The measurement of the mechanical properties of materials with submicron dimensions is extremely challenging, from the preparation and manipulation of specimens, to the application of small loads and ...extraction of accurate displacements. Here, we present results obtained on 250
nm-thick aluminium films using a novel versatile concept of micro and nano-machines allowing multiple loading configurations and geometries. The focus is put on the fracture strain defined either as the strain at necking under uniaxial tension or the local strain at cracking initiation. The ductility of free-standing thin metallic films is one of the mechanical properties which is rarely measured and discussed in the literature. The necking and fracture strains are found equal to 0.08 and 0.3, respectively. Depending on the application, such as the development of flexible electronics or the reliability of interconnects, and on the loading conditions, one or both of these ductility indices can be key in the definition of fail-safe designs. This study enlightens also the interest and potential of the new nanomechanical testing concept.
The effects on mechanical properties of partial crystallization of a zirconium based bulk amorphous alloy (Vit1) are investigated. Nanocomposites are produced by appropriate heat treatments at ...temperatures higher than the glass transition temperature. Mechanical properties at room temperature are investigated by compression tests and hardness measurements including nanoindentation. The variation of the fracture stress with the degree of crystallinity is related to the nature, the size and the dispersion of the crystals in the amorphous phase. The variations of microstructure are estimated thanks to differential scanning calorimetry, X-ray diffraction and transmission electron microscopy. A significant connexion between crystals induces a decrease of the fracture stress whereas hardness continuously increases with crystallinity. From nanoindentation tests, Young's modulus and apparent yield stresses were roughly estimated and it is concluded that crystallization tends to increase the yield stress. Nevertheless, AFM observations of the imprints after indentation suggest that the mechanism of deformation can vary significantly with crystallization.
The correlation between structure and mechanical behavior in the supercooled liquid region (SLR) of a Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass is investigated by compression tests, mechanical ...spectroscopy, differential scanning calorimetry and high resolution transmission electron microscopy. In the SLR, whatever the mechanical features, the alloy exhibits important change in mechanical behavior after a given time which is directly connected to the development of nanocrystallization. Moreover, in the studied experimental domain, strain-induced structural changes are very limited and the critical parameter remains the total annealing time undergone by the alloy. This result is attributed to the Newtonian rheology of the glass in the studied conditions.
On a modular domination game Gravier, Sylvain; Mhalla, Mehdi; Tannier, Eric
Theoretical computer science,
09/2003, Letnik:
306, Številka:
1-3
Journal Article
Recenzirano
Odprti dostop
We present a generalization of the so-called σ-game, introduced by Sutner (Math. Intelligencer 11 (1989) 49), a combinatorial game played on a graph, with relations to cellular automata, as well as ...odd domination in graphs. A configuration on a graph is an assignment of values in {0,…,p−1} (where p is an arbitrary positive integer) to all the vertices of G. One may think of a vertex v of G as a button the player can press at his discretion. If vertex v is chosen, the value of all the vertices adjacent to v increases by 1 modulo p. This defines an equivalence relation between the configurations: two configurations are in relation if it is possible to reach one from the other by a sequence of such operations. We investigate the number of equivalence classes that a given graph has, and we give formulas for trees and special regular graphs.
It has been a challenging problem to determine the smallest graph class where a problem is proved to be hard. In the literature, this has been pointed out to be very important in order to establish ...the real nature of a combinatorial problem.
An orientedk-coloring of an oriented graph G→=(V,E→) is a partition of V into k subsets such that there are no two adjacent vertices belonging to the same subset, and all the arcs between a pair of subsets have the same orientation. The decision problem k−oriented chromatic number (ocnk) consists of an oriented graph G→ and an integer k>0, plus the question if there exists an oriented k-coloring of G→. By its strong appeal, many papers have presented NP-completeness proofs for ocnk. It was not known the complexity status of ocnk when the input graph G→ satisfies that the underlying graph G has maximum degree 3.
In this paper we prove that ocn4 is NP-complete for an acyclic oriented graph G→ such that G is at same time: connected, planar, bipartite, and with maximum degree 3.
Our result defines a P versus NP-complete dichotomy with respect to the maximum degree Δ(G): ocnk is polynomial if Δ(G)<3 and NP-complete if Δ(G)≥3, since it is known that ocn3 is in P, and that ocnk is in P when the underlying graph has Δ(G)≤2.
Tremendous properties of bulk metallic glasses (BMGs) have led to numerous potential applications in the past few years. An obvious interest has been given to their potential as structural material ...given their high mechanical properties and their ability to be produced in bulk parts of several millimeters in size. Unlike their crystalline counterparts, they also show very promising insulating properties due to the absence of a periodic lattice. In the present work, the interest of using bulk amorphous metallic alloys as materials combining good structural properties and thermal insulation is discussed. The study of Hf-rich BMGs enables to reduce the thermal losses through a higher σc/κ performance ratio and thus shows very good potential for future insulating and structural applications.
Display omitted
•Zr substitution by Hf in (HfxZr1-x)52.5Ti5Cu17.9Ni14.6Al10 leads to lower thermal conductivity by around 15%.•The lower thermal conductivity is due to higher electrical resistivity as it represents 90% of the total thermal conductivity.•The low thermal conductivity of Hf-rich alloys leads to lower thermal losses through a higher σc/κ performance ratio.
In the last years new composite materials made of a metallic glass matrix with embedded nanocrystals have arisen as a promising alternative to the metallic glasses, due to their higher hardness. ...Although the effects of a partial nano-crystallization onto mechanical and magnetic properties have been widely investigated, nothing is known about thermal transport properties, interesting for recently proposed novel applications. Here we investigate how thermal transport is modified in presence of nanocrystalline inclusions in a Zr-based bulk metallic glass. By means of electric measurements and inelastic x ray scattering we are able to disentangle the effects of a partial nanocrystallization onto the two different contributions to heat transport, the electronic and the vibrational one. We show that no enhanced electrons or phonons scattering from the interfaces is observed, while the presence of crystalline nanoinclusions leads to an increase of both contributions, via an increased electric conductivity and transverse acoustic speed of sound. Surprisingly, while a gradual modification of the electric conductivity with the crystalline fraction is observed, even a low crystalline fraction is sufficient to modify elastic and vibrational properties. Our results indicate that low crystallinity composites are indeed promising alternative to both amorphous and crystalline alloys, thanks to their unique combination of high ductility, polycrystal-like vibrational properties and amorphous-like electric transport.
Display omitted
We use the link between the existence of tilings in Manhattan metric with {1}-bowls and minimum total dominating sets of Cartesian products of paths and cycles. From the existence of such a tiling, ...we deduce the asymptotical values of the total domination numbers of these graphs and we deduce the total domination numbers of some Cartesian products of cycles. Finally, we investigate the problem of total domination numbers for some Cartesian products of two paths.
PDF
