Physics-based crystal plasticity modeling of single crystal niobium

Crystal plasticity models based on thermally activated dislocationkinetics has been successful in predicting the deformation behavior ofcrystalline materials, particularly in face-centered cubic (fcc) metals.In body-centered cubic (bcc) metals success has been limited owing toill-defined slip planes. The flow stress of a bcc metal is stronglydependent on temperature and orientation due to the non-planar splittingof a/2<111> screw dislocations. As a consequence of this, bccmetals show two unique deformation characteristics: (a) thermally-activated glide of screw dislocations - the motion of screwcomponents with their non-planar core structure at the atomistic leveloccurs even at low stress through the nucleation (assisted by thermalactivation) and lateral propagation of dislocation kink pairs; (b)break-down of the Schmid Law, where dislocation slip is driven only bythe resolved shear stress.Since the split dislocation core has to constrict for a kink pairformation (and propagation), the non-planarity of bcc screw dislocationcores entails an influence of (shear) stress components acting on planesother than the primary glide plane on their mobility. Anotherconsequence of the asymmetric core splitting on the glide plane is adirection-sensitive slip resistance, which is termed twinning/atwinningsense of shear and should be taken into account when developingconstitutive models.Modeling thermally-activated flow including the above-mentionednon-Schmid effects in bcc metals has been the subject of much work,starting in the 1980s and gaining increased interest in recent times.The majority of these works focus on single crystal deformation ofcommonly used metals such as Iron (Fe), Molybdenum (Mo), and Tungsten(W), while very few published studies address deformation behavior inNiobium (Nb). Most of the work on Nb revolves around fitting parametersof phenomenological descriptions, which do not capture adequately themacroscopic multi-stage hardening behavior and evolution ofcrystallographic texture from a physical point of view. Therefore, weaim to develop a physics-based crystal plasticity model that can capturethese effects as a function of grain orientations, microstructureparameters, and temperature.To achieve this goal, first, a new dilatational constitutive model isdeveloped for simulating the deformation of non-compact geometries (foamsor geometries with free surfaces) using the spectral method. The modelhas been used to mimic the void-growth behavior of a biaxially loadedplate with a circular inclusion. The results show that the proposedformulation provides a much better description of void-like behaviorcompared to the pure elastic behavior of voids. Using the developeddilatational framework, periodic boundary conditions arising from thespectral solver has been relaxed to study the tensile deformationbehavior of dogbone-shaped Nb single crystals.Second, a dislocation density-based constitutive model with storage andrecovery laws derived from Discrete Dislocation Dynamics (DDD) isimplemented to model multi-stage strain hardening. The influence ofpre-deformed dislocation content, dislocation interaction strengths andmean free path on stage II hardening is then simulated and compared within-situ tensile experiments.