Investigation of flexural properties and failure behaviour of biaxial braided CFRP

In this research, the experimental tests of quasi-static three-point bending and three-point bending fatigue were carried out for a ±25° biaxial braided carbon fibre reinforced polymer (CFRP) manufactured using vacuum assisted resin transfer moulding (VARTM). A finite element (FE) model was also set up for quasi-static testing and the prediction results revealed that local fibre volume fraction (FVF) is a primary source affecting the mechanical properties of braided CFRP. The fatigue of the braided CFRP was defined as three different stages according to the flexural modulus results. The damage modes of the test specimens were observed via a digital microscope and scanning electron microscope (SEM) and the process-induced defects were summarised. With compiled results and observations, this study provides a better understanding of failure and fatigue behaviour of biaxial braided composites and their flexural properties which offers a good basis for any further research in fibre volume fractions, structure design and manufacturing for braided CFRP.     

Determination of Fibre Pore Structure: Influence of Salt,pH and Conventional Wet Strength Resins

It has been shown, in the present investigation, that the two methods used to investigate the pore size distribution of unbleached chemical pulps, i.e. inverse size exclusion chromatography (ISEC) and nuclear magnetic resonance (NMR), give different average pore radius for the pores inside the fibre wall. This is due to the way in which these experiments are performed and the sensitivity of the methods to different types of pores in the cell wall. It was also shown that the two methods gave different results when changing the pH and the ionic strength of the pulp suspension. The pore radius, as detected with ISEC, decreased with both increasing ionic strength and decreasing pH, indicating a loose structure of the exterior of the fibrillar network. However, the pore radius as detected with NMR, was virtually unaffected when increasing the ionic strength, indicating a very rigid structure of the interior of the fibre wall. Decreasing pH though, lead to a decrease in pore radius indicating that upon protonation of the carboxylic groups in the fibre wall, the electrostatic repulsion is diminished and the average pore radius decreases. The NMR technique was also used to study wet strength aid penetration into the fibre wall. It was shown that wet strength aids with a small molecular weight, penetrated the fibre wall, as detected by a decrease in pore radius. It was also shown that addition of different wet strength aids increased the tensile index of the sheet and decreased the fibre strength, measured as zero span-strength of the sheets.     

Flow prolongation of some tangent valued forms

We study the prolongation of semibasic projectable tangent valued k-forms on fibered manifolds with respect to a bundle functor F on local isomorphisms that is based on the flow prolongation of vector fields and uses an auxiliary linear r-th order connection on the base manifold, where r is the base order of F. We find a general condition under which the Frölicher-Nijenhuis bracket is preserved. Special attention is paid to the curvature of connections. The first order jet functor and the tangent functor are discussed in detail. Next we clarify how this prolongation procedure can be extended to arbitrary projectable tangent valued k-forms in the case F is a fiber product preserving bundle functor on the category of fibered manifolds with m-dimensional bases and local diffeomorphisms as base maps.     

XPM-induced intensity distortion due to dispersion in fibre Bragg grating filters

We investigate the conversion of cross-phase modulation (XPM) to intensity distortion due to dispersion in fibre Bragg grating (FBG) filters. We find that there can be significant XPM-induced intensity distortion, especially near the edges of the filter passband where the in-band dispersion is increasingly pronounced. Since FBG filter dispersion occurs above and beyond that in standard single-mode fibre, this enhances XPM-induced intensity distortion arising from dispersion and should be accounted for in system design.     

New construction of special Lagrangian submanifolds in <Emphasis Type="Italic">T</Emphasis>*R<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript> equipped with the standard metric

A class of twisted special Lagrangian submanifolds in T＊R^n and a kind of austere submanifold from conormal bundle of minimal surface of R^3 are constructed.     

Inertia and damping effects on the damage-dependent burst size distribution of fiber bundles

Distributions of simultaneous fiber failures—bursts—in loaded fiber bundles are studied considering inertia and damping. Resulting burst size distributions have universal properties: all approach the power law D_ΔΔ^−2.5 for larger burst sizes Δ. Momentary burst size distributions evolve with increasing damage and do not follow power laws but are still universal. Finally, it is briefly outlined how to use distribution progression to assess damage state.     

Poisson fiber bundles and coupling Dirac structures

Poisson fiber bundles are studied. We give sufficient conditions for the existence of a Dirac structure on the total space of a Poisson fiber bundle endowed with a compatible connection. We also provide some examples.      

Energy bands: Chern numbers and symmetry

Energy bands formed by rotation–vibrational states of molecules in the presence of symmetry and their qualitative modifications under variation of some control parameters are studied within the semi-quantum model. Rotational variables are treated as classical whereas a finite set of vibrational states is considered as quantum. In the two-state approximation the system is described in terms of a fiber bundle with the base space being a two-dimensional sphere, the classical phase space for rotational variables. Generically this rank 2 complex vector bundle can be decomposed into two complex line bundles characterized by a topological invariant, the first Chern class. A general method of explicit calculation of Chern classes and of their possible modifications under variation of control parameters in the presence of symmetry is suggested. The construction of iso-Chern diagrams which split the space of control parameters into connected domains with fixed Chern numbers is suggested. A detailed analysis of the rovibrational model Hamiltonian for a D₃ invariant molecule possessing two vibrational states transforming according to the two-dimensional irreducible representation is done to illustrate non-trivial restrictions imposed by symmetry on possible values of Chern classes.     

Convergence of Yang-Mills-Higgs flow for twist Higgs pairs on Riemann surfaces

We consider the gradient flow of the Yang-Mills-Higgs functional of twist Higgs pairs on a Hermitian vector bundle(E,H)over Riemann surface X.It is already known the gradient flow with initial data(A0,φ0)converges to a critical point(A∞,φ∞).Using a modified Chern-Weil type inequality,we prove that the limiting twist Higgs bundle(E,d′′A∞,φ∞)coincides with the graded twist Higgs bundle defined by the HarderNarasimhan-Seshadri filtration of the initial twist Higgs bundle(E,d′′A0,φ0),generalizing Wilkin’s results for untwist Higgs bundle.     

Lie algebroid modules and representations up to homotopy

We establish a relationship between two different generalizations of Lie algebroid representations: representation up to homotopy and Vaĭntrob’s Lie algebroid modules. Specifically, we show that there is a noncanonical way to obtain a representation up to homotopy from a given Lie algebroid module, and that any two representations up to homotopy obtained in this way are equivalent in a natural sense. We therefore obtain a one-to-one correspondence, up to equivalence.