Journal of Samara State Technical University, Ser. Physical and Mathematical SciencesJournal of Samara State Technical University, Ser. Physical and Mathematical Sciences1991-86152310-7081Samara State Technical University34666Research ArticleOrthotropic strip with central semi-infinite crack under arbitrary loads applied far apart from the crack tipUstinovKonstantin B.Doctor of physico-mathematical sciences, Head Scientist Researcherustinov@ipmnet.ruLisovenkoDmitry S.Doctor of physico-mathematical scienceslisovenk@ipmnet.ruChentsovAlexander VictorovichCandidate of physico-mathematical sciences, no statusIshlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences1512201923465767010062020Copyright © 2019, Samara State Technical University2019The exact analytical solution has been obtained for a problem of orthotropic strip with central semi-infinite crack loaded normally with self-balanced system of forces applied far enough from the crack tip to be considered as applied at infinity. The general solution is expressed as a superposition of solutions for two modes of loading: (i) symmetrically applied moments; (ii) symmetrically applied transverse forces with compensating moments. The exact expressions for stress intensity factor (SIF) have been obtained. Due to symmetry only the opening mode of SIF is present for each case of loading. For both cases of loading the stress states are determined by two dimensionless parameters composed by four elastic constants. Expression for SIF for the case of loading with symmetrically applied moments is obtained in terms of elementary functions and coincides with the elementary solution due to beam theory. Expression for SIF for the case of loading with symmetrically applied transverse forces with compensating moments has been obtained in terms of one function of one of the parameters expressed as a single integral, multiplied by a power function of the second parameter. The solution for this case demonstrated good agreement with the existing numerical solution for the range of parameters, for which the latter had been obtained. The obtained solution covers all possible range of parameters.stress intensity factordelaminationintegral transformWiener–Hopf techniqueкоэффициент интенсивности напряженийотслоениеинтегральное преобразованиеметод Винера–Хопфа[Suo Z., Bao G., Fan B., Wang T. C., "Orthotropy rescaling and implications for fracture in composites", Int. J. Solids Struct., 28:2 (1991), 235-248][Suo Z., "Domination specimens for orthotopic materials", J. Appl. Mech. - T. ASME, 57:3 (1990), 627-634][Bao G., Ho S., Suo Z., Fan B., "The role of material orthotropy in fracture specimens for composites", Int. J. Solids Struct., 29:9 (1992), 1105-1116][Li S., Wang J., Thouless M. D., "The effects of shear on delamination in layered materials", J. Mech. Phys. Sol., 52:1 (2004), 193-214][Massabo R., Brandinelli L., Cox B. N., "Mode I weight functions for an orthotropic double cantilever beam", Int. J. Eng. Sci., 41:13-14 (2003), 1497-1518][Brandinelli L., Massabo R., "Mode II weight functions for isotropic and orthotropic double cantilever beams", Int. J. Fract., 139:1 (2006), 1-25][Thouless M. D., "Phase angles and delamination of layered materials", Eng. Fract. Mech., 191 (2018), 153-167][Georgiadis H. G., Papadopoulos G. A., "Elastostatics of the orthotropic double-cantilever-beam fracture specimen", Z. angew. Math. Phys., 41:6 (1990), 889-899][Suo Z., Hutchinson J. W., "Interface crack between two elastic layers", Int. J. Fract., 43:1 (1990), 1-18][Hutchinson J. W., Suo Z., "Mixed mode cracking in layered materials", Adv. Appl. Mech., 29 (1991), 63-191][Begley M. R., Hutchinson J. W., The Mechanics and Reliability of Films, Multilayers and Coatings, Cambridge Univ. Press, Cambridge, United Kingdom, 2017, x+278 pp.][Ustinov K., "On semi-infinite interface crack in bi-material elastic layer", Eur. J. Mech. A-Solid., 75 (2019), 56-69][Low Frequency Properties of Dielectric Crystals. Second and Higher Order Elastic Constants, Landolt-Börnstein - Group III Condensed Matter, 29A, ed. D. F. Nelson, 1992][Лехницкий С. Г., Теория упругости анизотропного тела, Наука, М., 1977, 416 с.][Noble B., Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations, Chelsea Publ., New York, 1988, x+246 pp.][Устинов К. Б., "Об отслоении слоя от полуплоскости; условия упругой заделки для пластины, эквивалентной слою", Изв. РАН. МТТ, 2015, № 1, 75-95][Sih G. C.,Paris P. C.,Irwin G. R., "On cracks in rectilinearly anisotropic bodies", Int. J. Fract. Mech., 1:3 (1965), 189-203]