Sound Transmission Loss Analysis of a Double Plate-Acoustic Cavity Coupling System with In-Plane Functionally Graded Materials

In this paper, the isogeometric analysis (IGA) is employed to develop an acoustic radiation model for a double plate-acoustic cavity coupling system, with a focus on analyzing the sound transmission loss (STL). The functionally graded (FG) plate exhibits a different material properties in-plane, and the power-law rule is adopted as the governing principle for material mixing. To validate the harmonic response and demonstrate the accuracy and convergence of the isogeometric modeling, ANASYS is utilized to compare with numerical examples. A plane wave serves as the acoustic excitation, and the Rayleigh integral is applied to discretize the radiated plate. The STL results are compared with the literature, confirming the reliability of the coupling system. Finally, the investigation is conducted to study impact of cavity depth and power-law parameter on the STL.

Review of functionally graded materials processed by additive manufacturing

Additive manufacturing(AM)technology makes parts through layer-by-layer deposition,which can regulate the microstructure and properties of different parts of a single part well.It provides a new idea for the preparation of functionally gradient materials(FGM),and has become a research hotspot at present.By referring to and analyzing the recent research achievements in the additive manufacturing tech-nology of FGM,the latest research progress at domestic and abroad from four aspects were summaried:selective laser melting additive man-ufacturing,electron beam additive manufacturing,arc additive manufacturing,path planning,and material texture.Moreover,the existing problems in the research are pointed out,and the future research direction and focus are prospected.

The nonlocal solution of two parallel cracks in functionally graded materials subjected to harmonic anti-plane shear waves

In this paper, the dynamic interaction of two parallel cracks in functionally graded materials （FGMs） is investigated by means of the non-local theory. To make the analysis tractable, the shear modulus and the material density are assumed to vary exponentially with the coordinate vertical to the crack. To reduce mathematical difficulties, a one-dimensional non-local kernel is used instead of a twodimensional one for the dynamic problem to obtain stress fields near the crack tips. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces are expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularity is present at the crack tips. The non-local elastic solutions yield a finite hoop stress at the crack tips. The present result provides theoretical references helpful for evaluating relevant strength and preventing material failure of FGMs with initial cracks. The magnitude of the finite stress field depends on relevant parameters, such as the crack length, the distance between two parallel cracks, the parameter describing the FGMs, the frequency of the incident waves and the lattice parameter of materials.

Optimization design and residual thermal stress analysis of PDC functionally graded materials

The distribution of thermal stresses in functionally graded polycrystalline diamond compact (PDC) and in single coating of PDC are analyzed respectively by thermo-mechanical finite element analysis (FEA). It is shown that they each have a remarkable stress concentration at the edge of the interfaces. The diamond coatings usually suffer premature failure because of spallation, distortion or defects such as cracks near the interface due to these excessive residual stresses. Results showed that the axial tensile stress in FGM coating is reduced from 840 MPa to 229 MPa compared with single coating, and that the shear stress is reduced from 671 MPa to 471 MPa. Therefore, the single coating is more prone to spallation and cracking than the FGM coating. The effects of the volume compositional distribution factor (n) and the number of the graded layers (L) on the thermal stresses in FGM coating are also discussed respectively. Modelling results showed that the optimum value of the compositional distribution factor is 1.2, and that the best number of the graded layers is 6.

High Heat Flux Testing of B_4C/Cu and SiC/Cu Functionally Graded Materials Simulated by Laser and Electron Beam

B4C, SiC and C, Cu functionally graded-materials (FGMs) have been developed by plasma spraying and hot pressing. Their high-heat flux properties have been investigated by high energy laser and electron beam for the simulation of plasma disruption process of the future fusion reactors, And a study on eroded products of B4C/Cu FGM under transient thermal load of electron beam was performed. In the experiment, SEM and EDS analysis indicated that B4C and SiC were decomposed, carbon was preferentially evaporated under high thermal load, and a part of Si and Cu were melted, in addition, the splash of melted metal and the particle emission of brittle destruction were also found. Different erosive behaviors of carbon-based materials (CBMs) caused by laser and electron beam were also discussed.

3D analytical solution for a rotating transversely isotropic annular plate of functionally graded materials

The analytical solution for an annular plate rotating at a constant angular velocity is derived by means of direct displacement method from the elasticity equations for axisymmetric problems of functionally graded transversely isotropic media. The displacement components are assumed as a linear combination of certain explicit functions of the radial coordinate, with seven undetermined coefficients being functions of the axial coordinate z. Seven equations governing these z-dependent functions are derived and solved by a progressive integrating scheme. The present solution can be degenerated into the solution of a rotating isotropic functionally graded annular plate. The solution also can be degenerated into that for transversely isotropic or isotropic homogeneous materials. Finally, a special case is considered and the effect of the material gradient index on the elastic field is illustrated numerically.

Flexural strength of zirconia/stainless steel functionally graded materials

Zirconia/stainless steel (ZrO2/SUS316L) functionally graded materials (FGMs) were fabricated by tape casting and laminating. Microstructures of FGMs were observed by optical microscope. Fracture behavior of FGMs in different loading modes and influences of different gradient changes on flexural strength were investigated. The results show that ZrO2/ SUS316L FGMs with graded components at interlayers are obtained after they are sintered in vacuum and pressureless condition at 1 350 ℃. TheⅠ?Ⅱ mixed mode crack creates in composite layer and grows to both sides zigzag while loading on ZrO2 layer. Flexural strengths are 496.4,421.7 and 387.5 MPa when gradient changes are 10%,15% and 20%,but flexural strengths of the corresponding fracture layers are 387.1,334.6 and 282.3 MPa since cracks of FGMs are affected by three-dimensional stress,respectively. The cracks are generated in ZrO2 layer and extend to SUS316L layer while loading is added on SUS316L layer,flexural strength does not change with the graded components and keeps consistent basically.

Preparation of Al/Si functionally graded materials using ultrasonic separation method

Functionally graded materials （FGM） have been widely used in many industries such as aerospace, energy and electronics. In this experimental study of fabricating FGM, an approach was developed to prepare AI/Si FGM using power ultrasonic separation method. Material sample with continuously changing composition and performance/properties was successfully produced. Results showed that the microstructure of the FGM sample transited, from its top to bottom, from the hypereutectic structure with a large quantity of primary Si gradually to the eutectic, and finally to the hypoeutectic with numerous primary AI dendrites. The distribution of primary Si and microhardness of the FGM sample also presented graded characteristics, resulting that the wear resistance of the FGM sample decreased from top to bottom. Preliminary discussion was made on the mechanism of the formation of AI/Si FGM.

Hybrid graded element model for transient heat conduction in functionally graded materials

This paper presents a hybrid graded element model for the transient heat conduction problem in functionally graded materials （FGMs）. First, a Laplace transform approach is used to handle the time variable. Then, a fundamental solution in Laplace space for FGMs is constructed. Next, a hybrid graded element is formulated based on the obtained fundamental solution and a frame field. As a result, the graded properties of FGMs are naturally reflected by using the fundamental solution to interpolate the intra-element field. Further, Stefest＇s algorithm is employed to convert the results in Laplace space back into the time-space domain. Finally, the performance of the proposed method is assessed by several benchmark examples. The results demonstrate well the efficiency and accuracy of the proposed method.

COUPLED THERMAL/MECHANICAL ANALYSIS FOR THE FRACTURE OF FUNCTIONALLY GRADED MATERIALS UNDER TRANSIENT THERMAL LOADING

A comprehensive treatment of fracture of functionally gradedmaterials (FGMs) is provided. It is assumed that the materialproperties depend only on the coordinate perpendicular to the cracksurface And vary continuously along the crack faces. By using alaminated composite plate model to simulate the ma- Terialnon-homogeneity, an algorithm for solving the system based on Laplacetransform and Fourier transform Techniques is presented. Unlikeearlier studies that considered certain assumed propertydistributions and a Single crack problem, the current investigationstudies multiple crack problem in the FGMs with arbitrarily Varyingmaterial properties. Transient thermal stresses are presented.

DYNAMIC RESPONSE FOR FUNCTIONALLY GRADED MATERIALS WITH PENNY-SHAPED CRACKS

This paper provides a method for studying the penny-shaped cracksconfiguration in functionally graded material(FGM)structuressubjected to dynamic or steady loading. It is assumed that the FGMare transversely isotropic and all the material properties onlydepend on the axial coordi- nate z. In the analysis, the elasticregion is treated as a number of layers. The material properties aretaken to be constants for each layer. By utilizing the Laplacetransform and Hankel transform tech- nique, the general solution forthe layers are derived.

THERMAL AND THERMO-ELASTIC-PLASTIC RESPONSE OF CERAMIC-METAL FUNCTIONALLY GRADED MATERIALS—THERMAL SHOCK PROBLEM

The thermal and thermo-elastic-plastic response of newly developed ceramic-metal functionally graded materials under a thermal shock load is studied. The materials are heated at the ceramic surface with a sudden high-intensity heat flux input, and cooled at the metal surface with a flowing liquid nitrogen. Emphasis is placed on two aspects: (1) the influence of the graded composition of the materials on the temperature and stress response; and (2) the optimum design of the graded composition from a unified viewpoint of the heat insulation property and stress relaxation property. Moreover, a comparison between the thermoelastic stress and the thermo-elastic-plastic stress is also made to indicate the plasticity effect.

Mechanical properties of CNT reinforced hybrid functionally graded materials for bioimplants

The hybrid functionally graded materials(FGM) of hydroxyapatite(HA), stainless steel 316L(SS316L) and carbon nanotubes(CNT) were synthesized for biomedical implants. Three different types of FGM were produced by the combination of SS316 L and CNT to reinforce HA in discrete layers of FGM. In the first type of FGM, concentration of SS316 L was varied from 10% to 40%(mass fraction) with an increment of 10% to reinforce micro HA. In the second type of FGM, 0.5%(mass fraction) functionalized CNT was added by maintaining the rest of composition as that of the first type of FGM. In the third type of FGM, mixture of micro and nano HA(mass ratio1:1) was used, keeping rest of composition similar to the second type of FGM. All types of FGM were subjected to uniaxial compaction and sintered by pressureless sintering technique at similar compaction and sintering parameters. The results show that the densification is enhanced with the addition of CNT and nanocrystalline HA in the FGM. Hardness and fracture toughness increase in both FGM reinforced with CNT, but the increase of the hardness and fracture toughness are more pronounced in FGM with micro and nanocrystalline HA.

Evaluation of strongly singular domain integrals for internal stresses in functionally graded materials analyses using RIBEM

An accurate evaluation of strongly singular domain integral appearing in the stress representation formula is a crucial problem in the stress analysis of functionally graded materials using boundary element method.To solve this problem,a singularity separation technique is presented in the paper to split the singular integral into regular and singular parts by subtracting and adding a singular term.The singular domain integral is transformed into a boundary integral using the radial integration method.Analytical expressions of the radial integrals are obtained for two commonly used shear moduli varying with spatial coordinates.The regular domain integral,after expressing the displacements in terms of the radial basis functions,is also transformed to the boundary using the radial integration method.Finally,a boundary element method without internal cells is established for computing the stresses at internal nodes of the functionally graded materials with varying shear modulus.

Crack tip higher order stress fields for functionally graded materials with generalized form of gradation

A generalized form of material gradation applicable to a more broad range of functionally graded materials(FGMs) was presented.With the material model,analytical expressions of crack tip higher order stress fields in a series form for opening mode and shear mode cracks under quasi-static loading were developed through the approach of asymptotic analysis.Then,a numerical experiment was conducted to verify the accuracy of the developed expressions for representing crack tip stress fields and their validity in full field data analysis by using them to extract the stress intensity factors from the results of a finite element analysis by local collocation and then comparing the estimations with the existing solution.The expressions show that nonhomogeneity parameters are embedded in the angular functions associated with higher terms in a recursive manner and at least the first three terms in the expansions must be considered to explicitly account for material nonhomogeneity effects on crack tip stress fields in the case of FGMs.The numerical experiment further confirms that the addition of the nonhomogeneity specific terms in the expressions not only improves estimates of stress intensity factor,but also gives consistent estimates as the distance away from the crack tip increases.Hence,the analytical expressions are suitable for the representation of crack tip stress fields and the analysis of full field data.

Adaptive phase field modelling of crack propagation in orthotropic functionally graded materials

In this work,we extend the recently proposed adaptive phase field method to model fracture in orthotropic functionally graded materials(FGMs).A recovery type error indicator combined with quadtree decomposition is employed for adaptive mesh refinement.The proposed approach is capable of capturing the fracture process with a localized mesh refinement that provides notable gains in computational efficiency.The implementation is validated against experimental data and other numerical experiments on orthotropic materials with different material orientations.The results reveal an increase in the stiffness and the maximum force with increasing material orientation angle.The study is then extended to the analysis of orthotropic FGMs.It is observed that,if the gradation in fracture properties is neglected,the material gradient plays a secondary role,with the fracture behaviour being dominated by the orthotropy of the material.However,when the toughness increases along the crack propagation path,a substantial gain in fracture resistance is observed.

Single-pulse chaotic dynamics of functionally graded materials plate

Single-pulse chaos are studied for a functionally graded materials rectangular plate. By means of the global perturbation method, explicit conditions for the existence of a SiZnikov-type homoclinic orbit are obtained for this sys- tem, which suggests that chaos are likely to take place. Then, numerical simulations are given to test the analytical predic- tions. And from our analysis, when the chaotic motion oc- curs, there are a quasi-period motion in a two-dimensional subspace and chaos in another two-dimensional supplemen- tary subspace.

Interface microstructure and mechanical properties of selective laser melted multilayer functionally graded materials

Functionally graded material(FGM)can tailor properties of components such as wear resistance,corrosion resistance,and functionality to enhance the overall performance.The selective laser melting(SLM)additive manufacturing highlights the capability in manufacturing FGMs with a high geometrical complexity and manufacture flexibility.In this work,the 316L/CuSn10/18Ni300/CoCr four-type materials FGMs were fabricated using SLM.The microstructure and properties of the FGMs were investigated to reveal the effects of SLM processing parameters on the defects.A large number of microcracks were found at the 316L/CuSn10 interface,which initiated from the fusion boundary of 316L region and extended along the building direction.The elastic modulus and nano-hardness in the 18Ni300/CoCr fusion zone decreased significantly,less than those in the 18Ni300 region or the CoCr region.The iron and copper elements were well diffused in the 316L/CuSn10 fusion zone,while elements in the CuSn10/18Ni300 and the 18Ni300/CoCr fusion zones showed significantly gradient transitions.Compared with other regions,the width of the CuSn10/18Ni300 interface and the CuSn10 region expand significantly.The mechanisms of materials fusion and crack generation at the 316L/CuSn10 interface were discussed.In addition,FGM structures without macro-crack were built by only altering the deposition subsequence of 316L and CuSn10,which provides a guide for the additive manufacturing of FGM structures.

Design of Co-sedimentation Experiments Used to Fabricate Functionally Graded Materials with a Continuous Change of Composition

In the process of particle settling in a dilute,a density graded distribution of the liquid below the suspension needs to be designed according to the gravity of the suspension prior to sedimentation.In the present paper a compositionally graded W-Mo composite was formed via the settling of the W and Mo particles,with a density gradient distributed in the initial clear liquid along the settling direction.

Influence of Inclusion Shape on Thermoelasto-Plastic Optimun Design of Ceramic Metal Functionally Graded Materials

A nonlinear finite element method is applied to observe how inclusion shape influence the thermal response of a ceramic-metal functionally graded material (FGM). The elastic and plastic behaviors of the layers which are two-phase isotropic composites consisting of randomly oriented elastic spheroidal Inclusions and a ductile matrix are predicted by cc mean field method. The prediction results show that inclusion shape has remarkable influence on the overall behavior of the composite. The consequences of the thermal response analysis of the FGM are that the response is dependent on inclusion shape and its composition profile cooperatively and that the plastic behavior of each layer should be taken into account in optimum design of a ceramic-metal FGM.