Crystal plasticity finite element method based on crystal grain size and crystal grain morphology correlation

Abstract

The invention discloses a crystal plasticity finite element method based on crystal grain size and crystal grain morphology correlation, which comprises the following steps: S1, establishing a finite element model with a gradient crystal grain structure and morphology difference, and carrying out inversion based on crystal plasticity parameters updated by the finite element model; s2, an aluminum alloy laser welding experiment, welding joint microscopic observation and a uniaxial tensile test of a welding sample are carried out in sequence; s3, finite element simulation of the tensile test is carried out, and the macromechanical response of the welding joint is obtained from the grain level; according to the crystal plasticity finite element method, a mesoscopic crystal plasticity constitutive model is constructed based on the lens size form, the method is suitable for mechanical modeling analysis of a laser welding joint with a gradient grain structure, and a novel inversion method of crystal plasticity parameters is provided. The mechanical property difference and the failure mechanism of each area of the laser welding joint are systematically given from the perspective of a mesoscopic organization structure, and a theoretical basis is provided for research on the influence of the mechanical property gradient of the aluminum alloy laser welding joint.

Description

Technical Field

[0001] This invention relates to the field of aluminum alloy laser welding technology, specifically to a crystal plasticity finite element method based on grain size and grain morphology. Background Technology

[0002] Laser-strengthened welding technology for aluminum alloys features a small heat-affected zone, significantly improving the mechanical properties and corrosion resistance of the welded joint, reducing deformation and residual stress during welding, and increasing production efficiency. Laser-strengthened welding, through rapid heating and cooling processes or the addition of strengthening agents, strengthens the weld grain and grain boundary structure, reducing the size of the heat-affected zone and the loss of alloying elements, thereby improving the strength and durability of the weld. This technology offers significant advantages in lightweighting, automation, and cost control in structural design and manufacturing. Therefore, laser-strengthened welding technology for aluminum alloys helps promote the application of aluminum alloy materials in high-performance and high-precision structural components in aerospace, automotive manufacturing, and shipbuilding industries. Due to the thermomechanical effects during welding, the material undergoes complex mesoscopic structural changes, such as grain refinement, coarsening, and recrystallization. This gradient grain structure directly affects the macroscopic mechanical properties of the material. The gradient-varying columnar coarse grains near the laser-welded joint often lead to premature failure of the structure near the heat-affected zone. This not only reduces the service life of the laser-welded structure but also increases operating costs due to frequent maintenance and replacement, affecting the overall economic efficiency of the system.

[0003] The crystal plasticity finite element method can reveal the influence of mesoscopic structural changes, such as dislocation movement and accumulation, grain slip, and grain boundary interactions, on mechanical properties and the mechanisms of anisotropic behavior in materials. In existing techniques, Demir et al. developed crystal plasticity finite element models related to grain size and geometry, finding that crystal microstructure determines orientation evolution, elastic stiffness, and yield stress, having the most significant impact on the macroscopic mechanical response of weldments. Toursangsaraki et al. established a physics-based crystal plasticity finite element framework. According to the crystal plasticity model, after laser shot peening, the increase in dislocation density and crystal structure strength improves resistance to cyclic plastic deformation, and the texture heterogeneity decreases under the homogenization effect of crystal morphology.

[0004] The aforementioned existing technologies all focus on setting constitutive relations in crystal plasticity finite element analysis, and do not cover how to simply and quickly realize crystal plasticity modeling based on real structures, or how to use macroscopic strain field data to invert mesoscopic crystal plasticity constitutive parameters related to mesoscopic size and morphology gradients. Therefore, based on this, a crystal plasticity finite element method based on grain size and grain morphology is proposed. Summary of the Invention

[0005] The purpose of this invention is to provide a crystal plasticity finite element method based on grain size and grain morphology, in order to solve the problem mentioned in the background art of how to simply and quickly realize crystal plasticity modeling based on real structures and how to use macroscopic strain field data to invert mesoscopic crystal plasticity constitutive parameters related to mesoscopic size and morphology gradients.

[0006] Therefore, the present invention provides a crystal plasticity finite element method based on grain size and grain morphology, comprising the following steps: S1. Based on the classical crystal plasticity theory, a finite element model with gradient grain structure and morphological differences is established, and the crystal plasticity parameters updated by the finite element model are inverted. S2. Based on the constructed finite element model, mechanical data of the welded specimens were obtained and analyzed through aluminum alloy laser welding experiments, microscopic observation of the welded joints, and uniaxial tensile tests of the welded specimens. S3. Using the analyzed data, perform finite element simulation of the tensile test to obtain the macroscopic mechanical response of the welded joint at the grain level. S4. Analyze and summarize the obtained macroscopic mechanical response.

[0007] Preferably, in step S1, the construction of the finite element model specifically includes the following steps: In the engineering simulation finite element software, a two-dimensional rectangular plane stress finite element model with a size of 2mm×0.4mm was established, and the mesh was generated using the four-node plane stress reduced integral element CPS4R. Based on the established finite element model, 1000 polygonal grains with size gradients in the x-axis direction were randomly generated in the finite element model. From left to right, they are equiaxed small grains, long grains, equiaxed large grains, long grains, and equiaxed small grains.

[0008] Preferably, the constructed finite element model contains 128,000 elements and 128,961 nodes, with the smallest element size being 0.0125mm × 0.0125mm, used to capture deformation gradients between and within grains.

[0009] Preferably, in step S1, the specific steps for inverting crystal plasticity parameters are as follows: using a surrogate model to identify crystal plastic hardening parameters from strain data of macroscopic experiments, and dynamically correcting the grain plasticity parameters through an optimization algorithm.

[0010] Preferably, the specific steps of the aluminum alloy laser welding experiment in step S2 are as follows: The selected raw material is 2mm thick 6061-T651 aluminum alloy plate, and 1.2mm diameter ER4047 aluminum welding wire is used as welding filler. Before welding, use a wire brush to grind the surface of the area to be welded to remove the oxide film, and then wipe it clean with anhydrous ethanol. A laser with a maximum power of 10kW, a circular spot, a focal length of 300mm, and a spot diameter of 0.4mm at the focal point is used for butt laser welding without pre-grooving. During the welding process, the laser beam forms a 13° angle with the normal of the aluminum alloy plate, and the welding wire forms a 20° angle with the aluminum alloy plate. The fixture is constrained at 20mm from the weld on each of the two plates.

[0011] Preferably, in step S2, the specific steps of the tensile test are as follows: Using wire electrical discharge machining (EDM) technology, a dog-bone-shaped specimen was cut from the welded aluminum alloy plate and polished with metallographic sandpaper and diamond polishing paste. Next, the PMLAB3D-DIC system was calibrated, and black and white speckle patterns were sprayed onto the surface of the test piece to create random textures. The sample was fixed on the Instron 3345 universal testing machine and supplemented with a cold light source; Finally, two high-speed CCD cameras were placed at the same height with an angle of approximately 30° between them. The PMLAB3D-DIC system was used to measure the macroscopic mechanical response data, such as displacement and strain fields, of the material in the laser-welded joint area during the tensile test.

[0012] Preferably, during the tensile test, the tensile speed is set to 1 mm / min, the image acquisition frame rate of the 3D-DIC system is 2 fps, and the image size is 2048×1536 pixels.

[0013] Preferably, in step S2, the procedure for microscopic observation of the welded joint is as follows: A metallographic specimen measuring 8mm × 2mm × 2mm was cut from the weld seam in a position close to the tensile specimen and perpendicular to the weld seam direction. The specimen was then polished with metallographic sandpaper and diamond polishing paste. The scanning electron microscope acceleration voltage was set to 20kV, the specimen was tilted at 70°, and the acquisition speed was 108Hz to acquire the corresponding EBSD and reverse polarity images.

[0014] The present invention proposes a crystal plasticity finite element method based on grain size and grain morphology, the advantages of which are as follows: This crystal plasticity finite element method constructs a mesoscopic crystal plasticity constitutive model based on lens size and morphology, which is suitable for mechanical modeling and analysis of laser-welded joints with gradient grain structure. It also presents a new method for inverting crystal plasticity parameters and systematically explains the differences in mechanical properties and failure mechanisms of different regions of the laser-welded joint from the perspective of mesoscopic microstructure. This provides a theoretical basis for the study of the influence of mechanical property gradients on aluminum alloy laser-welded joints and is of great significance for improving the mechanical properties of aluminum alloy laser-welded joints. A finite element model update strategy is proposed. Under uniaxial tensile loading, the mesoscopic crystal plastic constitutive parameters related to the mesoscopic size morphology gradient are inverted using macroscopic strain field data. Numerical experiments demonstrate that the method has a fast convergence speed and the parameter identification error is less than 7% under noise conditions with a signal-to-noise ratio of less than 2%. The finite element simulation results of crystal plasticity are in good agreement with the actual macroscopic tensile test results. The results reflect the influence of grain size and morphology on mechanical properties in the weld area at the mesoscopic grain level. As the grain size increases, the yield strength of the material gradually decreases while the hardening modulus increases. As the grain morphology parameter η increases, both the yield strength and hardening modulus of the material decrease. Attached Figure Description

[0015] Figure 1 This is a flowchart of the crystal plasticity finite element method of the present invention; Figure 2 This is a finite element model diagram of the crystal plasticity of the present invention; Figure 3 This is a diagram showing the finite element model and stress distribution results of the present invention; Figure 4 The figure shows the welding test specimens of the present invention, where a is the welding test plate, b is the dog bone rod tensile part, and c and d are metallographic specimens. Figure 5 This is a strain field contour map of the present invention under different loads. Detailed Implementation

[0016] The technical solution of the present invention will now be described in detail through specific embodiments.

[0017] Example: Please see Figure 1-5 This invention provides a crystal plasticity finite element method based on grain size and grain morphology, comprising the following steps: S1. Based on the classical crystal plasticity theory, a finite element model with gradient grain structure and morphological differences is established, and the crystal plasticity parameters updated by the finite element model are inverted. S2. Based on the constructed finite element model, mechanical data of the welded specimens were obtained and analyzed through aluminum alloy laser welding experiments, microscopic observation of the welded joints, and uniaxial tensile tests of the welded specimens. S3. Using the analyzed data, perform finite element simulation of the tensile test to obtain the macroscopic mechanical response of the welded joint at the grain level. S4. Analyze and summarize the obtained macroscopic mechanical response.

[0018] See Figure 2 and Figure 3 The construction of a finite element model specifically includes the following steps: In the engineering simulation finite element software, a two-dimensional rectangular plane stress finite element model with a size of 2mm×0.4mm was established, and the mesh was generated using a four-node plane stress reduced integral element CPS4R. The constructed finite element model has a total of 128,000 elements and 128,961 nodes, with the smallest element size being 0.0125mm×0.0125mm, which is used to capture the deformation gradient between and within grains. Based on the established finite element model, 1000 polygonal grains with size gradients in the x-axis direction were randomly generated in the finite element model. From left to right, they are equiaxed small grains, long grains, equiaxed large grains, long grains, and equiaxed small grains.

[0019] The specific steps for inverting crystal plasticity parameters are as follows: using a surrogate model to identify crystal plastic hardening parameters from strain data of macroscopic experiments, and dynamically correcting the grain plasticity parameters through an optimization algorithm; In this embodiment: the simulation results show that under a small displacement load, such as 0.001 mm, the axial strain in the longitudinal section is uniformly distributed along the x-coordinate. This is because all grains undergo elastic deformation at this time, and the linear elastic constitutive relationship is independent of the grain size. As the displacement load increases, some regions first enter the yield stage and undergo plastic deformation. This is because the smaller the grain size and the smaller the ratio of grain size to minor axis, the greater the initial yield strength, and the grain size has a more significant influence. Therefore, the order of entering the yield stage is long grain region, equiaxed large grain region, and equiaxed small grain region. Thus, the axial strain distribution of the sample generally shows an "M"-shaped trend of first increasing and then decreasing from the center to both sides. Under the influence of the gradient grain size at various positions in the entire model, the longitudinal section strain shows a smooth gradient change, and this gradient change becomes more significant with the increase of displacement load, fully demonstrating the influence of the material's mesoscopic structure on macroscopic mechanical properties. The process for inverting crystal plasticity parameters involves combining the observed strain energy density in the x-direction of inhomogeneity, external load, and the calculation results from the finite element model into a weighted least squares optimization algorithm, as shown below:

[0020] Where i is the sequence number of time node ti, h is the thickness, and w is the width of the target region. These are the strain field distributions at time ti, , where represents the stress field distribution at time ti, FifemP represents the end load in the numerical simulation, wei(x,y) represents the weight distribution of the strain energy density measurement residual at time i, and wT represents the weight allocation of the external load measurement residual. Due to strain The grains are relatively uniformly distributed along the y-axis and exhibit a gradient grain distribution along the x-axis; therefore, the strain in the longitudinal section is used. Since the mean is approximated, it can be assumed that the numerically simulated and experimentally measured non-uniform strain along the x-axis can be expressed as εxifemP,x and εxiexpx, respectively: The average cross-sectional stress can be determined using the load and the cross-sectional area of ​​the target region: Substituting the equations, we obtain the following optimization problem:

[0021] Where L and W represent the x and y coordinate ranges of the rectangular specimen, respectively, Ω represents the region of the rectangular specimen, and wei(x) represents the weight distribution of the strain energy density measurement residual along the x-axis at time i. To ensure consistency in the solution range of the optimization variables and improve search accuracy, a normalized weight function is introduced, i.e.

[0022] The Levenberg-Marquardt algorithm is used to optimize the crystal plasticity parameters. The central difference method is used to calculate the partial derivatives of the design parameters. First, the Newton search direction is constructed. When the Hessian matrix approaches singularity, the search direction is changed to a direction closer to the negative gradient. Through this adjustment, the value of the objective function will decrease.

[0023] In step S2, the specific steps of the aluminum alloy laser welding experiment are as follows: The selected raw material is 2mm thick 6061-T651 aluminum alloy plate, and 1.2mm diameter ER4047 aluminum welding wire is used as welding filler. Before welding, use a wire brush to grind the surface of the area to be welded to remove the oxide film, and then wipe it clean with anhydrous ethanol. A laser with a maximum power of 10kW, a circular spot, a focal length of 300mm, and a spot diameter of 0.4mm at the focal point is used for butt laser welding without pre-grooving. During the welding process, the laser beam forms a 13° angle with the normal of the aluminum alloy plate, and the welding wire forms a 20° angle with the aluminum alloy plate. The fixture is constrained at 20mm from the weld on each of the two plates.

[0024] In this embodiment: the chemical composition table of the aluminum alloy plate is as follows:

[0025] The chemical composition table of aluminum welding wire is as follows:

[0026] An IPG YLS-10000 laser with a maximum power of 10kW and an IPG D50 wobble laser head was used. The laser spot was circular with a focal length of 300mm and a spot diameter of 0.4mm at the focal point. A KUKA KR60 six-axis welding robot and a Phonix KD4010 wire feeder were used for butt welding without pre-beveling. The welding parameters were as follows:

[0027] See Figure 4 and Figure 5 The specific steps of the tensile test are as follows: Using wire electrical discharge machining (EDM) technology, a dog-bone-shaped specimen was cut from the welded aluminum alloy plate and polished with metallographic sandpaper and diamond polishing paste. Next, the PMLAB3D-DIC system was calibrated, and black and white speckle patterns were sprayed onto the surface of the test piece to create random textures. The sample was fixed on the Instron 3345 universal testing machine and supplemented with a cold light source; Finally, two high-speed CCD cameras were placed at the same height with an angle of about 30° between them. The PMLAB 3D-DIC system was used to measure the macroscopic mechanical response data such as displacement field and strain field of the material in the laser welded joint area during the tensile test. During the tensile test, the tensile speed was set to 1 mm / min, the image acquisition frame rate of the 3D-DIC system was 2 fps, and the image size was 2048×1536 pixels. In this embodiment, the specimen is subjected to different loads during the tensile process. The strain cloud map, in which Figure 5 The rectangle in the figure shows its position. As can be seen from the figure, when the load is relatively small, the specimen is in an elastic state and the strain at each position is not much different. like Figure 5 b. As the load continues to increase, the HAZ and FZ of the weld zone... It starts to be greater than BZ, and becomes more pronounced as the load increases; like Figure 5 As shown in c, d, and e, the initial strength of the weld zone is lower because the grain size is larger than that of BZ. With further increases in load, the weld zone... Slightly larger than its adjacent BZ The two sides BZ that are farther away from the weld are Gradually extending beyond the weld zone; like Figure 5 As shown in f, g, and h, it eventually develops into BZ reaching its peak on one side. At its maximum value, the weldment fractured at point BZ; like Figure 5 The specific reason is that the ER4047 welding wire used in the experiment has a high silicon content. As the silicon content increases, the hardness of the weld zone generally increases. An appropriate amount of silicon can improve the tensile strength of the weld joint and is beneficial to improving the toughness of the weld joint. The thermal conductivity of high-Si welds is reduced, and the weld solidification rate is reduced, resulting in obvious coarsening of the weld grains. However, the solid solution strengthening effect brought about by the increase of the solid solution element Si content in the weld is far greater than the negative impact brought about by grain coarsening. The average hardness of high-Si welds is higher, and the yield strength and tensile strength of the welds are significantly improved.

[0028] In step S2, the procedure for microscopic observation of the welded joint is as follows: A metallographic specimen measuring 8mm × 2mm × 2mm was cut from the weld seam in a position close to the tensile specimen and perpendicular to the weld seam direction. The specimen was then polished with metallographic sandpaper and diamond polishing paste. The scanning electron microscope acceleration voltage was set to 20kV, the specimen was tilted at 70°, and the acquisition speed was 108Hz to acquire the corresponding EBSD and reverse polarity images.

[0029] In this embodiment, by comparing experimental and finite element results, it was found that using a grain size-dependent crystal plasticity model can simulate the mechanical behavior of actual laser-welded joints in tensile tests from a mesoscopic perspective. As the grain size increases, the material's yield strength gradually decreases while the hardening modulus increases. This may be because the large grain region undergoes a significant phase transformation during welding, incorporating the reinforcing phase from the ER4047 welding wire, thus enhancing its resistance to dislocation growth. Additionally, the 6061-T6 aluminum alloy base material may experience over-aging and softening behavior due to heat input during welding, leading to fracture of the entire test sample in the base material region. This application proposes a crystal plastic constitutive model related to grain size and morphology, and provides an inversion method for crystal plasticity parameters. This model is applied to the mechanical property characterization of ER4047 filler wire laser welded joints. Combining mesoscopic structure observation and macroscopic uniaxial tensile test, the mechanical property differences and failure mechanisms of various regions of the laser welded joints are systematically studied from the perspective of mesoscopic microstructure. EBSD scanning results showed that the weld joint's BZ, HAZ, and FZ regions exhibited different grain sizes and morphologies: the BZ displayed equiaxed small grains, the HAZ displayed slender columnar grains, and the FZ displayed equiaxed large grains. Macroscopic uniaxial tensile tests revealed differences in the mechanical properties of various regions of the weld joint. Although the weld zone, including the HAZ and FZ, had a lower yield strength, it showed stronger resistance to plastic deformation after yielding. The specimen ultimately fractured in the BZ. The finite element simulation results of crystal plasticity showed good agreement with the actual macroscopic tensile test results, analyzing the influence of grain size and morphology on mechanical properties within the weld region at the mesoscopic grain level. With increasing grain size, the yield strength gradually decreased, while the hardening modulus increased; conversely, with increasing grain morphology parameter η, both the yield strength and hardening modulus decreased.

[0030] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A finite element method for crystal plasticity based on grain size and grain morphology, characterized in that: Includes the following steps: S1. Based on the classical crystal plasticity theory, a finite element model with gradient grain structure and morphological differences is established, and the crystal plasticity parameters updated by the finite element model are inverted. S2. Based on the constructed finite element model, mechanical data of the welded specimens were obtained and analyzed through aluminum alloy laser welding experiments, microscopic observation of the welded joints, and uniaxial tensile tests of the welded specimens. S3. Using the analyzed data, perform finite element simulation of the tensile test to obtain the macroscopic mechanical response of the welded joint at the grain level. S4. Analyze and summarize the obtained macroscopic mechanical response.

2. The crystal plasticity finite element method based on grain size and grain morphology as described in claim 1, characterized in that: In step S1, the construction of the finite element model specifically includes the following steps: In the engineering simulation finite element software, a two-dimensional rectangular plane stress finite element model with a size of 2mm×0.4mm was established, and the mesh was generated using the four-node plane stress reduced integral element CPS4R. Based on the established finite element model, 1000 polygonal grains with size gradients in the x-axis direction were randomly generated in the finite element model. From left to right, they are equiaxed small grains, long grains, equiaxed large grains, long grains, and equiaxed small grains.

3. The crystal plasticity finite element method based on grain size and grain morphology according to claim 2, characterized in that: The constructed finite element model contains 128,000 elements and 128,961 nodes, with the smallest element size being 0.0125mm × 0.0125mm, used to capture deformation gradients between and within grains.

4. The crystal plasticity finite element method based on grain size and grain morphology as described in claim 1, characterized in that: In step S1, the specific steps for inverting crystal plasticity parameters are as follows: using a surrogate model to identify crystal plastic hardening parameters from strain data of macroscopic experiments, and dynamically correcting the grain plasticity parameters through an optimization algorithm.

5. The crystal plasticity finite element method based on grain size and grain morphology as described in claim 1, characterized in that: The specific steps of the aluminum alloy laser welding experiment in step S2 are as follows: The selected raw material is 2mm thick 6061-T651 aluminum alloy plate, and 1.2mm diameter ER4047 aluminum welding wire is used as welding filler. Before welding, use a wire brush to grind the surface of the area to be welded to remove the oxide film, and then wipe it clean with anhydrous ethanol. A laser with a maximum power of 10kW, a circular spot, a focal length of 300mm, and a spot diameter of 0.4mm at the focal point is used for butt laser welding without pre-grooving. During the welding process, the laser beam forms a 13° angle with the normal of the aluminum alloy plate, and the welding wire forms a 20° angle with the aluminum alloy plate. The fixture is constrained at 20mm from the weld on each of the two plates.

6. The crystal plasticity finite element method based on grain size and grain morphology as described in claim 5, characterized in that: In step S2, the specific steps of the tensile test are as follows: Using wire electrical discharge machining (EDM) technology, a dog-bone-shaped specimen was cut from the welded aluminum alloy plate and polished with metallographic sandpaper and diamond polishing paste. Next, the PMLAB3D-DIC system was calibrated, and black and white speckle patterns were sprayed onto the surface of the test piece to create random textures. The sample was fixed on the Instron 3345 universal testing machine and supplemented with a cold light source; Finally, two high-speed CCD cameras were placed at the same height with an angle of approximately 30° between them. The PMLAB3D-DIC system was used to measure the macroscopic mechanical response data, such as displacement and strain fields, of the material in the laser-welded joint area during the tensile test.

7. The crystal plasticity finite element method based on grain size and grain morphology as described in claim 5, characterized in that: During the tensile test, the tensile speed was set to 1 mm / min, the image acquisition frame rate of the 3D-DIC system was 2 fps, and the image size was 2048×1536 pixels.

8. The crystal plasticity finite element method based on grain size and grain morphology as described in claim 5, characterized in that: In step S2, the procedure for microscopic observation of the welded joint is as follows: A metallographic specimen measuring 8mm × 2mm × 2mm was cut from the weld seam in a position close to the tensile specimen and perpendicular to the weld seam direction. The specimen was then polished with metallographic sandpaper and diamond polishing paste. The scanning electron microscope acceleration voltage was set to 20kV, the specimen was tilted at 70°, and the acquisition speed was 108Hz to acquire the corresponding EBSD and reverse polarity images.

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