Analytical solution of a crack problem in a radially graded FGM

Çetin, Suat
The objective of this study is to determine stress intensity factors (SIFs) for a crack in a radially graded FGM layer on a substrate. Functionally graded coating with an edge crack perpendicular to the interface and a homogeneous substrate are bonded together. In order to make the problem analytically tractable, geometry is modeled as an FGM strip attached to a homogeneous layer. Introducing the elastic foundation underneath the homogeneous layer, an FGM coating on a thin walled cylinder can be modeled. At first, governing equations are obtained from stress displacement and equilibrium equations. Then using an assumed form of solution in terms of Fourier Transforms for displacements and applying the boundary conditions, a singular integral equation is obtained for the mode-I problem. Solving this singular integral equation numerically, stress intensity factors are obtained as functions of crack length, strip thicknesses and inhomogeneity parameter.


Three dimensional fracture analysis of FGM coatings
İnan, Özgür; Dağ, Serkan; Department of Mechanical Engineering (2004)
The main objective of this study is to model the three dimensional surface cracking problem in Functionally Graded Material (FGM) coatings bonded to homogeneous substrates. The FGM coating is assumed to be a (ZrO2) ا (Ti-6Al-4V) layer. Homogeneous ceramic, metal ا rich, ceramic ا rich and linear variation material compositions are considered in the analyses. The surface crack is assumed to have a semi ا circular crack front profile. The surface crack problem in the FGM coating ا substrate system is examined...
Three dimensional mixed mode fracture analysis of functionally graded materials
Köşker, Sadık; Dağ, Serkan; Department of Mechanical Engineering (2007)
The main objective of this study is to model and analyze a three dimensional inclined semi-elliptic surface crack in a Functionally Graded Material (FGM) coating bonded to a homogeneous substrate with a bond coat. The parametric analyses on FGMs are based upon zirconia-yttria (ZrO2-8wt%-Y2O3) FGM coating bonded to a substrate made of a nickel-based superalloy. It is assumed that there is a nickel-chromiumaluminumzirconium (NiCrAlY) bond coat between the FGM coating and substrate. Metal-rich, linear variatio...
Fatigue crack growth analysis models for funcionally graded materials
Sabuncuoğlu, Barış; Dağ, Serkan; Department of Mechanical Engineering (2006)
The objective of this study is to develop crack growth analysis methods for functionally graded materials under mode I cyclic loading by using finite element technique. The study starts with the analysis of test specimens which are given in ASTM standard E399. The material properties of specimens are assumed to be changing along the thickness direction according to a presumed variation function used for the modeling of functionally graded materials. The results of the study reveal the influence of different...
Exact solution of rotating FGM shaft problem in the elastoplastic state of stress
Akis, Tolga; Eraslan, Ahmet Nedim (Springer Science and Business Media LLC, 2007-10-01)
Plane strain analytical solutions to estimate purely elastic, partially plastic and fully plastic deformation behavior of rotating functionally graded (FGM) hollow shafts are presented. The modulus of elasticity of the shaft material is assumed to vary nonlinearly in the radial direction. Tresca's yield criterion and its associated flow rule are used to formulate three different plastic regions for an ideal plastic material. By considerina different material compositions as well as a wide range of bore radi...
Jk-integral formulation and implementation for thermally loaded orthotropic functionally graded materials
Arman, Eyüp Erhan; Dağ, Serkan; Department of Mechanical Engineering (2008)
The main aim of this study is to utilize a Jk-integral based computational method in order to calculate crack tip parameters for orthotropic functionally graded materials (FGMs). The crack is subjected to mixed mode thermal loading. Mixed mode thermal fracture analysis requires the calculation of mode-I and mode-II stress intensity factors (KI ,KII ). In addition to stress intensity factors, energy release rate and T-stress are calculated by means of Jk-integral. Jk-integral is defined as a line integral ov...
Citation Formats
S. Çetin, “Analytical solution of a crack problem in a radially graded FGM,” M.S. - Master of Science, Middle East Technical University, 2007.