Elastic characterization of CVD diamond by static and dynamic measurements

The present paper describes two different nondestructive approaches for the direct identification of the elastic constants of thin square isotropic plates. First a static method is presented, by which the identification of the Young's modulus and Poisson's ratio is carried out by the full field measurement of the out-of-plane displacements detected on the upper surface of the plate in two biaxial bending tests. Then a dynamic method is illustrated, by which the elastic constants are determined from two different natural frequency of a free vibrating plate. Both techniques, previously verified on a carbon steel specimen, have been applied to a CVD diamond specimen; a comparison between the two approach is reported and the influence of the measurement errors is also discussed.     

First‐Principles Study of Elastic,Structural, Electronic,Thermodynamical, and Optical Properties of Yttria (Y2O3) Ceramic in Cubic Phase

Structural, elastic, optical, thermodynamical, and electronic properties of yttrium oxide compound in cubic phase have been studied using the full‐potential augmented plane waves (FP‐LAPW) within density functional theory (DFT) framework. Four different approximations were used for exchange‐correlation potentials terms, comprised Perdew–Burke–Ernzerhof generalized parameterization of gradient approximation (GGA‐PBE), Wu–Cohen (WC‐GGA), local‐density approximation (LDA), and new approximation modified Becke and Johnson (mBJ‐GGA). The structural properties such as equilibrium lattice parameter, bulk modulus and its pressure derivative have been obtained using optimization method. Moreover, Elastic constants, Young's modulus, shear modulus, Poisson's ratio, sound velocities for longitudinal and shear waves, Debye average velocity, Debye temperature, and Grüneisen parameters have been calculated. Obtained structural, elastic and other parameters are consistent with experimental data. Moreover pressure dependence of the elastic moduli was studied. From electronic calculations, it has been found that the band gap was 5.7 eV at Г point in the Brillouin zone using mBJ‐GGA approximation. Optical properties, such as the dielectric function, refractive index, extinction index, and optical band gap, were calculated for radiation up to 14 eV. In addition, the unique type of bonding in Y₂O₃ was discussed by three method including effective charge, B/G ratio, and charge density distribution.     

Linear thermoelastic characterization of anisotropic poly(ethylene terephthalate) films

All nine independent elastic constants have been determined for a biaxially stretched poly(ethylene terephthalate) (PET) film using novel mechanical methods. The orthotropic directions and the in‐plane Poisson's ratios were first characterized using vibrational holographic interferometry of tensioned membrane samples. The out‐of‐plane Poisson's ratio was obtained by measuring the change in tension with the change in pressure for constant strain conditions. Pressure–volume–temperature (PVT) equipment was used to measure the bulk compressibility as well as the volumetric thermal expansion coefficient (TEC). The in‐plane Young's moduli were obtained by tensile tests, while the out‐of‐plane modulus was calculated from the compressibility and other elastic constants that describe the in‐plane behavior. The in‐plane TECs in the machine and transverse directions were determined using a thermal mechanical analyzer (TMA). The out‐of‐plane TEC was determined using these values and the volumetric TEC determined via PVT. The resulting compliance matrix satisfies all of the requirements of a positive‐definite energy criterion. The procedure of characterization utilized in this article can be applied to any orthotropic film. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 2937–2947, 2002     

Effective properties of cellular materials

This paper considers the effective properties of cellular materials. The present approach and some earlier proposed methods are compared and discussed. The main effort is placed upon the continuum mechanics approaches' ability to predict effective elastic properties. It is shown that two methods are distinctly better, namely a slight modification of the Mori‐Tanaka approach and a new approach by Dvorak and Srinivas, which is shown to predict the Young's modulus and shear modulus of the Divinycell H‐grade PVC foam almost exactly.     

A comparative study of physical properties in Fe3O4 nanoparticles prepared by coprecipitation and citrate methods

Magnetite exhibits unique structural, electronic, and magnetic properties in extreme conditions that are of great research interest. In this work, the effects of preparation technique on X‐ray peak broadening, magnetic and elastic moduli properties of Fe₃O₄ nanoparticles prepared by coprecipitation (FcP‐NPs) and citrate (FC‐NPs) methods have been investigated. The structural characterization of the samples is evidence for a cubic structure with Fd‐3m space group. The Williamson‐Hall analysis was used to study crystallite sizes and lattice strain of the samples and also stress and energy density. In addition, the crystallite sizes are compared with the particle sizes and the magnetic core sizes obtained from TEM and VSM methods, respectively. In addition, the cation distribution obtained from calculated inversion parameter indicate that in the smaller particles, more amount of Fe²⁺ on the tetrahedral sites can be related to higher stress induced in the FcP‐NPs compared to the FC‐NPs. The saturation magnetization of the FcP‐NPs is almost two times bigger than the saturation magnetization of the FC‐NPs. It could be attributed to the decrease in the negative interaction on the octahedral site and also the magnetic moment on the tetrahedral site of the FcP‐NPs. The increase in force constants of the FC‐NPs determined by infrared spectra analysis compared to FcP‐NPs suggests the strengthening of their interatomic bonding. The values of shear and longitudinal wave velocities obtained from force constants have been used to determine the values of Young's modulus, rigidity modulus, bulk modulus, and Debye temperature. By comparison of the elastic results of FC‐NPs with the FcP‐NPs, we can observe that the elastic properties of the F‐NPs have been improved by synthesis method, while Poisson's ratio almost remains constant. In addition, using the values of the compliance s_ij obtained from elastic stiffness constants, the values of Young's modulus and Poisson's ratio along the oriented direction [hkl] have been calculated for the samples.     

The determination of the axial Young's modulus of honeycomb specimens under bending

For solid specimens, Young's modulus is commonly determined from straightforward uniaxial tension experiments. However, honeycomb specimens are far more challenging to test in tension, and it is therefore desirable to conduct bending experiments to determine Young's modulus. The premise of this work is that the bending response of honeycomb specimens may be significantly different from that of solid specimens, and therefore it is necessary to establish a sound protocol for the determination of the axial Young's modulus of honeycomb specimens under bending. Toward this goal, we present results of a study that combines experimental, finite element simulation, and classical beam theory approaches. These results confirm that accurate measurements of Young's modulus of honeycombs require careful consideration of the specimen geometry and analysis of the data. We demonstrate that the use of conventional Bernoulli‐Euler's beam theory to interpret the data requires very slender specimens. We also show that less slender specimens can be used if the experimental data is interpreted on the basis of three‐dimensional elasticity theory and numerical simulations. A third option is to use a combination of moderately slender specimens and Timoshenko's beam theory.     

The effect of aspect ratio of inclusions on the elastic properties of unidirectionally aligned composites

This paper examines the influence of aspect ratio α, from zero to infinity, on the effective elastic moduli of a transversely isotropic composite. The reinforcing inclusions, which could be flakes or short fibers, are assumed to be spheroidal and unidirectionally aligned. Of the five independent elastic constants, the longitudinal Young's modulus E₁₁ and in-plane shear modulus μ₁₂ appear to increase with increasing aspect ratio, while the transverse Young's modulus E₂₂, out-plane shear modulus μ₂₃, and plane-strain bulk modulus K₂₃, generally decrease. It is further noted that E₁₁ is more sensitive to α when α > 1 but the others are more so when α < 1. The present analysis was carried out by the combination of Eshelby's and Mori-Tanaka's theories of inclusions.     

Matrix influence on the piezoelectric properties of piezoelectric ceramic/polymer composite exhibiting particle alignment

This study was addressed to the influence of an electric field strength applied at fabrication process and matrix properties, such as the dielectric constant and the Young's modulus, on “pseudo‐1‐3 piezoelectric ceramic/polymer composite” in order to further enhance the piezoelectricity of that. The pseudo‐1‐3 piezoelectric ceramic/polymer composite consists of linearly ordered piezoelectric ceramic particles in polymer material. Silicone gel, silicone rubber, urethane rubber, and poly‐methyl‐methacrylate, which exhibit different dielectric constants and Young's modulus, were used as matrices to evaluate the matrix influence. The piezoelectricity of the pseudo‐1‐3 piezoelectric ceramic/polymer composite was evaluated using the piezoelectric strain constant d₃₃. The d₃₃ is one of the indices of the piezoelectric properties for piezoelectric materials. As a result, it was confirmed that d₃₃ of the pseudo‐1‐3 piezoelectric ceramic/polymer composite increased with the increase of the electric filed strength applied at fabrication process, though, it reached a constant value at a certain strength value. Further it was confirmed that dielectric constant of the matrix had a small influence on d₃₃ of the pseudo‐1‐3 piezoelectric ceramic/polymer composite, however, in case of matrix of lower Young's modulus, d₃₃ was increase. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 41817.     

Intrinsic Mechanical Properties of 20 MAX‐Phase Compounds

The intrinsic mechanical properties of 20 MAX‐phase compounds are calculated using an ab initio method based on density functional theory. A stress versus strain approach is used to obtain the elastic coefficients and thereby obtain the bulk modulus, shear modulus, Young's modulus, and Poisson's ratio based on the Voigt–Reuss–Hill (VRH) approximation for polycrystals. The results are in good agreement with available experimental data. It is shown that there is an inverse correlation between Poisson's ratio and the Pugh ratio of shear modulus to bulk modulus in MAX phases. Our calculations also indicate that two MAX compounds, Ti₂AsC and Ti₂PC, show much higher ductility than the other compounds. It is concluded that the MAX‐phase compounds have a wide range of mechanical properties ranging from very ductile to brittle with the “A” in the MAX phase being the most important controlling element. The measured Vickers hardness in MAX compounds has no apparent correlation with any of the calculated mechanical parameters or their combinations.     

Determination of matrix-dominated mechanical properties of fiber composite lamina

A test methodology that utilizes unidirectional, hoop-wound tubes to determine matrix-dominated mechanical properties of unidirectional fiber composite lamina is described. Longitudinal shear modulus and strength as well as transverse Young's modulus, transverse tensile strength, and transverse compressive strength are obtained from a single thin-walled tube specimen and fixturing design. Data presented for two carbon-fiber-reinforced epoxy composite materials illustrate the simplicity and precision of the described procedure.     

Energy consistent modified molecular structural mechanics model for the determination of the elastic properties of single wall carbon nanotubes

A new, modified molecular structural mechanics model for the determination of the elastic properties of carbon nanotubes is presented. It is designed specifically to overcome drawbacks in existing molecular structural mechanics models, which are not consistent with their underlying chemical force fields in terms of energy. As a result, modifications are motivated, developed and implemented in order to create a new, energy consistent molecular structural mechanics model. Hence, the new model leads to a better prediction of the material parameters for single wall carbon nanotubes, while the simple applicability of the approach is maintained. The results calculated for the elastic constants (Young's modulus, Poisson ratio) of armchair and zig-zag CNTs are given and discussed. Both elastic constants were found to be dependent on the chirality as well as on the carbon nanotube diameter. An asymptotic value of approximately 800 GPa was obtained for the Young's modulus and a value of approximately 0.28 for the Poisson ratio.     

Auxetic polypropylene films

Auxetic materials are those exhibiting negative Poisson's ratio (ν) behavior. Polymeric auxetic extruded products in the form of cylinders and fibers have previously been reported. This article reports the successful production of auxetic polypropylene films (～0.15‐mm thick) using a melt extrusion process. Video extensometry and tensile testing techniques have been used to measure the in‐plane Poisson's ratios and Young's moduli of the auxetic film, both on an Instron tensile testing machine and a Deben microtensile testing machine. The film is elastically anisotropic with the Poisson's ratio and Young's modulus along the extrusion (x) direction being ν_xy = ?1.12 ± 0.06 and E_x = 0.34 ± 0.01GPa, respectively, while the Poisson's ratio and Young's modulus in the transverse (y) direction to the extrusion direction are ν_yx = ?0.77 ± 0.01 and E_y = 0.20 ± 0.01GPa, respectively. POLYM. ENG. SCI., 45:517–528, 2005. © 2005 Society of Plastics Engineers     

Predictions of young's modulus of inorganic fibrous particulate‐reinforced polymer composites

In this study, the factors affecting the Young's modulus of inorganic fibrous particulate‐reinforced polymer composites were analyzed, and a new expression of the Young's modulus was derived and was based on a simplified mechanical model. This equation was used to estimate the composite Young's modulus. The estimated relative Young's modulus increased nonlinearly with increasing filler volume fraction. Finally, we verified the equation preliminarily by quoting the measured Young's modulus values of poly(butylene terephthalate)/wollastonite, polypropylene/wollastonite, and nylon 6/wollastonite composites reported in the literature. Good agreement was shown between the predictions and the experimental data of the relative Young's modulus values for these three composite systems. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 2957–2961, 2013     

On the nonlinear behavior of Young's modulus of carbon‐bonded alumina at high temperatures

The origin of the nonlinear behavior of the Young's modulus (E) of carbon‐bonded alumina at high temperatures was addressed, based on the microstructural changes observed during processing and their thermo‐mechanical properties. Impulse excitation technique, thermogravimetric analysis, porosity measurement, and scanning electron microscopy were conducted in order to highlight and explain the E behavior. The finite element model of a virtual microstructure was simulated and the results attained are in good agreement with the experimental data. The tests revealed that the Young's modulus of a cured sample heated from room temperature up to 500°C was governed by the release of volatiles. Above this temperature, the thermal expansion mismatch among alumina, graphite, and the carbon matrix is dominant resulting in an increase in the effective Young's modulus. During cooling, crack networks and gaps between alumina particles and the carbon matrix were developed. The former were induced by volatile release and by the graphite's highly anisotropic thermal expansion. The latter was derived by the thermal expansion mismatch between the alumina and the carbon matrix. The closure of the gaps and cracks governed the expansion behavior during the second heating cycle and a nonlinear effective Young's modulus increase as a function of temperature was observed.     

Physicomechanical properties of α‐cellulose–filled styrene–butadiene rubber composites

In this research, the influence of adding α‐cellulose powder to styrene–butadiene rubber (SBR) compounds was investigated. Physicomechanical properties of SBR–α‐cellulose composites, including tensile strength, elongation, Young's modulus, tear strength, hardness, abrasion, resilience, and compression set, before and after ageing, were determined and analyzed. Young's modulus, hardness, and compression set increased and elongation and resilience decreased with increasing α‐cellulose loading in the composites, whereas tensile strength, tear strength, and abrasion resistance initially increased at low α‐cellulose concentration (5 phr), after which these properties decreased with increasing α‐cellulose content. Lower loadings of α‐cellulose (5 phr) showed better results than higher loadings, given that tensile strength, tear strength, and abrasion resistance increased at low α‐cellulose concentration. Theoretical prediction of elastic modulus was carried out using rule of mixtures, Hashin, Kerner, and Halpin–Tsai equations. Calculated results show that these equations are not suitable for accurate prediction for the work carried out. However, these models can be used with confidence for the prediction of elastic modulus because experimental results are higher than the calculated values. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 96: 2203–2211, 2005     

The amorphous contribution to the modulus of a semi-crystalline polymer

The amorphous contribution to the Young's modulus of a semi-crystalline polymer is calculated for two morphologies: the spherulite and the stacked lamellae structure. Four types of amorphous chains are considered: bridges (or tie molecules); cilia; loops; and floating, unattached chains. The statistics of a polymer chain between two, infinite, impenetrable, parallel walls are used in the modulus calculation. It is found that for each type of amorphous chain, the Young's modulus is greater in the stacked lamellae structure than in the spherulite. The Young's modulus of a cilium, loop and floating chain all increase with increasing chain contour length while the Young's modulus of a bridge passes through a minimum value. The behavior of the Young's modulus as a function of temperature is analogous. These results are discussed in terms of the relative importance of crystalline lamellar impenetrability and the inherent elastic nature of the amorphous chains, in the Young's modulus behavior.     

Effects of process conditions on Young's modulus and strength of extrudate in short‐fiber‐reinforced polypropylene

We examined the effects of process conditions on Young's modulus and tensile strength of extruded short‐fiber reinforced thermoplastics. With increasing extrusion ratio and decreasing extrusion temperature, the fiber alignment increases, the mean fiber length decreases, and the mechanical properties of the matrix are improved. The orientation parameter, mean fiber length, Young's modulus, and tensile strength of the matrix are described as a function of extrusion ratio and extrusion temperature. The models proposed by Fukuda and Kawata, and Fukuda and Chou are applied to predict Young's modulus and tensile strength of the composites using orientation parameter. By comparing the predicted Young's modulus and tensile strength with experimental results, the validity of the models is examined. The prediction of Young's modulus agreed quit with the experimental results. The tensile strength of composite extruded below the melting point nearly matched that of the neat matrix. There is no the strengthening effect of the fiber since the angle between fracture surface and fiber direction is very small. POLYM. COMPOS. 28:29–35, 2007. © 2007 Society of Plastics Engineers     

Fiber orientation control of short‐fiber reinforced thermoplastics by ram extrusion

In this study we examine the fiber orientation distribution, fiber length and Young's modulus of extruded short‐fiber reinforced thermoplastics such as polypropylene. Axial orientation distributions are presented to illustrate the influence of extrusion ratio on the orientation state of the fibrous phase. Fibers are markedly aligned parallel to the extrusion direction with increasing extrusion ratio. The orientation state of extruded fiber‐reinforced thermoplastics (FRTP) is almost uniform throughout the section. The control of fiber orientation can be easily achieved by means of ram extrusion. Experimental results are also presented for Young's modulus of extruded FRTP in the extrusion direction. Young's modulus follows a linear trend with increasing extrusion ratio because the degree of the molecular orientation and the fiber orientation increases. The model proposed by Cox, and Fukuda and Kawada describes the effect of fiber length and orientation on Young's modulus. The value of the orientation coefficient is calculated by assuming a rectangular orientation distribution and calculating the fiber distribution limit angle given by orientation parameters. By comparing the predicted Young's modulus with experimental results, the validity of the model is elucidated. The mean fiber length linearly decreases with increasing extrusion ratio because of fiber breakage due to plastic deformation. There is a small effect on Young's modulus due to fiber breakage by ram extrusion.     

Elastic properties of porous polycrystalline thoria—A relook

Elastic constant–porosity relation for polycrystalline thoria reported by previous researchers has been reanalyzed on the basis of the Mori–Tanaka mean field approach and a power law dependence of moduli with porosity. It indicates that the shear modulus dependence on Young's modulus is possibly related to the sintering characteristics of the material rather than pore morphology. A new method has been suggested for predicting variations of elastic properties and porosity with the progress in sintering of thoria based on experimental data at a single porosity only. The predicted values agree with the experimental data quite well.