Showing papers on "Functionally graded material published in 1996"

Crack problems in fgm layers under thermal stresses

Abstract: In this study an unconstrained elastic layer under statically self-equilibrating thermal or residual stresses is considered. The layer is assumed to be a functionally graded material (FGM), meaning that its thermo-mechanical properties are assumed to be continuous functions of the thickness coordinate. The layer contains an embedded or a surface crack perpendicular to its boundaries. Using superposition the problem is reduced to a perturbation problem in which the crack surface tractions are the only external forces. The dimensions, geometry, and loading conditions of the original problem are such that the perturbation problem may be approximated by a plane strain mode I crack problem for an infinite layer. After a general discussion of the thermal stress problem, the crack problem in the nonhomogeneous medium is formulated. With the application to graded coatings and interfacial zones in mind, the thickness variation of the thermo-mechanical properties is assumed to be monotonous. Thus, the functions suc...

Stress intensity relaxation at the tip of an edge crack in a functionally graded material subjected to a thermal shock

Abstract: We analyze thermal stresses and the stress intensity factor in an edge-cracked strip of a functionally graded material (FGM) subjected to sudden cooling at the cracked surface. It is assumed that the shear modulus of the material decreases hyperbolically with the higher value at the surface exposed to the thermal shock and that the thermal conductivity varies exponentially. Volume fractions of the constituents in a ceramic-metal FGM are then determined with the assumed shear modulus gradient using a three-phase model of conventional composites. The differences between the other assumed material properties and those predicted by the three-phase model are delineated and the applicability of the assumed FGM is discussed. It is shown that the maximum tensile thermal stress in the strip without cracks is substantially reduced by the assumed thermal conductivity gradient and that the magnitude of the compressive stress is increased. A strong compressive zone just away from the thermally shocked surface is devel...

Processing-microstructure-property relationships in graded materials

Abstract: The desired macroscopic properties of functionally graded components depend (1) directly on the local composition function P (c) and (2) indirectly, because important microstructural parameters (porosity grain size) that develop during processing are also strong functions of the local composition. These complex relationships are discussed for the case of functionally graded material (FGM) fabrication by powder compaction and sintering. The conclusion is that the real making of high quality graded components may be much more difficult than calculating an optimal composition profile P (x).

Curvature changes during thermal cycling of a compositionally graded NiAl2O3 multi-layered material

Abstract: The elastoplastic deformation characteristics of a plasma-sprayed, tri-layered composite plate subjected to thermal cycling from 20°C up to 800°C were studied experimentally and numerically. The tri-layered solid comprised polycrystalline Ni and Al2O3 outer layers and a 2.2 mm thick compositionally graded NiAl2O3 composite interlayer (FGM) wherein the composition varied approximately linearly along the layer thickness. The experiments involved in situ and ex situ measurements, employing a scanning laser technique, of the changes in the overall curvature of the unconstrained plate arising from the thermal mismatch between the constituent phases. The variations of curvature, accumulated plastic strains and thermal stresses at different locations in the layered solid were also assessed numerically with the aid of available continuum formulations, and the numerical predictions were compared with experiments, wherever appropriate. It is shown that when only small plastic strains exist in the Ni layer or in the Ni-rich end of the FGM layer, known formulations are capable of providing approximate predictions of the cyclic variations in curvature, the onset of plasticity and some features of the initiation of cracking (and its location). We also examine possible sources of error in the experimental measurements of curvature and in the interpretation of thermally induced deformation due to some processing conditions.

Analysis of thermal residual stress in a thick-walled ring of duralcan-base Al-SiC functionally graded material

Abstract: A ring-cutting test and an elastic theory were applied to evaluate the macroscopic residual stress in a thick-walled ring made of Al-SiC functionally graded material (FGM). The FGM ring specimens, with outer diameter 90 mm, radial thickness approximately 8.4 to 10 mm, and width 30 mm, were fabricated by the centrifugal casting method from an ingot of Duralcan F3D.20S of Al-20 vol pct SiC master composite. Because of a difference in centrifugal forces of SiC particles and of molten aluminum alloy, the rings had a graded composition of SiC particles in the radial direction. The volume fractions of SiC particles in each ring specimen varied in the range of 0 to 43 vol pct from the inner to the outer surface of the ring, depending on the applied mold spin speed. A ring diametral compression test was performed to validate an analytical formula based on the curved beam theory that can account for the graded properties of the material. Excellent agreement between the theory and the experiment was found. The residual stress was found to be generated by a cooling of Δt=140 K, which was from half the melting point corresponding stress-free condition to the ambient temperature. The hoop residual stresses in the FGM ring varied in the range of −50 to +35 MPa and from tension at the inner surface to compression at the outer surface because of the graded composition. With an increase in wall thickness and/or composition gradation, the residual stresses were found to increase.

Thermal stress and deformation in functionally graded material shells of revolution under thermal loading due to fluid

Abstract: This paper is concerned with an analytical formulation and a numerical solution of the thermal stress and deformation for axisymmetrical shells of functionally graded material(FGM) subjected to thermal loading due to fluid. The temperature distribution through the thickness is assumed to be a curve of high order, and the temperature field in the shell is determined using the equations of heat conduction and heat transfer. The equations of equilibrium and the relationships between the strains and displacements are derived from the Sanders elastic shell theory. The fundamental equations derived are numerically solved using the finite difference method. As numerical examples, functionally graded cylindrical shells composed of SUS 304 and ZrO 2 subjected to thermal loads due to fluid are analyzed. Numerical computations are carried out for various compositional distribution profiles in FGM. The results show that the present method gives correct temperature distributions and that the temperature distributions, stress distributions and deformations vary significantly depending on these compositional distribution profiles.

Effect of Microstructure on Thermal Shock Cracking of Functionally Graded Thermal Barrier Coatings Studied by Burner Heating Test

Abstract: The thermal shock fracture mechanism of metal/ceramic functionally graded thermal barrier coatings was studied by bumer heating tesL Discussions were made on the basis of fracture mechanics with special reference to the effect of microstructure on crack extension behavior. Two types of FGM coatings, having the same graded structure with different microstructures, were fabricated by slurry dipping and HIP sintering process: PSZ/IN 100 FGMs having finely mixed microstructure and PSZ/Inco 718 FGMs having rather coarse microstructure. The fracture toughness of each composition was determine by conventional vickers indentation method on uniform nonFGM specimens. It has been shown that the fracture toughness depends strongly on the microstructure following from the mixing conditions and the particle size of the raw material powders. In PSZ/IN 100 FGMs, the fracture toughness increased with increased in the metal phase content, while in PSZ/Inco718 FGMs it was fairly lower than that of PSZ/IN 100 FGMs, owing to roughly dispersed metal phase in the PSZ matrix. The results of bumer heating test revealed that the crack formation was always observed on the ceramic surface during cooling. By comparison between the fracture toughness and mode I stress intensity factor, the initiated vertical cracks in PSZ/ Inco718 FGMs were considered to extend into the interface of FGM/substrate without deflection. This crack extension behavior was confirmed by observing the cross-section of the tested sapmles. Although vertical cracks in PSZ/IN 100 FGMs tend to be arrested in the FGM coating, with the extension of the cracks into the graded layer, they deflected toward the direction parallel to the surface. The depth of the parallel cracks beneath the surface may correspond to a location of mode II stress intensity being equal to zero.

Applicability of Fracture Mechanics in Strength Evaluation of Functionally Graded Materials

Abstract: Elastic and elastic-plastic analyses of a crack in a particulate-dispersed functionally graded material (FGM) have been carried out using a newly developed finite element method based on Tohgo-Chou-Weng's(1994, 1996) constitutive relation for particulate-reinforced composites. By setting the mechanical properties of particles and a matrix and their content graded in the thickness direction, FGMs and non-FGM are designed. From comparison of the numerical results for the FGMs and non-FGM, the influence of the gradient of the mechanical properties on a stress intensity factor and the crack tip field is discussed. The following conclusions are derived: (1) The stress intensity factor of a crack under constant boundary conditions is considerably affected by the gradient of the mechanical properties. (2) The elastic and plastic stress singular fields around a crack tip in a FGM are basically described by the fracture mechanics parameters(K 1 and J 1 ) as well as in a non-FGM, using the mechanical properties of the material at the crack tip. (3) The size of the singular field decreases with an increase in the gradient of the mechanical properties. This means that the applicability of fracture mechanics, such as the small-scale-yielding condition and the validity of the J-integral, is affected by the gradient.

Elevated temperature erosion of range of composite layers of Ni-Cr based functionally graded material

Abstract: Functionally graded materials can be used in aggressive environments at elevated temperature because they provide the possibility of minimising wastage of materials. Gradation of the volume fraction of hard particles through the layers means that thermal cycling effects are less severe than for many conventional metal–substrate systems. Because such materials may provide resistance to wear and corrosion (by using a corrosion resistant matrix), it is thought that they may have applications to environments at elevated temperatures, in which materials selection involves a compromise between corrosion resistance and high yield strength. The object of the present study was to investigate the erosion resistance of the various layers of a candidate functionally graded material which consisted of WC particles in a Ni–Cr matrix. The performances of the various composite layers were considered separately in order to establish the variation of erosion rates through the graded structure. The effects of temper...

Thermal Stress and Deformation in Functionally Graded Material Shells of Revolution under Thermal Loading due to Fluid.

Abstract: This paper is concerned with an analytical formulation and a numerical solution of the thermal stress and deformation for axisymmetrical shells of functionally graded material (FGM) subjected to thermal loading due to fluid. The temperature distribution through the thickness is assumed to be a curve of high order, and the temperature field in the shell is determined using the equations of heat conduction and heat transfer. The equations of equilibrium and the relations between the strains and displacements are derived from the Sanders elastic shell theory. The fundamental equations derived are numerically solved using the finite difference method. As numerical examples, functionally graded cylindrical shells composed of SUS304 and ZrO2 subjected to thermal loads due to fluid are analyzed. Numerical computations are carried out for various compositional distribution profiles in FGM. The results show that the present method gives correct temperature distributions and that the temperature distributions, stress distributions and deformations vary significantly depending on these compositional distribution profiles.

Design and Development of Functionally Graded Material by Pulse Discharge Resistance Consolidation with Temperature Gradient Control

Abstract: A novel method of pulse electric discharge resistance consolidation with temperature gradient control has been developed for the design and fabrication of functionally graded materials (FGMs). The powder processing route employed makes it possible to select combinations of constituents with greatly different densification rates, controlling densification up to full density to produce a nanoscaled structure. A die with a specially designed outer shape makes it possible to achieve desired temperature profiles along a graded composition. Using a stepped graphite die with a temperature difference of more than 700 K within a width of 7 mm, a five layered material graded from TiAl intermetallic to partially stabilised zirconia (PSZ) can be fabricated. This structure shows full densification throughout its cross-section without any discontinuity and an increasing hardness from 650HV at the TiAl nanocrystalline layer to 1560HV at the PSZ layer, varying according to a mixture rule. PM/0716

Dynamic Thermal Stresses in a Composite Hollow Circular Cylinder with an Interlayer of Functionally Graded Material.

Abstract: This paper is concerned with the dynamic treatment of thermal stresses in a ceramic-metal composite hollow circular cylinder with an interlayer of functionally graded material (FGM) subjected to uniform impulsive electromagnetic radiation. Heating is assumed to be a step function in time, and to diminish exponentially with distance from the inner surface of the cylinder, assuming negligible heat conduction. In treating problems, the nature of the stress-wave buildup in the absorption cylinder is studied for the case of a temperature-dependent solid, i. e., material properties vary with temperature. The nonhomogeneous hollow circular cylinder is approximated as a laminated hollow circular cylinder consisting of different, homogeneous and isotropic cylindrical layers which are perfectly bonded to each neighboring layer. The numerical procedure employs the characteristic method based on the integration of the governing equations along the characteristics. Numerical examples are presented for several cases, which show the significance of the temperature-dependent properties of the material and the effects of the thickness and composition distribution of the FGM interlayer on the magnitude of the dynamic thermal stresses.

Mechanism of thermal shock crack extension in metal/ceramic sintered functionally graded materials

Abstract: The thermal shock fracture mechanism of metal/ceramic functionally graded materials was studied by burner heating test. Dependence of thermal shock crack initiation and propagation on controlled compositional gradients was virtually shown and discussions were made on the basis of fracture mechanics with special reference to the effect of compositional profile on crack extension behavior. Three types of FGMs, having the same thickness of graded layer with different compositional profiles, were fabricated by powder metallurgical process. The fracture toughness of each composition was determined by newly devised repeated vickers indentation method directly on FGM specimens. The fracture toughness increased with, increase in the metal phase content, owing to toughening mechanisms of thermal-strain-misfit and crack deflection. The FGMs were joined on cooling substrates and used for burner heating test. The crack formation was always observed on the ceramic surface during cooling due to large residual tensile stresses. By comparison between the fracture toughness and mode I stress intensity factor, vertical cracks in convex-profile FGMs were deflected toward the direction parallel to the surface. The depth of the parallel cracks beneath the surface may correspond well to a location of mode II stress intensity being equal to zero. On the other hand, initiated vertical cracks in concave-profile FGMs were considered to arrest without deflection.

Multi-Phase Functionally Graded Materials for Thermal Barrier Systems

Abstract: Jet engine and gas turbine hot section components can be protected from the 1,350--1,650 C combustion gases by thermal barrier coatings (TBCs). Metallic candidates for functionally graded material (FGM) coatings have been evaluated for potential use in bonding zirconia to a single crystal superalloy. Properties for four materials were studied for the low-expansion layer adjacent to the ceramic. Ingots were produced for these materials, and oxidation, expansion and modulus were determined. A finite element model was used to study effects of varying the FGM layers. Elastic modulus dominated stress generation, and a 20--25% reduction in thermal stress generated within the zirconia layer may be possible.