A rate-dependent, finite-deformation and crystal-mechanics-based constitutive theory was developed which described the twinning in single-crystal metallic materials. Central to the derivation of the constitutive equations were the use of fundamental thermodynamic laws and the principle of micro-force balance (Fried & Gurtin, 1994). A robust numerical algorithm based on the constitutive model has also been written and implemented in a finite-element program. Physical experiments in compression, cyclic tension-compression, plane-strain compression and three-point bending were conducted on an initially-martensitic shape-memory alloy single crystal. In order to determine the material parameters in the constitutive model, the stress–strain result from a finite-element simulation of the single crystal in simple compression was fitted to the corresponding result determined from the physical experiment. With the material parameters determined, it was shown that the stress–strain and force–displacement curves for the other aforementioned experiments were predicted to be in good accord by the present constitutive model. These calculations showed that the overall stress–strain responses and the microstructure evolution exhibited by the single crystal shape-memory alloy during the twinning process was highly dependent upon the initial microstructure, crystal orientation and the loading conditions e.g., tension vs. compression etc. Finally, it was shown that - by suitable augmentation of the free energy density with a gradient energy - the sensitivity of the calculated twin plane interface thickness to the density of the finite-element mesh could be minimized. This made the tracking of the twin plane interface during the twinning process possible without the aid of jump conditions.

The Evolution of Microstructure during Twinning: Constitutive Equations, Finite-Element Simulations and Experimental Verification. P.Thamburaja, H.Pan, F.S.Chau: International Journal of Plasticity, 2009, 25[11], 2141-68