Shear strength of chromia across multiple length scales: An LDA + U study

A method for predicting the shear strength of materials over multiple length scales is developed and tested. The method is based on renormalizing the energies and shear displacements obtained through electronic structure calculations of nanoscale models of the material of interest. All material- and size-dependent quantities are incorporated into the renormalization factors, yielding a universal model that can be applied to many materials and length scales. The model is used to predict the shear strength of Cr₂O₃ along three relevant slip planes and slip directions. The results demonstrate that the shear strengths of the nanoscale systems used in the calculations range from 19.4 to 29.4 GPa. These data are then renormalized to predict the shear strength of a grain that is 10 μm thick, yielding shear strengths ranging from 189 to 342 MPa. The large decrease in the shear strength with increasing grain size is consistent with the behavior of many materials. The ability to capture this change using electronic structure calculations that do not require experimental input may be useful in developing cohesive laws of novel materials for use in large-scale mechanical engineering simulations of materials failure.