Ressort de torsion | EPFL Graph Search

Le ressort de torsion est un ressort hélicoïdal. À part la forme spécifique de ses extrémités, ce ressort est identique à un ressort hélicoïdal de traction-compression à très faible angle d'hélice, ou même à un ressort de traction à spires jointives si l'on recherche un certain frottement interne, par exemple pour favoriser l'amortissement de vibrations. vignette Nous supposerons que notre ressort a des spires non jointives et très peu inclinées (travaillant en flexion presque pure) et que ses extrémités sont encastrées. Si tel n'était pas le cas la précision des formules serait passablement altérée et la répartition des contraintes modifiée dans un sens nettement défavorable. Il faut toutefois reconnaître que dans un très grand nombre de mécanismes où les critères de précision sont secondaires, les extrémités sont accrochées ou plus simplement encore appuyées. Condition de résistance C'est en fait la même que pour le ressort spiral, sauf que l'expression du moment d'

Fluid and glassy phases of vibrated granular matter studied with a torsion oscillator

Patrick Mayor

Granular matter submitted to external perturbations exhibits various behaviors depending on the vibration intensity: when strongly vibrated, the granular system has a fluid aspect, whereas under low intensity perturbations, it is in a quasi-solid phase. In this work, we clarify these analogies: we discuss to what extent a "granular fluid" is close to a standard liquid and, on the other hand, investigate the similarities between weakly perturbed granular materials and supercooled liquids undergoing a glass transition. We first consider the case where a granular medium undergoes vibrations of high intensity (with accelerations of about 1 to 10 times that of gravity). This vibrated system is investigated using an immersed torsion oscillator which is sensitive to the granular agitation and which, as a result, exhibits irregular angular deflections that can be analyzed to give information on the grains' motion. This oscillator can also be used in forced mode: applying a torque allows measures of the mechanical susceptibility, which displays a resonance peak similar to that of a damped oscillator. It is thus possible to introduce a viscosity parameter for the system, which is found to be inversely proportional to the vibration acceleration imposed to the container. Moreover, by considering both the fluctuations (given by the diffusive noise, with the oscillator in free mode) and the susceptibility (forced mode), the validity of the fluctuation-dissipation theorem can be tested. Surprisingly, it turns out that very complicated system, even though far from equilibrium, satisfies this basic law of equilibrium statistical mechanics in first approximation, and therefore behaves very much like a plain liquid. The immersed oscillator can thus be compared to a pollen particle exhibiting Brownian motion due to the continuous molecular – here, the granular – agitation. We can thus also introduce an "effective temperature" parameter for vibration-fluidized granular matter and discuss its properties. In particular, we observe that the temperature defined is inhomogeneous and anisotropic, contrary to usual liquids. An interesting issue is also studied carefully: when the damping becomes large (for when the imposed vibrations are lower, or when the oscillator is deeply immersed), a stiffening phenomenon is observed, in which the apparent elastic constant increases linearly with the friction. An elementary rheological model suggests that this may be caused by the appearance of a force chains fretwork resisting the probe rotation. Various granular materials are analyzed with this met hod. The grain mass seems to be an important parameter, as well as the grain surface state. Experiments in which the grains are etched with acid in order to modify the surface roughness are also discussed. While we know what happens to a liquid when its temperature is decreased one can wonder what happens to a granular system when the perturbations become critically low. By using vibrations of weak intensity (with accelerations below that of gravity), we study how the system reaches a "frozen" static configuration when the perturbation intensity is decreased. The observed diffusive noise appears to approach the final jammed state according to the Vogel-Fulcher-Tammann law, that also describes the temperature dependence of viscosity or diffusivity in supercooled liquids, thus showing strong analogies with the vitrification process. Here, the parameter playing the role of temperature in the equations is found to depend only on the vibration amplitude. Finally, we briefly discuss how a small modification of the experimental setup may allow to create a "Brownian motor" generating useful work out of the random agitation of the grains.

EPFL2005

Optimization of composition and structure of cemented carbide cutting tools

Samy Adjam

WC-Co cemented carbides are composites, which combine a hard phase consisting of WC grains and a metallic ductile phase as a binder. Their excellent mechanical properties, combining high hardness, toughness and refractory properties, make them excellent materials for cutting processes such as turning, drilling and milling. For such applications, cemented carbides are coated with thin ceramic films that increase their resistance to thermal stress as well as to the mechanical and chemical wear inherent in extreme machining conditions. Three main characteristics determine the performance and wear resistance of cutting tools: the cohesion of the hard phase above 1200 K, the ductility of the cobalt binder, and the mechanical and thermal resistance of the coatings. This work focuses on the impact of the microstructural behaviour of the cobalt binder on the tool-life of the cutting tools. The aim is to develop new binders for cemented carbides with improved impact resistance. The techniques of transmission electron microscopy at room temperature and in-situ at high temperature, as well as mechanical spectroscopy in a forced torsion pendulum have proved to be essential for the identification of the microstructure of cobalt and for the study of the relaxation phenomena occurring therein. Mechanical spectroscopy has evidenced the presence of two relaxation peaks, P1 and P2 in the cobalt phase and a peak (P3) related to WC-WC grain boundary sliding. The peak P1 appears to be correlated with the cutting tool life measured in interrupted cutting tests. In this work, the role of the binder is highlighted in particular by the identification of a glass-type transition observed for cobalt. The thermodynamics of the transition is evidenced by the behavior of P1 whose relaxation time diverges according to a Vogel-Fulcher-Tammann model, which is characteristic of glass transitions. The state of the material corresponding to temperatures below this transition shows a strong dependence on its thermomechanical history. This dependence is confirmed by a divergence in plastic deformations over two identical temperature cycles with different thermomechanical histories. Such a divergence on a standard protocol, called (ZFC/FC), seems to indicate a break in the thermodynamic hypothesis of ergodicity, even though it could not be attributed solely to the behaviour of cobalt. Transmission electron microscopy at room temperature has determined that the low temperature phase of the cobalt binder has a face-centred cubic structure and is composed of twinned nanodomains containing nanotwins. This state is therefore characterised by a short-range order without the long-range order, which is characteristic of glassy materials. In-situ observations have highlighted a detwinning process corresponding to the temperatures of the cobalt relaxation peak identified by mechanical spectroscopy. This detwinning process continues until the appearance of a long-range ordered face-centred cubic phase above 1050K, which is favourable to deformation. Mechanically, this transition is similar to a brittle-to-ductile transition, greatly influencing the properties of the material and its toughness. The cutting tool life could benefit from lowering the brittle to ductile transition temperature.

EPFL2021

Isogeny graphs of ordinary abelian varieties

Ernest Hunter Brooks, Dimitar Petkov Jetchev, Benjamin Pierre Charles Wesolowski

Fix a prime number l. Graphs of isogenies of degree a power of l are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ordinary abelian varieties over a finite field. We analyse graphs of so-called l-isogenies, resolving that, in arbitrary dimension, their structure is similar, but not identical, to the "volcanoes" occurring as graphs of isogenies of elliptic curves. Specializing to the case of principally polarizable abelian surfaces, we then exploit this structure to describe graphs of a particular class of isogenies known as (l, l)-isogenies: those whose kernels are maximal isotropic subgroups of the l-torsion for the Weil pairing. We use these two results to write an algorithm giving a path of computable isogenies from an arbitrary absolutely simple ordinary abelian surface towards one with maximal endomorphism ring, which has immediate consequences for the CM-method in genus 2, for computing explicit isogenies, and for the random self-reducibility of the discrete logarithm problem in genus 2 cryptography.