A Shear Fracture Criterion to Predict Limit Strains in Sheet Metal Forming

Abstract

Present work examines a mathematical model to predict the onset of shear fracture in the industrial processes of sheet metal forming such as biaxial stretching. Historically, sheet metal formability has been assessed by simple testing such as the Erichsen test. Lately, the concept of experimental Forming Limit Curve, FLC, was developed to evaluate formability. The Forming Limit Diagram shows the FLC which is the plot of principal strains in the sheet metal surface, ε₁ and ε₂, occurring at critical points obtained in the laboratory formability tests or in the fabrication process. Two types of undesirable failure mechanisms can occur in sheet metal forming operations: local necking and shear fracture. Therefore, two kinds of limit strain curves can be plotted: the local necking limit curve FLC-N and the shear fracture limit curve FLC-S. The D-Bressan shear instability criterion model proposed for the theoretical prediction of forming limit strain curve owing to the onset of local necking, FLC-N, in sheet metal forming is reformulated to predict the shear fracture strain limit, FLC-S, of sheet metal forming operations. Shear fracture is anticipated to initiate in the direction of pure shear when the shear stress attains some critical value. The Barlat Yld2000-2d anisotropic yield function proposed by Barlat et al. is employed and the material is assumed to display both planar and normal anisotropy. The new approach investigate the influence of mechanical plastic properties such us the plastic anisotropy parameters, pre-strain and work hardening coefficient in sheet metal formability. Some experimental and theoretical results of forming limit curve for aluminium obtained from present model for two values of the power coefficients a = 5 and 6 are shown. The relevant issues related with the FLC-S is presented and discussed.