Mechanical modeling of short-fibre-reinforced materials under static or cyclic loading.

Abstract

Fibre-Reinforced Composite (FRC) materials typically consist of two or more constituents combined at a macroscopic level. Due to their high mechanical properties (such as good tensile strength, fracture resistance, durability, corrosion resistance, enhanced wear and fatigue strength), composites are commonly used in advanced engineering applications. The mechanical properties of such multiphase materials depend on those of their constituents, i.e. the bulk material (matrix) and the reinforcing phase (such as fibres), as well as on their reciprocal interface bonding. The strength and durability design of composite structural elements must consider the typical damage phenomena occurring in such materials under in-service loading. Such degrading effects, usually responsible for a significant decrease of the structural mechanical performances, can be mainly related to the fibre-matrix delamination (also identified as debonding), fibre breaking, fibre buckling, matrix plastic deformation or cracking. The proper evaluation of the safety factor of composite materials during the service life and also at their limit state, is a crucial task in the design and durability assessment of structural components made by such materials.

The present Ph.D. Thesis deals with the development of a micro-mechanical-based approach for the assessment of the mechanical behaviour of short fibre reinforced composites under static and cyclic loading, by taking into account the principal damage failure modes. A homogenisation approach, based on an energetic formulation, has been generalised in order to take into account the spatial arrangement and distribution of the fibre reinforcing phase. Fibres effectiveness is considered by means of a proper parameter, the sliding function $s$, that quantifies the stress transfer capability of the fibre-matrix interface bond. Such a parameter has been determined through the fracture mechanics based approach proposed in this Ph.D. Thesis, in alternative to the classical "Shear Lag" model. A correlation between the present model and the shear lag one has been proposed in order to allow the quantification of the static critical interface parameters (such as fracture toughness and fracture energy), necessary to identified the condition of incipient detachment propagation. The progressive debonding due to the action of cyclic loads is quantified through a fatigue power law.

In order to consider all the micro-mechanical phenomena involved in static and fatigue problems, the mechanical behaviour of the single constituents of the composite are also analysed. The matrix is assumed to be characterised by a linear elastic, elastic-plastic or brittle mechanical behaviour in case of static loads, whereas an approach based on the experimental W\"ohler diagrams (S-N curves) is adopted to simulate fatigue effects. The fibre-reinforcing phase is assumed to present a linear elastic behaviour until reaching a suitable condition of failure at which the fibre breaks into two parts. Fibre-fibre reciprocal interaction is also considered, whereas the effect of the cycle loading on the fibre material has been neglected.

Finally, the formulation proposed has been implemented in a non-linear 2-D FE code and used for the simulation of simple structural elements under static and cyclic loads. Some of the obtained results have been reported, discussed and compared with literature available data.