Forming limit investigation of friction stir welded sheets: influence of shoulder diameter and plunge depth

The main aim of the present work is to analyze the influence of shoulder diameter and plunge depth on the formability of friction stir welded sheets. The base material used for welding and forming was AA6061-T6. Formability evaluation was performed through limiting dome height tests. The forming limit curve, FLC (only in the stretching region), thickness distribution, and strain hardening exponent of the weld region were monitored during formability studies. It is found from the work that the forming limit of friction stir welded sheets is better than unwelded sheets. In general, with an increase in shoulder diameter and plunge depth, the forming limit is found to improve considerably. With a decrease in thickness gradient severity and an increase in strain hardening exponent (n) of the weld region, the forming limit is found to increase. The increase in n value of the weld region is believed to occur because of the reduction in dislocation density. The maximum thickness difference is higher in the retreating side, rather than in the advancing side, of the weld. This is due to the differential straining and hardness levels attained by both sides during friction stir welding.

Revisiting some physics issues related to the new mass limit for magnetized white dwarfs

We clarify important physics issues related to the recently established new mass limit for magnetized white dwarfs which is significantly super-Chandrasekhar. The issues include, justification of high magnetic field and the corresponding formation of stable white dwarfs, contribution of the magnetic field to the total density and pressure, flux freezing, variation of magnetic field and related currents therein. We also attempt to address the observational connection of such highly magnetized white dwarfs.

REDUCING COMPUTATIONAL EFFORT IN SOLVING GEOMECHANICS PROBLEMS WITH UPPER BOUND FINITE ELEMENTS LIMIT ANALYSIS AND LINEAR OPTIMIZATION

This paper presents a simple technique for reducing the computational effort while solving any geotechnical stability problem by using the upper bound finite element limit analysis and linear optimization. In the proposed method, the problem domain is discretized into a number of different regions in which a particular order (number of sides) of the polygon is chosen to linearize the Mohr-Coulomb yield criterion. A greater order of the polygon needs to be selected only in that region wherein the rate of the plastic strains becomes higher. The computational effort required to solve the problem with this implementation reduces considerably. By using the proposed method, the bearing capacity has been computed for smooth and rough strip footings and the results are found to be quite satisfactory.

Calibration Curve with Improved Limit of Detection for Cadmium in Soil: An Approach to Minimize the Matrix Effect in Laser-Induced Breakdown Spectroscopic Analysis

The present article describes a working or combined calibration curve in laser-induced breakdown spectroscopic analysis, which is the cumulative result of the calibration curves obtained from neutral and singly ionized atomic emission spectral lines. This working calibration curve reduces the effect of change in matrix between different zone soils and certified soil samples because it includes both the species' (neutral and singly ionized) concentration of the element of interest. The limit of detection using a working calibration curve is found better as compared to its constituent calibration curves (i.e., individual calibration curves). The quantitative results obtained using the working calibration curve is in better agreement with the result of inductively coupled plasma-atomic emission spectroscopy as compared to the result obtained using its constituent calibration curves.

Solving Axisymmetric Stability Problems by Using Upper Bound Finite Elements, Limit Analysis, and Linear Optimization

A numerical formulation has been proposed for solving an axisymmetric stability problem in geomechanics with upper bound limit analysis, finite elements, and linear optimization. The Drucker-Prager yield criterion is linearized by simulating a sphere with a circumscribed truncated icosahedron. The analysis considers only the velocities and plastic multiplier rates, not the stresses, as the basic unknowns. The formulation is simple to implement, and it has been employed for finding the collapse loads of a circular footing placed over the surface of a cohesive-frictional material. The formulation can be used to solve any general axisymmetric geomechanics stability problem.

Effect of the Flow Rule on the Bearing Capacity of Strip Foundations on Sand by the Upper-Bound Limit Analysis and Slip Lines

The influence of the flow rule on the bearing capacity of strip foundations placed on sand was investigated using a new kinematic approach of upper-bound limit analysis. The method of stress characteristics was first used to find the mechanism of the failure and to compute the stress field by using the Mohr-Coulomb yield criterion. Once the failure mechanism had been established, the kinematics of the plastic deformation was established, based on the requirements of the upper-bound limit theorem. Both associated and nonassociated plastic flows were considered, and the bearing capacity was obtained by equating the rate of external plastic work to the rate of the internal energy dissipation for both smooth and rough base foundations. The results obtained from the analysis were compared with those available from the literature. (C) 2014 American Society of Civil Engineers.

Experimental investigation of forming limit, void coalescence and crystallographic textures of aluminum alloy 8011 sheet annealed at various temperatures

In this work, a combined forming and fracture limit diagram, fractured void coalescence and texture analysis have been experimentally evaluated for the commercially available aluminum alloy Al 8011 sheet annealed at different temperatures viz. 200 degrees C, 250 degrees C, 300 degrees C and 350 degrees C. The sheets were examined at different annealing temperatures on microstructure, tensile properties, formability and void coalescence. The fractured surfaces of the formed samples were examined using scanning electron microscope (SEM) and these images were correlated with fracture behavior and formability of sheet metals. Formability of Al 8011 was studied and examined at various annealing temperatures using their bulk X-ray crystallographic textures and ODF plots. Forming limit diagrams, void coalescence parameters and crystallographic textures were correlated with normal anisotropy of the sheet metals annealed at different temperatures. (C) 2013 Politechnika Wroclawska. Published by Elsevier Urban & Partner Sp. z o.o. All rights reserved.

Bearing capacity of circular foundations reinforced with geogrid sheets

The ultimate bearing capacity of a circular footing, placed over a soil mass which is reinforced with horizontal layers of circular reinforcement sheets, has been determined by using the upper bound theorem of the limit analysis in conjunction with finite elements and linear optimization. For performing the analysis, three different soil media have been separately considered, namely, (i) fully granular, (ii) cohesive frictional, and (iii) fully cohesive with an additional provision to account for an increase of cohesion with depth. The reinforcement sheets are assumed to be structurally strong to resist axial tension but without having any resistance to bending; such an approximation usually holds good for geogrid sheets. The shear failure between the reinforcement sheet and adjoining soil mass has been considered. The increase in the magnitudes of the bearing capacity factors (N-c and N-gamma) with an inclusion of the reinforcement has been computed in terms of the efficiency factors eta(c) and eta(gamma). The results have been obtained (i) for different values of phi in case of fully granular (c=0) and c-phi soils, and (ii) for different rates (m) at which the cohesion increases with depth for a purely cohesive soil (phi=0 degrees). The critical positions and corresponding optimum diameter of the reinforcement sheets, for achieving the maximum bearing capacity, have also been established. The increase in the bearing capacity with an employment of the reinforcement increases continuously with an increase in phi. The improvement in the bearing capacity becomes quite extensive for two layers of the reinforcements as compared to the single layer of the reinforcement. The results obtained from the study are found to compare well with the available theoretical and experimental data reported in literature. (C) 2014 The Japanese Geotechnical Society. Production and hosting by Elsevier B.V. All rights reserved.

Bearing Capacity of Circular Footings on Reinforced Soils

A method is presented for determining the ultimate bearing capacity of a circular footing reinforced with a horizontal circular sheet of reinforcement placed over granular and cohesive-frictional soils. It was assumed that the reinforcement sheet could bear axial tension but not the bending moment. The analysis was performed based on the lower-bound theorem of the limit analysis in combination with finite elements and linear optimization. The present research is an extension of recent work with strip foundations reinforced with different layers of reinforcement. To incorporate the effect of the reinforcement, the efficiency factors eta(gamma) and eta(c), which need to be multiplied by the bearing capacity factors N-gamma and N-c, were established. Results were obtained for different values of the soil internal friction angle (phi). The optimal positions of the reinforcements, which would lead to a maximum improvement in the bearing capacity, were also determined. The variations of the axial tensile force in the reinforcement sheet at different radial distances from the center were also studied. The results of the analysis were compared with those available from literature. (C) 2014 American Society of Civil Engineers.

Modified Einstein's gravity as a possible missing link between sub- and super-Chandrasekhar type Ia supernovae

We explore the effect of modification to Einstein's gravity in white dwarfs for the first time in the literature, to the best of our knowledge. This leads to significantly sub- and super-Chandrasekhar limiting masses of white dwarfs, determined by a single model parameter. On the other hand, type Ia supernovae (SNeIa), a key to unravel the evolutionary history of the universe, are believed to be triggered in white dwarfs having mass close to the Chandrasekhar limit. However, observations of several peculiar, under- and over-luminous SNeIa argue for exploding masses widely different from this limit. We argue that explosions of the modified gravity induced sub- and super-Chandrasekhar limiting mass white dwarfs result in under- and over-luminous SNeIa respectively, thus unifying these two apparently disjoint sub-classes and, hence, serving as a missing link. Our discovery raises two fundamental questions. Is the Chandrasekhar limit unique? Is Einstein's gravity the ultimate theory for understanding astronomical phenomena? Both the answers appear to be no!

Lower Bound Axisymmetric Limit Analysis Using Drucker-Prager Yield Cone and Simulation with Mohr-Coulomb Pyramid

This paper presents a lower bound limit analysis approach for solving an axisymmetric stability problem by using the Drucker-Prager (D-P) yield cone in conjunction with finite elements and nonlinear optimization. In principal stress space, the tip of the yield cone has been smoothened by applying the hyperbolic approximation. The nonlinear optimization has been performed by employing an interior point method based on the logarithmic barrier function. A new proposal has also been given to simulate the D-P yield cone with the Mohr-Coulomb hexagonal yield pyramid. For the sake of illustration, bearing capacity factors N-c, N-q and N-gamma have been computed, as a function of phi, both for smooth and rough circular foundations. The results obtained from the analysis compare quite well with the solutions reported from literature.

Bearing capacity factors for a conical footing using lower- and upper-bound finite elements limit analysis

Bearing capacity factors, N-c, N-q, and N-gamma, for a conical footing are determined by using the lower and upper bound axisymmetric formulation of the limit analysis in combination with finite elements and optimization. These factors are obtained in a bound form for a wide range of the values of cone apex angle (beta) and phi with delta = 0, 0.5 phi, and phi. The bearing capacity factors for a perfectly rough (delta = phi) conical footing generally increase with a decrease in beta. On the contrary, for delta = 0 degrees, the factors N-c and N-q reduce gradually with a decrease in beta. For delta = 0 degrees, the factor N-gamma for phi >= 35 degrees becomes a minimum for beta approximate to 90 degrees. For delta = 0 degrees, N-gamma for phi <= 30 degrees, as in the case of delta = phi, generally reduces with an increase in beta. The failure and nodal velocity patterns are also examined. The results compare well with different numerical solutions and centrifuge tests' data available from the literature.

Intrinsic Limit for Contact Resistance in Exfoliated Multilayered MoS2 FET

A new method for the separation of contact resistance (R-contact) into Schottky barrier resistance (R-SB) and interlayer resistance (R-IL) is proposed for multilayered MoS2 FETs. While R-SB varies exponentially with Schottky barrier height (Phi(bn)), R-IL essentially remains unchanged. An empirical model utilizing this dependence of R-contact versus Phi(bn) is proposed and fits to the experimental data. The results, on comparison with the existing reports of lowest R-contact, suggest that the extracted R-IL (1.53 k Omega.mu m) for an unaltered channel would determine the lower limit of intrinsic R-contact even for barrierless contacts for multilayered exfoliated MoS2 FETs.

Reply to Discussion on ``Bearing capacity of circular footings over rock mass by using axisymmetric quasi lower bound finite element limit analysis'' Comput. Geotech. 70 (2015) 138-149]

A discussion has been provided for the comments raised by the discusser (Clausen, 2015)1] on the article recently published by the authors (Chakraborty and Kumar, 2015). The effect of exponent alpha for values of GSI approximately smaller than 30 becomes more critical. On the other hand, for greater values of GSI, the results obtained by the authors earlier remain primarily independent of alpha and can be easily used. (C) 2015 Elsevier Ltd. All rights reserved.