Thermal stress problem for an FGM strip containing periodic cracks

Köse, Ayşe
In this study the plane linear elastic problem of a functionally graded layer which contains periodic cracks is considered. The main objective of this study is to determine the thermal stress intensity factors for edge cracks. In order to find an analytic solution, Young’s modulus and thermal conductivity are assumed to be varying exponentially across the thickness, whereas Poisson ratio and thermal diffusivity are taken as constant. First, one dimensional transient and steady state conduction problems are solved (heat flux being across the thickness) to determine the temperature distribution and the thermal stresses in a crack free layer. Then, the thermal stress distributions at the locations of the cracks are applied as crack surface tractions in the elasticity problem to find the stress intensity factors. By defining an appropriate auxiliary variable, elasticity problem is reduced to a singular integral equation, which is solved numerically. The influence of such parameters as the grading, crack length and crack period on the stress intensity factors is investigated


Dynamic frictional contact problems involving functionally graded materials
Balcı, Mehmet Nurullah; Dağ, Serkan; Department of Mechanical Engineering (2018)
The main aim of this study is to analyze the dynamic frictional contact problem of layered and functionally graded materials. Investigating contact problems including dynamic effects has a significant importance in mechanical engineering applications since many contact problems arise between moving structures. In moving contact problems, speed of the punch may not be so small to ignore dynamic effects. Hence, contact problem should be examined using elastodynamics theory. In this study, both frictional movi...
Nonlinear Vibration Analysis of Uniform and Functionally Graded Beams with Spectral Chebyshev Technique and Harmonic Balance Method
Dedekoy, Demir; Ciğeroğlu, Ender; Bediz, Bekir (2023-01-01)
In this paper, nonlinear forced vibrations of uniform and functionally graded Euler-Bernoulli beams with large deformation are studied. Spectral and temporal boundary value problems of beam vibrations do not always have closed-form analytical solutions. As a result, many approximate methods are used to obtain the solution by discretizing the spatial problem. Spectral Chebyshev technique (SCT) utilizes the Chebyshev polynomials for spatial discretization and applies Galerkin's method to obtain boundary condi...
Plane strain analytical solutions for a functionally graded elastic-plastic pressurized tube
Eraslan, Ahmet Nedim (Elsevier BV, 2006-09-01)
Plane strain analytical solutions to functionally graded elastic and elastic-plastic pressurized tube problems are obtained in the framework of small deformation theory. The modulus of elasticity and the uniaxial yield limit of the tube material are assumed to vary radially according to two parametric parabolic forms. The analytical plastic model is based on Tresca's yield criterion, its associated flow rule and ideally plastic material behaviour. Elastic, partially plastic and fully plastic stress states a...
Mixed-mode fracture analysis of orthotropic FGM coatings under mechanical and thermal loads
İlhan, Küçük Ayşe; Dağ, Serkan; Department of Mechanical Engineering (2007)
In this study, it is aimed to investigate the mixed-mode fracture behavior of orthotropic functionally graded material (FGM) coatings bonded to a homogeneous substrate through a homogeneous bond-coat. Analytical and computational methods are used to solve the embedded cracking problems under mechanical or thermal loading conditions. It is assumed that the material property gradation of the FGM coating is in the thickness direction and cracks are parallel to the boundaries. The principal axes of orthotropy a...
Periodic crack problem for a functionally graded half-plane an analytic solution
YILDIRIM, BORA; Kutlu, Ozge; Kadıoğlu, Fevzi Suat (Elsevier BV, 2011-10-15)
The plane elasticity problem of a functionally graded semi-infinite plane, containing periodic imbedded or edge cracks perpendicular to the free surface is considered. Cracks are subjected to mode one mechanical or thermal loadings, which are represented by crack surface tractions. Young's modulus, conduction coefficient, coefficient of thermal expansion are taken as exponentially varying functions of the depth coordinate where as Poisson ratio and thermal diffusivity are assumed to be constant. Fourier int...
Citation Formats
A. Köse, “Thermal stress problem for an FGM strip containing periodic cracks,” M.S. - Master of Science, Middle East Technical University, 2013.