The Stress Integration Algorithm In Pseudo-inverse Forming Approach For Automotive Panel

In the preliminary tool design stage, the one-step inverse forming FEM helps engineers to choose process parameters and evaluate parts forming performance. The one-step inverse forming FEM calculate optimal blank shape and physical distribution in the final parts by taking into account the assumptions of proportional loading and simplified tool actions. Nevertheless, the sheet forming process is a complicated problem, which depends on the loading history and requires the use of a path-dependant constitutive law. This one-step method is less accurate but much faster than classical incremental approaches. Numerous benchmark tests have proved that the one-step method gives fairly good strain estimation but poor stress estimation.To improve the strain, stress and other physical value estimation of the parts, based on one-step inverse forming theory, the pseudo-inverse approach was recently developed by domestic and foreign scholars:some realistic intermediate configurations are geometrically determined to consider the deformation paths; and a new algorithm of plastic integration is proposed to consider bending-unbending effects. However, the theories and methods of pseudo-inverse forming have not been developed:the existing methods of generating intermediate configurations, which have not a complete solution, will show difficulties in dealing with complex parts; the research of integrate constitutive algorithm is not sufficient, so there is lots of work to do in the material constitutive. Therefore, the two key issues in pseudo-inverse forming FEM are studied in this paper.(1) Firstly, supposing the sheet metal surface area is minimize under the constraints of the tool surface, sliding constraint surface of intermediate configurations is determined by the minimization of area of the surfaces. The sequential quadratic programming is used to solve this minimization problem. Secondly, a mesh mapping algorithm, based on the finite element mesh, is proposed. Part configuration and sliding constraint surface are unfolded to the plane by using one-step method. Then intermediate configurations are generated after the material nodes of part configuration are mapped onto sliding constraint surface. The scheme can be effective processing vertical or quasi-vertical walls of the parts.(2) To solve the constitutive integration in sheet forming, a complete implicit backward Euler return algorithm is demonstrated. In general, numerical integration of rate constitutive equations is accomplished in the following two steps. For a given strain increment, stresses are first computed by assuming a linear behavior to give an elastic predictor, and, if plastic loading occurs during this load increment, the elastic predictor is then returned to a suitably updated yield surface ensuring that plastic consistency is maintained. The backward Euler return algorithm is unconditionally stable and much more accuracy compared to the Euler forward algorithm. Using the notion of the equivalent stress and stress-strain curve, a scalar return algorithm is presented. The equivalent plastic strain increment estimated by scalar return algorithm is taken as the initial solution in backward Euler return algorithm, leading to a stable, efficient, and accurate plastic integration scheme.The above-mentioned improvements are implemented in our in-house inverse analysis software KMAS/PInverse module, developed in the COMX software platform with independent property rights. The forming of the square box and the blank shape of an electric vehicle B-pillar have been analyzed by KMAS/PInverse. The solution accuracy, in aspects of thickness, stress and blank shape, is higher than the results calculated by one-step inverse forming method.