(722j) Modeling Viscoelasticity and Stress Generation In Solidifying Coatings

As a polymer solution coating solidifies by drying, or a coating of monomer or oligomer solidifies by polymerization and crosslinking reactions, it acquires an elastic modulus. Subsequent departure of solvent or advance of curing reactions causes the coating's elastic stress-free state to shrink isotropically but possibly nonuniformly. Adhesion to a solid substrate frustrates the solidification-induced shrinkage in the coating plane and produces elastic strain and, consequently, elastic stress in the coating. The magnitude and directions of the state of stress depend on the type of material, its physical property and shrinkage history, and the topography of the coated surface. Predicting stress generation can show how undesired defects are formed in the coating and can suggest avenues for optimizing the solidification process to minimize the residual internal stress and reduce defects.

Calculating the stress generation mathematically shoes the entire state of internal stress in the coating domain. To calculate how a drying or curing material behaves, equations of momentum conservation and a constitutive equation must be combined and solved simultaneously. This research presents a novel implementation of the mathematics behind the viscoelastic phenomena seen in a solidifying coating material by manipulating the constitutive equation before inserting it into the equation of momentum conservation. The solution method is computationally less expensive than with standard constitutive and momentum equations. The partial-differential equations are solved using Galerkin's method with finite element basis functions. The final internal state of stress depends on the physical property change with solidification, shrinkage, heterogeneity, and substrate topography. In general, residual stress is caused by competing factors; modulus increase and shrinkage tend to create stress while relaxation destroys it. By varying the rates of shrinkage, modulus development, relaxation time development, and the substrate topography, two-dimensional stress profiles are generated that allow us to see spatially and time-dependent states of stress in a coating. We present the 2-dimensional stress profiles for an ultraviolet light cured system and show how the curing time and substrate topographic height and length change the stress maximum magnitude and location. Such profiles can be used to optimize curing schedules and substrate geometry.