Yield surfaces for perforated plates with square arrays of holes

Abstract

A symmetric model of a perforated plate containing a 3×3 array of circular holes, arranged in a square pattern, was chosen and elastoplastic finite element analyses were carried out to determine the limit stresses for both pitch and diagonal directions of loading, for different values of biaxiality ratios. Plane stress conditions were assumed and the Tresca and von Mises yield criteria were employed to obtain two different sets of results. Yield surfaces were constructed and ‘general cut-out factors’ were determined for four different ligament efficiencies. The FEM results obtained by the authors using the Tresca and von Mises yield criteria were compared with the corresponding results of [J. Pressure Vessel Technol. Trans. ASME (1975) 146–154] and [J. Pressure Vessel Technol. Trans. ASME (1997) 122–126], respectively. The results based on the Tresca yield criterion obtained by the present authors and those in [J. Pressure Vessel Technol. Trans. ASME (1975) 146–154] were found to agree well with each other. In the case of the von Mises yield criterion, the agreement with [J. Pressure Vessel Technol. Trans. ASME 122–126] is generally good. The estimates based on the Tresca yield criterion are seen to result in lower values of limit stresses and cut-out factors as compared to those based on the von Mises yield criterion. The difference is attributed to the yield criterion and the flow rule chosen for the analysis. The shape as well as the size of the yield surface was found to depend on the ligament efficiency.