numero25

J. Lachambre et alii, Frattura ed Integrità Strutturale, 25 (2013) 50-53 ; DOI: 10.3221/IGF-ESIS.25.08 51 E XPERIMENTAL he material used in this study is a nodular graphite cast iron with a homogeneous dispersion of graphite nodules which are used as natural markers for DVC [2]. The cracks are initiated from artificial defects produced by laser machining [3]. The fatigue cycles are applied on small dog bone samples (square cross section 1.5 mm 2 ) using a specially designed fatigue machine which allows to use a distance between the sample and the X-ray source lower than 20mm. A standard laboratory tomograph available at MATEIS [4] has been used. A current of 174µA and a mean of 3 radiography with an exposure time of 1 second have been used 720 angular positions have been recorded which corresponded to a scan time of 45 minutes. The reconstruction time (weighted filtered back projection, Feldkamp algorithm) takes approximately 15 minutes for a 560×560×900 voxels 3D image. The crack shape evolution is studied through the residual of the DVC which correspond to the difference between the reference and the deformed and corrected volumes [2]. Once the sample is set up in the tomograph, two scans are recorded at low stress (40 MPa) and a scan at high stress (290 MPa). The sample is cycled in situ at constant a stress amplitude of 300 MPa (load ratio: 0.1). In the beginning of the experiment 100,000 cycles are applied to the sample before a first scan is recorded. Then 2 scans are recorded every 15 kcycles, one at 40 MPa and an other at 290 MPa, to monitor the crack evolution as described in [2]. A C8-DVC multiscale algorithm with an eight node cubic element is used to compute the displacement fields in the loaded specimen [5]. Two kinds of correlation are performed during the experiment: first between a reference volume acquired before cycling under low stress and a deformed volume under high stress at each step of cycling. Then a correlation between the volume at low stress and the volume at high stress is also performed at each step. The first kind of analysis gives access to the crack shape evolution while the second is used to map the crack opening displacement (COD). R ESULTS he DVC analysis during cycling is carried out with 32 voxels elements, over a volume of 11×11×15 C8,elements. This mesh is quite coarse considering that, typically, at ~ 180 kc the crack is contained in only 8 elements. Nevertheless the crack morphology can be estimated from the DVC residual. Similar images have been obtained for the cracks emanating from a corner defect. Figure 1 : Surface crack evolution at 160 kc, 175 kc, 190 kc, 205 kc and 240 kc obtained from DVC residuals (the cross section of the sample is 1.5x1.5 mm 2 ). An extended version of DVC called X-DVC (based on the principle of the extended finite element method. [6]) is used to post process the 3D images recorded between the scans at low and high stress. The results of X-DVC on one corner and one surface crack can be visualised in Fig. 2. As the position of the crack front is not known, a discontinuous enrichment is added over the whole cross-section. Those displacement fields can be used to compute stress intensity factor values along the crack front using Williams series [7] as described in [2]. In this previous work, stress intensity factors were computed within parallel reconstructed sections containing the stress axis and the crack front normal. The crack was assumed to be straight and the planes used for fitting the Williams series were parallel. The crack front position was found by minimizing the super singular term n=-1 of the series for the mode I case. T