Deformation twinning during impact of a titanium cylinder  numerical calculations using a constitutive theory based on multiple natural configurations
It is well-known that polycrystalline metals (especially those with bcc or hcp structures), when subjected to impact, undergo two inelastic processes  slip and twinning. Since the work of Taylor [20] the former one has been studied extensively; while more recently, deformation twinning has attracted attention of some researchers, e.g. [3], [1]and[22]. Zerilli and Armstrong [22] suggested that the major effect of twinning is a refinement of the grain size. Based on this assumption, they proposed a model for twinning and showed that much better agreement with experiments can be obtained if, in addition to deformation by slip, deformation twinning is also considered. Similar conclusions were reached by Holt et al. [5] who analyzed the Taylor impact of a titanium specimen. In this work, we concentrate on the processes associated with deformation twinning. We model twinning by using the theory introduced by Rajagopal and Srinivasa [17]and[18], which is based on multiple natural configurations (an outline of the theory is given in Section 2). The theory considers the energetics associated with twinning and it can predict the volume fraction of the twinned material at each point and time. In this study, we model the Taylor impact of a titanium cylinder. We assume that the problem is axisymmetric and solve the full dynamic equations by using the Galerkin finite element method. Our results show that the energy absorbed during twinning and the deformation due to twinning are relatively small, and the material twins more near the center line. We also demonstrate the dependence of the results on the initial grain size of the material. Specifically, by modeling two materials of widely differing grain sizes, we show that the large-grained material twins substantially more than the small-grained material.
twinning impact natural configurations rate of dissipation stored energy