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. 2021 Feb 25;11(1):4531.
doi: 10.1038/s41598-021-83953-z.

Generalization of intrinsic ductile-to-brittle criteria by Pugh and Pettifor for materials with a cubic crystal structure

O N Senkov  1 , D B Miracle  2
Affiliations

Generalization of intrinsic ductile-to-brittle criteria by Pugh and Pettifor for materials with a cubic crystal structure

O N Senkov et al. Sci Rep. .

Abstract

Two classical criteria, by Pugh and Pettifor, have been widely used by metallurgists to predict whether a material will be brittle or ductile. A phenomenological correlation by Pugh between metal brittleness and its shear modulus to bulk modulus ratio was established more than 60 years ago. Nearly four decades later Pettifor conducted a quantum mechanical analysis of bond hybridization in a series of intermetallics and derived a separate ductility criterion based on the difference between two single-crystal elastic constants, C12-C44. In this paper, we discover the link between these two criteria and show that they are identical for materials with cubic crystal structures.

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Conflict of interest statement

The authors declare no competing interests.

Figures

Figure 1
Figure 1
(a) Correlation between C” = (C12 − C44) and G/B for 308 compounds and 24 metals given in Supplementary materials of; (b) a renormalized hyperbolic correlation between C” normalized by Young modulus E and G/B for all the data from (a). The horizontal dashed line corresponds to C” = 0 and the vertical dashed line corresponds to G/B = 0.57. (Compiled from.) A dashed yellow data trendline in (b) corresponds to Eq. (8).
Figure 2
Figure 2
Correlation between C”/B = (C12–C44)/B and G/B for 308 compounds (blue points) and 24 metals (brown points) with cubic crystal structures analyzed in. The linear trendlines are described by Eq. (6) for isotropic (A = 1) and highly anisotropic (A = 9) materials. The vertical band corresponds to G/B in the range of 0.42 to 0.6 to account for the effect of elastic anisotropy on the value of G at C12–C44 = 0.
See this image and copyright information in PMC

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