Yield Criterion for Thin Perforated Plates With Square Penetration Pattern

Abstract

Second and fourth order polynomials describing the yield criterion for perforated plates with square penetration pattern were developed following the methodology shown by Hill (1950) and later by Reinhardt (2001) for triangular penetration pattern. The inadequacy of Hill’s (1950) criterion to describe the yield surface of the equivalent solid plate was observed by Reinhardt (2001). Unlike in the case of triangular penetration pattern, the second-order polynomial satisfies the uniqueness of yield stresses after symmetric rotation in the case of square penetration pattern, even though the second order polynomial is incomplete as it cannot satisfy the yield criterion for pure shear. However, the fourth order polynomial is found to satisfy the symmetry and boundary conditions arising from biaxial loadings completely and shows closer agreement with the finite-element results obtained by the authors as compared to the second-order polynomial. Some of the finite-element results were compared with the experimental results of Litewka (1991) and the agreement between them was found to be satisfactory. The effect of out-of-plane stresses have not been considered in the present investigation as these are found to be negligible in case of thin perforated plates, for which plane stress condition was assumed in the finite element analysis.