Proposal of the Boltzmann-like superposition principle for nonlinear tensile creep of thermoplastics

Abstract

The Boltzmann superposition principle (BSP) valid for “standard linear solids” is presented in all textbooks on viscoelasticity. In practice, the BSP is not applicable to viscoelastic polymers because (i) the apparent limit (if any) of the stress–strain linearity is very low, (ii) real deformations (stresses) are not infinitesimal, and (iii) tensile deformations give rise to additional free volume, which affects all currently running deformation processes. Consistent application of the free volume approach, including the strain-induced free volume, allowed us to derive and verify a new type of the internal time–tensile strain superposition for a series of single-step nonlinear creeps [J. Kolařík, A. Pegoretti, Nonlinear tensile creep of polypropylene: time–strain superposition and creep prediction, Polymer 47 (1) (2006) 346]. The Boltzmann-like superposition principle for multistep nonlinear tensile creep, proposed in this paper, consists of (i) the separation of individual creeps, (ii) their reconstruction for the initial free volume by introducing a specific internal time, and (iii) the superposition of the reconstructed creeps. The procedure is demonstrated using creep data for three types of commercial polypropylene.