STRESS-INTENSITY FACTORS OF R-CRACKS IN FIBER-REINFORCED COMPOSITES UNDER THERMAL AND MECHANICAL LOADING

This paper is concerned with the problem of the calculation of stress- intensity factors at the tips of radial matrix cracks (r-cracks) in fi ber-reinforced composites under thermal and/or transverse uniaxial or biaxial mechanical loading. The crack is either located in the immedia te vicinity of a single fiber or it terminates at the interface betwee n the fiber and the matrix. The problem is stated and solved numerical ly within the framework of linear elasticity using Erdogan's integral equation technique. It is shown that the solutions for purely thermal and purely mechanical loading can simply be superimposed in order to o btain the results of the combined loading case. Stress-intensity facto rs (SIFs) are calculated for various lengths and distances of the crac k from the interface for each of these loading conditions. The behavio r of the SIFs for cracks growing towards or away from the interface is examined. The role of the elastic mismatch between the fibers and the matrix is emphasized and studied extensively using the so-called Dund urs' parameters. It is shown that an r-crack, which is remotely locate d from the fiber, can either be stabilized or destabilized depending o n both the elastic as well as the thermal mismatch of the fibrous comp osite. Furthermore, Dundurs' parameters are used to predict the expone nt of the singularity of the crack tip elastic field and the behavior of the corresponding SIFs for cracks which terminate at the interface. An analytical solution for the SIFs is derived for all three loading conditions under the assumption that the elastic constants of the matr ix and the fiber are equal. It is shown that the analytical solution i s in good agreement with the corresponding numerical results. Moreover , another analytical solution from the literature [15], which is based upon Paris' equation for the calculation of stress-intensity factors, is compared with the numerical results and it is shown to be valid on ly for extremely short r-cracks touching the interface. The numerical results presented are valid for practical fiber composites with r-crac ks close to or terminating at the interface provided the matrix materi al is brittle and the crack does not interact with other neighboring f ibers. They may be applied to predict the transverse mechanical behavi or of high strength fiber composites.