Effect of crack tip sharpness on the strength of vulcanized rubbers

The effect of crack tip sharpness on crack propagation in vulcanized rubbers has been studied. For very sharp cracks, tearing is found to occur on a small scale at very low energies not far above the threshold required for the onset of mechanical crack growth. The “small-scale” tearing energies show relatively little variation for rubbers that differ widely in tear strength as normally measured. Thus the latter property appears to be strongly influenced by variations in the ability of rubbers to promote tip blunting. The small-scale tear behavior is of relevance to other fracture phenomena, including cutting by sharp objects and tensile failure. Natural variations in tip sharpness occur during cyclic or time-dependent mechanical crack growth and influence the form of the crack growth characteristics.     

Superstring motivated gauge models based on a rank six subgroup ofE 6

We discuss gauge models based on a superstring motivated rank six subgroup ofE ₆. Lepton number is an accidental unbroken symmetry of the models which leads to an essentially stable proton. One of the neutral gauge bosons couples toB-L and may have mass below a TeV.     

Approximation algorithms for scheduling problems with a modified total weighted tardiness objective

We study the approximability of minimum total weighted tardiness with a modified objective which includes an additive constant. This ensures the existence of a positive lower bound for the minimum value. Moreover the new objective has a natural interpretation in just-in-time production systems.     

Some new integral inequalities of Bellman–Bihari type with delay for discontinuous functions

In this article we investigate some integral functional inequalities of Bellman–Bihari type for piecewise-continuous functions with some fixed points of discontinuity. We also prove a new analogy and generalization of results which were obtained by Bellman and Bihari to integro-sum inequalities with delay and discontinuities that do not belong to Lipschitz’s type.     

An unflexural refined model of deformation of multilayered plates on an undeformable foundation

The stress-strain state of multilayered plates on an undeformable foundation is investigated. The design diagram of a transversely loaded plate is formed by supplementing it with a symmetric one about the contact surface of the foundation. The double-thickness plate obtained becomes loaded bilaterally and symmetrically about its midsurface. In such a way, only unflexural deformations can be modeled, which reduces the number of unknowns and the general order of differentiation of the resolving system of equations. The refined continual model developed takes into account the deformations of transverse shear and transverse compression in high iterative approximations. The cases of a rigid contact between the foundation and the plate and frictionless slip of the plate over the foundation are considered. Calculations confirm the efficiency of such an approach, which allows one to obtain solutions qualitatively and quantitatively close to three-dimensional ones. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 643–654, September–October, 2006.     

Structure and mechanical properties of Al/AlN multilayer with different AlN layer thickness

Nanometer scale Al/AlN multilayers have been prepared by dc magnetron sputtering technique with a columnar target. A set of Al/AlN multilayers with the Al layer thickness of 2.9 nm and the AlN layer thickness variation from 1.13 to 6.81 nm were determined. Low angle X-ray diffraction (LAXRD) was used to analyze the layered structure of multilayers. The phase structure of the coatings was investigated with grazing angle XRD (GAXRD). Mechanical properties of these multilayers were thoroughly studied using a nanoindentation and ball-on-disk micro-tribometer. It was found that the multilayer hardness and reduced modulus showed no strong dependence on the AlN layer thickness. Al2.9 nm/AlN1.13 nm multilayer had more excellent tribological properties than single layers and other proportion multilayers with a lowest friction coefficient of 0.15. And the tribological properties of all the multilayers are superior to the AlN single layer.     

Linear Relations, Differential Inclusions, and Degenerate Semigroups

A generalized linear differential equation in a Banach space is studied. The construction of a phase space and solutions with the help of the spectral theory of linear operators, ergodic theorems, and degenerate semigroups of linear operators is carried out.     

Etude structurale des sulfotellurures de terres rares (LS)2Te1+x (L = Tb,Dy, Ho,Er, Tm et Y). I. Sous-structure de la phase ordonnée de (HoS)2Te1,34. Structure de la phase desordonnée de (TbS)2Te

The lanthanide sulfotellurides (LS)₂Te_1+x (0 ≤ x < 0.50) show order-disorder phenomena. Above 450°C, they crystallize in a partially disordered structure, orthorhombic with cell parameters a, b, and c close to 4.1, 5.2, and 13.6 Å, respectively. This structure is determined from diffractometer data on a (HoS)₂Te_1.34 crystal (R = 0.061). It is built up along the c axis from (L₄S) tetrahedra layers, separated by Te planes. Disorder and nonstoichiometry are related to the two vacant Te sites.