Plastic Exfoliation of a Thin Stiff Inclusion Parallel to the Boundary of Half Space in the Case of its Unilateral Conta
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PLASTIC EXFOLIATION OF A THIN STIFF INCLUSION PARALLEL TO THE BOUNDARY OF HALF SPACE IN THE CASE OF ITS UNILATERAL CONTACT WITH THE MEDIUM V. A. Kryven’,1,2 V. B. Valiashek,1 and M. I. Yavors’ka1
UDC 539.375
We obtain a numerical-analytic solution of the antiplane problem of stress-strain state of the elastoplastic half space with a thin rigid tunnel inclusion parallel to the boundary of the half space. It is assumed that, prior to loading, the inclusion is in unilateral mechanical contact with the medium. The specific features of plastic exfoliation of the inclusion are analyzed. Some partial cases are investigated. Keywords: unilaterally exfoliated inclusion, interface plastic strips, antiplane deformation, analytic solution.
At present, the stress-strain state of bodies with thin inclusions operating in perfect or imperfect contact with the medium is fairly comprehensively investigated within the framework of the linear elasticity theory [1, 2]. As for the more interesting and practically more important problems of plastic exfoliation of inclusions interacting with each other or with the boundary of the body, they require the models of elastoplastic deformation that are more complicated, less accessible for the analysis, and much less studied [3, 4]. These problems are especially important for the theory of composites because the strength of the body with interacting stresses concentrators can be higher or lower than the strength of the body with a similar single concentrator. Therefore, the influence of interaction of the stress concentrators is an important problem of mechanics and, in particular, of the theory of strength of reinforced materials. At the same time, the plastic exfoliation of the inclusions located near the boundary of the body remains insufficiently studied [5–7]. Statement of the Problem We now determine the stress-strain state of a perfectly elastoplastic half space x > 0 , – ∞ < y, z < ∞ , containing a stiff thin inclusion x = a , – l ≤ y ≤ l , parallel to its boundary under a quasistatically increasing shear load τ yz = τ ∞ , τ xz = 0 applied at infinity. We consider the case of unilateral contact of the inclusion with the
medium: prior to the application of the load, the inclusion was in perfect contact with the medium along the face x = a + 0 , – l ≤ y ≤ l ; at the same, it was not in contact with the medium along the face x = a − 0 , – l ≤ y ≤ l ( l is a half height of the inclusion and a is the distance from the inclusion to the boundary of the body) (Fig. 1). Assume that the material of the body is perfectly elastoplastic with the yield stress in shear equal to k and that the plastic strains are localized on the inclusion–medium boundary in the interface strips x = a + 0 , l − d ≤ y ≤ l ( d is the length of interface strips that depends on the applied load). 1 2
Pulyui Ternopil’ National Technical University, Ternopil, Ukraine. Corresponding author; e-mail: [email protected].
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 54, No. 2, pp. 64–69, March–April, 2018. Origi
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