Issue 49

S.A.G. Pereira et alii, Frattura ed Integrità Strutturale, 49(2019) 412-428; DOI: 10.3221/IGF-ESIS.49.40 417 Fig. 4 shows how the crack propagates in each of the cases considered above, using the XFEM tool made available by Abaqus, that enables the study of the initiation and propagation of a crack in quasi-static problems. Two different analytical methods presented in [17] are now compared with the analytical results obtained from Eqn. (14), for an angle of 60º. The following equations relate to the stress and deformation methods, Eqns. (15) and (16), respectively.    1 [ ) 2 xx xx T             (15) 1 2 x x dx dx T E dx dx                            (16) Fig. 5 shows a graphical comparison of the results achieved with these two methods. A similar approach is followed by [17]. Figure 5 : T for 60    . The stress method provided a non-dimensional T value of -0.51, while the deformation method provided a value of -0.49, both agreeing with -0.5 obtained analytically. Because of the singularity the points closer to the crack tip were neglected in the regression lines. The consideration of the points very close to the crack tip would introduce larges errors in the evaluation of T values. S PECIMENS our types of specimens in polymethyl methacrylate (PMMA) were considered. PMMA is a brittle material, transparent and colourless, which allows a direct observation of the crack tip. In this study cast PMMA was used, with Young´s modulus of 3.3 GPa, Poisson coefficient 0.3 and ultimate tensile strength 76 MPa. Fig. 7 a) shows the specimen used in the 4-point bending tests, and Fig. 7 b) the specimen used to achieve mixed mode in 3-point bending. Eleven 4-point bending tests were performed using an MTS servo-hydraulic machine under displacement control at 0.2 mm/min. The upper rollers had a diameter of 12.5 mm and the lower ones 30 mm. Since the lower part of the assembly had a predefined distance of 100 mm, the distance between supports was always maintained within the same 100 mm, varying only the supports position along the length of the specimen and its distance to the point of application of the load. For the 3-point bending, the same distance of 100 mm between rollers was maintained, as well as the displacement speed. The calibration of the non-standard 3-point bending specimen was performed using Abaqus software and J-integral. F