Showing papers in "Composites Part B-engineering in 1997"

FGM activities in Japan

Abstract: The concept of functionally graded materials (FGMs) was proposed in 1984 by materials scientists in the Sendai area as a means of preparing thermal barrier materials. Continuous changes in the composition, microstructure, porosity, etc. of these materials results in gradients in such properties as mechanical strength and thermal conductivity. In 1987, a national project was initiated entitled ‘Research on the Basic Technology for the Development of Functionally Gradient Materials for Relaxation of Thermal Stress’. In 1992 when the project was finished, samples of 300 mm square shell and 50 mm diameter hemispherical bowls for SiC-C FGM nose cones were prepared. The concept of FGMs is of interest not only in the practical design of super refractory materials, but also in the development of various functional materials. In 1993, the second national project was initiated for the research and development of FGMs as functional materials; ‘Research on Energy Conversion Materials with Functionally Gradient Structure’. This program aims to apply functionally graded structure technology to the improvement of energy conversion efficiency. The project will continue until the fiscal year 1997.

Fiber texture and mechanical graded structure of bamboo

Abstract: Among plants, bamboo has an unique structure which resembles that of a unidirectional, fiber-reinforced composite with many nodes along its length. Furthermore, bamboo's growth rate is very fast, producing an adult tree in only one year. This paper demonstrates that bamboo has a functionally graded and hierarchical structure. Bamboo's diameter, thickness and internodal length have a macroscopically graded structure while the fiber distribution exhibits a microscopically graded architecture, which lead to smart properties of bamboo. The reinforcing fibers are oriented along the bamboo's culm (trunk), whereas in the nodes the fibers become entangled in a complicated manner to produce nodes with isotropic properties that provide additional reinforcement for the culm.

Fabrication and properties of functionally graded dental implant

Abstract: Dental implants with functionally graded structures composed of titanium (Ti) and ceramic hydroxyapatite (HAP) were fabricated to satisfy both mechanical and biocompatible property requirements. Specimens containing up to Ti/50%HAP functionally graded material (FGM) with the dimensions 6Φ × 15 mm were successfully fabricated by CIP and sintering process. Miniature (2Φ × 10 mm) specimens of Ti, Ti/20%HAP FGM and Ti/30%HAP FGM implants were then made and inserted into femora of ten week-old Wistar strain rats to evaluate their biocompatibility. After 1, 2 and 4 weeks of implantation, the rats were killed and tissue blocks containing the implant material were embedded in resin. Observation of bone formation around the implant was performed by both the conventional method by optical microscopy using specimens stained with toluidine blue and the EPMA mapping method using unstained specimens. The observed area of new bone formation was in good agreement for both the light microscopy and EPMA elemental mapping method. Pure Ti and Ti/HAP FGM specimens showed no inflammation. When pure Ti and Ti/HAP FGM specimens were compared, Ti/HAP FGM showed better biocompatibility.

Finite element simulations of textile composite forming including the biaxial fabric behaviour

Abstract: A finite element simulation of fibre fabric shaping process is proposed. The behaviour of fabrics is experimentally studied from biaxial tensile tests on cross shaped specimens. These experiments permit to investigate the influence on the fabric behaviour of the undulation variations of the weaving and of the interactions between warp and weft yarns. A constitutive model including these aspects is proposed, validated and identified from the biaxial tests. Finite elements made of woven yarns are built in the field of non-linear kinematics. The deformation energy is calculated as the sum of the energy of each elementary cell for which the biaxial behaviour previously identified is considered. A drawing simulation with square punch and die is presented. It allows to distinguish the geometries of the tools which are possible or not for the shaping process. The influence of the undulation variations are studied in a second example.

Functionally graded materials synthesis via low vacuum directed vapor deposition

Abstract: The spatially distributed microstructures needed to implement many functionally graded material (FGM) designs are difficult to realize affordably with today's materials synthesis/processing technologies. To address this need, a new directed vapor deposition (DVD) technique has been developed and explored as a potential FGM synthesis tool. The technique exploits supersonic helium jets in combination with electron beam/resistive evaporation under low vacuum (10−3-10 Torr) conditions to atomistically spray deposit a wide variety of monolithic and composite materials. Two of the most important processing parameters (the carrier gas velocity and the deposition chamber pressure) that control deposition are identified, and their effect upon deposition efficiency for flat and fiber substrates is explored systematically. Under certain conditions, the DVD approach is found to deposit vapor onto fibers with a significantly higher efficiency than traditional high vacuum line-of-sight vapor deposition techniques. It can even deposit material onto surfaces that are not in the line-of-sight of the source. A computational fluid dynamics model has been used to interpret the experimental observations and to identify the role of carrier gas dynamics in controlling deposition efficiency and spatial distribution.

The static and dynamic axial crumbling of thin-walled fibreglass composite square tubes

Abstract: In the present paper we report on the behaviour and crashworthiness characteristics of square composite tubes subjected to static and dynamic axial compression exerted by a hydraulic press and a drop-hammer, respectively. The effect of specimen geometry, i.e. of thickness and axial length, and of the loading rate on the energy absorbing capability are studied in detail. Attention is directed towards the mechanics of the axial crumbling process from macroscopic and microscopic point of view for facilitating engineering design calculations of the amount of energy dissipated and for a somewhat more complete aspect on the actual fracture mechanism during the failure of the composite material tested. A theoretical analysis of the collapse mechanism of the components tested under axial compression is proposed, leading to a good approximation of the energy absorbed during crushing.

Functionally graded ceramic/ceramic and metal/ceramic composites by electrophoretic deposition

Abstract: Constant current electrophoretic deposition (EPD) has been used to synthesise Al2O3/YSZ,Al2O3/MoSi2, A12O3/Ni and YSZ/Ni functionally graded materials (FGM). EPD is a cheap and simple technique to fabricate complicated ceramic shapes. By this technique it is possible to synthesize step FGMs as well as continuous-profile FGMs. The profile can be controlled precisely by controlling the deposition current density, second component flow rate, suspension concentration, etc. The microstructures of the FGMs produced were characterized by optical and electron microcopy and micro-indentation was used to track the Vicker's hardness and fracture toughness variation across the composition profiles.

Dynamic pulse buckling of rectangular composite plates

Abstract: The elastic dynamic buckling of geometrically imperfect rectangular composite plates under a longitudinal compressive pulse is investigated. Specifically, the effects of fiber orientations of angle-ply laminated panels are studied. Geometric nonlinearities due to large deflections, as well as wave propagation effects due to inplane inertia terms, are included in the analysis. The applied load is either a force or displacement pulse. A numerical solution, through an explicit finite-difference integration scheme, is then developed. Appropriate dynamic buckling criteria are defined for both loading types, and buckling loads are determined for various loading durations and material lay-up configurations. It is found that the dynamic buckling loads are not always higher than the static ones; in some cases there is a range of loading frequencies near the fundamental frequency of the plate where dynamic buckling occurs for lower loads. Buckling under a displacement pulse occurs at a load higher than that for a force pulse of similar duration. Also, the critical axial displacement is not sensitive to the material configuration. Comparisons with results obtained through a finite-element analysis support the conclusions of the present analysis.

Development and characterization of a HDPE-sand-natural fiber composite

Abstract: A composite material consisting of HDPE, sand and short henequen fibers has been developed and characterized. It is shown that it is possible to incorporate as high as 50% w/w filler contents to the thermoplastic resin. A central composite design (Box-Hunter) was utilized to optimize the mechanical properties of the composite materials. The independent variables under study were: (i) sand content; (ii) henequen content and (iii) processing temperature. The selected response variables were the tensile and flexural properties of the composite. The tensile strength of the HDPE-sand composite does not seem to be affected by the processing temperature, for any filler content, but the tensile modulus shows similar behavior for filler contents greater than 15% w/w. The flexural strength shows a maximum at filler content of 30% w/w while the flexural modulus increase linearly. The flexural properties are not affected appreciably by the processing temperature. For the HDPE henequen composite, the processing temperature does seem to adversely effect the tensile strength but not the tensile modulus. The flexural properties are slightly increased by the processing temperature. It is shown that fiber-matrix adhesion does play an important role in the final properties of the composite. The HDPE-sand-henequen composite shows a more complicated behavior. An increase in filler content decreases the tensile strength. Similar behavior was found with an increase in the processing temperature. The processing temperature seems to have a more pronounced effect on the tensile modulus. At low temperatures the modulus behavior is governed by the sand content, while at higher temperatures, such behavior is governed by the fiber content. The flexural properties are also affected by the processing temperature. At low temperatures and sand contents below 30% w/w, the flexural strength increases with fiber content and at higher sand contents an opposite behavior is observed. At higher processing temperatures the behavior is the same as for lower temperatures, but the flexural properties are slightly decreased. It is also shown that adhesion between fiber and matrix plays an important role on the final mechanical properties.

Free vibration analysis of laminated composite cylindrical shells by DQM

Abstract: In this paper, free vibrations of laminated composite cylindrical shells are investigated by the global method of generalized differential quadrature (GDQ). The GDQ method was developed to improve the differential quadrature (DQ) method for the computation of weighting coefficients. The differential equations of motion are formulated using Love's first approximation classical shell theory. The spatial derivatives in both the governing equations and the boundary conditions are discretized by the GDQ method. The GDQ method is examined by comparing its results with those available in the literature. It is demonstrated that, with the use of the GDQ method, the natural frequencies can be easily and accurately obtained by using a considerably small number of grid points.

Dynamic analysis and damping of composite structures embedded with viscoelastic layers

Abstract: In recent years, it has been found that composites co-cured with viscoelastic materials can enhance the damping capacity of a composite structural system with little reduction in stiffness and strength. Because of the anisotropy of the constraining layers, the damping mechanism of co-cured composites is quite different from that of conventional structures with metal constraining layers. This paper presents an analysis of the dynamic properties of multiple damping layer, laminated composite beams with anisotropic stiffness layers, by means of the finite element-based modal strain energy method. ANSYS 4.4A finite element software has been used for this study. The variation of resonance frequencies and modal loss factors of various beam samples with temperature is studied. Some of these results are compared with the closed-form theoretical results of an earlier published work. For obtaining optimium dynamic properties, the effects of different parameters, such as layer orientation angle and compliant layering, are studied. Also, the effect of using a combination of different damping materials in the system for obtaining stable damping properties over a wide temperature range is studied.

A higher order theory for modeling composite laminates with induced strain actuators

Abstract: A refined higher order laminate theory is developed to analyze smart materials, surface bonded or embedded, in composite laminates. The analysis uses a refined displacement field which accounts for transverse shear stresses through the thickness. All boundary conditions are satisfied at the free surfaces. Non-linearities are introduced through the strain dependent piezoelectric coupling coefficients and the assumed strain distribution through the thickness. The analysis is implemented using the finite element method. The procedure is computationally efficient and allows for a detailed investigation of both the local and global effects due to the presence of actuators. The finite element model is shown to agree well with published experimental results. Numerical examples are presented for composite laminates of various thicknesses and the results are compared with those obtained using classical laminate theory. The refined theory captures important higher order effects which are not modeled by the classical laminate theory, resulting in significant deviations.

Mechanical and thermo-mechanical failure mechanism analysis of fiber/filler reinforced phenolic matrix composites

Abstract: Three groups of phenolic matrix composites were investigated in this study: (1) powder (glass, ceramic and carbon black) filled phenolic resin, (2) graphite fiber reinforced phenolic resin, and (3) graphite fiber/glass powder reinforced phenolic resin. In the first part of this study, the three-point bending test method was used to measure the mechanical properties of these composites. The graphite fiber/10 wt% glass powder filled phenolic composite exhibited higher flexural strength and flexural modulus than the unfilled graphite fiber reinforced phenolic resin composite. Samples were examined using an optical microscope and scanning electron microscope (SEM). The amount of wedge-shaped voids could be greatly reduced by introducing the glass powder to the phenolic resin. The filler acted to delay crack propagation by deflecting the crack such that it propagated along the interface of the carbon fiber and the matrix. In the second part of this study, the effects of temperature (up to 500°C) on the mechanical properties of graphite fiber reinforced phenolic (G/P) and graphite fiber/glass particle reinforced (G/g-P) composites were investigated. The results show that G/g-P composites exhibited higher flexural strength and flexural modulus than the G/P composites at exposure temperatures up to 360°C. The thermal stresses induced due to heating in the composite were analyzed by the Thick-Cylinder Model (TCM) and Selsing's model. At temperatures above 300°C, tensile thermal stresses tended to promote the formation of micro-cracks at the fiber/matrix interface, which degraded the properties of G/P composites. Debonding between the glass particle and the matrix occurred at a temperature above 360°C, which greatly degraded the properties of G/ g-P composites.

Some direction-dependent properties of matrix-inclusion type composites with given reinforcement orientation distributions

Abstract: A Mori-Tanaka mean-field approach for predicting the overall thermoelastic properties of multi-phase composites with given orientation distributions of the inclusion phases is used to study the influence of the inclusion orientation distribution on the effective material properties. The aim of this study is primarily to understand the effects of the inclusion orientations in short-fiber-reinforced composites and to identify the basic mechanisms of interaction between the phases which govern the overall thermoelastic behavior. Perfectly aligned discontinuous fibers, various orientation distributions as well as two-dimensional and three-dimensional random orientations of the inclusions are studied. The overall Young's moduli, shear moduli and coefficients of thermal expansion, as well as the onset of yielding of the matrix phase under thermal and mechanical loading conditions, are calculated. The results are evaluated both in terms of the orientation distributions of the inclusions and in terms of the direction dependences of the predicted overall moduli. From these findings useful information on the appropriate requirements for the design of composite materials and composite structures can be obtained.

Structural similitude for vibration response of laminated cylindrical shells with double curvature

Abstract: In order to understand the applicability of scaled down models in designing laminated composite structures, an analytical investigation was undertaken to assess the feasibility of their use. Employment of similitude theory to establish similarity among structural systems can save considerable expense and time, provided the proper scaling laws are found and validated. The developed methodology is demonstrated through application of similitude theory to laminated cylindrical shells. Particular emphasis is placed on the case of free vibration of cross-ply laminated cylindrical shells with double curvature. The results presented herein indicate that, for free vibration responses of laminated cylindrical shells of double curvature, based on structural similitude, a set of scaling laws can be found which are used to develop design rules for designing small scale models. This analytical study indicates that distorted models with a different number of layers, geometries and material properties than those of the prototype can predict the behavior of the prototype with good accuracy. However, it is shown that a scaled down model with distorted curvature is incapable of predicting the response of the prototype.

On the effect of particle shape and orientation on elastic properties of metal matrix composites

Abstract: In this investigation, an aluminum alloy, A1 2124-T6, matrix composite containing alumina particles is examined. Both a standard mechanical approach and the homogenization method are employed to calculate effective elastic material constants. A periodic cubic array of particles is assumed leading to three-dimensional finite element analyses. Effective elastic properties are determined. The ceramic particles are assumed to be of four shapes: spherical, cylindrical, cubic and rectangular parallelepiped. For the latter two particles, the effect of particle orientation is examined. These lead to a lack of symmetry which produce effective elastic constants which are not usually observed. Rectangular parallelepiped particles appear to produce some benefits for effective axial elastic moduli.

Modal analysis of cracked, unidirectional composite beam

Abstract: In this paper, a model and an algorithm for creation of the characteristic matrices of a composite beam with a single transverse fatigue crack are presented. The element developed has been applied in analysing the influence of the crack parameters (position and relative depth) and the material parameters (relative volume and fibre angle) on changes in the first four transverse natural frequencies of the composite beam made from unidirectional composite material.

The use of transient FGM interlayers for joining advanced ceramics

Abstract: Functionally graded materials are designed to exhibit a desirable gradient in a property, due either to a gradient in composition, or microstructure, or both. In this paper, progress in the use of multilayer interlayers with microdesigned gradient structures for the purpose of joining is summarized. In contrast to conventional FGMs, the gradient structures of specific interest are not designed to be permanent, but are instead designed to facilitate processing by forming a thin layer of a transient liquid phase (TLP). This allows joining by a process that resembles brazing, but allows the formation of refractory joints at reduced processing temperatures, and provides access to joining chemistries that are not accessible by conventional joining methods. The method has been applied to the joining of A1 2 O 3 , Si 3 N 4 , and SiC, and is now being applied to the joining of SiC-SiC composites. Prior work is reviewed and recent progress in joining of these materials is described.

Bending strength of an AlAl3Ni functionally graded material

Abstract: The gradient of bending strength of an Al-Al3Ni functionally graded material (FGM) has been examined using 3-point bending tests. Specimens with rectangular cross-sections of 6 × 6 mm2 were machined from a thick-walled FGM tube such that the thickness direction of the specimen coincided with the radial direction of the tube. Thus the specimens had a graded composition of the A13Ni phase in the thickness direction. Four types of specimens characterized by four nominal volume fractions of the Al3Ni phase at the crack initiation plane, namely Vf= 0, 24, 49 and 53 vol%, were employed in the study. Fracture surfaces consisted of cleavage facets of the Al3Ni phase surrounded by dimples of the aluminum phase. Brittle fracture of Al3Ni dominated the fracture process of Al-Al3Ni FGM. Fracture strengths of the four types of specimens were plotted on the standard normal and Weibull probability paper. The trends of each data set exhibited good linearity, making it difficult to determine the differences in the fit between the two kinds of probability papers. Maximum average fracture stress of 156 MPa was obtained from the Vf= 24 vol% specimen, and decreased in the following order with specimen type: Vf= 24, 49, 53 and 0 vol%. Fracture strength of Al-Al3Ni FGM attained a maximum value of 160 MPa at Vf≈10 vol% and decreased with an increase in the A13Ni volume fraction due to the size effect that controls the strength of the brittle Al3Ni phase.

Microstructural optimization of functionally graded composites subjected to a thermal gradient via the coupled higher-order theory

Abstract: A recently developed higher-order theory for the response of a functionally graded composite plate subjected to a through-thickness thermal gradient is employed to optimize the composite's microstructure. The higher-order theory explicitly couples the microstructural and macrostructural effects, thereby providing a rational methodology for analyzing the response of functionally graded materials, typically analyzed using the standard uncoupled micromechanics approach, which often produces erroneous results. Herein, the higher-order theory is incorporated into an optimization algorithm to determine optimal through-thickness distributions of the reinforcement phase in a composite plate subjected to a thermal gradient that minimize the inplane moment resultant, and thus the tendency of the plate to bend about an axis. The results indicate that the manner of constraining the plate from bending due to the thermal gradient is a major factor that governs the optimal reinforcement phase distributions.

Numerical and experimental determination of residual stresses in graded materials

Abstract: When an FGM part is cooled down from its processing or heat treatment temperature to room remperature, residual stresses are generated in the composite due to the thermal expansion mismatch between the different materials. As the residual stresses may influence the performance of the part significantly, the efforts put into the development of theoretical models to predict these stresses are justified. The aim of the paper is to compare the theoretical results with those obtained from various experimental techniques using three different FGM systems, namely Cu-Ni, CrNi-ZrO2 and WC-Co, as examples.

Stress intensity factors as the fracture parameters for delamination crack growth in composite laminates

Abstract: A “mutual integral” approach is used to calculate the mixed-mode stress intensity factors for a free-edge delamination crack in a laminate under tensile loading conditions. This “mutual integral” approach, for generalized plane strain conditions, is based on the application of the path-independent J integral to a linear combination of three solutions: one, the problem of the laminate to be solved using the quasi 3-D finite element method, the second, an “auxiliary” solution with a known asymptotic singular solution, and the third, the particular solution due to the out-of-plane loading. A comparison with the exact solutions is made to determine the accuracy and efficiency of this numerical method. With this “mutual integral” approach, it was found that the calculated mixed-mode stress intensity factors of the free-edge delamination crack remain relatively constant as the crack propagates into the laminate. It was also found that the fracture criterion based on the mixed-mode stress intensity factors is more consistent with the experimental observations than the criterion based on the total energy release rate, and hence demonstrates the importance of the ability to calculate each individual component of the stress intensity factors. Furthermore, it was found that the fracture toughness measurements from double cantilever beam specimens can be used directly to predict the onset of delamination crack growth between two dissimilar laminae. Using these fracture toughness measurements from the double cantilever beam specimens, some examples are given to show that the fracture criterion based on the mixed-mode stress intensity factors can accurately predict the failure load for various laminates under tensile loading conditions.

Evaluation of the higher-order theory for functionally graded materials via the finite-element method

Abstract: A comparison is presented between the predictions of the finite-element analysis and a recently developed higher-order theory for functionally graded materials subjected to a through-thickness temperature gradient. In contrast to existing micromechanical theories that utilize classical (i.e. uncoupled) homogenization schemes to calculate micro-level and macro-level stress and displacement fields in materials with uniform or nonuniform fibre spacing (i.e. functionally graded materials), the new theory explicitly couples the microstructural details with the macrostructure of the composite. Previous thermo-elastic analysis has demonstrated that such coupling is necessary when: the temperature gradient is large with respect to the dimension of the reinforcement; the characteristic dimension of the reinforcement is large relative to the global dimensions of the composite and the number of reinforcing fibers or inclusions is small. In these circumstances, the standard micromechanical analyses based on the concept of the representative volume element used to determine average or effective properties of macroscopically homogeneous composites produce questionable results. The comparison between the results of the finite-element method and the higher-order theory presented herein establishes the theory's accuracy in predicting thermal and stress fields within composites with a finite number of fibers in the thickness direction subjected to a through-thickness thermal gradient.

A technique for analyzing elastodynamic responses of anisotropic laminated plates to line loads

Abstract: A new technique is presented to modify the hybrid numerical method (HNM) proposed earlier by the authors for analyzing the responses of anisotropic laminated plates subjected to time-step and time-pulse line loads. In the modified HNM, eigenfrequencies and modal factor functions for wave modes in the plate are computed at equally spaced points on the wavenumber axis. In each interval of the points, the eigenfrequencies and modal factor functions are replaced by straight lines, and the inverse Fourier integrations are then carried out analytically. The proposed modification can significantly reduce the sampling points in the inverse integrations. The modified HNM is much more efficient than the original HNM, and can be used to compute not only near-field and short-time but also far-field and long-time responses for anisotropic laminated plates, without increasing the sampling points. Numerical examples are presented to demonstrate the modified HNM.

Free vibration of a laminated composite circular cylindrical shell partially filled with fluid

Abstract: Free vibrations of partially fluid-filled laminated composite circular cylindrical shells including transverse shear deformation are investigated using a semi-analytical procedure. In this approach, displacements and rotations of the shell and the dynamic pressure of the fluid are modelled by Fourier series and finite elements in the circumferential and axial directions, respectively, whereas the dynamic pressure of the fluid is expanded as a power series in the radial direction. The coupling between symmetric and antisymmetric modes is taken into account in the formulation. Numerical examples are given for free vibrations of partially fluid-filled laminated composite circular cylindrical shells with various boundary conditions. Parametric studies including circumferential wave number, fluid depth, thickness to mean radius ratio, length to mean radius ratio and boundary condition are carried out.

Levy-type piezothermoelastic solution for hybrid plate by using first-order shear deformation theory

Abstract: A Levy-type solution is presented for hybrid rectangular plates, with two opposite edges simply supported, made of a cross-ply composite laminate with attached piezoelectric layers, and subjected to thermoelectromechanical load. First-order shear deformation and classical lamination theories are used. A mixed formulation is employed for the solution. The effect of the width-to-depth ratio and aspect ratio on deflection and force resultants has been illustrated for a uniform load on plates with various boundary conditions. The effect of shear deformation on deflection and force resultants for moderately thick plates is generally more pronounced for the mechanical load case than for the self-straining cases of thermal and electric loads.

Creep behavior of carbon-fiber-reinforced polyetheretherketone (PEEK) [ ±45]4s laminated composites (I)

Abstract: The creep properties of AS-4/PEEK [ ± 45]4s laminated composites have been investigated. The temperature dependence of the viscoelastic behavior of the matrix composite and the bulk resin was studied by dynamic mechanical analysis. The tensile properties were measured at elevated temperature. The tensile failure morphology at elevated temperature was investigated by scanning electron microscopy. The accelerated characterization of the creep response due to the effect of temperature and stress was studied. Short-term creep tests were performed at various stress levels and at elevated temperatures. The creep strain data were fitted by using the Findley equation. It was found that results predicted by the Findley equation showed good agreement with the experimental data. Coupling with the Findley equation, a master curve was constructed by using the time-temperature-stress superposition principle (TTSSP) with a reference condition at 85°C and 94.38 MPa. From the short-term creep test obtained after 600 min, a smooth master curve was obtained by the proposed procedure of accelerated characterization and a creep strain of 106.29 min can be predicted.

Evaluation of thermomechanical performance for thermal barrier type of sintered functionally graded materials

Abstract: Thermomechanical properties of metal/ceramic functionally graded materials were evaluated by a burner heating test using a H 2 /O 2 combustion flame, which simulated the real environment of the heated inner wall of a rocket combustor. Disk-shaped graded samples of a material combination of partially stabilized zirconia and stainless steel were used for the test, in which the ceramic surface of the sample was heated with a burner flame and the back surface was cooled with flowing water. The critical temperature of the first crack formation, which was always observed on the ceramic surface during cooling, was determined in the test. The stress distributions in the sample during heating and cooling cycles, calculated by the finite element method, show the generation of large compressive and tensile stresses during heating and cooling, respectively, which are attributed to the non-elastic deformation of the heated sample surface due to an excess compressive stress. The fracture mechanism in terms of crack formation and spalling in the FGMs is discussed on the basis of the stress distributions in addition to a fracture mechanics approach.

Plane strain/stress solutions for piezoelectric solids

Abstract: Piezoceramics are increasingly used in the fabrication of smart composite structures. In view of these applications, there is a growing interest in the development of analytical and computational tools for stress analysis of piezoelectric solids and mechanics problems related to smart composite elements. The coupled equations governing two-dimensional electroelastic fields of a piezoelectric solid are solved in this paper by applying Fourier integral transforms. The piezoelectric medium is assumed to be hexagonally symmetric about or polarized along the vertical direction. Analytical general solutions are presented for all components of the electroelastic field. Closed-form analytical solutions are derived for a solid subjected to concentrated line loads and an electric charge. Solutions for line loads and an electric charge applied to the boundary of a piezoelectric solid are also derived. Selected numerical results are presented to portray the salient features of the electroelastic fields. A significant dependence of the electroelastic fields on the material properties is noted including complex spatial variations and coupling effects. The closed-form solutions presented in this paper are the kernel functions required in the two-dimensional boundary element analysis of composite elements with embedded or surface-mounted piezoceramic actuators.