Abstract
This article examines the time to activate Frank–Read sources in response to macroscopic strain rates ranging from 101s−1 to 1010s−1 in aluminium under athermal conditions. We develop analytical models of the bowing of a pinned dislocation segment as well as numerical simulations of three dimensional dislocation dynamics. We find that the strain rate has a direct influence on both the activation time and the source strength of Frank–Read sources at strain rates up to 106s−1, and the source strength increases in almost direct proportion to the strain rate. This contributes to the increase in the yield stress of materials at these strain rates. Above 106s−1, the speed of the bowing segments reaches values that exceed the domain of validity of the linear viscous drag law, and the drag law is modified to account for inertial effects on the motion of the dislocation. As a result the activation times of Frank–Read sources reach a finite limit at strain rates greater than 108s−1, suggesting that Frank–Read sources are unable to operate before homogeneous nucleation relaxes elastic stresses at the higher strain rates of shock loading. Elastodynamic calculations are carried out to compare the contributions of Frank–Read sources and homogeneous nucleation of dislocations to plastic relaxation. We find that at strain rates of 5×107s−1 homogeneous nucleation becomes the dominant generation mechanism.
Highlights
The plastic response of metals subjected to loads imposed at different rates varies from the quasi-static response observed in conventional tensile tests, to one characterised by the formation of shock waves under high strain rate loading
We address the activation of Frank–Read sources at imposed strain rates below 106 sÀ1. At these strain rates dislocations may be modelled as Volterra discontinuities in an elastostatic continuum. By employing both analytical models and a three-dimensional model of discrete dislocation dynamics, we explore the effect of increasing the strain rate on the time and critical stress to activate a Frank–Read source
We have examined the finite times required for Frank–Read sources to operate in relation to imposed strain rates ranging from quasistatic to shock loading
Summary
The plastic response of metals subjected to loads imposed at different rates varies from the quasi-static response observed in conventional tensile tests (vid. Reed-Hill et al, 2009; Argon, 2008), to one characterised by the formation of shock waves under high strain rate loading (vid. Meyers, 1994; Swegle and Grady, 1985; Grady, 2010). The plastic response of metals subjected to loads imposed at different rates varies from the quasi-static response observed in conventional tensile tests Meyers, 1994; Swegle and Grady, 1985; Grady, 2010) In both regimes, plastic deformation is governed by the kinetics of the generation and motion of dislocations (Hirth and Lothe, 1982). In the quasi-static regime, plastic behaviour is governed by phenomena ranging from thermally activated motion of dislocations during creep and rupture to the plastic yielding of materials subjected to relatively small loads applied at low strain rates where slip is governed by the motion of pre-existing dislocations and by the generation of additional dislocations at Frank–Read sources (Hirth and Lothe, 1982)
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