Revisiting the fracture forming limits of bulk forming under biaxial tension

Abstract

The formability limits of bulk metal forming in principal strain space and in the effective strain vs. stress-triaxiality space are characterized by an uncertainty region in which cracks may be triggered by tension (mode I of fracture mechanics) or by out-of-plane shear (mode III). The problem in obtaining experimental data in this region has been known for a long time and the main objective of this paper is to present a new upset formability test geometry that can effectively contribute to the characterization of the formability limits of bulk metal forming parts subjected to biaxial tension. Alongside with this objective, this paper also presents an analytical expression for converting the fracture forming limit line corresponding to crack opening by mode III in principal strain space into a hyperbolic fracture limit curve in the effective strain vs. stress-triaxiality space. The overall methodology employed by the authors combines experimentation along with analytical and numerical modelling, and the contents of the paper is a step towards diminishing the actual lack of knowledge regarding failure by fracture in bulk metal forming parts subject to stress-triaxiality values beyond uniaxial tension. Results show that a new uncoupled ductile fracture criterion built upon combination of the integrands of the Cockcroft-Latham and McClintock criteria can be successfully used to model the physics of the bulk metal forming limits for the entire range of stress-triaxiality values corresponding to cracking on free surfaces.