Enlargement of a Circular Hole in Strain Hardening Materials Under Uniaxial Tension

Deformation contour of a circular hole in a flat thin sheet has been investigated under uniaxial tension by using engineering materials of copper, brass, aluminum and the low carbon steel of SS-41. By elastic and plastic constraints around the hole, especially the strong constraint of the zone about the minimum section in the perforated sheet, the circular holes intrcduced in copper and brass which have strain hardening exponents varying from 0.30 to 0.52 deform into nearly elliptical holes as the tensile load increases. The hole in the aluminum sheet, due to its low exponent of about 0.22,deforms quite differently from the ones in the above materials. The hole in the low carbon steel sheet, having upper and lower yield points and yield elongation, takes in three steps to deform into a nearly elliptical hole. In all cases the diameter (2b) parallel to the tensile axis is elongated and the one (2a) perpendicular to it contracts as the plastic tensile strain increases. The axial ratio (b/a) is shown as functions of the plastic strain applied as well as the strain hardening exponent of materials.