Stress relaxation phenomena: Multiple box distribution treatment of relaxation times

Abstract

AbstractThe box distribution of relaxation times was generalized for the interpretation of stress relaxation of viscoelastic material under small constant strain. The generalization consists of the use of a number of box distribution functions, each of which is characterized by three parameters; namely, modulus constant, Cj; largest relaxation time, τmj; and width of spectrum. The logarithms of Cj and τmj obtained by applying the multiple box distribution function to published stress relaxation data for polyisobutylene, polystyrene, and GR‐S vulcanizate are linear functions of the reciprocal of absolute temperature, 1/T. The log Cj versus 1/T curves divide into two groups. The group showing relatively small change with temperature is likely due to interchain forces, while the other group, increasing rapidly with decreasing temperature, can be attributed to intrachain forces. Each curve of the latter group consists of three distinct segments of straight line with the middle segment bracketing the glass transition temperature. Thus, the transition from rubbery to glassy state covers a temperature range which can be determined by stress relaxation. Other viscoelastic properties, such as viscosity, activation energy, and tensile stress—strain at various strain rates are discussed on the basis of multiple box distribution.