Estimation of tensile strength distribution for carbon fiber with diameter variation along fiber

Abstract

Tensile strength distribution of carbon fibers was investigated for different gauge lengths ranging from 2 to 100 min. In tensile tests, the fiber diameter was determined as the three-point minimum diameter d3 at neighborhoods of both ends and the center of gauge section by using an optical microscope. Weibull analysis of the data and the effective volume model for tensile strength of carbon fiber showed that the shape parameter a was not constant for different gauge lengths and the effective volume model could not be applied effectively to the results. It was found that these were caused by the fact that the diameter was never constant along a carbon fiber. Consequently, in this study, it was aimed to derive the distribution of the tensile strength σ0 for the true minimum diameter d0 along the gauge length. In order to do this, two-dimensional distributions of d3 and d0 were derived from the data of diameter measured at every 0.1 mm along a single fiber with the gauge length of 100 mm. Combining these distributions of d3 and d0 with the distribution of the tensile strength σ3 for the diameter d3, the distribution of the strength σ0 was derived analytically, and calculated by using numerical values of included parameters. The distributions of σ0 obtained for respective gauge lengths mutually agreed very well and could be represented by a single normal distribution, and this showed the validity of the present analysis.