Characterization of crack-tip strain singularity in brittle-microcracking materials by means of the photoelastic-coating method

The strain fields ahead of crack tips in rock, mortar, and graphite were measured using a photoelastic coating method. A transparent ferroelectric ceramic was used as a coating material to observe the photoelastic fringe pattern. A coating plate of 110–150 μm thick was placed on single-edge-notch specimens, and photoelasticity experiments were conducted in three-point bending under a polarizing microscope. The results show that the principal-strain difference ahead of the crack tip is given by $$\Delta \in = \Delta \in _o [(J/\sigma _{ult} )/r]^m $$ whereσ _ult is the ultimate tensile strength,r is the distance from the crack tip, and9? _o andm are material constants. Based on this observation, the use of theJ _Ic concept in determining the fracture toughness of brittle-microcracking materials is discussed.     

Flow of solids during forming and extrusion: Some aspects of numerical solutions

In the extrusion and forming of solids the plastic (or viscoplastic) deformations are so large that the elastic strain is negligible. The problem thus becomes one of incompressible viscous, non-Newtonian flow with prescribed boundary velocities. Various formulations of such problems (analogous to those of incompressible solid mechanics) are possible, and the paper investigates two basic processes.Details of application to some examples of steady state flow in extrusion, drawing and rolling are given and transient free surface solutions are demonstrated for stretch forming and deep drawing. The formulation is shown to be capable of dealing with boundary friction and strain hardening. The coupling with thermal effects is demonstrated in the last section of the paper, and in addition, some practical problems of elastic spring-back which occur on the removal of load are discussed.     

Effects of local surface residual stresses on the near resonance vibrations of nano-beams

The effects of surface residual stresses on nano-beams including mid-plane stretching under near resonance vibrations, are studied. The nonlinear vibration equations are separated into two complementary parts: static, which includes the surface residual moments and yields a residual deflection, and dynamic, for the beam vibrations associated with the residual deflection via geometrical nonlinearity. The dynamic response is expressed by a shape mode expansion with time dependent coefficients, governed by a set of coupled ordinary differential equations. An approximated solution is extracted analytically by a combination of the asymptotic straight-forward expansion and multiple scale method. Results exhibit fine correspondence with finite element simulations. It is found that the non-uniformities in the surface residual stresses change the resonance frequency of the beam, shifts its amplitude-response curve and reduce its phase. Applications for nano-sensors are demonstrated and optimization possibilities are discussed.     

Localized surface plasmon resonances of anisotropic semiconductor nanocrystals

We demonstrate that anisotropic semiconductor nanocrystals display localized surface plasmon resonances that are dependent on the nanocrystal shape and cover a broad spectral region in the near-IR wavelengths. In-plane and out-of-plane dipolar resonances were observed for colloidal dispersions of Cu(2-x)S nanodisks, and the wavelengths of these resonances are in good agreement with calculations carried out in the electrostatic limit. The wavelength, line shape, and relative intensities of these plasmon bands can be tuned during the synthetic process by controlling the geometric aspect ratio of the disk or using a postsynthetic thermal-processing step to increase the free carrier densities.     

F-(H2O)+CH3I Ligand Exchange Reaction Dynamics

Single hydration of the gas phase F\begin{document}$^-$\end{document}+CH\begin{document}$_3$\end{document}I\begin{document}$\rightarrow$\end{document} I\begin{document}$^-$\end{document}+CH\begin{document}$_3$\end{document}F reaction allows to probe solvent effects on a fundamental nucleophilic substitution reaction. At the same time, the addition of a solvent molecule opens alternative product channels. Here, we present crossed beam imaging results on the dynamics of the F\begin{document}$^-$\end{document}(H\begin{document}$_2$\end{document}O)+CH\begin{document}$_3$\end{document}I\begin{document}$\rightarrow$\end{document}[FCH\begin{document}$_3$\end{document}I]\begin{document}$^-$\end{document}+H\begin{document}$_2$\end{document}O ligand exchange pathway at collision energies between 0.3 and 2.6 eV. Product kinetic energies are constrained by the stability requirement of the weakly bound product complexes. This implies substantial internal excitation of the water molecule and disfavors efficient energy redistribution in an intermediate complex, which is reflected by the suppression of low kinetic energies as collision energy increases. At 0.3 eV, internal nucleophilic displacement is important and is discussed in light of the competing nucleophilic substitution pathways that form I\begin{document}$^-$\end{document} and I\begin{document}$^-$\end{document}(H\begin{document}$_2$\end{document}O).     

Structural investigation of water‐induced phase transitions of poly(ethylene imine). III. The thermal behavior of hydrates and the construction of a phase diagram

The thermal behavior of poly(ethylene imine) (PEI) hydrates in a water vapor atmosphere was investigated through temperature‐dependent measurements of infrared spectra and X‐ray diffraction. Almost perfectly dried anhydrate melted at about 60 °C during the heating process. Anhydrate containing a small amount of water showed a phase transition to a mixture of hemihydrate and sesquihydrate around 40 °C, at which point the ethylene imine (EI)/water ratio was 1/0.5 in the hemihydrate and 1/1.5 in the sesquihydrate. The hemihydrate transferred to the sesquihydrate around 60 °C, and the latter melted above 80 °C. When the starting PEI sample contained a greater amount of water and consisted of hemihydrate and sesquihydrate, the hemihydrate transferred to the sesquihydrate via heating, and the latter melted around 75 °C. For a sample of dihydrate (EI/water ratio = 1/2) containing an appreciably large amount of water, it transferred to the sesquihydrate around 65 °C, and the latter melted above 90 °C. A sample of dihydrate with a much higher water content existed up to 110 °C and then melted; during this period, no transition to the sesquihydrate was observed. In this way, the starting crystalline phases were found to change for anhydrate and various types of hydrates. Their transition behaviors varied according to the water content. From these data, a phase diagram was successfully derived as a function of the temperature and water content. This phase diagram allowed us to predict the transition behavior during the hydration process at various constant temperatures. For example, at 60 °C, a molten sample should crystallize into a mixture of hemihydrate and sesquihydrate at first, and the hemihydrate should transfer to the sesquihydrate with increasing water content. The latter should change to the dihydrate in the final stage. This prediction was checked with time‐resolved measurements of X‐ray diffraction and infrared spectra during the hydration process at the corresponding temperature; this led to the establishment of the phase diagram. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2937–2948, 2003     

Strong duality of the Monge–Kantorovich mass transfer problem in metric spaces

This paper studies the Monge–Kantorovich mass transfer (MT) problem on metric spaces and with an unbounded cost function. Conditions are given under which the strong duality condition holds; that is, MT and its dual MT are both solvable and their optimal values coincide. Received: 21 July 2000; in final form: 4 December 2000 / Published online: 18 January 2002     

Self-assembly of perfunctionalized beta-cyclodextrins on a quartz crystal microbalance for real-time chiral recognition

This study reports the development of novel chiral sensors based on the self-assembly of perfunctionalized beta-cyclodextrins (beta-CD) on a quartz crystal microbalance transducer for real time chiral recognition. Ten chiral sensors immobilized with mercaptyl perfunctionalized beta-cyclodextrins were found to exhibit promising enantioselectivity in the gas phase. Well-defined sizes of molecular cavities of the modified beta-CDs associated with cooperative weak interactions with the host molecules afforded enhanced chiral discrimination. This study contributes to the realization of novel chiral sensors applicable for real-time recognition and analysis of enantiomeric alcohols and lactates.