Shear-Lag Attenuation of Interfacial Damage Kinetics in Aligned Carbon Nanotube/Polydimethylsiloxane Composites

Aligned carbon nanotube/polydimethylsiloxane (CNT/PDMS) composites soften under repeated loading, but the microscopic rate of interfacial degradation has not been related in closed form to the macroscopic rate of stiffness loss. This paper derives that relation for a Krenchel-type, orientation-averaged Cox shear-lag homogenization whose interfacial load-transfer efficiency decays exponentially with cycle number at a prescribed rate κ. Because that efficiency enters the modulus nonlinearly—under a square root, then a saturating length-efficiency function—the instantaneous macroscopic decay rate is κ times an exact dimensionless sensitivity function S(x) of one operating point, x = βs, the shear-lag parameter times the aspect ratio. S is proved to be a strictly decreasing bijection from (0, ∞) onto (0, 1) with closed-form limits, so the mapping inverts uniquely; the rate apparent over a finite window is likewise exact, so the attenuation depends on the window length as well as the operating point. At the illustrative operating points, a least-squares rate fitted to sparse checkpoints understates the interfacial rate by a factor of about three, and the exact 50-cycle window-averaged rate understates it by a factor of up to 6.32. Both scale with the prescribed, uncalibrated shear-lag prefactor, and the fitted-constant factor exceeds 1.4 throughout. All model-derived results are analytical; no experimental validation is claimed.