Background
Tungsten is the leading armour material for nuclear fusion plasma-facing components, combining the highest melting point of any metal (3695 K) with high thermal conductivity, a low sputtering yield and low tritium retention. Its use is constrained by the ductile-to-brittle transition: below the transition temperature it fractures by cleavage, and because recrystallisation and neutron irradiation raise that temperature, it can fall within the operating range of a reactor that cycles through start-up and shut-down every pulse. No neutron source yet reproduces the neutron spectrum of a nuclear fusion reactor, so the irradiated transition cannot be measured under representative conditions, and validated assessment methods for brittle armour materials remain lacking.
Approach
I implemented a continuum dislocation dynamics model of a single tungsten grain in Julia (around 1,300 lines, with no external dislocation library). Screw dislocation glide is governed by thermally activated kink-pair nucleation, so glide velocity varies by around twelve orders of magnitude across the temperature range. Frank–Read sources multiply dislocations, impenetrable grain boundaries force pile-ups whose back-stress throttles further plasticity, and the grain unloads against its surroundings as plastic strain accumulates. The plastic work dissipated in a fixed 120 s window was computed at 30 temperatures between 100 and 3000 K, and the transition temperature was taken from the inflection of the resulting curve, with nothing fitted to measured transition data.
The model was verified in stages against analytical and published values. The simulated pile-up converged to within 1.1% of the Eshelby–Frank–Nabarro solution under mesh refinement, and correcting a dimensional inconsistency in the published kink-barrier amplitude brought the kink-pair energy to 1.574 eV, within 10% of the 1.75 eV measured on high-purity single crystals.
Findings
The model reproduces the lower shelf, steep transition and upper plateau characteristic of experimental transition curves directly from the dislocation kinetics, with the transition arising from the coupled loss of dislocation mobility and source emission at low temperature. It predicts a transition temperature of 386 K (347–425 K for ±10%), between the 348 K and 398 K measured on warm-rolled pure tungsten.
Coarser grains raised the transition temperature by 63 K across a fivefold increase in grain size, while plateau work increased 21-fold, consistent with dissipative capacity scaling with grain area. Irradiation raised the transition steeply before saturating, with 80% of the shift reached by 0.5 dpa and a predicted shift of 614 K at 1 dpa against approximately 650 K measured experimentally. Because a full 30-point sweep runs in under a minute on a single desktop core, the model serves as an inexpensive, mechanism-based screening tool for conditions beyond practical experimental reach.
