An analytical incremental model for the analysis of the cup drawing

Purpose: of this paper Develop an analytical model for the cup drawing process to solve for the induced stresses and strains over the deforming sheet at any stage of deformation until a full cup is formed. Design/methodology/approach: An analytical model is developed for the cup drawing process by determining the variation of stresses and strains over the deforming sheet. The model uses finite difference approach and numerical procedures to solve for equilibrium, continuity, and plasticity equations in an incremental fashion. Findings: The developed analytical model results showed good correlation with experimental ones from the literature. Also, the analytical model was found to be useful in conducting parametric studies in order to determine how the different process parameters can affect the deforming cup. Research limitations/implications: This paper includes the development of an analytical model to analyze the deep drawing of axisymmetric cups. This model is then used as the solution engine for the optimization of the blank holder force for such cups avoiding failure by wrinkling or tearing. This model also gives an insight of the modes of deformation in the deep drawing process. Practical implications: This paper is part of a procedure that leads to the optimization of the blank holder loading scheme. The full procedure as presented in the two parts of the work may be applied in industry to minimize the maximum punch load or the work done during deep drawing process by modifying the blank holder force and at the same time avoid failures by wrinkling or tearing. Originality/value: Developing a predictive/corrective technique for solving the unknown boundaries of the deforming sheet.