Delamination growth in composite materials

The Double Cantilever Beam (DCB) and the End Notched Flexure (ENF) specimens are employed to characterize MODE I and MODE II interlaminar fracture resistance of graphite/epoxy (CYCOM 982) and graphite/PEEK (APC2) composites. Sizing of test specimen geometries to achieve crack growth in the linear elastic regime is presented. Data reduction schemes based upon beam theory are derived for the ENF specimen and include the effects of shear deformation and friction between crack surfaces on compliance, C, and strain energy release rate, G sub II. Finite element (FE) analyses of the ENF geometry including the contact problem with friction are presented to assess the accuracy of beam theory expressions for C and G sub II. Virtual crack closure techniques verify that the ENF specimen is a pure Mode II test. Beam theory expressions are shown to be conservative by 20 to 40 percent for typical unidirectional test specimen geometries. A FE parametric study investigating the influence of delamination length and depth, span, thickness and material properties on G sub II is presented. Mode I and II interlaminar fracture test results are presented. Important experimental parameters are isolated, such as precracking techniques, rate effects, and nonlinear load-deflection response. It is found that subcritical crack growth and inelastic materials behavior, responsible for the observed nonlinearities, are highly rate-dependent phenomena with high rates generally leading to linear elastic response

Delamination growth in composite materials

Research related to growth of an imbedded through-width delamination (ITWD) in a compression loaded composite structural element is presented. Composites with widely different interlaminar fracture resistance were examined, viz., graphite/epoxy (CYCOM 982) and graphite/PEEK (APC-2). The initial part of the program consisted of characterizing the material in tension, compression and shear mainly to obtain consistent material properties for analysis, but also as a check of the processing method developed for the thermoplastic APC-2 material. The characterization of the delamination growth in the ITWD specimen, which for the unidirectional case is essentially a mixed Mode 1 and 2 geometry, requires verified mixed-mode growth criteria for the two materials involved. For this purpose the main emphasis during this part of the investigation was on Mode 1 and 2 fracture specimens, namely the Double Cantilever Beam (DCB) and End Notched Flexure (ENF) specimens

Multi-Bunch Solutions of Differential-Difference Equation for Traffic Flow

Newell-Whitham type car-following model with hyperbolic tangent optimal velocity function in a one-lane circuit has a finite set of the exact solutions for steady traveling wave, which expressed by elliptic theta function. Each solution of the set describes a density wave with definite number of car-bunches in the circuit. By the numerical simulation, we observe a transition process from a uniform flow to the one-bunch analytic solution, which seems to be an attractor of the system. In the process, the system shows a series of cascade transitions visiting the configurations closely similar to the higher multi-bunch solutions in the set.Comment: revtex, 7 pages, 5 figure

Solvable Optimal Velocity Models and Asymptotic Trajectory

In the Optimal Velocity Model proposed as a new version of Car Following Model, it has been found that a congested flow is generated spontaneously from a homogeneous flow for a certain range of the traffic density. A well-established congested flow obtained in a numerical simulation shows a remarkable repetitive property such that the velocity of a vehicle evolves exactly in the same way as that of its preceding one except a time delay $T$. This leads to a global pattern formation in time development of vehicles' motion, and gives rise to a closed trajectory on $\Delta x$-$v$ (headway-velocity) plane connecting congested and free flow points. To obtain the closed trajectory analytically, we propose a new approach to the pattern formation, which makes it possible to reduce the coupled car following equations to a single difference-differential equation (Rondo equation). To demonstrate our approach, we employ a class of linear models which are exactly solvable. We also introduce the concept of ``asymptotic trajectory'' to determine $T$ and $v_B$ (the backward velocity of the pattern), the global parameters associated with vehicles' collective motion in a congested flow, in terms of parameters such as the sensitivity $a$, which appeared in the original coupled equations.Comment: 25 pages, 15 eps figures, LaTe

Mechanical properties of nanotube sheets: Alterations in joint morphology and achievable moduli in manufacturable materials

Nanotube sheets, or “bucky papers,” have been proposed for use in actuating, structural and electrochemical systems, based in part on their potential mechanical properties. Here, we present results of detailed simulations of networks of nanotubes/ropes, with special emphasis on the effect of joint morphology. We perform detailed simulations of three-dimensional joint deformation, and use the results to inform simulations of two-dimensional (2D) networks with intertube connections represented by torsion springs. Upper bounds are established on moduli of nanotube sheets, using the 2D Euler beam-network simulations. Comparisons of experimental and simulated response for HiPco-nanotube and laser-ablated nanotube sheets, indicate that ∼2–30-fold increases in moduli may be achievable in these materials. Increasing the numbers of interrope connections appears to be the best target for improving nanotube sheet stiffnesses in materials containing straight segments. © 2004 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70283/2/JAPIAU-95-8-4335-1.pd

Maxwell Model of Traffic Flows

We investigate traffic flows using the kinetic Boltzmann equations with a Maxwell collision integral. This approach allows analytical determination of the transient behavior and the size distributions. The relaxation of the car and cluster velocity distributions towards steady state is characterized by a wide range of velocity dependent relaxation scales, $R^{1/2}<\tau(v)<R$, with $R$ the ratio of the passing and the collision rates. Furthermore, these relaxation time scales decrease with the velocity, with the smallest scale corresponding to the decay of the overall density. The steady state cluster size distribution follows an unusual scaling form $P_m \sim ^{-4} \Psi(m/< m>^2)$. This distribution is primarily algebraic, $P_m\sim m^{-3/2}$, for $m\ll ^2$, and is exponential otherwise.Comment: revtex, 10 page

The band-gap structure and the singular character of the bounded large array of potential barriers

The bounded one dimensional multibarrier potential shows signs of chaos, phase transition and a transmission probability of unity for certain values of its total length $L$ and the ratio $c$ of total interval to total width. Like the infinite Kronig-Penney system, which is arranged along the whole spatial region, the bounded multibarrier potential has a band-gap structure in its energy spectrum. But unlike the Kronig-Penney system, in which the gaps disappear for large energies, these gaps do not disappear for certain values of $L$ and $c$. The energy is discontinuous even in parts of the spectrum with no gaps at all. These results imply that the energy spectrum of the bounded multibarrier system is singular.Comment: 22 pages, 7 PS figures, former text removed and a new one inserte

Christian Higher Education in Europe: A Historical Overview

The history of Christian higher education in Europe may be analyzed in terms of seven eras. From their medieval origins in scholasticism and the practical needs of students and rulers, universities passed through Renaissance humanism to a period of decay, yet remained substantially Christian in intent. The Enlightenment exercised a partially secularizing influence, and the neohumanist reaction against it also tended to dilute the faith. The recent era of the late 20th and early 21st centuries has been associated with the rise of postmodernism and the involvement of the state in the quest for relevance. A Christian response to contemporary circumstances is to engage with the cultural currents of the present day and, in drawing on the thought of John Henry Newman and Sir Walter Moberly, to ensure the integration of Christianity into higher education so that discussion of ultimate questions is informed by the Christian faith