Thermal shock analysis for a functionally graded plate with a surface crack

Summary The fracture behavior of a functionally graded material (FGM) plate subjected to a thermal shock is studied. A surface crack is considered. The thermomechanical properties of the FGM plate are assumed to vary along the thickness direction. By using a perturbation method, the transient temperature field is solved. Then the transient thermal stresses and the corresponding thermal stress intensity factor (TSIF) are obtained. The transient thermal stresses and TSIF in an FGM ceramic/metal (ZrO₂/Ti-6Al-4V) plate are shown in figures. Dedicated to Professor Franz Ziegler on the occasion of his 70th birthday     

TiC／Ni3Al系梯度材料的残余应力与工作应力计算及结构优化

测定了TiC／Ni3Al复合材料的物性参数．对TiC／Ni3Al系梯度材料在制备过程中产生的残余应力以及在隔热使用时产生的工作应力，进行了热弹性假设下的有限元模拟在综合考虑热应力最小、应力强度比值最小以及纯TiC侧应力状态的基础上，完成了FGM的热应力缓和设计与结构优化结果表明，按线性组成分布设计是体系的最佳设计．     

New approach to MoSi2/SiC intermetallic-ceramic composite with B4C

The effects of SiC and B₄C additives in the MoSi₂ matrix on the microstructures and mechanical properties at room temperature were investigated. Their coefficients of thermal expansion (CTE) were also evaluated up to 1200°C by a thermal mechanical analysis (TMA). The experimental results show that the Mo₂B₅ reinforced phase was formed in situ in the hot-pressed MoSi₂/SiC/B₄C composites. Both the Mo₂B₅ phase and the SiC phase significantly improved the mechanical behavior of MoSi₂. Besides, the SiC with a high content up to 40 vol% could be added into the MoSi₂ composite with the B₄C additive. As a result, a dense and homogenous MoSi₂/SiC/B₄C composite was obtained, which possessed a relatively high bending strength and fracture toughness. Meanwhile, the CTE of the MoSi₂/SiC/B₄C composites linearly decreased with the increasing SiC content, which dropped to 21% at 1200°C in comparison with the pure MoSi₂ when adding 40 vol% SiC. This MoSi₂/SiC/B₄C composite system is very important for developing new applications at elevated temperature, particularly for high-temperature coating applications.     

Crack Spacing Effect on the Brittle Fracture Characteristics of Semi-infinite Functionally Graded Materials with Periodic Edge Cracks

The effect of crack spacing on the brittle fracture characteristics of a semi-infinite functionally graded material (FGM) with periodic edge cracks is discussed. The incompatible eigenstrain induced in the material due to mismatch in the coefficients of thermal expansion is considered in the analysis. The nonhomogeneity of the material is simulated by an equivalent eigenstrain, whereby the problem is reduced to that of a cracked homogeneous material with incompatible and equivalent eigenstrains. A method is then formulated to calculate the stress intensity factor of periodic edge cracks in such a semi-infinite homogeneous medium and applied to calculate apparent fracture toughness of a semi-infinite FGM from its prescribed composition profile. Inverse calculation is also carried out to compute composition profile from prescribed apparent fracture toughness of the semi-infinite FGM. Numerical calculations are carried out for semi-infinite TiC/Al₂O₃ FGM and the results are shown in the figures.     

Synthesis and wear of Al based,free standing functionally gradient materials: effects of different reinforcements

Abstract

In the present study, three aluminium based functionally gradient materials (FGMs), reinforced with different ceramic particulates (silicon carbide, aluminium oxide, and titanium carbide), were successfully synthesised using the innovative gradient slurry disintegration and deposition (GSDD) technique. The results for Al/SiC and Al/Al₂O₃ revealed, in common, an increase in the weight percentage of reinforcement along the direction of deposition, to result in an increase in porosity and microhardness. However, for Al/TiC, the reverse trend was observed, with porosity and microhardness decreasing with increasing distance from the base of the ingot. The porosity levels for Al/TiC were also found to be significantly lower than those ofthe other two FGMs. Thermomechanical analysis of the FGMs showed thatthe average coefficient of thermal expansion of the high reinforcement end was reduced, as compared to the high aluminium end. Sliding wear test results also revealed that the high reinforcement end was more wear resistant than the high aluminium end, except for the case of Al/Al₂O₃. An attempt is made to interrelate the effects of different types of particulates, with microstructural development, microhardness and wear rate results obtained in the present study.     

Stress intensity factors of two diametrically opposed edge cracks in a thick-walled functionally graded material cylinder

A method is developed to evaluate stress intensity factors for two diametrically-opposed edge cracks emanating from the inner surface of a thick-walled functionally graded material (FGM) cylinder. The crack and the cylinder inner surfaces are subjected to an internal pressure. The thermal eigenstrain induced in the cylinder material due to nonuniform coefficient of thermal expansion after cooling from the sintering temperature is taken into account. First, the FGM cylinder is homogenized by simulating its nonhomogeneous material properties by an equivalent eigenstrain, whereby the problem is reduced to the solution of a cracked homogenized cylinder with an induced thermal and an equivalent eigenstrains and under an internal pressure. Then, representing the cracks by a continuous distribution of edge dislocations and using their complex potential functions, generalized formulations are developed to calculate stress intensity factors for the cracks in the homogenized cylinder. The stress intensity factors calculated for the cracks in homogenized cylinder represents the stress intensity factors for the same cracks in the FGM cylinder. The application of the formulations are demonstrated for a thick-walled TiC/Al₂O₃ FGM cylinder and some numerical results of stress intensity factors are presented for different profiles of material distribution in the FGM cylinder.     

Room and high temperature tensile behaviour of a P/M 2124/MoSi2 composite at different heat treatment conditions

In the present work, a 2124/15 vol%MoSi₂ composite was obtained by powder metallurgy. Its microstructure and mechanical properties were investigated at room and at high temperature (up to 200°C) in conditions T351, T4 and after heat treatments at 495°C for up to 100 h. Up to 150°C, tensile properties of 2124/MoSi₂ in T351 resulted similar to those of a ceramic reinforced 2124/SiC composite. Yield stress of the 2124/MoSi₂ material, after heating at 495°C for up to 100 h, resulted higher than that of the monolith 2124 alloy heated for the same periods. No diffusion reaction phases were formed surrounding the MoSi₂ reinforcing particles during such long exposures to high temperature. Only at 100 h, large plate-like precipitates that contain Al, Cu, Mg and Si appeared. The high thermal stability of this 2124/MoSi₂ composite and its good mechanical properties at room and at elevated temperature makes MoSi₂ intermetallic a competitor of ceramic reinforcements.     

Study of indentation induced cracks in MoSi2-reaction bonded SiC ceramics

MoSi₂-RBSC composite samples were prepared by infiltration of Si-2 at.% Mo melt into a preform of commercial SiC and petroleum coke powder. The infiltrated sample had a density > 92% of the theoretical density (TD) and microstructurally contained SiC, MoSi₂, residual Si and unreacted C. The material was tested for indentation fracture toughness at room temperature with a Vicker’s indenter andK _IC was found to be 4.42 MPa√m which is around 39% higher than the conventional RBSC material. Enhancement in indentation fracture toughness is explained in terms of bowing of propagating cracks through MoSi₂/SiC interface which is under high thermal stress arising from the thermal expansion mismatch between MoSi₂ and SiC.     

Inverse problem of material distribution for desired fracture characteristics in a thick-walled functionally graded material cylinder with two diametrically-opposed edge cracks

This study concerns the inverse problem of evaluating the optimum material distribution for desired fracture characteristics in a thick-walled functionally graded material (FGM) cylinder containing two diametrically-opposed edge cracks emanating from the inner surface of the cylinder. The thermal eigenstrain developed in the cylinder material due to nonuniform coefficient of thermal expansion as a result of cooling from sintering temperature is taken into account. Based on a generalized method of evaluating stress intensity factors developed in a previous study, an inverse method is developed to optimize material distribution intending to realize prescribed apparent fracture toughness in the FGM cylinder. To present some numerical results, a TiC/Al₂O₃ FGM cylinder is considered and the inverse problems are solved to evaluate material distributions for two examples of prescribed apparent fracture toughness. The effect of cylinder wall thickness on the material distribution and comparison of material distributions corresponding to a single and two cracks are also discussed. The numerical results reveal that the apparent fracture toughness of FGM cylinders can be controlled by choosing the material distributions properly.     

Fracture Mechanics Analysis Model for Functionally Graded Materials with Arbitrarily Distributed Properties

Functionally Graded Materials (FGMs) have been developed as super-resistant materials for propulsion systems and airframe of space-planes in order to decrease thermal stresses and to increase the effect of protection from heat. It has been experimentally observed that surface cracking in FGMs is the most common failure mode of a metal-ceramic FGM when it is subjected to a thermal shock. Therefore, it is very important to consider the thermally induced fracture behaviors of FGMs. In this paper, a functionally graded material strip containing an embedded or a surface crack perpendicular to its boundaries is considered. The graded region is treated as a large number of single layers, with each layer being homogeneous material. The problem is reduced to an integral equation and is solved numerically. Unlike most of the existing researches, which considered only certain assumed material distributions, the method developed in this paper can be used to investigate functionally graded materials with arbitrarily varied material properties.     

Influence of the particle size and phase type of zirconia on the fabrication and residual stress of zirconia/stainless-steel 304 functionally gradient material

Tetragonal zirconia polycrystal (TZP)/stainless steel 304 (SUS304)- and ZT [50 vol % monoclinic zirconia polycrystal (MZP) + 50 vol % TZP]/SUS304-functionally gradient material (FGM) were fabricated by pressureless sintering, and the sintering properties and residual stresses of this proposed FGM were compared with directly jointed material. The defects in the sintered specimens, such as warping, frustum formation, delamination, and cracking, which originated from the different shrinkage and sintering behavior of ceramic and metal, could be controlled by the adjustments in terms of the particle size and phase type of zirconia. The residual stresses induced on the ceramic and metal regions of FGM were characterized by the X-ray diffraction method, which were relaxed as the thickness and number of compositional gradient layers were increased. The residual stresses in TZP/SUS304-FGM show irregular patterns resulting from sintering defects and thermal expansion mismatch. In ZT/SUS304-FGM, compressive stress is induced on the ceramic regions by the volume expansion of MZP that resulted from the t m ZrO₂ phase transformation on cooling. Also, compressive stress is induced on the metal regions by the constraint of warping and frustum formation that must be created to the metal direction caused by the difference of the coefficient of thermal expansions. As a consequence, it has been verified that the residual stresses generated on FGM are dominantly influenced by the thickness and number of compositional gradient layers, and the sintering defects and residual stresses can be controlled by the decrease of the difference of the shrinkage and sintering behavior of each component.     

Application of poly(methylsilane) and Nicalon® polycarbosilane precursors as binders for metal/ceramic powders in preparation of functionally graded materials

For the first time, ceramic precursors were applied in the powder metallurgy (P/M) preparation of Functionally Graded Materials (FGM). Two types of FGMs were prepared: Al/SiC for possible aerospace applications and Cu/SiC for dynamic seal applications. There are two main advantages of using ceramic precursors for P/M preparation of FGMs (1) avoidance of the commercially used debinding step and (2) shrinkage control of the individual layers of the composite. This revised version was published online in November 2006 with corrections to the Cover Date.     

Nonlinear thermal bending response of FGM plates due to heat conduction

Nonlinear thermal bending analysis is presented for a simply supported, shear deformable functionally graded plate without or with piezoelectric actuators subjected to the combined action of thermal and electrical loads. Heat conduction and temperature-dependent material properties are both taken into account. The temperature field considered is assumed to be a uniform distribution over the plate surface and varied in the thickness direction and the electric field considered only has non-zero-valued component E_Z. The material properties of functionally graded materials (FGMs) are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and the material properties of both FGM and piezoelectric layers are assumed to be temperature-dependent. The governing equations of an FGM plate are based on a higher order shear deformation plate theory that includes thermo-piezoelectric effects. A two step perturbation technique is employed to determine the thermal load–deflection and thermal load–bending moment curves. The numerical illustrations concern nonlinear bending response of FGM plates without or with surface bonded piezoelectric actuators due to heat conduction and under different sets of electric loading conditions. The results reveal that for the case of heat conduction the nonlinear thermal bending responses are quite different to those of FGM plates subjected to transverse mechanical loads, and the temperature-dependency of FGMs could not be neglected in the thermal bending analysis.     

Inverse problems of material distributions for prescribed apparent fracture toughness in FGM coatings around a circular hole in infinite elastic media

This study is concerned with the inverse problem of calculating material distributions intending to realize prescribed apparent fracture toughness in functionally graded material (FGM) coatings around a circular hole in infinite elastic media. The incompatible eigenstrain induced in the FGM coatings after cooling from the sintering temperature, due to mismatch in the coefficients of thermal expansion, is taken into consideration. An approximation method of determining stress intensity factors is introduced for a crack in the FGM coatings in which the FGM coatings are homogenized simulating the nonhomogeneous material properties by a distribution of equivalent eigenstrain. A radial edge crack emanating from the circular hole in the homogenized coatings is considered for the case of a uniform pressure applied to the surfaces of the hole and the crack. The stress intensity factors determined for the crack in the homogenized coatings represent the approximate values of the stress intensity factors for the same crack in the FGM coatings, and are used in the inverse problem of calculating material distributions in the FGM coatings intending to realize prescribed apparent fracture toughness in the coatings. Numerical results are obtained for a TiC/Al₂O₃ FGM coating, which reveal that the apparent fracture toughness in FGM coatings around a circular hole in infinite elastic media can be controlled within possible limits by choosing an appropriate material distribution profile in the coatings.     

Effect of different reinforcements on composite-strengthening in aluminium

In the development of metal-matrix composites, reinforcements of aluminium and its alloys with ceramic materials has been pursued with keen interest for quite sometime now. However, a systematic comparison of the effect of different reinforcements in powder-processed aluminium and its alloys is not freely available in the published literature. This study examines the influence of SiC, TiC, TiB₂ and B₄C on the modulus and strength of pure aluminium. B₄C appears slightly superior as a reinforcement when comparing the effect of SiC, TiC, B₄C and TiB₂ on specific modulus and specific strength values of composites. However, TiC appears to be a more effective reinforcement, yielding the best modulus and strength values among those considered in this study. The differences in thermal expansion characteristics between aluminium and the reinforcements do not seem to explain this observation. The other advantage of TiC is that it is economically a more viable candidate as compared to B₄C and TiB₂ for reinforcing aluminium alloys. It is suggested that the superior effect of TiC as a reinforcement is probably related to the high integrity of the bond at the Al-TiC interface.     

Time-resolved penetration into pre-damaged hot-pressed silicon carbide

We have conducted a series of experiments to examine projectile penetration of cylindrical hot-pressed silicon carbide (SiC) ceramic targets that are pre-damaged to varying degrees under controlled laboratory conditions prior to ballistic testing. SiC was thermally shocked to introduce non-contiguous cracks. Another set of targets was thermally shocked and then additional damage was induced by load–unload cycling in an MTS machine while the ceramic specimen was confined in a 7075-T6 aluminum sleeve. Finally, targets were made by compacting SiC powder into a 7075-T6 aluminum sleeve. For each of these target types, long gold rod penetration was measured as a function of impact velocity v_p over the approximate range of 1–3 km/s, with most data between 1.5 and 3 km/s. Penetration as a function of time was measured using multiple independently timed flash X-rays. Results are compared with previous results for non-damaged (intact) SiC targets. Key results from these experiments include the following: (1) penetration is nominally steady state for v_p>1.5 km/s; (2) for all target types, the penetration velocity u is a linear function of v_p (except for the lowest impact velocities); and (3) it is found that u_intact<u_pre-damaged<u_{in-situ comminuted}<u_powder<u_hydrodynamic.     

Microstructure and thermal shock resistance of Al2O3 fiber/ZrO2 and SiC fiber/ZrO2 composites fabricated by hot pressing

Al₂O₃ chopped fiber/ZrO₂ and SiC continuous fiber/ZrO₂ composites were fabricated by hot pressing at 1550°C and 15 MPa in vacuum. The mechanical properties of thermally shocked composites were measured at room temperature by four-point bending. The addition of Al₂O₃ fibers into ZrO₂ matrix degraded the fracture strength, but improved significantly the thermal shock resistance. In addition, the mechanical properties of SiC fiber/ZrO₂ composites were much lower than those of monolithic ZrO₂ because of the presence of microcracks on the surface. The SiC fiber/ZrO₂ composites showed an excellent thermal shock resistance.     

Effect of FGM coating thickness on apparent fracture toughness of a thick-walled cylinder

This study describes the effect of FGM coating thickness on apparent fracture toughness (AFT) of a thick-walled cylinder containing two diametrically-opposed edge cracks emanating from the inner surface of the cylinder. The incompatible eigenstrain developed in the cylinder due to nonuniform coefficient of thermal expansion because of cooling from sintering temperature is taken into account. Based on a generalized method of evaluating stress intensity factor (SIF) addressed in a previous study, an approach is developed to calculate AFT. Some numerical results of AFT are presented for a TiC/Al₂O₃ FGM coating at the inner surface of an Al₂O₃ thick-walled cylinder.     

Thermal conductivity investigation of zirconia co-doped with yttria and niobia EB-PVD TBCs

A technique used to improve the life cycle and/or the working temperature of the turbine blades uses ceramic coatings over metallic material applied by electron beam-physical vapor deposition (EB-PVD). The most usual material for this application is yttria doped zirconia. Addition of niobia, as a co-dopant in the Y₂O₃–ZrO₂ system, can reduce thermal conductivity. The purpose of this work is to evaluate the influence of the addition of niobia on the microstructure and thermal properties of the ceramic coatings. This new formulation will, in the future, be able to become an alternative to the composition currently used by the aerospace field in EB-PVD thermal barrier coatings (TBC). A significant reduction of the thermal conductivity, measured by laser flash technique, in the zirconia ceramic coatings co-doped with yttria and niobia when compared with zirconia–yttria coatings was observed.