Fillet Stress Evolution

Analysis: The fillet radius creates a geometric discontinuity that amplifies thermal stress. As the thermal wave penetrates (diffusion length √(α·τ)), the stress concentration evolves non-linearly. Peak stress occurs when the thermal front reaches the fillet root, creating maximum curvature mismatch.

For r/t = —, the theoretical static Kₜ ≈ —. However, under dynamic loading at — °C/s, the transient amplification factor reaches —x.

This is why the frozen brisket cracks: the thermal shock exceeds the yield strength before the core can equilibrate.