Bora Yildirim

EDGE CRACK PROBLEMS IN HOMOGENOUS AND FUNCTIONALLY GRADED MATERIAL THERMAL BARRIER COATINGS UNDER UNIFORM THERMAL LOADING

In this study the axisymmetric crack problem for thermal barrier coatings under a uniform temperature change is considered. Modes I and II stress intensity factors and the strain energy release rate are calculated for various sizes and locations of the crack. The main variables in the problem are the material inhomogeneity parameter of the functionally graded material coating, the size and the location of the crack, and the relative dimensions of the specimen. The effect of the temperature dependence of the material properties on the stress intensity factors and the strain energy release rate is also investigated. The finite element method is used to solve the problem. The material property grading is accounted for by developing special inhomogeneous elements and the stress intensity factors are calculated by using enriched crack tip elements.

An Equivalent Domain Integral Method for Fracture Analysis of Functionally Graded Materials Under Thermal Stresses

This paper presents the formulation and finite element implementation of the equivalent domain integral (EDI) for fracture analysis of functionally graded materials (FGMs) under thermal stresses. By carrying out the neccesary modifications resulting from material nonhomogeneity and thermal strains, the generalized J-integral is converted to an equivalent domain integral around the crack tip for both plane stress and plane strain problems of thermoelasticity. The developed procedure is integrated in a fracture analysis code FRAC2D using graded and cubic finite elements in order to calculate the stress intensity factor under mode I steady-state and transient thermal loading conditions. Temperature distribution profiles in FGMs are calculated using the finite elements based heat transfer analysis code HEAT2D. Comparisons of the computed thermal stress intensity factors to the results available in the literature and to those calculated by an enriched finite element method show that developed EDI approach produces highly accurate results and possesses the required domain independence. Detailed parametric analyses are performed in order to examine the influences of material property variation profiles and geometrical parameters on the mode I stress intensity factors. It is shown that variation profiles of the thermomechanical parameters such as Poissons ratio, thermal expansion coefficient and thermal conductivity significantly influence both the amplitude of the stress intensity factors and the transient crack closure behavior.

Computation of Thermal Fracture Parameters for Inclined Cracks in Functionally Graded Materials Using J k -Integral

This article describes the formulation and implementation of the J k -integral for the analysis of inclined cracks located in functionally graded materials (FGMs) that are subjected to thermal stresses. The generalized definition of the J k -integral over a vanishingly small curve at the tip of an inclined crack is converted to a domain independent form that consists of area and line integrals defined over finite domains. A numerical procedure based on the finite element method is then developed, which allows the evaluation of the components of the J k -integral, the modes I and II stress intensity factors and the T-stresses at the crack tips. The developed procedure is validated and the domain independence is demonstrated by providing comparisons to the results obtained by means of the displacement correlation technique (DCT). Detailed parametric analyses are conducted by considering an inclined crack in an FGM layer that is subjected to steady-state thermal stresses. Numerical results show the influences of the thermal conductivity and thermal expansion coefficient variation profiles and the crack inclination angle on the mixed-mode fracture parameters.

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.

Subsurface stresses in graded coatings subjected to frictional contact with heat generation

ABSTRACT In this article, the thermoelastic contact problem involving a functionally graded coating and a homogenous substrate is considered. Determination of subsurface stresses is highly critical in the design of mechanical assemblages due to fatigue and fracture failures resulting from contact loading. In such contact problems, cracking generally initiates at the locations of high subsurface stresses. The present study proposes a finite element methodology for the computation of subsurface stresses in functionally graded coatings subjected to frictional contact with heat generation. The method developed is based on iterations continued until convergence is observed in the contact zone heat flux values. Presented results illustrate the influences of various geometric and material parameters upon the subsurface stresses.

Computational Methods for Inclined Cracks in Orthotropic Functionally Graded Materials Under Thermal Stresses

This article sets forth two different computational methods developed to evaluate fracture parameters for inclined cracks lying in orthotropic functionally graded materials, that are under the effect of thermal stresses. The first method is based on the J k -integral, whereas the second entails the use of the J 1-integral and the asymptotic displacement fields. The procedures introduced are implemented by means of the finite element method and integrated into a general purpose finite element analysis software. Numerical results are generated for an inclined edge crack in an orthotropic functionally graded layer subjected to steady-state thermal stresses. Comparisons of the mixed-mode stress intensity factors computed by the use of the proposed methods to those calculated by the displacement correlation technique point out that both approaches lead to numerical results of high accuracy. Further results are provided in order to illustrate the influences of inclination angle, material property gradation, and crack length upon the thermal fracture parameters.

Hygrothermal Fracture Analysis of Orthotropic Materials Using J k -Integral

A new computational method based on the J k -integral is put forward for the purpose of conducting fracture analysis of orthotropic materials subjected to hygrothermal stresses. By utilizing the constitutive relations of plane orthotropic hygrothermoelasticity, an alternative expression for the J k -integral is derived to replace the general limit definition. A numerical procedure is developed and integrated into a finite element analysis software to implement the proposed form of the J k -integral. Temperature and specific moisture concentration fields, which are required in fracture calculations, are also computed through finite element analysis. Numerical results are generated by considering an embedded crack in a polymer matrix fibrous composite laminate, that is subjected to steady-state hygrothermal loading. Comparisons of the mixed-mode stress intensity factors computed by the J k -integral based method to those evaluated via the displacement correlation technique demonstrate that, the proposed form of the J k -integral is domain independent and leads to numerical results of high accuracy. Presented parametric analyses illustrate the influences of the fiber volume fraction and the crack location on the modes I and II stress intensity factors, the energy release rate, and the T-stress.

Three Dimensional Analysis of Periodic Cracking in FGM Coatings under Thermal Stresses

A three dimensional finite element method is used to examine periodic surface cracking problem in a functionally graded coating subjected to transient thermal loads. The ceramic/metal FGM coating is assumed to contain periodic semi‐elliptical cracks and to be perfectly bonded to a homogeneous substrate. The composite structure is subjected to transient residual/thermal stresses. Temperature and displacement fields are computed using a three dimensional finite element approach. Finite element models are created by considering a unit cell in the periodic structure. Mode I stress intensity factors are evaluated by means of the displacement correlation technique (DCT). Presented results illustrate the influence of crack periodicity on the transient behavior of the stress intensity factors.

Design of a vibration-free platform: Stabilization of a beam mounted on bicycle model of a car

Many high-precision measurement and control devices must be mounted on vibration-free platforms. Accuracy of those devices’ output are adversely affected by the base excitation motion, so motion of these platforms must be isolated from the excitation source. In this paper, a flexible platform, which is mounted on a car, is considered as a base on which many such measurement and control devices can be attached. To this end, mixed finite element and lumped parameter model of the platform and vehicle are used to derive the model of such a system; this results in a discrete-model with finite degree of freedom. This lumped parameter model of the system is then controlled by a linear quadratic regulator, which minimizes the amplitude of vibration at finite number of points on the platform. The mathematical model of this system was simulated on a computer and it has been shown that it is possible to minimize the vibration of this flexible platform.

Fatigue Crack Growth Analysis Models for Functionally Graded Materials

The objective of this study is to develop crack growth analysis methods for functionally graded materials (FGMs) subjected to mode I cyclic loading. The study presents finite elements based computational procedures for both two and three dimensional problems to examine fatigue crack growth in functionally graded materials. Developed methods allow the computation of crack length and generation of crack front profile for a graded medium subjected to fluctuating stresses. The results presented for an elliptical crack embedded in a functionally graded medium, illustrate the competing effects of ellipse aspect ratio and material property gradation on the fatigue crack growth behavior.