An approach for modeling resistance spot welding of thin-gauge, dissimilar metal sheets with high electrical conductivity is presented in this work. In this scenario, the electrical and thermal contact resistances play a dominant role in heat generation and temperature evolution within the workpieces; these interactions ultimately control the weld geometry. Existing models are limited in modeling these interactions, especially for dissimilar and thin-gauge metal sheets, and at higher temperatures when the multiphysics becomes increasingly interdependent. The approach presented here uses resistivity measurements, combined with thermal modeling and known bulk resistance relationships to infer the relationship between electrical contact resistance and temperature for each of the different material interfaces in the welding process. Corresponding thermal contact resistance models are developed using the Wiedemann-Franz law combined with a scaling factor to account for nonmetallic behavior. Experimental and simulation voltage histories and final weld diameter were used to validate this model for a Cu/Al/Cu and a Cu/Al/Cu/Al/Cu stack-ups. This model was then used to study the effect of Ni-P coating on resistance spot welding of Cu and Al sheets in terms of weld formation, mechanical deformation, and contact resistance. Contact resistance and current density distribution are highly dependent on contact pressure and temperature distribution at the Cu/Al interface in the presence of alumina. The Ni-P coating helps evolve a partially-bonded donut shaped weld into a fully-bonded hourglass-shaped weld by decreasing the dependence of contact resistance and current density distribution on contact pressure and temperature distribution at the Cu/Al interface. This work also provides an approach to minimize distortion due to offset-rolling in thin aluminum sheets by optimizing the stiffening feature geometry. The distortion is minimized using particle swarm optimization. The objective function is a function of distortion and smallest radius of curvature in the geometry. Doubling the minimum allowable radius of curvature nearly doubles the reduction in distortion from the stadium shape for a quarter model. Reduction in distortion in the quarter model extends to the full-scale model with the best design performing 5.3% and 27% better than the corresponding nominal design for a quarter and full-scale model, respectively.

A method for modelling the interactions of dislocations with inclusions has been developed to analyse toughening mechanisms in alloys. This method is different from the superposition method in that infinite domain solutions and image stress fields are not superimposed. The method is based on the extended finite element method (XFEM) in which the dislocations are modelled according to the Volterra dislocation model. Interior discontinuities are introduced across dislocation glide planes using enrichment functions and the resulting boundary value problem is solved through the standard finite element variational approach. The level set method is used to describe the geometry of the dislocation glide planes without any explicit treatment of the interface geometry which provides a convenient and an appealing means for describing the dislocation. A method for estimating the Peach-Koehler force by the domain form of J-integral is considered. The convergence and accuracy of the method are studied for an edge dislocation interacting with a free surface where analytical solutions are available. The force converges to the exact solution at an optimal rate for linear finite elements. The applicability of the method to dislocation interactions with inclusions is illustrated with a system of Aluminium matrix containing Aluminium-copper precipitates. The effect of size, shape and orientation of the inclusions on an edge dislocation for a difference in stiffness and coefficient of thermal expansion of the inclusions and matrix is considered. The force on the dislocation due to a hard inclusion increased by 8% in approaching the sharp corners of a square inclusion than a circular inclusion of equal area. The dislocation experienced 24% more force in moving towards the edges of a square shaped inclusion than towards its centre. When the areas of the inclusions were halved, 30% less force was exerted on the dislocation. This method was used to analyse interfaces with mismatch strains. Introducing eigenstrains equal to 0.004 to the elastic mismatch increased the force by 15 times for a circular inclusion. The energy needed to move an edge dislocation through a domain filled with circular inclusions is 4% more than that needed for a domain with square shaped inclusions.