Criteria for prediction of flow instabilities and microstructural manifestations during warm working of AISI 304L stainless steel

The deformation characteristics of 304L stainless steel in compression in the temperature range 20–700°C and strain rate range 0·001–100 s−1 have been studied with the aim of characterising the .flow instabilities occurring in the microstructure. At higher temperatures and strain rates the stainless steel exhibits flow localisation, whereas at temperatures below 500°C and strain rates lower than 0·1 s−1 the flow instabilities are due to dynamic strain aging. Strain induced martensite formation is responsible for the flow instabilities at room temperature and low strain rates (0·01 s−1). In view of the occurrence of these instabilities, cold working is preferable to warm working to achieve dimensional tolerance and reproducible properties in the product. Among the different criteria tested to explain the occurrence of instabilities, the continuum criterion, developed on the basis of the principles of maximum rate of entropy production and separability of the dissipation function, predicts accurately all the above instability features.

Critical phenomena in polymer solutions: Scaling of the free energy

The thermodynamics of monodisperse solutions of polymers in the neighborhood of the phase separation temperature is studied by means of Wilson’s recursion relation approach, starting from an effective ϕ4 Hamiltonian derived from a continuum model of a many‐chain system in poor solvents. Details of the chain statistics are contained in the coefficients of the field variables ϕ, so that the parameter space of the Hamiltonian includes the temperature, coupling constant, molecular weight, and excluded volume interaction. The recursion relations are solved under a series of simplifying assumptions, providing the scaling forms of the relevant parameters, which are then used to determine the scaling form of the free energy. The free energy, in turn, is used to calculate the other singular thermodynamic properties of the solution. These are characteristically power laws in the reduced temperature and molecular weight, with the temperature exponents being the same as those of the 3d Ising model. The molecular weight exponents are unique to polymer solutions, and the calculated values compare well with the available experimental data.

Minimum weight design of fiber-reinforced laminated composite structures with maximum stress and Tsai-Wu failure criteria

In this article, a minimum weight design of carbon/epoxy laminates is carried out using genetic algorithms. New failure envelopes have been developed by the combination of two commonly used phenomenological failure criteria, namely Maximum Stress (MS) and Tsai-Wu (TW) are used to obtain the minimum weight of the laminate. These failure envelopes are the most conservative failure envelope (MCFE) and the least conservative failure envelope (LCFE). Uniaxial and biaxial loading conditions are considered for the study and the differences in the optimal weight of the laminate are compared for the MCFE and LCFE. The MCFE can be used for design of critical load-carrying composites, while the LCFE could be used for the design of composite structures where weight reduction is much more important than safety such as unmanned air vehicles.

Supercritical age-dependent branching Markov processes and their scaling limits

This paper studies the long-time behavior of the empirical distribution of age and normalized position of an age-dependent supercritical branching Markov process. The motion of each individual during its life is a random function of its age. It is shown that the empirical distribution of the age and the normalized position of all individuals alive at time t converges as t -> infinity to a deterministic product measure.

Prediction of nonlocal scaling parameter for armchair and zigzag single-walled carbon nanotubes based on molecular structural mechanics, nonlocal elasticity and wave propagation

Atomic vibration in the Carbon Nanotubes (CNTs) gives rise to non-local interactions. In this paper, an expression for the non-local scaling parameter is derived as a function of the geometric and electronic properties of the rolled graphene sheet in single-walled CNTs. A self-consistent method is developed for the linearization of the problem of ultrasonic wave propagation in CNTs. We show that (i) the general three-dimensional elastic problem leads to a single non-local scaling parameter (e(0)), (ii) e(0) is almost constant irrespective of chirality of CNT in the case of longitudinal wave propagation, (iii) e(0) is a linear function of diameter of CNT for the case of torsional mode of wave propagation, (iv) e(0) in the case of coupled longitudinal-torsional modes of wave propagation, is a function which exponentially converges to that of axial mode at large diameters and to torsional mode at smaller diameters. These results are valid in the long-wavelength limit. (C) 2011 Elsevier Ltd. All rights reserved.

Performance and scaling of a 1.2 V/1.5 Ah nickel/metal hydride cell to a 6 V/1.5 Ah battery

A 1.2 V/1.5 Ah positive-limited nickel/metal hydride cell has been studied to determine its charge-discharge characteristics at different rates in conjunction with its AC impedance data. The faradaic efficiency of the cell is found to be maximum at similar to 70% charge input. The cell has been scaled to a 6 V/1.5 Ah battery. The cycle-life data on the battery suggest that it can sustain a prolonged charge-discharge schedule with little deterioration in its performance.

Temperature scaling in a dense vibrofluidized granular material

The leading order "temperature" of a dense two-dimensional granular material fluidized by external vibrations is determined. The grain interactions are characterized by inelastic collisions, but the coefficient of restitution is considered to be close to 1, so that the dissipation of energy during a collision is small compared to the average energy of a particle. An asymptotic solution is obtained where the particles are considered to be elastic in the leading approximation. The velocity distribution is a Maxwell-Boltzmann distribution in the leading approximation,. The density profile is determined by solving the momentum balance equation in the vertical direction, where the relation between the pressure and density is provided by the virial equation of state. The temperature is determined by relating the source of energy due to the vibrating surface and the energy dissipation due to inelastic collisions. The predictions of the present analysis show good agreement with simulation results at higher densities where theories for a dilute vibrated granular material, with the pressure-density relation provided by the ideal gas law, sire in error. [:S1063-651X(99)04408-6].

In-situ power monitoring scheme and its application in dynamic voltage and threshold scaling for digital CMOS integrated circuits

An in-situ power monitoring technique for Dynamic Voltage and Threshold scaling (DVTS) systems is proposed which measures total power consumed by load circuit using sleep transistor acting as power sensor. Design details of power monitor are examined using simulation framework in UMC 90nm CMOS process. Experimental results of test chip fabricated in AMS 0.35µm CMOS process are presented. The test chip has variable activity between 0.05 and 0.5 and has PMOS VTH control through nWell contact. Maximum resolution obtained from power monitor is 0.25mV. Overhead of power monitor in terms of its power consumption is 0.244 mW (2.2% of total power of load circuit). Lastly, power monitor is used to demonstrate closed loop DVTS system. DVTS algorithm shows 46.3% power savings using in-situ power monitor.

Scaling analysis of momentum and heat transport in gas tungsten arc weld pools

A systematic procedure is outlined for scaling analysis of momentum and heat transfer in gas tungsten arc weld pools. With suitable selections of non-dimentionalised parameters, the governing equations coupled with appropriate boundary conditions are first scaled, and the relative significance of various terms appearing in them is analysed accordingly. The analysis is then used to predict the orders of magnitude of some important quantities, such as the velocity scene lit the top surface, velocity boundary layer thickness, maximum temperature increase in the pool, and time required for initiation of melting. Some of the quantities predicted from the scaling analysis can also be used for optimised selection of appropriate grid size and time steps for full numerical simulation of the process. The scaling predictions are finally assessed by comparison with numerical results quoted in the literature, and a good qualitative agreement is observed.

Scaling analysis of momentum, heat, and mass transfer in binary alloy solidification problems

A systematic approach is developed for scaling analysis of momentum, heat and species conservation equations pertaining to the case of solidification of a binary mixture. The problem formulation and description of boundary conditions are kept fairly general, so that a large class of problems can be addressed. Analysis of the momentum equations coupled with phase change considerations leads to the establishment of an advection velocity scale. Analysis of the energy equation leads to an estimation of the solid layer thickness. Different regimes corresponding to different dominant modes of transport are simultaneously identified. A comparative study involving several cases of possible thermal boundary conditions is also performed. Finally, a scaling analysis of the species conservation equation is carried out, revealing the effect of a non-equilibrium solidification model on solute segregation and species distribution. It is shown that non-equilibrium effects result in an enhanced macrosegregation compared with the case of an equilibrium model. For the sake of assessment of the scaling analysis, the predictions are validated against corresponding computational results.

A scaling analysis of momentum and heat transport in laser surface melting

In this paper, we outline a systematic procedure for scaling analysis of momentum and heat transfer in laser melted pools. With suitable choices of non-dimensionalising parameters, the governing equations coupled with appropriate boundary conditions are first scaled, and the relative significance of various terms appearing in them are accordingly analysed. The analysis is then utilised to predict the orders of magnitude of some important quantities, such as the velocity scale at the top surface, velocity boundary layer thickness, maximum temperature rise in the pool, fully developed pool-depth, and time required for initiation of melting. Using the scaling predictions, the influence of various processing parameters on the system variables can be well recognised, which enables us to develop a deeper insight into the physical problem of interest. Moreover, some of the quantities predicted from the scaling analysis can be utilised for optimised selection of appropriate grid-size and time-steps for full numerical simulation of the process. The scaling predictions are finally assessed by comparison with experimental and numerical results quoted in the literature, and an excellent qualitative agreement is observed.

Minimum error solutions of the Boltzmann equation for shock structure

‘Best’ solutions for the shock-structure problem are obtained by solving the Boltzmann equation for a rigid sphere gas by applying minimum error criteria on the Mott-Smith ansatz. The use of two such criteria minimizing respectively the local and total errors, as well as independent computations of the remaining error, establish the high accuracy of the solutions, although it is shown that the Mott-Smith distribution is not an exact solution of the Boltzmann equation even at infinite Mach number. The minimum local error method is found to be particularly simple and efficient. Adopting the present solutions as the standard of comparison, it is found that the widely used v2x-moment solutions can be as much as a third in error, but that results based on Rosen's method provide good approximations. Finally, it is shown that if the Maxwell mean free path on the hot side of the shock is chosen as the scaling length, the value of the density-slope shock thickness is relatively insensitive to the intermolecular potential. A comparison is made on this basis of present results with experiment, and very satisfactory quantitative agreement is obtained.

On the criteria for reverse transition in a two-dimensional boundary layer flow

Experiments on reverse transition were conducted in two-dimensional accelerated incompressible turbulent boundary layers. Mean velocity profiles, longitudinal velocity fluctuations $\tilde{u}^{\prime}(=(\overline{u^{\prime 2}})^{\frac{1}{2}})$ and the wall-shearing stress (TW) were measured. The mean velocity profiles show that the wall region adjusts itself to laminar conditions earlier than the outer region. During the reverse transition process, increases in the shape parameter (H) are accompanied by a decrease in the skin friction coefficient (Cf). Profiles of turbulent intensity (u’2) exhibit near similarity in the turbulence decay region. The breakdown of the law of the wall is characterized by the parameter \[ \Delta_p (=\nu[dP/dx]/\rho U^{*3}) = - 0.02, \] where U* is the friction velocity. Downstream of this region the decay of $\tilde{u}^{\prime}$ fluctuations occurred when the momentum thickness Reynolds number (R) decreased roughly below 400.

Universality and scaling behavior of injected power in elastic turbulence in wormlike micellar gel

We study the statistical properties of spatially averaged global injected power fluctuations for Taylor-Couette flow of a wormlike micellar gel formed by surfactant cetyltrimethylammonium tosylate. At sufficiently high Weissenberg numbers the shear rate, and hence the injected power p(t), at a constant applied stress shows large irregular fluctuations in time. The nature of the probability distribution function (PDF) of p(t) and the power-law decay of its power spectrum are very similar to that observed in recent studies of elastic turbulence for polymer solutions. Remarkably, these non-Gaussian PDFs can be well described by a universal, large deviation functional form given by the generalized Gumbel distribution observed in the context of spatially averaged global measures in diverse classes of highly correlated systems. We show by in situ rheology and polarized light scattering experiments that in the elastic turbulent regime the flow is spatially smooth but random in time, in agreement with a recent hypothesis for elastic turbulence.