JOURNAL OF MATERIALS SCIENCE 28(1993) 4489-4496 Prediction of fibre strength at the critical length: a simulation theory and experimental verification for bimodally distributed carbon fibre strengths TAEHWAN JUNG, R. V. SUBRAMANIAN, V. S. MANORANJAN* Department of Mechanical and Materials Engineering, and *Department of Mathematics, Washington State University, Pullman, WA 99164, USA A computer simulation model of fragment distribution with respect to the fibre strength in a single-filament composite test is developed using the bimodal Weibull statistics. The predictions of the theory are examined with experimental results for AU carbon fibres coated by zirconium-n-propoxide or a zircoaluminate complex. Weibull analysis reveals a bimodal distribution of fibre strengths, in which the fractions of low- and high-strength populations vary with gauge length. It is seen that the simulation results are in good agreement with experimental data if the best fit model of strength distribution is applied. Thus, the use of a bimodal distribution term in the simulation theory yields a predicted strength at the critical length which is in good agreement with the results of extrapolation of experimental data, while the unimodal distribution term leads to overestimation of the strength. 1. Introduction Carbon fibre-reinforced composite materials have be- come very attractive structural materials in many branches of aerospace and other industries because of their light weight combined with high strength and modulus. In the fibre-reinforced composite system, one of the most important controlling factors is the interracial property which relates to the capacity of stress transfer from the matrix to the reinforcing fibre. Although the high strength of a composite is due to strong bonding between the fibre and the matrix, a low interfacial bonding strength due to a relatively weak bonding improves the fracture toughness of the composite. For this important reason, many investiga- tions are devoted to research characterizing the inter- facial behaviour in the composite system. There are various techniques to characterize inter- facial shear strength between the fibre and matrix [l]. Among them, the single-filament composite (SFC) test is frequently used to study interracial shear strength in the composite [2-6]. This test was originally used to investigate the interfacial shear strength in the fibre/metal composite system by Kelly and Tyson [2]. The method is based on force balance when tensile stress is transferred to the interface parallel to the fibre axis. Assuming that the matrix is perfectly plastic, the shear stress, z, is a constant along the critical length, Ic. Therefore, the relationship between fibre strength, sf, and the shear stress at the critical length is Sf.d - 21 c (1) 0022-2461 ~ 1993 Chapman & Hall where d is the diameter of the fibre. In Equation 1, the critical length and diameter of the fibre can be ob- tained from the SFC test. However, it is impractical to measure directly the fibre strength at the critical length, because the critical length is too short for measurement by conventional tensile tests. It is the usual practice to extrapolate tensile strength data at measurable gauge lengths to the critical length using an approximately linear relationship between the fibre strength and the logarithm of gauge length [7]. Recently, a probability model and a Monte Carlo method were used to predict a realistic value for the interracial strength between the fibre and the matrix [8, 9]. A notable new development [10] is the formula- tion of an exact theory to express the relationship between the fibre fragmentation and the underlying fibre statistical strength iri the SFC test. These simu- lation theories are based on the unimodal Weibull distribution for the fibre fracture. Generally, the unimodal Weibull distribution does not fit well the experimental data because of the presence of various kinds of imperfections such as surface defects, and internal defects including misoriented crystallites and undetectable defects [11-14]. But, the Weibull dis- tribution curve predicted from the bimodal distribu- tion is known to be a better fit with the experimental data than the unimodal distribution 1-15, 16]. For this reason, the unimodal distribution model used in simu- lation theories needs to be modified to a multimodal distribution model if the fibre strength data reveal more than one type of defect. The objective of this paper is to obtain the fibre 4489