On the determination of forming limits in thin-walled tubes

Abstract

This paper proposes a methodology to determine the formability limits of thin-walled tubes and to plot them in principal strain space and in the space of effective strain vs. stress-triaxiality. Digital image correlation (DIC), combined either with time-dependent methodologies or strain-force approaches, is utilized to identify the onset of failure by necking and obtain the corresponding limit strains. Thickness measurements and determination of the gauge length strains across the cracked regions are utilized to characterize the onset of fracture and to evaluate the fracture limit strains.Results show that the utilization of tube expansion with rigid punches and elastomers allow obtaining strain loading paths and fracture loci by necking and fracture across a wide range of tube forming conditions ranging from biaxial stretching in the first quadrant to pure tension in the second quadrant of principal strain space. The fracture forming line (FFL) is the first time ever determined for thin-walled tubes. The forming limit curve (FLC) and the FFL resemble those of sheet and strip materials and their use is of paramount importance in the design and optimization of tube forming processes.