield strength of the material; ε0, K, n, σ s , N and p are model parameters.

3. The method according to claim 2, characterized in that, The nonlinear damage accumulation fracture criterion defines a failure increment ΔD, and the evolution equation of the failure increment ΔD is as follows: ； In the formula: The equivalent plastic failure strain is a function of the stress triaxiality η. This represents the equivalent plastic strain increment. n is the material damage coefficient, used to define the degree of nonlinear damage to the material; This is an invalid value.

4. The method according to claim 3, characterized in that, Calculating the correction coefficient K includes: Two sets of butt weld joint specimens with the same material and process were prepared. The first set retained the original weld reinforcement, while the second set had the weld reinforcement milled off and ground flat to the same thickness as the base material. Quasi-static tensile tests were performed on the two sets of specimens. The average maximum load F1 of the first set of butt weld joint specimens and the average maximum load F2 of the second set of butt weld joint specimens were extracted. The correction coefficient K = F1 / F2.

5. The method according to claim 4, characterized in that, When correcting the excess height of the flow stress of the shell element corresponding to the weld zone, the correction coefficient K is applied as a multiplier to the flow stress of the weld zone material, so that the corrected flow stress is the original flow stress multiplied by the correction coefficient K, and then the corrected flow stress is extrapolated by large strain hardening.

6. The method according to claim 5, characterized in that, The nonlinear damage accumulation fracture criterion also defines the instability coefficient increment ΔF, and the evolution equation of the instability coefficient increment ΔF is as follows: ； In the formula: Let F be the equivalent instability plastic strain under different stress states, and let F be the variable representing the material softening behavior.

7. The method according to claim 6, characterized in that, When defining a nonlinear damage accumulation fracture criterion for the shell elements in the modified shell element model, the shell elements corresponding to the base material region are calibrated separately first, and then the calibrated base material region parameters are used as boundary conditions to calibrate the shell elements corresponding to the heat-affected zone and the weld zone in sequence.

8. The method according to claim 1, characterized in that, For the portion of the base material region in the butt weld joint specimen, a uniaxial tensile test simulation model with different mesh sizes is established. Based on the load-displacement curve, the mesh dependence factor value corresponding to each mesh size is obtained by inverse parameter calculation, and the relationship curve between the mesh dependence factor and the mesh size is obtained.

9. The method according to claim 8, characterized in that, The load-displacement curve was obtained in the following manner: Butt weld joint specimens under different stress states were subjected to quasi-static tensile testing on a universal testing machine at a tensile speed of 4.2 mm / min. Digital image correlation technology was used to record the full-field strain during the deformation process of the specimens. Five experiments were conducted for each type of specimen. The experimental data were processed to obtain the load-displacement curves under each stress state.

10. The method according to claim 9, characterized in that, The butt weld joint specimens under different stress states consist of six types of specimens: R5 notched tensile specimen, R20 notched tensile specimen, R4 tensile specimen with center hole, R7.5 tensile specimen with center hole, mixed tensile-shear specimen, and simple shear specimen.

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