A Theory for Designing Ductile Materials with Anisotropy
A predictive theory is presented which enables projections of relative ductility and toughness in a wide class of anisotropic materials. Qualitative, and potentially quantitative, trends for stress-state-dependent ductility and fracture toughness are obtained with no experimental input other than the basic stress–strain curves, evidence of failure by progressive cavitation, and basic information about the inclusion content. A key concept is the anisotropy-effect-on-ductility (AED) index, which correlates complex three-dimensional anisotropy attributes of a material to a single scalar index of ductility and toughness. This index has a fundamental meaning as it emerges from a scale transition operation by means of micromechanics. A proof of concept is presented. The theory is relevant to lightweight metals whose anisotropy is inherent (Mg, Al), and eventually induced by processing (sheet metal). It is also relevant to additively manufactured metals where both porosity and process-induced anisotropy seem unavoidable so that the theory is useful in ductility–strength–cost tradeoffs.
Support from the National Science Foundation under Grant Number CMMI-1563580 is gratefully acknowledged.
- 6.R. Hill. A theory of yielding and plastic flow of anisotropic solids. Proceedings of the Royal Society of London A, 193:281–297, 1948.Google Scholar