Modeling the Fatigue Behavior of Amorphous Polymers
arXiv:2607.14994
The paper derives Basquin's law for fatigue in amorphous polymers using a linearized Long plasticity model, predicts the fatigue exponent m = 3, provides an expression for the prefactor, and validates the theory against experimental data for PS, PMMA, and PVC.
Abstract
Prediction of material durability is both very important and very difficult. In many cases, material durability is measured by subjecting a sample to repeating oscillatory cycles (in shear or tension-compression) until it fails in either ductile or brittle fashion. Typically, the stress amplitude is denoted S, and the number of cycles N, so the resulting dependence is known as the SN-curve. For many materials, SN curve has been shown to obey the empirical Basquin's law, N = AS^(-m), where the prefactor A was a function of the temperature, load frequency, and sample history, and the power law m was a real number, usually between 3 and 12. Here, we derive the Basquin's law using a linearized version of the Long's plasticity model and demonstrate that within this framework, m = 3. We also derive the expression for the prefactor A. Finally, we show that our theory successfully describes experimental data for three amorphous polymers, PS, PMMA, and PVC.
17 pages, 4 figures, 1 table