Comparison of stress singularities of kinked carbon and glass fibres weakening compressed unidirectional composites: a three-dimensional trimaterial junction stress singularity analysis

A three-dimensional eigenfunction expansion technique, based in part on separation of the thickness variable and partly utilizing a modified Frobenius-type series expansion in conjunction with the Eshelby-Stroh formalism, is used to compute the local stress singularity, in the vicinity of a kinked fibre/matrix trimaterial junction front, representing a measure of the degree of inherent flaw sensitivity of unidirectional carbon-fibre-reinforced composites under compression. Micro-kinking, more prominent in the misaligned regions of carbon fibres, is caused by crystallite disorientations, as detected by the Raman and X-ray measurements, as well as dislocation glide in crystallites and intra/intercrystallite disorders. The present analysis explains the test results relating to propagation of failure from such discontinuities in a unidirectional composite under compression. Numerical results presented include the effect of fibre wedge aperture angle on the strengths of the mode I and mode II singularities. Of special practical interest is the comparison of the inherent flaw sensitivity of carbon/epoxy and glass/epoxy composites, because improvement of the compressive strength and kink toughness was earlier accomplished through commingling of highly anisotropic (and crystalline) carbon and isotropic (and amorphous) glass fibres at the tow level. Compression fracture of these composites can be fully explained and quantified by the present three-dimensional linear elastic stress singularity analysis-based method. Finally, numerical results, pertaining to the through-thickness variation of 'stress intensity factor' for symmetric uniform load and its skew-symmetric counterpart that also satisfies the boundary conditions on the top and bottom surfaces of a compressed composite monolayer, in the vicinity of a trimaterial junction front, are also presented.