Issue 38

N.O. Larrosa et alii, Frattura ed Integrità Strutturale, 38 (2016) 266-272; DOI: 10.3221/IGF-ESIS.38.36 267 typically 2-6 mm in height [3]. Both these aspects result in reduced crack tip constraint in the component compared to the deeply notched standard specimens. Furthermore, there is experimental evidence showing that panels loaded in tension exhibit higher resistance to fracture since these conditions lead to lower constraint around the crack [4]. As a result, in these cases, the material capacity to withstand load is underestimated and it would be useful to perform assessments with a fracture resistance value obtained from a test specimen with a crack tip constraint condition similar to that in the actual component [5]. Materials can exhibit a change in toughness with specimen geometry for both cleavage and ductile fracture modes. Here, attention is focussed on ductile crack propagation behaviour (microvoid coalescence). A ductile fracture simulation approach has been implemented in previous work [6,7] to evaluate the fracture resistance curves ( J -R) for different test specimens. Although these procedures are useful tools to evaluate fracture resistance for structural components, the development and calibration of the finite element assessment (FEA) model requires extensive expertise and the application of the procedures becomes prohibitive for routine assessments. An alternative framework is then of interest for more rapid assessments. The J–Q two-parameter fracture mechanics [8,9] approach has been extensively used to characterize elastic–plastic crack front fields. The parameter Q characterizes the degree of crack tip constraint, by quantifying the level of deviation of stress/strain fields from reference fields. In this work, we conduct investigations on the J-Q two parameter characterisation approach to compare the constraint conditions of a pipe under different loading modes with those observed in C(T) and SE(T) specimens. The aim of this is to support the use of a low constraint fracture toughness value by showing that at the same applied driving force ( J ), the level of constraint ( Q ) at the pipe is similar to that in the SE(T) specimen. T HEORETICAL BACKGROUND Two parameter J-Q theory n small-scale yielding, there is always a zone of single parameter (K, J , CTOD) dominance. The crack-tip conditions are fully defined by the single parameter, whose value depends on load, crack size and geometry. The situation changes as plasticity develops when the loss of constraint becomes apparent (e.g., fully plastic response or shallow cracks), and single parameter dominance does not hold. Under these circumstances, the stresses near the crack tip are not given by the single parameter but also depend on the configuration (loading type, geometry and material properties). In low constraint geometries the near tip stress distribution can be significantly lower than the high constraint J -dominant state. The J-Q approach to elastic-plastic fracture mechanics was introduced to remove some of the conservatism inherent in the single parameter approach based on the J integral. The following equation provides an approximate description of the near tip stress field, over physically significant distances [8,9]: ref ij ij ij Q 0       (1) where ij  is the Kronecker delta, 0  is the yield stress and ref ij  is a reference field, often taken as the HRR field, the near crack tip fields for power-law plastic materials derived in [10,11]. Thus, the Q- factor quantifies the difference between the actual local stress at a certain reference location near the crack tip and the theoretical HRR-stress field and is given by: ref ij ij Q 0 -     (2) The actual stress field in a component and the HRR field in the forward sector of the crack-tip region differ by an approximately uniform hydrostatic stress independently of distance from the crack tip, for given values of J [8,9]. Therefore, eq (1) means that with the addition of the second parameter, a range of stress states can be obtained at a fixed deformation level (as characterised by J ), differing by a hydrostatic stress (as characterised by Q ). In practice, the stress field is more complex than eq. (1) but this simplification has been found to apply for the region at the crack tip where [8,9], corresponding to the near crack tip zone where the fracture process zone (FPZ) for both cleavage and ductile I