Deterministic and stochastic analysis of failure in sheet metal forming operations

Numerical simulation can be successfully applied to evaluate product manufacturability and predict possible defects. Material breakage, wrinkling and shape defects due to springback are most frequent defects in sheet metal forming operations. In this paper we shall deal with prediction of sheet breakage during stamping process. The breakage possibility in our study is evaluated using Forming Limit Diagrams (FLD) commonly used in industrial practice. Typically deterministic analysis of sheet forming process is carried out. The first part of the paper includes an example of such simulation. Sheet forming operations, however, are characterised with a significant scatter of the results. This can be caused by differences that can occur in forming of each part. The second part of the paper presents a stochastic approach to assessment of sheet metal failure during forming operation. Methodology developed is based on the application of reliability analysis of structures to estimate probability of sheet breakage in metal forming operations. Numerical examples illustrate the stochastic approach to failure analysis in sheet forming processes. In recent years a substantial progress has been made in sheet metal forming technology to meet higher technical and economical requirements. Technical advances have been possible in great part thanks to development in the area of computer simulation methods for the forming operations - a number of specific techniques and simulation programs are now in widespread use. As a rule they allow for the determination of deformation and stresses at every point in the simulated sheet at any stage of the forming process. It is very rare, however, that the numerical simulations accounted in a truly rational way for the inherent variability of various parameters governing the response of the sheet under consideration. Process characteristics may be affected essentially by the stochastic nature of the problem. This paper shows the possibility of sheet breakage prediction by typical deterministic analysis as well as more advanced stochastic analysis of sheet failure. The latter is carried out by employing system reliability assessment techniques in sheet forming simulation. Finite element modelling of sheet forming Different formulations can be used in the simulation of sheet forming operations. Within the finite element method the analysis of these processes can be performed employing either dynamic or quasistatic models, cf. [1]. Considering the solution method we have either implicit or explicit formulation. Because of its efficiency in the analysis of largescale systems the explicitly integrated dynamic approach has become very popular in sheet stamping simulation. In the present work the explicit dynamic program Stampack has been used [2]. Sheet was discretized using a simple triangular shell element with translational degrees of freedom only, known as the BST (Basic Shell Triangle) element [3]. The BST shell element has only three displacement variables at each node which makes the element computationally efficient and suitable for large scale analysis such as the simulation of industrial sheet stamping problems. Elasto-plastic constitutive models implemented in the program Stampack for simulation of sheet metal forming employ the Huber-Mises yield criterion for isotropic materials and the Hill'48 [4], Hill'79 [5] or Hill'90 [6] criteria for anisotropic plastic behaviour. The stress-strain curve will be defined analytically by the following equation () n p Y Ka σe =+