Abstract
In this paper a new criterion for fracture investigation of orthotropic materials with cracks under mixed mode I/II loading is presented. In this fracture criterion, orthotropic material will be considered as a reinforced isotropic material. It is supposed that the crack will grow in the matrix of the orthotropic material. A new definition named here as “isotropic–orthotropic stress reduction factor” (IO-SRF) is utilized to consider the effects of the fracture process zone by a macro-mechanics approach. Also, the stress reduction factors will present a valuable relationship between the orthotropic and isotropic fracture toughness. Experimental and finite element methods will be introduced for computing the stress reduction factors. The SRFs are calculated for samples of glass–epoxy as an orthotropic material and samples of epoxy as a related isotropic one. Experimental tests under mixed mode I/II are performed on glass–epoxy composite samples to evaluate the validity of the presented mixed mode fracture criterion. The results of experimental tests on composite samples show a good agreement with the results of the presented criterion. Thus, the proposed criterion could be utilized as an efficient criterion for investigating the fracture of orthotropic materials under mixed mode I/II loading.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Talreja, R.: Assessment of the fundamentals of failure theories for composite materials. Compos. Sci. Technol. 105, 190–201 (2014)
Benveniste, Y., Aboudi, J.: Crack propagation in a laminated composite material modeled by a two-dimensional mixture theory. Acta Mech. 29(1), 213–227 (1978)
Li, Y.D., Xiong, T., Zhao, H.: Interfacial fracture analysis of a piezoelectric-polythene composite cylindrical shell patch under axial shear. Acta Mech. 225(2), 543 (2014)
Li, Y.D., Xiong, T., Cai, Q.G.: Coupled interfacial imperfections and their effects on the fracture behavior of a layered multiferroic cylinder. Acta Mech. 226(4), 1183–1199 (2015)
Sih, G.C.: Strain-energy-density factor applied to mixed mode crack problems. Int. J. Fract. 10(3), 305–321 (1974)
Hussain, M.A., Pu, S.L., Underwood, J.: Strain energy release rate for a crack under combined mode I and mode II. In: Fracture Analysis: Proceedings of the 1973 National Symposium on Fracture Mechanics, Part II. ASTM International (1974)
Erdogan, F., Sih, G.C.: On the crack extension in plates under plane loading and transverse shear. J. Basic Eng. 85(4), 519–525 (1963)
Fakoor, M., Khansari, N.M.: Mixed mode I/II fracture criterion for orthotropic materials based on damage zone properties. Eng. Fract. Mech. 153, 407–420 (2016)
Lin, W.H., Tsai, Y.M.: Fracture of hybrid laminates containing a pair of collinear cracks in the central layer. Acta Mech. 82(3), 159–173 (1990)
Wu, E.M.: Application of fracture mechanics to anisotropic plates. J. Appl. Mech. 34(4), 967–74 (1967)
Leicester, R.H.: Applications of linear fracture mechanics in the design of timber structures. In: Conference of the Australian Fracture Group, Melbourne, pp. 156–164 (1974)
Williams, J.G., Birch, M.W.: Mixed mode fracture in anisotropic media. ASTM STP 601, 125–37 (1976)
Woo, C.W., Chow, C.L.: Mixed mode fracture in orthotropic media. In: Sih, G.C., Valluri, S.R. (eds.) Fracture Mechanics in Engineering Application, pp. 387–96. Sijthoff and Noordhoff, Rockville (1979)
Hunt, D.G., Croager, W.P.: Mode II fracture toughness of wood measured by a mixed-mode test method. J. Mater. Sci. Lett. 1(2), 77–9 (1982)
Mall, S., Murphy, J.F., Shottafer, J.E.: Criterion for mixed mode fracture in wood. J. Eng. Mech. 109(3), 680–690 (1983)
Jernkvist, L.O.: Fracture of wood under mixed mode loading: I. Derivation of fracture criteria. Eng. Fract. Mech. 68(5), 549–563 (2001)
Jernkvist, L.O.: Fracture of wood under mixed mode loading: II. Experimental investigation of Picea abies. Eng. Fract. Mech. 68(5), 565–576 (2001)
Romanowicz, M., Seweryn, A.: Verification of a non-local stress criterion for mixed mode fracture in wood. Eng. Fract. Mech. 75(10), 3141–60 (2008)
Gowhari Anaraki, A.R., Fakoor, M.: General mixed mode I/II fracture criterion for wood considering T-stress effects. Mater. Des. 31, 4461–4469 (2010)
Van der Put, T.A.C.M.: A new fracture mechanics theory for orthotropic materials like wood. Eng. Fract. Mech. 74, 771–781 (2007)
Gowhari Anaraki, A.R., Fakoor, M.: Mixed mode fracture criterion for wood based on a reinforcement microcrack damage model. Mater. Sci. Eng. A 527, 7184–7191 (2010)
Gowhari-Anaraki, A.R., Fakoor, M.: A new mixed-mode fracture criterion for orthotropic materials, based on strength properties. J. Strain Anal. IMechE (2010). https://doi.org/10.1243/03093247JSA667
Fakoor, M., Rafiee, R.,: Fracture investigation of wood under mixed mode I/II loading based on the maximum shear stress criterion. Strength Mater. 45(3), 378–385 (2013)
Carraro, P.A., Zappalorto, M., Quaresimin, M.: A comprehensive description of interfibre failure in fibre reinforced composites. Theor. Appl. Fract. Mech. 79, 91–97 (2015)
Buczek, M.B., Herakovich, C.T.: A normal stress criterion for crack extension direction in orthotropic composite materials. J. Compos. Mater. 19(6), 544–553 (1985)
Gregory, M.A., Herakovich, C.T.: Predicting crack growth direction in unidirectional composites. J. Compos. Mater. 20(1), 67–85 (1986)
Saouma, V.E., Ayari, M.L., Leavell, D.A.: Mixed mode crack propagation in homogeneous anisotropic solids. Eng. Fract. Mech. 27(2), 171–184 (1987)
Buczek, M.B., Herakovich, C.T.: A normal stress criterion for crack extension direction in orthotropic composite materials. J. Compos. Mater. 19(6), 544–53 (1985)
Wei-yang, Y., Shao-qin, Z., Yuan-duo, J.: On J-integrals in the plane fracture of composite materials. Appl. Math. Mech. 13(3), 281–287 (1992)
Saucedo, L., Rena, C.Y., Ruiz, G.: Fully-developed FPZ length in quasi-brittle materials. Int. J. Fract. 178(1–2), 97–112 (2012)
Fakoor, M., Rafiee, R., Sheikhansari, M.: The influence of fiber-crack angle on the crack tip parameters in orthotropic materials. In: Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 0954406215617195 (2015)
He, Q.L., Wu, L., Li, M., Yu, H.: Prediction of mode I crack growth resistance based on a comparative investigation of J-integral and energy dissipation rate concept. Acta Mech. 215(1–4), 175–191 (2010)
Agarwal, B.D., Broutman, L.J., Chandrashekhara, K.: Analysis and Performance of Fiber Composites. Wiley, Hoboken (2006)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Fakoor, M., Shokrollahi, M.S. A new macro-mechanical approach for investigation of damage zone effects on mixed mode I/II fracture of orthotropic materials. Acta Mech 229, 3537–3556 (2018). https://doi.org/10.1007/s00707-018-2132-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-018-2132-4