The stress-strain response and ultimate strength of filled elastomers

A constitutive model is derived for the mechanical behavior of reinforced elastomers at finite strains. A polymer is treated as a rigid-rod network, whose rupture is tantamount to breakage of chains treated as bond scission. Adjustable parameters in the stress-strain relations are found by fitting observations in tensile tests for filled and unfilled ethylene-octene copolymers. It is demonstrated that the model correctly describes stress-strain curves up to the break points. We analyze the effects of temperature, the degree of crystallinity and the filler content on Young's modulus and the ultimate strain per bond. It is shown that the dependences of material constants on the volume fraction of carbon black are substantially altered at the critical filler contents which correspond to the percolation thresholds found by dc conductivity measurements.