Measurement of the forming limit stress curve using a multi-axial tube expansion test with a digital image correlation system

A servo-controlled tension-internal pressure testing machine with an optical 3D deformation analysis system (ARAMIS) was used to measure the multi-axial plastic deformation behavior of a high-strength steel sheet for a range of strain from initial yield to fracture. The testing machine is capable of applying arbitrary principal stress or strain paths to a tubular specimen using an electrical, closed-loop servo-control system for axial force and internal pressure. Tubular specimens with an inner diameter of 44.6 mm were fabricated from a high-strength steel sheet with a tensile strength of 590 MPa and a thickness of 1.2 mm by roller bending and laser welding. Several linear and non-linear stress paths in the first quadrant of the stress space were applied to the tubular specimens in order to measure the forming limit curve (FLC) and forming limit stress curve (FLSC) of the as-received test material, in addition to the contours of plastic work and the directions of plastic strain rates. The contours of plastic work and the directions of plastic strain rates measured for the linear stress path experiments were compared with those calculated using selected yield functions in order to identify the most appropriate yield function for the test material. Moreover, a Marciniak-Kuczyński type (M-K) forming limit analysis was performed using the most appropriate yield function. The calculated and measured FLC and FLSC were compared in order to validate the M-K approach. The path-dependence of the FLC and FLSC was also investigated