Dislocation-mechanics-based constitutive relations for material dynamics calculations

TLDR

The constitutive relations are simple, broadly applicable to fcc materials, and extendable to bcc materials, though bcc behavior is incomplete due to missing twinning effects, and each crystal structure has its own dislocation‑based behavior. The study proposes a method for accounting for twinning in bcc materials, to be detailed in future work. The authors incorporated strain hardening, strain‑rate hardening, thermal softening, and grain‑size effects into a dislocation‑mechanics‑based constitutive relation for copper. The new relations provide an improved description of copper and iron Taylor‑test impact results, and an iron relation is also presented.

Abstract

An improved description of copper- and iron-cylinder impact (Taylor) test results has been obtained through the use of dislocation-mechanics-based constitutive relations in the Lagrangian material dynamics computer program EPIC-2. The effects of strain hardening, strain-rate hardening, and thermal softening based on thermal activation analysis have been incorporated into a reasonably accurate constitutive relation for copper. The relation has a relatively simple expression and should be applicable to a wide range of fcc materials. The effect of grain size is included. A relation for iron is also presented. It also has a simple expression and is applicable to other bcc materials but is presently incomplete, since the important effect of deformation twinning in bcc materials is not included. A possible method of acounting for twinning is discussed and will be reported on more fully in future work. A main point made here is that each material structure type (fcc, bcc, hcp) will have its own constitutive behavior, dependent on the dislocation characteristics for that particular structure.