Generalised forming limit diagrams showing increased forming limits with non-planar stress states

The forming limit diagram and its associated analytical and experimental techniques has been widely used for 40 years with the assumption that sheet deformation occurs inplane-stress. Some hydro-forming type processes induce significant normal stress across the workpiece and this has led to a small number of extended formability analyses. However, recent work on the incremental sheet forming process which is known to give higher formability than conventional sheet pressing has shown that the repeated passage of a tool over the sheet leads to significant through-thickness shear strains being induced in the workpiece. Accordingly this paper explores the forming limits of sheet forming processes which induce any possible proportional loading, including all six components of the symmetric stress tensor. Marciniak and Kuczyinski’s famous (1967) analysis is extended to allow such loading, and a new generalised forming limit diagram (GFLD) is proposed to allow visual representation of the resulting forming limit strains. The GFLD demonstrates that forming limits can be increased significantly by both normal compressive stress and through-thickness shear. This increased formability is confirmed by experiments on a specially designed ‘linear paddle testing’ apparatus in which a conventional uniaxial test is augmented by the action of a paddle that ‘strokes’ the sample while also applying a normal force. Tests on the rig show that the paddle action leads to enhanced engineering strains at failure up to 300%. The insight gained in this paper is significant for process analysts, as it may explain existing discrepancies between prediction and experience of forming limits, and is important for designers who may be able to use it to expand process operating windows.