Two parameter engineering fracture mechanics
The object of this work was to investigate and expand on previously carried out research into elastic-plastic crack tip fields using the first two terms of the Williams expansion to characterise the degree of crack tip constraint. As a precursor to this research a history of fracture mechanics is also presented. In the present work crack tip fields in small scale yielding have been detennined using modified boundary layer formulations in an attempt to model the influence of the second order term of the Williams expansion, the T -stress. The prime object of this thesis was to investigate and expand on previously carried out research into a two parameter characterisation of elastic-plastic crack tip fields using the second parameter of the Williams expansion(T), which attempts to characterise the degree of crack tip constraint. Modified Boundary Layer formulations in conditions of plane strain were implemented to derive a suitable reference solutions, against which the effects of out of plane strains can be compared and the validity of presently established reference fields can be gauged. The effect of out of plane non-singular stress, S, on the crack tip stress field were also considered, where constraint was largely determined by T. A wide range of analyses have been carried out, from the microstructural scale to complete engineering components in an attempt to characterise crack tip stress fields. The ability to apply two parameter fracture concepts to real engineering structures requires methods for calculating T for complex components with realistic semi-elliptical defects. A simple engineering method for achieving this was developed making use of linespring elements in the finite element package ABAQUS. This approach was validated by the calculation of T for semi-elliptical cracks at the chord-brace intersection of a tubular welded joint, modelled using the mesh generation program PATRAN. The micromechanics of cleavage, using the Ritchie-Knott-Rice model have also been constructed. This work relates the ratio of J for unconstrained and constrained geometries to critical microstructural distance, critical cleavage stress and the toughness ratio on the strainhardening effect. The elastic-plastic behaviour of short and deeply cracked bend bars has previously been described by Betegon and Hancock based on the first two terms of the Williams expansion. A local cleavage criterion has been applied to these fields to indicate the effect of loss of constraint on lower shelf toughness of shallow cracked bend bars. The work models the maximum temperature at which cleavage can occur in these geometries to show the effect of constraint and aJW ratio of cracked bend bars on the ductile-brittle transition temperature. This has also been backed by a significant experimental research program. Finally constraint dependent toughness has been considered in relation to failure assessment methodologies. A simple engineering method for modifying these Failure Assesssment Diagrams has been presented, this consists of considering the constraint matched toughness of the strucutre. This procedure recovers the original Failure Assessment Line and unifies the constraint dependent fracture toughness within defect assessment schemes which utilise Failure Assessment Diagrams.