Deformation and spallation of shocked Cu bicrystals with $\Sigma$3 coherent and symmetric incoherent twin boundaries

We perform molecular dynamics simulations of Cu bicrystals with two important grain boundaries (GBs), Σ3 coherent twin boundaries (CTB), and symmetric incoherent twin boundaries (SITB) under planar shock wave loading. It is revealed that the shock response (deformation and spallation) of the Cu bicrystals strongly depends on the GB characteristics. At the shock compression stage, elastic shock wave can readily trigger GB plasticity at SITB but not at CTB. The SITB can induce considerable wave attenuation such as the elastic precursor decay via activating GB dislocations. For example, our simulations of a Cu multilayer structure with 53 SITBs (∼1.5-μm thick) demonstrate a ∼80$\%$ elastic shock decay. At the tension stage, spallation tends to occur at CTB but not at SITB due to the high mobility of SITB. The SITB region transforms into a threefold twin via a sequential partial dislocation slip mechanism, while CTB preserves its integrity before spallation. In addition, deformation twinning is a mechanism for inducing surface step during shock tension stage. The drastically different shock response of CTB and SITB could in principle be exploited for, or benefit, interface engineering and materials design.

Figure 1

Schematic configurations of Cu bicrystals with a CTB (a) and a SITB (b), and shock loading geometry. Shock loading is along the $x$-axis.

Figure 2

(a)–(d) Snapshots of shock compression, release and spallation in the CTB bicrystal loaded at $u_{\mathrm{p}}$ = 0.75 km/s, and (e) the corresponding $x$-$t$ diagram. The impact plane is at $x$ = 0. Color coding in (e) is based on σ${}_{11}$. Region O: unshocked; S: shocked; R: release; T: tension.

Figure 3

The $x$-$t$ diagrams for the CTB (a) and SITB (b) bicrytsals shock-loaded at $u_{\mathrm{p}}$ = 0.375 km/s. The impact plane is at $x$ = 0. Color coding is based on local von Mises stress. Region P: impact plane plastic wave; GB-P: grain boundary plasticity.

Figure 4

(a) The initial atomic configuration of SITB. SITB contains a set of Shockley partial dislocations on a {111} plane with a repeating sequence of b${}_3$:b${}_1$:b${}_2$; (b) Projection onto a {111} plane showing the ABCABC stacking sequence. The stacking can be altered by the glide of any of the three Shockley partial dislocations.

Figure 5

Snapshots of the CTB response to the elastic and plastic shocks ($u_{\mathrm{p}}$ = 0.375 km/s): (a) no GB plasticity upon the passage of the elastic precursor; (b) and (c) GB steps produced by the plastic shock (dislocation slip).

Figure 6

GB-plasticity induced by the elastic shock at SITB for different shock strengths at $t$ = 16 ps. The 9R structure denotes the repeating stacking sequence of ABCBCACAB.

Figure 7

Evolution of the stress wave profiles for CTB (a) and SITB (b) shock-loaded at $u_{\mathrm{p}}$ = 0.75 km/s. GB locations are marked with the dashed lines. Also see text.

Figure 8

(a) The $x$-$t$ diagram for shock loading of the Cu multilayers contain 53 SITBs at $u_{\mathrm{p}}$ = 0.375 km/s. Color coding is based on pressure ($P$ = (σ${}_{11}$ + σ${}_{22}$ + σ${}_{33}$)/3), and the arrow indicates the reflection of the elastic shock wave front at the free surface. $E$ and $P$ ($P_1$ and $P_2$) stand for elastic wave and plastic wave, respectively. (b) The elastic precursor decay due to GB plasticity. The position refers to the elastic shock front position during its propagation. Atomic configurations at $t$ = 270 ps near the impact end (c) and the free surface end (d).

Figure 9

Structural variation of SITB during shock, tension and spallation for $u_{\mathrm{p}}$ = 0.5 km/s: (a) before the elastic shock arrival; (b) GB plasticity during elastic and plastic shock compression; (c) the first partial dislocation (b${}_{\mathrm{p}1}$) nucleation at SITB which slips in Gain I during tension; (d) the second partial dislocation (b${}_{\mathrm{p}2}$) formation in SITB which slips in Grain II; (e) partial transformation of the SITB into a threefold twin during tension; (f) void nucleation in Grain I, away from the original SITB.

Figure 10

Difference in void nucleation for CTB (a) and SITB (b) shock loaded at $u_{\mathrm{p}}$ = 0.5 km/s.

Figure 11

Formation sequence of a twinning-induced surface step for SITB shock-loaded at $u_{\mathrm{p}}$ = 0.75 km/s. (a) A bamboo-like deformation twin produces a surface step at the free surface of Grain II at $t$ = 60 ps. (b) to (h) Detailed deformation twin formation process at $t$ = 33.6, 34, 36, 38.8, 40, 42.8, and 60 ps, respectively; its thickening and propagation lead to the surface step. SP denotes slip plane.

Figure 12

The $x$-$t$ diagrams for shock loading of the Cu bicrystal with SITB at $u_{\mathrm{p}}$ = 0.75 km/s. Color coding is based on σ${}_{31}$. The region marked by the ellipse shows the strong shear stress region in Grain II during tension and spallation stage.