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The fracture mechanics are established for a large plate containing an embedded crack of finite length taking account of: (1) the anisotropy of the material, (2) the effect of residual stresses arising from isothermal temperature changes, and (3) the effect of tractions applied to the crack surfaces resulting from the mechanical effect of crack-bridging ligaments. An expression for the crack-opening displacement distribution in terms of the crack-bridging traction distribution is derived together with the corresponding fracture criterion based on energy considerations.
Assuming that the relationship is known between the bridging traction and the crack-opening displacement, it is shown how integral equations may be derived to solve bridged crack problems for both a linear and a nonlinear case. For the special case when the preexisting crack is long enough, how a simple relation can be derived which controls the initiation of crack growth is demonstrated.
In general terms, how the relationship between the crack-bridging tractions and the crack opening can be derived from micromechanical models of stress transfer is shown. Both unidirectional composites and cross-ply laminates are considered for the case of long bridged cracks. It is shown how the results can be used for short cracks if the macroscopic shear strains are neglected.
Applications of the techniques developed in this paper are described in an accompanying paper.
Head of Fracture and Performance Section, National Physical Laboratory, Teddington, Middlesex
Stock #: CTR10091J