Rubber toughening and damage competition theory. In material selection it is important to look at the interaction between the matrix and the secondary phase. For example, crosslinking within the rubber phase will promote high strength fibril formation that will toughen the rubber, preventing particle fracture. Carboxyl-terminated butadiene-acrylotnitrile (CTBN) is often used to toughen epoxies, but using CTBN alone increases the toughness at the cost of stiffness and heat resistance. Amine-terminated butadiene acrylonitrile (ATBN) is also used. Using ultra-fine full-vulcanized powdered rubber (UFPR) researchers have been able to improve all three, toughness, stiffness, and heat resistance simultaneously, resetting the stage for rubber toughening
Rubber elasticity could be backwards or forwards, so the net time average formula_19 will be zero. However, one can use the root mean square as a useful measure of that distance. Ideally, the polymer chain's movement is purely entropic (no enthalpic, or heat-related, forces involved). By using the following basic equations for entropy and Helmholtz free energy, we can model the driving force of entropy "pulling" the polymer into an unstretched conformation. Note that the force equation resembles that of a spring: "F=kx". Note that the elastic coefficient formula_22 is temperature dependent. If we increase the rubber temperature, the elastic coefficient also