Onset of Void Coalescence during Dynamic Fracture of Ductile Metals

Molecular dynamics simulations in three-dimensional copper are performed to quantify the void coalescence process leading to fracture. The correlated growth of the voids during their linking is investigated both in terms of the onset of coalescence and the ensuing dynamical interactions through the rate of reduction of the distance between the voids and the directional growth of the voids. The critical intervoid ligament distance marking the onset of coalescence is shown to be approximately one void radius in both measures.

Figure 1

Snapshots of the slices of the two-void system at $\dot{\epsilon }={10}^9/\mathrm{s}$ with only those atoms shown that are in dislocation cores, stacking faults, void surfaces, or other defects (see text). The dashed loop in panel (c) is drawn around a slice of a prismatic dislocation loop. The plane shown passes through the centers of both voids. The snapshots show the initial plasticity (a),(b), interacting plastic zones (c),(d), and the final coalescence (e),(f). The frames correspond to strains of $\epsilon =1.72\%$, 2.42%, 3.47%, 3.89%, 4.52%, and 5.21%, respectively.

Figure 2

The dynamical ILD, the distance between the surfaces of the voids along the line connecting the original center positions, plotted versus the mean void size ${\overline{f}}^{1/3}$ for various initial ${\mathrm{I}\mathrm{L}\mathrm{D}}_0$’s. The ILD is plotted in units of the average void diameter $d$ calculated at each instant using the formula $d=2[3/(4\pi )\overline{f}V{]}^{1/3}$, assuming roughly spherical voids. For reference, thin lines are plotted to show the relationship for spherical voids impinging freely on each other (see text). The red line shows the hypothetical ILD computed by duplicating the single void at fixed centers with ${\mathrm{I}\mathrm{L}\mathrm{D}}_0=1.8$. The horizontal line is at $\mathrm{I}\mathrm{L}\mathrm{D}=0.5d$.

Figure 3

Distance $d_{cv}$ from the original center of void to the instantaneous void center, projected onto the line connecting the original void centers, plotted versus the average void size to the point of coalescence ($\mathrm{I}\mathrm{L}\mathrm{D}\simeq 0$). The sign of the distance $d_{cv}$ is positive for motion toward the other void. ${\mathrm{I}\mathrm{L}\mathrm{D}}_0=1.8$. The thin solid line is for a single void in the same size of the box and with the same radius and $\dot{\epsilon }={10}^9/\mathrm{s}$ projected to the same line. Here the distance $d_{cv}$ is given in the units of the original void diameter $d_0$.

Figure 4

Growth of the voids until coalescence presented by void fraction for ${\mathrm{I}\mathrm{L}\mathrm{D}}_0=0.5$, 1.0, 1.2, 1.5, 1.8, and 4.6 diameters as well as in a single void case (in the same box size) at $\dot{\epsilon }={10}^9/\mathrm{s}$. The asymptotic behavior (before finite size effects) is exponential growth with $\exp (200ϵ)$ as seen in the inset for the single void case. In the main figure the void fraction $f$ has been scaled with the exponential. The circles point to where the dynamical ILD’s cross the line $\mathrm{I}\mathrm{L}\mathrm{D}=0.5$ in Fig. 2.