A phase-field model for brittle fracture is proposed and evaluated for strength and fracture analyses of composites. In addition to the elastic properties, this approach makes use of only the fracture toughness and the strength of the material. The capability of the method is shown in analyses of composites at two scales. In laminates, strengths of notched laminates are estimated, including hole size effects. In a lamina, cracks developed in both transverse tension and compression are analyzed and compared to other numerical methods in the literature. The effects of a spectral and a hydrostatic-deviatoric decomposition of the strain energy density, two variants often used in phase-field formulations, are studied. It is shown that the choice of the decomposition affects the fracture development. Results are compared to experiments and simulations in the literature showing the capabilities of the phase-field approach.

The influence of boundary conditions (BCs) in the estimation of elastic properties of periodic structures is investigated using computational homogenization with special focus on planar structures. Uniform displacement, uniform traction, periodic, in-plane periodic and a proposed mix of periodic and traction BCs are used. First, the effect of the BCs is demonstrated in structures with one-, two- and three-dimensional periodicity. Mixed BCs are shown to most accurately represent the behavior of layered structures with a small number of repeating unit cells. Then, BCs are imposed on a twill woven composite architecture. Special attention is devoted to investigate the sensitivity of the estimated properties with respect to the BCs and to show differences when considering a single lamina or a laminate. High sensitivity of the in-plane extensional modulus and Poisson's ratio with respect to the type of BCs is found. Moreover, it is shown that the mix of BCs and in-plane periodic BCs are capable to represent an experimental strain field.

The free-edge effects and relative layer shifting in the interlaminar and intralaminar stresses of plain woven composite laminates under uniaxial extension is investigated numerically using a finite element approach. A computational framework of the free-edge problem for periodic structures with finite width is applied to woven laminates. First, two-layered laminates with three different shifting configurations are studied considering repeating unit cells simulating finite and infinite width. For each configuration, two different widths are considered by trimming the model at different locations in order to investigate different free-edge effects. Then, two four-layered laminates with no shifting and a maximum shifting configuration are analyzed to illustrate the effect of neighboring layers in the stresses. For each shifting configuration, different delamination mechanisms are expected. When considering more layers, it is found that the stacking configuration affects the state of stress and the free-edge effects depending on the shifting. In general, a different behavior than that of unidirectional tape laminates is found, since the interlaminar and intralaminar stresses can be higher than those generated at the free-edges. Particularly, for the maximum shifting configuration results are in agreement with experimental results in the literature where no debonding between yarns was observed at the free-edges.

Failure in woven composite laminates subject to global shear load is studied. Laminates are manufactured, tested and analyzed using X-ray computed tomography, scanning electron microscopy and finite element models. It is found that the stress distribution along the thickness direction is dependent on the layer shifting that alters different yarn interactions, which in turn, affects delamination and failure onset A suggested failure mechanism is in agreement with experimental observations.

A phase-field approach to fracture is used to simulate transverse cracking kinetics in composite laminates. First, a typical unidirectional tape laminate is modeled and the transverse cracking evolution with the consequent reduction in the in-plane modulus of elasticity is estimated. Then, a four-layered plain weave composite is modeled using different layer shifting configurations. Predictions in the transverse cracking evolution become improved as the shifting configuration of the laminate model become closer to experimental observations. Simulations predict that some cracks do not form perpendicularly to the loading direction, as it has been observed experimentally in similar locations. Only the fracture toughness and the in situ transverse strength of the ply are required without prior knowledge of the position of the cracks or an ad hoc criterion for crack evolution. All the simulations are compared qualitatively and quantitatively to experiments published elsewhere.