Deterministic method of describing rupture probability application to the analysis of high-modulus carbon fibres

Abstract

The fitting of experimental fibre strength distribution by a Weibull distribution function must theoretically allow the prediction of strength distribution in other conditions as, for example, other gauge lengths, because it is the hypothesis of the Weibull model that the material is well described. It may be assured that this last assumption is almost always fully unrealistic, and applied to the case of aluminium-coated high-modulus carbon fibres, the Weibull statistics do not lead to any convenient prediction of the size effect. A new approach is proposed. It is based on a precise description of the real population of defects and no longer on an idealized and a priori simplified distribution as proposed by the Weibull model. It is completely deterministic and does not require any parameter adjustment. It permits an extremely precise prediction of the experimental strength distribution at other gauge lengths, exactly describing, for example, the experimentally observed jumps in the curve (P r-σ r). Moreover, it results in a very significant optimization of testing procedure, in determining only the necessary gauge lengths at which strength measurements have to be made in order to allow a complete description of the defect population and thus a confident strength prediction at every gauge length. Therefore, by giving a quantitative representation of the critical defect distribution in the material by a function of their failure probability, the damage, caused by annealing treatment or chemical reaction, may be thoroughly analysed as a function of the microstructure of the material and particularly at the level of the critical defects, whose evolution (increasing of failure propensity) may be easily followed. This method has been applied very successfully in the case of aluminium-coated high-modulus HM35 carbon fibres.