Investigation into the effects of foaming variables on the cellular structure and expansion ratio of foamed TPU using response surface methodology

Thermoplastic polyurethane elastomer (TPU) foams were prepared using the high-pressure autoclave with supercritical fluid carbon dioxide (SC-CO2). The effects of foaming variables (i.e. saturation temperature, saturation pressure, and depressurization rate) on cellular structure and expansion ratio were investigated. The model between expansion ratio and foaming variables was constructed using the Box-Behnken design (BBD) of response surface methodology (RSM), and analysis of variance (ANOVA) was conducted to evaluate the validity and significance of the model. Finally, the interactive effects of foaming variables on the expansion ratio were investigated, and the expansion ratios of maximum and center point from numerical model were verified by experiment. The result showed higher saturation pressure and depressurization rate resulted in the more uniform cellular structure and higher cell density, however the higher saturation temperature resulted in the bigger cell and nonuniform structure. The ranges of average cell diameter and cell density were 15.26–45.4 μm and 0.32 × 108 to 6.24 × 108 cells/cm3, respectively. The model obtained using BBD of RSM was valid to predict the expansion ratio in the design window. The saturation temperature was the most important factor influencing the expansion ratio. With the increase of saturation temperature, the expansion ratio always increases in the design window. The maximum expansion ratio from numerical optimization was 4.91, which was located at saturation temperature 190°C, saturation pressure 12.51 MPa, and depressurization rate 5 MPa/s, and the corresponding experiment value was 4.56. The error between them was 7.13%.