We consider the problem of determination of the elastoplastic stress-strain state of a matrix containing an elliptic inclusion of a different material in the presence of an arc-shaped crack on the interface under the action of mechanical loads applied at infinity, which can be arbitrarily oriented relative to the crack. The appearance of contact macrozones between the crack faces is regarded as possible. We use the model of isotropic hardening of the materials with bilinear approximation of the “stress–strain” curves. We consider numerical solutions of the elastic and elastoplastic problems. It is shown that disagreement between the corresponding results increases in the course of transition from the elastic to elastoplastic state as the level of loading increases.
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References
A. J. Hodes and V. V. Loboda, “Arc crack in a homogeneous electrostrictive material,” Mat. Met. Fiz.-Mekh. Polya, 58, No. 1, 92–102 (2015); English translation: J. Math. Sci., 222, No. 2, 114–130 (2017); https://doi.org/10.1007/s10958-017-3286-7.
L. M. Kachanov, Fundamentals of the Theory of Plasticity [in Russian], Nauka, Moscow (1969).
I. M. Kershtein, V. D. Klyushnikov, E. V. Lomakin, and A. S. Shesterikov, Fundamentals of Experimental Fracture Mechanics [in Russian], Moscow State University, Moscow (1989).
A. Ulitko and V. Ostryk, “Interface crack on the interface of a circular inclusion and s matrix,” Fiz.-Mat. Modelyuv. Inform. Tekhnol., Issue 3, 138–149 (2006).
R. D. Bhargava and R. Narayan, “Circular inhomogeneity and two concentric symmetric circular arc cracks problem in an infinite isotropic elastic plate under tension,” Int. J. Fract., 11, No. 3, 509–520 (1975); https://doi.org/10.1007/BF00033537.
B. Cotterell and J. R. Rice, “Slightly curved or kinked cracks,” Int. J. Fract., 16, No. 2, 155–169 (1980); https://doi.org/10.1007/BF00012619.
D.-H. Chen and S. Nakamichi, “Plane problem of cracks generated from the interface of an elliptical inclusion,” JSME Int. J. Ser. A.: Solid Mech. Mater. Eng., 40, No. 3, 275–282 (1997); https://doi.org/10.1299/jsmea.40.275.
D.-H. Chen and S. Nakamichi, “Stress intensity factors for an interface crack along an elliptical inclusion,” Int. J. Fract., 82, No. 2, 131–152 (1996); https://doi.org/10.1007/BF00034660.
A. H. England, “An arc crack around a circular elastic inclusion,” Trans. ASME, J. Appl. Mech., 33, No. 3, 637–640 (1966); https://doi.org/10.1115/1.3625132.
Y. L. Gao, C. L. Tan, and A. P. S. Selvadurai, “Stress intensity factors for cracks around or penetrating an elliptic inclusion using the boundary element method,” Eng. Anal. Bound. Elem., 10, No. 1, 59–68 (1992); https://doi.org/10.1016/0955-7997(92)90079-M.
N. Hasebe and Y. Yamamoto, “A crack initiation and two debondings development at the interface of a circular rigid inclusion under uniform loading,” Int. J. Damage Mech., 24, No. 7, 965–982 (2015); https://doi.org/10.1177/1056789514560774.
A. Piva, “A crack along a circular interface between dissimilar media,” Meccanica, 17, No. 2, 85–90 (1982); https://doi.org/10.1007/BF02135007.
H. Shen, P. Schiavone, C. Q. Ru, and A. Mioduchowski, “Stress analysis of an elliptic inclusion with imperfect interface in plane elasticity,” J. Elasticity, 62, No. 1, 25–46 (2001); https://doi.org/10.1023/A:1010911813697.
M. Toya, “A crack along the interface of a rigid circular inclusion embedded in an elastic solid,” Int. J. Fract., 9, No. 4, 463-470 (1973); https://doi.org/10.1007/BF00036326.
M. Toya, “Debonding along the interface of an elliptic rigid inclusion,” Int. J. Fract., 11, No. 6, 989–1002 (1975); https://doi.org/10.1007/BF00033845.
E. Viola and A. Piva, “Fracture behaviour by two cracks around an elliptic rigid inclusion,” Eng. Fract. Mech., 15, No. 3-4, 303–325 (1981); https://doi.org/10.1016/0013-7944(81)90063-1.
E. Viola and A. Piva, “Two arc cracks around a circular rigid inclusion,” Meccanica, 15, No. 3, 166–176 (1980); https://doi.org/10.1007/BF02128927.
O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method for Solid and Structural Mechanics, Vol. 2, Elsevier, Oxford (2005).
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 63, No. 1, pp. 65–74, January–March, 2020.
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Adlucky, V.J., Loboda, V.V. Finite-Element Analysis of the Elastoplastic State of a Plane with Elliptic Inclusion in the Presence of Interface Crack. J Math Sci 270, 76–86 (2023). https://doi.org/10.1007/s10958-023-06333-0
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DOI: https://doi.org/10.1007/s10958-023-06333-0