Size Effect on Onset and Subsequent Evolution of Adiabatic Shear Band: Theoretical and Numerical Analysis

The adiabatic shear instability of ductile materials has attracted more and more attentions of researchers and groups, who have been sparing no effort in further understanding of the underlying mechanism since the first experimental depiction of adiabatic shear instability by Zener and Hollomon. As for the adiabatic shear instability, many factors account for its occurrence, including heat conduction, inertia effect, microstructure effect and so on. However, lots of experimental evidence has shown that metal materials display a strong size effect when the characteristic length scale is in the order of microns. The size effect has also been observed in the analysis of shear band in the ductile materials because the order of the bandwidth stays within the microscale range. However, a comprehensive understanding of the whole process of adiabatic shear banding (ASB), including the early onset and the subsequent evolution, is still lacking. In this work, a gradient plasticity model based on the Taylor-based nonlocal theory feasible for the linear perturbation analysis and convenient for numerical calculation is proposed to investigate the strain gradient on the onset of ASB and the coupling effect of heat conduction, inertia effect and strain gradient at the early stage, as well as on the subsequent evolution process at later stages. As for the onset of ASB, the linear perturbation method is used to consider the effect on the initial formation of ASB. After the investigation of the onset of ASB, the characteristic line method is applied to describe the subsequent nonlinear evolution process of ASB. Three stages of ASB evolution are clearly depicted during the evolution process, and the significance of size effect on the ASB nonlinear evolution process of ASB at different stages is analyzed. With the help of linear perturbation analysis and characteristic line method, a comprehensive description of the role of strain gradient in the ASB from the early onset to the end of the evolution is provided.