Crack formation analysis during transient thermal pyrolysis of a heated annular disk

Abstract

Solid fuel combustion involves chemical pyrolysis which liberates volatile reactants that feed the active flame. If the pyrolytic reaction is char forming then the resulting solid degradation involves generalized fracture processes with complex crack and craze morphologies. We model this for an annular thin disk heated at its inner hole boundary. Pyrolytic mass loss gives a state of plane stress which is simply analyzed prior to crack formation because of the circular symmetry. Cracking breaks this symmetry. We model the ensuing fracture using both a critical stress criterion as well as a phase field model. The former is characterized by a critical stress material parameter ${\sigma }_c$. The latter is characterized by the energy release rate $G_c$ and the characteristic length $l_c$. Cracks initiate at the heated surface in both models and then advance into the disk. At issue is the resulting crack morphology and the extent to which the advancing pattern is or is not tightly correlated to the advancing char process zone across which the solid material density transitions from its original virgin value to its fully charred value. Crack pattern morphology is found to vary with both ${\sigma }_c$ and the pair $(G_c,l_c)$ for the two treatments. Certain morphologies are highly branched, in which case lagging crack tips eventually arrest. Active crack tips are found to keep pace with the advancing char process zone in a manner that is often relatively insensitive to material parameters. Comparisons are made so as to gauge the effect of a standard presumption that ${\sigma }_c\sim \sqrt{G_c/l_c}$.