Young's Modulus Ratio Research Articles

Temperature dependence of the tensile properties of single-walled carbon nanotubes:O(N)tight-binding molecular-dynamics simulations

This paper examines the effect of temperature on the structural stability and mechanical properties of 20-layered (10,10) single-walled carbon nanotubes (SWCNTs) under tensile loading using an $\mathrm{O}(N)$ tight-binding molecular-dynamics simulation method. We observed that (10,10) tube can sustain its structural stability for the strain values of 0.23 in elongation and 0.06 in compression at $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Bond-breaking strain value decreases with increasing temperature under stretching but not under compression. The elastic limit, Young's modulus, tensile strength, and Poisson ratio are calculated as 0.10, $0.395\phantom{\rule{0.3em}{0ex}}\mathrm{TPa}$, $83.23\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, and 0.285, respectively, at $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. In the temperature range from $300\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}900\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, Young's modulus and the tensile strengths decrease with increasing temperature while the Poisson ratio increases. At higher temperatures, Young's modulus starts to increase while the Poisson ratio and tensile strength decrease. In the temperature range from $1200\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}1800\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the SWCNT is already deformed and softened. Applying strain on these deformed and softened SWCNTs does not follow the same pattern as in the temperature range of $300\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}900\phantom{\rule{0.3em}{0ex}}\mathrm{K}$.

Determination of Young's modulus and Poisson's ratio for coatings

Designing thin-film coatings to meet engineering needs requires the knowledge of accurate mechanical properties of the coatings. Young's modulus and Poisson's ratio are two basic mechanical properties of materials, which should be conveniently measured. This paper reports a direct and non-destructive method for the measurement of the Young's modulus and Poisson's ratio of a thin-film coating and its substrate based on the extended Hertz theory for the contact of coated bodies. The theory is used to analyze load–displacement data from a spherical indentation in the elastic range, in which the substrate effect is intrinsically modeled. The Young's modulus and Poisson's ratio are determined at the same time through minimizing the difference between the measured and specially defined modified Young's moduli. Two sets of validation experiments are also reported. This new method does not require any assumptions on pressure distribution and Poisson's ratio and can be easily incorporated into current indentation analysis systems.

PLASTICITY CHARACTERISTICS OBTAINED THROUGH INSTRUMENTAL INDENTATION

AbstractThe nanohardness and microhardness testing of crystalline materials with different types of interatomic bonds and different crystal structures was performed with Berkovich indenter.The plasticity characteristics for crystalline materials with different types of interatomic bonds and different crystalline structures were determined by microindentation and by nanoindentation. The relation between these characteristics and parameters of material (Meyer hardness, Young's modulus and Poisson's ratio) was assigned. Plasticity characteristic may be used for characterization of mechanical behavior of materials which are brittle at standard mechanical tests and for coatings.

Nanoindentation and nanofriction on DLC films

Diamond-like carbon (DLC) coatings have been studied for many years as wear-resistant and low friction materials. Their tribological behaviour depends on the nature of the coating, which is determined by the deposition process. It is also strongly affected by environmental conditions. In this study, the nanomechanical properties and nanofriction behaviour of two a-C:H coatings deposited on a silicon substrate and exhibiting different macroscopic friction behaviours were investigated using a three-axial surface force apparatus equipped with a diamond tip. The hardness, Young's modulus and Poisson's ratio of the two coatings were determined. Viscous recovery of the indents was observed a few days after the indentation tests. Low friction coefficients (around 0.06) were measured for the coating that exhibited macroscopic low friction. For the coating that exhibited a higher friction coefficient, dissipative behaviour measured during nanofriction test was enhanced by sliding, compared to the dissipative behaviour measured during normal indentation, suggesting a link between normal viscous dissipation at nanoscale and high friction.

Influence of indenter tip roundness on hardness behavior in nanoindentation

In this paper, the effect of indenter tip roundness on hardness behavior for two typical elastic perfectly plastic materials is studied by means of finite element simulation. A rigid conical indenter of semi apex angle 70.3° fitted smoothly with a spherical tip is employed. It is shown that as the indentation depth increases hardness first rises from zero, reaches a maximum and then decreases slowly approaching asymptotically the limiting value equal to that due to a conical indenter of ideally sharp tip. The range within which hardness varies appreciably is comparable to the radius of the indenter tip. The difference between the maximum value and the limiting value depends on the yield stress over the Young's modulus ratio. The smaller this ratio the greater the difference is. Numerical simulation also provides an opportunity for checking the accuracy and limitations of the widely used Oliver–Pharr method.

An engineering-oriented embedded-atom-method potential fitting procedure for pure fcc and bcc metals

A numerical fitting procedure for developing embedded-atom-method (EAM) potentials for pure fcc and bcc metals is presented in this paper. The focus is on developing an approximate EAM potential that suffices for engineering applications to pure metals. The EAM inter-atomic potential consists of two parts: the pair-potential and the embedding function. By assuming a parameterized form for the pair-potential, the embedding function is numerically fit into the hydrostatic linear-elastic stress equations of the metal at hand. Following this, the single crystal anisotropic Young's modulus and Poisson's ratio of the metal are calculated through a uniaxial molecular dynamics (MD) simulation, and are compared to experimental values. The parameter of the pair-potential is then changed and the embedding function recalculated until the Young's modulus and Poisson's ratio are satisfactorily predicted. Following this, a parameterized relation between temperature and kinetic energy is fit into the thermal expansion data of the metal, and a temperature dependent volume factor for calculating Young's modulus at 0 and 100 K accurately is numerically fit. Finally, the potential is adjusted without changing the slopes (i.e. forces) to fit the cohesive energy of the metal. The resulting EAM potential for pure copper is tested to see how accurately the thermal and elastic properties of single crystal copper are predicted. The thermal and elastic properties are found to be predicted accurately. This shows that the EAM potential fitting procedure thus developed is suitable for atomic-level engineering applications.

Validation of stresses and stress intensity factor in a notched bilayer system under four point bending, as determined by the solution of the Navier's equation

We use a previously formulated solution of the Navier's equation to calculate stress intensity factor in a notched bar bonded to a substrate. We evolve a procedure for determining the stress distribution. We validate the stress analysis in four-point bending by measuring surface strains for different combination of materials in the bilayer (the Young's modulus ratio of the materials in the bilayer varied from 28 to 86). We also determine the stress intensity factor (SIF) experimentally using a notched photoelastic bar bonded to a substrate and validate our estimation of SIF.

Controls of grain-size distribution on geomechanical properties of reservoir rock—A case study: Cretaceous Khafji Member, Zuluf Field, offshore Arabian Gulf

The Khafji Member of the Cretaceous Wasia Formation in Zuluf Field, offshore Saudi Arabia is an important siliciclastic hydrocarbon reservoir. The reservoir consists of a lower Main Sand and an upper Stringer Sand. The present study investigated the relationships between the geomechanical attributes (Young's modulus and Poisson's ratio) of the reservoir and its grain size distribution. In addition, an attempt was also made to relate the reservoir quality with the depositional environments deduced from factor analysis of the grain size distribution data. The Young's modulus for the Khafji reservoir range from a low of 8.43×10 5 psi at 1000 psi confining pressure (1.13×10 6 psi at 2900 psi confining pressure) to a high of 1.27×10 6 psi at 1000 psi (1.91×10 6 psi at 2900 psi). The study shows that there is no significant relationship between grain size parameters (mean, median, skewness, and kurtosis) and geomechanical properties. However, a good correlation was observed between geomechanical parameters and sands deposited in different environments. The clean sand showing moderate to good sorting and interpreted as beach sand showed low Young's modulus (average 1.07×10 6 psi) and Poisson's ratio (average 0.16), while the parameters were higher (average of 1.57×10 6 psi Young's modulus and 0.204 Poisson's ratio) for the fine-grained sediments representing possible lagoonal or offshore environment.

On Applying the Shell Theory to Single Layer Graphitic Structures

The validity of on applying the shell theory to single layer graphitic structures, such as buckball, single-walled carbon nanotube and so on is discussed by analyzing the results obtained from the first-principles calculations. It is shown that the classic shell theory based on 3-dimensional (M) isotropic materials is inapplicable to describe the elasticity of the single layer graphitic structures, while a generalized shell theory based on 2D isotropic materials holds. The reasonable concepts in the elastic theory of single layer graphitic structures are rigidity coefficients rather than the Young's modulus and Poisson ratio.

An experimental investigation of sill formation and propagation in layered elastic media

A series of experiments are described where dyed water (a magma analogue) was intruded into solid gelatine (a crustal analogue) to investigate the formation of sills. We considered a layered gelatine system with contrasting adjacent layers. By varying the density and rigidity of the gelatine we found that experimental sills form when the upper layer is more rigid than the lower layer, with intrusion occurring in a plane directly below the interface. Experimental dykes were observed to propagate to the surface when the Young's Modulus ratio of upper to lower gelatine layers was less than one. Experimental dyke arrest occurred when the upper layer was more rigid and the interface was strong. Two varieties of experimental sill formed when the upper layer was more rigid than the lower layer and the interface was sufficiently weak. The form of the intrusion depends on the balance of driving pressures and the Young's Modulus ratio of contrasting adjacent layers. When the rigidity ratio is high and there is a large driving pressure the experimental feeder dyke completely converts to propagate as a sill. However, when the rigidity ratio and driving pressure are both close to one a dyke–sill hybrid forms. Under these conditions the experimental sill formation is accompanied by contemporaneous dyke intrusion into the overlying more rigid layer. During sill propagation deformation structures such as faults and en echelon fractures are formed into the lower layer. Experimental sill propagation dynamics are controlled by viscous dissipation along the length of the sill; causing acceleration with increasing length. Our study suggests that rigidity contrasts may play a major role in the location of sills and development of igneous complexes. In ancient cratonic areas the Moho is a suitable site for the preferential formation of sills with higher rigidity continental crust overlying weaker mantle. Mantle plumes impacting ancient continents provide a situation in which large sills can form to fractionate prior to eruption of flood basalts. The boundary between the upper and lower crust (Conrad discontinuity) may provide a preferential focus for the emplacement of sheets of silicic magma at continental arcs where the lower crust is weakened by prolonged heating and possible hydration.

Mechanical characterization of a polysiloxane-derived SiOC glass

Silicon oxycarbide glass with the composition Si 1.0O 1.6C 0.8 was synthesized from a commercial polysiloxane by polymer pyrolysis. Dense SiOC samples were obtained by cross linking of the polysiloxane followed by warm pressing to form cylindrical samples and subsequent pyrolysis of the shaped polymer at 1100 °C in Ar. Hardness ( H), Young's modulus ( E) and Poisson's ratio ( ν) of the as-prepared SiOC glass were evaluated from indentation studies and from acoustic microscopy. Indentation studies showed that E depends on the applied load and amounts to 90 GPa for low load and to 180 GPa for high load. Average values of 6.4 and 101 GPa were obtained for H and E, respectively, by the Vickers indentation method. Acoustic microscopy analysis yielded values of 96 GPa and 0.11 for E and ν, respectively. Compared to vitreous silica, the Young's modulus of the SiOC glass is about 1.3–1.5 times higher. To the knowledge of the present authors, the measured Poisson's ratio ( ν = 0.11) is the lowest reported so far for glasses and polycrystalline ceramics.

Tensile deformation behavior of plasma-sprayed Ni–45Cr coatings

Deformation behavior of plasma-sprayed Ni–45Cr coatings was studied in terms of stress–strain relation and modulus changes under tensile loading. The tensile loading was applied in both directions parallel and perpendicular to the lamellar plane of the coatings. The influences of spray distance on Young's modulus and Poisson's ratio of the coatings were investigated. The Young's modulus was measured from both directions parallel and perpendicular to the lamellar plane. Results showed a linear relation between the stress and strain in the direction parallel to the lamellar plane. The similar linear stress–strain relation in the direction perpendicular to the lamellar plane was revealed only when the tensile loading with up to a certain value was applied, while a nonlinear stress–strain relation prevailed under a higher tensile load. The increase of the proportional limit of the coating was observed under repetitive tensile loading perpendicular to the lamellar plane. The modulus measured from the direction parallel to the lamellar plane changed from 78 GPa to 92 GPa. Spray distance showed minor effect on the Young's modulus. Moreover, the modulus measured from the direction perpendicular to the lamellar plane, changing from 48 GPa to 64 GPa, was lower than that obtained from the direction parallel to the lamellar plane. It is clear that plasma-sprayed metallic coating presented an anisotropic elastic behavior. In addition, it was found that the coatings yielded a Poisson's ratio of 0.13–0.15 which is lower than that of bulk materials. Spray distance also has no significant influence on the Poisson's ratio of coatings.

Evaluation of the effectiveness of representative methods for determining Young's modulus and hardness from instrumented indentation data

The effectiveness of Oliver & Pharr's (O&P's) method, Cheng & Cheng's (C&C’s) method, and a new method developed by our group for estimating Young's modulus and hardness based on instrumented indentation was evaluated for the case of yield stress to reduced Young's modulus ratio (σy/Er) ≥ 4.55 × 10−4 and hardening coefficient (n) ≤ 0.45. Dimensional theorem and finite element simulations were applied to produce reference results for this purpose. Both O&P's and C&C's methods overestimated the Young's modulus under some conditions, whereas the error can be controlled within ±16% if the formulation was modified with appropriate correction functions. Similar modification was not introduced to our method for determining Young's modulus, while the maximum error of results was around ±13%. The errors of hardness values obtained from all the three methods could be even larger and were irreducible with any correction scheme. It is therefore suggested that when hardness values of different materials are concerned, relative comparison of the data obtained from a single standard measurement technique would be more practically useful. It is noted that the ranges of error derived from the analysis could be different if different ranges of material parameters σy/Er and n are considered.

Size-Dependent Elastic Moduli of FCC Crystal Nanofilms

ABSTRACTA semi-continuum model is constructed to study the size effects on the mechanical properties of face-cubic-center crystal structure nanofilms. Unlike the classical continuum theory, the current model directly takes the discrete nature in the thickness direction into consideration. In-plane and out-plane Poisson's ratios as well as in-plane Young's modulus are investigated with this model. It is found that the values of the Young's modulus and Poisson's ratio depend on the film thickness and approach the respective bulk values asymptotically.

Synthesis, characterization and devitrification behaviour of an yttrium containing boroaluminate glass

The glass forming region in the B2O3-Al2O3-Y2O3 composition diagram has been determined by a melting and quenching procedure at temperatures up to 1800°C. Different physical characteristics (density, coefficient of thermal expansion, glass transition and crystallization peak temperatures) have been determined for a 35B2O3-40Al2O3-25Y2O3 glass composition (in mol.%). By using a predictive model and some NMR structural data, different elastic moduli (Young's modulus, bulk modulus, shear modulus and Poisson's ratio) have been calculated. The devitrification behaviour has also been studied. Internal crystallization is the dominant mechanism and a new (Y, Al)BO3 ternary phase has been characterized by X-ray powder diffraction. The temperature and time nucleation dependence have been determined from DTA experiments as well as the crystallization kinetics (i.e. the Avrami exponent and the activation energy for crystal growth).

Determination of the elastic properties of some coated materials by simulation of the analogue signal of the reflection acoustic microscope

We discuss in this work the elastic properties of monolayer materials (layer/substrate). We consider both cases of quick/slow and slow/quick systems. We calculate Young's modulus, shear modulus and Poisson's ratio of the following four systems: Cr/Fe, TiN/Fe, Al/Si and Al/SiC. We make it evident that the use of the simulated acoustic signal of the reflection acoustic microscope yields to the determination of the wave propagation velocity of different modes in the layer/substrate according to the frequency and the thickness of the layer. We demonstrate that Victorov relation is not applicable in this case. A new method, that we called ‘method of homogenization’ is proposed to resolve the problem of dispersion. For the considered materials, the calculations have been carried out in a large range of frequencies (50 MHz–3.5 GHz) and coating layer thickness (0.5–150 μm). We show that for the studied materials the elastic constants take the values of the material layer beyond a thickness of 30–40 μm.

EQUIVALENT CONTINUUM MODELING OF GRAPHENE SHEETS

Carbon nanotubes have drawn tremendous interest due to their excellent mechanical and electronic properties. Carbon nanotubes have a similar molecular structure as that of graphene sheets. Hence, characterization of mechanical properties of graphene sheet based on equivalent continuum modelling is of considerable importance. Our initial studies are carried out on a single carbon ring/cell. The ring is then modelled as a truss (finite) element assemblage and equivalent Young's modulus is computed for a few fundamental modes. Next, these studies have been extended to model graphene sheet as a planar continuum to determine the mechanical properties (Young's modulus, shear modulus and Poisson's ratio) for typical modes of deformation. Further research is in progress to investigate how this set of different values can be integrated together towards a meaningful continuum characterization of the inherent discrete structure.

Mechanical properties of the novel organometallic polymer poly(ferrocenyldimethylsilane)

AbstractA study of the mechanical properties of poly(ferrocenyldimethylsilane) [Fe(η‐C5H4)2SiMe2]n, 3, a novel organometallic polymer, has been performed on thin films of this material. The Young's modulus and Poisson's ratio of film samples (15 × 1 × 1 mm) of 3 were measured in quasi‐static tension using a video extensometer. For 3, the values of the Young's moduli (E) and Poisson's ratios (ν) were similar between axes in the plane and independent of the splicing direction used during sample preparation. The mean and standard deviation of the Young's modulus and Poisson's ratio were 0.78 ± 0.08 GPa and 0.37 ± 0.06 GPa, respectively. Thermomechanical analysis of 3 revealed a steady decrease of E from a room temperature value of approximately 0.70 GPa. Additionally, it was found that at 150 °C, 3 was unable to support even small stresses, consistent with the onset of a melt transition (ca. 135 °C). A mathematical model based on molecular geometry is developed to describe the results. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2280–2288, 2005

An extended modeling of the micropipette aspiration experiment for the characterization of the Young's modulus and Poisson's ratio of adherent thin biological samples: Numerical and experimental studies

The micropipette aspiration (MA) experiment remains a quite widely used micromanipulation technique for quantifying the elastic modulus of cells and, less frequently, of other biological samples. However, moduli estimations derived from MA experiments are only valid if the probed sample is non-adherent to the rigid substrate. This study extends this standard formulation by taking into account the influence of the sample adhesion. Using a finite element analysis of the sample aspiration into the micropipette, we derived a new expression of the aspirated length for linear elastic materials. Our results establish that (i) below a critical value, the thickness h of the probed sample must be considered to get an accurate value of its Young's modulus (ii) this critical value depends both on the Poisson's ratio and on the sample adhesivity. Additionally, we propose a novel method which allows the computation of the intrinsic Young's modulus of the adherent probed sample from its measured apparent elasticity modulus. Thanks to the set of computational graphs we derived from our theoretical analysis, we successfully validate this method by experiments performed on polyacrylamide gels. Interestingly, the original procedure we proposed allows a simultaneous quantification of the Young's modulus and of the Poisson's ratio of the adherent gel. Thus, our revisited analysis of MA experiments extends the application domain of this technique, while contributing to decrease the dispersion of elastic modulus values obtained by this method.

New developments in the Integrated Stress Determination Method and their application to rock stress data at the Äspö HRL, Sweden

The Integrated Stress Determination Method (ISDM) is a powerful tool for estimating the regional stress tensor from in-situ measurements of local stress tensors using a wide variety of stress measuring techniques. This study presents new developments of the ISDM: The stress field may be described with up to 12 model parameters; and is applicable to data from CSIR- and CSIRO HI-type of overcoring devices, hydraulic fracturing, hydraulic tests of pre-existing fractures (HTPF), as well as to combined data sets. Furthermore, in combined data sets, the hydraulic fracturing and/or HTPF data may be used to constrain the average elastic parameters, Young's modulus and Poisson's ratio. The new ISDM developments were applied to the extensive and recently re-analysed rock stress data at the Äspö Hard Rock Laboratory. The results reveal a good fit of the re-analysed data. Overall, the re-analysis indicates that the stress field at Äspö HRL is relatively well constrained and consistent with depth. The NE-2 Fracture Zone influences the stresses, and dividing the regional stress field into a NW and a SE stress domain. When the hydraulic fracturing data were used to constrain the average elastic parameters, Young's modulus, E, and Poisson's ratio, ν, quite similar results were obtained ( E = 50.8 GPa and ν = 0.33 ) compared with results from biaxial tests of overcore samples ( E = 61.6 MPa and ν = 0.26 ).