Towards a theory of flow stress in multimodal polycrystalline aggregates. Effects of dispersion hardening

TL;DR

This paper extends the theory of flow stress to multimodal polycrystalline aggregates, incorporating dispersion hardening and analyzing effects on yield strength across different crystalline structures and temperatures.

Contribution

It introduces a generalized two-phase model for multimodal polycrystals, including dispersion hardening effects, and derives analytical relations for various crystal lattices.

Findings

Maximum yield strength shifts with grain mode and phase composition.

Dispersion hardening influences the extremal grain size for strength.

Temperature affects the yield strength in multimodal aggregates.

Abstract

We elaborate the recently introduced theory of flow stress, including yield strength, in polycrystalline materials under quasi-static plastic deformations, thereby extending the case of single-mode aggregates to multimodal ones in the framework of a two-phase model which is characterized by the presence of crystalline and grain-boundary phases. Both analytic and graphic forms of the generalized Hall-Petch relations are obtained for multimodal samples with BCC ($\alpha$-phase Fe), FCC (Cu, Al, Ni) and HCP (Cu, Al, Ni) and HCP ($\alpha$-Ti, Zr) crystalline lattices at $T=300K$ with different values of the grain-boundary (second) phase. The case of dispersion hardening due to a natural incorporation into the model of a third phase including additional particles of doping materials is considered. The maximum of yield strength and the respective extremal grain size of samples are shifted by changing both the input from different grain modes and the values at the second and third phases. We study the influence of multimodality and dispersion hardening on the temperature-dimensional effect for yield strength within the range of $150-350K$.