PDF《pure metals》

s own elastic self-energy. Since dislocations move to minimise the elastic free energy of the system [3], the mobility law usually expresses the effect of the external stimuli in terms of the PeachCKoehler force [4]: σ ξ = ε f B i ijk lj l k (1) where ≡ f f i PK is the PeachCKoehler force, εijk the Levi-Civita tensor, σlj the external stress ?tensor, Bl the Burgers vector, and ξk the direction of the dislocation line. Equally, the effect of the lattice resistance is expressed as a drag force, the nature of which depends on the speed the dislocation is moving at. At low stresses and low strain rates, dislo- cation motion is naturally impeded by the Peierls barrier, and the motion is governed by the thermally assisted probability of overcoming that barrier [5]. At higher stress levels, disloca- tions are able to overcome the barrier and enter a free glide regime where the drag force is said to resemble a viscous drag force [5], where the glide speed is reported to be proportional to the applied resolved shear stress, τ: τ = v B d glide (2) where d is a drag coefficient and =| | B B the magnitude of the Burgers vector, both dependent on the material. This '

free glide'

or '

pure drag'

regime and, consequently, equation?(2), neglect the impor- tance the dislocation'

s self-energy may have in its own motion. It is known that the latter increases with the dislocation'

s speed [5C7], and that according to first order linear elastic- ity, it diverges at the transverse speed of sound, which has led the latter to be regarded as a limiting speed of dislocations [5]. This effect results in a well-attested [5, 6, 8, 9] saturation of the speed a dislocation may achieve with respect to increasing PeachCKoehler force;

due to its similarity with the relativistic motion of electric charges, this regime is often referred to as relativistic regime. Additional likely effects resulting from the fast moving dislocations [8, 10], suggest that the intrinsic lattice resistance may be different from the viscous drag given by equation?(2), which complicates the proposal of a univocally clear mobility law valid in the relativistic regime. This is particularly relevant for shock loading, where due to the magnitude of the applied loads, most dislocations are believed to glide in either the pure drag regime or, more usually, in the relativistic regime (see [5, 8]). Most of the proposed dislocation mobility laws that can be employed in shock loading are therefore speculative at best. Nonetheless, there seems to be B Gurrutxaga-Lerma? Modelling Simul. Mater. Sci. Eng.

24 (2016)

065006 3 a large consensus in that the dislocation'

s speed should saturate as it approaches the transverse speed of sound [5, 6, 9, 11C14] or, in the presence of free surfaces, the Rayleigh wave speed [5, 15]. This article examines the role mobility laws may have in determining the plastic relaxation of a shock front propagating through FCC aluminium employing dynamic discrete dislocation plasticity (D3P). Therefore, all results presented here apply for the motion of pure edge dis- locations in pure metals, thereby lacking impurities or any other such defects that may affect the dislocation'

s drag. In section?2, the mobility laws that will be put to test are introduced. Section?3 presents the details of the D3P simulations where the mobility laws will be tested, as well as their significance to the study of plastic relaxation in shock loading. Section?4 presents the results of this study, and offers a physical interpretation of the latter. Section?5 summarises the main findings of this work. 2.? Mobility laws of high speed dislocations The requirement that the dislocation'