Issue 49

S.A.G. Pereira et alii, Frattura ed Integrità Strutturale, 49(2019) 412-428; DOI: 10.3221/IGF-ESIS.49.40 427 C ONCLUDING REMARKS racture tests on 4- and 3-point bending specimens of PMMA were carried out for mixed mode fracture analysis and numerical assessment with the extended finite element method (XFEM). Unlike other works, in the present experimental results no correlation between T-stress and the toughness level was found: all fracture points are above the MTS theoretical values, a result similar to the early tests of Erdogan and Sih in their classical tests of flat plates of PMMA with inclined cracks. The strain energy density (SED) criterion provides an improved lower bound fit of the experimental data points. Nevertheless, most of the experimental points are above of this curve, requiring further studies to evaluate this effect. Concerning the crack path prediction with XFEM implemented in Abaqus, generally good agreement with experiments was obtained, particularly in the initial steps of crack propagation. XFEM analysis were performed using the MTS criterion, and it is noted that the crack path simulation may be slightly affected by the fracture criteria considered. The results found for the inclined central crack plate remotely loaded by a tensile stress, show good consistency between T - stress results obtained either by analytical methods or directly or indirectly through Abaqus software. A CKNOWLEDGEMENTS he cooperation of Miguel Figueiredo and Rui Silva in the experiments is acknowledged. R EFERENCES [1] Alkan, U., Tutluoglu, L. (2016). Investigation of beam specimen geometries under four-point asymmetric bending for shear mode fracture toughness measurements of rocks, Pap. ARMA (American Rock Mech. Assoc. 16-183, (October). [2] Erdogan, F., Sih, G.C. (1963). On the crack extension in plates under plane loading and transverse shear, J. Basic Eng., 85(4), pp. 519. [3] Smith, D.J., Ayatollahi, M.R., Pavier, M.J. (2000). The role of T-stress in brittle fracture for linear elastic materials under mixed mode loading, Fatigue Fract. Eng. Mater. Struct., 24(2), pp. 137–150. [4] Richard, H.A. (1981). A new compact shear specimen, Int. J. Fract. 17(5), pp. 105–107. [5] Atkinson, C., Smelser, R. E., Sanchez, J. (1982). Combined mode fracture via the cracked Brazilian disk test, Int. J. Fract. 18(4), pp. 279–291. [6] Krueger, R. (2004). Virtual crack closure technique: history, approach, and applications, Appl. Mech. Rev. 57(2), pp. 109–143. [7] Belytschko, T., & Black, T. (1999). Elastic crack growth in finite elements with minimal remeshing, Int. J. Numer. Methods Eng. 45(5), pp. 601–20. [8] Rebelo, C.A.C.C. (1987).Caracterização do Comportamento à Fractura de Resinas Poliester Insaturadas, tese de Mestrado em Materiais e Processos de Fabrico. FEUP, 1987. [9] He, M.Y., Hutchinson, J.W. (2000). Asymmetric four-point crack specimen, J. Appl. Mech., 67(March 2000), pp. 207– 209. [10] Ayatollahi, M.R., Aliha, M.R.M. (2011). On the use of an anti-symmetric four-point bend specimen for mode II fracture experiments, Fatigue Fract. Eng. Mater. Struct., 34(11), pp. 898–907. [11] Wang, C., Zhu, Z.M., Liu, H.J. (2016). On the I–II mixed mode fracture of granite using four-point bend specimen, Fatigue Fract. Eng. Mater. Struct., 39(10), pp. 1193–1203. [12] Belli, R., Wendler, M., Petschelt, A., Lohbauer, U. (2017). Mixed-mode fracture toughness of texturized LS2 glass- ceramics using the three-point bending with eccentric notch test, Dent. Mater., 33(12), pp. 1473–1477. [13] Fett, T. (1991). Mixed-mode stress intensity factors for the thee-point bending bars, Int. J. Fract., 48, pp. 67–74. [14] Williams, M.L. (1957). On the stress distribution at the base of a stationary crack, J. Appl. Mech., 24, pp. 109–114. [15] Irwin, G.R. (1957). Analysis of stresses and strains near the end of a crack traversing a plate, J. Appl. Mech., 24, pp. 361–364. [16] Arteiro, A.J.C., de Castro, P.M.S.T. (2014). Mecânica da Fratura e Fadiga: Exemplos de cálculo e aplicação, FEUP F T