Matrix cracking with bonded interfaces in unidirectional fibre-reinforced composites

Abstract

Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6119, USA The mechanical properties of a material can be significantly improved by incorporating strong fibres aligned with the loading direction [1-6]. The initial damage in unidirectional fibre-reinforced composites is often in the form of a crack (or cracks) extending through the matrix with unbroken fibres bridging the crack surfaces. Several models have been proposed to analyse the critical loading stress on the composite for matrix cracking [7-14]. Depending upon the bonding strength between the fibre and the matrix, the interface either remains bonded [8, 9] or becomes debonded [7, 9-14] during the matrix cracking and fibre bridging processes. For the case of debonded interfaces, the analysis has been performed in a companion work [14] and compared with other existing analyses [7, 9]. Hence, the analysis of the present study is limited to the case of bonded interfaces. Firstly, the existing models [8, 9] are summarized, then a new model is proposed. Finally, comparison is made between the present solution and the existing solutions. The steady-state matrix cracking stress with bonded interfaces was first analysed by Aveston and Kelly [8]. A fibre surrounded by a hexagonal matrix was adopted as a representative volume element of the composite. A shear lag model [15] was used to analyse the stress transfer between the fibre and the matrix in the presence of matrix cracking. The stress-transfer solutions were based on the assumption that the average displacement in the matrix could be represented by the displacement in the matrix at a radial distance R from the centre of the fibre. The solutions were then used to calculate the work done by the applied stress during matrix cracking. Finally, the energy balance condition was used to derive the matrix cracking stress, and the result was [8]: