Three-dimensional thermomechanical buckling analysis for functionally graded composite plates

Three-dimensional thermomechanical buckling analysis is investigated for functionally graded composite structures that composed of ceramic, functionally graded material (FGM), and metal layers. Material properties are assumed to be temperature dependent, and in FGM layer, they are varied continuously in the thickness direction according to a simple power law distribution in terms of the ceramic and metal volume fractions. The finite element model is adopted by using an 18-node solid element to analyze more accurately the variation of material properties and temperature field in the thickness direction. Temperature at each node is obtained by solving the thermomechanical equations. For a time discretization, Crank–Nicolson method is used. In numerical results, the thermal buckling behavior of FGM composite structures due to FGM thickness ratios, volume fraction distributions, and system geometric parameters are analyzed.     

Autofrettage of layered and functionally graded metal–ceramic composite vessels

The residual compressive stresses induced by the autofrettage process in a metal vessel are limited by metal plasticity. Here we showed that the autofrettage of layered metal–ceramic composite vessels leads to considerably higher residual compressive stresses compared to the counterpart metal vessel. To calculate the residual stresses in a composite vessel, an extension of the Variable Material Properties (X-VMP) method for materials with varying elastic and plastic properties was employed. We also investigated the autofrettage of composite vessels made of functionally graded material (FGM). The significant advantage of this configuration is in avoiding the negative effects of abrupt changes in material properties in a layered vessel – and thus, inherently, in the stress and strain distributions induced by the autofrettage process. A parametric study was carried out to obtain near-optimized distribution of ceramic particles through the vessel thickness that results in maximum residual stresses in an autofrettaged functionally graded composite vessel. Selected finite element results were also presented to establish the validity of the X-VMP method.     

功能梯度板壳的力学研究进展

功能梯度材料(FGM)是一种材料组分或微观结构沿一个或几个方向连续变化的新型复合材料。FGM中基本消除了宏观界面,同时具有很好的可设计性,设计人员可以有目的地改变材料组成,以获得所期望的性能。由FGM构成的功能梯度板壳结构在许多工程领域中有着广阔的应用前景,评述了FGM板壳结构的弯曲、屈曲和后屈曲、振动和动力稳定性等力学问题研究的发展现状,阐述了常用方法和理论的优缺点,并提出了未来的发展趋势和需要研究的方向。     

Cohesive fracture modeling of elastic-plastic crack growth in functionally graded materials

This work investigates elastic-plastic crack growth in ceramic/metal functionally graded materials (FGMs). The study employs a phenomenological, cohesive zone model proposed by the authors and simulates crack growth by the gradual degradation of cohesive surfaces ahead of the crack front. The cohesive zone model uses six material-dependent parameters (the cohesive energy densities and the peak cohesive tractions of the ceramic and metal phases, respectively, and two cohesive gradation parameters) to describe the constitutive response of the material in the cohesive zone. A volume fraction based, elastic-plastic model (extension of the original Tamura-Tomota-Ozawa model) describes the elastic-plastic response of the bulk background material. The numerical analyses are performed using WARP3D, a fracture mechanics research finite element code, which incorporates solid elements with graded elastic and plastic properties and interface-cohesive elements coupled with the functionally graded cohesive zone model. Numerical values of volume fractions for the constituents specified at nodes of the finite element model set the spatial gradation of material properties with isoparametric interpolations inside interface elements and background solid elements to define pointwise material property values. The paper describes applications of the cohesive zone model and the computational scheme to analyze crack growth in a single-edge notch bend, SE(B), specimen made of a TiB/Ti FGM. Cohesive parameters are calibrated using the experimentally measured load versus average crack extension (across the thickness) responses of both Ti metal and TiB/Ti FGM SE(B) specimens. The numerical results show that with the calibrated cohesive gradation parameters for the TiB/Ti system, the load to cause crack extension in the FGM is much smaller than that for the metal. However, the crack initiation load for the TiB/Ti FGM with reduced cohesive gradation parameters (which may be achieved under different manufacturing conditions) could compare to that for the metal. Crack growth responses vary strongly with values of the exponent describing the volume fraction profile for the metal. The investigation also shows significant crack tunneling in the Ti metal SE(B) specimen. For the TiB/Ti FGM system, however, crack tunneling is pronounced only for a metal-rich specimen with relatively smaller cohesive gradation parameter for the metal.     

Parametric study of development of Inconel-steel functionally graded materials by laser direct metal deposition

Laser direct metal deposition (LDMD) has developed from a prototyping to a single and multiple metals manufacturing technique. It offers an opportunity to produce graded components, with differing elemental composition, phase and microstructure at different locations. In this work, continuously graded Stainless Steel 316L and Inconel 718 thin wall structures made by direct laser metal deposition process have been explored. The paper considers the effects of process parameters including laser power levels and powder mass flow rates of SS316L and Inconel 718 during the deposition of the Steel–Ni graded structures. Microstructure characterisation and phase identification are performed by optical microscopy and X-ray diffraction techniques. Mechanical testing, using methods such as hardness, wear resistance and tensile testing have been carried out on the structures. XRD results show the presence of the NbC and Fe₂Nb phases formed during the deposition. The effect of experimental parameters on the microstructure and physical properties are determined and discussed. Work shows that mechanical properties can be controlled by input parameters and generation of carbides provides an opportunity to selectively control the hardness and wear resistance of the functionally graded material.     

Thixotropic casting of ceramic-metal functionally gradient materials

Functionally gradient materials (FGM), a recent development in composite materials, consist of a continuously graded interface between two component phases. Previously reported FGM fabrication methods are reviewed, including vapour deposition, plasma spraying, electrophoretic deposition, controlled powder mixing, slipcasting, sedimentation forming, centrifugal forming, laser cladding, metal infiltration, controlled volatilization, and self propagating high-temperature synthesis. A novel approach to FGM fabrication is presented involving thixotropic casting — vibratory casting of highly concentrated highly thixotropic suspensions castable only under vibration. The hydroxyapatite/316L stainless steel system (a biocompatible ceramic/metal system) was used due to appropriate matches in true densities, thermal expansion, and sintering temperatures. Solids loadings from 76.08–82.67 wt% were trialled. Solids loading was found to be critical. At 78.17 wt%, an ideal continuous FGM formed, showing a gradual transition from pure ceramic to pure metal across 60 mm. At the nearest increments trialled (±0.3 wt%) gradation was far from optimal: 77.87 wt% gave a sharp ceramic/metal interface with negligible grading; 78.47 wt% gave a relatively homogeneous sample with only a small degree of grading, from a slightly metal-rich end to a slightly metal-poor end.     

The role of gradation on the improvement of effective properties of highly heterogeneous multilayered thermoviscoplastic materials under simple shearing

In this paper we study the role of the gradation on the effective properties of heterogeneous multilayered thermoviscoplastic materials with discontinuous properties under simple shearing. Starting from the bimetallic multilayered material, we produce a new multicomponent material with discontinuous gradation having improved effective properties. We also present the effective properties of the continuously graded material functionally graded material (FGM). The main results are illustrated with some numerical examples.     

On the shear stress distribution between a functionally graded piezoelectric actuator and an elastic substrate and the reduction of its concentration

Recent advances in material processing technologies allow the production of piezoelectric materials with functionally graded material properties. We investigate the implications of functionally graded piezoelectric materials when used as actuators for structural control by examining the distribution of the actuating shear stress under a piezoelectric actuator of a functionally graded material (FGM) on an isotropic elastic half-space. It is shown that FGM materials can be used to adjust the shear stress distribution. In particular, the concentration near the edges of a conventional homogeneous piezoelectric actuator can be significantly reduced in an FGM actuator.     

功能梯度材料的制备与应用进展

功能梯度材料(FGM)是由日本人首先提出的一种新型复合材料,从提出后到现在已经得到了深入的研究和广泛的应用.阐述了功能梯度材料的概念及其产生背景,重点评述了功能梯度材料各种制备技术的原理和特点,以及国内外在应用方面取得的各种成果,探讨了功能梯度材料的发展方向.     

Stochastic Finite element analysis of the free vibration of functionally graded material plates

The superior properties of functionally graded materials (FGM) are usually accompanied by randomness in their properties due to difficulties in tailoring the gradients during manufacturing processes. Using the stochastic finite element method (SFEM) proved to be a powerful tool in studying the sensitivity of the static response of FGM plates to uncertainties in their material properties. This tool is yet to be used in studying free vibration of FGM plates. The aim of this work is to use both a First Order Reliability Method (FORM) and the Second Order Reliability Method (SORM), combined with a nine-noded isoparametric Lagrangian element based on the third order shear deformation theory to investigate sensitivity of the fundamental frequency of FGM plates to material uncertainties. These include the effect of uncertainties on both the metal and ceramic constituents. The basic random variables include ceramic and metal Young’s modulus and Poisson’s ratio, their densities and ceramic volume fraction. The developed code utilizes MATLAB capabilities to derive the derivatives of the stiffness and mass matrices symbolically with a considerable reduction in calculation time. Calculating the eigenvectors at the mean values of the variables proves to be a reasonable simplification which significantly increases solution speed. The stochastic finite element code is validated using available data in the literature, in addition to comparisons with results of the well-established Monte Carlo simulation technique with importance sampling. Results show that SORM is an excellent rapid tool in the stochastic analysis of free vibration of FGM plates, when compared to the slower Monte Carlo simulation techniques.     

Rapid additive manufacturing of functionally graded structures using simultaneous wire and powder laser deposition

Laser additive fabrication allows the manufacturing of functionally graded structures that are not possible using conventional subtractive manufacturing. Laser deposition of injected powders with varying compositions, layer-by-layer, is often used for the building up of functionally graded fully dense structures or materials. This approach, however, has some drawbacks: the un-used powders (normally 60-80%) cannot be recycled as they will be contaminated by the powder mixture. In addition, multiple passes are needed to develop functionally graded structures. This paper reports the feasibility and characteristics of using simultaneous powder and wire feeding laser deposition to produce functionally graded structures in a single step. This approach has been shown to eliminate the above problems associated with powder feed laser deposition. In this work, copper powder and nickel wire have been used to deposit functionally grated copper/nickel/iron structures on H13 tool steel. A 1.5-kW diode laser is used for the build-up process. Electron probe microanalysis (EPMA), scanning electron microscopy (SEM), energy dispersive X-ray spectroscopy (EDS), X-ray diffraction (XRD) and optical microscopy are used to analyse the deposited materials in terms of morphology, composition distributions, microstructures and phases formed. Successful deposition of functionally graded Cu-Ni-Fe structures has been demonstrated. Comparisons are made with the dual powder feed deposition process, which shows the inclusion of un-melted Ni powders in the Cu layer as a result of melting temperature difference of the two materials.     

The ballistic performance of SiC–AA7075 functionally graded composite produced by powder metallurgy

The potential of silicon carbide reinforced Functionally Gradient Material (FGM) to be used as armor material was investigated under the impact of armor piercing projectile. For this purpose, the SiC–Aluminum Alloy (AA) 7075 functionally graded composite at different thicknesses was produced from the metallic and ceramic powders via powder metallurgy method. Before the ballistic testing, the precipitation hardening behavior of the samples was determined. And also, the microstructural characterizations of the samples were done with the aid of microscopy techniques. Next, the FGM samples were tested using armor piercing projectile to analyze their impact behavior. In the produced samples, some pore formation was detected. The ballistic experiments showed that the investigated FGMs (up to a thickness of 25 mm) did not withstand the impact of the projectile. At the tested samples, some major cracks and plug formation were detected at macrolevel while there were some microcracks, deformed and elongated grains in the regions near to the deformation zone of the samples.     

Rapid additive manufacturing of functionally graded structures using simultaneous wire and powder laser deposition

Laser additive fabrication allows the manufacturing of functionally graded structures that are not possible using conventional subtractive manufacturing. Laser deposition of injected powders with varying compositions, layer-by-layer, is often used for the building up of functionally graded fully dense structures or materials. This approach, however, has some drawbacks: the un-used powders (normally 60–80%) cannot be recycled as they will be contaminated by the powder mixture. In addition, multiple passes are needed to develop functionally graded structures. This paper reports the feasibility and characteristics of using simultaneous powder and wire feeding laser deposition to produce functionally graded structures in a single step. This approach has been shown to eliminate the above problems associated with powder feed laser deposition. In this work, copper powder and nickel wire have been used to deposit functionally grated copper/nickel/iron structures on H13 tool steel. A 1.5-kW diode laser is used for the build-up process. Electron probe microanalysis (EPMA), scanning electron microscopy (SEM), energy dispersive X-ray spectroscopy (EDS), X-ray diffraction (XRD) and optical microscopy are used to analyse the deposited materials in terms of morphology, composition distributions, microstructures and phases formed. Successful deposition of functionally graded Cu–Ni–Fe structures has been demonstrated. Comparisons are made with the dual powder feed deposition process, which shows the inclusion of un-melted Ni powders in the Cu layer as a result of melting temperature difference of the two materials.     

功能梯度材料的断裂与屈曲驱动断裂的简化分析

作为一类先进的复合材料,功能梯度材料(FGM)能综合利用多种材料的物理性能,同时材料性质的连续变化也使其具有许多优越的力学性能。本文对功能梯度材料中平行于界面的裂纹的断裂参数进行了计算,并分析了梯度变化的薄膜在压应力作用下的屈曲驱动扩展。研究结果表明:功能梯度材料能有效地减小界面中的应力集中及它对材料中缺陷的作用,从而不同程度地提高了材料的强度和韧性。     

The effect of notch depth on J-integral and critical fracture load in plates made of functionally graded aluminum–silicone carbide composite with U-notches under bending

The present paper deals with the effect of notch depth on J-integral and critical fracture load in a plate made of functionally graded aluminum–silicone carbide composite (Al–SiC) with U-notch under bending. The weight fraction of SiC particles varies from 0% to 20% through the specimen width. Using three criteria namely mean stress (MS), point stress (PS), and averaged strain-energy density (ASED), the critical fracture load has been predicted and its variation with respect to the notch depth has been studied. A comparison of the J-integral between functionally graded and homogeneous Al–SiC composite were made, where the notch tip in the functionally graded material is situated in a layer with same mechanical properties as the homogeneous composite. The results indicated that in the case where the notch scene is toward brittleness increment the critical J-integral in functionally graded material (FGM) is larger than that of in homogeneous material with the same mechanical properties at the notch tip. Therefore, FGM is more convenient than homogeneous material against fracture.     

Buckling of FGM cylindrical shells subjected to pure bending load

In this paper, buckling behaviors of composite cylindrical shells made from functionally graded materials (FGMs) subjected to pure bending load were investigated. The material properties were assumed to be graded along the thickness. The non-uniform bending force on the shell section was considered in the buckling government equation of FGM cylindrical shells based on the Donnell shallow shell theory. The prebuckling deformation of the FGM cylindrical shells was neglected and the buckling mode was assumed to occur non-uniformly in local district along the shell circumferential direction. The eigenvalue method was used to obtain the buckling critical condition. The theoretical results were in excellent agreement with those of ABAQUS code. Results show that the inhomogenity of the materials is significant for buckling of FGM cylindrical shells.     

非保守功能梯度材料杆的后屈曲分析

对受切向均布随从力作用的右端可移简支功能梯度材料(FGM)杆,基于轴线可伸长杆的大变形理论建立了非线性控制微分方程组,用打靶法对由金属和陶瓷所构成的FGM杆的后屈曲特性进行了数值分析,给出了不同梯度指标下FGM杆的后屈曲特征曲线,并与金属和陶瓷两种单相材料杆的相应特性进行了比较,讨论了FGM杆长高比对其后屈曲特性的影响。     

Crack growth resistance behavior of a functionally graded material: computational studies

This paper describes crack growth resistance simulation in a ceramic/metal functionally graded material (FGM) using a cohesive zone ahead of the crack front. The plasticity in the background (bulk) material follows J₂ flow theory with the flow properties determined by a volume fraction based, elastic-plastic model (extension of the original Tamura-Tomota-Ozawa model). A phenomenological, cohesive zone model with six material-dependent parameters (the cohesive energy densities and the peak cohesive tractions of the ceramic and metal phases, respectively, and two cohesive gradation parameters) describes the constitutive response of the cohesive zone. Crack growth occurs when the complete separation of the cohesive surfaces takes place. The crack growth resistance of the FGM is characterized by a rising J-integral with crack extension (averaged over the specimen thickness) computed using a domain integral (DI) formulation. The 3-D analyses are performed using WARP3D, a fracture mechanics research finite element code, which incorporates solid elements with graded elastic and plastic properties and interface-cohesive elements coupled with the functionally graded cohesive zone model. The paper describes applications of the cohesive zone model and the DI method to compute the J resistance curves for both single-edge notch bend, SE(B), and single-edge notch tension, SE(T), specimens having properties of a TiB/Ti FGM. The numerical results show that the TiB/Ti FGM exhibits significant crack growth resistance behavior when the crack grows from the ceramic-rich region into the metal-rich region. Under these conditions, the J-integral is generally higher than the cohesive energy density at the crack tip even when the background material response remains linearly elastic, which contrasts with the case for homogeneous materials wherein the J-integral equals the cohesive energy density for a quasi-statically growing crack.     

Free vibration analysis of pre-twisted rotating FGM beams

The natural frequencies of vibration of a rotating pre-twisted functionally graded cantilever beam are investigated. Rotating cantilever beam with pre-twist made of a functionally gradient material (FGM) consisting of metal and ceramic is considered for the study. The material properties of the FGM beam symmetrically vary continuously in thickness direction from core at mid section to the outer surfaces according to a power-law form. Equations of motion for free vibration are derived using Lagrange’s equation and the natural frequencies are determined using Rayleigh–Ritz method. The effect of parameters such as the pre-twist angle, power law index, hub radius and rotational speed on the natural frequencies of rotating functionally graded pre-twisted cantilever beams are examined through numerical studies and comparison is made with the numerical results obtained using other methods reported in literature. The effect of coupling between chordwise and flapwise bending modes on the natural frequencies has also been investigated.     

Fabrication and characterization of vacuum plasma sprayed W/Cu-composites for extreme thermal conditions

The joining of tungsten to copper and the ongoing search for commercially viable production techniques is one of the challenging issues in the field of composite materials. The reason why this material combination is of essential importance is its ability to withstand erosion and high temperatures on the tungsten side and to remove big quantities of heat on the copper side. Due to the mismatch of thermal expansion and Young’s moduli, the direct joining of these two materials results in high residual and thermal stresses at the interface, ultimately reducing component lifetime. One potential answer to this problem is functionally graded structures of W and Cu, which smoothen the transition of material properties. The present study focuses on vacuum plasma spraying (120 mbar, Ar) of W/Cu-gradients and composites with defined mixing ratios. The influence of the fabrication process and the W:Cu ratio on the microstructure has been investigated and results from thermo-mechanical and thermo-physical results analyses are presented. Finite element modeling has been used to demonstrate the positive effect of gradients on the elastic and elastic–plastic response within two different model-geometries. Partial gradients, ranging from pure tungsten to 75 vol.% tungsten, exhibit the best results and improve the expected life-time performance significantly by reducing the stresses at both interfaces, W/FGM and FGM/Cu, compared to a reference interface between W and Cu.