# A Numerical Approach for the Efficient Concept Design of Laser-Based Hybrid Joints
## 2 Method and Models
### Automated Generation of Microstructure Concepts  
The automated generation of microstructure concepts while considering the manufacturing constraints is an important factor to enable the efficient design of laser-based joints. Otherwise, the designer would have to manually define the microstructure for each new component with new requirements and materials and, in the end, perform iterative experiments to ensure that the strength and cost requirements are satisfied. Therefore, a method is needed that can be automated without requiring special domain knowledge of the laser manufacturing constraints. The state of the art provides numerous design methods for classical joints, such as riveting or bolting, which are well documented in standards such as the VDI 2230 for the systematic design and calculation for bolted joints [30]. Typically, step-by-step analytical tests are carried out for highly simplified geometries and load cases while for more complex cases the use of numerical models is required. Existing methodological approaches are only valid for the manufacturing constraints of the corresponding joining  
Figure 2: Approach for the automated design of laser-based plastic–metal joints. technologies. Since the manufacturing constraints of the laser technology are different, the existing approaches cannot be applied. The key challenge for laser-based joints is that manufacturing constraints, the local stress, the characteristic anisotropy, and the manufacturing costs must be considered simultaneously and automatically in order to design joining zones for this technology holistically. The manufacturing constraints are discussed as follows. Based on the current state of technology, the primary manufacturing constraint is that the structures must be continuous lines with a constant distance between them. Curves are not possible due to the complex process control of the laser system at high speeds. Furthermore, the application is currently limited to two-dimensional surfaces. It is also important to note that the laser process always introduces thermal energy into the metal, which can result in deformation of the metal. The deformation might then lead to fluctuations in the mechanical properties, although this effect on the joint strength currently cannot be precisely quantified. The mechanical behavior of the cavities is anisotropic. This means that it depends on the load direction. The strength as a function of the load-direction (out-of-plane angle theta) for different distances (300 \(\upmu\)m, 600 \(\upmu\)m, and 900 \(\upmu\)m) is shown in Figure 3. The results shown were generated by FE simulation (Polymer: PP-GF40; Metal: 1.4301) of a single cavity. The load angle (out-of-plane angle theta) was varied in 1 degree increments from 0 to 90 degrees and the fracture strength was determined. In the tensile direction (out-of-plane angle theta = 90\({}^{\circ}\)), the strength is substantially lower than in the shear direction (out-of-plane angle theta = 0\({}^{\circ}\)). In addition, the strength depends on the geometry of the cavities. Especially in the tensile direction cavities with a distinct undercut show a higher strength [22]. However, for undercuts multiple laser runs are required, which increases the production time (see Section 2.3). Another important factor is the distance between the cavities. Specifically, the greater the distance, the lower the joint strength is, and vice versa. However, with larger distances, the number of cavities also decreases and thus so do the production time and costs (see also Section 2.3). With the presented approach in step 1, a FE model of the component was created. For this FE model, boundary conditions, materials, and the load case need to be defined and included (see Figure 2 step 1). Between the plastic and the metal where the components shall be joined, a thin interlayer (\(t_{\text{interlayer}}/t_{\text{plastic}}<<1\)) was implemented and tied to both components. The microstructure was defined in later steps and thus generic material properties were used.