An Approximate Explicit Solution for Polar Strain of Hydraulically Bulged Circular Diaphragms

Abstract

Requirements for practical bulging tests of sheet metals favor small die aperture and surface extensometry with relatively large gage length. The practice of equating the meridional strain at the pole with the hoop strain indicated by the extensometer introduces significant error into the evaluation of representative strain under these conditions. Exact solutions, based on the measured chord and the embraced segment height, are implicit functions of the diaphragm thickness and require prior knowledge of the material’s properties: they are, therefore, unsuitable for materials testing purposes. An approximate explicit expression for representative polar strain is developed and shown to have good accuracy.