Link Statistics of Dislocation Network during Strain Hardening

Dislocations are line defects in crystals that multiply and self-organize into a complex network during strain hardening. The length of dislocation links, connecting neighboring nodes within this network, contains crucial information about the evolving dislocation microstructure. By analyzing data from Discrete Dislocation Dynamics (DDD) simulations in face-centered cubic (fcc) Cu, we characterize the statistical distribution of link lengths of dislocation networks during strain hardening on individual slip systems. Our analysis reveals that link lengths on active slip systems follow a double-exponential distribution, while those on inactive slip systems conform to a single-exponential distribution. The distinctive long tail observed in the double-exponential distribution is attributed to the stress-induced bowing out of long links on active slip systems, a feature that disappears upon removal of the applied stress. We further demonstrate that both observed link length distributions can be explained by extending a one-dimensional Poisson process to include different growth functions. Specifically, the double-exponential distribution emerges when the growth rate for links exceeding a critical length becomes super-linear, which aligns with the physical phenomenon of long links bowing out under stress. This work advances our understanding of dislocation microstructure evolution during strain hardening and elucidates the underlying physical mechanisms governing its formation.

💡 Research Summary

This paper investigates the statistical distribution of dislocation link lengths in face‑centered cubic (fcc) copper during strain hardening, with a focus on individual slip systems. Using a large set of discrete dislocation dynamics (DDD) simulations performed with the ParaDiS code, the authors generated dislocation networks for 118 different loading orientations covering the entire stereographic triangle. For each simulation snapshot, links were defined as sequences of dislocation segments sharing the same Burgers vector and glide plane. The link lengths were normalized by the average link length for the corresponding slip system, and histograms were built using 125 bins spanning a normalized length range of 0–25. By averaging these normalized histograms over all time steps within a strain window of 0.9 %–1.05 % shear strain, the authors obtained link‑length density data spanning six orders of magnitude, far exceeding the range accessible in earlier studies that considered all slip systems together.

The key observation is that the link‑length distribution depends strongly on slip‑system activity. Slip systems with high Schmid factors (typically > 0.3) – i.e., the active systems – display a clear deviation from a simple exponential decay. Their distributions are accurately captured by a sum of two exponential terms:

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