A micro-kink theory for determination of shear modulus of a unidirectional composite lamina

A hitherto unavailable concept of fiber micro-kink responsible for microscopic shear damage is introduced. Fiber micro-kinking is caused by crystallite disorientations, as detected by the Raman and X-ray measurements, inside a carbon fiber. In addition, the fibers themselves, constituting a unidirectional composite lamina, may contain micro-flaws such as fiber misalignment. The matrix material is assumed to be linear elastic. A mechanistic (as opposed to empirical) approach for derivation of the constitutive relation in shear, based on the concept of micro-kinking (caused by crystallite disorientations) and fiber misalignment, is developed. This is the shear counterpart of the micro-cracking theory for damage assessment of composites under tension. An expression for the nonlinear shear modulus is derived based on the assumption of uniform distribution of micro-kinks and fiber misalignment defects.