STRESS-STRAIN STATE OF THE CUP WALL IN AXISYMMETRIC DEEP DRAWING UNDER THE INFLUENCE OF TOOL CLEARANCE, DIE RADIUS, AND BLANK-HOLDER FORCE

The stress–strain state in the cup wall plays a central role in axisymmetric deep drawing but is often simplified as uniaxial tension in analytical and numerical analyses. This study presents a numerical investigation of the cup-wall stress–strain state using axisymmetric finite element simulations in DEFORM-2D to assess the validity of this assumption. The effects of punch–die clearance, die corner radius, and blank-holder force are examined using a Box–Behnken design as a structured sampling of the process parameter space. Stress and strain components are extracted at three representative locations across the wall thickness, near the punch side, mid-thickness, and near the die side, at a consistent forming stage corresponding to the onset of stable wall formation. Principal stresses, principal strains, equivalent stress, and stress triaxiality are evaluated to characterize local mechanical states. The results reveal pronounced through-thickness heterogeneity of the stress–strain state. The punch-side region is dominated by compressive or mixed stress states, the mid-thickness exhibits a plane-stress-dominated biaxial tension that may approach but does not reach uniaxial tension under large clearance conditions, and the die-side region shows a stable tensile-dominated response. No strictly uniaxial tensile stress state is observed in the cup wall. These findings clarify the limitations of simplified stress assumptions and emphasize the need for three-dimensional stress analysis in deep drawing.