A computationally-efficient micromechanical model for the fatigue life of unidirectional composites under tension-tension loading

Abstract

Failure of fibre-reinforced composites is affected by fatigue, which increases the challenge in designing safe and reliable composite structures. This paper presents an analytical model to predict the fatigue life of unidirectional composites under longitudinal tension-tension. The matrix and fibre-matrix interface are represented through a cohesive constitutive law, and a Paris law is used to model fatigue due to interfacial cracks propagating from fibre-breaks. The strength of single-fibres is modelled by a Weibull distribution, which is scaled hierarchically though a stochastic failure analysis of composite fibre-bundles, computing stochastic S-N curves of lab-scaled specimens in less than one minute. Model predictions are successfully validated against experiments from the literature. This model can be used to reduce the need for fatigue testing, and also to evaluate the impact of constituent properties on the fatigue life of composites.

Predicting damage accumulation and fatigue life of UD composites under longitudinal tension

“…Cyclic loading progressively reduces the ability of the interface to transfer shear-stresses near the fibre-break, up to the moment when a crack-tip is formed. It has been previous shown [9] number of cycles required to form this crack tip is…”

“…The strength of a single fibre under a uniform stress ∞ follows a Weibull distribution with shape parameter and scale parameter f 0 , measured at the reference length f 0 [11]. Therefore, the survival probability of a single fibre ( Figure 1: Hierarchical generation of composite fibre-bundles [7,8,9]. …”

“…This shear-lag process homogenises the contributions of the matrix and fibre-matrix interface, which will hereafter be simply referred to as the interface between fibres and/or sub-bundles [9]. The static shear-lag response will be governed by a linear cohesive law, defined by a shear strength ( int ) and mode-II fracture toughness ( int IIc ); the growth rate of mode-II interface cracks along a level…”

“…In this scenario, a subsequent number of load cycles ( ) under a loading ratio ∞ will lead to a bi-lateral increase of the effective recovery length governed by the mode-II Paris law of the interface [9]:…”

“…An overview of the hierarchical scaling law previously developed to predict the fatigue life of unidirectional composites [9] is provided in Sections 2.1-2.3; this is then used in Sections 2.4-2.6 to predict damage accumulation under longitudinal tensile fatigue, by extending our previously proposed static formulation [8]. Model results are presented and compared against experiments in Section 3, and discussed in Section 4.…”