Paolo Nevone Blasi

Influence of micro-cracking and contact on the effective properties of composite materials

Abstract In the present work a novel micro-mechanical approach to analyze the influence of micro-crack evolution and contact on the effective properties of elastic composite materials is proposed, based on homogenization techniques, interface models and fracture mechanics concepts. By means of the finite element method, enhanced non-linear macroscopic constitutive laws are developed by taking into account changes in micro-structural configuration associated with the growth of micro-cracks and with contact between crack faces. Numerical simulations are carried out for the cases of a porous composite with edge cracks and of a debonded fibre reinforced composite, loaded along extension/compression uniaxial macro-strain paths. Micro-crack propagation is modelled by using an original methodology based on the J-integral technique in conjunction with an interface model taking into account the unilateral contact of crack faces. In the context of a micro-to-macro transition obtained by controlling the macro-deformation of the micro-structure, the effects of adopting three types of boundary conditions on the macroscopic constitutive law, namely linear deformation, uniform tractions and periodic deformations and anti-periodic tractions, are studied. As a consequence, the proposed method can be applied to a large class of problems including periodic, locally periodic and irregular composite materials. Micro-crack and contact evolution result in a progressive loss of stiffness and can lead to failure for homogeneous macro-deformations associated with unstable crack propagation.

Prediction of Microscopic Interface Crack Onset in Fiber-Reinforced Composites by Using a Multi-Scale Homogenization Procedure

A two-scale method able to carry out a macroscopic failure analysis of a composite structure in presence of microscopic mixed mode interface crack initiation, is proposed. The method is able to accurately predict local failure quantities (fiber/matrix interfacial stresses, energy release and mode mixity for an interface crack) in an arbitrary cell from the results of a macroscopic homogenized analysis. Microscopic crack initiation is thus analyzed by using a coupled stress and energy failure criterion in term of these local quantities. Numerical results are obtained for a plane strain model of a locally periodic fiber-reinforced composite material subjected to shear loading and characterized by initially undamaged fiber/matrix interfaces. Predictions for the critical load factor and interface crack length at crack onset obtained by the proposed model are compared with those obtained by means of a direct simulation.

Edge Debonding Prediction in Beams Strengthened by FRP Composite Plates

Edge debonding initiation and propagation in beams strengthened with fiber-reinforced composite plates is here studied. The structural system is composed by three physical components, namely the beam, the adhesive layer and the bonded plate, which are modeled by one or several first-order shear deformable layers according to a multi-layer formulation, wherein both strong and weak interface constitutive relations are introduced to model interfaces. Debonding onset is predicted with the aid of a mixed mode coupled stress and energetic criterion, and propagation in different locations across the adhesive thickness is studied by using a mixed mode fracture criterion. The proposed models are implemented according to the 1D finite element technique, allowing accurate evaluation of interlaminar stresses and fracture energies.

Macroscopic Stability Analysis in Periodic Composite Solids

A theoretical and numerical investigation of the effects of microscopic instabilities on the homogenized response for solids with periodic microstructure is here carried out. The theory is formulated for materials characterized by an incrementally linear constitutive law. Novel macroscopic measures of microstructural stability are introduced corresponding to the positive definiteness of the homogenized moduli tensors relative to a class of conjugate stress-strain pairs and their effectiveness to obtain a conservative prediction of microscopic primary instability load is pointed out. Numerical applications, devoted to hyperelastic microstructures representative of cellular solids and reinforced composites, are developed by implementing a one-way coupled finite element approach. Both uniaxial and equibiaxial loading conditions are considered. Comparisons between the exact microscopic stability region in the macro-strain space, obtained by taking into account microstructural details, and the macroscopic stability regions, determined by investigating the homogenized material properties, are shown. Results evidence that an appropriate definition of macroscopic stability measure depending on the type of loading condition (tensile or compressive) and the kind of microstructure may lead to a conservative stability prediction.