Tensile modulus of polymer halloysite nanotubes nanocomposites assuming stress transferring through an imperfect interphase

In this work, Hui-Shia model is developed to reveal the efficiency of a deficient interphase on the tensile modulus of polymer halloysite nanotube (HNT) nanocomposites. "L_c" as essential HNT length providing full stress transferring is defined and effective HNT size, effective HNT concentration, and efficiency of stress transferring (Q) are expressed by "L_c". Furthermore, the influences of all terms on the "Q" and nanocomposite's modulus are clarified, and also the calculations of the model are linked to the tested data of some nanocomposites. Original Hui-Shia model overpredicts the moduli, but the innovative model's predictions appropriately fit the measured data. L_c = 200 nm maximizes the sample's modulus to 2.6 GPa, but the modulus reduces to 2.11 GPa at L_c = 700 nm. Therefore, there is a reverse relation between the sample's modulus and "L_c". Q = 0.5 produces the system's modulus of 2.1 GPa, while the modulus of 2.35 GPa is achieved at Q = 1 providing a direct relation between the nanocomposite's modulus and "Q". Generally, narrow and big HNTs, along with a low "L_c", enhance the "Q", because a lower "L_c", reveals a tougher interphase improving the stress transferring.