Abstract
The effect of physical aging on the mechanics of amorphous solids as well as mechanical rejuvenation is modeled with nonequilibrium thermodynamics, using the concept of two thermal subsystems, namely a kinetic one and a configurational one. Earlier work (Semkiv and Hütter in J Non-Equilib Thermodyn 41(2):79–88, 2016) is extended to account for a fully general coupling of the two thermal subsystems. This coupling gives rise to hypoelastic-type contributions in the expression for the Cauchy stress tensor, that reduces to the more common hyperelastic case for sufficiently long aging. The general model, particularly the reversible and irreversible couplings between the thermal subsystems, is compared in detail with models in the literature (Boyce et al. in Mech Mater 7:15–33, 1988; Buckley et al. in J Mech Phys Solids 52:2355–2377, 2004; Klompen et al. in Macromolecules 38:6997–7008, 2005; Kamrin and Bouchbinder in J Mech Phys Solids 73:269–288 2014; Xiao and Nguyen in J Mech Phys Solids 82:62–81, 2015). It is found that only for the case of Kamrin and Bouchbinder (J Mech Phys Solids 73:269–288, 2014) there is a nontrivial coupling between the thermal subsystems in the reversible dynamics, for which the Jacobi identity is automatically satisfied. Moreover, in their work as well as in Boyce et al. (Mech Mater 7:15–33, 1988), viscoplastic deformation is driven by the deviatoric part of the Cauchy stress tensor, while for Buckley et al. (J Mech Phys Solids 52:2355–2377, 2004) and Xiao and Nguyen (J Mech Phys Solids 82:62–81, 2015) this is not the case.
Highlights
The mechanical properties of solids often depend on the way they are produced
+ θ −1 ˆ,ηs,Fe σγημ + σγ[sμη]η (∇μvγ ) + θ η + σμν Dt Fμeε Fεeν,−1. This completes the formulation of the model for physical aging and mechanical rejuvenation of glasses using subsystem entropies, and of alternative formulations of it in terms of other variables for the kinetic and configurational subsystems, namely temperatures or kinetic energies
4 Discussion: comparison with the literature In Sect. 3, we have presented a general model to describe physical aging and mechanical rejuvenation of amorphous solids, by considering the evolution of two thermal degrees of freedom, i.e., kinetic and configurational entropies, or the corresponding temperatures or internal energies, respectively
Summary
The mechanical properties of solids often depend on the way they are produced. For example, in the case of semicrystalline polymers, the processing conditions determine the crystal structure, which in turn affects, e.g., the yield stress. Models have been developed for the evolution of the kinetic and configurational thermal degrees of freedom [10,11,12,13,14,15], as well as constitutive expressions have been formulated for a stress tensor and for a plastic flow rule for the mechanical deformation of aging solids. In these models the mutual interaction of the kinetic and configurational subsystems is in general incomplete, as discussed in the sequel of this paper, and leaves room for further investigation and generalization. Adαβ denotes the deviatoric part of the tensor Aαβ , i.e., Adαβ ≡ Aαβ − ( Aμμ/3)δαβ
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