Issue 47

J. P. Manaia et alii, Frattura ed Integrità Strutturale, 47 (2019) 82-103; DOI: 10.3221/IGF-ESIS.47.08 86 Figure 3 : Butterfly specimen shape, dimensions in millimeters. The relevance of this geometry was analysed and optimized by 3D FE calculations. The FE calculations confirmed that the specimen shoulders deform elastically, while the central gauge section exhibits large plastic deformations. Also, the shoulders dimensions provide sufficient gripping area. The complex loft surface in the gauge section of the specimen, lowers the likelihood of fracture in the vicinity of the specimen boundaries. Consequently, the onset of fracture processes is confined to initiate near the specimen centre in the gauge section under all loading combinations and at the same time the specimen experiences a wide range of stress states (stress triaxiality). The analytical formula for initial stress triaxiality was derived by Dunand and Mohr, in their study to optimize butterfly specimen for the multiaxial ductile fracture experiments on sheet metals [13]:           2 3 12 sign (5) The stress triaxiality is zero for shear dominant loading      0 while it approaches its maximum value of   1 3 as the pure tension becomes dominant      [13]. To sum up, the biaxial loading allows exploring initial stress triaxialities ranged from 0 for pure shear  = 0° (Fig. 4 (2)) to 0.58 for pure tension  = 90° (Fig. 4 (3)) and 0.19 for  = 30° (both combined shear and tension) (Fig. 4 (4)). Figure 4 : Butterfly specimen at four different loading angles: (1) designed arcan apparatus with the butterfly specimen, (2)  = 0° (pure shear), (3)  = 90° (pure tension) and (4)  = 30° (combined shear and tension). For the present biaxial experiments, an arcan apparatus, was designed and manufactured (Fig. 4 (1)). The designed arcan apparatus is a modification based on the work by Doyoyo and Wierzbicki [14], which in turn is based on the original specimen presented by Arcan et al. to study the biaxial failure of unidirectional fiber-reinforced composites [15]. The loading (1) (2) (3) (4)