Andrzej Kaczyński

On the three-dimensional interface crack problems in periodic two-layered composites

Within the framework of the linear thermoelasticity with microlocal parameters the solutions of some three-dimensional interface crack problems in a two-layered periodic space are obtained. Effective results have been achieved through the use of similarity in governing equations of the homogenized model for the laminated body and transversely isotropic elastic solid. Some specific examples concerning interface crack problems have been considered and discussed from the point of view of fracture theory.

Three-dimensional thermoelastic problems of interface cracks in periodic two-layered composites

Abstract This paper outlines the potential function method for solving three-dimensional interface crack problems of a two-layered periodic space, treated within the framework of linear stationary thennoelasticity with microlocal parameters. By constructing the appropriate harmonic functions, the resulting boundary-value problems regarding an interface crack are reduced to corresponding ordinary problems dealing with mechanical loading in homogeneous isothermal elasticity. This result—known as an analogy between the thermal crack problems and their mechanical counterparts—may be exploited to yield closed-form solutions following directly from that obtained in the isotropic case. In connection with the theory of fracture mechanics, the thermal stress singularities as well as the effects of the geometrical and mechanical parameters of the composite structure on them are discussed.

Thermal stresses in a laminate composite with a row of interface cracks

Abstract In this paper two-dimensional stationary problems of periodic two-layered thermoelastic space weakened by a finite or infinite periodic system of interface thermally insulated cracks under a uniform heat flux are investigated. The analysis is performed on the basis of a homogenized model with microlocal parameters presented in Refs [11–14]. We have derived a complex potential representation suitable for solving the interface crack problems and exact solutions of those are obtained. The stress singularities at the crack tips are discussed.

Stress intensity factors for an interface crack in a periodic two-layered composite under the action of heat sources

The state of thermal stresses for a periodic two-layered elastic space weakened by an interface thermally insulated Griffith crack and loaded by concentrated line heat sources is investigated. The analysis is performed within the framework of the homogenized model with microlocal parameters. The stress intensity factors at the crack tips are determined. Two examples of the application of the results obtained are detailed.

On the stress distribution in a periodic reinforced elastic composite with partially unbonded fiber

Abstract This paper deals with the antiplane static problem of a periodic reinforced elastic composite with a partially unbonded fiber. The composite is composed of an elastic matrix and unidirectional periodically distributed elastic fibers with identical rectangular cross-sections. The exact solution of the problem is obtained with the framework of the homogenized model with microlocal parameters.

On 3D Anticrack Problem of Thermoelectroelasticity

Abstract A solution is presented for the static problem of thermoelectroelasticity involving a transversely isotropic space with a heat-insulated rigid sheet-like inclusion (anticrack) located in the isotropy plane. It is assumed that far from this defect the body is in a uniform heat flow perpendicular to the inclusion plane. Besides, considered is the case where the electric potential on the anticrack faces is equal to zero. Accurate results are obtained by constructing suitable potential solutions and reducing the thermoelectromechanical problem to its thermomechanical counterpart. The governing boundary integral equation for a planar anticrack of arbitrary shape is obtained in terms of a normal stress discontinuity. As an illustration, a closed-form solution is given and discussed for a circular rigid inclusion.

AN ANTICRACK IN A TRANSVERSELY ISOTROPIC SPACE

Abstract An absolutely rigid inclusion (anticrack) embedded in an unbound transversely isotropic elastic solid with the axis of elastic symmetry normal to the inclusion plane is considered. A general method of solving the anticrack problem is presented. Effective results have been achieved by constructing the appropriate harmonic potentials. With the use of the Fourier transform technique, the governing system of two-dimensional equations of Newtonian potential type for the stress jump functions on the opposite surfaces of the inclusion is obtained. For illustration, a complete solution to the problem of a penny-shaped anticrack under perpendicular tension at infinity is given and discussed from the point of view of material failure.