Reconstruction of cracks of different types from far‐field measurements

In this paper, we deal with the acoustic inverse scattering problem for reconstructing cracks of possibly different types from the far‐field map. The scattering problem models the diffraction of waves by thin two‐sided cylindrical screens. The cracks are characterized by their shapes, the type of boundary conditions and the boundary coefficients (surface impedance). We give explicit formulas of the indicator function of the probe method, which can be used to reconstruct the shape of the cracks, distinguish their types of boundary conditions, the two faces of each of them and reconstruct the possible material coefficients on them by using the far‐field map. To test the validity of these formulas, we present some numerical implementations for a single crack, which show the efficiency of the proposed method for suitably distributed surface impedances. The difficulties for numerically recovering the properties of the crack in the concave side as well as near the tips are presented and some explanations are given. Copyright © 2009 John Wiley & Sons, Ltd.     

Decay and nonexistence of global solutions of a quasilinear riser equation

We study qualitative properties of a quasilinear wave equation of fourth order that models the mechanical vibrations of a marine riser. Our analysis characterizes global and nonglobal solutions with respect to the norm of some Hilbert space, if energy is strictly less than the potential well depth. We employ invariant sets to show our results. In particular, we show that globality implies exponential decay to zero, and nonglobality is due to blow up. Both results are shown with respect to the norm of the solution in the Hilbert space. Copyright © 2009 John Wiley & Sons, Ltd.     

Long Time Behavior of the Cahn-Hilliard Equation with Irregular Potentials and Dynamic Boundary Conditions

The Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions is considered.The existence of the global attractor is proved and the long time behavior of the trajectories,namely,the convergence to steady states,is studied.     

Numerical damage assessment of Haghia Sophia bell tower by nonlinear FE modeling

In the present paper, the numerical damage assessment of the masonry bell tower called “Haghia Sophia” in Trabzon, Turkey is performed by nonlinear 3D finite element modeling. The behavior of bell tower is determined under several different conditions: nonlinear static analysis containing dead and wind loads and nonlinear seismic analysis. In addition to, an assessment of the tower’s stability with respect to the tilt of the tower is carried out by means of a nonlinear analysis. In the nonlinear dynamic analysis, the east–west component of 1992 Erzincan earthquake is used. Cracking and crushing of the masonry have been taken into account, as well as the influence of material nonlinearity. The numerical analysis has given a valuable picture of possible damage evolution, providing useful hints for the prosecution of structural monitoring. The displacement and stress fields, as well as the distribution of cracking have been calculated and compared to the actual distribution of fractures in the tower. It is seen from the numerical results that there is a good agreement with present damages of the bell tower.     

High-Temperature dispersion zones in cross-linked natural rubber

The complex dielectric constant of natural rubber samples cross-linked by sulfur and dicumyl peroxide has been measured over a frequency range from 1.5 to 3.0 × 10⁵ cps by the bridge method and from 3.0 to 1.0 × 10⁴ cps by the relaxation method. Two dispersion peaks were detected which lay in the measured frequency range at temperatures above the main dispersion zone. Temperature and cross-link density-dependent shift of these peaks were studied and compared with the results obtained by Ferry et al. from complex compliance measurements performed on analogous systems.     

Influence of Thermal Treatment on the Thermal Behavior of Poly‐L‐lactide

The influences of thermal treatment on cold crystallization and the thermal behavior of poly‐L‐lactide (PLLA) were investigated by DSC and polarizing microscopy. Both the cooling and heating rates had effects on cold crystallization. Double peaks were observed for the samples on subsequently heating at 10°C min^?1 after cooling between 5 and 20°C min^?1. The degrees of crystallinity dramatically increased with decreasing cooling rate, and the size of PLLA spherulites increased with a decrease in the cooling rate. Double cold crystallization peaks were also observed during heating traces at higher rates for this material after fast cooling (20°C min^?1) from the melt. The competition between the crystallization from the nuclei formed during cooling, and that from spontaneous nucleation might be responsible for the appearance of double peaks.     

Thermal Cross‐Linking of Poly(Vinyl Methyl Ether). I. Effect of Cross‐Linking Process on the Viscoelastic Properties

Abstract

Thermal cross‐linking of poly(vinyl methyl ether) (PVME) in the absence of cross‐linking agent, was detected rheologically. The linear viscoelastic properties of PVME were found to be greatly changed by the onset of the cross‐linking process. The viscoelastic material functions, such as dynamic shear moduli, G′ and G″, complex shear viscosity, η*, and loss tangent, tan δ, were found to be sensitive to the structure changes during the cross‐linking process and the formation of a three‐dimensional polymer network. At the onset temperature of the cross‐linking process, an abrupt increase in G′, G″, and η* (several orders of magnitude) during dynamic temperature ramps (2°C/min heating rate) was observed with some frequency dependence. The temperature dependence of tan δ was found to be frequency independent at the gel‐point, T _gel, that is, the crossover in tan δ regardless of the value of frequency can be taken as an accurate method for determination of T _gel. The coincidence of G′ and G″ at the gel‐point cannot be considered a general method for evaluation of T _gel due to its high frequency dependence, that is, T _gel determined from the crossover of G′ and G″ in the dynamic temperature ramp at 1 rad/sec is about 20°C less than at 100 rad/sec. Furthermore, a dramatic increase in η₀ above the minimum (“v” shape) was observed at T = T _gel in agreement with the value obtained from tan δ vs. T (190°C). The time–temperature‐superposition principle was found to be valid only for temperatures lower than the T _gel (190°C); the principle failed at T ≥ 190°C. This was clearly seen in the low‐frequency region as a deviation from the terminal slope in the G′ curve. Similar behavior was observed in the modified Cole–Cole analyses (G″ vs. G′) that is, the curves start to deviate at 190°C.     

Compatibilization of Poly(Trimethylene Terephthalate)/Polycarbonate Blends by Epoxy. Part 2. Melting Behavior and Spherulite Morphology

The melting behaviors of poly(trimethylene terephthalate)/polycarbonate (PTT/PC) blends, compatibilized by epoxy, and PTT spherulite morphology in the blends were investigated. When epoxy was present during blending, the melting behaviors of PTT/PC blends changed substantially; glass transition temperatures (T_g's) and cold crystallization temperature (T_cc's) of the PTT‐rich phase shifted to higher temperatures, while T_m's shifted slightly to lower temperatures, indicating that epoxy suppressed considerably all processes of dynamic movements pertinent to molecular (or segmental) movements. The cold crystallization process responded sensitively to thermal history. Changes of T_cc's with composition suggested that the epoxy's compatibilization effect was pronounced when PTT and PC were in near equal content.

Recrystallization or reorganization exotherms appeared before melting for isothermally crystallized PTT/PC and PTT/PC epoxy (E) blends. A wide angle X‐ray diffraction (WAXD) analysis showed that, although the perfection of PTT crystallites was influenced either by PC content and the presence of compatibilizer or by the crystallization temperature and crystallization time, PTT's crystal structure was independent of these variables.

The polarized light microscopy (PLM) observations showed that PTT spherulite morphology was very sensitive to blend composition. Epoxy addition interfered severely with the growth of PTT spherulites, causing them to be much less developed. When the spherulites grew under a condition of varied composition, they would exhibit diversified spherulite morphology, though in one spherulite.     

Correlation Between Structural and Dynamic‐Mechanical Transitions of Different Syndiotactic Polypropylene Polymorphs

Abstract

We prepared several well‐characterized syndiotactic polypropylene (sPP) polymorphs so as to correlate their thermal and dynamic‐mechanical behaviors. A sample was crystallized in pure form I at 100°C; a second sample containing only the trans‐planar mesophase was prepared by directly drawing a quenched sample at 0°C; a third sample, drawn at room temperature, contained both the trans‐planar mesophase and a fraction of the helical form II. By annealing this sample at increasing temperatures, we obtained a series of samples containing either trans‐planar mesophase, or form II and form I crystallinities.

In the dynamic‐mechanical analysis, the sample containing form I crystallinity showed only the amorphous glass transition, at 19°C, before melting at a high temperature. The trans‐planar mesophase transformed, at temperatures higher than 50°C, into the helical forms, and this transition was completed at 80°C. The dynamic mechanical curve of the sample containing only the mesophase showed a peak, centered at 50°C, which could be clearly associated to this transition. The sample containing the trans‐planar mesophase and the helical form II, showed in the dynamic‐mechanical curve a third peak that can be associated with the melting recrystallization of form II into the most stable form I. These results are important, because it was possible to directly correlate the structural transitions of the sPP polymorphs to the dynamic‐mechanical behavior. Moreover, a dynamic‐mechanical analysis could help recognize the presence of the trans‐planar mesophase or of the helical form II in more complex structural organizations.