Issue 49

S.A.G. Pereira et alii, Frattura ed Integrità Strutturale, 49(2019) 412-428; DOI: 10.3221/IGF-ESIS.49.40 413 consideration, see e.g. [1]. In mixed-mode fracture the fit of theoretical models and experimental data displays some variation, as exemplified by PMMA results of Erdogan and Sih [2] or Smith, Ayatollahi, Pavier [3]. Given the continued interest in the topic of mixed mode fracture, the present work discusses mixed mode fracture modelling and testing, illustrating the levels of approximation attained using several techniques, with PMMA as an experimental case study. Fracture mechanics under mixed mode loading in planar structures has been less explored than the pure mode I, due to the difficulty of the crack behavior characterization in mode II and III. Several testing methods, based on different geometries and loading conditions, are available in the literature. For instance, in planar geometries, the Compact Tension Shear (CTS) [4] and the Brazilian disk [5] are common geometries for mixed mode fracture testing, allowing to evaluate the material behavior for different degrees of mixity. However, other simple geometries can be used for these studies, as is the case of the Single Edge Notch specimen (SEN). Considering conventional axial testing machines, two types of tests are possible for planar geometries: (i) axial tension/compression tests and (ii) bending tests. Bending tests are advantageous for testing in mixed mode since crack growth with any combination of mode I/mode II can be performed by changing the position of the crack in relation to the load locations. In this work, SEN specimens were tested in bending for the characterization of toughness of Poly(methyl methacrylate) (PMMA) under mixed mode conditions, and advanced numerical formulations were used to simulate non-pure mode I loading conditions. Possible influence of T -stress in the results was assessed and results were compared with those obtained using flat plates with inclined cracks tested by Erdogan and Sih, [2]. For planar specimens, crack path predictions are based on 2D Finite Element (FE) analysis and consideration of I K and II K in the frame of suitable eq K criteria; numerical tools, such as the modified virtual crack closure technique (mVCCT), [6], and the extended finite element method (XFEM), [7], are used. The experimental results are compared with the results obtain by Erdogan and Sih, [2], and Rebelo, [8], among others. The 4-point asymmetric bending test allows to study the behaviour of a specimen subjected pure mode II or mixed mode I-II, see e.g. [9,10]. Considering an asymmetric load, it is possible to measure the fracture toughness in pure mode II ( IIc K ) and to vary the ratio / I II K K or / II I K K by changing the distance of application of the load to the plane of the crack ( 0 S ), Fig. 1. Figure 1 : Mixed mode I-II in a 4-point bending test. For 0 0 S  (force applied in the plane of the crack) the bending moment is null and there is only shear force; representing a situation of pure mode II. For mixed-mode analysis, the variation of 0 S influences the mode I component, resulting in different shear stress and bending moment combinations at the plane of the crack. According to Wang et al., [11], the stress intensity factors for mixed mode are given by: I I Q a K Y Wt    (1) II II Q a K Y Wt   (2)