Serkan Dag

A surface crack in a graded medium loaded by a sliding rigid stamp

In this article the coupled problem of crack/contact mechanics in a nonhomogeneous medium is considered. The underlying physical problem to which the results might be applicable is the initiation and the subcritical growth of surface cracks in a graded medium loaded by a sliding rigid stamp in the presence of friction. The dimensions of the graded medium are assumed to be very large in comparison with the local length parameters of the crack/contact region. Thus in formulating the problem the graded medium is assumed to be semi-infinite. The objective of the study is to determine, in addition to contact stresses, the in-plane component of the surface stress and the stress intensity factors at the crack tip. These are the primary load factors controlling the initiation and the subsequent growth of surface cracks in the graded medium. The coupled mixed boundary value problem is solved and the results are presented for various combinations of friction coefficient, material nonhomogeneity constant and crack/contact length parameters.

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.

A Surface Crack in a Graded Medium Under General Loading Conditions

In this study the problem of a surface crack in a semi-infinite elastic graded medium under general loading conditions is considered. It is assumed that first by solving the problem in the absence of a crack it is reduced to a local perturbation problem with arbitrary self-equilibrating crack surface tractions. The local problem is then solved by approximating the normal and shear tractions on the crack surfaces by polynomials and the normalized modes I and II stress intensity factors are given. As an example the results for a graded half-plane loaded by a sliding rigid circular stamp are presented. ©2002 ASME

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.

Mixed-Mode Fracture Analysis of Orthotropic Functionally Graded Material Coatings Using Analytical and Computational Methods

This article presents analytical and computational methods for mixed-mode fracture analysis of an orthotropic functionally graded material (FGM) coating-bond coat-substrate structure. The analytical solution is developed by considering an embedded crack in the orthotropic FGM coating. The embedded crack is assumed to be loaded through arbitrary self-equilibrating mixed-mode tractions that are applied to its surfaces. Governing partial differential equations for each of the layers in the trilayer structure are derived in terms of the effective parameters of plane orthotropic elasticity. The problem is then reduced to a system of two singular integral equations, which is solved numerically to evaluate the mixed-mode crack tip parameters. The computational approach is based on the finite element method and is developed by applying the displacement correlation technique. The use of two separate methods in the analyses allowed direct comparisons of the results obtained for an embedded crack in the orthotropic FGM coating, leading to a highly accurate numerical predictive capability. The finite element based approach is used to generate further numerical results by considering periodic cracking in the orthotropic FGM coating. Parametric analyses presented in this article illustrate the influences of the material nonhomogeneity and orthotropy constants, the bond coat thickness, and the crack periodicity on the mixed-mode stress intensity factors and the energy release rate.

Mixed-Mode Fracture Analysis of Functionally Graded Materials Under Thermal Stresses: A New Approach Using J k -Integral

A new computational method based on the J k -integral is developed in order to calculate crack tip parameters for functionally graded materials (FGMs) that are subjected to mixed-mode thermal loading. By using the constitutive relations of plane thermoelasticity, J k -integral is modified and reduced to a domain independent form that contains area and line integrals. Temperature fields in FGMs and the components of the J k -integral are computed by means of the finite element method. In both thermal and mechanical analyses, finite element models are created utilizing special graded isoparametric elements that possess cubic interpolation. Numerical results are generated by considering an embedded crack under steady-state thermal stresses and periodic interface cracks subjected to thermal shock heating. The J k -integral approach is validated and domain independence is demonstrated by providing comparisons of the mixed-mode stress intensity factors to those calculated using an enriched finite element technique. Presented results illustrate the influences of material property gradation and crack geometry on the modes I and II stress intensity factors, energy release rate and the T-stress.

Manufacturing of Functionally Graded Porous Products by Selective Laser Sintering

Selective laser sintering (SLS) is a rapid prototyping technique which is used to manufacture plastic and metal models. The porosity of the final product obtained by SLS can be controlled by changing the energy density level used during the manufacturing process. The energy density level is itself dependent upon manufacturing parameters such as laser power, hatching distance and scanning speed. Through mechanical characterization techniques, it is possible to quantitatively relate the energy density levels to particular strength values. The present study is directed towards manufacturing functionally graded polyamide products by changing the energy density level in a predetermined manner. The mechanical properties of the functionally graded components are characterized by means of tensile testing. Both homogeneous and functionally graded specimens are produced and tested in order to examine the influence of the energy density level on the mechanical response and on the ultimate tensile and rupture strengths. Selective laser sintering is shown to possess the potential to produce functionally graded porous specimens with controlled variations in physical and mechanical properties.

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.

Three Dimensional Fracture Analysis of FGM Coatings

In this study the three – dimensional surface cracking of a graded coating bonded to a homogeneous substrate is considered. The main objective is to model the subcritical crack growth process in the coated medium under a cyclic mechanical or thermal loading. Because of symmetry, along the crack front conditions of mode I fracture and plane strain deformations are assumed to be satisfied. Thus, at a given location on the crack front the crack propagation rate would be a function of the mode I stress intensity factor. A three – dimensional finite element technique for nonhomogeneous elastic solids is used to solve the problem and the displacement correlation technique is used to calculate the stress intensity factor.

Production of graded porous polyamide structures and polyamide-epoxy composites via selective laser sintering

Selective laser sintering was used for producing uniformly porous and graded porous polyamide structures. The porous structures were infiltrated with epoxy to produce composites. The porous and composite specimens were physically and mechanically characterized. Within the capabilities of the selective laser sintering machine and the materials used, porosities in the range 5–29% could be obtained in a controlled, repeatable manner. The ultimate tensile strength of the produced uniformly porous polyamide structures ranged from 20 MPa (for 29% porosity) to 44 MPa (for 5% porosity). The graded porous structures exhibited continuously changing porosity grades. As the number of grade increments rose, the grade profile fit closely with the design grade profile. The grades need to be constructed at porosities 9% or more for clear grade variation. Five percent porosity remained in all epoxy-polyamide composites after infiltration of the polyamide preforms with epoxy resin. Improvement in strength with epoxy infiltration was observed for preform porosities above 9%. The composite strength varied from 37 MPa to 44 MPa with respect to epoxy resin volume fraction. The maximum strength of the composites was found to be the same as the strength of the sintered polyamide powder (44 MPa).