Review of the Basic Elastic Mechanical Properties and Their Realignment to Establish Ductile Versus Brittle Failure Behaviors

The underlying formalism of isotropic elasticity theory is shown to benefit from a review and re-examination of its structure thereby yielding a re-alignment of the basic moduli type properties. When this is accomplished the pathway to understanding ductile versus brittle failure behaviors becomes much more accessible. The ductile/brittle transition in uni-axial tension then admits a simple and direct specification in terms of the two elastic moduli 2 μ and k. The consequences of these results are discussed in the context of general failure theory.