Determining the optimum thickness ratio of two-layer metallic sheets using multi-objective genetic algorithm

Nowadays, two-layer sheets have many applications in various industries due to their superlative characteristics. Characteristics such as weight and formability of two-layer sheet depend on the material and the thickness of the layers which compose the two-layer sheet. Plastic instability and occurrence of localized necking limit the forming of the sheets. Forming limit diagram is used to evaluate the formability of sheet. In this paper, a multi-objective genetic algorithm is applied to optimize the thickness ratio of layers in Al3105-St14 two-layer sheet. The optimal model minimizes the weight and maximizes the formability of two-layer sheet simultaneously. Forming limit diagram of two-layer sheet is determined by analytical model based on Marciniak and Kuckzinsky (M-K) method using Barlat and Lian non-quadratic yield criterion. Experiments are also carried out on Al3105-St14 two-layer sheet in order to examine the validity of the theoretical results. Pareto-based multi-objective optimization is used in order to make the objective function of weight per unit area minimized and the objective function of formability maximized. The Pareto front provides a set of optimal solutions. In addition, the knee point as the most satisfactory solution from Pareto-set is determined using minimum distance method.