Nonlinear Finite Element Analysis and Optimum Design of Spot-Welded Joints and Weld-Bonded Joints

Resistance spot welding and hybrid weld bonding have wide applications in the body work construction within the automobile industry. The integrity of the spot welds and applied adhesives determines the body assembly rigidity and dynamic performance. Incorporating contact nonlinearity and geometric nonlinearity, finite element analysis (FEA) have been carried out to investigate the structural stiffness and strength of both spot-welded and weld-bonded assemblies. Topology optimization has been performed to reveal the distributions of material effectiveness in the overlap regions and suggest a feasible method for removing underutilized material for weight reduction. Design optimization has been conducted with an aim to reduce the maximum von Mises stress in the assembly to minimum by choosing optimum values for a set of design variables, including the weld spacing, weld diameter and overlap width.


Introduction
Spot welding is a quick welding process and can be easily adapted for automation when combined with robots and control systems. The weld-bonded joining is a technology in which both adhesives and spot-welds are utilized to fasten metal sheets. Spot-welding and weld-bonding have been the conventional joining technologies for assembling metal sheets together for decades, notably for How to cite this paper: Zhang, S.Y. (2020) Nonlinear Finite Element Analysis and Optimum Design of Spot-Welded Joints and Journal of Applied Mathematics and Physics vehicle body construction. A modern automobile has its body structure comprised of stamped panels fastened with several thousands of spot welds and adhesive bonding. The integrity of the spot welds and the applied adhesives determines the body stiffness and dynamic performance. Higher body stiffness, including both the bending stiffness and torsional stiffness, is deemed to be better by designers. Body stiffness has an impact on the automotive NVH parameters as well. For example, the annoying squeak and rattle noise resulting from the relative motion between joined components indicates a poor quality of an automotive body structure.
Murray [1] studied the loaded behavior of spot-welded thin-walled structures from the perspective of vehicle crashworthiness. Experimental testing on transverse joints in the floorpans demonstrated the effects of the spot weld pattern on the energy absorbing capacity of the joints. Thin-walled tubular members fastened with spot welds were investigated to study the influence of the spot weld spacing on the energy absorbing capacity as well. Deng has found more and more applications in the construction of vehicle body structures. Tanegashimaa, Akebonoa, Katoa et al. [4] conducted experimental testing on thin-walled, spot-welded members made of HSS. The growing of cracks in the spot-welded joints was observed to study the fatigue properties when the joints were subjected to variable loads. Dhawaleb and Ronge [5] developed a mathematical model to predict the tensile shear strength of spot-welded joints using the design and process parameters. Three design variables and two process variables were involved in the developed model. Experimental testing was conducted for validation of the analytical results.
Both experimental and numerical studies on the weld-bended joints have been carried out since it was developed. Finite element analysis was carried out in references [6] [7] to study the structural performance of weld-bonded joints. The stress distributions in the lap zone of a single-point lap weld-bonded joint were calculated and compared with those of spot-welded joint and adhesive-bonded joint. It was found that the stresses in the weld-bonded joints were low and uniform. The stress concentration that occurred around the nugget in spot-welded joints was avoided, leading to a better fatigue performance. It was concluded that the tearing strength of weld-bonded joints was superior to that of adhesive-bonded Journal of Applied Mathematics and Physics joints because of the existence of spot-welds. Testing results illustrated the load distribution in the lap zone corresponding to different elastic modulus of adhesives. It was concluded that application of adhesive with large elastic modulus will help uniform stress distribution. Fujiia, Tohgo, Suzukib, et al. [8] compared spot-welded joints and weld-bonded joints on their fatigue strength. Strain was measured to study the development and propagation of fractures in the applied adhesive. It was concluded that the cracks likely initiated at the edge of overlap region in adhesive bonded joints. Almeida, Camilo, Silva et al. [9] conducted numerical and experimental studies on three different adhesives and compared with each other on the aspect of joint strength. It was concluded that a weld-bonded joint enhanced strength, stiffness, and peel resistance than that of a spot-welded joint.
FEA-based topology optimization and design optimization have been performed for spot-welded joints and weld-bonded joints in this study. FEA is conducted in which the nonlinear responses due to sheet contacting and large displacement are involved. Topology optimum results reveal the distributions of material effectiveness in the overlap regions and suggest a feasible method for removing underutilized material for weight reduction. Design optimization has been conducted with an aim to reduce the maximum von Mises stress in the assembly to minimum under specified constraints.     It is clear that the two sheets come into contact and interfere with each other in the overlap region. The existing contact and interference will result in unreliable FEA results, including the assembly compliance and strength. It suggests that the nonlinearity due to the contacting surfaces should be involved in the FEA for accurate simulation of structural performance. Surface contacting is a process involving boundary nonlinearity which is too complicate to be analyzed with analytical models. Many researches rely on numerical methods for approximating this nonlinear contacting process. In this study, 3D flexible-flexible, surface contact elements are utilized to prevent inter-penetration of sheets during the deformation process. Figure 3(b) shows the deformation of the assembly under the same prescribed loadings. Compared to Figure 3(a), it is clear that the inter-penetration between the two sheets has been prevented with the application of the contact pair elements.

Finite Element Analysis with Geometric Nonlinearity
The weld-bonded joint investigated in this study is the same in its dimensions as the spot-welded one shown in Figure 1  as that for the spot-welded assembly. Figure 9 shows the assembly is experiencing a large displacement under the specified loading. Large displacement will incur geometric nonlinearity in the responses, resulting in a reduction in the assembly stiffness. The von Mises stress is plotted in Figure 10. Figure 11(a) and Figure 11

Design Optimization
The

Conclusion
Resistance

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.