Time limited self-organised criticality in the high rate deformation of face centred cubic metals

Abstract

Plastic deformation is a fundamentally important physical process, ultimately determining how materials can be used. Metal plasticity is governed by dislocation dynamics and lattice twinning. Although many continuum constitutive models exist, plasticity is now known to occur in discrete events arising from the self-organisation of dislocations into ‘avalanches’ under applied stress. Here we extend avalanche plasticity to high strain rates, by introducing time limitation to self-organisation. At high rates large avalanches fail to form; the system must self-organise around new constraints. Various macroscopic consequences include an increasing rate of work hardening with strain rate. We perform new measurements on high purity copper that distinguish between instantaneous and permanent strength contributions across a strength transition at 104 s−1, showing the transition to be a change in structural evolution. Strong model agreement validates our time limited self-organisation approach. Our work results in a unified, physically realistic framework for plasticity, with wide applicability.

Dislocation Mechanics of Extremely High Rate Deformations in Iron and Tantalum

“…Fig. 1 A compilation [6,12,16] of copper conventional and split Hopkinson pressure bar measurements leading at higher pressures to two stress dependencies [15,17] proposed to be applicable for shock-induced strength behaviors.…”

“…Figure 1 illustrates the behavioral transition for very recently reported [16] split Hopkinson pressure bar (SHPB) measurements made on copper material, with and without stress interruption, in comparison with a previous compilation [6,12] of conventional, SHPB, and shock results. The lower, approximately linear, stress dependencies, at two strain values, apply for Eq.…”

High-Rate Crystal/Polycrystal Dislocation Dynamics

“…Figure 1 provides a compilation of SHPB and shock measurements based on the recent work of Lea et al [2] and including the previous Follansbee et al and dislocation mechanics descriptions of high-rate deformations [6]. The open-diamond and filled-circle measurements from Lea et al also include open-circle measurements made afterwards at the indicated strain rates to demonstrate that the strain hardening had been largely retained, as normally occurs for "shock hardening".…”

“…The open-diamond and filled-circle measurements from Lea et al also include open-circle measurements made afterwards at the indicated strain rates to demonstrate that the strain hardening had been largely retained, as normally occurs for "shock hardening". The approximately linear-fitted lower strain rate Lea et al and Follansbee et al measurements, in the latter case made at a compressive strain, ε = 0.15, are matched in the figure in each case with the face-centered cubic (fcc) form of the Z-A relationship for the flow stress, σ ε , that is expressed as [7] σ ε = σ Gε + B 0 [ε r (1 [1], ε = 0.15, SHPB measurements fitted to a Z-A relationship [7] and follow-on ε = 0.10 measurements reported by Lea et al [2], also shown in relation to extrapolation to the lower stress regime of experimental Swegle and Grady [5] and dislocation mechanics-based shock [4] descriptions.…”

“…Initial σ ε measurements had been reported for polycrystalline copper by Follansbee, Regazzoni and Kocks [1]. More recently, additional SHPB measurements were reported by Lea, Brown and Jardine [2] and compared with the work by Follansbee et al Another favorable compilation of copper measurements was presented recently by Jia, Rusinek, Pesci et al [3] as part of their study of the analogous high-strain-rate behavior exhibited in shear tests of 304 stainless steel material. The upturn in the strain-rate-dependent σ ε was initially proposed to be due to the onset of a "phonon drag resistance" to the motion of individual dislocations.…”