Comparative study of extrapolation and direct methods for FLD prediction in friction stir welded aluminum sheets

Abstract

The present work involves numerical modeling of the Forming Limit Diagram (FLD) in a heterogeneous weld bead generated by FSW of two aluminum alloys (AA2139-T8 and AA7020-T651) through Nakazima test simulation using Abaqus software and the second derivative of the large deformation criterion to locate the necking. A concept is proposed to determine the FLD of welded bi-material sheet by the extrapolation method and the direct method. In the extrapolation method, FLDs have been predetermined for each of the seven weld zones and extrapolated into FSW configuration. In the direct method, a simplified geometrical model limiting FSW zones is used to determine the FLD for the global FSW bi-material assembled sheet. Results show that the extrapolation method is slightly lower, they agree well with the direct method that shows acceptable values of the major and minor strains, particularly in the expansion region, thus providing good indicative strain values during drawing. The direct method was found to provide a more conservative and realistic prediction of forming limits, especially in strain paths representative of deep-drawing operations, where failure is governed by the material behavior in the expansion region. It was also observed that the heat affected zones govern the onset of localized necking, while the base material AA2139-T8 exhibits the highest formability level among all weld zones. This is the first study to compare two different simulation approaches for FLD extraction in a fully heterogeneous FSW weld bead. The proposed methodology provides a practical numerical framework for predicting the formability of dissimilar aluminum welded sheets and can assist in the design and optimization of lightweight components in the aerospace, automotive, and structural industries. • 1-Numerical modeling of the Forming Limit Diagram (FLD) in a heterogeneous weld bead using finite element simulations. • 2️-Two FLD determination methods (extrapolation and direct method) are developed and compared for friction stir welded (FSW) bi-material sheets. • 3️-Nakazima test simulations in Abaqus are used to predict localized necking in aluminum alloys (AA2139-T8 and AA7020-T651). • 4️-Results provide valuable insights for optimizing forming processes in aerospace and automotive applications.