A finite element framework for the evolution of bond strength in joining-by-forming processes

Joining-by-forming processes are widely used to permanently join two or more metals through plastic deformation. In the numerical simulation of joining-by-forming processes using finite element methods or models based on the elementary theory, it is common practice not to model the generation of the bond. Either, the workpieces to be joined are tied firmly together, as it is done in simulations of roll bonding processes, or the workpieces are treated as separate bodies throughout the simulation, as it is often done in friction welding simulations. Both approaches are problematic when shear stresses occur in the interface. Shear may initially help increase the bond strength, but it may also cause failure of the bond once it is created. Hence, to arrive at a realistic simulation of joining-by-forming processes with interface shear, a model is needed which allows for the simulation of the generation of a bond between two initially separate deformable bodies, and for the release of the bond when detrimental loading conditions occur. In this paper, a finite element framework is presented, in which the development of bonding is simulated using an adapted contact formulation, which allows for the calculation of bond strength as a function of local influence factors. To describe the evolution of bond strength, a model proposed by Zhang and Bay has been extended by a tangential bond strength and implemented into the framework. The model implementation is validated using simple numerical tests. In addition, the generation of bond strength in roll bonding of two aluminum alloys with a large difference in yield strength is analyzed. It is shown that due to the large yield stress difference, shear stresses that are generated in the roll gap can exceed the tangential bond strength, so that the bond that is created at the roll gap entry breaks near the roll gap exit.