Micromechanics: Crystal Plasticity Links for Deformation Twinning
Paudel, Yub Raj
AdvisorEl Kadiri, Haitham
CommitteeBarrett, Christopher D.
Priddy, Matthew W.
Tschopp, Mark A.
Historically, the ability of crystal plasticity to incorporate the Schmid’s law at each integration point has been a powerful tool to simulate and predict the slip behavior at the grain level and the succeeding heterogeneous stress/strain localization and texture evolution at the macroscopic level. Unfortunately, this remarkable capability has not been replicated for materials where twinning becomes a noticeable deformation mechanism, namely in the case of low-stacking fault energy cubic, orthorhombic, and hexagonal close packed structures. This dissertation is an attempt to gain understanding on the heterogeneous deformation due to twinning through various techniques including micromechanics, discrete dislocation dipole loops, and digital image correlation (DIC) analyses, and then bring the collected small scale information up to the full-field crystal plasticity scale using fast Fourier Trans- forms. Results indicate that the twin spacing depends primarily upon the height of the twin, and the stress relaxation from the twinning depends upon the thickness of the twin. Furthermore, in a homogenous stress state, discrete dislocation dipole loop-based twinning model showed that the lenticular shape has the minimum stable energy rather than the lamellar or ellipsoidal twin morphology. Our study on the evolution of twinning under three-point bending condition in strongly basal textured magnesium alloy allowed us to build a strategy to incorporate characteristic twin spacing parameter in the crystal plasticity framework. Inspired by results from molecular dynamics (MD) simulations stressing the effect of shuffles on twin nucleation and disconnection core width, we developed an explicit twinning nucleation criterion based on hydrostatic stress gradient and volume fraction of twin inside a grain. Characteristic twin spacing parameter is used as a function of twin height to determine site specific nucleation points in case of multiple twinnings. This ap- proach offered a good reproduction of the microstructure evolution as affected by twinning in a tri-crystal system.