Homogenization of heat diffusion in a cracked medium

We develop in this note a homogenization method to tackle the problem of a diffusion process through a cracked medium. We show that the cracked surface of the domain induces a source term in the homogenized equation. We assume that the cracks are orthogonal to the surface of the material, where an incoming heat flux is applied. The cracks are supposed to be of depth 1, of small width, and periodically arranged.Comment: 28 pages, 10 figure

Application of homogeneously precipitated nanosized Fe-doped alumina powders to carbon nanotube growth.

Homogeneous precipitation of hydroxides was investigated as an alternative method to synthesize Fe-doped aluminum oxide (α-Al2−2xFe2xO3) particles over which carbon nanotubes (CNTs) were grown via a catalytic chemical vapor deposition (CCVD) method. Performance of the homogeneously precipitated particles for CNT growth was quantitatively compared with that of the combustion-synthesized particles. The main advantage of the homogeneous precipitation of hydroxides and subsequent calcination process against to the combustion synthesis and other commonly practiced chemical routes is the ability to tailor the Fe-doped Al2O3 precursor powder characteristics such as size and specific surface area (SSA) without requiring any milling step and also to control the phase composition of the oxide powder with high Fe content, and subsequently the quality and quantity of CNTs during CCVD process. The particle size of the precipitated and calcined α-Al2−2xFe2xO3 powders varies between ∼50 and 400 nm for 5–10 cat.% Fe-containing systems. The monodispersed particle size distribution and optimum phase composition of the homogeneously precipitated powders, particularly for a 10 cat.% Fe content in the starting oxide, and their much higher SSA than similar materials prepared by other chemical routes lead to production of high amounts of good quality CNTs

Catalytic CVD Synthesis of Double and Triple-walled Carbon Nanotubes by the Control of the Catalyst Preparation

We report the influence of catalyst preparation conditions for the synthesis of carbon nanotubes (CNTs) by catalytic chemical vapour deposition (CCVD). Catalysts were prepared by the combustion route using either urea or citric acid as the fuel. We found that the milder combustion conditions obtained in the case of citric acid can either limit the formation of carbon nanofibres (defined as carbon structures not composed of perfectly co-axial walls or only partially tubular) or increase the selectivity of the CCVD synthesis towards CNTs with fewer walls, depending on the catalyst composition. It is thus for example possible in the same CCVD conditions to prepare (with a catalyst of identical chemical composition) either a sample containing more than 90% double- and triple-walled CNTs, or a sample containing almost 80% double-walled CNTs

The weight and density of carbon nanotubes versus the number of walls and diameter

The weight and density of carbon nanotubes are calculated as a function of their characteristics (inner diameter, outer diameter, and number of walls). The results are reported in the form of diagrams which may be useful to other researchers, in particular in the fields of synthesis/production, materials and composites, health/toxicity studies

On shakedown of shape memory alloys with permanent inelasticity

International audienceShape memory alloys (SMAs) offer interesting perspectives in various fields such as aeronautics, robotics, biomedical sciences, or structural engineering. The distinctive properties of those materials stem from a solid/solid phase transformation occuring at a microscopic level. Modeling the rather complex behavior of SMAs is a topic of active research. Lately, SMA models coupling phase-transformation with permanent inelasticity have been proposed to capture degradation effects which are frequently observed experimentally for cyclic loadings. In this paper, the classical static and kinematic shakedown of plasticity theory are extended to such material models. Those results gives conditions for the energy dissipation to remain bounded, and might be relevant for the fatigue design of SMA systems

Shakedown of elastic-perfectly plastic materials with temperature-dependent elastic moduli

International audienceFor elastic-perfectly plastic structures under prescribed loading histories, the celebrated Melan's theorem gives a sufficient condition for the evolution to become elastic in the large-time limit. That situation, classically referred to as shakedown, is associated with the intuitive idea that the plastic strain tends to a limit as time tends to infinity. The Melan's theorem has the distinctive property of being path-independent, i.e. independent on the initial state of the structure. Regarding fatigue design, shakedown corresponds to the most beneficial regime of high-cycle fatigue, as opposed to the regime of low-cycle fatigue which typically occurs if the plastic strain does not converge towards a stabilized value.This communication addresses the extension of Melan's theorem to situations in which the elastic moduli are fluctuating in time. Such time fluctuations may result from significant variations of the temperature. In a lot of practical situations, structural elements are indeed submitted to thermomechanical loading histories in which variations of the temperature are large enough for the temperature dependence of the material not to be negligible. It has been conjectured that Melan's theorem could be extended to temperature dependent (or time-dependent) elastic moduli , but no theoretical result is available. This communication aims at providing results in that direction, with a special emphasis on time-periodic variations. If Melan's condition is satisfied, we show that shakedown indeed occurs provided the time fluctuations of the elastic moduli satisfy a certain condition (which in particular is fulfilled if the time fluctuations are not too large). We provide a counterexample which shows that setting such a constraint on the elastic moduli is necessary to reach path-independent theorems as proposed. A simple mechanical system is studied as an illustrative example

CCVD synthesis of carbon nanotubes from (Mg,Co,Mo)O catalysts: influence of the proportions of cobalt and molybdenum

Carbon nanotubes have been synthesised by catalytic chemical vapour deposition of a H2–CH4 mixture (18 mol% CH4) over (Mg,Co,Mo)O catalysts. The total amount of cobalt and molybdenum has been kept constant at 1 cat% and the proportion of molybdenum with respect to cobalt has been varied from x(Mo) = 0.25–1.0. This variation has important effects on both the yield and the nature (number of walls, straight walls or bamboo-like structures) of the carbon nanotubes. It also has an influence on the purity of the samples (amount of encapsulated metal particles, presence or not of amorphous carbon deposits). For x = 0.25, the nanotubes were mainly double- and triple-walled (inner diameter less than 3 nm); samples prepared from catalysts with higher molybdenum ratios contained larger multi-walled carbon nanotubes (inner diameter up to 9 nm), having up to 13 concentric walls. It is proposed that different growth mechanisms may occur depending on the initial composition of the catalyst

Organized growth of carbon nanotubes on Fe-doped alumina ceramic substrates

Polycrystalline Fe-doped alumina (Al2O3) ceramics have been produced and used as a substrate for organized carbon nanotubes (CNTs) growth by catalytic chemical vapor deposition (CCVD). In these substrates, Fe3+ cations, which are the catalyst source, are initially substituted to Al3+ in a-Al2O3, instead of being simply deposited as a thin Fe layer on the surface of the substrate. The selective reduction of these substrates resulted in in situ formation of homogeneously distributed Fe nanoparticles forming patterns at nanometerscale steps and kinks. These nanoparticles then catalyzed the growth of high quality CNTs, with some degree of organization thanks to their interaction with the topography of the substrate

Preparation-microstructure-property relationships in double-walled carbon nanotubes/alumina composites

Double-walled carbon nanotube/alumina composite powders with low carbon contents (2– 3 wt.%) are prepared using three different methods and densified by spark plasma sintering. The mechanical properties and electrical conductivity are investigated and correlated with the microstructure of the dense materials. Samples prepared by in situ synthesis of carbon nanotubes (CNTs) in impregnated submicronic alumina are highly homogeneous and present the higher electrical conductivity (2.2–3.5 Scm-1) but carbon films at grain boundaries induce a poor cohesion of the materials. Composites prepared by mixing using moderate sonication of as-prepared double-walled CNTs and lyophilisation, with little damage to the CNTs, have a fracture strength higher (+30%) and a fracture toughness similar (5.6 vs 5.4 MPa m1/2) to alumina with a similar submicronic grain size. This is correlated with crack-bridging by CNTs on a large scale, despite a lack of homogeneity of the CNT distribution

In situ CCVD synthesis of carbon nanotubes within a commercial ceramic foam

Consolidated nanocomposite foams containing a large quantity of carbon nanotubes (CNTs) within millimetre-sized pores are prepared for the first time. A commercial ceramic foam is impregnated by a 60 g L21 slurry of a (Mg(12x)(Co0.75Mo0.25)xO solid solution (x = 0.01, 0.05, 0.1 and 0.2) powder in ethanol. Three successive impregnations led to deposits several tens of mm thick, with a good coverage of the commercial-ceramic pore walls but without closing the pores. The materials were submitted to a CCVD treatment in H2–CH4 atmosphere in order to synthesise the CNTs. When using attrition-milled powders, the carbon is mostly in the form of nanofibres or disordered carbon rather than CNTs. Using non-milled powders produces a less-compact deposit of catalytic material with a higher adherence to the walls of the ceramic foam. After CCVD, the carbon is mostly in the form of high-quality CNTs, as when using powder beds, their quantity being 2.5 times higher. The so-obtained consolidated nanocomposite materials show a multi-scale pore structuration