Issue 49

S.A.G. Pereira et alii, Frattura ed Integrità Strutturale, 49(2019) 412-428; DOI: 10.3221/IGF-ESIS.49.40 415   2 2 1 3 cos cos sin sin 2 2 2 2 I II K K T O r r                  (9)     1 cos sin 3cos 1 sin cos 2 2 2 r I II K K T O r r                  (10) where higher order terms   O r are ignored near the crack tip, since their contribution is negligible compared with the other terms. The crack tip parameters I K , II K and depend on the geometry and loading configurations and can vary considerably for different specimens, [3], [11]. Equivalent stress intensity factor In this study the equivalent stress intensity factor proposed by Irwin, [15], was considered: 2 2 eq I II K K K   (11) Organization of the paper The ‘Introduction’ and the next section (‘Inclined central crack’) briefly present the concepts used throughout the work. The paper is organized into two main subjects: the experimental work performed, describing specimens, testing conditions and results, and the simulation of crack path for several mixed mode situations tested, using the finite element method and the Abaqus software. The development of numerical tools allows to evaluate the influence of non-mode I loadings in the crack path and in the growth rate. The aim of this work is to analyse the propagation of pre-existing cracks under pure mode I, pure mode II and unstable mixed mode I-II loading conditions. Numerical simulations with two-dimensional models created in Abaqus software were performed, and validated by comparison with the analytical and experimental results. T- stress and stress intensity factors were obtained using the finite element method, together with the modified virtual crack closure technique (mVCCT) and/or the J-integral. Finally, the extended finite element method (XFEM) was used to predict the crack trajectory under different loading conditions. I NCLINED C ENTRAL C RACK s found in most textbooks, e.g. [16], the stress intensity factors in mode I and II, for the case of a inclined central crack subjected to a remote tension are, [2]: 2 sin I y K a a         (12) sin cos II xy K a a          (13) Later, T -stress for that geometry was found to be, e.g. [3]:   cos 2 T a     (14) Fig. 3 compares these analytical solutions with numerical values obtained with mVCCT and J-integral techniques. In this Figure, the stress intensity factor values are made non-dimensional by a   . Fig. 3 recalls the variation of the stress intensity factors as function of the angle β . For β =90° the stress intensity factor in mode I is obtained, but for β =0° both modes I and II disappear; T is the only non-zero parameter, implying that, for low β values, the fracture is dominated by T . It is also verified that, as expected, normalized T ( T/ σ ) varies between -1 and 1, that is, between remote T    for β =90° and remote T   for β =0°. A