Bridging in uniaxial reinforced ceramic composites

Abstract

In this study, a unidirectional fibre reinforced infinite composite plate under uniaxial stress which has a central through crack is considered. The bridging relations which express the relation between the stress in the fibre and the crack opening displacement along the crack axis as elastic bridging relation used by Hsuech (1988) and frictional bridging relation used by Marshall et al. (1985) which are consistent with infinite brittle fibre-reinforced composite behaviour are chosen to be utilised in the formulation of the problem. The differential equation which contains Airy stress functions of a centrally cracked orlhotropic plate is solved through Fourier transform techniques and the stresses in plane are obtained in terms of the crack surface derivative. The singular integral equation system obtained for the formulation of the problem, is reduced to the solution of a non-linear system of algebraic equations by introducing Chebyshev polynomials which have closer roots near to crack tips. Stress intensity factor at crack tips, crack opening displacement and the point where the bridging type considered changes on the crack axis can be calculated. $S_iC/AI_2O_3$ is chosen as an example of brittle fibre-reinforced composite material and the effect of the variations of the fibre volume ratio is presented.

Özet

Bu çalışmada, tek eksenli gerilme altında, merkezi bir çatlağı olan, çatlak eksenine dik lifler ile kuvvetlendirilmiş sonsuz kompozit levha gözönüne alınmıştır. Problemin formülasyonunda kullanmak üzere, çatlak boyunca lifteki gerilme ve çatlak açılması ilişkisini ifade eden köprülenme bağıntıları olan Hsuech (l988)'in kullandığı elastik köprülenme bağıntısı ve Marshall ve diğerleri (1985)'nin kullandığı sürtünmeli köprülenme bağıntısı seçilmiştir. Problemin formülasyonunda elde edilen tekil integral denklem, Chebyshev polinomları yardımı ile lineer olmayan bir cebirsel denklem sistemine indirgenmiştir. Gevrek lifler ile kuvvetlendirilmiş kompozitlere örnek malzeme olarak $S_iC/AI_2O_3$ seçilmiş ve lif hacim oranının değişimine göre çözümler elde edilmiştir.