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.

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.

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.

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.

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.

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.

THERMO ELASTO—PLASTIC OPTIMUM DESIGN OF CERAMIC—METAL FUNCTIONALLY GRADED MATERIALS-Ⅰ.MICROMECHANICAL AND GEOMETRICAL EFFECTS

The thermo elasto-plastic optimum design of ceramic-metal functionally graded materials (FGMs)was investigated in this paper. The inelastic properties were first evaluated using micromechanical approaches, then an elasto-plastic finite element model was used to calculate the thermal stress in the material . The effects of micromechanical approaches, plasticity and graded interlayer thickness on the thermal stress relaxation characteristics and stress distributions were studied. The results show that: (1) the macro elas-to-plastic response given by the mean-field micromechanics and self-consistent micromechanics is nearly the same but the response given by the rule of mixture is different; (2)the thermo elasto-plastic behavior must be considered to realistically evaluate stress reduction, and the elasto-plastic optimum design can get helpful information to determine the graded interlayer thicknesses;and(3) to optimize the microstructure of the graded material achieves reductions in critical stress components and rational stress distributions.

Design and Synthesis of Ti-ZrO_2 Functionally Graded Materials

Functionally graded materials (FGMs) based on titanium-zirconia system have been prepared by powder metallurgical method. The graded interlayer number and the compositional distribution have been designed by elastic finite element method. The interfacial microstructure between layers, the combining state of phases between Ti and ZrO2 have been investigated by means of XRD (X-ray diffraction), SEM (scanning electron microscope), EDS (energy dispersive spectrometer) and so on. The co-existing region of Ti and ZrO2 has been determined by thermodynamic calculation to control the sintering atmosphere. The experimental results show that the joint between Ti and ZrO2 phases is physical in this composite and ZrO2 mainly exists as tetragonal phase. The microstructure of Ti-ZrO2 system FGM exhibits a transition from a zirconia particle dispersion in a titanium matrix to an inverse dispersion of titanium in zirconia. The gradient structure of titanium and zirconia can relieve thermal stress.

In-situ powder mixing for laser-based directed energy deposition of functionally graded materials

The mixing of powders is a highly relevant field under additive manufacturing,however,it has attracted limited interest to date.The in-situ mixing of various powders remains a significant challenge.This paper proposes a new method utilizing a static mixer for the in-situ mixing of multiple powders through the laser-based directed energy deposition(DED)of functionally graded materials.Firstly,a powder-mixing experimental platform was established;WC and 316L powders were selected for the mixing experiments.Secondly,scanning electron microscopy,energy dispersive spectroscopy,and image processing were used to visually evaluate the homogeneity and proportion of the in-situ mixed powder.Furthermore,powder-mixing simulations were conducted to determine the powder-mixing mechanism.In the simulations,a powder carrier gas flow field and particle mixing were employed.Finally,a WC/316L metal matrix composite sample was produced using laser-based DED to verify the application potential of the static mixer.It was found that the static mixer could adjust the powder ratio online,and a response time of 1–2 s should be considered when adjusting the ratio of the mixed powder.A feasible approach for in-situ powder mixing for laser-based DED was demonstrated and investigated,creating the basis for functionally graded materials.

Multi-material additive manufacturing-functionally graded materials by means of laser remelting during laser powder bed fusion

Many processes may be used for manufacturing functionally graded materials.Among them,additive manufacturing seems to be predestined due to near-net shape manufacturing of complex geometries combined with the possibility of applying different materials in one component.By adjusting the powder composition of the starting material layer by layer,a macroscopic and step-like gradient can be achieved.To further improve the step-like gradient,an enhancement of the in-situ mixing degree,which is limited according to the state of the art,is necessary.In this paper,a novel technique for an enhancement of the in-situ material mixing degree in the melt pool by applying laser remelting(LR)is described.The effect of layer-wise LR on the formation of the interface was investigated using pure copper and low-alloy steel in a laser powder bed fusion process.Subsequent cross-sectional selective electron microscopic analyses were carried out.By applying LR,the mixing degree was enhanced,and the reaction zone thickness between the materials was increased.Moreover,an additional copper and iron-based phase was formed in the interface,resulting in a smoother gradient of the chemical composition than the case without LR.The Marangoni convection flow and thermal diffusion are the driving forces for the observed effect.

Dynamic Characteristics of Functionally Graded Timoshenko Beams by Improved Differential Quadrature Method

This study proposes an effective method to enhance the accuracy of the Differential Quadrature Method(DQM)for calculating the dynamic characteristics of functionally graded beams by improving the form of discrete node distribution.Firstly,based on the first-order shear deformation theory,the governing equation of free vibration of a functionally graded beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam axial displacement,transverse displacement,and cross-sectional rotation angle by considering the effects of shear deformation and rotational inertia of the beam cross-section.Then,ignoring the shear deformation of the beam section and only considering the effect of the rotational inertia of the section,the governing equation of the beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam transverse displacement.Based on the differential quadrature method theory,the eigenvalue problem of ordinary differential equations is transformed into the eigenvalue problem of standard generalized algebraic equations.Finally,the first several natural frequencies of the beam can be calculated.The feasibility and accuracy of the improved DQM are verified using the finite element method(FEM)and combined with the results of relevant literature.

Metallic Functionally Graded Materials:A Specific Class of Advanced Composites

Functionally graded materials, including their characterization, properties and production methods are a new rapidly developing field of materials science. The aims of this review are to systematize the basic production techniques for manufacturing functionally graded materials. Attention is paid to the principles for obtaining graded structure mainly in the metal based functionally graded materials. Several unpublished results obtained by the authors have been discussed briefly. Experimental methods and theoretical analysis for qualitative and quantitative estimation of graded properties have also been presented. The article can be useful for people who work in the field of functionally graded structures and materials, and who need a compact informative review of recent experimental and theoretical activity in this area.

A High Order Control Volume Finite Element Method for Transient Heat Conduction Analysis of Multilayer Functionally Graded Materials with Mixed Grids

This paper describes a new two-dimensional(2-D)control volume finite element method(CV-FEM)for transient heat conduction in multilayer functionally graded materials(FGMs).To deal with the mixed-grid problem,9-node quadrilateral grids and 6-node triangular grids are used.The unknown temperature and material properties are stored at the node.By using quadratic triangular grids and quadratic quadrilateral grids,the present method offers greater geometric flexibility and the potential for higher accuracy than the linear CV-FEM.The properties of the FGMs are described by exponential,quadratic and trigonometric grading functions.Some numerical tests are studied to demonstrate the performance of the developed method.First,the present CV-FEM with mixed high-order girds provides a higher accuracy than the linear CV-FEM based on the same grid size.Second,the material properties defined location is proved to have a significant effect on the accuracy of the numerical results.Third,the present method provides better numerical solutions than the conventional FEM for the FGMs in conjunction with course high-order grids.Finally,the present method is also capable of analysis of transient heat conduction in multilayer FGM.

Hot-pressed sintering of W/Cu functionally graded materials prepared from copper-coated tungsten powders

The three-layered(W-60 vol%Cu/W-40 vol%Cu/W-20 vol%Cu)W/Cu functionally graded material(FGM)containing a Cu network structure was fabricated at different temperatures by hot-pressed sintering produced from copper-coated tungsten powders.The effects of various sintering temperatures on relative density,microstructure,thermal conductivity,hardness and flexural strength were investigated.Scanning electron microscopy(SEM)and X-ray diffraction(XRD)analysis show that a Cu network extends throughout the W/Cu FGM specimens sintered at 1065℃and the graded structure can be retained perfectly,and W particles are distributed homogeneously.The low-temperature sintering densification of W/Cu FGM arises because the sintering mode of the copper-coated tungsten particles includes just sintering Cu to Cu,rather than Cu to W,Cu to Cu and W to W,as required for conventional powder particles.The relative density of W/Cu FGM sintered at 1065℃for 3 h under a load of25 MPa is 96.1%.The thermal conductivity is up to204 W·m^-1·K^-1 at normal temperature and 150 W·m^-1·K^-1at 800℃.And the Vickers hardness varies with the gradient of different layers from 3.34 to 4.05 GPa.