Crystal Plasticity Constitutive Modeling of Grain Size-Texture Coupling with Application to Mg-4Al

Abstract

Grain refinement is a common strategy to improve the yield strength of magnesium (Mg) alloys quantified via the empirical Hall-Petch equation. Due to the hexagonal close-packed (HCP) crystal structure of Mg alloys, the Hall-Petch effect, which characterizes the sensitivity of the yield stress to the grain size, has been observed to be strongly dependent on the underlying crystallographic texture, arising through the effect of grain boundaries (GBs) as evidenced by several experimental studies. Crystal plasticity (CP) simulations form a powerful modeling tool to model and simulate the elastoplastic mechanical behavior of crystalline materials. Classical CP models do not include the effect of grain size in the constitutive model and hence are unable to simulate the Hall-Petch effect. There are also very few studies targeted towards developing constitutive models which account for the effect of grain size on the yield stress of the material. More so, those few studies do not account for the underlying microstructural aspects due to which the coupling between texture and grain size is not explicitly considered.

This thesis presents efforts towards developing such a constitutive model accounting for this grain size-texture coupling by integrating high-resolution electron backscatter diffraction experiments with dislocation pile-up theory and CP simulations. A rate-dependent CP constitutive model was first developed within the PRISMS-Plasticity framework, an open-source parallelized finite element code to simulate the elasto-viscoplastic behavior of materials. In the context of the Hall-Petch effect, a continuum dislocation pile-up model was used to fit pile-up stress measurements ahead of basal slip bands blocked by GBs in Mg-4Al, which along with some simplifying assumptions, yields the micro-Hall-Petch parameters for basal slip for nine GBs. The basal micro-Hall-Petch parameters were then related to GB metrics using an empirical power-law equation to obtain the basal micro-Hall-Petch coefficients - the micro-Hall-Petch multiplier and exponent. The GB metrics were constructed from incoming and potential outgoing slip system information obtained from CP simulations of GB neighborhoods of the GBs considered. Extending a similar procedure to prismatic slip, the prismatic micro-Hall-Petch parameters were then related to GB metrics to obtain the prismatic micro-Hall-Petch coefficients - the micro-Hall-Petch multiplier and exponent. The potential outgoing slip system information required to construct the GB metrics was obtained from CP simulations of GB neighborhoods. The experimental work does not as yet consider a micro-Hall-Petch equation for the pyramidal slip or extension twinning systems. The micro-Hall-Petch model was implemented into PRISMS-Plasticity and calibrated against experimental stress-strain curves obtained from samples of different textures and grain sizes. The model is used to study the modulation of the grain size effect due to additional parameters including texture, loading direction, and the grain aspect ratio. From the studies involving modulation of texture and loading direction, we find that the relative competition between basal and prismatic slip activity with texture changes determines the variations in the Hall-Petch slope. From the aspect ratio study, we obtain an asymmetric variation in the yield stress with the aspect ratio, which is justified using theoretical arguments. This approach provides the foundation to quantitatively model and design microstructural features to enhance the engineering properties of Mg alloys.