Microbuckle initiation from a patch of large amplitude fibre waviness in a composite under compression and bending

A finite element couple stress formulation is used to predict microbuckle initiation from a patch of fibre waviness in a unidirectional fibre composite under remote compression and bending. Attention is focused on the knock-down in strength due to large amplitude waviness, with the effects of the physical size of the imperfection included by incorporating the fibre bending resistance within the formulation. The predicted strengths deviate significantly from the simpler kinking theory which neglects the role of fibre bending. Initial imperfections in the form of an infinite band and a circular wavy patch are considered: when these imperfections are of large spatial extent and possess a large misalignment angle, the compressive strength approximates the steady state band broadening stress for an infinite band. The effect of an imposed spatial gradient of stress within the composite is explored by determining the compressive strength of beams of finite height B for the loading cases of pure bending and axial compression. It is found that the compressive strength is sensitive to the magnitude of the imposed stress gradient: the compressive strength of the outer fibres of the beam in bending increases with diminishing height of the beam. This size dependence is much reduced for the case of uniform compression.