Quantitative analysis of the micro-indentation behaviour of ®bre-reinforced composites: development and validation of an analytical model Mondher Zidi a,b, *, Luc Carpentier b , Antoine Chateauminois c , FrancËois Sidoro b a Laboratoire de Me Âcanique des Solides, Ecole Nationale d'Inge Ânieurs de Monastir, Avenue Ibn Eljazzar, 5019 Monastir, Tunisia b Laboratoire de Tribologie et Dynamique des Syste Ámes, UMR CNRS 5513, Ecole Centrale de Lyon, BP 163, 69131 Ecully Cedex, France c Laboratoire d'IngeÂnierie et Fonctionnalisation des Syste Ámes, UMR CNRS 5621, Ecole Centrale de Lyon, BP 163, 69131 Ecully Cedex, France Received 5 January 1999; accepted 30 September 1999 Abstract A shear-lag model has been developed in order to assess interfacial shear strength from micro-indentation experiments. The treatment of the experimental load/displacement curves is based upon the quanti®cation of the two components of the indenter displacement, i.e. (i) the elasto-plastic indentation of the ®bre surface by the Vickers indenter, and (ii) the displacement of the ®bre surface due to its compression and to the de¯ection of the matrix. The latter component has been modelled by using an analytical shear-lag model which takes into account both ®bre/matrix debonding and ®bre sliding in the debonded areas. Some of the basic hypothesis of this analytical approach have been checked by ®nite-element (FE) simulations with appropriate model con®gurations. By means of this model, the critical shear debonding stress can be obtained from the experimental indentation curves. Moreover, the data-reduction scheme takes into account separately the local environment of each indented ®bre. This method has been suc- cessfully applied to experimental data by using a unidirectional E-glass/epoxy composite. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Glass ®bres; B. Debonding; B. Interfacial strength; Micro-indentation 1. Introduction The ®bre/matrix interface plays an essential part in the mechanical behaviour, fatigue life and durability of ®bre-reinforced composite materials and much work has been devoted to its mechanical characterisation. An easily operated and quantitatively reliable test would be desirable for assessing the interfacial strength properties and their dependence on ®bre sizing and processing parameters. Such a test would also be of interest for the evaluation of interfacial degradation as a result of environmental ageing or mechanical damage. Within this framework, the micro-indentation test provides an ecient solution [1±6]. Its basic principle is very simple: starting from a polished surface perpendicular to the ®bres of the composite under investigation, a single ®bre is selected and its cross-section indented with a Vickers indenter. The basic result from this test is the indenta- tion curve giving the normal load as a function of the penetration depth. This micro-indentation test is now well understood and widely used in many situations and various areas of material science. In this particular case, it has many advantages, the greatest of which is prob- ably the fact that it allows characterisation of the real interface in a real material. Its interpretation is not straightforward, however, and a careful mechanical analysis is required to obtain intrinsic material properties from the global response of a complicated system involving the whole ®bre envir- onment (interface, matrix, neighbouring ®bres) under a highly heterogeneous stress state. Some simplifying assumptions have to be made in order to obtain satisfactory results. Most of the existing analyses of experimental data are based on some kind of shear- lag argument, which was initially derived by Cox [7] with very crude approximations regarding the stress distribution [8,9]. Of course, this approximation may be 0266-3538/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0266-3538(99)00143-8 Composites Science and Technology 60 (2000) 429±437 * Corresponding author. E-mail address: mondher.zidi@enim.rnu.tn (M. Zidi).