ANALYSIS OF CRITICAL STATES OF INHOMOGENEOUS JOINTS WITH AN INDIRECT CONTACT BOUNDARY

V. L. Dilman, A. E. Kashcheeva

Abstract


Mathematical models of critical states of discrete heterogeneous joints under conditions of plane deformation are considered. The boundary between sections of different strengths is assumed to be a two-link polyline or contains such a fragment. The purpose of the work is to study the features of the characteristic fields (sliding lines) of such models and to find the stress state at the inner boundary. A characteristic variant of such a field is given; possible locations of stress rupture lines (lines of violation of smoothness of characteristics) and zones of plastic flow in a durable part of the joint are indicated. It has been established how the value of the coefficient of heterogeneity affects the appearance of a plastic section in a durable part of the joint.

Keywords


discretely heterogeneous joints; critical states; stress state; conjugation problem; quasi-linear hyperbolic equations; characteristics

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References


Prandtl L. Examples of the Application of Hencky’s Theorem to the Equilibrium of Plastic Bodies. Theory of Plasticity, Izdatel’stvo Inostr. Literatury, Moscow, 1948, pp. 102–113.

Kachanov L.M. Fundamentals of the Theory of Plasticity. Moscow, Nauka, 1974. (in Russian)

Bakshi O.A., Shakhmatov M.V., Yerofeyev V.V. [On the Effect of the Degree of Mechanical Heterogeneity on the Static Strength of Welded Joints]. Svarochnoe proizvodstvo, 1983, no. 4, pp. 1–4. (in Russian)

Bakshi O.A. [On Taking into Account the Factor of Mechanical Heterogeneity of Welded Joints during Tensile Testing]. Svarochnoe proizvodstvo, 1985, no. 7, pp. 32–34. (in Russian)

Dilman V.L., Ostsemin A.A. [About the Stress-Strain State during Stretching of a Plastic Layer with Two Axes of Symmetry]. Izv. RAN. MTT, 2001, no. 6, pp. 115–124. (in Russian)

Kim Y.-J., Schwalbe K.-H. Numerical Analysis of Strength Mismatch Effect on Local Stresses for Ideally Plastic Material. Engineering Fracture Mechanics, 2004, vol. 71, pp. 1177–1199.

Schnabl S., Saje M., Turk G., Planninc I. Analytic Solution of Two-layer Beam Taking into Account Interlayer Slip and Shear Deformation. Journal of Structural Engineering, 2007, vol. 133, issue 6, pp. 886–894.

Kozak D., Gubeljak N., Konjatic S.J. Yield Load Solutions of Heterogeneous Welded Joints. International Journal of Pressure Vessels and Piping, 2009, vol. 86, pp. 807–812.

Shakhmatov M.V., Yerofeyev V.V. Engineering Calculations of Welded Shell Structures. Chelyabinsk, CHSTU, 1995. (in Russian)

Dilman V.L. Mathematical Models of Stress States of Heterogeneous Thin-walled Cylindrical Shells. Chelyabinsk, Publishing center SUSU, 2007. (in Russian)

Dilman V.L., Eroshkina T.V. Mathematical Modeling of Critical States of Soft Layers in Heterogeneous Compounds. Chelyabinsk, Publishing Center SUSU, 2011. (in Russian)

Dilman V.L., Kashcheeva A.E. Mathematical Modeling of Critical States of Discrete Inhomogeneous Connections with a Boundary in the Form of a Two-link Broken Line. Chelyabinsk Physical and Mathematical Journal, 2025, vol. 10, no. 1, pp. 126–134. DOI: 10.47475/2500-0101-2025-10-1-126-134 (in Russian)

Dilman V.L., Nosacheva A.I. Numerical Analysis of Stresses on an Inclined Contact Surface under Tension of a Discretely Inhomogeneous Body. Bulletin of the South Ural State University. Series Mathematical Modeling and Programming, 2012, no. 40 (299), pp. 164–168. (in Russian)

Kachanov L.M. Fundamentals of the Theory of Plasticity. Moscow, Nauka, 1974. (in Russian)

Dilman V.L. Stress State and Strength of an Inhomogeneous Plastic Strip with a Defect in a Stronger Part. Mekhanika tverdogo tela, 2010, no. 2, pp. 89–102. (in Russian)


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