Geometrical Size Effect Research Articles

The effect of point defects and nanoparticles on thermal conductivity of magnesium silicide

We compute thermal conductivity (κ) of magnesium silicide (Mg2Si) with point defects and nanoparticles through molecular dynamics simulation. To describe an alloy with complex defect structures, the extended modified embedded atom method is utilized in this simulation study. The calculated phonon dispersion and κ of pristine Mg2Si are in close agreement with first-principles calculations and experimental results. We compared the effect of intrinsic point defects and nanoparticles on heat transfer in Mg2Si at the same stoichiometry. We find that point defects could be more effective than nanoparticles to reduce κ. The geometric size effect is also investigated for Mg and Si nanoparticles. Smaller Mg nanoparticles can significantly reduce κ. However, Si nanoparticles demonstrate little size effect on κ. Our simulation results show that phonon transport in Mg2Si has more contribution from strain scattering than mass defect scattering. These findings can provide guidance for experiments to more effectively engineer bulk Mg2Si with nanostructured defects for thermoelectric applications.

Mode-I crack in a magnetoelectroelastic layer sandwiched by two elastic half-planes

In this paper we study the impermeable opening crack problem in a magnetoelectroelastic layer sandwiched between dissimilar elastic half-planes under in-plane mechanical, electric and magnetic loadings. Fourier transforms are applied to reduce the crack problem to dual integral equations, which can be further reduced to solving a system of simultaneous Fredholm integral equations. Numerical solutions of the integral equations can be obtained by using the collocation method, and the explicit form solution of the near crack-tip fields is obtained asymptotically. The field intensity factors are obtained and the effects of material properties, geometric size, and loadings are analyzed.

Parametric Study of a Horizontal Tube Heat Exchanger for LNG Submerged Combustion Vaporiser

LNG (Liquefied Natural Gas) submerged combustion vaporiser is applied to convert Liquefied natural gas to gas phase natural gas through using the hot combustion gas generated from submerged combustion. This paper investigated the vaporisation and heat transfer process of a single horizontal tube, a simplified model, to simulate the heat transfer of circular tube heat exchanger used in LNG submerged combustion vaporiser. This work provides a useful computer model for the design of heat exchanger used in LNG submerged combustion vaporiser. The overall heat transfer and vaporisation process of the tube was separated into single-phase liquid, two-phase mixture and single-phase vapour heat transfer regions for calculation and analysis. Through development of a dedicated computer model, a parametric study was carried out to analyse the effects of geometrical size and operating conditions on inner surface convective heat transfer of tube. The results of study suggested that the preferable tube surface temperature for design was found between 280 K and 288 K in order to avoid frost deposition. The minimum tube length required for the overall vaporisation is predicted to be about 16 m when the inner tube diameter set between 0.24 m and 0.28 m.

Size Effects at Dwell Stage of Micro-Indentation for Pure Aluminum

Abstract Pure aluminum L2 was used to study the size effect during the dwell stage of micro-indentation. The experiments reveal that an indentation depth increases further and then a load-displacement platform appears when the load is held in a constant after reaching the maximum load. The results show that the emergency of instantly formed load-displacement platform has a little relevance to the dwell time. Subsequently the micro-plastic constitutive model with intrinsic material length and the reduced intrinsic material length was imported into the FEM of whole indentation process. The abnormal phenomenon at the dwell stage could be treated as a rule through comparative analysis from simulated and experimental results. The intrinsic length of pure aluminum L2 was obtained as 5.09 μm, while the reduced intrinsic length at the end of the dwell stage decreased to 4.90 μm. The simulated results indicate that depth variances at the dwell stage are mainly affected by the reduction of the strain gradient. This is equivalent to that the density of geometrically necessary dislocations (GNDs) reduces to about 96.27% compared with that of the beginning of the dwell stage. It is summarized that the forming mechanism of the load-displacement platform may be attributed to the geometric size effect and the mechanical size effect.

On a 2D hydro-mechanical lattice approach for modelling hydraulic fracture

A 2D lattice approach to describe hydraulic fracturing is presented. The interaction of fluid pressure and mechanical response is described by Biot's theory. The lattice model is applied to the analysis of a thick-walled cylinder, for which an analytical solution for the elastic response is derived. The numerical results obtained with the lattice model agree well with the analytical solution. Furthermore, the coupled lattice approach is applied to the fracture analysis of the thick-walled cylinder. It is shown that the proposed lattice approach provides results that are independent of the mesh size. Moreover, a strong geometrical size effect on nominal strength is observed which lies between analytically derived lower and upper bounds. This size effect decreases with increasing Biot's coefficient.

Electromagnetically induced transparency in a two-dimensional quantum pseudo-dot system: Effects of geometrical size and external magnetic field

Electromagnetically induced transparency in a two-dimensional quantum pseudo-dot system, under the influence of a uniform magnetic field, is theoretically investigated. In this regard, the effects of external magnetic field and the geometrical size of the pseudo-dot system on the absorption as well as refractive index and the group velocity of the probe light pulse are investigated. The results show that the electromagnetically induced transparency occurs in the system and its frequency, transparency window and group velocity of the probe field are affected by the external magnetic field and the geometrical size of the pseudo-dot system. Also, electromagnetically induced transparency and the group velocity of light can be controlled via the external magnetic field and geometrical size.

The Influence of Notch Geometric Size in the Fatigue Strength of Steel

The fatigue behavior of notch specimens has been investigated in this manuscript. It is shown that notch geometric size has apparent effect for fatigue strength of specimens. The blunt notch is used in test. It is concluded that geometric size effect depends on the stress gradient and can be estimated with the help of the linear elastic fracture mechanics. The influence of notch size for fatigue strength can be explained with geometric factor. The plastic strain play an important role in fatigue crack initiation with notch gets sharper reach certain magnitude limit, and fatigue strength is lower than the predicted by geometric size factor effect. The method does not apply fatigue strength of the sharper notch. Another estimation method shall be used to that kind of notches.

Geometrical size effect on the interface diffusion of micro solder joint in electro-thermal coupling aging

This paper investigates the influence of diffusion layer (solder layer) thickness (δ) on interface diffusion in both thermal aging and electro-thermal coupling aging. The different δ (δ = 60, 120 and 240 μm) of Cu/Sn–3.0Ag–0.5Cu (SAC305)/Cu butt solder joints are used. The results indicate that the geometrical size (solder layer thickness) of solder joint has significant effect on element diffusion behavior. The diffusion coefficient, time exponent, element concentrations and diffusion flux are greatly dependent upon δ. The effects of δ on the interface diffusion is different between thermal aging and electro-thermal coupling aging, due to driving force for diffusion is different. During thermal aging, concentration gradient is the main driving force of diffusion, and diffusion coefficient, time exponent and diffusion flux are relatively low for a thin solder layer. However, under electro-thermal coupling condition, the electron wind force provides the dominating driving force for diffusion, and diffusion coefficient and diffusion flux of thin δ are significantly larger than the thick ones. The Cu concentration of the area near interface is relatively high for a thin solder layer in both tests. Under the same experimental temperature, the effects of δ on the electro-thermal coupling aging are more obvious than thermal aging.

Mechanical and acoustic response of an underwater structure subjected to mechanical excitation

In this paper, an underwater structure is modeled as a cylindrical shell with internal bulkheads, and closed by a truncated conical shell, and it consists of metal substrate and sound absorbing coating, whose FGM core is considered. Suppose the inner cavity and outer space of the structure are filled with air and fluid mediums, the mechanical response of the underwater structure is calculated with Galerkin method while the acoustic response is investigated by means of the Helmholtz integral. Some numerical examples are given and the effect of geometrical size and material parameters on mechanical and acoustic response is discussed.

Piezoelectric effect of one-dimensional gear-shaped ZnO microwires

In this work the piezoelectric effect of one-dimensional ZnO gear-shaped microwires (GMWs) is studied by the finite element method. By calculating the piezopotential of substrate-bound gear-shaped ZnO microwires oriented along the c-axis with gear groove depth of 0–5 μm, we demonstrate that the GMW has more advantage for piezoelectric nanogenerators than the common hexagonal microwire (HMW). To understand the anisotropic electricity generation, the calculated piezopotential distribution in the bent ZnO GMW and HMW has been analyzed under an external force with the different directions. Moreover, the calculation also indicates that the effect of geometric size on piezopotential for the GMW is similar to the HMW. Our results will be a guidance for the design of high-efficiency energy harvesting devices.

Geometrical Size Effect in High Cycle Fatigue Strength of Heavy-walled Ductile Cast Iron GJS400: Weakest Link vs Defect-based Approach

Fatigue strength is known to decrease with increasing dimension of the component. This is due to a technological size effect, related to the production process, and to a geometrical size effect, due to a higher probability of finding a large defect. To investigate the latter, an heavy-walled component made of Ductile Cast Iron (DCI) has been trepanned and a fatigue test plan has been carried out using 4 different specimen geometries. An attempt has been made to relate the resulting fatigue strength using a weakest-link approach based on the effective volumes and surfaces. This approach seems to work well only in cases of different specimen's lengths. Some of the fracture surfaces were analyzed by means of SEM and the initiating defects were identified and measured. An approach in which the defects population can be randomly distributed in the specimen has been tried. Virtual fatigue tests have been carried out by considering pure propagation of the worst defect. The resulting fatigue curves showed that this approach is promising but needs further description of the initiation phase.

Geometrical size effect in high cycle fatigue strength of heavy-walled Ductile Cast Iron GJS400: Weakest link vs. defect-based approach

Fatigue strength is known to decrease with increasing dimension of the component. This is due to a technological size effect, related to the production process, and to a geometrical size effect, due to a higher probability of finding a large defect. To investigate the latter, an heavy-walled component made of Ductile Cast Iron (DCI) has been trepanned and a fatigue test plan has been carried out using 4 different specimen geometries. An attempt has been made to relate the resulting fatigue strength using a weakest-link approach based on the effective volumes and surfaces. This approach seems to work well only in cases of different specimen's lengths. Some of the fracture surfaces were analyzed by means of SEM and the initiating defects were identified and measured. An approach in which the defects population can be randomly distributed in the specimen has been tried. Virtual fatigue tests have been carried out by considering pure propagation of the worst defect. The resulting fatigue curves showed that this approach is promising but needs further description of the initiation phase.

Transferability of fatigue resistance data for welded joints

The original notch stress approach for fatigue design is limited to thick sheet structures and a fixed notch radius of 1 mm. Concepts utilizing the effective notch stress claim to account for the variation of the weld shape parameters, however, size effects are not taken into account. Therefore, an expansion of the notch stress approach has been developed, which includes consideration of the geometrical and statistical size effect in order to extend the application to thin and thick sheet structures. It is also capable of evaluating highly localized three-dimensional stress concentrations at weld start and end points. To validate the quality of this approach, experimentally determined fatigue data for thin steel sheet specimens from the Institute of Material Mechanics, including weld start and end points, and data from the literature regarding conventional thick sheet components without weld start and end points were reevaluated. The final result is a unified scatter band of fatigue lives of thin and thick sheet specimens, with and without weld start and end points, including also several modes of seam weld end point loading: transversal and longitudinal tension compression as well as shear loading at seam welds.

Linear and nonlinear optical properties of multilayered spherical quantum dots: Effects of geometrical size, hydrogenic impurity, hydrostatic pressure and temperature

Based on the effective mass and parabolic one band approximations, simultaneous effects of the geometrical size, hydrogenic impurity, hydrostatic pressure, and temperature on the intersubband optical absorption coefficients and refractive index changes in multilayered spherical quantum dots are studied. Energy eigenvalues and eigenvectors are calculated using the fourth-order Runge–Kutta method and optical properties are obtained using the compact density matrix approach. The results indicate that the hydrogenic impurity, hydrostatic pressure, temperature and geometrical parameters such as the well and barrier widths have a great influence on the linear, the third-order nonlinear and the total optical absorption coefficients and refractive index changes.

Electron Raman scattering in single and multilayered spherical quantum dots: Effects of hydrogenic impurity and geometrical size

Based on the effective mass and parabolic one-band approximations, the differential cross-section for the intersubband electron Raman scattering process in a single and multilayered spherical quantum dots is investigated. The influence of an on-center hydrogenic impurity and geometrical parameters such as the well and barrier widths on the differential cross-section is studied. Results show that the number, the position and the magnitude of the peaks of emission spectra, considerably depend on the presence of the hydrogenic impurity as well as geometrical parameters. Results also reveal that the magnitude of the peaks significantly depend on the polarization vectors of incident and scattered lights. • Hydrogenic impurity effects on ERS in single and multilayered SQDs are investigated. • Light polarization vectors and geometrical size effects the ERS are also studied. • Number, position and magnitude of the peaks, depend on the presence of the impurity. • The light polarization vectors have a great influence on the magnitude of the peaks. • Geometrical parameters considerably change the peaks number, position and magnitude.

Nonlinear vibration analysis of micro-plates based on strain gradient elasticity theory

In this study, non-linear free vibration of micro-plates based on strain gradient elasticity theory is investigated. A general form of Mindlin’s first-strain gradient elasticity theory is employed to obtain a general Kirchhoff micro-plate formulation. The von Karman strain tensor is used to capture the geometric non-linearity. The governing equations of motion and boundary conditions are obtained in a variational framework. The Homotopy analysis method is employed to obtain an accurate analytical expression for the non-linear natural frequency of vibration. For some specific values of the gradient-based material parameters, the general plate formulation can be reduced to those based on some special forms of strain gradient elasticity theory. Accordingly, three different micro-plate formulations are introduced, which are based on three special strain gradient elasticity theories. It is found that both geometric non-linearity and size effect increase the natural frequency of vibration. In a micro-plate having a thickness comparable with the material length scale parameter, the strain gradient effect on increasing the non-linear natural frequency is higher than that of the geometric non-linearity. By increasing the plate thickness, the strain gradient effect decreases or even diminishes. In this case, geometric non-linearity plays the main role on increasing the natural frequency of vibration. In addition, it is shown that for micro-plates with some specific thickness to length scale parameter ratios, both geometric non-linearity and size effect have significant role on increasing the frequency of non-linear vibration.

Thermo-mechanical coupling and size effects in micro and nano resonators

Existing models for thermoelastic damping consider geometric size effects only, the focus of this study is on tuning of thermoelastic damping with mechanical strain, which reduces both relaxation rate and thermal conductivity at the nanoscale. We developed a model that accounts for the contribution of tensile force and thermal conductivity in a clamped-clamped configuration nano-resonator. Experimentally measured thermal conductivity is then coupled with the model suggests the existence of a critical length scale (inversion point) below which quality factor increases with increase in thickness and vice versa. The nanoscale strain-thermal conductivity coupling is found to be most effective at and around this inversion point.

Third harmonic generation in a coaxial cylindrical quantum well wire: Magnetic field and geometrical size effects

Third harmonic generation coefficient of typical GaAs/AlxGa1−xAs single and coaxial cylindrical quantum well wires under the influence of an external magnetic field is investigated. The fourth-order Runge–Kutta method is used to obtain energy eigenvalues and eigenvectors of the system. Results indicate that for a single CQWW, the maximum values of the third harmonic generation coefficient increase with the increase of the wire radius and magnetic field. The results also reveal that because of the anti-crossing effect between adjacent subbands with similar azimuthal quantum number, the external magnetic field has a great influence on the third harmonic generation coefficient of the coaxial cylindrical quantum well wire. We also found that the largest value of the third harmonic generation coefficient of coaxial cylindrical quantum well wire can be obtained with an appropriate choice of the barrier width.

On the competition between in-plane and out-of-plane deformations in laser thermal adjustment

Laser thermal adjustment as an application of laser forming in micro systems has received considerable attentions in recent years. The deformations of thin sheets in laser thermal adjustment are decoupled into in-plane and out-of-plane deformation components through re-distributing the plastic deformation zone. In order to understand the competition between these two deformations, the effects of geometric size and material property on deformation behavior are numerically investigated by changing the temperature distribution in laser heating process. The out-of-plane bending dominates if thicker plates are used, while samples with smaller width favor the in-plane deformation. Moreover, it is an effective way to choose materials with higher thermal conductivity and lower yield stress in laser thermal adjustment process for achieving larger in-plane deformation.

Statistical and geometrical size effects in notched members based on weakest-link and short-crack modelling

Cracks originate at defects of numerous kinds spread in the material. The fatigue life is – besides many other factors – governed by the large defects in the highly stressed area. The statistical size effect may be taken into account by identifying the highly stressed surface of a structure. The geometrical size effect is strictly interpreted from the viewpoint of fracture mechanics. Endurance limit stresses are correlated with thresholds of fatigue crack growth. For short cracks the increase of the threshold with crack length may be steeper than the increase of the applied stress intensity factor. In terms of applied local stresses this phenomenon of non propagating cracks can be expressed as a support factor. Additionally, some metals may show stable cyclic plastic deformation at the endurance limit. If proofs of the fatigue strength are based on the Theory of Elasticity a hypothetical stress state in accordance with the theory must be found which corresponds with the real stresses and strains at the critical locations of components. Neuber’s formula is used to supply this correlation expressed as a macro support factor. The paper describes a multiplicative ansatz for considering these combined effects in a design environment. A validation of the system of factors against experimental evidence is provided.