Engineering Transactions, 27, 4, pp. 559-574, 1979

Stress Concentrations in Non-Homogeneous Elastic Layer Weakened by Cracks

M. Matczyński
Institute of Fundamental Technological Research, Warszawa

The paper presents the statical problem of stress concentrations around the tips of two semi-infinite cracks situated within an infinite, non-homogenous elastic layer. The conditions of antiplane state of strain are assumed to be satisfied. The outer boundaries of the layer are rigidly clamped,
while the crack surfaces are loaded by presciribed forces.
The application of the complex exponential Fourier transform reduces the problem of determining the stress intensity factors at the crack tips to the solution of a corresponding system of Wiener-Hopf equations. By assuming the cracks to be located symmetrically with respect to the interface between the two elastic materials, the system of equations splite un inta taio canarata Wiener-Hopf equations; their exact solutions are derived. Stress intensity factors at the two crack tips are determined and several particular cases are discussed. The solution is illustrated by an example in which the displacements are prescribed along the boundaries of the layer, the crack surfaces being free from loading.

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E. C. TITCHMARSH, Theory of Fourier integrals, Oxford Univ. Press, 1939.

B. NOBLE, Methods based on the Wiener-Hopf technique, Pergamon Press, London-New York-Paris-Los Angeles, 1958.

B. VAN DER POL, H. BREMMER, Operational calculus based on the two-sided Laplace integral, Cambridge 1950.

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