Stress Effects in Drying Polymer Films
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S.Y. TAM, L.E. SCRIVEN*, H.K. STOLARSKI
Dept. of Civil & Mineral Engineering, University of Minnesota, MN 55455 *Dept. of Chemical Eng'g & Material Science, University of Minnesota, MN 55455 ABSTRACT A model is developed to predict the magnitude and pattern of stress due to drying of polymer films, This model combines diffusion-and-convection equation with large deformation elastoviscoplasticity, utilizing concentration dependent elastic and viscoplastic material properties to better represent the behavior of drying thin films. The results show that the highest stress occurs at film surface where the concentration depletion is the highest. The magnitude of this stress is induced by increasing mass transfer across the film surface but reduced by increasing diffusion coefficient. The edge effect is significant but local, limited to about four film thicknesses. Similarly, change in substrate induces extra stress. INTRODUCTION Drying of polymer films often results in appreciable shrinkage. Even though drying usually occurs at elevated temperature, thermal effects on coating contribute only a small amount of volume change compared to the shrinkage caused by evaporation of solvent. Thermal effects are therefore ignored in this study. Adhesion of the film to the substrate restrains the natural deformation of the coated material in the drying process. Such restraint causes departure of the actual deformation state from the stress free state and the associated development of stress. In addition, evaporation of solvent through the surface of the film causes nonuniform shrinkage throughout the volume of the film. This nonuniformity causes further departure of the actual deformation state from the stress free state.
Furthermore, nonuniformities such as topography of the substrate and initial defects lead to additional redistribution of stress, so can yielding when it occurs. When the magnitude of compound residual stress exceeds the material strength, drying defects are intiated. The accuracy of predicted values of stress depends on the quality of data describing material properties, and understanding of the drying mechanism. Most polymeric coatings are to some extent viscous but elastic and plastic properties may develop as drying progresses. Even with the relaxation due to viscous effects, residual stress may well exceed the elastic limits. The relevant material properties, namely elastic moduli, yield stress and post-yield viscosity change throughout the drying process as solvent is removed and the coating solidifies. Viscoplastic model is chosen to represent this inelastic behavior. Large volume changes during drying call for large deformation and large strain representation. Previous studies of coating-substrate assemblies [1-4] did not include geometric nonlinearities and varying material properties. To understand better the stress development mechanisms, the model constructed here includes large deformations and changing elasto-viscoplastic material properties, and is coupled with the Fickian diffusion model of drying
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