Issue 41

V. Rizov, Frattura ed Integrità Strutturale, 41 (2017) 491-503; DOI: 10.3221/IGF-ESIS.41.61 502 present study indicate that the longitudinal fracture in two-dimensional functionally graded beams with material non- linearity can be efficiently regulated in their design stage by employing appropriate material gradients. Besides for the beam shown in Fig. 1, the analysis developed in the present paper can be applied to determine the strain energy release rate for longitudinal cracks in two-dimensional functionally graded non-linear elastic beam configurations loaded in pure bending (for instance, the double cantilever beam loaded with uneven bending moments, the four-point bending beam when the crack tip is located in middle beam portion which is loaded in pure bending). It should be noted that the approach developed in the present paper is applicable also for beam configurations loaded by a vertical load when the shear stresses can be neglected, i.e. when the span to height ratio of the beam is large. A CKNOWLEDGMENTS he present study was supported financially by the Research and Design Centre (CNIP) of the UACEG, Sofia (Contract BN – 198/2017). R EFERENCES [1] Butcher, R.J., Rousseau, C.E., Tippur, H.V., A functionally graded particulate composite: Measurements and Failure Analysis, Acta Matererialia, 47 (1999) 259-268. [2] Gasik, M.M., Functionally graded materials: bulk processing techniques, International Journal of Materials and Product Technology, 39 (1995) 20-29. [3] Hirai, T., Chen, L., Recent and prospective development of functionally graded materials in Japan, Material Science Forum, 308-311 (1999) 509-514. [4] Mortensen, A., Suresh, S., Functionally graded metals and metal-ceramic composites: Part 1 Processing, International Materials Review, 40 (1995) 239-265. [5] Nemat-Allal, M.M., Ata, M.H., Bayoumi, M.R., Khair-Eldeen, W., Powder metallurgical fabrication and microstructural investigations of Aluminum/Steel functionally graded material, Materials Sciences and Applications, 2 (2011) 1708-1718. [6] Neubrand, A., Rödel, J., Gradient materials: An overview of a novel concept, Zeit f Met, 88 (1997) 358-371. [7] Suresh, S., Mortensen, A., Fundamentals of functionally graded materials, IOM Communications Ltd, London (1998). [8] Tokova, L., Yasinskyy, A., Ma, C.-C, Effect of the layer inhomogeneity on the distribution of stresses and displacements in an elastic multilayer cylinder, Acta Mechanica, (2016) DOI: 10.1007/s00707-015-1519-8, 1 – 13. [9] Tokovyy, Y., Ma, C.-C, Three-dimensional temperature and thermal stress analysis of an inhomogeneous layer, Journal of Thermal Stresses, 36 (2013) 790 – 808, DOI: 10.1080/01495739.2013.787853. [10] Tokovyy, Y., Ma, C.-C, Axisymmetric stresses in an elastic radially inhomogeneous cylinder under length-varying loadings, ASME Journal of Applied Mechanics, 83 (2016), DOI: 10.1115/1.4034459. [11] Uslu Uysal, M., Kremzer, M., Buckling behaviour of short cylindrical functionally gradient polymeric materials, Acta Physica Polonica A, 127 (2015) 1355-1357, DOI:10.12693/APhysPolA.127.1355. [12] Uslu Uysal, M., Buckling behaviours of functionally graded polymeric thin-walled hemispherical shells, Steel and Composite Structures, An International Journal, 21 (2016) 849-862. [13] Szekrenyes, A., Fracture analysis in the modified split-cantilever beam using the classical theories of strength of materials, Journal of Physics: Conference Series, 240 (2010) 012030. [14] Szekrenyes, A., Vicente, W.M., Interlaminar fracture analysis in the GII-GIII plane using prestressed transparent composite beams, Composites Part A: Applied Science and Manufacturing, 43 (2012) 95-103. [15] Szekrenyes, A., Semi-layerwise analysis of laminated plates with nonsingular delamination - The theorem of autocontinuity, Applied Mathematical Modelling, 40 (2016) 1344 – 1371. [16] Bohidar, S.K., Sharma, R., Mishra, P.R., Functionally graded materials: A critical review, International Journal of Research, 1 (2014) 289-301. [17] Erdogan, F., Fracture mechanics of functionally graded materials, Computational Engineering, 5 (1995) 753-770. [18] Paulino, G.C., Fracture in functionally graded materials, Engineering Fracture Mechanics, 69 (2002) 1519-1530. T