Lamination-dependent shear deformation models for bending of angle-ply laminated plates

Lamination-dependent shear corrective terms in the analysis of bending of laminated plates are derived from a priori assumed linear thicknesswise distributions for gradients of transverse shear stresses by using CLPT inplane stresses in the two in-plane equilibrium equations of elasticity in each ply. In the development of a general model for angle-ply laminated plates, special cases like cylindrical bending of laminates in either direction, symmetric laminates, cross-ply laminates, antisymmetric angle-ply laminates, homogeneous plates are taken into consideration. Adding these corrective terms to the assumed displacements in (i) Classical Laminate Plate Theory (CLPT) and (ii) Classical Laminate Shear Deformation Theory (CLSDT), two new refined lamination-dependent shear deformation models are developed. Closed form solutions from these models are obtained for antisymmetric angle-ply laminates under sinusoidal load for a type of simply supported boundary conditions. Results obtained from the present models and also from Ren's model (1987) are compared with each other.

Lamination-dependent shear deformation models for cylindrical bending of angle-ply laminates

Lamination-dependent shear corrective terms in the analysis of flexure of laminates are derived from a priori assumed linear thicknesswise distributions for gradients of transverse shear stresses and using them in the two in-plane equilibrium equations of elasticity in each ply. Adding these corrective terms to (i) Classical Laminate Plate Theory (CLPT) displacements and (ii) Classical Laminate Shear Deformation Theory (CLSDT) displacements, four new refined lamination-dependent shear deformation models for angle-ply laminates are developed. Performance of these models is evaluated by comparing the results from these models with those from exact elasticity solutions for antisymmetric 2-ply laminates and for 4-ply [15/-15](s) laminates. In general, the model with shear corrective terms based on CLPT and added to CLSDT displacements is sufficient and predicts good estimates, both qualitatively and quantitatively, for all displacements and stresses.

Mechanistic approach to the shear strength behaviour of allophanic soils

The presence of allophane minerals imparts special engineering features to the volcanic ash soils. This study examines the reasons for the allophanic soils exhibiting unusual shear strength properties in comparison to sedimentary clays. The theories of residual shear strength developed for natural soils and artificial soil mixtures and the unusual surface charge properties of the allophane particle are invoked to explain the high shear strength values of these residual soils. The lack of any reasonable correlation between phi' (effective stress-strength parameter) and plasticity index values for allophanic soils is explained on the basis of the unusual structure of the allophane particle. The reasons as to why natural soil slopes in allophanic soil areas (example, Dominica, West Indies) are stable at much steeper angles than natural slopes in sedimentary clay deposits (London clay areas) are explained in light of the hypothesis developed in this study.

Discontinuous shear thickening in confined dilute carbon nanotube suspensions

A monotonic decrease in viscosity with increasing shear stress is a known rheological response to shear flow in complex fluids in general and for flocculated suspensions in particular. Here we demonstrate a discontinuous shear-thickening transition on varying shear stress where the viscosity jumps sharply by four to six orders of magnitude in flocculated suspensions of multiwalled carbon nanotubes (MWNT) at very low weight fractions (approximately 0.5%). Rheooptical observations reveal the shear-thickened state as a percolated structure of MWNT flocs spanning the system size. We present a dynamic phase diagram of the non-Brownian MWNT dispersions revealing a starting jammed state followed by shear-thinning and shear-thickened states. The present study further suggests that the shear-thickened state obtained as a function of shear stress is likely to be a generic feature of fractal clusters under flow, albeit under confinement. An understanding of the shear-thickening phenomena in confined geometries is pertinent for flow-controlled fabrication techniques in enhancing the mechanical strength and transport properties of thin films and wires of nanostructured composites as well as in lubrication issues.

Punching shear strength of flat slab corner column connections .1. Reinforced concrete connections

This paper presents the details of an experimental study on punching shear strength and behaviour of reinforced concrete corner column connections in flat slabs; a quasi-empirical method is proposed for computing the punching shear strength. The method has also been extended for punching shear strength prediction at interior and edge column connections. The test results compare better with the strengths predicted by the proposed method than those by Ingvarson, Zaglool and Pollet available in the literature. Further, the experimental strengths of interior, edge and corner column connections have been compared with the strengths predicted by the proposed method and the two codes of practice, viz. ACI and BS code, to demonstrate the usefulness of the method.

Punching shear strength of flat slab corner column connections .2. Fibre-reinforced concrete connections

This paper gives the details of the studies undertaken to examine the strength and behaviour of fibre-reinforced concrete corner column connections in flat slabs. Tests have been conducted on 16 specimens with varying reinforcement ratio, moment/shear ratio (load eccentricity) and volume fraction of fibres. A quasi-empirical method has been proposed for computing the punching shear strength. The method has also been extended to fibre-reinforced concrete interior column connections, tests on which are available in the literature. The test results have been compared with the strength predicted by the proposed method for corner column as well as interior column connections and a satisfactory agreement noticed.

Modified Kirchhoffs theory of plates including transverse shear deformations

A primary flexure problem defined by Kirchhoff theory of plates in bending is considered. Significance of auxiliary function introduced earlier in the in-plane displacements in resolving Poisson-Kirchhoffs boundary conditions paradox is reexamined with reference to reported sixth order shear deformation theories, in particular, Reissner's theory and Hencky's theory. Sixth order modified Kirchhoff's theory is extended here to include shear deformations in the analysis. (C) 2011 Elsevier Ltd. All rights reserved.

Velocity distribution function for a dilute granular material in shear flow

The velocity distribution function for the steady shear flow of disks (in two dimensions) and spheres (in three dimensions) in a channel is determined in the limit where the frequency of particle-wall collisions is large compared to particle-particle collisions. An asymptotic analysis is used in the small parameter epsilon, which is naL in two dimensions and na(2)L in three dimensions, where; n is the number density of particles (per unit area in two dimensions and per unit volume in three dimensions), L is the separation of the walls of the channel and a is the particle diameter. The particle-wall collisions are inelastic, and are described by simple relations which involve coefficients of restitution e(t) and e(n) in the tangential and normal directions, and both elastic and inelastic binary collisions between particles are considered. In the absence of binary collisions between particles, it is found that the particle velocities converge to two constant values (u(x), u(y)) = (+/-V, O) after repeated collisions with the wall, where u(x) and u(y) are the velocities tangential and normal to the wall, V = (1 - e(t))V-w/(1 + e(t)), and V-w and -V-w, are the tangential velocities of the walls of the channel. The effect of binary collisions is included using a self-consistent calculation, and the distribution function is determined using the condition that the net collisional flux of particles at any point in velocity space is zero at steady state. Certain approximations are made regarding the velocities of particles undergoing binary collisions :in order to obtain analytical results for the distribution function, and these approximations are justified analytically by showing that the error incurred decreases proportional to epsilon(1/2) in the limit epsilon --> 0. A numerical calculation of the mean square of the difference between the exact flux and the approximate flux confirms that the error decreases proportional to epsilon(1/2) in the limit epsilon --> 0. The moments of the velocity distribution function are evaluated, and it is found that [u(x)(2)] --> V-2, [u(y)(2)] similar to V-2 epsilon and -[u(x)u(y)] similar to V-2 epsilon log(epsilon(-1)) in the limit epsilon --> 0. It is found that the distribution function and the scaling laws for the velocity moments are similar for both two- and three-dimensional systems.

Evolution of crystallographic texture during deformation of submicron grain size titanium

Evolution of deformation texture in commercially pure titanium with submicron grain size (SMG) was studied using x-ray diffraction (XRD) and electron back scatter diffraction (EBSD) methods. The material was deformed by rolling at room temperature. The deformation mechanism was found to be slip dominated with a pyramidal slip system facilitating plastic deformation. No evidence of tensile or compressive twinning was detected, as generally seen in the case of titanium with conventional microcrystalline grain size. The absence of twinning and the propensity of the pyramidal slip system in the SMG Ti is attributed to the lack of coordinated motion of zonal partial dislocations that leads to twinning.

Analysis of shear bands in slow granular flows using a frictional Cosserat model

The slow flow of granular materials is often marked by the existence of narrow shear layers, adjacent to large regions that suffer little or no deformation. This behaviour, in the regime where shear stress is generated primarily by the frictional interactions between grains, has so far eluded theoretical description. In this paper, we present a rigid-plastic frictional Cosserat model that captures thin shear layers by incorporating a microscopic length scale. We treat the granular medium as a Cosserat continuum, which allows the existence of localised couple stresses and, therefore, the possibility of an asymmetric stress tensor. In addition, the local rotation is an independent field variable and is not necessarily equal to the vorticity. The angular momentum balance, which is implicitly satisfied for a classical continuum, must now be solved in conjunction with the linear momentum balances. We extend the critical state model, used in soil plasticity, for a Cosserat continuum and obtain predictions for flow in plane and cylindrical Couette devices. The velocity profile predicted by our model is in qualitative agreement with available experimental data. In addition, our model can predict scaling laws for the shear layer thickness as a function of the Couette gap, which must be verified in future experiments. Most significantly, our model can determine the velocity field in viscometric flows, which classical plasticity-based model cannot.

Texture evolution in an Al-Cu alloy during equal channel angular pressing: the effect of starting microstructure

In this article, the effect of initial microstructure on the texture evolution in 2014 Al alloy during equal channel angular pressing (ECAP) through route A has been reported. Three heat treatment conditions were chosen to generate the initial microstructures, namely (i) the recrystallization anneal (as-received), (ii) solution treatment at 768 K for 1 h, and (iii) solution treatment (768 K for 1 h) plus aging at 468 K for 5 h. Texture analyses were performed using orientation distribution function (ODF) method. The texture strength after ECAP processing was different for the three samples in the order, solutionised > solutionised plus aged condition > as-received. The prominent texture components were A (E) /(A) over bar (E) and B(E)/(B) over bar (E) in addition to several weaker components for the three materials. The strong texture evolution in solutionised condition has been attributed to higher strain hardening of the matrix due to higher amount of solute. In case of the as-received as well as solutionised plus aged alloy, the weaker texture could be due to the strain scattering from extensive precipitate fragmentation and dissolution during ECAP.

Solidification Microstructure and Texture in Grain-refined Titanium alloys

In the present study, solidification microstructure and texture evolution in grain-refined Ti-6Al-4V and γ-TiAl alloys via trace boron addition are compared with their baseline counterparts. Boron addition resulted in dramatic grain refinement by almost an order of magnitude. The texture developed in these alloys is also markedly different from the baseline alloys.