Constraint estimation schemes in fracture mechanics
Elastic-plastic crack tip constraint has been estimated for the common planar crack geometries. These include single edge cracked bars in tension and bending, centre cracked panels, and double edge cracked bars. The description of the stress field has been modified from a one parameter characterisation, based on K or J, to include a second term. The second parameter is a non-singular term, described either in terms of an elastic T-stress or a Q field. The limits of one and two parameter characterisation are discussed for single edge bars in tension and bending and for centre cracked panels. For the single edge geometries the two parameter characterisation was found to extend the characterisation well beyond the one parameter approach. For the centre cracked panels the two parameter characterisation in terms of a J-Q approach was found to be more accurate than a J-T approach at high levels of deformation. For the single edge cracked bending and tension geometries the second parameter Q is divided into two components named QT and QP. QT is an elastic term which depends on the elastic T stress and is independent of the distance from the crack tip. The second component, QP, arises from global bending on the uncracked ligament. This is a distance dependent term which depends on the level of deformation and can either be expressed as a function of the load normalised by the limit load or as a function of the plastic component of the J-integral. For single edge bend bars the constraint estimation provides a basis for a method of predicting fracture toughness using local failure approach, where the failure criterion is expressed in terms of the stress level ahead of the crack tip. Finally the constraint of mixed mode problem has been analysed and compared with that of pure Mode I problems.