Complications of cylindrical anisotropy on the properties of fibres

Abstract

Cylindrically orthotropic materials having linear elastic stress-strain relations can possess a unique type of coupling between the radial and tangential directions. This type of anisotropy occurs when fibres have onion skin or radial morphologies which are characteristic of some graphite fibres and poly- p-phenylene terephthalamide fibres. Pulling on a long slender fibre having this type of anisotropy does not produce a uniaxial state of stress because the unequal Poisson ratios also cause both radial and tangential stresses. The magnitude of these predicted transverse stresses in relation to the axial stress is similar to the relationship of strengths in these principal directions. Hence, it is conceivable that fibre failure could be caused by fibre splitting from high transverse stresses rather than the longitudinal tensile stresses. Temperature changes and other factors causing dimensional changes such as swelling and pressure can similarly cause large stresses if the radial and tangential expansion coefficients are different. This type of axial-transverse coupling is known to limit certain designs in composite structures having this type of anisotropy, yet little has been done to understand fibres possessing these characteristics. This paper examines the complex state of stress that can result in fibres having cylindrically orthotropic linear elastic properties for several simple modes of deformation.