First-principles theory of work hardening and dislocation patterning
In plain words
As a metal is deformed it gets harder, and its dislocations arrange themselves into cells and walls whose size shrinks as the stress grows. Neither the hardening rate nor the pattern has been derived from the motion of individual dislocations.
Precise statement
In FCC single crystals (Cu, Al, Ni) the stage II hardening rate $\theta_{II} = d \tau / d \gamma$ is of order $\mu/200$ to $\mu/300$ ($\mu$ the shear modulus), nearly independent of material and temperature, and dislocation cells obey the similitude relation $\Lambda = K \mu b / \tau$ with $K$ of order 10 ($b$ the Burgers vector). Derive $\theta_{II}$ and the emergence and wavelength of cell structures from discrete or continuum dislocation dynamics without fitted hardening parameters. An answer is computed $\theta_{II}/\mu$ and $K$ within 20 percent of experiment.
What would settle it
Large-scale dislocation dynamics or a coarse-grained theory derived from it that reproduces $\theta_{II}$ and $K$ for at least two FCC metals.