scholarly journals Displacement Approach to Determine the Effective Tensile and Torsional Modulus of Nanowires

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Lin Fang ◽  
Quan Yuan ◽  
Bin Wu ◽  
Honglin Li ◽  
Mengyang Huang
Keyword(s):  
Young’S Modulus ◽  
Effective Properties ◽  
Young's Modulus ◽  
Axial Strain ◽  
Surface Elasticity ◽  
Volume Ratio ◽  
Field Equations ◽  
Surface Residual Stresses ◽  
Residual Strains ◽  
Displacement Approach

Surface elasticity and residual stress have a strong influence on the effective properties of nanowire (NW) due to its excessively large surface area-to-volume ratio. Here, the classical displacement method is used to solve the field equations of the core-surface layer model subjected to tension and torsion. The effective Young’s modulus is defined as the ratio of normal stress to axial strain, which decreases with the increase in NW radius and gradually reaches the bulk value. The positive or negative surface residual stresses will increase or decrease Young’s modulus and shear modulus due to the surface residual strains. Nonzero radial and circumferential strains enhance the influence of surface moduli on the effective modulus.

Effective properties of composite materials containing voids

1993 ◽  
Vol 440 (1909) ◽  
pp. 461-473 ◽  
Keyword(s):  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Effective Properties ◽  
Young's Modulus ◽  
Matrix Material ◽  
Practical Importance ◽  
Three Dimensional ◽  
Poisson's Ratio ◽  
Two Dimensional ◽  
Isotropic Composite

Recent results of theoretical and practical importance prove that the two-dimensional (in-plane) effective (average) Young’s modulus for an isotropic elastic material containing voids is independent of the Poisson’s ratio of the matrix material. This result is true regardless of the shape and morphology of the voids so long as isotropy is maintained. The present work uses this proof to obtain explicit analytical forms for the effective Young’s modulus property, forms which simplify greatly because of this characteristic. In some cases, the optimal morphology for the voids can be identified, giving the shapes of the voids, at fixed volume, that maximize the effective Young’s modulus in the two-dimensional situation. Recognizing that two-dimensional isotropy is a subset of three-dimensional transversely isotropic media, it is shown in this more general case that three of the five properties are independent of Poisson’s ratio, leaving only two that depend upon it. For three-dimensionally isotropic composite media containing voids, it is shown that a somewhat comparable situation exists whereby the three-dimensional Young’s modulus is insensitive to variations in Poisson’s ratio, v m , over the range 0 ≤ v m ≤ ½, although the same is not true for negative values of v m . This further extends the practical usefulness of the two-dimensional result to three-dimensional conditions for realistic values of v m .

scholarly journals Effects of Intrinsic Strain on the Structural Stability and Mechanical Properties of Phosphorene Nanotubes

2016 ◽  
Author(s):  
Xiangbiao Liao ◽  
Xi Chen
Keyword(s):  
Mechanical Properties ◽  
Young’S Modulus ◽  
Structural Stability ◽  
Young's Modulus ◽  
Axial Strain ◽  
Md Simulations ◽  
Column Buckling ◽  
Instability Modes ◽  
Higher Temperature ◽  
Intrinsic Strain

Using molecular dynamics (MD) simulations, we explore the structural stability and mechanical integrity of phosphorene nanotubes (PNTs), where the intrinsic strain in the tubular PNT structure plays an important role. It is proposed that the atomic structure of larger-diameter armchair PNTs (armPNTs) can remain stable at higher temperature, but the high intrinsic strain in the hoop direction renders zigzag PNTs (zigPNTs) less favorable. The mechanical properties of PNTs, including the Young’s modulus and fracture strength, are sensitive to the diameter, showing a size dependence. A simple model is proposed to express the Young’s modulus as a function of the intrinsic axial strain which in turns depends on the diameter of PNTs. In addition, the compressive buckling of armPNTs is length-dependent, whose instability modes transit from column buckling to shell buckling are observed as the ratio of diameter/length increases.

Surface effect on size dependent Young’s modulus of nanowires: Exponentially decreased surface elasticity model

2022 ◽  
Vol 307 ◽  
pp. 131001
Author(s):  
Jiangang Li ◽  
Xiao Lei ◽  
Jianhua Ding ◽  
Zhixiang Gao ◽  
Hua Wang ◽  
...  
Keyword(s):  
Young’S Modulus ◽  
Surface Effect ◽  
Young's Modulus ◽  
Surface Elasticity ◽  
Size Dependent

scholarly journals Investigation of the Young’s Modulus and the Residual Stress of 4H-SiC Circular Membranes on 4H-SiC Substrates

Micromachines ◽  
2019 ◽  
Vol 10 (12) ◽  
pp. 801 ◽  
Author(s):  
Jaweb Ben Messaoud ◽  
Jean-François Michaud ◽  
Dominique Certon ◽  
Massimo Camarda ◽  
Nicolò Piluso ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Residual Stress ◽  
Young’S Modulus ◽  
Microelectromechanical Systems ◽  
Film Growth ◽  
Electrochemical Etching ◽  
Young's Modulus ◽  
Fabrication Process ◽  
Bulge Test ◽  
Residual Strains

The stress state is a crucial parameter for the design of innovative microelectromechanical systems based on silicon carbide (SiC) material. Hence, mechanical properties of such structures highly depend on the fabrication process. Despite significant progresses in thin-film growth and fabrication process, monitoring the strain of the suspended SiC thin-films is still challenging. However, 3C-SiC membranes on silicon (Si) substrates have been demonstrated, but due to the low quality of the SiC/Si heteroepitaxy, high levels of residual strains were always observed. In order to achieve promising self-standing films with low residual stress, an alternative micromachining technique based on electrochemical etching of high quality homoepitaxy 4H-SiC layers was evaluated. This work is dedicated to the determination of their mechanical properties and more specifically, to the characterization of a 4H-SiC freestanding film with a circular shape. An inverse problem method was implemented, where experimental results obtained from bulge test are fitted with theoretical static load-deflection curves of the stressed membrane. To assess data validity, the dynamic behavior of the membrane was also investigated: Experimentally, by means of laser Doppler vibrometry (LDV) and theoretically, by means of finite element computations. The two methods provided very similar results since one obtained a Young’s modulus of 410 GPa and a residual stress value of 41 MPa from bulge test against 400 GPa and 30 MPa for the LDV analysis. The determined Young’s modulus is in good agreement with literature values. Moreover, residual stress values demonstrate that the fabrication of low-stressed SiC films is achievable thanks to the micromachining process developed.

Nanomechanics of carbon nanotubes and composites

2003 ◽  
Vol 56 (2) ◽  
pp. 215-230 ◽  
Author(s):  
Deepak Srivastava and ◽  
Chenyu Wei ◽  
Kyeongjae Cho
Keyword(s):  
Carbon Nanotubes ◽  
Young’S Modulus ◽  
Elastic Limit ◽  
Young's Modulus ◽  
Axial Strain ◽  
Torsional Stiffness ◽  
Strain Rates ◽  
Polyethylene Composite ◽  
Single Wall Nanotubes ◽  
And Diffusion

Computer simulation and modeling results for the nanomechanics of carbon nanotubes and carbon nanotube-polyethylene composite materials are described and compared with experimental observations. Young’s modulus of individual single-wall nanotubes is found to be in the range of 1 TPa within the elastic limit. At room temperature and experimentally realizable strain rates, the tubes typically yield at about 5–10% axial strain; bending and torsional stiffness and different mechanisms of plastic yielding of individual single-wall nanotubes are discussed in detail. For nanotube-polyethylene composites, we find that thermal expansion and diffusion coefficients increase significantly, over their bulk polyethylene values, above glass transition temperature, and Young’s modulus of the composite is found to increase through van der Waals interaction. This review article cites 54 references.

scholarly journals Experimental Deformation of Opalinus Clay at Elevated Temperature and Pressure Conditions: Mechanical Properties and the Influence of Rock Fabric

2021 ◽  
Author(s):  
Valerian Schuster ◽  
Erik Rybacki ◽  
Audrey Bonnelye ◽  
Johannes Herrmann ◽  
Anja M. Schleicher ◽  
...  
Keyword(s):  
Young’S Modulus ◽  
Deformation Behavior ◽  
Water Saturation ◽  
Young's Modulus ◽  
Axial Strain ◽  
Shear Zones ◽  
Opalinus Clay ◽  
Triaxial Tests ◽  
Influence Of Water ◽  
Confining Pressures

AbstractThe mechanical behavior of the sandy facies of Opalinus Clay (OPA) was investigated in 42 triaxial tests performed on dry samples at unconsolidated, undrained conditions at confining pressures (pc) of 50–100 MPa, temperatures (T) between 25 and 200 °C and strain rates ($$\dot{\varepsilon }$$ ε ˙ ) of 1 × 10–3–5 × 10–6 s−1. Using a Paterson-type deformation apparatus, samples oriented at 0°, 45° and 90° to bedding were deformed up to about 15% axial strain. Additionally, the influence of water content, drainage condition and pre-consolidation was investigated at fixed pc–T conditions, using dry and re-saturated samples. Deformed samples display brittle to semi-brittle deformation behavior, characterized by cataclastic flow in quartz-rich sandy layers and granular flow in phyllosilicate-rich layers. Samples loaded parallel to bedding are less compliant compared to the other loading directions. With the exception of samples deformed 45° and 90° to bedding at pc = 100 MPa, strain is localized in discrete shear zones. Compressive strength (σmax) increases with increasing pc, resulting in an internal friction coefficient of ≈ 0.31 for samples deformed at 45° and 90° to bedding, and ≈ 0.44 for samples deformed parallel to bedding. In contrast, pre-consolidation, drainage condition, T and $$\dot{\varepsilon }$$ ε ˙ do not significantly affect deformation behavior of dried samples. However, σmax and Young’s modulus (E) decrease substantially with increasing water saturation. Compared to the clay-rich shaly facies of OPA, sandy facies specimens display higher strength σmax and Young’s modulus E at similar deformation conditions. Strength and Young’s modulus of samples deformed 90° and 45° to bedding are close to the iso-stress Reuss bound, suggesting a strong influence of weak clay-rich layers on the deformation behavior.

The Influence of the Fixed Negative Charges on Mechanical and Electrical Behaviors of Articular Cartilage Under Unconfined Compression

2004 ◽  
Vol 126 (1) ◽  
pp. 6-16 ◽  
Author(s):  
D. D. Sun ◽  
X. E. Guo ◽  
M. Likhitpanichkul ◽  
W. M. Lai ◽  
V. C. Mow
Keyword(s):  
Articular Cartilage ◽  
Osmotic Pressure ◽  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Young's Modulus ◽  
Axial Strain ◽  
Fluid Pressure ◽  
Poisson's Ratio ◽  
Unconfined Compression ◽  
Fixed Charges

Unconfined compression test has been frequently used to study the mechanical behaviors of articular cartilage, both theoretically and experimentally. It has also been used in explant and gel-cell-complex studies in tissue engineering. In biphasic and poroelastic theories, the effect of charges fixed on the proteoglycan macromolecules in articular cartilage is embodied in the apparent compressive Young’s modulus and the apparent Poisson’s ratio of the tissue, and the fluid pressure is considered to be the portion above the osmotic pressure. In order to understand how proteoglycan fixed charges might affect the mechanical behaviors of articular cartilage, and in order to predict the osmotic pressure and electric fields inside the tissue in this experimental configuration, it is necessary to use a model that explicitly takes into account the charged nature of the tissue and the flow of ions within its porous interstices. In this paper, we used a finite element model based on the triphasic theory to study how fixed charges in the porous-permeable soft tissue can modulate its mechanical and electrochemical responses under a step displacement in unconfined compression. The results from finite element calculations showed that: 1) A charged tissue always supports a larger load than an uncharged tissue of the same intrinsic elastic moduli. 2) The apparent Young’s modulus (the ratio of the equilibrium axial stress to the axial strain) is always greater than the intrinsic Young’s modulus of an uncharged tissue. 3) The apparent Poisson’s ratio (the negative ratio of the lateral strain to the axial strain) is always larger than the intrinsic Poisson’s ratio of an uncharged tissue. 4) Load support derives from three sources: intrinsic matrix stiffness, hydraulic pressure and osmotic pressure. Under the unconfined compression, the Donnan osmotic pressure can constitute between 13%–22% of the total load support at equilibrium. 5) During the stress-relaxation process following the initial instant of loading, the diffusion potential (due to the gradient of the fixed charge density and the associated gradient of ion concentrations) and the streaming potential (due to fluid convection) compete against each other. Within the physiological range of material parameters, the polarity of the electric potential depends on both the mechanical properties and the fixed charge density (FCD) of the tissue. For softer tissues, the diffusion effects dominate the electromechanical response, while for stiffer tissues, the streaming potential dominates this response. 6) Fixed charges do not affect the instantaneous strain field relative to the initial equilibrium state. However, there is a sudden increase in the fluid pressure above the initial equilibrium osmotic pressure. These new findings are relevant and necessary for the understanding of cartilage mechanics, cartilage biosynthesis, electromechanical signal transduction by chondrocytes, and tissue engineering.

Experimental Measurement of Dynamical Young's Modulus and Shear Modulus of Low-Impedance Materials

2004 ◽  
Vol 261-263 ◽  
pp. 325-330
Author(s):  
Shao Chiu Shih ◽  
Yong Zhong Wang ◽  
Bing Yu ◽  
Li Li Wang
Keyword(s):  
Young’S Modulus ◽  
Effective Stress ◽  
Aluminum Foam ◽  
Young's Modulus ◽  
Axial Strain ◽  
Front Face ◽  
Pvdf Film ◽  
Strain History ◽  
Stress History ◽  
Average Value

A new dynamical measurement technique that combines PVDF film piezoelectric gages with resistor strain gages in conventional SHPB is developed to study the dynamical mechanical behavior of low-impedance aluminum foam. The average value of the stresses measured by PVDF gages from the front face and the back face of the specimen at each time is taken as the effective stress history of the specimen. This effective stress history is combined with the measured axial strain history in the specimen by eliminating time t. Then the initial part of the stress-strain relationship of the material can be determined reliably. From its slope, the dynamical Young’s modulus of low-impedance aluminum foam can be determined. For the aluminum foam with a density of 1.2×103 Kg/cm3 at a given strain rate (ε& =814/s), we get: E =1.15 GPa, G=0.44GPa.

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