Integration of self-consistent polycrystal plasticity with dislocation density based hardening laws within an implicit finite element framework: Application to low-symmetry metals

Strain rate and temperature effects on the selection of primary and secondary slip and twinning systems in HCP Zr

“…The barriers for twin activation and propagation within each crystal follow a different model than slip and this twinning model will be reviewed last. In several prior studies, this same basic modeling framework has been successfully applied to a variety of metals of different crystal structures: Zr [45,46], Be [47,48], and Mg [49,50], BCC Ta [51][52][53], an FCC cobalt alloy [54], and orthorhombic uranium [55,56]. However, to meet the objectives of this work, we found it necessary to extend the framework to treat multiple modes of twins per crystal, interactions between slip modes, and lattice reorientation by secondary (internal) twinning.…”

“…Such calculations are possible with full-field models based on finite elements [17,72] or Green's functions [73] that consider explicitly the grain structure of the metal [74] but not the mean-field formulation adopted here. Nevertheless, to first order, prior work using mean-field models has demonstrated that assuming that the twins associated with the highest Schmid factor variant can lead to reasonable predictions for twin volume fraction and texture for many low-symmetry metals including Zr [7,23,45,46], Be [47,48], Mg [49,50,75], Ti [6] and U [55,56]. This success likely results because the thicker twins usually correspond to twins with the higher Schmid factor [68,76].…”

A multi-scale model for texture development in Zr/Nb nanolayered composites processed by accumulative roll bonding

“…This physically based dislocation density (DD) model replaces the empirical hardening laws that are sometimes used in CPFE modeling. In prior work, the DD hardening model used here [50] has been successfully applied to a broad variety of metals, differing in crystal structure, such as bcc "Haynes 25" [51], Nb [25], Mg [52], Zr [24,50,53], Be [54], and uranium [55][56][57]. All the foregoing studies implemented the DD model into the mean-field polycrystal visco-plastic self-consistent (VPSC) [50,58] scheme.…”

Thermomechanical Response of Polycrystalline alpha-Uranium

“…More recently, Knezevic et al utilized the VPSC model in conjunction with finite element methods to predict the response in four-point bending [41]. The model was able to capture the texture evolution through the thickness and plastic deformation state of the beam after loading.…”

“…Finally, the 1 2 h112i{021} mode, denoted roof slip, has four slip systems and the largest CRSS among all the modes, up to the transformation temperature of ↵-uranium. Roof slip is usually observed only near the transition temperature in single crystals [2], but has been considered in crystal plasticity modeling of low temperature deformation [41] as it is necessary to close the single crystal yield surface [9]. The interplay between these di↵erent deformation mechanisms has been recently investigated [1,8,30,31,35].…”