The evolution of microstructure during twinning: Constitutive equations, finite-element simulations and experimental verification

In this work, we develop a rate-dependent, finite-deformation and crystal-mechanics-based constitutive theory which describes the twinning in single-crystal metallic materials. Central to the derivation of the constitutive equations are the use of fundamental thermodynamic laws and the principle of micro-force balance [Fried, E., Gurtin, M., 1994. Dynamic solid–solid transitions with phase characterized by an order parameter. Physica D 72, 287–308]. A robust numerical algorithm based on the constitutive model has also been written and implemented in the ABAQUS/Explicit [Abaqus reference manuals, 2007. SIMULIA, Providence, R.I.] finite-element program. Physical experiments in compression, cyclic tension-compression, plane-strain compression and three-point bending have been 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, we show that the stress–strain and force–displacement curves for the other aforementioned experiments were predicted to be in good accord by our constitutive model. Our calculations show that the overall stress–strain responses and the microstructure evolution exhibited by the single crystal shape-memory alloy during the twinning process is highly dependent on the initial microstructure, crystal orientation and the loading conditions e.g., tension vs. compression etc. Finally, we show 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 can be minimized. This makes the tracking of the twin plane interface during the twinning process possible without the aid of jump conditions.