Issue 41

P. Lopez-Crespo et alii, Frattura ed Integrità Strutturale, 41 (2017) 203-210; DOI: 10.3221/IGF-ESIS.41.28 205 M APPING OF ELASTIC STRAIN he strain mapping experiments were conducted on beamline ID15A of the European Synchrotron Radiation Facility (France). Energy dispersive mode was used, following the configuration previously applied with high qauality results [15,21]. Two solid state X-ray detectors were mounted to measure two in-plane directions of strain ( ε xx and ε yy ). The scattering angle was 2θ = 5º. The elastic strain was evaluated according to Bragg’s law:    0 0 hkl hkl hkl hkl d d d (1) where hkl d is the lattice parameter of crystallographic plane (hkl) measured at a certain load and 0 hkl d is the strain-free lattice parameter of the same crystallographic plane. Here the plane (211) was used. The incident beam slits were opened to 60 × 60 µm, giving a lateral resolution (x, y) of 60 µm and a nominal gauge length through-thickness (z) of around 1.4 mm [17]. The gauge length was diamond shaped and centred on the mid-plane (z=0). Attention was paid to locate the origin of coordinates at the crack tip [22]. Fig. 2 shows an elastic strain field in the crack opening direction for a sample subjected to 5.3 kN. The two black solid lines in Fig. 2 emanating from the origin of coordinates towards negative coordinates in the crack growing direction represent the crack. Figure 2 : The elastic strain field based on the (211) peak local to the crack in the crack opening direction (ε yy ) for a 13 mm crack length subjected to 5.3 kN. The area sampled by each point is 60 x 60  m. The parameters relating to the area of interest are also illustrated: inner radius of the data array, R int , outer radius of the data array, R out , and angle between the end of the data array and the crack plane, α. F ITTING THE EXPERIMENTAL TO AN ELASTIC MODEL he elastic strains were fitted to an analytical model following a multi-point over-deterministic scheme [23]. The analytical model was based on Williams’ series development used to describe the elastic behaviour of the region surrounding the crack tip [24]. The strains in the crack opening direction can be written as [25]:                                          1 1 2 2 2 0 0 1 3 cos 1 1 2  cos 1 1 2 2 2 2 2 yy E A r sin sin B A r sin T T