Dislocation Mechanics of Shock-Induced Plasticity

Abstract

The constitutive deformation behavior of copper, Armco iron, and tantalum materials is described over a range of strain rates from conventional compressive/tensile testing, through split Hopkinson pressure bar (SHPB) test results, to shock-determined Hugoniot elastic limit (HEL) stresses and the follow-on shock-induced plasticity. A mismatch between the so-called ZerilliArmstrong (Z-A) constitutive equation description of pioneering SHPB measurements for copper provided initial evidence of a transition from the plastic strain rate being controlled by movement of the resident dislocation population to the strain rate being controlled by dislocation generation at the shock front, not by a retarding effect of dislocation drag. The transition is experimentally confirmed by connection with Swegle-Grady-type shock vs plastic strain rate measurements reported for all three materials but with an important role for twinning in the case of Armco iron and tantalum. A model description of the shock-induced plasticity results leads to a pronounced linear dependence of effective stress on the logarithm of the plastic strain rate. Taking into account the Hall-Petch grain size dependence is important in specifying the slip vs twinning transition for Armco iron at increasing strain rates.

Attenuation of the Dynamic Yield Point of Shocked Aluminum Using Elastodynamic Simulations of Dislocation Dynamics

“…The mobility law of dislocations is adjusted to account for the likely presence of high speed dislocations [1,18,21,[23][24][25][26][27][28]; data about the mobility of dislocations is extracted from MD simulations of aluminum [22] (see Supplementary Materials).…”

“…Thus, faster dislocation generation mechanisms must be considered. Smith [29], Hornbogen [30], Meyers and coworkers [31,32], Shehadeh et al [37] (using elastostatics) and Armstrong et al [21] have all proposed dislocation generation processes involving homogeneous nucleation. Recent simulations show that the stress levels required to nucleate dislocations homogeneously are about the ideal shear lattice resistance (µ/18 − µ/(4π)), easily achievable in shock loading (vid.…”

Transition of mechanisms underlying the rate effects and its significance

“…The effect has been widely observed in experiments of metals and alloys [2][3][4]. Experimental results were obtained from different technics [4][5][6], such as conventional compressive/tensile testing, split Hopkinson pressure bar, shock-determined Hugoniot elastic limit stresses and femtosecond laser pulses [6], over a wide strain rate range from 10 À4 to almost 10 9 s À1 . Several constitutive models had been proposed to describe the strain, stress and strain-rate relations [7][8][9].…”

Rate effect and coupled evolution of atomic motions and potential landscapes

“…It is reported that rate effects exist in a wide range of materials [2][3][4][5]. Strain rates in most experiments range from 10 −5 to 10 7 s −1 ; and rate effect mainly emerges in plastic deformation and fracture, e.g., yield stress, flow stress, strength and fracture toughness [3,6,7].…”

“…A distinct transition has been observed in the relationship of flow stress and strain rate in a number of metals, like copper, iron, etc. This indicates that there might be different mechanisms which can govern the rate effect [1,3]. So far, several mechanisms have been proposed, like dislocation mobility [3,8], shock controlled mechanism of dislocation or twinning [1,9,10], etc.…”