Modeling Stress and Failure in Shrinking Coatings

摘要

Drying or curing of a coating after vitrification or gelation is accompanied by stress development. Evaporation of solvent, polymerization, cross-linking, and cooling all cause shrinkage, but adhesion of the coating to the substrate prevents shrinkage to a stress-free state. The interaction of shrinkage and restraint creates strain and stress. If the local stress grows above the local strength of the coating, it can produce cracking, delamination, or other defects. A large deformation elastic model based on the Galerkin/finite element method is developed to analyze stress development in coatings subject to uniform shrinkage. The model is used to analyze effects of delamination and surface cracks. The strain energy release rates in both delamination and surface cracking are computed at different crack lengths. In both cases, results show that thicker coatings have larger energy release rates and are more vulnerable to cracking. A key conclusion of this modeling is that a crack can propagate only from an inherent flaw greater than a certain size. If the coating is thin enough so that the maximum energy release rate is less than the crack growth resistance, then no inherent flaws in the coating can grow into a crack, and so the coating remains crack-free. The model also shows how to calculate a critical coating thickness, i.e., the maximum thickness of a coating that can remain crack-free.