Power law relationship between yield stress and shear modulus for glassy polymers

The published data on the yielding of glassy polymers under a variety of testing conditions reveal that the yield stress increases with the elastic modulus. However, fundamental understanding of the interrelation has not yet been established. In this paper, a power law relation between the shear yield stress τ_y and the shear modulus G is presented: T₀τ_y/Tτ_y0 = (T₀G/TG₀)ⁿ, where T is the absolute temperature, T₀. is reference temperature, and τ_y0 and G₀ are, respectively, the shear yield stress and the shear modules at T₀. The exponent n takes a value 1.63 for amorphous polymers without exception, whereas it is about 0.8–0.9 for crystalline polymers. The exponent 1.63 for amorphous polymers is in good agreement with the value derived from the approximation of the Bowden–Raha dislocation analog. This law may enable us to investigate a model for the yielding of glassy polymers.