Effects of interfacial roughness on fibre push-out

Single-fibre push-out tests have been performed on Nicalon fibre-reinforced SiC composites, and roughness on the surface of the pushed-out fibre has been observed [1]. Analyses of the loading stress against fibre-end displacement relation during the fibre pushout process (i.e. the push-out curve) were performed to include the roughness effect, and a methodology was developed recently to evaluate the interfacial properties from the measured push-out curve for Nicalon/SiC composites [2]. However, only assumptions and analytical results of the roughness effect were summarized in [2]. The purpose of this study is to present the detailed derivations for the roughness effect. Modelling for a single-fibre push-out test is shown schematically in Fig. 1. A fibre with radius a is surrounded by a coaxial shell of matrix with outer radius b. A compressive stress, o0, is applied to the fibre in the axial direction, and a critical applied stress, od, is required to initiate interfacial debonding. When o0 exceeds od, interfacial debonding and sliding occur within a length h, such that the axial stress in the fibre is in equilibrium with od at the end of the sliding zone. The loaded end of the fibre has displacement u0 in the loading direction. The specimen has thickness t and rests on a slotted stage, such that the fibre can be pushed out of the specimen when the interface is fully debonded. The general features of the push-out curve (i.e. the o0 against u0 relation) are depicted in Fig. 2a. The curve shows an initial linear relationship corresponding to elastic loading of the composite with a bonded interface. This linear relationship terminates when initial debonding occurs, which is followed by progressive debonding and sliding. During progressive debonding, the stress increases with increasing displacement at a decreasing rate, and reaches a maximum, o . At this point, catastrophic debonding occurs along the remaining portion of the bonded interface. The stress suddenly drops to a new value, which is defined as the push-out stress, opo, and fibre push-out starts. The important role of interfacial asperities (i.e. roughness) on the fibre sliding behaviour has been identified [3–10]. Experimental evidence of the interfacial roughness effect has been obtained from the fibre push-back test [4, 6, 8–10]. This test is performed by turning over the push-out specimen and then pushing back the pushed-out fibre, which completely debonds from and slightly protrudes out of the matrix due to the original push-out test. The general features of the push-back curve are depicted in Fig. 2b. During the push-back test, the stress increases with the displacement initially until fibre sliding occurs along the entire interface. At this point, the stress drops and reaches a plateau value. When the fibre slides through its original position, the load drops to a stress defined as the fibre reseating stress, ors. This is then followed by the load increasing to a peak as the fibre is pushed beyond its origin. After this peak, the load returns to its plateau value. During the fibre push-out process, the interface is subjected to Coulomb friction after it is debonded. Hence, the interfacial shear stress at the frictional interface is proportional to the interfacial radial compressive stress. Ignoring the roughness effect, this compressive stress can result from (i) oc, the stress due to the thermomechanical mismatch between the fibre and the matrix, which is uniform along the frictional interface, and (ii) op, the stress induced by Poisson’s effect when the fibre is subjected to loading in the axial direction, which varies along the frictional interface [11–15]. The