Prediction of Kink Width in Compressed Fiber Composites

Couple stress theory is used in the prediction of the size of the kink band width that occurs in the compressive failure of a fiber composite by microbuckling. The composite is assumed to be inextensible in the fiber direction, and to deform as a Ramberg-Osgood solid in shear and in transverse tension. Predictions are given for the kink width as a function of the fiber diameter, modulus and strength; the material nonlinearity of the composite; and the amplitude and wavelength of fiber waviness. The kink width scales with fiber diameter but is fairly insensitive to variations in other material properties and in the amplitude and wavelength of initial fiber waviness. For typical polymer matrix composites, the predicted kink width is of the order of 10–15 fiber diameters, in agreement with observed values. The couple stress theory is also used to assess the role of fiber bending resistance in the compressive strength of fiber composites that fail by microbuckling. It is found that although the compressive strength is sensitive to the amplitude of the initial waviness, it is not very sensitive to its wavelength.