Aspects on finite element simulation of sheet metal forming processes
Abstract: This thesis has focused on four different aspects of finite element simulation of sheet metal forming processes. Four substantial research areas are the development of a methodology for predicting the limiting strains in connection with the Forming Limit Diagram, the applicable mode of procedure for finite element simulation of the hydromechanical deep drawing process, the adaptive mesh refinement strategy based on gradients of the effective plastic stresses and strains; and the reliability and sensitivity assessments within sheet metal forming processes. The fundamental understanding of the mechanics of failure during the sheet metal forming process and the development of a method to predict the critical strains are within the scope of the first part of this study. This work contributes to the fact that a first-principle analysis, using an appropriate constitutive law, accurately predicts potential necking. Thus, the forming limit diagram is a redundant information, i.e., it is not needed to predict necking in the simulation of sheet metal forming. The second aim of this work is to enhance the accuracy of the numerical simulation of hydroforming processes in order to achieve improved results. For this purpose different strategies in process modelling are investigated and developed. Two mesh refinement indicators based on gradients of the effective plastic stresses and strains, respectively, are proposed for adaptive finite element analysis using shell elements. It has been shown that the implemented refinement indicators effectively can identify those finite elements, which have high gradients of the effective plastic stresses and strains such that the mesh can be refined in regions undergoing the most severe deformations. Finally, a methodology has been developed to provide an analytical tool for estimation of robustness and response variation within a pre-defined process window. In order to exemplify the developed methodology, the stochastic simulation technique is used for a sheet metal forming application. The conclusions of this study are that the applied method gives a possibility to illustrate and interpret the variation of the response versus a design parameter variation. Consequently, it gives significant insights into the usefulness of individual design parameters. It has been shown that the method enables us to estimate the admissible design parameter variations and to predict the actual safe margin for given process parameters. Furthermore, the dominating design parameters can be predicated using sensitivity analysis and this in turn clarifies how the reliability criteria are met.
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