Abstract
The problem of partial contact of faces of a rectilinear crack in a uniform elastic plane under given tensile and shear stresses at infinity as well as two compressive concentrated forces applied near the crack is investigated. Three variants of problem statement are considered: smooth contact, sliding contact, and contact with slip and adhesion between the faces of the crack. Using Kolosov–Muskhelishvili complex potentials, the problem is reduced to a conjugation problem, and a solution of the last one is obtained in analytic form. Transcendental equations to determine the boundaries of contact area and adhesion zone are derived. Conditions are found for cases when the contact area of crack faces degenerates into a point or takes an entire crack. It is shown that an adhesion zone disappears and a mutual slip of crack faces occurs along an entire contact area, if a ratio of tangential and normal stresses given at infinity is larger than a certain value. The results of calculation of boundaries of contact area and adhesion zone, stress intensity factors, and distributions of normal and tangential contact stresses are presented.
Similar content being viewed by others
References
Mossakovsky, V.I., Zagubizhenko, P.A.: On a mixed problem of elasticity theory for a plane, weakened by a rectilinear gap. Rep. USSR Acad. Sci. 94(3), 409–412 (1954). (in Russian)
Mossakovsky, V.I., Zagubizhenko, P.A.: On a compression of an elastic isotropic plane, weakened by a rectilinear crack. Rep. Ukr. SSR Acad. Sci. 5, 385–390 (1954). (in Ukrainian)
Aksogan, O.: Partial closure of a Griffith crack under a general loading. Int. J. Fract. 11(4), 659–670 (1975)
Bowie, O.L., Freese, C.E.: On the “overlapping” problem in crack analysis. Eng. Fract. Mech. 8(2), 373–379 (1976)
Grilytsky, N.D., Kit, G.S.: On a stress–strain state in the vicinity of a crack with partially contacting faces. Math. Methods Physicomech. Fields 8, 35–39 (1978). (in Ukrainian)
Zozulya, V.V.: Bending of a plate weakened by a crack with contacting edges under dynamic loading. Rep. USSR Acad. Sci. 4, 56–60 (1991). (in Ukrainian)
Shatsky, I.P.: Developing a model of a contact of crack faces in bending plate. Theor. Appl. Mech. (31), 91–97 (2000). (in Russian)
Zozulya, V.M., Men’shikov, A.V.: Contact interaction of the faces of a rectangular crack under normally incident tension–compression waves. Int. Appl. Mech. 38(3), 302–307 (2002)
Omidvar, B., Rahimian, M., DorMohammadi, A.A.: Simultaneous analysis of dynamic crack growth and contact of crack faces in single-region boundary element method. Am. Eurasian J. Agric. Environ. Sci. 5(2), 273–283 (2009)
Opanasovych, V.K., Yatsyk, I.M., Sulym, H.T.: Bending of Reissner’s plate containing a through-the-thickness crack by concentrated moments taking into account the width of a contact zone of its faces. J. Math. Sci. 187(5), 620–634 (2012)
Dhondt, G.: Effect of contact between the crack faces on crack propagation. Key Eng. Mater. 577–578, 61–64 (2014)
Kaminsky, A.O., Selivanov, M.F., Chornoivan, YuO: Determination of contact stresses between faces of a crack of normal separation. Rep. Natl. Acad. Sci. Ukr. 5, 36–42 (2016). (in Ukrainian)
Muskhelishvili, N.I.: Some Basic Problems of Mathematical Theory of Elasticity. Noordhoff, Groningen (1953)
Muskhelishvili, N.I.: Singular Integral Equations. Nauka, Moscow (1968). (in Russian)
Bateman, H., Erdelyi, A.: Higher Transcendental Functions, vol. 3. McGraw-Hill, New York (1955)
Fromm, H.: Berechnung des Schlupfes beim Rollen deformierbarer Scheiben. Z. Angew. Math. Mech. 7(1), 27–58 (1927). (in German)
Spence, D.A.: An eigenvalue problem for elastic contact with finite fraction. Proc. Camb. Philos. Soc. 73, 249–268 (1973)
Ostrik, V.I.: Indentation of a punch into an elastic strip with friction and adhesion. Mech. Solids 46(5), 755–765 (2011)
Ostryk, V.I.: Axisymmetric contact of a punch of polynomial profile with an elastic half-space when there is friction and adhesion. J. Appl. Math. Mech. 77(4), 433–444 (2013)
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
Ostrik, V.I. Contact of faces of a rectilinear crack under complex loading and various contact conditions. Acta Mech 230, 3741–3758 (2019). https://doi.org/10.1007/s00707-019-02477-w
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-019-02477-w