Suat Kadıoğlu

Crack problem for a functionally graded layer on an elastic foundation

In this paper internal and edge crack problems for an FGM layer attached to an elastic foundation are considered. This model can be used to simulate circumferential crack problem for a thin walled cylinder. It is assumed that the mechanical properties of the layer are varying in thickness direction. Crack is assumed to be perpendicular to the surfaces. For this geometry stress intensity factors are calculated for a number of different crack surface tractions. By using the calculated stress intensity factors and the principle of superposition it is possible to obtain solutions for physically meaningful cases such as fixed grip constant strain loading, membrane loading and bending.

Circumferential crack problem for an FGM cylinder under thermal stresses

The main objective of this study is to determine the stress intensity factors associated with a circumferential crack in a thin-walled cylinder subjected to quasi-static thermal loading. The cylinder is assumed to be a functionally graded material. In order to make the problem analytically tractable, the thin-walled cylinder is modeled as a layer on an elastic foundation whose thermal and mechanical properties are exponential functions of the thickness coordinate. Hence a plane strain crack problem is obtained. First temperature and thermal stress distributions for a crack-free layer are determined. Then using these solutions, the crack problem is reduced to a local perturbation problem where the only nonzero loads are the crack surface tractions. Both internal and edge cracks are considered. Stress intensity factors are computed as functions of crack geometry, material properties, and time.

Delamination of Compressively Stressed Orthotropic Functionally Graded Material Coatings Under Thermal Loading

The objective of this study is to investigate a particular type of crack problem in a layered structure consisting of a substrate, a bond coat, and an orthotropic functionally graded material coating. There is an internal crack in the orthotropic coating layer. It is parallel to the coating bond-coat interface and perpendicular to the material gradation of the coating. The position of the crack inside the coating is kept as a variable. Hence, the case of interface crack is also addressed. The top and bottom surfaces of the three layer structure are subjected to different temperatures and a two-dimensional steady-state temperature distribution develops. The case of compressively stressed coating is considered. Under this condition, buckling can occur, the crack can propagate, and the coating is prone to delamination. To predict the onset of delamination, one needs to know the fracture mechanics parameters, namely, Mode I and Mode II stress intensity factors and energy release rates. Hence, temperature distributions and fracture parameters are calculated by using finite element method and displacement correlation technique. Results of this study present the effects of boundary conditions, geometric parameters (crack length and crack position), and the type of gradation on fracture parameters.

The free-end interface crack problem for bonded orthotropic layers

Abstract The plane elasticity problem of two bonded orthotropic layers containing cracks perpendicular to and along the interface is considered. The cracks are extended to intersect the boundaries and each other in such a way that a crack configuration suitable to study the edge debonding problem associated with bonded dissimilar materials is obtained. The problem is reduced to the solution of a system of singular integral equations with Cauchy type singularities. Numerical results for stress intensity factors and energy release rates are presented for various loading conditions and for isotropic as well as orthotropic material pairs. These results indicate that elementary strength of material type calculations for energy release rates provide a very good approximation to the actual elasticity solution even for relatively short cracks under some practical loading conditions such as thermal loading, as long as the thicknesses of the layers are not very different.

Free Edge Problem for Bonded Orthotropic Elastic Layers

In this paper the plane elasticity problem of two bonded orthotropic infinite strips containing collinear cracks perpendicular to the interface is considered. By extending the cracks to the boundaries and to the interfacethe problem of a crack terminating at an interface and the free edge problem are addressed. An asymptotic analysis of the kernels of the related integral equations reveals that the stresses may display a singular behaviour at the intersection of the edge and the interface. Determination of these singularities and the stress intensity factors associated with them for various material pairs and thickness ratios is the main purpose of this study. For a crack terminating at or crossing the interface it is shown that the singularity depends on two material and three bimaterial parameters. A number of numerical examples are presented for some material pairs and different crack configurations.

T-shaped crack problem for bonded orthotropic layers

The plane elasticity problem of two perfectly bonded orthotropic layers containing cracks perpendicular to and along the interface is considered. Cracks are extended to intersect the boundaries and each other in such a way that a crack configuration suitable to study the T-shaped crack problem is obtained. The problem is reduced to the solution of a system of singular integral equations with Cauchy type singularities. Numerical results for stress intensity factors and energy release rates are presented for various loading conditions and for isotropic as well as orthotropic material pairs. These results indicate that elementary strength of material type calculations for energy release rates provide a good approximation to the actual elasticity solution even for relatively short cracks, as long as the layer thicknesses are not very different.

Shock failure analysis of metallic structures by using strain energy density method

Failure of metallic structures operating under shock loading is a common occurrence in engineering applications. It is difficult to estimate the response of complicated systems analytically, due to structure’s dynamic characteristics and varying loadings. Therefore, experimental, numerical, or a combination of both methods is used for evaluations. In this study, test pieces made of two different materials are subjected to shock loads stemming from firing of a Gatling gun. Strain measurements are made, and finite element analysis of the test piece is performed. As a result of this study, strain energy density theory is applied to predict the shock failure of metallic structures.

Analytical Solution of a Crack Problem in a Radially Graded FGM

The objective of this study is to determine stress intensity factors (SIFs) for a crack in a functionally graded layer bonded to a homogeneous substrate. Functionally graded coating contains an edge crack perpendicular to the interface. It is assumed that plane strain conditions prevail and the crack is subjected to mode I loading. By introducing an elastic foundation underneath the homogeneous layer, the plane strain problem under consideration is used as an approximate model for an FGM coating with radial grading on a thin walled cylinder. The plane elasticity problem is reduced to the solution of a singular integral equation. Constant strain loading is considered. Stress intensity factors are obtained as a function of crack length, strip thicknesses, foundation modulus, and inhomogeneity parameter.

Indentation of a cantilever beam or plate

In this paper the general plane problem for a semi-infinite strip fixed at its short end, containing a crack perpendicular to its voundaries is considered. The strip is under the effect of a stamp. By extending the crack to the surfaces, one can reduce the problem to that of c cantilever beam or plate. Integral transform technique is used to provide an exact formulation of this problem, in terms of a system of four singular integral equations one of them being second kind. Stress singularities at the corners of the fixed-end, at the crack tips and at the end points of the contact region undermeath the stamp are obtained from the singular integral equations which are then solved numerically.