Nonhomogeneous Materials Research Articles

Thermoelastic analysis of nonhomogeneous structural materials with an interface crack under uniform heat flow

Many modern materials are layered material systems. Interfaces are inherent to these materials because they are heterogeneities, such as thermal and residual stresses in the elastic properties. In this paper, we study a partially insulated interface crack between two different functionally graded materials bonded to a homogeneous material subjected to a steady-state heat flux away from the crack region as well as mechanical crack surface stresses. The problem is solved under the assumption of plane strain and generalized plane stress conditions. The properties of the functionally graded materials vary as exponential function in the thickness direction. Using the Fourier transform and a superposition technique, the singular integral equations for the temperature and the displacement fields are derived. The total strain energy release rate and strain energy density are obtained. Critical parametric studies are conducted for non-homogeneity parameter, the thermal stress intensity factors and minimum strain energy density.

Optimized ultrasonic attenuation measures for non-homogeneous materials

In this paper the study of frequency-dependent ultrasonic attenuation in strongly heterogeneous materials is addressed. To determine the attenuation accurately over a wide frequency range, it is necessary to have suitable excitation techniques. Three kinds of transmitted signals have been analysed, grouped according to their bandwidth: narrowband and broadband signals. The mathematical formulation has revealed the relation between the distribution of energy in their spectra and their immunity to noise. Sinusoidal and burst signals have higher signal-to-noise ratios (SNRs) but need many measurements to cover their frequency range. However, linear swept-frequency signals (chirp) improve the effective bandwidth covering a wide frequency range with a single measurement and equivalent accuracy, at the expense of a lower SNR. In the case of highly attenuating materials, it is proposed to use different configurations of chirp signals, enabling injecting more energy, and therefore, improving the sensitivity of the technique without a high time cost. Thus, if the attenuation of the material and the sensitivity of the measuring equipment allows the use of broadband signals, the combination of this kind of signal and suitable signal processing results in an optimal estimate of frequency-dependent attenuation with a minimum measurement time.

Analysis of a propagating crack tip in orthotropic functionally graded materials

Crack tip stress and displacement fields for a propagating crack at constant velocity along a gradient in orthotropic functionally graded materials (OFGMs) with an exponential variation of the shear modulus and density are developed. The crack tip fields are obtained by using wave potentials and the Airy stress function through an asymptotic analysis. Solutions are obtained for orthotropic characteristics of two kinds. Using the stress fields, the effects of material nonhomogeneity on the stress components are investigated. In addition, contours of the constant maximum shear stress at a propagating crack tip are generated and the effects of material nonhomogeneity on the isochromatics are discussed.

Dyakonov–Tamm waves guided by the planar interface of a rugate filter and a columnar thin film

Dyakonov–Tamm waves guided by a planar interface of an anisotropic, homogeneous dielectric material, and an isotropic, periodically nonhomogeneous dielectric material was investigated in a canonical boundary-value problem. The former material was taken to be a columnar thin film (CTF) and the latter was a rugate filter. Dyakonov–Tamm waves are surface electromagnetic waves that have negligible propagation losses. In the chosen setup, multiple Dyakonov–Tamm waves of different phase speeds, degrees of localization, and spatial field profiles, but of the same frequency were found to exist. The effect of direction of propagation with respect to the morphologically significant plane of the CTF, the phase and the amplitude of modulation of the rugate filter was investigated. The number of Dyakonov–Tamm waves depends on the direction of propagation with respect to the morphologically significant plane of the CTF. The relative wavenumber and the degree of localization of the Dyakonov–Tamm waves increase with an increase in the amplitude of modulation of the rugate filter.

Effects of rotary inertia shear deformation and non-homogeneity on frequencies of beam

In the present study, separate and combined effects of rotary inertia, shear deformation and material non-homogeneity (MNH) on the values of natural frequencies of the simply supported beam are examined. MNH is characterized considering the parabolic variations of the Young's modulus and density along the thickness direction of the beam, while the value of Poisson's ratio is assumed to remain constant. At first, the equation of the motion including the effects of the rotary inertia, shear deformation and MNH is provided. Then the solutions including frequencies of the first three modes for various combinations of the parameters of the MNH, depth to length ratios, and shear corrections factors are reported. To show the accuracy of the present results, two comparisons are carried out and good agreements are found.

The Influence of Non-Homogeneous Material Propertieson ElasticWave Propagation in Fluid-Filled Boreholes

The Influence of Non-Homogeneous Material Propertieson ElasticWave Propagation in Fluid-Filled Boreholes

Effect of non-homogeneity on asymmetric vibrations of non-uniform circular plates

This paper investigates asymmetric vibrations of non-homogeneous circular plates of parabolically varying thickness on the basis of classical plate theory. The non-homogeneity of the plate material is assumed to arise due to exponential variation in Young’s modulus as well as density along radial direction in distinct manner. First three natural frequencies of clamped, simply supported and free plates have been obtained using Ritz method. The basis functions have been chosen as polynomial co-ordinate functions satisfying the essential boundary conditions. Thereafter, the effects of taper parameter, non-homogeneity parameter, density parameter and nodal diameter have been analysed for first three modes of vibration. The results obtained are compared with those available in literature for homogeneous and non-homogeneous plates.

Wear Behaviour and Cutting Performance of Surfaced Inserts for Wood Machining

achining, in general, and wood machining, in particular, is a complex to explain and describe many influencing factors. Natural wood is nonhomogeneous biological material, so each species of wood requires different machining conditions and tools. Understanding of wood properties, proper selection of cutting tools and machining parameters provides possibilities to improve quality of wooden products, to increase production efficiency, and to improve machining. The aim of this works was to find the most suitable cutting tools for machining of oak wood grown in Lithuania. This paper cover tests of two commercial cutting inserts made of high speed tool steel (CT01M-LA2 and 8X6FT) and two experimental inserts (EI) made by surfacing using submerged arc welding (SAW) technique and mixture of alloying elements spread on the surface under the industrial flux. Results of conducted milling tests demonstrated the suitability of suggested surfaced inserts for machining oak wood. All tool wear parameters have been evaluated and compared, such as cutting edge radius, edge recession, nose width, and cutting power. Cutting edge radius of EI after 3200 m of cutting length was ~ 4.00 μm, 3 – 4 times lower than wear of standard tool, while edge recession of surfaced inserts showed 2 – 3 times lower results. Received results confirmed that the cutting power increases on growing of feed per cutter. Surfaced inserts can replace commercial inserts used for wood machining.

Mode III stress intensity factor in two-dimensional functionally graded material with lengthwise linearly varying properties

Mode III fracture is considered in a two-dimensional functionally graded material with an internal crack. The material properties are assumed to vary linearly along two planar directions. The problem has been analyzed via two different methods. Primarily, the governing partial differential equations are derived, and using the method of separating variables and Hankel transforms, the equations are solved. Then, finite element technique is employed to analyze the problem. The effects of material non-homogeneity on the value of stress intensity factor are studied. Finally, the obtained stress intensity factors, calculated by two different methods, are compared.

Dyakonov–Tamm waves-based optical sensing using sculptured nematic thin film

Dyakonov–Tamm (DT) waves are highly sensitive to the constitutive properties of the partnering materials near the interface. DT waves are excited at the interface of two dielectric materials of which at least one is anisotropic and periodically nonhomogeneous normal to their interface. Sculptured nematic thin film (SNTF) is a good candidate for the periodically nonhomogeneous dielectric partner for optical sensing of a fluid due to its porosity. The nanoscale parameters of an uninfiltrated SNTF obtained from the inverse Bruggeman homogenization formalism were used in the forward Bruggeman homogenization formalism to determine the constitutive parameters for the infiltrated SNTF. The sensitivity of DT waves to the refractive index was analyzed for two possible sensing modalities and it was found that the sensitivity was comparable to that of the chiral sculptured thin films (STFs) made of the same material as of the SNTF. This implies that the sensing with DT waves is robust, is independent of the morphology of the partnering nonhomogeneous dielectric material and could make the sensing easier since SNTFs are easier to fabricate than the chiral STFs.

Group and Phase Velocity of Love Waves Propagating in Elastic Functionally Graded Materials

AbstractThis paper presents a theoretical study of the propagation behaviour of surface Love waves in nonhomogeneous functionally graded elastic materials, which is a vital problem in acoustics. The elastic properties (shear modulus) of a semi-infinite elastic half-space vary monotonically with the depth (distance from the surface of the material). Two Love wave waveguide structures are analyzed: 1) a nonhomogeneous elastic surface layer deposited on a homogeneous elastic substrate, and 2) a semi-infinite nonhomogeneous elastic half-space. The Direct Sturm-Liouville Problem that describes the propagation of Love waves in nonhomogeneous elastic functionally graded materials is formulated and solved 1) analytically in the case of the step profile, exponential profile and 1cosh2type profile, and 2) numerically in the case of the power type profiles (i.e. linear and quadratic), by using two numerical methods: i.e. a) Finite Difference Method, and b) Haskell-Thompson Transfer Matrix Method.The dispersion curves of phase and group velocity of surface Love waves in inhomogeneous elastic graded materials are evaluated. The integral formula for the group velocity of Love waves in nonhomogeneous elastic graded materials has been established. The results obtained in this paper can give a deeper insight into the nature of Love waves propagation in elastic nonhomogeneous functionally graded materials.

Gradient estimates in generalized Morrey spaces for parabolic operators

We obtain global regularity in generalized Morrey spaces for the gradient of the weak solutions to divergence form linear parabolic operators with measurable data. Assuming partial BMO smallness of the coefficients and Reifenberg flatness of the boundary of the underlying domain, we develop a Calderón‐Zygmund type theory for such operators. Problems like the considered here arise in the modeling of composite materials and in the mechanics of membranes and films of simple nonhomogeneous materials which form a linear laminated medium.

Thermoelastic analysis of non-uniform pressurized functionally graded cylinder with variable thickness using first order shear deformation theory(FSDT) and perturbation method

Recently application of functionally graded materials(FGMs) have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.

Nonlinear dynamic response and damage analysis for functionally graded metal shallow spherical shell under low-velocity impact

The nonlinear dynamic response and damage evolution of functionally graded shallow spherical shell under low-velocity impact are investigated in this work. Basing on continuum damage theory, a damage constitutive relation is established for functionally graded material and the Kachanov damage evolution law is adopted to predict the damage propagation in the structure. A modified contact model suitable for non-homogenous material (functionally graded material) is applied to model the contact force in impacting process. The laminated modeling method is adopted to model the functionally graded shell with varying material constants along the thickness by dividing the shell to N plies with the constant material properties for each ply. With the established damage constitutive relations and nonlinear geometric relations of FGM shallow spherical shell with elastic modulus varying as a power-law function, the nonlinear motion equations of FGM shallow spherical under low-velocity impact have been obtained in the term of displacement functions. The problems are solved by using the orthogonal collocation point method, the Newmark method and the iterative method synthetically. Some numerical examples are carried out to validate present impacting model and the calculating methods, and parametrical analysis are presented to discuss the effects of the material properties, the geometrical size and impacting velocity on damage state and dynamic response of the structure when under low-velocity impact.

Rolling induced size effects in elastic–viscoplastic sheet metals

Rolling processes for which the characteristic length scale reaches into the range where size effects become important are receiving increased interest. In particularly, this is owed to the roll-molding process under development for high-throughput of micron-scale surface features. The study presented revolves around the rolling induced effect of visco-plasticity (ranging hot and cold rolling) in combination with strain gradient hardening – including both dissipative and energetic contributions. To bring out first order effects on rolling at small scale, the modeling efforts are limited to flat sheet rolling, where a non-homogeneous material deformation takes place between the rollers. Large strain gradients develop where the rollers first come in contact with the sheet, and a higher order plasticity model is employed to illustrate their influence at small scales. The study reveals that the energetic length parameter has negligible effect on the rolling quantities of interest, while the contribution coming from the dissipative length parameter can be dominant. Considering a slow and a fast moving sheet, respectively, convergence towards the rate independent limit is demonstrated, and a characteristic velocity is identified, for which the torque and punch force applied to the roller becomes independent of the material rate-sensitivity.

Conditions of Single-Valuedness of Rotation and Displacements for Non-Homogeneous Materials in Plane Thermoelasticity

The conditions of single-valuedness of rotation and displacements in the multiply connected regions for non-homogeneous materials are discussed theoretically by using the stress function. As an example of a multiply connected region, we have considered the steady thermal stresses in a functionally graded hollow circular body with an eccentric outer circular boundary. The material properties are expressed by the power law of the radius of the inner circle. The inner boundary conditions are satisfied strictly, whereas the outer boundary conditions are satisfied numerically using a point-matching method. Steady thermal stresses in the body are shown for ZrO2/Ti-6Al-4 V functionally graded materials (FGMs). The results were verified by comparing with those of a functionally graded hollow circular cylinder.

Influence of steel fibre on micropore structure of concrete

As a kind of non-homogeneous porous material, the strength and durability (impermeability, freeze resistance, carbonisation resistance, etc.) of concrete are affected by the inherent micropore structure. In this paper, the micropore structure of steel fibre reinforced concrete was analysed by mercury intrusion pore and scanning electron microscope, and the effect of fibre content (0–2%) on the micropore structure of concrete was also studied. Then, the effects of fibre content on the mechanical property and durability of concrete were summarised based on the fibre content: the micropore structure turns out to be better when the steel fibre content increases from 0 to 1·5%. However, the micropore structure will change for the worse because of the increase of large pore when the fibre content increases to 2%.

Generalized domain-independent interaction integral for solving the stress intensity factors of nonhomogeneous materials

The generalized domain-independent interaction integral (DII-integral) is investigated due to its extremely promising application in solving the stress intensity factors (SIFs) of nonhomogeneous materials with complex interfaces. A recent study revealed that the DII-integral, which is domain-independent for material interfaces, can be established by defining an appropriate auxiliary field. Regrettably, the kind of auxiliary field that can be used is not very clear. This work first discusses the conditions that the auxiliary field must satisfy for establishing a DII-integral and provides a framework for designing more applicable auxiliary fields. In this framework, a generalized auxiliary field and the corresponding generalized DII-integral are derived. The generalized auxiliary field contains two free constants and can be expressed as the linear combination of a widely used auxiliary field and a new auxiliary field, which are referred to as the crack face traction-free auxiliary field and the zero mean stress auxiliary field, respectively. The generalized auxiliary field is effective in establishing the DII-integral for purely mechanical loading, and the zero mean stress auxiliary field is also effective in the establishment of the DII-integral for isotropic mismatch strain problems. The generalized DII-integral is the linear function of mode-I and mode-II SIFs and its expression does not involve the free constants in the generalized auxiliary field. Then, a patched extended finite element method (XFEM) is briefly introduced to remove the crack-tip enrichment and instead employ a patched mesh in the modeling. The patched XFEM does not depend on the material constitutive relations and thus has a larger applicable scale than does the traditional XFEM. Finally, the DII-integral combined with the patched XFEM is employed to investigate four representative crack problems. Numerical examples show that the generalized DII-integral exhibits good domain-independence for homogeneous, nonhomogeneous, and discontinuous properties. Although the numerical values of the DII-integral do not remain constant for different values of the free constants due to numerical errors, good numerical precision can be achieved if the free constants do not deviate too much from those used in the crack face traction-free auxiliary field. In addition, the DII-integral using the zero mean stress auxiliary field is demonstrated to be reliable and convenient in solving the SIFs of particulate composites under an initial thermal strain.

Effects of gradient density on effective heat capacity of charring ablative material for re-entry vehicles

Purpose – The effective heat capacity is a key index to estimate the thermal protection performance of charring ablative materials in reentry vehicles subjected to aerodynamic heat loads. The purpose of this paper is to investigate the effects of gradient density on the effective heat capacity. Design/methodology/approach – Based on the Fourier law and the pyrolysis interface model, the authors establish the governing equations for the transient heat conduction with variable density, and then simulate one-dimensional transient thermal behavior of a homogeneous and three types of non-homogeneous charring ablative material in reentry capsules by using the implicit numerical method. Findings – The moving rate of pyrolysis interface and the surface temperature of charring ablative material depend on not only the surface heating history, but also the gradient density. And the gradient density can improve the insulation performance of charring materials, e.g. the effective heat capacity in the bilinear design is larger than that in the homogeneous design under a given heat flux condition. Originality/value – This study will help the design of the thermal protection system in reentry vehicles.

Damping in composite materials: Properties and models

The present review aims at gathering the available literature on damping in composite materials. A chronological review of test methods for damping estimation is presented in order to describe the time-line of the theoretical knowledge development in this field. In the last years many new material configurations have emerged that deserve investigation, such as nano-composites, hybrid laminates and sandwich materials. Damping models specifically meant for non-homogeneous materials are reported to provide a background for understanding this problem. Although not widely exploited yet, fibre reinforced polymers has the potential to be tailored for damping by acting on constituents, geometry and boundary conditions. Nano-composites, for instance, are shown to possess a high potential for damping purposes. New hybrid and sandwich-type structures are emerging as noise and vibration control solutions in lightweight applications. The effort devoted to mathematical and numerical model in view of Finite Element integration of damping properties is also addressed. Finally, the conclusions summarise the ideas of the authors on needed steps to advance the state-of-the-art in each of the described topic.