Quantification of constraint in three-dimensional fracture mechanics

• Main Author: Terfas, Osama Abdulhamid
• Published: University of Glasgow 2010
• Subjects: 620.110287; TJ Mechanical engineering and machinery
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.523362

Abstract The role of crack tip constraint in three dimensional fracture mechanics has been investigated under elastic-plastic conditions using finite element techniques. Out-of-plane constraint loss has been identified by comparing the mean stress of the three dimensional cracked body with a reference plane strain configuration. This has allowed the quantification of constraint loss due to thickness. This is important for fitness-for-service procedures where the use of standard thick deeply cracked samples inherently leads to conservative assessments. The proximity to plane–strain conditions was investigated, as well as the J-integral along the crack fronts of typical fracture mechanics specimens. It was shown that deep cracks (a/w=0.5) were significantly affected by out-of-plane constraint loss, while the effect was smaller for shallow cracks (a/w=0.1) when in-plane effects were dominant, where a is the crack length and w is the width of the specimen. The out-of-plane effect was confirmed experimentally with a series of fracture mechanics tests on thin and thick deeply cracked fracture mechanics samples. Computational and experimental studies showed that geometries with B/w=0.2 maintained high constraint conditions at the centre plane and exhibited a low fracture toughness, where B is the thickness of the specimen. As such they can be used to measure the plane strain fracture toughness (JIc) as long as the thickness and the ligament exceed 20J/σ0. The increased slope of the resistance JR curve and enhanced fracture toughness were correlated to the loss of out-of-plane constraint that developed in thinner samples (B/w=0.1). A procedure to incorporate the effects of out-of-plane constraint in the R6 failure assessment diagram was proposed. A procedure was developed to determine ductile crack growth of semi-elliptical surface cracks in flat plates. The procedure used the J-a resistance curve developed from standard high and low constraint geometries in conjunction with an analysis of the crack tip stress field using finite element modelling. This allowed the evolution of crack shape under ductile tearing to be modelled. The majority of the work was devoted to the study of surface breaking semi-elliptical cracks subject to bending, uniaxial tension or biaxial loading. Both the mean stress and J-integral were geometry and load dependent, and were non-uniformly distributed around the crack front. Crack growth was dependent on the level of crack tip constraint, and the original crack shape was generally not retained after ductile tearing. In bending the crack growth was suppressed in the thickness direction and the crack extended significantly sub-surface in a stable manner so that the crack adopted a boat shape. In tension the crack extended through the thickness and this was accompanied with extensive growth in the angular range 45ْ-70ْ. In biaxial loading higher constraint levels were observed, however the overall trend of crack growth was similar to uniaxial tension. Finally, the results from the finite element modelling and the crack growth procedure were verified with experimental data. Excellent agreement in the crack shape patterns was observed between the test data and the crack growth models.