Slip band formation and mobile dislocation density generation in high rate deformation of single fcc crystals

Abstract

The mechanisms for the nucleation, thickening, and growth of crystallographic slip bands from the sub-nanoscale to the microscale are studied using three-dimensional dislocation dynamics. In the simulations, a single fcc crystal is strained along the [111] direction at three different high strain rates: 10⁴, 10⁵, and 10⁶ s^− 1. Dislocation inertia and drag are included and the simulations were conducted with and without cross-slip. With cross-slip, slip bands form parallel to active (111) planes as a result of double cross-slip onto fresh glide planes within localized regions of the crystal. In this manner, fine nanoscale slip bands nucleate throughout the crystal, and, with further straining, build up to larger bands by a proposed self-replicating mechanism. It is shown that slip bands are regions of concentrated glide, high dislocation multiplication rates, and high dislocation velocities. Cross-slip increases in activity proportionally with the product of the total dislocation density and the square root of the applied stress. Effects of cross-slip on work hardening are attributed to the role of cross-slip on mobile dislocation generation, rather than slip band formation. A new dislocation density evolution law is presented for high rates, which introduces the mobile density, a state variable that is missing in most constitutive laws.

Keywords:

• slip bands
• high strain rate
• inertial effects
• cross-slip
• microbands
• dislocation dynamics

Acknowledgements

The work of Z.Q. Wang and I.J. Beyerlein was supported by the Advanced Simulation and Computing Program at Los Alamos National Laboratory (LANL). LANL is operated by the Los Alamos National Security, LLC, for the National Nuclear Security Administration of the United States Department of Energy (US DOE) under contract DE-AC52-06NA25396. RL gratefully acknowledges Iowa State University for its support.

Notes

Notes

1. The stresses on the segments that are too short to cross-slip are re-calculated only after a number of time steps rather than every time step 30. This is an optional feature that reduces computation time without having a noticeable impact on the results 30.

2. For crystals tested along the [100] direction, 30, the same power law represented in Equation (15) was applied to the generation of the total ρ. It was found that at 10⁶ and 10⁵ s⁻¹, n  = −0.3 and −0.2, respectively. Because of the multiple slip conditions in [100] (all four planes were equally active), the values for n cannot be compared with those for in Figure 14. Additional expressions for the interactions between active slip planes and possible nucleation of new Frank–Read sources (ω_cs  ≠ 0) are needed in the [100] load case.