Frequency f and strain rate ̇εn dependences of linear dynamic shear modulus were measured for glassy epoxy network during uniaxial stretching processes. With increasing strain εn, the storage shear modulus G´ slightly decreased to a steady value appearing at post-yield strain-hardening range of strain. The loss shear modulus G˝ markedly increased in the same strain range, where G´ decreased, and then leveled off. These variations of G´ and G˝ indicated that the glassy structure in the epoxy network changed into more unstable ones by stretching. When compared at a fixed condition of α= ̇εn/f, the functional relation between strain-induced increment of G˝ and εn was identical independently of ̇εn of stretching. Thus, frequency dispersion of the nonlinear relaxation was found to be determined only by the relative distance from the timescale of deformation and the amount of imposed strain. Whereas the decrement of G´ at a fixed α was not superposable when plotted against εn, because of (εn ) ̇ dependence of their steady values. The variation of G´ was affected not only by destabilization of glassy structure due to deformation. The observed f and ̇εn dependences of G´-εn and G˝-εn relations for glassy epoxy network during stretching were qualitatively the same as those observed for poly(methyl methacrylate) (PMMA). Thus, the dependence on εn, f and ̇εn of the nonlinear relaxation under constant-speed deformation conditions reported here is presumably universal for glassy polymers. The strain-induced variation of G´ and G˝ was smaller for epoxy network compared with PMMA stretched exactly at the identical condition. This result indicates that glassy structures in the epoxy network before stretching are more unstable because of constraint arising from crosslinked molecular structures.
The single relaxation time of epoxy glass, a thermoset having crosslinked molecular structures, was evaluated during tensile yielding process by using a nonlinear single relaxation model. The model consisted of two elastic springs expressing linear viscoelastic behavior and a dashpot with variable viscosity as a single parameter representing strain-induced structural change. We calculated the strain-dependent relaxation time τSS by fitting the model to experimental stress-strain curves observed at various strain rates and temperatures. The relaxation time τSS steeply decreased with increasing strain at the beginning of stretching, and then attained to low steady values at strains slightly larger than the yield strain. The steady values of τSS were almost inversely proportional to the strain rate, and slightly shorter at a higher stretching temperature. These dependences of τSS for epoxy glass on strain, strain rate and temperature were qualitatively identical to those for thermoplastic glassy polymers without crosslinked molecular structures. Strain-dependent relaxation times for thermoplastic glassy polymers are known as the result of change in glassy structures. Thus, it is concluded that the nonlinear viscoelastic behavior of crosslinked epoxy glass arises from strain-induced structural change.
Variation of complex shear modulus of glassy poly(methyl methacrylate) (PMMA) was monitored during uniaxial stretching to investigate the frequency dispersion of strain-induced nonlinear relaxation. With increasing strain εn, the storage modulus G' decreased to a steady value appearing at post-yield range of strain accompanied by a marked increase of the loss modulus G", indicating that glassy structures changed into more unstable ones due to stretching. The variation of the moduli was more remarkable when the timescale of observation, i.e. frequency ƒ of dynamic measurement, was closer to that of deformation, i.e. strain rate εn. Increment of G" as a function of εn was identical independently of εn when observed at a fixed condition of α = εn/ƒ. This observation indicates that β relaxation is not altered by imposition of large strain and that the frequency dispersion of the nonlinear stress relaxation is determined by relative distance from the timescale of deformation and the amount of imposed strain. Relationships between ΔG', decrement of G', and εn were not superposable at a fixed α, because of negative εn dependence of ΔG' in the post-yield regime. This presumably shows that strain aging, structural relaxation of the strain-induced unstable glassy structures under finite stress, occurs during deformation.
