A viscoelastoplastic stiffening model for plant fibre unidirectional reinforced composite behaviour under monotonic and cyclic tensile loading

Abstract At room conditions and standard strain rate ( e ˙ ∼ 10 − 4 s − 1 ), unidirectional (UD) plant-based reinforced organic polymers often exhibit nonlinear mechanical behaviour in tension. A viscoelastoplastic model (VEP model) for the simulation of UD plant fibre composite mechanical behaviour in tension, previously validated from twisted flax yarn epoxy composite under room conditions and standard strain rate, is calibrated with new data obtained from flax fibre epoxy composite under repeated progressive loading and a wide range of strain rates ( e ˙ ∼ 10 − 3 to 10 − 7 s − 1 ). The VEP model does not reproduce well the experimental observations. There seems to be a lack of stiffening in this phenomenological model. We propose an improved VEP model, developed within the frameworks of thermodynamics and limited to uniaxial tension and infinitesimal strains. An internal variable s representing the stiffening is added to create a VEP-stiffening model. This internal variable represents the coupled effects of reorienting cellulose microfibrils in kink band areas, spiral spring-like extension of cellulose microfibrils, and shear-stress-induced crystallization of the amorphous cellulose of flax fibres. The stiffening phenomenon was considered viscous, without a threshold, and was related to the tension energy in the direction of the fibres. Three viscosity coefficients drive the three phenomena: η (elastic), K (plastic), and K s (stiffening). In the chosen formalism, this leads to two thermodynamic potentials φ V E P s and Ω V E P s in which the stiffening phenomenon is strongly coupled with all the others. This VEP-stiffening model of the UD flax fibre epoxy composite correlates well with experimental observations. The paper also explores the evolution of the three viscous phenomena (elastic, plastic, and stiffening) by simulation of different loading conditions: monotonic, cyclic, and creep. This VEP-stiffening model can easily enrich existing multiaxial models of UD behaviour in the fibre direction. Implemented in a finite element model, it could be used at different length scales to numerically explore the origin of the mechanical behaviour of plant-based reinforced polymers.