Issue 39

J. Sobek et alii, Frattura ed Integrità Strutturale, 39 (2017) 129-142; DOI: 10.3221/IGF-ESIS.39.14 141  Variant con 180° (0°), which represents the nodal selection governed by a uniform distribution from the whole body of the test specimen, seems to be the best choice (and was used as the reference for the next analysis step).  Nodal selection of variant ring 5 mm is still comparable with the uniform nodal distribution variant. This is true up to the highest number of the used Williams series terms that was tested in this study, i.e. N = 11.  Using of variant ring 0.5 mm provides a sufficiently accurate results only up to the number of Williams expansion terms N = 4. This is not valid for the (very) close vicinity of the crack tip, where the results are still accurate enough. Future work will provide analysis of variant ring 5 mm (or other convenient value of the ring radius) with a particular focus on how many terms N of the Williams series are optimal for the crack-tip field reconstruction at a given distance from the crack tip. Physical significance of the higher order terms of the Williams series should be better explained and will be analysed via a real experiment (with utilization of digital image correlation technique, similarly to the case of [28]), which is under preparation by authors of this paper. However, for the purpose of the analysis shown in this paper this knowledge is not relevant – the coefficients of terms of the regression are not used here as fracture parameters as it is within the classical or the two-parameter fracture mechanics ( K or/and T ). Here, they are used only as coefficients of a regression function for the stress field approximation. The aim of this approach is to use the approximation of the field in further fracture- mechanical application (i.e. the plastic zone or the fracture process zone size and shape estimation, etc.). A CKNOWLEDGMENT his paper has been worked out under the project No. LO1408 “AdMaS UP – Advanced Materials, Structures and Technologies” , supported by Ministry of Education, Youth and Sports under the “National Sustainability Programme I” . R EFERENCES [1] Williams, M.L., On the stress distribution at the base of a stationary crack, Journal of Applied Mechanics (ASME), 24 (1957) 109–114. [2] Anderson, T.L., Fracture mechanics. Fundamentals and Applications, Boca Raton: CRC Press, (2005). [3] Berto, F., Lazzarin, P., On higher order terms in the crack tip stress field, International Journal of Fracture, 161 (2010) 221–226. [4] Pook, L.P., The linear elastic analysis of cracked bodies and crack paths, Theoretical and Applied Fracture Mechanics, 79 (2015) 34–50. [5] Ayatollahi, M.R., Rashidi Moghaddam, M., Razavi, S.M.J., Berto, F., Geometry effects on fracture trajectory of PMMA samples under pure mode-I loading, Engineering Fracture Mechanics, (2016), in press. [6] Pook, L.P., The linear elastic analysis of cracked bodies, crack paths and some practical crack path examples, Engineering Fracture Mechanics, (2016), in press. [7] Berto, F., Lazzarin, P., Kotousov, A., On higher order terms and out-of-plane singular mode, Mechanics of Materials, 43 (2011) 332–341. [8] Berto, F., Lazzarin, P., Multiparametric full-field representations of the in-plane stress fields ahead of cracked components under mixed mode loading, International Journal of Fatigue, 46 (2013) 16–26. [9] Pook, L.P., Berto, F., Campagnolo, A., Lazzarin, P., Coupled fracture mode of a cracked disc under anti-plane loading, Engineering Fracture Mechanics, 128 (2014) 22–36. [10] Ayatollahi, M.R., Rashidi Moghaddam, M., Berto, F., A generalized strain energy density criterion for mixed mode fracture analysis in brittle and quasi-brittle materials, Theoretical and Applied Fracture Mechanics, 79 (2015) 70–76. [11] Pook, L.P., Campagnolo, A., Berto, F., Lazzarin, P., Coupled fracture mode of a cracked plate under anti-plane loading, Engineering Fracture Mechanics, 134 (2015) 391–403. [12] Saboori, B., Ayatollahi, M.R., Torabi, A.R., Berto, F., Mixed mode I/III brittle fracture in round-tip V-notches, Theoretical and Applied Fracture Mechanics, 83 (2016) 135–151. [13] Berto, F., Lazzarin, P., Recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, Material Science and Engineering R, 75 (2014) 1–48. T