Combined Modeling of the Volume, Dielectric, and Stress Relaxation and Fatigue Behavior in Glassy Polymers

We combine our recently developed two-state amorphous material model, “SL-TS2”¹ with simple linear elasticity describing the affine bulk and shear deformations. Due to the hierarchy of timescales, the slowest (“α”) relaxation process is described by the nonlinear Trachenko-Zaccone² equation. We show that for the mechanical stress relaxation (shear or tensile/compressive), this equation can be re-written as the Eyring plasticity equation,³ resulting in the asymptotic Guiu-Pratt⁴ logarithmic solution. Interestingly, the same solution can be also approximated by the Kohlrausch-Williams-Watts (KWW) function, at least in the intermediate time range. Finally, we describe the potential application of the model to the prediction of a material fatigue lifetime based on a simplified approach of Janssen et al.,⁵ and discuss other applications and modifications of the proposed theory. References: 1. Ginzburg, V. V; Zaccone, A.; Casalini, R. Soft Matter 2022, 18, 8456–8466. 2. Trachenko, K.; Zaccone, A. Journal of Physics: Condensed Matter 2021, 33 (31), 315101. 3. Eyring, H. J Chem Phys 1936, 4 (4), 283–291. 4. Guiu, F.; Pratt, P. L. Physica status solidi (b) 1964, 6 (1), 111–120. 5. Janssen, R. P. M.; Govaert, L. E.; Meijer, H. E. H. Macromolecules 2008, 41 (7), 2531–2540.