Procedures for construction of anisotropic elastic-plastic property closures for face-centered cubic polycrystals using first-order bounding relations

Microstructure-sensitive design (MSD) is a novel mathematical framework that facilitates a rigorous consideration of the material microstructure as a continuous design variable in the engineering design enterprise [Adams, B.L., Henrie, A., Henrie, B., Lyon, M., Kalidindi, S.R., Garmestani, H., 2001. Microstructure-sensitive design of a compliant beam. J. Mech. Phys. Solids 49(8), 1639-1663; Adams, B.L., Lyon, M., Henrie, B., 2004. Microstructures by design: linear problems in elastic-plastic design. Int. J. Plasticity 20(8-9), 1577-1602; Kalidindi, S.R., Houskamp, J.R., Lyons, M., Adams, B.L., 2004. Microstructure sensitive design of an orthotropic plate subjected to tensile load. Int. J. Plasticity 20(8-9), 1561-1575]. MSD employs spectral representations of the local state distribution functions in describing the microstructure quantitatively, and these in turn enable development of invertible linkages between microstructure and effective properties using established homogenization (composite) theories. As a natural extension of the recent publications in MSD, we provide in this paper a detailed account of the methods that can be readily used by mechanical designers to construct first-order elastic-plastic property closures. The main focus in this paper is on the crystallographic texture (also called Orientation Distribution Function or ODF) as the main microstructural parameter controlling the elastic and yield properties of cubic (fcc and bcc) polycrystalline metals. The following specific advances are described in this paper: (i) derivation of rigorous first-order bounds for the off-diagonal terms of the effective elastic stiffness tensor and their incorporation in the MSD framework, (ii) delineation of the union of the property closures corresponding to both the upper and lower bound theories resulting in comprehensive first-order closures, (iii) development of generalized and readily usable expressions for effective anisotropic elastic-plastic properties that could be applied to all cubic polycrystals, and (iv) identification of the locations of readily available or easily processable ODFs (e.g. textures that are produced by rolling, drawing, etc.) on the property closures. It is anticipated that the advances communicated in this paper will make the mathematical framework of MSD highly accessible to the mechanical designers.     

Trifluoromethanesulfonic Acid Catalyzed Alkylation of Arenes with Methyl (2R)‐Glycidate

Methyl (R)‐glycidate (=methyl (R)‐oxiranecarboxylate; 2 ) in superacidic trifluoromethanesulfonic acid medium reacts with electron‐rich arenes to give α‐hydroxy‐β‐arylpropanoate derivatives 3a – 3f with high stereospecificity. At the same time, the observed high regioselectivity has been attributed to superelectrophilic activation of the glycidate.     

A four-arm Sagnac interferometric switch

A four-arm Sagnac interferometric switch is demonstrated. The switch works on the nonlinearity of the Pancharatnam's phase in a Young's interference set-up with differently polarized coherent laser beams.     

Dynamics of a supercooled liquid

The theory of collective motion in liquids suggested by the authors has been found to explain successfully the recent experimental results of temperature dependent disorder in supercooled liquid gallium. Metastability limit is exhibited through a singularity of S(k, ω = 0) and corresponds to a critical value of correlation between different particles beyond which the supercooled liquid goes to the thermodynamically stable solid state.     

Stable Carbodications

Methods developed for the generation and study of stable carbomonocations can also be employed for similar investigations on carbodications. Trivalent (classical) as well as hexacoordinate (non-classical) carbodications studied under long-lived ion conditions are reviewed with special emphasis on their structural features, and investigated primarily by ¹H- and ¹³C-NMR spectroscopy.     

Trace analysis of mercury by a radiochemical displacement method using cobalt(III) diethyldithiocarbamate

A radiochemical displacement method was utilized for the determination of traces of mercury in water taking advantage of its ability to displace cobalt from cobalt(III) diethyldithiocarbamate tagged with⁶⁰Co. The method is found to be applicable in the concentration range of 50–200 g/ml mercury. The interfernces from various cations like Fe(III), Co(II), Cu(II), Pb(II) and Ag(I) ions were studied.     

Diffraction of sound pulses by a rigid cylinder in an inhomogeneous medium

We consider the problem of scattering of two-dimensional sound pulses by a rigid circular cylinder embedded in a cylindrically stratified inhomogeneous medium. The line source is parallel to the axis of the cylinder. It is assumed that the velocity of soundc is given byc ^?1=pr ^q, wherep andq are real constants andp>0. The method of dual integral transformation developed by Friedlander is used. The solution in terms of pulse propagation modes gives the diffracted pulse and the method of steepest descents yields the geometrical acoustic field.