Hybrid Bishop-Hill Model for Elastic-Yield Limited Design With Non-orthorhombic Polycrystalline Metals

A method is presented for adapting the classical Bishop-Hill model to the requirements of elastic/yield-limited design in metals of arbitrary crystallographic texture. The proposed Hybrid Bishop-Hill (HBH) model, which will be applied to ductile FCC metals, retains the “stress corners” of the polyhedral Bishop-Hill yield surface. However, it replaces the ‘maximum work criterion’ with a criterion that maximizes the projection of the applicable local corner stress state onto the macroscopic stress state. This compromise leads to a model that is much more accessible to yield-limited design problems. Demonstration of performance for the HBH model is presented for an extensive database for oxygen free electronic copper. The design problem considered is a hole-in-a-plate configuration of thin sheets loaded in uniaxial tension in arbitrary directions relative to the principal directions of material orthorhombicity. Results obtained demonstrate that HBH-based elastic/yield limited design is capable of predicting complex and highly nonintuitive behaviors, even within standard problems.