Fiber-size effects on the onset of fiber–matrix debonding under transverse tension: A comparison between cohesive zone and finite fracture mechanics models I.G. García a,⇑ , M. Paggi b , V. Mantic ˇ a a Grupo de Elasticidad y Resistencia de Materiales, E.T.S. de Ingeniería, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain b Politecnico di Torino, Department of Structural, Geotechnical and Building Engineering, Corso Duca degli Abruzzi 24, 10129 Torino, Italy article info Article history: Received 9 November 2012 Received in revised form 5 August 2013 Accepted 19 October 2013 Available online 4 November 2013 Keywords: Fiber–matrix debonding Size effect Cohesive Zone Model Finite Fracture Mechanics Circular inclusion Interface crack abstract The problem of fiber–matrix debonding due to transverse loading is revisited. Predictions of the critical load for the debond onset obtained by a Cohesive Zone Model combined with contact mechanics and by a Finite Fracture Mechanics model based on a coupled stress and energy criterion are compared. Both models predict a strong nonlinear dependence of the critical load on the fiber size. A good agreement between the predictions provided by these models is found for large and medium fiber radii. However, different scaling laws for small fiber radii are noticed. A discussion of the asymptotic trends for very small and very large fiber radii is presented. Limitations of both models are also discussed. For very small fibers, it is shown that matrix plasticity can prevail over fiber–matrix debonding, leading to an upper bound for the critical load. When fiber–matrix debonding prevails over plasticity for large enough fibers, the predictions provided by the two models are still in fair good agreement. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction The study of the micromechanical fiber–matrix behavior has demonstrated to be very useful for explaining some macro- scopic phenomena in Fiber Reinforced Composites (FRCs). A few examples are: the effect of the reinforcement size on the superplastic deformation properties observed in fiber reinforced metal matrix composites [6,51], the macroscopic effect of the interface properties [50], the features of failure under transverse tension [28,39,42] and compression [12,13] and the influence of a transverse compression on the failure under dominant transverse tension [29,30,38] in FRC laminates. In particular, the plane strain problem of a long cylindrical inclusion (sometimes referred to as inhomogeneity) sur- rounded by a matrix has been studied since 1930s when Goodier [18] deduced the elastic solution of the problem of an elas- tic circular inclusion perfectly bonded to an elastic matrix subjected to transverse tension. The problem of partial debonding at the fiber–matrix interface under a rather general transverse load was solved, assuming the open model of interface cracks, in Toya’s [44] seminal work in 1970s. Toya’s solution provided analytical expressions for displacements, stresses and the En- ergy Release Rate (ERR). Later, analytical solutions were presented considering the interface as a continuous distribution of linear springs for a circular inclusion in [17,26] and for an elliptical inclusion in [47]. Many numerical studies have been carried out with the aim of understanding the micromechanical behavior of the fiber– matrix system using different techniques. Boundary Element Method (BEM) codes with contact were used in [12,37,39,46] to analyze the growth of a partial debond at the interface and its subsequent kink towards the matrix. Several Cohesive Zone 0013-7944/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.engfracmech.2013.10.014 ⇑ Corresponding author. Tel.: +34 954487300; fax: +34 954461637. E-mail addresses: israelgarcia@us.es (I.G. García), marco.paggi@polito.it (M. Paggi), mantic@etsi.us.es (V. Mantic ˇ). Engineering Fracture Mechanics 115 (2014) 96–110 Contents lists available at ScienceDirect Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech