Efficient Robust Optimization of Metal Forming Processes using a Sequential Metamodel Based Strategy

The coupling of Finite Element (FE) simulations to mathematical optimization techniques has contributed significantly to product improvements and cost reductions in the metal forming industries. The next challenge is to bridge the gap between deterministic optimization techniques and the industrial need for robustness. This paper introduces a new and generally applicable structured methodology for modeling and solving robust optimization problems. Stochastic design variables or noise variables are taken into account explicitly in the optimization procedure. The metamodel-based strategy is combined with a sequential improvement algorithm to efficiently increase the accuracy of the objective function prediction. This is only done at regions of interest containing the optimal robust design. Application of the methodology to an industrial V-bending process resulted in valuable process insights and an improved robust process design. Moreover, a significant improvement of the robustness (> 2s ) was obtained by minimizing the deteriorating effects of several noise variables. The robust optimization results demonstrate the general applicability of the robust optimization strategy and underline the importance of including uncertainty and robustness explicitly in the numerical optimization procedure

Sequential optimization of strip bending process using multiquadric radial basis function surrogate models

Surrogate models are used within the sequential optimization strategy for forming processes. A sequential improvement (SI) scheme is used to refine the surrogate model in the optimal region. One of the popular surrogate modeling methods for SI is Kriging. However, the global response of Kriging models deteriorates in some cases due to local model refinement within SI. This may be problematic for multimodal optimization problems and for other applications where correct prediction of the global response is needed. In this paper the deteriorating global behavior of the Kriging surrogate modeling technique is shown for a model of a strip bending process. It is shown that a Radial Basis Function (RBF) surrogate model with Multiquadric (MQ) basis functions performs equally well in terms of optimization efficiency and better in terms of global predictive accuracy. The local point density is taken into account in the model formulatio

Multi-stage metal forming: Variation and transformation

During precision forming of metal parts made of metastable austenitic stainless steels, the relationship between the scatter on the initial parameters like the strip thickness, yield stress, etc. on the product accuracy need to be known. This becomes complex if the material is instable, i.e. martensite forms very easily. The transformation rate depends on the stress state, which is related to friction. It also depends on the temperature, which is related to deformation heat. A greater understanding of these phenomena is obtained by doing a process window study, using design and analysis of computer experiments (DACE). This paper demonstrates how to perform a DACE study on a three-stage metal forming process, using distributed computing. The study focuses on:\ud \ud •Hardening due to strain-induced and stress-assisted transformation.\ud •The influence of metal forming parameters on the product accuracy

A Plasticity Induced Anisotropic Damage Model for Sheet Forming Processes

Plastic deformation induces damage in Advanced High Strength Steels (AHSS). Therefore damage development in these steels shall be studied and incorporated in the simulations for accurate failure predictions in forming processes and for determination of the product properties after forming. An efficient anisotropic damage model suitable for large scale metal forming applications has been developed. The standard Lemaitre anisotropic damage model was modified to incorporate lower damage evolution under compression, strain rate dependency in damage and Material Induced Anisotropic Damage (MIAD). Viscoplastic regularization proved to be effective in removing the pathological mesh dependence of the presented local damage model. Anisotropic damage development was characterized in Dual Phase (DP600) steel. The damage model parameters for DP600 were determined from experiments. The Modified Lemaitre’s (ML) anisotropic damage model was validated with experiments