Axial shear modulus of a fiber-reinforced composite with random fiber cross-sections. (1982)

• Record Type: Journal Article
• Authors: Bose, S. K.; Debnath, L.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 5:Number 2(1982)
• Page Start: 393
• Page End: 401
• Publication Date: 1982
• Subjects: axial shear modulus -- fiber-reinforced composites -- random distributions -- random cross-sections -- coarse-graining -- bounds on moduli; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171282000386
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : A study is made of the effective axial shear modulus of a fiber reinforced material with random fiber cross-sections so that the micromechanics is governed by stochastic differential equations. A coarse-graining procedure is adopted to investigate the macroscopic behavior of the material. This analysis leads to the formula for the effective axial shear modulusμ ∗ = μ 1 / { 1 − 2 c ( μ 2 − μ 1 ) / ( μ 2 + μ 1 ) }, whereμ 1 andμ 2 are the shear modulus of the matrix and fibers respectively andc is the concentration of the fibers less that0.5 . Forc > 0.5, the fiber and matrix moduli are to be interchanged andc is to be replaced by1 − c . The results of this study are compared with those of the theory of fibre reinforced materials. Finally, a numerical example is presented with graphical representation.