Validation of Homogenization Techniques for Locally Periodic Fiber-reinforced Composites with Interfacial Debonding

Macroscopic properties of fiber-reinforced composites are strongly affected by fiber/matrix debonding phenomena and often the assumption of a perfectly periodic microstructure may be not appropriate in practical applications, especially in presence of damage mechanisms. To this end, in the present work a numerical investigation on the validity of homogenization based approaches to predict the fracture behavior of locally periodic composites with fiber/matrix debonding, has been developed. Firstly, a technique able to determine the nonlinear homogenized constitutive response incorporating mixed mode interface crack propagation and contact is illustrated and applied in plane strain for uniaxial macrostrain paths, both in tension and compression. An original formulation based on the J-integral technique is proposed to compute energy release rate and mode mixity for an interface crack. Then a localization technique is proposed in order to obtain microscopic variables from the results of the composite homogenized analysis. Numerical applications are carried out with reference to a 2D locally periodic fiber-reinforced composite structure, by developing comparisons in terms of energy release rate, mode mixity and fiber/matrix interface stresses, between results obtained by a direct analysis (which takes into account microstructural details), and those computed by using the homogenized properties of the composite. Results show that the accuracy of the predictions obtained from the homogenized analysis by means of the adopted localization technique, strictly depends on the distance from the composite structure boundary.