Journal of Mechanical Science and Technology 23 (2009) 54~63 www.springerlink.com/content/1738-494x DOI 10.1007/s12206-008-0810-1 Journal of Mechanical Science and Technology Evaluation of elastic modulus for unidirectionally aligned short fiber composites † Hong Gun Kim and Lee Ku Kwac * Department of Mechanical and Automotive Engineering, Jeonju University, Jeonju, 560 - 759, Korea (Manuscript Received March 18, 2008; Revised August 3, 2008; Accepted August 8, 2008) -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Abstract An analytical approach of to reinforcement for of short fiber reinforced composites has been extended to include the estimation of elastic modulus. The model is based on the theoretical development of shear lag theory developed by Cox for unidirectionally Aligned aligned Short short Fiber fiber Compositescomposites. Thus, the evolution of conventional models is described in detail along with the effect on the modulus of various parameters. Results are shown with ex- perimental data as well as the comparison of other theories. It is found that the present model agrees well with experi- mental data and resolves some of the discrepancies among the previous models. It is also found that the present model is very accurate yet relatively simple to predict Young's modulus of discontinuous composites and has the capability to correctly predict the effects of fiber aspect ratio, fiber volume fraction, and fiber/matrix modulus ratio. Keywords: Piezoelectric hollow cylinder; Thermal gradient; Electric potential; Radial stress; Hoop stress -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction Composite materials are among the strongest candi- dates as a structural material for many automobile, aerospace and other applications [1, 2]. Among them, short fiber reinforced composites or discontinuous composites are not as strong or as stiff as continuous fiber reinforced composites and are not likely to be used in critical structural applications such as aircraft primary structures. However, they do have several attractive characteristics that make them worthy of consideration for other applications. Therefore, short fiber reinforced composite materials have been exten- sively investigated because they are more economical and impact resistant [3]. One of the earliest attempts to explain the reinforc- ing effect of short fibers was described by Cox [4], and is now referred to as the shear lag theory which considers long straight discontinuous fibers com- pletely embedded in a continuous matrix [1, 4]. It is the most conventional version of the shear model which can be considered as debonded at fiber ends, assuming that no stress is transferred across the fiber ends. However, the prediction of composite modulus calculated by Cox model does not provide sufficiently accurate strengthening predictions when the fiber as- pect ratio is small [5, 6]. The predicted modulus value obtained by Cox model is significantly smaller than the experimentally observed values in the short fiber composites. In fact, the Cox model gives an underes- timation of the strength due to the neglect of stress transfer across the fiber ends [3, 7, 8]. Over the years, several ways of accounting fiber end stresses have been proposed. Nardone and Prewo at- tempted to modify the conventional shear lag model to take into account the tensile transfer of load from the matrix to the discontinuous reinforcement [5]. Their modified shear lag model is well fitted with the ex- perimental data for prediction of yield strength of dis- continuous composites. However, it is limited to pre- †This paper was recommended for publication in revised form by Associate Editor Chongdu Cho * Corresponding author. Tel.: +82 63 220 3063, Fax.: +82 63 220 2959 E-mail address: kwac29@jj.ac.kr © KSME & Springer 2009