Considered in this study are the axially-symmetric problems of fracture of composite materials with interacting cracks, which are subjected to initial (residual) stresses acting along the cracks planes. An analytical approach within the framework of three-dimensional linearized mechanics of solids is used. Two geometric schemes of cracks location are studied: a circular crack is located parallel to the surface of a semi-infinite composite with initial stresses, and two parallel co-axial penny-shaped cracks are contained in an infinite composite material with initial stresses. The cracks are assumed to be under a normal or a radial shear load. Analysis involves reducing the problems to systems of second-kind Fredholm integral equations, where the solutions are identified with harmonic potential functions. Representations of the stress intensity factors near the cracks edges are obtained. These stress intensity factors are influenced by the initial stresses. The presence of the free boundary and the interaction between cracks has a significant effect on the stress intensity factors as well. The parameters of fracture for two types of composites (a laminar composite made of aluminum/boron/silicate glass with epoxy-maleic resin and a carbon/plastic composite with stochastic reinforcement by short ellipsoidal carbon fibers) are analyzed numerically. The dependence of the stress intensity factors on the initial stresses, physical-mechanical parameters of the composites, and the geometric parameters of the problem are investigated.
Similar content being viewed by others
References
V. M. Babich, A. N. Guz, and V. M. Nazarenko, “Disk-shaped normal-rupture crack near the surface of a semiinfinite body with initial stresses,” Sov. Appl. Mech., 27, No. 7, 637–643 (1991).
A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer, Berlin (1999).
A. N. Guz, Brittle Fracture of Materials with Initial Stresses [in Russian], Naukova Dumka, Kiev (1992).
A. N. Guz, “On non-classical problems of fracture mechanics taking into account the stresses along cracks,” Int. Appl. Mech., 40, No. 8, 138–144 (2004).
A. N. Guz, “On the development of brittle-fracture mechanics of materials with initial stresses,” Int. Appl. Mech., 32, No. 4, 316–323 (1996).
A. N. Guz, M. Sh. Dyshel’, and V. M. Nazarenko, “Fracture and stability of materials and structural members with cracks: Approaches and results,” Int. Appl. Mech., 40, No. 12, 1323–1359 (2004).
A. N. Guz and V. M. Nazarenko, “Symmetric failure of the halfspace with penny-shaped cracks in compression,” Theor. Appl. Fract. Mech., 3, No. 3, 233–245 (1985).
A. N. Guz, V. M. Nazarenko, and V. L. Bogdanov, “Fracture under initial stresses acting along cracks: Approach, concept and results,” Theor. Appl. Fract. Mech., 48, 285–303 (2007).
M. K. Kassir and G. C. Sih, Mechanics of Fracture. Three-Dimensional Crack Problems, Vol. 2, Noordhoff, Leyden (1975).
L. P. Khoroshun, B. P. Maslov, E. N. Shikula, and L. V. Nazarenko, Statistical Mechanics and the Effective Properties of Materials [in Russian], Naukova Dumka, Kiev (1993).
V. M. Nazarenko, V. L. Bogdanov, and H. Altenbach, “Influence of initial stress on fracture of a halfspace containing a penny-shaped crack under radial shear,” Int. J. Fract., 104, 275–289 (2000).
Ya. S. Uflyand, Dual-equation Method in Mathematical Physics Problems [in Russian], Nauka, Leningrad (1977).
Author information
Authors and Affiliations
Additional information
Published in Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 3, pp. 176–185, July–September, 2008.
Rights and permissions
About this article
Cite this article
Bogdanov, V.L. Influence of initial stresses on fracture of composite materials containing interacting cracks. J Math Sci 165, 371–384 (2010). https://doi.org/10.1007/s10958-010-9805-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-010-9805-4