Transient analysis on hygroscopic swelling characterization using sequentially coupled moisture diffusion and hygroscopic stress modeling method

The characterization of hygroscopic swelling properties for polymeric materials in electronic packaging presents unique challenges that have not been adequately addressed in existing literature. One of those challenges is the accurate determination of the coefficient of hygroscopic swelling. Due to the fact that the moisture diffusion is a slow process, specimens used in hygroscopic swelling measurements are often subjected to a non-uniform moisture distribution condition during measurement period. This introduces potential sources of hidden errors in obtaining the coefficient of hygroscopic swelling. Previously analytical solutions have been devised to predict the errors caused by the non-uniform moisture distribution and the use of averaged approach. The elastic deformation by non-uniform hygroscopic swelling was not considered. However, when the non-uniform moisture distribution is present, it is inevitable that the measured deformation includes both hygroscopic and elastic deformation. It is vital to separate the elastic deformation from the total deformation so that only hygroscopic swelling strain is documented. The transient analysis using sequentially coupled moisture diffusion and hygroscopic stress finite element modelling has been applied in this paper to simulate the TMA hygroscopic swelling characterization process. Results showed that the elastic strain caused by the hygroscopic stress accounts for about one-third of the total strain during the measurement period. It is also found that the elastic strain along the thickness direction changes from tensile state to compressive state, thus the overall contribution of elastic deformation to the total deformation along the thickness direction is negligible. The simulation results confirmed the excellent agreement with the previous analytical study without considering elastic deformation. This implies that the previously developed analytical solutions are still valid and accurate in analyzing the characterization of swelling property.