numero25

C. J. Christopher, Frattura ed Integrità Strutturale, 25 (2013) 161-166; DOI: 10.3221/IGF-ESIS.25.23 164 1 1 2 2 x y r i 1 1 2 2 r i 1 1 1 2 2 2 r i C (u iu ) 2(B iB )z z 4 C z (B iB 2E)z z ln(z) 4 C (A i3B )z z ln(z 2 2Ez ln( ) z) E D 2Dz z 2                                        (9) Where x u and y u are the horizontal and vertical displacements respectively, E 2(1 )     ; 3 4     (plane strain) or 3 1       (plane stress). x u and y u are shown explicitly below with the assumption D E 0   . 1 1 1 2 2 2 x r r i i r 1 1 2 2 i 2 ( A (2B (B 2E)cos B sin E ln(r ) 3 u r 2B 2E)cos r 3B )sin r 2 2 2 3 3 3 r r (1 2 )cos sin (1 2 )sin 2 2 2 2 2 C r(1 )c 4 co os s                                                    (10) 1 1 1 2 2 2 i i r r r 1 1 2 2 i y 2 ( 2B (A (B 2E)sin B cos E ln(r ) 3 u r 3B )cos r 2B 2E)sin r 2 2 2 3 3 3 r r sin (1 2 )sin (1 2 )cos 2 2 2 2 2 C r(3 )sin 4 cos                                                   (11) A PPLICATION OF THE MODEL TO MIXED MODE CRACK GROWTH hus far, the model has been tested against limited data obtained from an inclined crack in a 2mm thick 2024-T6 aluminium CT specimen with non-standard dimensions, which is shown in Fig. 2. A jeweller’s saw with blade thickness of 0.15 mm was used to extend the notch tip into a 45° slit some 5 mm long, which is schematically shown in Fig. 2. A fatigue crack some 2 mm long was then grown in Mode I collinear with this slit. This was achieved by starting with a larger dimension CT specimen with additional loading holes in a similar fashion to the disk-shaped compact specimen described by Ding et al [2]. The specimen was then machined to final dimensions and approximately 100 cycles of loading was applied in the usual orientation, so as to put the fatigue crack under a combination of mixed Mode I and Mode II loading. The applied load ratio was R = 0.1 and the peak load was 1.2 kN. A Dantec digital image correlation (DIC) system operating in 2D mode was used to measure the crack tip displacement field and to compare the predictions of the CJP model with the measured strain field data. A facet size of 17 pixels with a centre-line pitch of 17 pixels was used with a scale of 107 pixels per millimetre. It is acknowledged that this method of cracking is not optimum, as it produces a Mode I plastic wake, rather than one that reflects mixed mode loading. However, the technique gives data for a mixed mode crack tip strain field and a Mode I crack wake and this is not dissimilar to the data acquired by many other workers, e.g. [2]. Attention will be given in the immediate future to testing cracks of various inclinations, i.e. various mode-mixity ratios, which have been developed under true mixed mode loading, as well as under Mode I loading. Fig. 3 presents a comparison between the measured x and y components of the crack tip displacement and those predicted by the 5-parameter CJP mixed mode model, whilst Fig. 4 show typical stress intensity data measured through a loading half cycle. In Fig. 4 the stress intensity factors are all defined with respect to the local crack plane, i.e. K F and K II values are defined as respectively being perpendicular to, and parallel with, the plane of the inclined crack. The stress intensity factors can be fairly easily re-defined using simple geometry, with Cartesian coordinates defined in terms of the load line T