Comment on "Modified Coulomb Law in a Strongly Magnetized Vacuum"

This is a comment on Phys. Rev. Lett. 98, 180403 (2007) [arXiv:0704.2162].Comment: 1 page, comment on arXiv:0704.2162, published versio

Interlaminar crack growth in fiber reinforced composites during fatigue, part 3

Interlaminar crack growth behavior in fiber-reinforced composites subjected to fatigue loading was investigated experimentally and theoretically. In the experimental phase, inter-laminar crack propagation rates and mechanisms were determined for the cases of various geometries, laminate parameters and cyclic stress levels. A singular hybrid-stress finite element method was used in conjuction with the experimental results to examine the local crack-tip behavior and to characterize the crack propagation during fatigue. Results elucidate the basic nature of the cyclic delamination damage, and relate the interlaminar crack growth rate to the range of mixed-mode crack-tip stress intensity factors. The results show that crack growth rates are directly related to the range of the mixed-mode cyclic stress intensity factors by a power law relationship

Manufacturing method and performance assessment for variable lead vacuum rotors

In recent years variable lead rotors have been produced, mainly for vacuum applications, involving a multiple pass manufacturing process which is necessarily time-consuming. A faster method of manufacturing such rotors uses a full profiled disc-type milling or grinding tool but involves clearance variations along the length. These effects have been assessed by computer modelling to quantify any disadvantages. The results indicate that the effects on performance are negligible and the profiled disk tool process is suitable for such components

The mechanics of delamination in fiber-reinforced composite materials. Part 2: Delamination behavior and fracture mechanics parameters

Based on theories of laminate anisotropic elasticity and interlaminar fracture, the complete solution structure associated with a composite delamination is determined. Fracture mechanics parameters characterizing the interlaminar crack behavior are defined from asymptotic stress solutions for delaminations with different crack-tip deformation configurations. A numerical method employing singular finite elements is developed to study delaminations in fiber composites with any arbitrary combinations of lamination, material, geometric, and crack variables. The special finite elements include the exact delamination stress singularity in its formulation. The method is shown to be computationally accurate and efficient, and operationally simple. To illustrate the basic nature of composite delamination, solutions are shown for edge-delaminated (0/-0/-0/0) and (+ or - 0/+ or - 0/90/90 deg) graphite-epoxy systems under uniform axial extenstion. Three-dimensional crack-tip stress intensity factors, associated energy release rates, and delamination crack-closure are determined for each individual case. The basic mechanics and mechanisms of composite delamination are studied, and fundamental characteristics unique to recently proposed tests for interlaminar fracture toughness of fiber composite laminates are examined

The mechanics of delamination in fiber-reinforced composite materials. Part 1: Stress singularities and solution structure

The fundamental mechanics of delamination in fiber composite laminates is studied. Mathematical formulation of the problem is based on laminate anisotropic elasticity theory and interlaminar fracture mechanics concepts. Stress singularities and complete solution structures associated with general composite delaminations are determined. For a fully open delamination with traction-free surfaces, oscillatory stress singularities always appear, leading to physically inadmissible field solutions. A refined model is introduced by considering a partially closed delamination with crack surfaces in finite-length contact. Stress singularities associated with a partially closed delamination having frictional crack-surface contact are determined, and are found to be diferent from the inverse square-root one of the frictionless-contact case. In the case of a delamination with very small area of crack closure, a simplified model having a square-root stress singularity is employed by taking the limit of the partially closed delamination. The possible presence of logarithmic-type stress singularity is examined; no logarithmic singularity of any kind is found in the composite delamination problem. Numerical examples of dominant stress singularities are shown for delaminations having crack-tip closure with different frictional coefficients between general (1) and (2) graphite-epoxy composites

Compressive failure of thick-section composite laminates with and without cutouts subjected to biaxial loading

The composites studied are fiber composite laminate plates made of carbon fibers and a thermoplastic matrix material. Tests and results are given for: the solution convergence for transverse shear in a clamped plate without cutout under compression; the effects of cutout and laminate thickness on maximum shear in buckling and postbuckling response of a clamped plate under biaxial compression; the effects of cutout and laminate thickness on maximum shear in buckling and postbuckling response of a clamped plate under biaxial compression; and the effects of laminate thickness and cutout of the lowest three eigenvalues of a clamped plate under biaxial compression. Additional test results are given

Group corings

We introduce group corings, and study functors between categories of comodules over group corings, and the relationship to graded modules over graded rings. Galois group corings are defined, and a Structure Theorem for the $G$-comodules over a Galois group coring is given. We study (graded) Morita contexts associated to a group coring. Our theory is applied to group corings associated to a comodule algebra over a Hopf group coalgebra.Comment: 38 page

Legendrian Gronwall conjecture

The Gronwall conjecture states that a planar 3-web of foliations which admits more than one distinct linearizations is locally equivalent to an algebraic web. We propose an analogue of the Gronwall conjecture for the 3-web of foliations by Legendrian curves in a contact three manifold. The Legendrian Gronwall conjecture states that a Legendrian 3-web admits at most one distinct local linearization, with the only exception when it is locally equivalent to the dual linear Legendrian 3-web of the Legendrian twisted cubic in \,\PP^3. We give a partial answer to the conjecture in the affirmative for the class of Legendrian 3-webs of maximum rank. We also show that a linear Legendrian 3-web which is sufficiently flat at a reference point is rigid under local linear Legendrian deformation.Comment: 15 page