Analysis of holes and spot weld joints using sub models and superelements

Components of press hardened boron steel joined by spot welds can show a brittle behavior during certain load cases which may lead to crack initiation. To capture cracks in a FEM simulation, the mesh must be very detailed and if the fully detailed system is modeled it will lead to long and expensive simulations. The approach to solve this is using a global/local method where the part is divided into two models. First a coarse mesh is created of the components excluding the small details and this model is called the global model. The other model is called the local model and contains a fine mesh of the small details. After simulating the global model one step, displacements from the global model are transferred to the local. Then the local model is simulated applying these displacements as boundary conditions during the simulation. In the next step the global model is updated with the reduced stiffness matrix of the local model, which is returned to the global model through a superelement. To develop the method, a simpler model of a component with a hole is used, instead of creating a model of a spot weld. This model is used to develop a routine to capture cracks near the edge of the hole. The routine reduces the stiffness matrix of the local model, to get all the stiffness information of the local model to the nodes shared with the global model, which are called master nodes. This is done through a series of simulations using the definition of the stiffness matrix coefficients to retrieve the reduced stiffness matrix: the stiffness coefficient with index ij, is equal to the force at degree of freedom i, due to the unit displacement of degree of freedom j. In the simulations all boundary degree of freedoms are constrained not to move except one master node’s degree of freedom, which is constrained to move a small distance. Also the boundary nodes between this master node and the surrounding ones are constrained to move. Their displacements are linearly interpolated from the surrounding master nodes’ displacements. The tangential stiffness is obtained by calculating the difference in force, before and after the perturbation of the master node and dividing with the prescribed displacement of the master node. However, the boundary nodes between the master nodes also have a prescribed displacement and therefore they will affect the master nodes. The equivalent force is derived by calculating the work these nodes will perform on the master nodes. The result is that the equivalent force is equal to the reaction force of the master node multiplied with the interpolation constants from the interpolated displacement. These equivalent forces are added to the master node’s forces when calculating the tangential stiffness. The function used to import the superelement into the global model treats the superelement linearly and this means that the reaction force from the superelement will not be the correct one. By calculating the difference in the reaction force used and the one that should be used, it can be compensated by applying external forces equal to this difference. The results show that that the routine needs to be further tested and developed before it can be used as a structural mechanics simulation tool for systems with small holes. Especially when the response of the local model is non-linear, the reduction of the stiffness matrix works poorly. The method using LS-DYNA to return the local model properties through a superelement is verified through a script, using an elastic model and decreasing the stiffness in the middle of the simulation.Validerat; 20101217 (root