On the shear deformation theory for dynamic analysis of beams

Timoshenko's shear deformation theory is widely used for the dynamical analysis of shear-flexible beams. This paper presents a comparative study of the shear deformation theory with a higher order model, of which Timoshenko's shear deformation model is a special case. Results indicate that while Timoshenko's shear deformation theory gives reasonably accurate information regarding the set of bending natural frequencies, there are considerable discrepancies in the information it gives regarding the mode shapes and dynamic response, and so there is a need to consider higher order models for the dynamical analysis of flexure of beams.

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.

A study of the deformation slip lines in quenched and aged Al-2% Ge alloy

Optical microscopy has been employed to observe the slip lines in deformed Al-2% Ge alloy samples. Slip lines have been observed in the as-quenched, partially-aged, fully-aged and over-aged states. The lines tend to traverse fairly straight paths in the case of quenched and partially-aged conditions. Fully-aged samples also reveal such straight running lines when tested at low-temperatures. However, the density of the lines generally decreases as the peak-aged state is approached. These results are in agreement with the idea that thermally activated shearing of the precipitates is occurring in the alloy aged up to peak-hardness. The irregular lines for the over-aged specimens support the view that the moving dislocations by-pass the precipitates during deformation. The influence of test-temperature on the appearance of slip traces has been briefly examined.

Effect of Strain Rate on Evolution of the Deformation Microstructure and Texture in Polycrystalline Copper and Nickel

The evolution of crystallographic texture in polycrystalline copper and nickel has been studied. The deformation texture evolution in these two materials over seven orders of magnitude of strain rate from 3 x 10(-4) to similar to 2.0 x 10(+3) s(-1) show little dependence on the stacking fault energy (SFE) and the amount of deformation. Higher strain rate deformation in nickel leads to weakerh < 101 > texture because of extensive microband formation and grain fragmentation. This behavior, in turn, causes less plastic spin and hence retards texture evolution. Copper maintains the stable end < 101 > component over large strain rates (from 3 x 10(-4) to 10(+2) s(-1)) because of its higher strain-hardening rate that resists formation of deformation heterogeneities. At higher strain rates of the order of 2 x 10(+3) s(-1), the adiabatic temperature rise assists in continuous dynamic recrystallization that leads to an increase in the volume fraction of the < 101 > component. Thus, strain-hardening behavior plays a significant role in the texture evolution of face-centered cubic materials. In addition, factors governing the onset of restoration mechanisms like purity and melting point govern texture evolution at high strain rates. SFE may play a secondary role by governing the propensity of cross slip that in turn helps in the activation of restoration processes.

A Non-contact measurement technique to measure micro surface stress and obtain deformation profiles of the order of 1nm in Micro-cantilever based structures by single image Optical Diffraction method

A new method based on analysis of a single diffraction pattern is proposed to measure deflections in micro-cantilever (MC) based sensor probes, achieving typical deflection resolutions of 1nm and surface stress changes of 50 mu N/m. The proposed method employs a double MC structure where the deflection of one of the micro-cantilevers relative to the other due to surface stress changes results in a linear shift of intensity maxima of the Fraunhofer diffraction pattern of the transilluminated MC. Measurement of such shifts in the intensity maxima of a particular order along the length of the structure can be done to an accuracy of 0.01mm leading to the proposed sensitivity of deflection measurement in a typical microcantilever. This method can overcome the fundamental measurement sensitivity limit set by diffraction and pointing stability of laser beam in the widely used Optical Beam Deflection method (OBDM).

Nucleation and growth characteristics of cavities during the early stages of tensile creep deformation in a superplastic zirconia-20 wt% alumina composite

Constant-stress tensile creep experiments on a superplastic 3-mol%-yttria-stabilized tetragonal zirconia composite with 20 wt% alumina revealed that cavities nucleate relatively early during tensile deformation. The number of cavities nucleated increases with increasing imposed stress. The cavities nucleate at triple points associated largely with an alumina grain, and then grow rapidly in a cracklike manner to attain dimensions on the order of the grain facet size. It is suggested that coarser-grained superplastic ceramics exhibit lower ductility due to the ease in formation of such grain boundary facet-cracks and their interlinkage to form a macroscopic crack of critical dimensions.

Role of indenter angle on the plastic deformation underneath a sharp indenter and on representative strains: An experimental and numerical study

The subsurface microhardness mapping technique of Chaudhri was utilized to determine the shape, size and distribution of plastic strain underneath conical indenters of varying semi-apex angles, alpha (55 degrees, 65 degrees and 75 degrees). Results show that the elastic-plastic boundary under the indenters is elliptical in nature, contradicting the expanding cavity model, and the ellipticity increases with alpha. The maximum plastic strain immediately under the indenter was found to decrease with increasing alpha. Complementary finite-element analysis was conducted to examine the ability of simulations to capture the experimental observations. A comparison of computational and experimental results indicates that the plastic strain distributions as well as the maximum strains immediately beneath the indenter do not match, suggesting that simulation of sharp indentation requires further detailed studies for complete comprehension. Representative strains, epsilon(r), evaluated as the volume-average strains within the elastic-plastic boundary, decrease with increasing alpha and are in agreement with those estimated by using the dimensional analysis. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Effect of strain rate and temperature on the plastic deformation behaviour of a bulk metallic glass composite

The composites consisting of amorphous matrix reinforced with crystalline dendrites offer extraordinary combinations of strength, stiffness, and toughness and can be processed in bulk. Hence, they have been receiving intense research interest, with a primary focus to study their mechanical properties. In this paper, the temperature and strain rate effects on the uniaxial compression response of a tailored bulk metallic glass (BMG) composite has been investigated. Experimental results show that at temperatures ranging between ambient to 500 K and at all strain rates; the onset of plastic deformation in the composite is controlled by that in the dendrites. As the temperature is increased to the glass transition temperature of the matrix and beyond, flow in the amorphous matrix occurs readily and hence it dictates the composite's response. The role of the constituent phases in controlling the deformation mechanism of the composite has been verified by assessing the strain rate sensitivity and the activation volume for deformation. The composite is rate sensitive at room temperature with values of strain rate sensitivity and activation volume being similar to that of the dendrites. At test temperatures near to the glass transition temperature, the composite however becomes rate-insensitive corresponding to that of the matrix phase. At low strain rates, serrated flow akin to that of dynamic strain ageing in crystalline alloys was observed and the serration magnitude decreases with increasing temperature. Initiation of the shear bands at the dendrite/matrix interface and propagation of them through the matrix ligaments until their arrest at another interface is the responsible mechanism for this. (C) 2011 Elsevier B.V. All rights reserved.

New insights into the development of microstructure and deformation texture in nickel-60 wt.% cobalt alloy

The present study investigates the critical role of deformation twinning and Bs-type shear bands in the evolution of deformation texture in a low stacking fault energy Ni-60Co alloy up to very large rolling strain (epsilon(t) approximate to 4). The alloy develops a strong brass-type rolling texture, and its formation is initiated at the early stages of deformation. Extensive twinning is observed at the intermediate stages of deformation, which causes significant texture reorientation towards alpha-fiber. A pseudo-in-situ electron back-scattered diffraction technique adopted to capture orientation changes within individual grains during the early stages suggests that twinning should be subsequently aided by crystallographic slip to attain alpha-fiber (< 1 1 0 >parallel to ND) orientations. Beyond 40% reduction, deformation is dominated by Bs-type shear bands, and the banding coincides with the evolution of < 1 1 1 >parallel to ND components. The volume fraction of shear bands is significant at higher strains, and crystallites within the bands preferentially show < 1 1 0 >parallel to ND components. The absence of the Cu {1 1 2}< 1 1 1 > component in the initial texture, and subsequently during rolling, indicates that, for the evolution of a brass-type texture, the presence of the Cu component is not a necessary condition. The final rolling texture is a synergistic effect of deformation twinning and shear banding. (C) 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

On the stability of the L-p-norm of the Riemannian curvature tensor

We consider the Riemannian functional defined on the space of Riemannian metrics with unit volume on a closed smooth manifold M where R(g) and dv (g) denote the corresponding Riemannian curvature tensor and volume form and p a (0, a). First we prove that the Riemannian metrics with non-zero constant sectional curvature are strictly stable for for certain values of p. Then we conclude that they are strict local minimizers for for those values of p. Finally generalizing this result we prove that product of space forms of same type and dimension are strict local minimizer for for certain values of p.

SOME UNSTABLE CRITICAL METRICS FOR THE L-n/2-NORM OF THE CURVATURE TENSOR

We consider the Riemannian functional defined on the space of Riemannian metrics with unit volume on a closed smooth manifold M given by R-n/2(g) := integral(M) vertical bar R(g)vertical bar(n//2) dv(g) where R(g), dv(g) denote the Riemannian curvature and volume form corresponding to g. We show that there are locally symmetric spaces which are unstable critical points for this functional.

Temperature characteristics of the billet and the dies in a small batch forging production

The work reported herein is part of an on-going programme to develop a computer code which, given the geometrical, process and material parameters of the forging operation, is able to predict the die and the billet cooling/heating characteristics in forging production. The code has been experimentally validated earlier for a single forging cycle and is now validated for a small batch production. To facilitate a step-by-step development of the code, the billet deformation has so far been limited to its surface layers, a situation akin to coining. The code has been used here to study the effects of die preheat-temperature, machine speed and rate of deformation the cooling/heating of the billet and the dies over a small batch of 150 forgings. The study shows: that there is a pre-heat temperature at which the billet temperature changes little from one forging to the next; that beyond a particular number of forgings, the machine speed ceases to have any pronounced influence on the temperature characteristics of the billet; and that increasing the rate of deformation reduces the heat loss from the billet and gives the billet a stable temperature profile with respect to the number of forgings. The code, which is simple to use, is being extended to bulk-deformation problems. Given a practical range of possible machine, billet and process specifics, the code should be able to arrive at a combination of these parameters which will give the best thermal characteristics of the die-billet system. The code is also envisaged as being useful in the design of isothermal dies and processes.

A simulation study of the mixing, atomic flow and velocity profiles of crystalline materials during sliding

Self-contained Non-Equilibrium Molecular Dynamics (NEMD) simulations using Lennard-Jones potentials were performed to identify the origin and mechanisms of atomic scale interfacial behavior between sliding metals. The mixing sequence and velocity profiles were compared via MD simulations for three cases, viz.: sell-mated, similar and hard-softvcrystal pairs. The results showed shear instability, atomic scale mixing, and generation of eddies at the sliding interface. Vorticity at the interface suggests that atomic flow during sliding is similar to fluid flow under Kelvin-Helmholtz instability and this is supported by velocity profiles from the simulations. The initial step-function velocity profile spreads during sliding. However the velocity profile does not change much at later stages of the simulation and it eventually stops spreading. The steady state friction coefficient during simulation was monitored as a function of sliding velocity. Frictional behavior can be explained on the basis of plastic deformation and adiabatic effects. The mixing layer growth kinetics was also investigated.

Evidence of episodic brittle faulting in the cratonic part of the Peninsular India and its implications for seismic hazard in slow deforming regions

The region around Waclakkancheri, in the province of Kerala, India, which lies in the vicinity of Palghat-Cauvery ;hear zone (within the Precambrian crystalline terrain), has been a site of microseismic activity since 1989. Earlier studies had identified a prominent WNW-ESE structure overprinting on the E-W trending lineaments associated with Palghat-Cauvery shear zone. We have mapped this structure, located in a chamockite quarry near Desamangalam, Waclakkancheri, which we identify as a ca. 30 km-long south dipping reverse fault. This article presents the characteristics of this fault zone exposed on the exhumed crystalline basement and discusses its significance in understanding the earthquake potential of the region. This brittle deformation zone consists of fracture sets with small-scale displacement and slip planes with embedded fault gouges. The macroscopic as well as the microscopic studies of this fault zone indicate that it evolved through different episodes of faulting in the presence of fluids. The distinct zones within consolidated gouge and the cross cutting relationship of fractures indicate episodic fault activity. At least four faulting episodes can be recognized based on the sequential development of different structural elements in the fault rocks. The repeated ruptures are evident along this shear zone and the cyclic behavior of this fault consists of co-seismic ruptures alternating with inter-seismic periods, which is characterized by the sealed fractures and consolidated gouge. The fault zone shows a minimum accumulated dip/oblique slip of 2.1 m in the reverse direction with a possible characteristic slip of 52 cm (for each event). The ESR dating of fault gouge indicates that the deformation zone records a major event in the Middle Quaternary. The empirical relationships between fault length and slip show that this fault may generate events M >= 6. The above factors suggest that this fault may be characterized as potentially active. Our study offers some new pointers that can be used in other slow deforming cratonic hinterlands in exploring the discrete active faults.