Effective elastic moduli of two-dimensional solids with multiple cracks

An accurate method which directly accounts for the interactions between different microcracks is used for analyzing the elastic problem of multiple cracks solids. The effective elastic moduli for randomly oriented cracks and parallel cracks are evaluated for the representative volume element (RVE) with microcracks in infinite media. The numerical results are compared with those from various micromechanics models and experimental data. These results show that the present method is simple and provides a direct and efficient approach to dealing with elastic solids containing multiple cracks.

The Surface- And Size-Dependent Elastic Moduli Of Nanostructures

A theoretical model is presented to investigate the size-dependent elastic moduli of nanostructures with the effects of the surface relaxation surface energy taken into consideration. At nanoscale, due to the large ratios of the surface-to-volume, the surface effects, which include surface relaxation surface energy, etc., can play important roles. Thus, the elastic moduli of nanostructures become surface- and size-dependent. In the research, the three-dimensional continuum model of the nanofilm with the surface effects is investigated. The analytical expressions of five nonzero elastic moduli of the nanofilm are derived, and then the dependence of the elastic moduli is discussed on the surface effects and the characteristic dimensions of nanofilms.

Effective elastic moduli of inhomogeneous solids by embedded cell model

An embedded cell model is presented to obtain the effective elastic moduli for three-dimensional two-phase composites which is an exact analytic formula without any simplified approximation and can be expressed in an explicit form. For the different cells such as spherical inclusions and cracks surrounded by sphere and oblate ellipsoidal matrix, the effective elastic moduli are evaluated and the results are compared with those from various micromechanics models. These results show that the present model is direct, simple and efficient to deal with three-dimensional tyro-phase composites.

The surface- and size-dependent elastic moduli of nanostructures

A theoretical model is presented to investigate the size-dependent elastic moduli of nanostructures with the effects of the surface relaxation surface energy taken into consideration. At nanoscale, due to the large ratios of the surface-to-volume, the surface effects, which include surface relaxation surface energy, etc., can play important roles. Thus, the elastic moduli of nanostructures become surface- and size-dependent. In the research, the three-dimensional continuum model of the nanofilm with the surface effects is investigated. The analytical expressions of five nonzero elastic moduli of the nanofilm are derived, and then the dependence of the elastic moduli is discussed on the surface effects and the characteristic dimensions of nanofilms.

Prediction of Effective Moduli of Carbon Nanotube-Reinforced Composites with Waviness and Debonding

Carbon nanotubes (CNTs) have been regarded as ideal reinforcements of high-performance composites with enormous applications. However, the waviness of the CNTs and the interfacial bonding condition between them and the matrix are two key factors that influence the reinforcing efficiency. In this paper, the effects of the waviness of the CNTs and the interfacial debonding between them and the matrix on the effective moduli of CNT-reinforced composites are studied. A simple analytical model is presented to investigate the influence of the waviness on the effective moduli. Then, two methods are proposed to examine the influence of the debonding. It is shown that both the waviness and debonding can significantly reduce the stiffening effect of the CNTs. The effective moduli are very sensitive to the waviness when the latter is small, and this sensitivity decreases with the increase of the waviness. (C) 2008 Elsevier Ltd. All rights reserved.

Investigation of Chemical Bond Characteristics, Thermal Expansion Coefficients and Bulk Moduli of alpha-R2MoO6 and R2Mo2O7 (R = rare earths) by Using a Dielectric Chemical Bond Method

Theoretical researches are performed on the alpha-R2MoO6 (R = Y, Gd, Tb Dy, Ho, Er, Tm and Yb) and pyrochlore-type R2Mo2O7 (R = Y, Nd, Sm, Gd, Tb and Dy) rare earth molybdates by using chemical bond theory of dielectric description. The chemical bonding characteristics and their relationship with thermal expansion property and compressibility are explored. The calculated values of linear thermal expansion coefficient (LTEC) and bulk modulus agree well with the available experimental values. The calculations reveal that the LTECs and the bulk moduli do have linear relationship with the ionic radii of the lanthanides: the LTEC decreases from 6.80 to 6.62 10(-6)/K and the bulk modulus increases from 141 to 154 GPa when R goes in the order Gd, Tb Dy, Ho, Er, Tm, and Yb in the alpha-R2MoO6 series; while in the R2Mo2O7 series, the LTEC ranges from 6.80 to 6.61 10(-6)/K and the bulk modulus ranges from 147 to 163 GPa when R varies in the order Nd, Sm, Gd, Tb and Dy.

Elasticity, stability, and ideal strength of beta-SiC in plane-wave-based ab initio calculations

On the basis of the pseudopotential plane-wave method and the local-density-functional theory, this paper studies energetics, stress-strain relation, stability, and ideal strength of beta-SiC under various loading modes, where uniform uniaxial extension and tension and biaxial proportional extension are considered along directions [001] and [111]. The lattice constant, elastic constants, and moduli of equilibrium state are calculated and the results agree well with the experimental data. As the four SI-C bonds along directions [111], [(1) over bar 11], [11(1) over bar] and [111] are not the same under the loading along [111], internal relaxation and the corresponding internal displacements must be considered. We find that, at the beginning of loading, the effect of internal displacement through the shuffle and glide plane diminishes the difference among the four Si-C bonds lengths, but will increase the difference at the subsequent loading, which will result in a crack nucleated on the {111} shuffle plane and a subsequently cleavage fracture. Thus the corresponding theoretical strength is 50.8 GPa, which agrees well with the recent experiment value, 53.4 GPa. However, with the loading along [001], internal relaxation is not important for tetragonal symmetry. Elastic constants during the uniaxial tension along [001] are calculated. Based on the stability analysis with stiffness coefficients, we find that the spinodal and Born instabilities are triggered almost at the same strain, which agrees with the previous molecular-dynamics simulation. During biaxial proportional extension, stress and strength vary proportionally with the biaxial loading ratio at the same longitudinal strain.

The Size-Dependent Elastic Properties of Nanofilms with Surface Effects

Size-dependent elastic constants are investigated theoretically with reference to a nanoscale single-crystal thin film. A three-dimensional _3D_ model is presented with the relaxation on the surface of the nanofilm taken into consideration. The constitutive relation of the 3D model is derived by using the energy approach, and analytical expressions for the four nonzero elastic constants of the nanofilm are obtained. The size effects of the four elastic constants are then discussed, and the dependence of these elastic constants on the surface relaxation and the ambiguity in the definition of the thickness of the nanofilm are also analyzed. In addition, the elastic moduli of the nanofilm in two kinds of plane problem are obtained and discussed in the case of a special boundary condition.

Novel Mechanical Behavior Of Zno Nanorods

A novel stress-strain relation with two stages of linear elastic deformation is observed in [0 0 0 1]-oriented ZnO nanorods under uniaxial tensile loading. This phenomenon results from a phase transformation from wurtzite (WZ, P6(3)mc space group) to a body-centered tetragonal structure with four-atom rings (denoted as BCT-4) belonging to the P4(2)/mnm space group. The analysis here focuses on the effects of nanorod size and temperature on the phase transformation and the associated mechanical behavior. It is found that as size is increased from 19.5 to 45.5 angstrom, the critical stress for nucleation of the transformation decreases by 25% from 21.90 to 16.50 GPa and the elastic moduli of the WZ- and BCT-4-structured nanorods decrease by 24% (from 299.49 to 227.51 GPa) and 38% (from 269.29 to 166.86 GPa), respectively. A significant temperature effect is also observed, with the critical stress for transformation initiation decreasing 87.8% from 17.89 to 2.19 GPa as temperature increases from 300 to 1500 K. (c) 2007 Elsevier B.V. All rights reserved.

Regularity of strain distribution in short-fiber/whisker reinforced composites

Based on studies on the strain distribution in short-fiber/whisker reinforced metal matrix composites, a deformation characteristic parameter, lambda is defined as a ratio of root-mean-square strain of the reinforcers identically oriented to the macro-linear strain along the same direction. Quantitative relation between lambda and microstructure parameters of composites is obtained. By using lambda, the stiffness moduli of composites with arbitrary reinforcer orientation density function and under arbitrary loading condition are derived. The upper-bound and lower-bound of the present prediction are the same as those from the equal-strain theory and equal-stress theory, respectively. The present theory provides a physical explanation and theoretical base for the present commonly-used empirical formulae. Compared with the microscopic mechanical theories, the present theory is competent for stiffness modulus prediction of practical engineering composites in accuracy and simplicity.

Micromechanics of elastic solids weakened by a large number of cracks

This paper presents a micromechanics analysis of the elastic solids weakened by a large number of microcracks in a plane problem. A new cell model is proposed. Each cell is an ellipse subregion and contains a microcrack. The effective moduli and the stress intensity factors for an ellipse cell are obtained. The analytic closed formulas of concentration factor tensor for an isotropic matrix containing an anisotropic inclusion are derived. Based on a self-consistent method, the effective elastic moduli of the solids weakened by randomly oriented microcracks are obtained.

Fracture Properties of LPCVD Silicon Nitride and Thermally Grown Silicon Oxide Thin Films From the Load-Deflection of Long Si3N4 and SiO2/Si3N4 Diaphragms

The bulge test is successfully extended to the determination of the fracture properties of silicon nitride and oxide thin films. This is achieved by using long diaphragms made of silicon nitride single layers and oxide/nitride bilayers, and applying comprehensive mechanical model that describes the mechanical response of the diaphragms under uniform differential pressure. The model is valid for thin films with arbitrary z-dependent plane-strain modulus and prestress, where z denotes the coordinate perpendicular to the diaphragm. It takes into account the bending rigidity and stretching stiffness of the layered materials and the compliance of the supporting edges. This enables the accurate computation of the load-deflection response and stress distribution throughout the composite diaphragm as a function of the load, in particular at the critical pressure leading to the fracture of the diaphragms. The method is applied to diaphragms made of single layers of 300-nm-thick silicon nitride deposited by low-pressure chemical vapor deposition and composite diaphragms of silicon nitride grown on top of thermal silicon oxide films produced by wet thermal oxidation at 950 degrees C and 1050 degrees C with target thicknesses of 500, 750, and 1000 mn. All films characterized have an amorphous structure. Plane-strain moduli E-ps and prestress levels sigma(0) of 304.8 +/- 12.2 GPa and 1132.3 +/- 34.4 MPa, respectively, are extracted for Si3N4, whereas E-ps = 49.1 +/- 7.4 GPa and sigma(0) = -258.6 +/- 23.1 MPa are obtained for SiO2 films. The fracture data are analyzed using the standardized form of the Weibull distribution. The Si3N4 films present relatively high values of maximum stress at fracture and Weibull moduli, i.e., sigma(max) = 7.89 +/- 0.23 GPa and m = 50.0 +/- 3.6, respectively, when compared to the thermal oxides (sigma(max) = 0.89 +/- 0.07 GPa and m = 12.1 +/- 0.5 for 507-nm-thick 950 degrees C layers). A marginal decrease of sigma(max) with thickness is observed for SiO2, with no significant differences between the films grown at 950 degrees C and 1050 degrees C. Weibull moduli of oxide thin films are found to lie between 4.5 +/- 1.2 and 19.8 +/- 4.2, depending on the oxidation temperature and film thickness.

Fracture properties of silicon carbide thin films by bulge test of long rectangular membrane

This paper reports the mechanical properties and fracture behavior of silicon carbide (3C-SiC) thin films grown on silicon substrates. Using bulge testing combined with a refined load-deflection model of long rectangular membranes, which takes into account the bending stiffness and prestress of the membrane material, the Young's modulus, prestress, and fracture strength for the 3C-SiC thin films with thicknesses of 0.40 and 1.42 mu m were extracted. The stress distribution in the membranes under a load was calculated analytically. The prestresses for the two films were 322 +/- 47 and 201 +/- 34 MPa, respectively. The thinner 3C-SiC film with a strong (111) orientation has a plane-gstrain moduli of 415 +/- 61 GPa, whereas the thicker film with a mixture of both (111) and (110) orientations exhibited a plane-strain moduli of 329 +/- 49 GPa. The corresponding fracture strengths for the two kinds of SiC films were 6.49 +/- 0.88 and 3.16 +/- 0.38 GPa, respectively. The reference stresses were computed by integrating the local stress of the membrane at the fracture over edge, surface, and volume of the specimens and were fitted with Weibull distribution function. For the 0.40-mu m-thick membranes, the surface integration has a better agreement between the data and the model, implying that the surface flaws are the dominant fracture origin. For the 1.42-mu m-thick membranes, the surface integration presented only a slightly better fitting quality than the other two, and therefore, it is difficult to rule out unambiguously the effects of the volume and edge flaws.

NOVEL COMPOSITES OF POLY(L-LACTIDE) AND SURFACE MODIFIED BIOACTIVE SiO2-CaO-P2O5 GEL NANOPARTICLES: MECHANICAL AND BIOLOGICAL PROPERTIES

Bioactive SiO2-CaO-P2O5 gel (BAG) nanoparticles with 40 nm in diameter were synthesized by the sol-gel route and further modified via the ring-opening polymerization of lactide on the surface of particles. Surface modified BAG (mBAG) was introduced in poly(L-lactide) (PLLA) matrix as bioactive filler. The dispersibility of mBAG in PLLA matrix was much higher than that of rough BAG particles. Tensile strength of the mBAG/PLLA composite could be increased to 61.2 MPa at 2 wt% filler content from 53.4 MPa for pure PLLA. The variation of moduli of the BAG/PLLA and mBAG/PLLA composites always showed an enhancement tendency with the increasing content of filler loading. The SEM photographs of the fracture surfaces showed that mBAG could be homogeneously dispersed in the PLLA matrix, and the corrugated deformation could absorb the rupture energy effectively during the breaking of materials. In vitro bioactivity tests showed that both BAG and mBAG particles could endow the composites with ability of the calcium sediment in SBF, but the surface modification of BAG particles could weaken this capability to some extent. Biocompatibility tests showed that both BAG and mBAG particles could facilitate the attachment and proliferation of the marrow cells on the surface of the composite.

Synthesis and gas permeability of novel fluorinated poly(phenylene-co-naphthalimide)s

A new class of high-performance polymers [poly(phenylene-co-naphthalimide)s] was prepared through the Ni(0) catalytic coupling of N-(4-chloro-2-trifluromethylphenyl)-5-chloro-1,8-naphthalimide and 2,5-dichlorobenzophenone. The resulting copolymers exhibited high molecular weights (high inherent viscosities) and a combination of desirable properties such as good solubility in dipolar aprotic solvents, film-forming capability, and mechanical properties. The glass-transition temperatures of the copolymers ranged from 320 to 403 degrees C and increased as the content of the naphthalimide moiety increased. Tough polymer films, obtained via casting from N-methylpyrrolidone solutions, had tensile strengths of 64-107 MPa and tensile moduli of 3.4-4.7 GPa. The gas permeability coefficients of the copolymers were measured for H-2, CO2, O-2, CH4, and N-2. They showed oxygen permeability coefficients and permeability selectivity of oxygen to nitrogen (permeability coefficient for O-2/permeability coefficient for N-2) in the ranges of 1.39-4.31 and 4.92-5.38 barrer, respectively.