Issue 38

N.O. Larrosa et alii, Frattura ed Integrità Strutturale, 38 (2016) 266-272; DOI: 10.3221/IGF-ESIS.38.36 270 R ESULTS he numerical J -R curves obtained by the implementation of the damage model are shown in Fig. 3. A standard deeply cracked C(T) specimen and a shallow cracked SE(T) specimen are modelled. The use of the ESIS P2 procedure [2] for the estimation of the effective initiation fracture toughness is illustrated. Next, the J-Q approach is applied to the pipe component for internal pressure and pure bending in order to show the effect of the loading mode on constraint level. In general, the value of Q depends on load magnitude (and therefore on J ) as well as loading mode, being proportional to load in small-scale yielding but weakly dependent on J at large loads. The values of Q have therefore been evaluated at applied J values, see Fig. 4, for the pipe at loads which cover the range of J at initiation in C(T) and SE(T) specimens. It can be seen that at these values, the stress fields in the pipe when plotted against normalised distance are weakly dependent on J . Hence, Q is also weakly dependent on J in this practical range. It can then be assumed that the pipe would have the same effective initiation toughness as a specimen with the same J-Q value. For fracture assessments where it is not possible to match the Q value of the pipe with that of a test specimen, the specimen with the closest higher value of Q will be a conservative choice. The Q- stress is generally evaluated at the distance r = 2J/σ 0 from the crack tip and using the opening stress obtained by detailed finite element analysis, Eq. (2). The reference field in Eq. (1) is obtained from a boundary layer analysis at the same applied J with T=0, as this enables the approach to be applied to materials which do not follow the power-law form which enables the HRR field to be used as the reference field in Eq. (1). 0.0 0.2 0.4 0.6 0.8 1.0 0 200 400 600 800 1000 1200 ESIS-P2 (J 0.2 ) Domain integral C(T), a o /W=0.5 SE(T), a o /W=0.2 J-integral (kJ/m 2 )  a(mm) API X65 J SE(T) 0.2 J C(T) 0.2 Figure 3 . J -R curves of shallow cracked SE(T) and deeply cracked C(T) specimens. Fig. 4 shows the normalised values of the crack tip opening stress field for the test specimens, the pipe component under two loading types and the modified boundary layer model. It is readily observed from the figure that, from all the components assessed here, the severest stress field is that of the C(T) specimen. The vertical distance from any of the curves to the MBL curve gives the value of Q. As the stress field in the SE(T) specimen is greater than that in the pipe for both loading conditions (more negative value of Q), can be used as a conservative critical value for crack initiation for the pipe under either loading condition for the crack size assessed. C ONCLUSIONS rack size, loading mode and material properties can have a strong effect on constraint conditions, affecting the material resistance to fracture. In this work, finite element ductile fracture simulation has been used to construct J -R curves for 2 test specimens with different constraint conditions. The ductile fracture model only considers a small area ahead of the crack tip T C