Definition
A Frank–Read source is a dislocation generation mechanism in crystalline materials whereby a pinned segment of a dislocation line bows out under applied shear stress, eventually forming a loop that detaches and leaves the original segment ready to repeat the process. This mechanism provides a continuous source of mobile dislocations that contribute to plastic deformation.
Overview
First described in 1950 by physicists Frederick C. Frank and Thornton Read, the Frank–Read source explains how a single dislocation line can multiply, thereby increasing the dislocation density during plastic flow. In a crystal, obstacles such as impurity atoms, precipitates, grain boundaries, or other dislocations can pin the ends of a straight dislocation segment. When a resolved shear stress exceeds a critical value, the segment bows outward between the pinning points, forming a semi‑circular shape. As the stress continues, the bowed segment expands until it touches itself, creating a closed dislocation loop that detaches from the original line. The remaining segment is again pinned and can generate additional loops under continued loading. This process is a key component of the dislocation theory of work hardening.
Etymology/Origin
The term combines the surnames of the two scientists who introduced the concept: Frederick C. Frank, an American physicist, and Thornton Read, a British metallurgist. Their joint publication in Philosophical Magazine (1950) presented the theoretical analysis of the mechanism, which has since borne their names.
Characteristics
- Pinning Points: Fixed obstacles at the ends of the dislocation segment; can be point defects, precipitates, or grain boundaries.
- Critical Stress: The shear stress required to initiate bowing, given by τ_c = (2Gb) / (L), where G is the shear modulus, b the Burgers vector magnitude, and L the length of the pinned segment.
- Loop Geometry: The emitted loop is generally circular (or elliptical) and lies in the slip plane of the original dislocation.
- Source Length Dependence: Longer pinned segments generate loops at lower stresses but produce larger loops; shorter segments require higher stresses and yield smaller loops.
- Multiplication Rate: The rate at which loops are emitted depends on the applied stress, temperature (which influences dislocation mobility), and the density of available pinning sites.
- Contribution to Work Hardening: As loops intersect existing dislocations, they increase the overall dislocation density, raising the material’s flow stress.
Related Topics
- Dislocation theory of plasticity
- Slip systems in crystalline solids
- Work hardening (strain hardening)
- Orowan mechanism (dislocation bypass of obstacles)
- Grain boundary strengthening (Hall–Petch relationship)
- Cottrell atmosphere (solute atoms pinning dislocations)
- Crystal defects (vacancies, interstitials, stacking faults)
This entry reflects information established in peer‑reviewed materials science literature and textbooks.