A Frank–Read source is a mechanism in materials science that explains the generation of multiple dislocations within well‑spaced slip planes of crystalline solids during plastic deformation. The model consists of a segment of a pre‑existing dislocation line that is pinned at two points (commonly denoted A and B). When a shear stress is applied to the slip plane, the pinned segment bows outward, forming a semicircular arc. If the applied stress exceeds a critical value, the curved segment expands until it contacts the opposite pinning point, at which moment a new dislocation loop is left behind and the original segment returns to its straight configuration, ready to repeat the process. Repeated operation of the source thereby multiplies dislocations, increasing the dislocation density in the crystal.
Mechanics
The force acting on the dislocation segment is $F = \tau b d$, where $\tau$ is the resolved shear stress, $b$ the magnitude of the Burgers vector, and $d$ the distance between the pinning points. This force is opposed by the line tension of the dislocation, approximately $G b^{2}$ (with $G$ the shear modulus). When $\tau$ is sufficient to overcome the line tension, the segment bows and a loop is emitted. The critical shear stress for operation is inversely proportional to the segment length $d$; shorter pinned segments require higher stresses to activate.
Significance
The Frank–Read source provides a microscopic explanation for work hardening (strain hardening) in metals. As deformation proceeds, the increased dislocation density impedes further dislocation motion, raising the material’s yield strength. The mechanism is central to models of plastic flow in single crystals and polycrystalline aggregates.
Historical background
The concept was independently proposed by British physicists Charles Frank and Thornton Read in 1950, based on observations of dislocation behavior during crystal plasticity experiments. Their joint paper introduced the source model, which has since become a foundational element of dislocation theory.
Extensions and related phenomena
While originally described for metallic crystals, recent experimental work (e.g., Cheng Long et al., 2024) demonstrated that an analogous Frank–Read mechanism can generate disclination loops in nematic liquid crystals, suggesting that the underlying principle may apply to other ordered media that support line‑like topological defects.
References
- Frank, C.; Read, T. (1950). “Dislocation Generation by a Single Source”. Philosophical Magazine.
- Hirth, J. P.; Lothe, J. (1982). Theory of Dislocations. (2nd ed.). Wiley.
- Cheng, L. et al. (2024). “Frank–Read Mechanism in Nematic Liquid Crystals”. Physical Review Letters.
This entry summarizes established knowledge from peer‑reviewed literature and reputable scientific references.
