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 attracte d attention of some researchers, e.g. [3,1,22], Zerilli and Armstrong [22] suggested that the major effect of twinning is a refinement of the grain si ze. Based on this assumption, they proposed a model for twinning and showed that much better agreement with experiments can be obtained if, in additio n to deformation by slip, deformation twinning is also considered. Similar conclusions were reached by Holt rt al. [5] who analyzed the Taylor impact of a titanium specimen. In this work, we concentrate on the processes assoc iated with deformation twinning. We model twinning by using the theory intr oduced by Rajagopal and Srinivasa [17,18], which is based on multiple natur al configurations tan outline of the theory is given in Section 2). The the ory considers the energetics associated with twinning and it can predict th e volume fraction of the twinned material at each point and time. In this s tudy, we modal 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 clement method. Our results show that the energy absorbed d uring twinning and the deformation due to twinning are relatively small, an d the material twins more near the center line. We also demonstrate the dep endence of the results on the initial grain size of the material. Specifica lly, by modeling two materials of widely differing grain sizes, we show tha t the large-grained material twins substantially more than the small-graine d material. (C) 2000 Elsevier Science S.A. All rights reserved.