Modelling and simulation of the joining zone during the tailored forming process

Figure 1: Volume element with a tesselation of 100 Voronoi cells representing the different phases of the joining zone. The discretisation is realised by dividing each Voronoi cell in several 10-noded tetrahedral elements.

In the subproject C4, micromechanically motivated thermo-chemo-mechanical material models are developed in order to achieve a high mechanical strength of the hybrid solid components. Due to the significant differences of material properties as well as due to the formation of an intermetallic phase between the base materials aluminium and steel, the resulting high stresses in the joining zone might lead to damage and failure. To avoid this, the developed material models are used to evaluate the sensitivity of different process parameters after joining and during forming and heat treatment. Moreover, with the aid of the evaluation results the material behaviour of the joining zone can be accurately adjusted during the Tailored Forming process. Later, the developed material model will be used by other subprojects of the CRC 1153 (A2, B1, B3, C1, C2, C3) to improve their simulations.

On the microscopic length scale, a geometric model is generated representing the polycrystalline microstructure of the joining zone between aluminium and steel (Figure 1). Based on a Voronoi tesselation, the model captures characteristic sizes of the grains, different morphologies (non-convex or elongated grains), a randomly distributed orientation of the atomic lattice and optionally generated pores. In the model for the joining zone, the thermoplastic material behaviour of aluminium and steel, the thermoelastic material behaviour of the intermetallic phase as well as their correlation is considered. For the thermoplastic material models, the microscopic behaviour of dislocations and point defects is described in a continuum mechanics framework. In addition, diffusion processes are taken into account that lead to an increase of hardening due to the diffusion of foreign substitutional atoms and the growth of the intermetallic phase.

The microscopic processes described above, result in the macroscopically observable thermoplastic material behaviour. Hence, the effective material model of the joining zone obtained from the microscopic model, will be transformed into a macroscopic element formulation called InTEx and developed in the subproject C4. Here, advantages of Cohesive Zone Elements like the simple discretisation as well as advantages of volume elements like the representation of all loading directions are combined by an Internal Thickness Extrapolation (InTEx).

With the developed material models, validation of the microscopic material models and microscopic simulations of the forming, the heat treatment and investigations on residual stresses formed due to temperature decrease after joining will be performed in cooperation with several subprojects of the CRC 1153 (A1, A2, B4, C1). The macroscopic material model will be validated in cooperation with other subprojects (B1, B3, C1, C3) and used for their simulations.