Ideal Strength And Ductility In Metals From Second- And Third-Order Elastic Constants

Under tensile loading the ideal strength of a solid is governed by mechanical instabilities corresponding to failure in tension or shear, indicative of intrinsically brittle or ductile behavior, respectively. Ideal-strength first-principles calculations are performed in this work on several hexagonal-close-packed (hcp) and body-centeredcubic (bcc) metals. It is shown that some metals fail in tension under uniaxial loading, whereas others fail in shear. The observed behavior is rationalized with a simple analytical model based on second-order and third-order elastic constants. This formalism correctly predicts the failure mode of all but one of the metals studied in this work and leads to fundamental insights into why some classes of metals are intrinsically brittle or ductile. Further, for the transition metals, filling of the d bands is shown to correlate with the type of mechanical instability encountered, thus providing insights into the effect of alloying on the intrinsic mechanical behavior of hcp and bcc metals.