**1. Introduction**

The industrial e fforts to reduce the mass of vehicles in order to save fuel and reduce CO2 emissions result, inter alia, in the use of hybrid components and thus in the demand for new joining techniques of dissimilar materials. In order to achieve a reduction in mass at low cost, the combination of aluminum and steel has lately received substantial attention. The joining of 6xxx series aluminum alloys and steel has extensively been investigated using several joining processes, such as laser welding [1], friction stir welding [2], friction welding [3], compound forging [4] or co-extrusion [5]. The occurrence of intermetallic phases presents a challenge for both fusion welding and solid-state joining processes, as these phases are very hard and brittle and can reduce the strength of the hybrid component. Control of the resulting phase seam width is therefore essential to achieve reliable compounds [6]. The growth of intermetallic phases is di ffusion controlled, and thus strongly dependent on the prevailing temperature and time [7].

Intermetallic phases typically exhibit low crystal symmetry, which curtails dislocation movements. Due to the low mobility of the dislocations, intermetallic phases are generally characterized by high hardness values and a particularly brittle material behavior [8]. For this reason, the thickness of the intermetallic phase seam is an indispensable aspect in assessing the strength of hybrid components. Intermetallic phase seams with a given width often consist of different intermetallic phases, which in the case of the Fe-Al system, are Fe3Al, FeAl, FeAl2, Fe2Al5 and FeAl3. When joining aluminum and steel in the solid state, the phase Fe2Al5 is mainly formed [9].

The effect of intermetallic phases on the mechanical properties of a joint has been evaluated by several authors. Yamamoto et al. report a linear decrease in the joint strength with an increase in the thickness of the intermetallic layer [10]. Kimapong and Watanabe state that the joint strength increases exponentially with a decrease in the intermetallic seam thickness [11]. Yilmaz et al. determined that the highest strength can be achieved by the thinnest possible intermetallic phase in friction welding [12]. According to Fukuora, even with a thickness of the intermetallic layer less than 1 μm, the joint demonstrated premature fracture at the interface in friction bonding of high-strength Al alloys to steels [13].

Clearly, it is crucial for these hybrid materials to control the thickness of the intermetallic phase seam that forms at the interface during bonding and to characterize its properties, especially the mechanical ones. Nanoindentation enables to probe the local hardness at the nanometer scale, and was used by several authors to investigate the mechanical properties of intermetallic phases. Ogura et al. determined the nano hardness of different Fe-Al intermetallic phases. They stated that the nano hardness of intermetallic phases of type Fe*x*Al*y* increases with increasing proportion of aluminum, with the exception of the FeAl3 phase, which is less hard than FeAl2 and Fe2Al5. The increase in hardness can be explained by the increasing complexity of the lattice structures [6].

Within the framework of the Collaborative Research Centre 1153, co-extrusion is used to produce coaxial hybrid profiles of aluminum and steel. In the further course of the process chain, these profiles are used as joined hybrid semi-finished workpieces for the die forging of bearing bushings. The use of already joined semi-finished workpieces allows a geometrical and thermomechanical tailoring of the joining zone, resulting in improved mechanical properties. For a sufficient formability of these hybrid semi-finished products, the intermetallic phase seam must not exceed a certain size after co-extrusion. In order to consider the resulting phase seam thickness already in the numerical process design, a phenomenological model was developed that can predict the phase seam width during the post-processing of a commercial finite element (FE) system. In the present study, the influence of the process parameters temperature, time and force on the resulting intermetallic phase seam thickness were investigated using analogy experiments and subsequent scanning electron microscopy (SEM) analysis. In the following, the numerical model being developed and its implementation into the FE software are presented. The parameters required to describe the development of the intermetallic phase seam thickness were determined from the analogy experiment. To correlate the properties of the joining zone with the formed intermetallic phases, additional nanoindentation and energy dispersive X-ray measurements (EDS) were carried out.

#### **2. Materials and Methods**
