Critical Thickness Ratio Research Articles

Analytical model and material equivalent methods for steady state heat partition coefficient between two contact discs in multi-disc clutch

The heat partition coefficient between two finite thickness contact discs during long-time sliding is studied with a coupled finite element method. Results show that the heat partition coefficient varies from its initial value to another steady state value rapidly instead of being a constant all the time. An analytical solution of the temperature field under invariant heat flux input is deduced, which tells that there exists a unique critical thickness ratio between the contact discs that keeps the heat partition coefficient a constant. An equivalent method for single-material contact bodies is proposed that is capable of calculating the steady state heat partition coefficient for any thickness ratio. It reveals that the steady state heat partition coefficient only has relationship with the mass density and the heat capacity of the materials and the thickness ratio. Based on this method, a two-step material equivalent method is further proposed for the contact discs that have friction linings on them. The solution shows that the steady state heat partition coefficient in this situation is also only determined by the material properties and the layer thicknesses. A test bench of multi-disc clutch is set up and a series of sliding experiments are conducted to validate the proposed equivalent methods and solutions of steady state heat partition coefficient. The measured experimental temperature variations show that the temperature level of the separator disc in the clutch is overestimated with the constant heat partition coefficient of semi-infinite model, while it is close to those calculated results with steady state heat partition coefficient. Therefore, the temperature fields of the contact discs during long-time sliding with constant speed can be figured out efficiently using the steady state heat partition coefficient with only small error, and these equivalent methods benefit the multi-disc clutch design and temperature estimation in practical applications.

Numerical analysis of the flow and heat transfer in cylindrical clothing microclimates – Influence of the microclimate thickness ratio

Clothing microclimates, i.e. the space between the skin and the clothing, can play a central role in the heat and mass exchanges from or to the body. This is especially true for protective clothing, where microclimates are generally thicker and natural convection is more likely to occur. We used a computational fluid dynamics approach to perform numerical studies of fluid flow and heat transfer across cylindrical clothing microclimates for Reynolds number of 3900. Transient simulations were performed for three different values of microclimate thickness to diameter ratio (0.05, 0.10 and 0.25), considering a two-dimensional cross-section of a human limb surrounded by a porous fabric and exposed to cool external air (10°C). The obtained local heat transfer along the skin shows that increasing the microclimate thickness ratio from 0.05 to 0.25 decreases the convective heat fluxes by up to 100% in the upstream regions of the microclimate, and increases them up to 190% in the downstream regions. This asymmetry, which indicates an increasingly important role of natural convection as the microclimate thickness ratio is increased, is often overlooked in space-averaged approaches due to the opposite changes in the different regions of the microclimate. Local variations in temperature along the outer fabric and in convective fluxes along the skin were significant, reaching up to 14K and 90%, respectively. The critical thickness ratio above which natural convection should not be ignored was found to be 0.1 (e.g. corresponding to a microclimate thicknesses of 11 mm or 8 mm, around an upper arm or forearm, respectively).

Scaling behavior of nanoimprint and nanoprinting lithography for producing nanostructures of molybdenum disulfide

Top-down lithography techniques are needed for manufacturing uniform device structures based on emerging 2D-layered materials. Mechanical exfoliation approaches based on nanoimprint and nanoprint principles are capable of producing ordered arrays of multilayer transition metal dichalcogenide microstructures with a high uniformity of feature dimensions. In this study, we present a study on the applicability of nanoimprint-assisted shear exfoliation for generating ultrathin monolayer and few-layer MoS2 structures as well as the critical limits of feature dimensions produced via such nanoimprint and nanoprint-based processes. In particular, this work shows that give a lateral feature size of MoS2 structures that are pre-patterned on a bulk stamp, there exists a critical thickness or aspect ratio value, below which the exfoliated layered structures exhibit major defects. To exfoliate a high-quality, uniform monolayer or few-layer structures, the characteristic lateral feature sizes of such structures need to be in the sub-100 nm regimes. In addition, the exfoliated MoS2 flakes of critical thicknesses exhibit prominent interlayer twisting features on their cleaved surfaces. Field-effect transistors made from these MoS2 flakes exhibit multiple (or quasi-analog-tunable) charge memory states. This work advances the knowledge regarding the limitations and application scope of nanoimprint and nanoprint processes in manufacturing nano/microstructures based on layered materials and provides a method for producing multi-bit charge memory devices.

Analytical determination of process windows for bilayer slot die coating

Slot die coating is a film casting process with a highly diverse variety of everyday applications. As a pre-metered process it not only guarantees excellent film uniformity, but is also suitable for simultaneously applied multilayer coatings. Characteristic singularities like the behavior of the liquid–liquid interface and the impact of the additional mid-lip on film uniformity were already investigated before. However, the effect of an altered gap pressure regime on commonly used coating windows has not yet been discussed. In this work, we therefore extended available single-layer coating windows for Newtonian and power-law liquids to the bilayer case. Here, the emphasis was laid on the air entrainment limit. Subsequently, the theoretical results were compared to experimental data. It was found that the onset of air entrainment strongly depends on the top to bottom film thickness ratio for bilayer coatings. A critical film thickness ratio which delivers similar coating limits as those for single-layer coatings was derived and confirmed by experimentally gained results.

Critical thickness ratio for buckled and wrinkled fruits and vegetables

This work aims at establishing the geometrical constraint for buckled and wrinkled shapes by modeling a fruit/vegetable with exocarp and sarcocarp as a hyperelastic layer-substrate structure subjected to uniaxial compression. A careful analysis on the derived bifurcation condition leads to the finding of a critical thickness ratio which separates the buckling and wrinkling modes, and remarkably, which is independent of the material stiffnesses. More specifically, it is found that if the thickness ratio is smaller than this critical value a fruit/vegetable should be in a buckled shape (under a sufficient stress); if a fruit/vegetable is in a wrinkled shape the thickness ratio is always larger than this critical value. To verify the theoretical prediction, we consider four types of buckled fruits/vegetables and four types of wrinkled fruits/vegetables with three samples in each type. The geometrical parameters for the 24 samples are measured and it is found that indeed all the data fall into the theoretically predicted buckling or wrinkling domains.

Ultra-wide Low-Frequency Band Gap of One-Dimensional Superconducting Photonic Crystals Containing Metamaterials

In this paper, the low-frequency band gap properties of one-dimensional superconducting photonic crystal which is composed of superconductor and metamaterials have been theoretically investigated by the Bloch theorem together with the transfer matrix method. Numerical results show that the width of the low-frequency band gap increases first and then decreases with the increase of thickness ratio, which is defined as the ratio of the thickness of the metamaterials layer to that of the superconductor layer. A critical thickness ratio is found at which the ultra-wide low-frequency band gap appears. The influence of the metamaterials layer’s relative permittivity, the superconductor layer thicknesses and the operating temperature on the ultra-wide low-frequency band gap are also investigated in this paper.

Theoretical analysis of the characteristics of the solid oxide fuel cells with a bi-layer electrolyte

From the analytical model derived earlier [17], analytical expressions for the relative thickness ratio rs of a bi-layer electrolyte and the maximum power density of a fuel cell are developed. Using these expressions, together with the other relationships from the analytical model, the characteristics of solid oxide fuel cells (SOFCs) with a bi-layer electrolyte are analyzed and theoretical analysis of the effect of the configuration of a bi-layer electrolyte on the SOFC performance is performed. The results show that the effectiveness of the bi-layer electrolyte depends strongly on its configuration. In the analyses, the variations of open circuit voltage and the maximum power density with the thickness ratio at different total electrolyte thicknesses and different operating temperatures are obtained. Furthermore, by taking into considerations of the oxygen partial pressure at the interface between the two layers of electrolytes, an analytical expression for the critical relative thickness ratio, above which, the electrolyte is stable, is obtained.

Effect of the Thickness Ratio on the Failure Modes of Tailor Welded Blanks

Tailor welded blanks (TWBs) offer several notable benefits including decreased part weight, reduced manufacturing costs, increased environmental friendliness, and improved dimensional consistency. To take full advantage of these benefits, however, one needs to overcome the reduced formability of TWBs and be able to accurately predict the failure modes depending on the thickness ratio between the thicker and thinner sheets of a tailor welded blank with similar base materials early in the design process. In this paper, we studied the effect of the thickness ratio on the limit dome height of TWBs by using finite element method and experiments, analyzed the effect of TR on the failure mode of TWBs. A concept of the critical thickness ratio was presented to predict the failure modes of TWBs. The results show that the rapture originates on the weld of TWBs when the thickness ratio is less than the critical thickness ratio and on the thinner side when the thickness ratio exceeds the critical thickness ratio.

Modeling of Magnetomechanical Actuators in Laminated Structures

A magnetomechanical plate model (MMPM) has been developed to predict the elastic and magnetostrictive strains and mechanical stress in laminated structures with magnetostrictive and non-magnetic layers under the simultaneous effect of quasi-static mechanical stress and magnetic field. This model was obtained by combining an energy-based statistical magnetomechanical model with the classical laminated plate theory. The magnetomechanical plate model was used to study a unimorph structure having a magnetostrictive iron—gallium (Galfenol) patch attached to different non-magnetic substrates. The actuation response from the patch was obtained for in-plane axial magnetic field acting on the unimorph. The MMPM was used to predict the normalized tip displacement due to induced-strain actuation in a unimorph cantilever beam and the results were compared with existing modeling techniques. The model was used to study the effect of tensile and compressive axial pre-loads on the actuation response of the structure. A study was also performed to understand the effect of total thickness of the structure, the ratio of the active/ passive layer thickness and the effect of the mechanical properties of different substrate materials on the actuator performance. A non-dimensional parameter ST i (percentage strain transfer) was introduced to explain the behavior of the actuator in extension and bending dominated regimes and a critical thickness ratio (trc) was defined to demarcate these two regimes. The results demonstrate that the model captures the non-linearity in the magnetomechanical process and the different structural couplings.

Intermixing criteria for reaction synthesis of Ni/Al multilayered microfoils

Abstract Intermixing criteria are proposed for determining the microstructure of the reaction products during the reaction synthesis of Ni/Al multilayered microfoils. The critical thickness and thickness ratio for the formation of monolithic intermetallic depend on the conductive heat loss through the Ni layer and are verified by analytical thermophysical modeling.

Two-layer hydraulic falls over an obstacle

Motions in a forced channel flow of two contiguous homogeneous fluids of different constant densities and different thicknesses are considered. The total depth is finite and the upper surface is constrained to be planar (rigid lid approximation). The forcing is due to a bottom obstruction. The existence of a critical thickness ratio, obtained when the square of the thickness ratio is equal to the density ratio, leads to major differences with the one-layer case. The present study concentrates on this critical case. Moreover it is restricted to hydraulic falls, which are steady flows over an obstacle providing a transition between a subcritical and a supercritical flow. A weakly nonlinear analysis is performed. At leading order the problem reduces to a forced modified Korteweg–de Vries equation which can be integrated exactly. The weakly nonlinear results are validated by comparison with a numerical integration of the full governing equations. The numerical method is based on boundary integral equation techniques. The differences with the one-layer case are the existence of a second family of subcritical hydraulic falls when the thickness ratio is below critical, and the existence of supercritical hydraulic falls described by four parameters instead of three for all thickness ratios.

Linear stability of multilayer plane Poiseuille flows of Oldroyd B fluids

The linear stability of plane Poiseuille flows of two and three-symmetrical layers is studied by using both longwave and moderate wavelength analysis. The considered fluids follow Oldroyd-B constitutive equations and hence the stability is controlled by the viscous and elastic stratifications and the layer thicknesses. For the three symmetrical-layer Poiseuille flow, competition between varicose (symmetrical) and sinuous (antisymmetrical) mode is considered. In both cases (two and three symmetrical layers), the additive character of the longwave formula with respect to viscous and elastic terms is largely used to determine stable arrangements at vanishing Reynolds number. It is found that if the stability of such arrangements is due simultaneously to viscous and elastic stratification (the flow is stable for longwave disturbance and the Poiseuille velocity profile is convex), then the Poiseuille flow is also stable with respect to moderate wavelength disturbances and the critical thickness ratio around which the configurations becomes unstable is given by longwave analysis. Note that a convex velocity profile means a positive jump of shear rate at the interface. Finally, the destabilization due to a moderate increase in the Reynolds number is considered and two distinct behaviors are pointed according to the convexity of the Poiseuille velocity profile. Moreover, an important influence of the thickness ratio on the critical wavenumber is found for three symmetrical layer case (for two layer case, the critical wave number is of order one and depends weakly on the thickness ratio).

Multiple cracking in metal-ceramic laminates

There have been observations showing that relatively thick metal layers in metal-ceramic laminates lead to the formation of multiple periodic cracks within a zone near a pre-crack, distributing damage and significantly enhancing the composite's toughness. Several models including linear elastic fracture mechanics and shear-lag analysis are developed in the present work in order to study the competition between multiple cracking and single-crack extension as damage modes. It is established that there is a critical thickness ratio for metal-ceramic layers above which multiple cracking dominates. Moreover, this critical thickness ratio is inversely proportional to the corresponding moduli ratio such that the competition between damage modes is governed by the metal-ceramic layer stiffness ratio. Plastic hardening of metals helps to activate the multiple-cracking damage mode, while plastic yielding does the opposite.

Autorotation of rectangular plates

A series of tests have been conducted on the autorotation of plates of rectangular section and thickness to chord ratios of from 0.1 to 1.0. The major difference from previous work was that the plates spanned the full width of the wind tunnel, i.e. the flow was essentially two-dimensional. The results show major differences from predictions of infinite aspect ratio plates inferred from finite aspect ratio tests as given by Iversen (1979). Moreover, they give excellent correlation with the two-dimensional numerical solution of Lugt (1980) for a 10% thick plate. In contrast to previous results which indicate no autorotation for square cylinders (t/c = 1.0), it is found that autorotation is easily achieved. A new result is that tipspeed ratios are found to be independent of thickness ratio, at approximately the Lugt value over the full range of thickness ratios. Drag coefficients are found to be independent of thickness ratio. There appears to be a critical thickness ratio above and below which the lift coefficients are constant, but are of different magnitude.

Solitary Waves on a Two-Layer Fluid

This paper deals with weakly nonlinear long gravity waves on a stably stratified two-layer fluid. By using the reductive perturbation method, it is found that the fast mode is always governed by a Korteweg-de Vries (K-dV) equation whose coefficients depend on the thickness ratio and the density ratio. On the other hand, the slow mode is also governed, in general, by another K-dV equation except near and at the critical thickness ratio. At the critical thickness ratio, however, the slow mode is shown to be governed by a modified K-dV equation with cubic nonlinearity and near the critical thickness ratio it is governed by an equation of a combined form of the K-dV and modified K-dV equation. Steady solitary wave solutions to these equations are investigated in detail. A special solution representing a dispersive bore or hydraulic jump is also found.

Lateral Diffusion in Ag–Se Thin-Film Couples

A study has been made of the diffusion of Ag along thin evaporated Se films using optical and transmission electron microscopy. The effect on the growth rate of varying both the Ag and Se film thicknesses and the temperature has been studied. Thin-film diffusion rates were considerably faster than in bulk diffusion couples, indicating some short-circuit diffusion mechanism. An important result of the investigation was the demonstration of a critical thickness ratio of Ag to Se which had to be exceeded in order for diffusion to occur. This critical ratio depended only on the stoichiometry of the Ag2Se phase formed during diffusion.