Dislocation Networks and the Microstructural Origin of Strain Hardening

When metals plastically deform, the density of line defects called dislocations increases and the microstructure is continuously refined, leading to the strain hardening behavior. Using discrete dislocation dynamics simulations, we demonstrate the fundamental role of junction formation in connecting dislocation microstructure evolution and strain hardening in face-centered cubic (fcc) Cu. The dislocation network formed consists of line segments whose lengths closely follow an exponential distribution. This exponential distribution is a consequence of junction formation, which can be modeled as a one-dimensional Poisson process. According to the exponential distribution, two non-dimensional parameters control microstructure evolution, with the hardening rate dictated by the rate of stable junction formation. Among the types of junctions in fcc crystals, we find that glissile junctions make the dominant contribution to strain hardening.

Figure 1

Shear stress-strain curves of single crystalline Cu deformed along [001] axis. Thick curves are predictions by DDD simulations for an initial dislocation density ${\rho }_0=0.7\times {10}^{12}{\mathrm{m}}^{-2}$ at two different strain rates $\dot{ϵ}$. The thin solid line is extracted from experimental data [33] at strain rate of $\dot{ϵ}=3\times {10}^{-3}{\mathrm{s}}^{-1}$. The dashed lines are translated from the thin solid line to show the consistency of the strain hardening rate between simulations and experiments.

Figure 2

(a) Snapshot from a DDD simulation at $\gamma =0.87\%$ shear strain, with $\dot{ϵ}={10}^3{\mathrm{s}}^{-1}$ and ${\rho }_0=0.7\times {10}^{12}{\mathrm{m}}^{-2}$. (b) Dislocation link length distribution $n(L)$ for the structure shown in (a) (after being relaxed to zero stress) compared to Eq. (3).

Figure 3

$\varphi -\beta$ values during DDD simulations at strain rates $\dot{ϵ}={10}^3{\mathrm{s}}^{-1}$ and $10^2{\mathrm{s}}^{-1}$. Dashed lines are guide to the eye for the range of $\varphi -\beta$ values. The * symbol indicates the critical value ${\varphi }_{\mathrm{c}}$, beyond which Eq. (7) becomes valid.

Figure 4

Shear stress-strain curves and (inset) strain hardening rates for specialized DDD simulations with selected types of junctions suppressed; ${\rho }_0=0.7\times {10}^{12}{\mathrm{m}}^{-2}$ and $\dot{ϵ}={10}^3{\mathrm{s}}^{-1}$. The legend shows the type of junctions that are allowed to form during the simulation.