Sun, Chen, and colleagues developed a three-way coupled thermo-mechanical fracture model for sintered alpha-silicon carbide spanning 20 to 1400 degrees Celsius. The model, implemented in MOOSE, integrates elasticity, damage phase field analysis, and heat conduction into a single framework. Flexural strength predictions fell within the uncertainty envelope of experimental data across the full temperature range. More revealing than the accuracy was what the model required: analytical derivations of crack length scales under tension and shear that change with temperature, not just material constants but temperature-dependent geometric parameters governing how far damage can propagate before arresting.

The through-claim is that brittle materials fail not at a threshold stress but at a threshold length. The critical question is not how much force the material can bear but how far a crack can run before the geometry of the stress field forces it to stop. Temperature changes this length, not merely by weakening bonds but by altering the spatial envelope within which energy concentrates. The same applied stress can be harmless at one temperature and catastrophic at another, not because the material is weaker but because the characteristic damage distance has grown past a geometric boundary.

This reframes failure prediction in any brittle system. Software systems crash not when the bug is severe enough but when the error propagation path is long enough to reach a critical boundary. Financial contagion depends less on the size of the initial loss than on the chain length between counterparties. Fragility is a spatial property — it lives in the distance damage can travel, not in the force applied.

(arXiv:2603.04753)