The properties of rubber in pure homogeneous strain

Abstract

Measurements are reported on the relationship between the principal stresses t1 and t2 and the corresponding extension ratios lambda 1 and lambda 2 in the general biaxial strain of a rubber sheet. The resulting data are shown to be consistent with the Valanis-Landel hypothesis, according to which the strain energy W is a separable function w( lambda ) of the principal extension ratios. The formulation of the series for lambda (dw/d lambda ) in terms of strain invariants I1 and I2 enables delta W/ delta I1 and delta W/ delta I2 to be accurately calculated for any values of I1 and I2. It is concluded that both delta W/ delta I1 and delta W/ delta I2 are functions of both I1 and I2. The results confirm the conclusions of earlier workers that the empirical Mooney constants derived from uniaxial extension or compression bear no direct relation to the values of delta W/ delta I1 and delta W/ delta I2.