The dominating dimensionless numbers of adiabatic shear localization

Adiabatic shear is a complex phenomenon involving thermo-mechanical coupled failure mechanisms, which is affected by material properties, loads, and geometries. In this study, four dimensionless numbers which only contain input parameters and can fully reflect the influence of adiabatic shear are determined by reducing the conservation equations of shear localization to dimensionless terms. The dimensional analysis method of adiabatic shear, along with predictive models for the characteristic parameters of adiabatic shear, are systematically provided by revealing the physical significance of the dimensionless numbers. Based on data analysis, a dimensional analysis method of adiabatic shear for multi-physical processes is proposed, which has been successfully applied to explosively-driven metal shells, to realize the prediction and control of adiabatic shear. This study demonstrates that the prediction models of adiabatic shear-band spacing and width can be unified through a relationship involving the Prandtl number, P_r. Furthermore, the classical prediction models of spacing and width are improved based on the experimental data. It is clearly pointed out that the more favorable the formation of shear localization, the smaller the width and spacing of the shear band, which illustrates the influence of material properties and loads on the spatial distribution of shear bands. In addition, a new prediction model for the propagation velocity of the shear band including P_r is proposed by using dimensional analysis. Compared with the classical model, the new model has higher accuracy, and can correctly reflect the influence of loads, material mechanical and thermophysical properties on the shear-band velocity.