Finite difference calculations of one-dimensional, convection-conduction, non-reacting heat flow are described, focusing on near-cannon-bore temperatures using time-dependent combustion gas temperatures and convection coefficient data derived from cannon interior ballistic codes. Temperatures are obtained for a 0.1-to-1.0 mm thickness range of chromium or tantalum coating over pressure vessel steel substrate, using temperature-dependent conductivity and diffusivity data for pure chromium and tantalum and ASTM A723 steel. In-situ verification of calculated temperature profiles is done by comparing with metallographic observation of depths of the steel phase transformation at its well characterized temperature. The temperature profiles are used to estimate the thermal shear stress at the interface of a crack-generated coating segment, with segment length characteristic of that observed from cannon firing. Finite element thermo-mechanical analysis is used to verify that the temperature difference used to estimate interface shear stress and the resulting stress values are realistic. Results show that: [i] temperatures and interface stress are somewhat higher for Ta than Cr coatings due to the lower heat capacity of Ta; [ii] interface stress is higher for thinner coatings, as expected, but reaches a maximum at 0.1 to 0.2 mm thickness, because of the limited temperature range that can be present in a thinner coating; [iii] the characteristic length of coating segment relative to coating thickness has important control over interface shear stress, with the longer segment observed for tantalum coatings providing a significant reduction in average shear stress compared to the stress for the smaller segments observed with chromium coatings.

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