Mechanics of adhesive contact on a power-law graded elastic half-space

We consider adhesive contact between a rigid sphere of radius R and a graded elastic half-space with Young's modulus varying with depth according to a power law E = E-0(z/c(0))(k) (0 < k < 1) while Poisson's ratio v remaining a constant. Closed-form analytical solutions are established for the critical force, the critical radius of contact area and the critical interfacial stress at pull-off. We highlight that the pull-off force has a simple solution of P-cr= -(k+3)pi R Delta gamma/2 where Delta gamma is the work of adhesion and make further discussions with respect to three interesting limits: the classical JKR solution when k = 0, the Gibson solid when k --> 1 and v = 0.5, and the strength limit in which the interfacial stress reaches the theoretical strength of adhesion at pull-off. (C) 2009 Elsevier Ltd. All rights reserved.

An extension of the two dimensional JKR theory to the case with a large contact width

In the Hertz and JKR theories, parabolic assumptions for the rounded profiles of the sphere or cylinder are adopted under the condition that the contact radius (width) should be very small compared to the radius of the sphere or cylinder. However, a large contact radius (width) is often found in experiments even under a zero external loading. We aim at extending the plane strain JKR theory to the case with a large contact width. The relation between the external loading and the contact width is given. Solutions for the Hertz, JKR and rounded-profile cases are compared and analyzed. It is found that when the ratio of a/R is approximately larger than about 0.4, the parabolic assumptions in the Hertz and JKR theories are no longer valid and the exact rounded profile function should be used.

On the contact width in generalized plain strain JKR model for isotropic solids

Adhesive contact model between an elastic cylinder and an elastic half space is studied in the present paper, in which an external pulling force is acted on the above cylinder with an arbitrary direction and the contact width is assumed to be asymmetric with respect to the structure. Solutions to the asymmetric model are obtained and the effect of the asymmetric contact width on the whole pulling process is mainly discussed. It is found that the smaller the absolute value of Dundurs' parameter beta or the larger the pulling angle theta, the more reasonable the symmetric model would be to approximate the asymmetric one.

Influence of Contact Angle and Tube Size on Capillary-Driven Flow Under Microgravity

The influence of contact angle and tube radius on the capillary-driven flow for circular cylindrical tubes is studied systematically by microgravity experiments using the drop tower. Experimental results show that the velocity of the capillary flow decreases monotonically with an increase in the contact angle. However, the time-evolution of the velocity of the capillary flow is different for different sized tubes. At the beginning of the microgravity period, the capillary flow in a thinner tube moves faster than that in a thicker tube, and then the latter overtakes the former. Therefore, there is an intersection between the curves of meniscus velocity vs microgravity time for two differently sized tubes. In addition, for two given sized tubes this intersection is delayed when the contact angle increases. The experimental results are analyzed theoretically and also supported by numerical computations.

Sessile Drop in Microgravity: Creation, Contact Angle and Interface

We present in this paper the results obtained from a parabolic flight campaign regarding the contact angle and the drop interface behavior of sessile drops created under terrestrial gravity (1g) or in microgravity (mu g). This is a preliminary study before further investigations on sessile drops evaporation under microgravity. In this study, drops are created by the mean of a syringe pump by injection through the substrate. The created drops are recorded using a video camera to extract the drops contact angles. Three fluids have been used in this study : de-ionized water, HFE-7100 and FC-72 and two heating surfaces: aluminum and PTFE. The results obtained evidence the feasibility of sessile drop creation in microgravity even for low surface tension liquids (below 15 mN m (-aEuro parts per thousand 1)) such as FC-72 and HFE-7100. We also evidence the contact angle behavior depending of the drop diameter and the gravity level. A second objective of this study is to analyze the drop interface shape in microgravity. The goal of the these experiments is to obtain reference data on the sessile drop behavior in microgravity for future experiments to be performed in an French-Chinese scientific instrument (IMPACHT).

Plankton periodicity and some physicochemical parameters of the intake channel of Lake Chad

This study examines zooplankton periodicity and some physicochemical parameters of the intake channel of Lake Chad (Nigeria). Nine different zooplankton species were identified at the sampling station 1, while seven different zooplankton species were identified at the sampling station 2 (the intake channel of Lake Chad). Each identified zooplankton species was grouped according to its major group of copepods, Cladocera or Rotifera. The copepods dominated the zooplankton community with the highest numbers of occurrence as Cyclopedia species throughout the course of the study at both station l and 2. There was a clear evidence of the influence of organic manure nutrients on total zooplankton population at station 1 when compared to that of station 2. The water quality variables measured in the course of this study show that the surface water temperature in station 1 ranges from 27.5 degree C to 30.5 degree C. The pH ranges from 6.8 to 8.5, while D.O. contents ranges from 2.9mg/L to 6.1mg/L and alkalinity recorded was 172.00 to 208.00. At the station 2 the water quality parameters obtained show that surface water temperature ranges from 27.3 degree C to 30.2 degree C, pH ranges between 6.9 to 8.5, while the D.O contents ranges from 3.0 mg/L to 6.2 mg/L.Alkalinity ranges from 172mg/L to 212 mg/L

Estimation and inference for grasping and manipulation tasks using vision and kinesthetic sensors

This thesis presents a novel framework for state estimation in the context of robotic grasping and manipulation. The overall estimation approach is based on fusing various visual cues for manipulator tracking, namely appearance and feature-based, shape-based, and silhouette-based visual cues. Similarly, a framework is developed to fuse the above visual cues, but also kinesthetic cues such as force-torque and tactile measurements, for in-hand object pose estimation. The cues are extracted from multiple sensor modalities and are fused in a variety of Kalman filters.

A hybrid estimator is developed to estimate both a continuous state (robot and object states) and discrete states, called contact modes, which specify how each finger contacts a particular object surface. A static multiple model estimator is used to compute and maintain this mode probability. The thesis also develops an estimation framework for estimating model parameters associated with object grasping. Dual and joint state-parameter estimation is explored for parameter estimation of a grasped object's mass and center of mass. Experimental results demonstrate simultaneous object localization and center of mass estimation.

Dual-arm estimation is developed for two arm robotic manipulation tasks. Two types of filters are explored; the first is an augmented filter that contains both arms in the state vector while the second runs two filters in parallel, one for each arm. These two frameworks and their performance is compared in a dual-arm task of removing a wheel from a hub.

This thesis also presents a new method for action selection involving touch. This next best touch method selects an available action for interacting with an object that will gain the most information. The algorithm employs information theory to compute an information gain metric that is based on a probabilistic belief suitable for the task. An estimation framework is used to maintain this belief over time. Kinesthetic measurements such as contact and tactile measurements are used to update the state belief after every interactive action. Simulation and experimental results are demonstrated using next best touch for object localization, specifically a door handle on a door. The next best touch theory is extended for model parameter determination. Since many objects within a particular object category share the same rough shape, principle component analysis may be used to parametrize the object mesh models. These parameters can be estimated using the action selection technique that selects the touching action which best both localizes and estimates these parameters. Simulation results are then presented involving localizing and determining a parameter of a screwdriver.

Lastly, the next best touch theory is further extended to model classes. Instead of estimating parameters, object class determination is incorporated into the information gain metric calculation. The best touching action is selected in order to best discern between the possible model classes. Simulation results are presented to validate the theory.

Plume Parameters and Thruster Properties of a Low Power Arcjet

Abstract. A low power arcjet-thruster of 1 kW-class with gas mixture of H2-N2 or pure argon as the propellant is fired at a chamber pressure about 10 Pa. The nozzle temperature is detected with an infrared pyrometer; a plate set perpendicular to the plume axis and connected to a force sensor is used to measure the thrust; a probe with a tapered head is used for measuring the impact pressure in the plume flow; and a double-electrostatic probe system is applied to evaluate the electron temperature. Results indicate that the high nozzle temperature could adversely affect the conversion from enthalpy to kinetic energy. The plume flow deviates evidently from the LTE condition, and the rarefied-gas dynamic effect should be considered under the high temperature and low-pressure condition in analyzing the experimental phenomena.

The assessment of physico-chemical parameters of Shiroro Lake and its major tributaries

The physico-chemical parameters of the surface water of Shiroro Lake and its major tributaries at their entry point to the reservoir were assessed over a period of eighteen months. As in other African inland water bodies there were seasonal variations in the parameters measured. The hydrological regime of the lake, precipitation chemistry, bedrock chemistry and hydro-electric power generation influence and determine the inputs of dissolved organic carbon, nutrient levels and water quality of the lake. The added nutrients to the lake by means of the major tributary rivers and inundation of surrounding areas also influence the water quality of the lake. The wet season mean values for water and air temperature were significantly (P <0.05) higher than dry season mean values in all stations. However, for pH, Dissolved oxygen and Phosphate-phosphorus the dry season mean values were higher than wet season mean values

I. Rigid body penetration into brittle materials. II. Phase change effect on shock wave propagation

Part I.

We have developed a technique for measuring the depth time history of rigid body penetration into brittle materials (hard rocks and concretes) under a deceleration of ~ 10⁵ g. The technique includes bar-coded projectile, sabot-projectile separation, detection and recording systems. Because the technique can give very dense data on penetration depth time history, penetration velocity can be deduced. Error analysis shows that the technique has a small intrinsic error of ~ 3-4 % in time during penetration, and 0.3 to 0.7 mm in penetration depth. A series of 4140 steel projectile penetration into G-mixture mortar targets have been conducted using the Caltech 40 mm gas/ powder gun in the velocity range of 100 to 500 m/s.

We report, for the first time, the whole depth-time history of rigid body penetration into brittle materials (the G-mixture mortar) under 10⁵ g deceleration. Based on the experimental results, including penetration depth time history, damage of recovered target and projectile materials and theoretical analysis, we find:

1. Target materials are damaged via compacting in the region in front of a projectile and via brittle radial and lateral crack propagation in the region surrounding the penetration path. The results suggest that expected cracks in front of penetrators may be stopped by a comminuted region that is induced by wave propagation. Aggregate erosion on the projectile lateral surface is < 20% of the final penetration depth. This result suggests that the effect of lateral friction on the penetration process can be ignored.

2. Final penetration depth, P_max, is linearly scaled with initial projectile energy per unit cross-section area, e_s , when targets are intact after impact. Based on the experimental data on the mortar targets, the relation is P_max(mm) 1.15e_s (J/mm² ) + 16.39.

3. Estimation of the energy needed to create an unit penetration volume suggests that the average pressure acting on the target material during penetration is ~ 10 to 20 times higher than the unconfined strength of target materials under quasi-static loading, and 3 to 4 times higher than the possible highest pressure due to friction and material strength and its rate dependence. In addition, the experimental data show that the interaction between cracks and the target free surface significantly affects the penetration process.

4. Based on the fact that the penetration duration, t_max, increases slowly with e_s and does not depend on projectile radius approximately, the dependence of t_max on projectile length is suggested to be described by t_max(μs) = 2.08e_s (J/mm² + 349.0 x m/(πR²), in which m is the projectile mass in grams and R is the projectile radius in mm. The prediction from this relation is in reasonable agreement with the experimental data for different projectile lengths.

5. Deduced penetration velocity time histories suggest that whole penetration history is divided into three stages: (1) An initial stage in which the projectile velocity change is small due to very small contact area between the projectile and target materials; (2) A steady penetration stage in which projectile velocity continues to decrease smoothly; (3) A penetration stop stage in which projectile deceleration jumps up when velocities are close to a critical value of ~ 35 m/s.

6. Deduced averaged deceleration, a, in the steady penetration stage for projectiles with same dimensions is found to be a(g) = 192.4v + 1.89 x 10⁴, where v is initial projectile velocity in m/s. The average pressure acting on target materials during penetration is estimated to be very comparable to shock wave pressure.

7. A similarity of penetration process is found to be described by a relation between normalized penetration depth, P/P_max, and normalized penetration time, t/t_max, as P/P_max = f(t/t_max, where f is a function of t/t_max. After f(t/t_max is determined using experimental data for projectiles with 150 mm length, the penetration depth time history for projectiles with 100 mm length predicted by this relation is in good agreement with experimental data. This similarity also predicts that average deceleration increases with decreasing projectile length, that is verified by the experimental data.

8. Based on the penetration process analysis and the present data, a first principle model for rigid body penetration is suggested. The model incorporates the models for contact area between projectile and target materials, friction coefficient, penetration stop criterion, and normal stress on the projectile surface. The most important assumptions used in the model are: (1) The penetration process can be treated as a series of impact events, therefore, pressure normal to projectile surface is estimated using the Hugoniot relation of target material; (2) The necessary condition for penetration is that the pressure acting on target materials is not lower than the Hugoniot elastic limit; (3) The friction force on projectile lateral surface can be ignored due to cavitation during penetration. All the parameters involved in the model are determined based on independent experimental data. The penetration depth time histories predicted from the model are in good agreement with the experimental data.

9. Based on planar impact and previous quasi-static experimental data, the strain rate dependence of the mortar compressive strength is described by σ_f/σ⁰_f = exp(0.0905(log(έ/έ_0) ^1.14, in the strain rate range of 10^-7/s to 10³/s (σ⁰_f and έ are reference compressive strength and strain rate, respectively). The non-dispersive Hugoniot elastic wave in the G-mixture has an amplitude of ~ 0.14 GPa and a velocity of ~ 4.3 km/s.

Part II.

Stress wave profiles in vitreous GeO₂ were measured using piezoresistance gauges in the pressure range of 5 to 18 GPa under planar plate and spherical projectile impact. Experimental data show that the response of vitreous GeO₂ to planar shock loading can be divided into three stages: (1) A ramp elastic precursor has peak amplitude of 4 GPa and peak particle velocity of 333 m/s. Wave velocity decreases from initial longitudinal elastic wave velocity of 3.5 km/s to 2.9 km/s at 4 GPa; (2) A ramp wave with amplitude of 2.11 GPa follows the precursor when peak loading pressure is 8.4 GPa. Wave velocity drops to the value below bulk wave velocity in this stage; (3) A shock wave achieving final shock state forms when peak pressure is > 6 GPa. The Hugoniot relation is D = 0.917 + 1.711u (km/s) using present data and the data of Jackson and Ahrens [1979] when shock wave pressure is between 6 and 40 GPa for ρ₀ = 3.655 gj cm³ . Based on the present data, the phase change from 4-fold to 6-fold coordination of Ge⁺⁴ with O^-2 in vitreous GeO₂ occurs in the pressure range of 4 to 15 ± 1 GPa under planar shock loading. Comparison of the shock loading data for fused SiO₂ to that on vitreous GeO₂ demonstrates that transformation to the rutile structure in both media are similar. The Hugoniots of vitreous GeO₂ and fused SiO₂ are found to coincide approximately if pressure in fused SiO₂ is scaled by the ratio of fused SiO₂to vitreous GeO₂ density. This result, as well as the same structure, provides the basis for considering vitreous Ge0₂ as an analogous material to fused SiO₂ under shock loading. Experimental results from the spherical projectile impact demonstrate: (1) The supported elastic shock in fused SiO₂ decays less rapidly than a linear elastic wave when elastic wave stress amplitude is higher than 4 GPa. The supported elastic shock in vitreous GeO₂ decays faster than a linear elastic wave; (2) In vitreous GeO₂ , unsupported shock waves decays with peak pressure in the phase transition range (4-15 GPa) with propagation distance, x, as α 1/x^-3.35 , close to the prediction of Chen et al. [1998]. Based on a simple analysis on spherical wave propagation, we find that the different decay rates of a spherical elastic wave in fused SiO₂ and vitreous GeO₂ is predictable on the base of the compressibility variation with stress under one-dimensional strain condition in the two materials.

Analysis and optimization of stress wave propagation in two-dimensional granular crystals with defects

Granular crystals are compact periodic assemblies of elastic particles in Hertzian contact whose dynamic response can be tuned from strongly nonlinear to linear by the addition of a static precompression force. This unique feature allows for a wide range of studies that include the investigation of new fundamental nonlinear phenomena in discrete systems such as solitary waves, shock waves, discrete breathers and other defect modes. In the absence of precompression, a particularly interesting property of these systems is their ability to support the formation and propagation of spatially localized soliton-like waves with highly tunable properties. The wealth of parameters one can modify (particle size, geometry and material properties, periodicity of the crystal, presence of a static force, type of excitation, etc.) makes them ideal candidates for the design of new materials for practical applications. This thesis describes several ways to optimally control and tailor the propagation of stress waves in granular crystals through the use of heterogeneities (interstitial defect particles and material heterogeneities) in otherwise perfectly ordered systems. We focus on uncompressed two-dimensional granular crystals with interstitial spherical intruders and composite hexagonal packings and study their dynamic response using a combination of experimental, numerical and analytical techniques. We first investigate the interaction of defect particles with a solitary wave and utilize this fundamental knowledge in the optimal design of novel composite wave guides, shock or vibration absorbers obtained using gradient-based optimization methods.

The relationship between some physicochemical parameters and plankton composition on fish production in ponds

The effect of physico-chemical parameters and plankton composition on fish production in ponds was investigated in six fish farms for eight weeks. The physicochemical parameters investigated were temperature=25-30 plus or minus C, transparency=0.45-0.57m, dissolved oxygen=3.0-10.9mg/l, pH=6.0-7.7, dissolved carbon dioxide=5.46-28.3mg/l, total alkalinity=44.37-80.0ppm, chemical oxygen demand=31.88-72.18mg/l and biological oxygen demand=0.66-48.34mg/l. Plankton composition varies and was made of four families of phytoplankton namely; Cyanophyceae, Chlorophyceae, Dinophyceae and Diatomida; and four families of zooplankton viz; Protozoa, Rotifera, Copepoda and Dinoflagellates. Farm 1 and 6 recorded the highest average weight of about 1.0kg and average total length of about 40.0cm for the two fish species. This study showed that fish yield was dependable on the quality and management of pond water characteristics