Rheological Behaviour for Polymer Melts and Concentrated SolutionsPart Ⅱ: Material Function with Nagai Chain Constraints and Determination of Their Parameters from Flow Curves

An integral constitutive equation and a set of material functions for describing the strain history of polymer melts were formulated in terms of the Cauchy-Green and Finger tensors. A simple memory function and the dependence of ηo and τt on M3.4 were derived from the theory of non-linear viscoelasticity with constraints of entanglements for polymer melts and substituted into the Oldroye-Walters-Fredickson constitutive equation. An integral constitutive equation for polymer melts was consequently obtained. Some material functions of the constitutive equation related to certain 'test flow' are examined as follows : (1) simple steady shear flow; (2) steady elongation flow; (3) small-amplitude oscillatory shear flow; (4) stress growth upon the inception of steady shear elongation flow; (5) stress relaxation (modulus and compllance). These theoretical relations for simple steady shear flow were compared with experimental data from our laboratory and references for various polymer melts and concentrated solutions. A good agreement between the theory and experiment was achieved.

Transfer matrix method for free and forced vibrations of multi-level functionally graded material stepped beams with different boundary conditions

Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method.Under the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable approach.Then,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are presented.To demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also given.On this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out.The results show the accuracy and efficiency of the TMM.

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 action mechanisms and structures designs of F-containing functional materials for high performance oxygen electrocatalysis

Non-renewable fossil fuels have led to serious problems such as global warming,environmental pollution,etc.Oxygen electrocatalysis including oxygen reduction reaction(ORR)and oxygen evolution reaction(OER)plays a central role in clean energy conversion,enabling a number of sustainable processes for future air battery technologies.Fluorine,as the most electronegative element(4.0)not only can induce more efficient regulation for the electronic structure,but also can bring more abundant defects and other novel effects in materials selection and preparation for favorable catalysis with respect to the other nonmetal elements.However,an individual and comprehensive overview of fluorine-containing functional materials for oxygen electrocatalysis field is still blank.Therefore,it is very meaningful to review the recent progresses of fluorine-containing oxygen electrocatalysts.In this review,we first systematically summarize the controllable preparation methods and their possible development directions based on fluorine-containing materials from four preparation methods.Due to the strong electron-withdrawing properties of fluorine,its control of the electronic structure can effectively enhance the oxygen electrocatalytic activity of the materials.In addition,the catalytic enhancement effect of fluorine on carbonbased materials also includes the prevent oxidation and the layer peeling,and realizes the precise atomic control.And the catalytic improvement mechanism of fluorine containing metal-based compounds also includes the hydration of metal site,the crystal transformation,and the oxygen vacancy induction.Then,based on their various dimensions(0D–3D),we also have summarized the advantages of different morphologies on oxygen electrocatalytic performances.Finally,the prospects and possible future researching direction of F-containing oxygen electrocatalysts are presented(e.g.,novel pathways,advanced methods for measurement and simulation,field assistance and multi-functions).The review is considered valuable and helpful in exploring the novel designs and mechanism analyses of advanced fluorine-containing electrocatalysts.

Crystalline framework nanosheets as platforms for functional materials

The integration of organic and inorganic materials has been widely used in various applications to generate novel functional nanomaterials characterized by unique properties.Functional crystalline framework nanosheets and their synergistic effects have been studied recently for possessing the advantages of functional species as well as crystalline framework nanosheets.Hence,we have focused on the preparation methods and applications of functional crystalline framework nanosheets in this review.We introduced crystalline framework nanosheets and discussed the importance of integrating functional species with nanosheets to form functional crystalline framework nanosheets.Then,two aspects of the preparation methods of functional crystalline framework nanosheets were reviewed:in situ synthesis and post-synthesis modification.Subsequently,we discussed the properties of the crystalline framework nanosheets combined with various functional species and summarized their applications in catalysis,sensing,separation,and energy storage.Finally,we have shared our insights on the challenges of functional crystalline framework nanosheets,hoping to contribute to the knowledge base for optimizing the preparation methods,expanding categories,improving stability,and exploring potential applications.

Complete solutions for elastic fields induced by point load vector in functionally graded material model with transverse isotropy

The paper develops and examines the complete solutions for the elastic field induced by the point load vector in a general functionally graded material(FGM)model with transverse isotropy.The FGMs are approximated with n-layered materials.Each of the n-layered materials is homogeneous and transversely isotropic.The complete solutions of the displacement and stress fields are explicitly expressed in the forms of fifteen classical Hankel transform integrals with ten kernel functions.The ten kernel functions are explicitly expressed in the forms of backward transfer matrices and have clear mathematical properties.The singular terms of the complete solutions are analytically isolated and expressed in exact closed forms in terms of elementary harmonic functions.Numerical results show that the computation of the complete solutions can be achieved with high accuracy and efficiency.

Research progress and application prospect of functional adhesive materials in the field of oil and gas drilling and production

By summarizing the composition,classification,and performance characterization of functional adhesive materials,the adhesion mechanisms of functional adhesive materials,such as adsorption/surface reaction,diffusion,mechanical interlocking,and electrostatic adsorption,are expounded.The research status of these materials in oil and gas drilling and production engineering field such as lost circulation prevention/control,wellbore stabilization,hydraulic fracturing,and profile control and water plugging,and their application challenges and prospects in oil and gas drilling and production are introduced comprehensively.According to the applications of functional adhesive materials in the field of oil and gas drilling and production at this stage,the key research directions of functional adhesive materials in the area of oil and gas drilling and production are proposed:(1)blending and modifying thermoplastic resins or designing curable thermoplastic resins to improve the bonding performance and pressure bearing capacity of adhesive lost circulation materials;(2)introducing low-cost adhesive groups and positive charge structures into polymers to reduce the cost of wellbore strengthening agents and improve their adhesion performance on the wellbore;(3)introducing thermally reversible covalent bond into thermosetting resin to prevent backflow of proppant and improve the compressive strength of adhesive proppant;(4)introducing thermally reversible covalent bonds into thermoplastic polymers to improve the temperature resistance,salt-resistance and water shutoff performance of adhesive water shutoff agents.

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.

DESIGN AND PROPERTIES OF A FUNCTIONALLY GRADIENT CERAMIC TOOL MATERIAL

Based on the analyses of the severity of cutting process as well as the failure mechanisms of ceramic tools, a model for designing functionally gradient ceramic tool materials with symmetrical distribution is presented, by which a Al 2O 3/(W,Ti)C ceramic tool material FG 2 was developed. Multi objective optimization method was employed in designing the compositional distribution of this ceramic tool material. The results of both continuous and intermittent cutting tests are indicative of the much better cutting behavior of the functionally gradient ceramic tool FG 2 than that of the common ceramic tool SG 4.

Functional porous carbon-based composite electrode materials for lithium secondary batteries

The synthetic routes of porous carbons and the applications of the functional porous carbon-based composite electrode materials for lithium secondary batteries are reviewed. The synthetic methods have made great breakthroughs to control the pore size and volume, wall thickness, surface area, and connectivity of porous carbons, which result in the development of functional porous carbon-based composite electrode materials. The effects of porous carbons on the electrochemical properties are further discussed. The porous carbons as ideal matrixes to incorporate active materials make a great improvement on the electrochemical properties because of high surface area and pore volume, excellent electronic conductivity, and strong adsorption capacity. Large numbers of the composite electrode materials have been used for the devices of electrochemical energy conversion and storage, such as lithium-ion batteries （LIBs）, Li-S batteries, and Li-O2 batteries. It is believed that functional porous carbon-based composite electrode materials will continuously contribute to the field of lithium secondary batteries.

Solution-based Chemical Strategies to Purposely Control the Microstructure of Functional Materials

Micro/nanostructured crystals with controlled architectures are desirable for many applications in optics, electronics, biology, medicine, and energy conversions. Low-temperature, aqueous chemical routes have been widely investigated for the synthesis of particles, and arrays of oriented nanorods and nanotubes. In this paper, based on the ideal crystal shapes predicted by the chemical bonding theory, we have developed some potential chemical strategies to tune the microstructure of functional materials, ZnS and Nb205 nanotube arrays, MgO wiskers and nestlike spheres, and cubic phase Cu2O microcrystals were synthesized here to elucidate these strategies. We describe their controlled crystallization processes and illustrate the detailed key factors controlling their growth by examining various reaction parameters. Current results demonstrate that our designed chemical strategies for tuning microstructure of functional materials are applicable to several technologically important materials, and therefore may be used as a versatile and effective route to the controllable synthesis of other inorganic functional materials.

The Influence of Mineral Functional Materials on Chloride Ion Penetration of Concrete

The mechanism of chloride ion penetration in high performance concrete was analy zed. The experimental results indicate that there are two important reasons that influence the anti-chloride penetration of high performance concrete. One is the function effect of mineral functional material, so that it increases conc rete's capability to resist chloride ion penetration. The other is combined acti on of mineral functional material's original capability of binding the chloride ion (physical adsorption) and physicochemical adsorption after hydration.

NVESTIGATION OF PRODUCTOPN OF FUNCTIONALLY GRADIENT MATERIAL BY ELECTROLESS PLATING

Thispaper proposed a new methodof producing Ceramic/ Metalfunctionally gradient mate rialby electroless platingtechnique. The experimentof producing SiC/ Ni PFGM wascar ried out with self made electroless plating facilities. The results show that the thickness of FGMcoating andthegradientdistribution ofcompositioncanbecontrolled byoptimizingelec trolessplating technology and changing the parameters such as plating time, the additionspeed and concentration of SiCparticles. Analysisdemonstratesthatthereisastrongrelation ship amongthe SiCcontent,the microstructureandthe mechanicalproperty ofthe FGM.

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.

Free vibration of functionally graded material beams with surface-bonded piezoelectric layers in thermal environment

Free vibration of statically thermal postbuckled functionally graded material （FGM） beams with surface-bonded piezoelectric layers subject to both temperature rise and voltage is studied. By accurately considering the axial extension and based on the Euler-Bernoulli beam theory, geometrically nonlinear dynamic governing equations for FGM beams with surface-bonded piezoelectric layers subject to thermo-electro- mechanical loadings are formulated. It is assumed that the material properties of the middle FGM layer vary continuously as a power law function of the thickness coordinate, and the piezoelectric layers are isotropic and homogenous. By assuming that the amplitude of the beam vibration is small and its response is harmonic, the above mentioned non-linear partial differential equations are reduced to two sets of coupled ordinary differential equations. One is for the postbuckling, and the other is for the linear vibration of the beam superimposed upon the postbuckled configuration. Using a shooting method to solve the two sets of ordinary differential equations with fixed-fixed boundary conditions numerically, the response of postbuckling and free vibration in the vicinity of the postbuckled configuration of the beam with fixed-fixed ends and subject to transversely nonuniform heating and uniform electric field is obtained. Thermo-electric postbuckling equilibrium paths and characteristic curves of the first three natural frequencies versus the temperature, the electricity, and the material gradient parameters are plotted. It is found that the three lowest frequencies of the prebuckled beam decrease with the increase of the temperature, but those of a buckled beam increase monotonically with the temperature rise. The results also show that the tensional force produced in the piezoelectric layers by the voltage can efficiently increase the critical buckling temperature and the natural frequency.

DIRECT AND ADAPTIVE SLICING ON CAD MODEL OF IDEAL FUNCTIONAL MATERIAL COMPONENTS (IFMC)

A brand new direct and adaptive slicing approach is proposed, which canapparently improve the part accuracy and reduce the building time. At least two stages are includedin this operation: getting the crossing contour of the cutting plane with the solid part anddetermining the layer thickness. Apart from usual SPI algorithm, slicing of the solid model has itsspecial requirements. Enabling the contour line segments of the cross-section as long as possible isone of them, which is for improving manufacturing efficiency and is reached by adaptively adjustingthe step direction and the step size at every crossing point to obtain optimized secant height. Thelayer thickness determination can be divided into two phases: the geometry-based thicknessestimation and the material-based thickness verifying. During the former phase, the geometrytolerance is divided into two parts: a variety of curves are approximated by a circular arc, whichintroduces the first part, and the deviation error between the contour line in LM process and thecircular arc generates the second part. The latter phase is mainly verifying the layer thicknessestimated in the former stage and determining a new one if necessary. In addition, an example usingthis slicing algorithm is also illustrated.

Crack tip field in functionally gradient material with exponential variation of elastic constants in two directions

This paper presents an exact solution of the crack tip field in functionally gradient material with exponential variation of elastic constants. The dimensionless Poisson＇s ratios v0 of the engineering materials （iron, glass …… ） are far less than one; therefore, neglecting them, one can simplify the basic equation and the exact solution is easy to obtain. Although the exact solution for the case v0 ≠ 0 is also obtained, it is very complicated and the main result is the same with the case v0 = 0 （it will be dealt with in Appendix VII）. It has been found that the exponential term exp（ax ＋ by） in the constitutive equations becomes exp（ ax /2 ＋ by/2- kr /2 ） in the exact solution.

Development of Mathematical Model on Preparation of Functionally Graded Material by Co-sedimentation

From the process of sedimentation the mathematical relationships among deposition volume and powder properties as well as sedimentation parameters were deduced. Based on the formula a mathematical model was set up and simulated through the computer. At last the validity of mathematical model was supported by the representative experiment on Ti-Mo system FGM prepared by co-sedimentation.

Generalized thermoelastic interaction in functional graded material with fractional order three-phase lag heat transfer

The present work is concerned with the solution of a problem on thermoelastic interactions in a functional graded material due to thermal shock in the context of the fractional order three-phase lag model. The governing equations of fractional order generalized thermoelasticity with three-phase lag model for functionally graded materials(FGM)(i.e., material with spatially varying material properties) are established. The analytical solution in the transform domain is obtained by using the eigenvalue approach.The inversion of Laplace transform is done numerically. The graphical results indicate that the fractional parameter has significant effects on all the physical quantities. Thus, we can consider the theory of fractional order generalized thermoelasticity an improvement on studying elastic materials.