Statistics for the strength and size effects of microcomposites with four carbon fibers in epoxy resin

Experimental results are presented for the strength distribution and length effects of carbon/epoxy microcomposites consisting of four carbon fibers (Hercules AS4) embedded in one of two different epoxies approximately in a square array at a fiber volume fraction of about 0.7. One epoxy (Dow DER 331 with Dow DEH 26 hardener) was stiff in bulk with a strain to failure of less than 10%, and the other (50% by weight of Dow DER 331 blended with 50% Dow DER 732 and Dow DEH 26 hardener) was very flexible in bulk with large apparent ductility and a strain to failure of 40%. Individual fibers tested at two gauge lengths, 1 and 20 cm, yielded a Weibull shape parameter of about 5 at each length, but the strength versus length plot for the scale parameter on log-log coordinates suggested a Weibull shape parameter of about 8.3. Therefore, the ratio alpha was about 0.6 rather than unity as in previous work in microcomposites. Thus a modified statistical theory for microcomposite strength as a function of length was developed to incorporate this alpha effect. Experimental verification of both the size effect and alpha effect are the two major advantages of the present model over previous Weibull fiber composite models. Strength data for microcomposites at two gauge lengths, 1 and 20 cm, for both epoxies were generated and plotted on Weibull coordinates, where both the expected doubling and tripling of the Weibull shape parameter as compared to that of the fiber and the predicted alpha effect for microcomposite length were observed. The stiff epoxy produced stronger composites at both gauge lengths. On the other hand, the length effect was more severe than predicted in the 20 cm flexible epoxy microcomposite apparently due to a combination of epoxy yielding in shear and fiber/matrix debonding at fiber breaks, and a lower matrix ultimate strength, leading to longer effective load transfer lengths, delta.