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This thesis describes the investigation and development of damage modelling for composites materials at their micro-scale (e.g. fibre, matrix). A damage model for elastic materials, based on a "local" damage approach, has been introduced to predict failure onset and simulate the post-failure behaviour of unidirectional threedimensional representative volume elements (RVE) or unit cells with hexagonal distribution of the fibres over the cross section. The damage model consists of three parts: an elastic model, a failure criterion and the post-failure behaviour. Modifications of von Mises criteria and Maximum Principal Stress criterion have been considered to evaluate failure in the matrix whilst for the fibre in general the Maximum Principal Stress criterion has been used. The damage model has been implemented into the commercial code ABAQUS with subroutines in FORTRAN (UMAT and USDFLD). The material properties in the residual stress analyses are considered temperature dependant to simulate the volumetric contraction during the manufacturing process. Hence, the overall residual stress introduced from curing was determined by considering two ontributions: volume shrinkage of matrix resin from the crosslink polymerization during isothermal curing and thermal contraction of both resin and fibre as a result of cooling from the curing temperature to room temperature. Finally, three different typologies of 3D unit cells have been investigated. The first kind of micro-model is based on a symmetric distribution of the fibres and the unit cells have two phases, i.e.: matrix and fibre. The second typology of unit cells is still based on a uniform architecture but include a three-dimensional interphase between fibre and matrix. As in real composites at their constituent level fibres are randomly distributed. The mutual distance between fibres represents a critical factor for the ultimate mechanical properties of the micro-composites. Hence the last kind of micro-models account for this non-uniform position of fibres within the RVE although they consists of only two phases. FEM analyses have indicated that predicted damage initiation and evolution are clearly influenced by the presence of residual stresses in all the three different typologies of unit cells analysed. The numerical analyses on the numerical models have proved that, in general, the overall mechanical properties are strongly influenced by the presence of residual stress, fibre volume fraction, fibre distribution and interphasial properties. In particular on transverse tensile loading, residual stresses produces beneficial results in terms of ultimate strength while in the case of longitudinal loading (parallel to the fibres) the matrix, due to the high compressive stress, undergoes a premature failure although.

Three-dimensional numerical analyses, using the finite element method (FEM), have been adopted to simulate fatigue crack propagation in a hollow cylindrical specimen, under pure axial or combined axial-torsion loading conditions. Specimens, made of Al alloys B95AT and D16T, have been experimentally tested under pure axial load and combined in-phase constant amplitude axial and torsional loadings. The stress intensity factors (SIFs) have been calculated, according to the J-integral approach, along the front of a part through crack, initiated in correspondence of the outer surface of a hollow cylindrical specimen. The crack path is evaluated by using the maximum energy release rate (MERR) criterion, whereas the Paris law is used to calculate crack growth rates. A numerical and experimental comparison of the results is presented, showing a good agreement in terms of crack growth rates and paths.