Analytical and numerical bound analysis of hygroscopic swelling characterization

In this paper, a comprehensive study is developed on the effects of non-uniform moisture distribution and hygroscopic stress in hygroscopic swelling characterization. Two different averaged methods are introduced to analyze the experimental data obtained using TMA/TGA techniques with respect to the different reference states chosen, i.e., absolute dry and saturation conditions, respectively. It turns out that these two methods give the upper and lower bound estimates of the coefficient of hygroscopic swelling of materials. Three-dimensional moisture diffusion solution is employed to consider the non-uniform moisture distribution. The analytical expressions of both methods are obtained for the averaged coefficient of hygroscopic swelling, which are functions of time, diffusivity and specimen dimensions. The effects of aspect ratio, and time-dependency on measurement accuracy are discussed. Mathematical proof and numerical results are given for the lower and upper bound analysis. The analytical predication shows a remarkable agreement with the experiment results. Because the analytical solutions are developed without considering the effect of the hygroscopic stress induced deformation, a sequentially coupled moisture diffusion and hygroscopic stress analysis is utilized to investigate the impact of hygroscopic stresses in the hygroscopic swelling characterization. It is interesting to notice that even through the elastic strain caused by hygroscopic stress accounts for about one third of the total strain, the displacement induced by the elastic deformation at probe measurement point is negligible compared to the displacement of hygroscopic swelling. We conclude that our analytical solutions give the accurate analysis of hygroscopic swelling characterization