This thesis deals with three inter-related topics. The first topic is concerned with the solution of a cracked transversely isotropic—orthotrOpic composite laminate of finite thickness. The transversely isotropic sublaminate which is sandwiched between orthotropic outer sublarninates contains a central crack or an array of periodically distributed cracks which are perpendicular to the interfaces between the two media. When the crack is wholly within the sublaminate, solutions are obtained for the stress intensity factors and the crack-induced interfacial stresses in three loading modes. When the crack tips touch the interfaces, the stress singularities are no longer the usual square-root type but are determined by the mechanical properties of the media. In this case, solutions are obtained for stress singularities and the corresponding stress intensity factors. The degenerate case when the outer sublarninates are also isotropic but dissimilar from the central sublaminate is also solved.
The second topic concerns the application of the above fracture mechanics solutions to crack problems of laminates composed of unidirectional fibre-reinforced composites. In view of the fact that unidirectional fibre-reinforced composites are prone to transverse cracking and that laminates made from unidirectional plies are prone to delamination, a cracked [(il9),,2 /(900)n1 ]s symmetric laminate is studied with a view to examining the mutual constraining effect of plies on transverse cracking and the role of transverse cracks in causing delamination. The fracture mechanics framework is used to reveal the mechanisms behind the enhancement of the socalled in situ strengths of unidirectional laminae in multidirectional laminates. When the tips of a transverse crack touch the interfaces, the effect of the properties of the constraining sublarninates on the stress singularities and stress intensities at the tips of the crack is investigated.
The third topic is concerned with two types of optimum strength design of composites laminates. First, for a fibre-reinforced antisymmetric [(:l:0°)n2 / (90°)n1 / (2120),,2] angle-ply laminate, the design variables of the laminate, viz. the ply angle 0 and relative ply thickness, are chosen in such a way as to minimize the stress intensity factor at the crack tip in the (900),“ lamina without exceeding the interfacial maximum principal tensile stress. Secondly, based upon the extensive fracture mechanics analysis (from topics one and two), a set of in situ strength parameters for unidirectional laminae in a multidirectional laminate is proposed. The in situ strength parameters take into account the influence of adjacent laminae and thickness of a particular lamina upon its transverse tensile and in-plane shear strengths when it is used in a multidirectional laminate. These strength parameters are then employed to calculate a stress norm which determines how close the stress state in the lamina is to its failure state. The stress norm is incorporated into the formalism of an optimization problem in order to enhance the load bearing capacity of multidirectional laminates
