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 minimizes the Euclidean distance between the applicable local corner stress state and 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 (OFE) copper. The study also implements the HBH model to the polycrystalline yield surface via standard finite element analysis (FEA) tools to carry out microstructure-sensitive design. Anisotropic elastic properties are incorporated into the FEA software, as defined by the sample texture. The derived local stress tensor is assessed using the HBH approach to determine a safety factor relating to the distance from the yield surface, and thereby highlighting vulnerable spots in the component and obtaining a quantitative ranking for suitability of the given design. By following standard inverse design techniques, an ideal microstructure (meaning texture in this context) may be arrived at. The design problems considered is a hole-in-plate configuration of sheets loaded in uniaxial tension and simple compliant mechanisms. The further improvement of HBH model is discussed by introducing geometrically necessary dislocation (GND) densities in addition to the crystal orientations procedure in standard microstructure-based method. The correlations between crystal orientations and GND densities are studied. The shape of the yield surface most influenced by the texture of the material, while the volume of the envelope scales in accordance with the GND density. However, correlations between crystal orientation and GND content modify the yield surface shape and size. While correlations between GND density and crystal orientation are not strong for most copper samples, there are sufficient dependencies to demonstrate the benefits of the detailed four-parameter model. The four-parameter approach has potential for improving estimates of elastic-yield limit in all polycrystalline FCC materials.



College and Department

Ira A. Fulton College of Engineering and Technology; Mechanical Engineering



Date Submitted


Document Type





Bishop-Hill model, microstructure, FCC metals, elastic/plastic yield limit, design space, stress, yield surface, OFE copper