PSI - Issue 7

Jean-Yves Buffiere / Procedia Structural Integrity 7 (2017) 27 – 32 Jean-Yves Bu ffi ere / Structural Integrity Procedia 00 (2017) 000–000

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Fig. 2. 3D rendering of a micro shrinkage in a cast Al alloy (voxel size = 0.7 µ m synchrotron tomography) multiple crack internal initiation is observed (in green + orange arrow) from high stress concentration areas. The stress axis is vertical (Serrano-Munoz (2014)).

a fully characterized set of grains (Herbig et al. (2011); King et al. (2010)). Such experimental data is extremely rich and o ff er a real challenge for modeling techniques such as crystal plasticity which, for the moment, can only partly tackle this degree of details, see for example Chen et al. (2017)), for crack initiation or Proudhon et al. (2016) for propagation. This type of studies might however be intrinsically limited for two reasons. First, in the simulations, the loading conditions are generally assumed to be perfect ( e.g. perfectly uniaxial) which is seldom the case, specially for the fatigue rigs which are small / light enough to be installed on tomographic rotations. An unwanted misalignment of the sample might have a large influence on the level of plasticity achieved in the di ff erent grains contained in the sample gauge length and therefore comparison with simulation might be considered with care. Secondly, it is now generally admitted that cracks cross grain boundaries by a combination of tilts and twists which account for the di ff erence in crystallographic orientations of the two neighboring grains. However except in some special microstructures (planar slip resulting in crystallographic facets such as in Al-Li alloys (Zhai et al. (2000)) such mechanisms occur at a nano metric scale (Schaef et al. (2011)) in order to optimize the amount of surface energy required for crossing the grain boundary. It can be seen on figure 1 that, for the moment, if phase contrast tomography can describe the ”global” crack path within a sample with a good accuracy ( ∼ 1 µ m ), very local deviation mechanisms (typical scale ∼ 100 nm) are hardly detected and the local orientation of the imaged crack surface is an average (in that case a < 100 > direction) which is di ffi cult to physically interpret / simulate. At the scale where crack fronts can be accurately imaged in 3D, therefore, the relevant parameters for model ing initiation and propagation could be, respectively, the local values of the stress concentration factor ( K t ) or the Stress Intensity Factor (K), respectively, provided that conditions required to apply Linear Elastic Fracture Mechanics (LEFM) prevail. Such values can be obtained by Finite Element (FE) simulations based on real 3D geometries of the initiating defects. Figure 2 shows an example of small cracks initiated form a shrinkage pore in a cast Al alloy. It can be shown (Serrano-Munoz (2014)) that the crack locations correspond very well to the regions at the surface of the pore where the highest values of K t are predicted by an elastic (and therefore approximate) FE calculation . For crack propagation one should be able to compute the local stress values of K along the crack front. This can be done based solely on the crack shape as in Ferrie et al. (2006), but more complex calculations based on curved and irregular crack fronts remain to be carried out. Here the challenges lie in the calculation of K values at singular points ( e.g. pinned parts of the crack front). An alternative is to try to infer the local crack driving force from the 3D measurement of displacement fields at the crack tip (Toda et al. (2004)) measured using Digital Volume Correlation (DVC). For materials with a suitable microstructure ( i.e. presenting natural markers) this has been done on 3D through cracks with an approximately straight front (Limodin et al. (2010)) but, for the moment, with limited success on part through cracks (Lachambre et al. (2015)). Nevertheless, any anisotropic propagation rate along a part of the crack front tends to be smoothed out by the corresponding increase / decrease of the SIF value, as shown by Morris et al. (1980). This leads gradually to a more