Dislocation Glide: Why Metals Yield 1000× Below Theoretical Strength

The theoretical strength problem

Frenkel's 1926 calculation estimated the shear stress needed to slide one perfect atomic plane over the next: τ_th ≈ G/2π, roughly G/6 by common approximation. For iron, with shear modulus G ≈ 80 GPa, that predicts a theoretical strength around 13 GPa. Measured shear yield stress for annealed polycrystalline iron at room temperature is only 25–30 MPa — a discrepancy of 500 to 1,000 times. Something had to be moving atoms far more cheaply than sliding whole planes at once.

Glide: moving one row of bonds at a time

The resolution, proposed independently by Taylor, Orowan and Polanyi in 1934, is the dislocation. Rather than breaking every bond across a slip plane simultaneously, a dislocation lets the crystal shear by breaking and reforming just the bonds at its core, then advancing one atomic spacing — like a ripple pushed across a carpet rather than dragging the whole carpet at once:

Energy required to move a dislocation ∝ line length, not swept area
→ stress needed drops by 2-4 orders of magnitude vs the theoretical limit

Peter Hirsch's group (Cambridge, 1956) first observed dislocations
gliding directly, using transmission electron microscopy

Glide happens preferentially on slip systems — close-packed planes in close-packed directions, where atoms are densest and the Burgers vector is smallest. FCC metals get 12 independent {111}⟨110⟩ slip systems and are correspondingly ductile; BCC metals, lacking a truly close-packed plane, need higher stress to activate slip and are stronger but less formable at room temperature.

Work-hardening: dislocations breeding dislocations

A crystal starts with a dislocation density around 10¹⁰–10¹² m⁻² of line length per unit volume, but heavy cold work drives it up to 10¹⁵–10¹⁶ m⁻². The mechanism is the Frank-Read source: a dislocation segment pinned at two points bows outward under stress until it wraps around and pinches off a full loop, then re-forms and repeats — one source can emit thousands of loops per second:

Frank-Read critical stress: τ_FR = α·G·b / L
Example (L=1 µm, G=80 GPa, b=0.25 nm): τ_FR ≈ 10 MPa

Taylor hardening: Δσ = α·G·b·√ρ    (α ≈ 0.2–0.5)
As ρ rises, dislocations tangle and block each other → the metal
gets harder to deform further — this is work-hardening.

This is why bending a paperclip back and forth makes each successive bend stiffer, and why cold-rolled steel sheet is measurably stronger than the same alloy annealed. Heating reverses it: annealing lets dislocations rearrange and annihilate, restoring ductility — the cold-work-then-anneal cycle is the backbone of sheet-metal manufacturing.

Engineering the glide, not just the alloy

Once dislocation glide is understood as the mechanism of plasticity, strengthening becomes a game of putting obstacles in its way. Precipitation hardening disperses nanometre-scale particles (Cu-rich θ' phase in aerospace Al-Cu alloys) that dislocations must cut through or bow around. Dispersion strengthening uses incoherent oxide particles that survive the high temperatures where precipitates would coarsen away, as in nickel superalloy turbine blades running at 1,100°C. In semiconductors the goal flips entirely: dislocations create deep-level electronic traps, so Czochralski-grown silicon aims for effectively zero dislocation density instead.

Frequently asked questions

Try it live

Everything above runs in your browser — open Dislocation Glide and apply shear stress to watch an edge dislocation sweep across its slip plane while the surrounding stress field updates in real time. Nothing is installed, nothing is uploaded.