17/06/13 meb. Open access paper, OK to pub

a b s t r a c tThis article examines the time to activate Frank-Read sources in response to macroscopic strain rates ranging from 10 1 s À 1 to 10 10 s À 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 FrankRead sources at strain rates up to 10 6 s À 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 10 6 s À 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 10 8 s À 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 Â 10 7 s À 1 homogeneous nucleation becomes the dominant generation mechanism.

Despite numerous theoretical models and simulation results, a clear physical picture of dislocations traveling at velocities comparable to the speed of sound in the medium remains elusive. Using two complementary atomistic methods to model uniformly moving screw dislocations, lattice dynamics and molecular dynamics, the existence of mechanical instabilities in the system is shown. These instabilities are found at material-dependent velocities far below the speed of sound. We show that these are the onset of an atomistic kinematic generation mechanism, which ultimately results in an avalanche of further dislocations. This homogeneous nucleation mechanism, observed but never fully explained before, is relevant in moderate and high strain rate phenomena including adiabatic shear banding, dynamic fracture, and shock loading. In principle, these mechanical instabilities do not prevent supersonic motion of dislocations.

The elastodynamic image forces on edge and screw dislocations in the presence of a planar-free surface are derived. The explicit form of the elastodynamic fields of an injected, quiescent screw dislocation are also derived. The resulting image forces are affected by retardation effects: the dislocations experience no image force for a period of time defined by the arrival and reflection at the free surface of the dislocation fields. For the case of injected, stationary dislocations, it is shown that the elastodynamic image force tends asymptotically to the elastotatic prediction. For the case of injected, moving dislocations, it is shown that the elastodynamic image force on both the edge and the screw dislocations is magnified by inertial effects, and becomes increasingly divergent with time; this additional effect, missing in the elastostatic description, is shown to be substantial even for slow moving dislocations. Finally, it is shown that the elastodynamic image force of an edge dislocation moving towards the surface at the Rayleigh wave speed becomes repulsive, rather than attractive; this is suggestive of instabilities at the core of the dislocation, and likely resonances with the free surface.

When a metal is subjected to extremely rapid compression, a shock wave is launched that generates dislocations as it propagates. The shock wave evolves into a characteristic two-wave structure, with an elastic wave preceding a plastic front. It has been known for more than six decades that the amplitude of the elastic wave decays the further it travels into the metal: this is known as "the decay of the elastic precursor". The amplitude of the elastic precursor is a dynamic yield point because it marks the transition from elastic to plastic behaviour. In this letter we provide a full explanation of this attenuation using the first method of dislocation dynamics to treat the time dependence of the elastic fields of dislocations explicitly. We show that the decay of the elastic precursor is a result of the interference of the elastic shock wave with elastic waves emanating from dislocations nucleated in the shock front. Our simulations reproduce quantitatively recent experiments on the decay of the elastic precursor in aluminum, and its dependence on strain rate.The dynamic behaviour of crystalline solids subjected to shock compression plays a central role in diverse applications, including bird strikes in aerospace [1], crashworthiness in the automobile industry [2], and manufacturing processes such as laser shock peening [3], amongst many others. Upon being shocked within a range of strain rates and pressures of typically 10 6 − 10 10 s −1 and 5 − 50GPa [1], the shock front in crystalline materials often displays a characteristic two-wave structure near the loading surface: the plastic wave front leading to the Hugoniot shocked state is preceded by an elastic precursor wave [1]. The amplitude of the elastic precursor wave decays as the wave front advances[1, 4]-a phenomenon known as the 'decay of the elastic precursor'. The amplitude of the elastic wave marks the onset of plasticity, i.e. it is the dynamic yield point. The subsequent plastic wave is commonly ascribed to the generation and motion of dislocations, the agents of plasticity in crystalline solids [9].The cause of its attenuation remains unclear after six decades [4][5][6][7][8]. Clifton and Markenscoff [4] calculated analytically the amplitude attenuation of a planar elastic shock wave caused by the destructive interference of elastic wavelets emanating from pre-existing dislocations set into motion by the passage of a shock wave of infinite strain rate; dislocation generation by the shock was neglected. Consequently, the elastic precursor decay was attributed to the density and initial velocity of pre-existing dislocations. Armstrong et al.[10] studied the dislocation relaxation mechanisms during high strain rate shock loading, concluding that dislocation generation dominates plastic relaxation under shock loading. This is because the number of pre-existing dislocations is about two to three orders of magnitude less than that generated during the shock [1,4,7].In this letter we show that we can account for the experimentally observed residual disloca...