Instability analysis of shear bands using the instantaneous growth-rate method. (January 2016) - Arriaga, Miguel; McAuliffe, Colin; Waisman, Haim
Abstract: Shear banding, as an unstable process of localization, is a common precursor to fracture in materials under high strain rate loadings, making the detection of the instability point after which localization will occur of significant importance. Stability analysis based on the perturbation method or the acoustic tensor have been employed. However, these methodologies are limited to certain class of problems and are difficult to generalize. In this work we propose an alternative for identifying the instability point by employing the concept of generalized stability analysis. In this framework, a stability measure is obtained by computing the instantaneous growth rate of the vector tangent to the solution. Such an approach is more appropriate for non-orthogonal problems and is easier to generalize to difficult dynamic fracture problems. Under conditions where the local instability triggers the non-homogeneous solution growth, i.e. problems that are homogeneous until the appearance of local instability, the generalized stability analysis and the modal stability analysis will closely match. Therefore, the non-homogeneous growth can be approximated by the Rayleigh Quotient of the vector tangent to the solution, which is easier to compute. We show that for a particular class of problems that respect the aforementioned conditions, in 1D and 2D examples, both quantities successfully find the instability point predicted analytically and validated experimentally in past literature results. This methodology is general and can be applied to a wide array of dynamic fracture problems, for which instability that leads to localization is important. Highlights: Stability of shear bands is studied using the instantaneous growth-rate method. Proposed method is appropriate to non-orthogonal problems and easier to generalize. Numerical results show the recovering of the traditional stability criteria.