Finite-element simulation of springback in sheet metal forming using local interpolation for tool surfaces

Graduate School of Energy Science, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan; Volume-CAD System Research Program, The Institute of Physical and Chemical Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan; LPMTM-CNRS, University Paris 13, 93430 Villetaneuse, France
International Journal of Mechanical Sciences (Impact Factor: 1.61). 01/2008; DOI: 10.1016/j.ijmecsci.2007.07.005

ABSTRACT This paper describes new techniques for the sheet metal forming simulation using a local interpolation for tool surfaces proposed by Nagata [Simple local interpolation of surfaces using normal vectors. Computer Aided Geometric Design 2005;22:327–47] and the effect of tool modeling accuracy on springback simulation of a high strength steel sheet. The Nagata patch enables the creation of tool models that are much more accurate, in terms of not only shape but also normal vectors, than those of conventional polyhedral representations. Besides allowing an improved description of the contact between the sheet nodes and the tool surfaces, the proposed techniques have the advantage of relatively straightforward numerical implementation. Springback simulations of a two-dimensional draw bending process of a high strength steel sheet are then carried out using the polyhedral and Nagata patch models. It is found that the simulation results are largely influenced by the tool mesh when using polyhedral representations, while they are rather independent when using the Nagata patch representations. This demonstrates the efficiency and reliability of the numerical solution using the Nagata patch model.

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    ABSTRACT: This study deals with different tool surface description methods used in the finite element analysis of sheet metal forming processes. The description of arbitrarily-shaped tool surfaces using the traditional linear finite elements is compared with two distinct smooth surface description approaches: (i) Bézier patches obtained from the Computer-Aided Design model and (ii) smoothing the finite element mesh using Nagata patches. The contact search algorithm is presented for each approach, exploiting its special features in order to ensure an accurate and efficient contact detection. The influence of the tool modelling accuracy on the numerical results is analysed using two sheet forming examples, the unconstrained cylindrical bending and the reverse deep drawing of a cylindrical cup. Smoothing the contact surfaces with Nagata patches allows creating more accurate tool models, both in terms of shape and normal vectors, when compared with the conventional linear finite element mesh. The computational efficiency is evaluated in this study through the total number of increments and the required CPU time. The mesh refinement in the faceted description approach is not effective in terms of computational efficiency due to large discontinuities in the normal vector field across facets, even when adopting fine meshes.
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    ABSTRACT: The accurate solution of large deformation frictional contact problems using the finite element method is still a challenging task due to the strong nonlinearities involved. This paper presents a smoothing method applicable to 3D contact surfaces discretized with an arbitrary mesh topology. The quadratic Nagata patch interpolation is adopted to define the smooth surface. The resulting contact surface passes through all nodes of the mesh while providing a smooth description, with at least G1 continuity at the nodes and quasi-G1 continuity between the patches. Thus, the proposed method avoids the non-physical oscillations in the contact force, which are induced by the traditionally used faceted contact surfaces description, when slave nodes slide over several master segments. Moreover, it allows the accurate evaluation of kinematic variables, leading to important improvements in terms of convergence rate within the Newton–Raphson iteration loop. The developed global and local contact search algorithms, designed for contact surfaces described by Nagata patches, are described in detail. Three numerical examples were selected to illustrate the advantages of the proposed smoothing method, including a complex industrial example of sheet metal forming process. The results show the significant improvements attained with the proposed approach, in terms of efficiency, robustness and accuracy, when compared with the traditional faceted contact surfaces description.
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    ABSTRACT: Springback is a really troublesome effect in sheet metal forming processes. In fact changes in geometry after springback are a big and costly problem in the automotive industry. In this paper the authors want to analyse the springback phenomenon experimentally in sheet metal hydroforming. Compared with conventional deep drawing, sheet hydroforming technology has many remarkable advantages, such as a higher drawing ratio, better surface quality, less springback, better dimensional freezing and capability to manufacture complicated shapes. The springback phenomenon has been extensively analysed in deep drawing processes but there are not many works in the literature about springback in sheet metal hydroforming. In order to study it, the authors have performed an accurate measuring phase on the chosen test cases through a coordinate measuring machine and the obtained measurements have been utilised for the determination of springback parameters, taking into account the method proposed by Makinouchi et al. The authors have focused their attention on the possibility of adopting a modified Makinouchi et al. approach in order to measure the springback of the large size considered test cases. Through the implemented methodology it has been possible to calculate the values of the springback parameters. The obtained results correspond to the observed experimental deformations. Analysing the springback parameter values of the different combinations investigated experimentally, the authors have also studied the pre-bulging influence on the springback amount.
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Jun 4, 2014