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1

Antiplane deformation of a bimaterial with thin interfacial nonlinear elastic inclusion

Sulym H., Piskozub Y., Polanski J.

Acta Mechanica et Automatica

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2018

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Vol. 12, no. 3

190--195

EN

The problem of longitudinal shear of bimaterial with thin nonlinear elastic inclusion at the interface of matrix materials is considered. Solution of the problem is constructed using the boundary value problem of combining analytical functions and jump functions method. The model of the thin inclusion with nonlinear resilient parameters is built. Solution of the problem is reduced to a system of singular integral equations with variable coefficients. The convergent iterative method for solving such a system is offered for various nonlinear strain models, including Ramberg-Osgood law. Numerical calculations are carried out for different values of non-linearity characteristic parameters for the inclusion material. Their parameters are analysed for the tensely-deformed matrix under loading a uniformly distributed shear stresses and for a balanced system of the concentrated forces.

2

Longitudinal shear of a bi-material with frictional sliding contact in the interfacial crack

Sulym H., Pasternak I., Piskozub L., Piskozub Y.

Journal of Theoretical and Applied Mechanics

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2016

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Vol. 54 nr 2

529--539

EN

We construct an analytical solution to the anti-plane problem of an inhomogeneous bi- -material medium with the interfacial crack considering sliding friction. The medium is exposed to an arbitrary normal and shear loading in the longitudinal direction. Using the jump function method, the problem is reduced to a solution to singular integral equations for the jumps of displacements and stresses in the areas with sliding friction. Explicit expressions for displacements, stress intensity factors and energy dissipation are obtained. Critical load values for determination of the onset of slippage are investigated. The effect of friction and loading parameters on the size of the slip zone, stress intensity factors and energy dissipation is numerically analyzed.

3

Antiplane deformation of a bimaterial containing an interfacial crack with the account of friction. [P.] 1, Single loading

Sulym H., Piskozub L., Piskozub Y., Pasternak I.

Acta Mechanica et Automatica

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2015

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Vol. 9, no. 2

115--121

EN

The paper presents the exact analytic solution to the antiplane problem for a non-homogeneous bimaterial medium containing closed interfacial cracks, which faces can move relatively to each other with dry friction. The medium is subjected to the action of normal and arbitrary single loading in a longitudinal direction. Based on the discontinuity function method the problem is reduced to the solution of the system of singular integral-differential equations for stress and displacement discontinuities at the possible slippage zones. Influence of loading parameters and the effects of friction on the sizes of these zones is analyzed. The stress intensity factors, stress and displacement discontinuities, energy dissipation are determined for several characteristic types of external loading.

4

Antiplane deformation of a bimaterial containing an interfacial crack with the account of friction 2. Repeating and cyclic loading

Sulym H., Piskozub L., Piskozub Y., Pasternak I.

Acta Mechanica et Automatica

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2015

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Vol. 9, no. 3

178--184

EN

The paper presents the exact solution of the antiplane problem for an inhomogeneous bimaterial with the interface crack exposed to the normal load and cyclic loading by a concentrated force in the longitudinal direction. Using discontinuity function method the problem is reduced to the solution of singular integral equations for the displacement and stress discontinuities at the domains with sliding friction. The paper provides the analysis of the effect of friction and loading parameters on the size of these zones. Hysteretic behaviour of the stress and displacement discontinuities in these domains is observed.

5

Verification of brittle fracture criteria for bimaterial structures

Mieczkowski G., Molski K.

Acta Mechanica et Automatica

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2014

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Vol. 8, no. 1

44--48

EN

The increasing application of composite materials in the construction of machines causes strong need for modelling and evaluat-ing their strength. There are many well known hypotheses used for homogeneous materials subjected to monotone and cyclic loading conditions, which have been verified experimentally by various authors. These hypotheses should be verified also for composite materials. This paper provides experimental and theoretical results of such verifications for bimaterial structures with interfacial cracks. Three well known fracture hypotheses of: Griffith, McClintock and Novozhilov were chosen. The theoretical critical load values arising from each hy-potheses were compared with the experimental data including uni and multi-axial loading conditions. All tests were carried out with using specially prepared specimens of steel and PMMA.

6

Problemy modelowania rozwoju pęknięć międzyfazowych

Molski K.

Zeszyty Naukowe Politechniki Białostockiej. Mechanika

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2000

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Z. 22

143-159

PL

Praca dotyczy zagadnienia wytrzymałości struktury materiałowej osłabionej szczeliną umiejscowioną wzdłuż granicy dwóch różnych ośrodków sprężystych w złożonym stanie obciążenia. Przedstawiono problemy związane z analitycznym opisem pól naprężeń w okolicy wierzchołkowej, spowodowane obecnością zespolonego wykładnika potęgowego. Omówiono trudności powstające przy próbie obliczania kumulacji uszkodzenia oraz przewidywaniu prędkości i kierunku rozwoju takich pęknięć. Zaproponowano definicje zmodyfikowanych współczynników intensywności naprężeń KI* i KII*, podano wzory opisujące ich funkcje wagowe oraz wyrażenia analityczne na komponenty pola naprężeń wokół wierzchołka szczeliny, których dokładność zweryfikowano numeryczną metodą elementu brzegowego MEB. Zwrócono uwagę na konsekwencje występowania, zasięg oddziaływania i interpretację fizyczną członów oscylacyjnych pojawiających się w analitycznym opisie pól naprężeń. Zaproponowano sposób całkowania funkcji naprężeń w warunkach występowania oscylacji oraz przedstawiono zalety stosowania w tych przypadkach kryterium kumulacji uszkodzenia według Seweryna i Mroza (1995, 1998).

EN

The present paper deals with the assessment of strength and fatigue life of a structure with a crack located between two different elastic materials subjected to multi-axial loading. Some problems of analytical description of stresses around the crack tip and oscillatory singularity due to the complex exponent of the elastic stress field are discussed. New modified stress intensity factors KI* i KII* are proposed and analytical formulae of stress components are given. Theoretical results of the stresses are compared to the numerical ones obtained by means of the boundary element method. Normalised weight functions are also obtained which enable the determination of numerical values of the stress intensity factors for any normal and shear loading distributed on the crack surfaces. Finally some problems related to modelling of damage accumulation process are discussed and the application of calculating procedures based on the non-local Seweryn-Mróz criteria are also proposed.

7

A pair of equal collinear interfacial griffith cracks

Das S., Patra B.

Applied Mechanics and Engineering

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1999

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Vol. 4, no 1

97-112

EN

The plane strain problem of determining stress intensity factors and crack energy for a pair of equal collinear moving Griffith cracks situated at the interface of two bonded dissimilar orthotropic half planes has been considered. The problem is reduced to solving a pair of simultaneous singular integral equations which have finally been solved by using Jacobi polynomials. Expressions for stress intensity factors and crack energy are obtained for some particular cases and the results are presented graphically.