Numerical and experimental study of the thermal behaviour of coining and upsetting processes

A numerical simulation technique has been employed to study the thermal behavior of hot-forging type forming processes. Experiments on the coining and upsetting of an aluminum billet were conducted to validate the numerical predictions. Typical forming conditions for both the coining and upsetting processes were then studied in detail. an electrical analogy scheme was used to determine the thermal contact resistance. This scheme can conviniently provide the interface characteristics for typical processing conditions, which normally involve high pressures and temperatures. A single forging cycle was first considered, and then a batch of twenty-five forgings was studied. Each forging cycle includes the billet mounting, ascent, loading, dwelling, unloading, descent, and billet removal stages. The temperature distribution in the first forging to be formed is found to be significantly different from that at the end of the batch. In industry, forging is essentially a batch operation. The influence of forming speed and reduction on thermal characteristics was investigated also. The variations that can occur in the process design by considering differences in temperature characteristics are discussed also.

Direct numerical simulations of statistically steady, homogeneous, isotropic fluid turbulence with polymer additives

We carry out a direct numerical simulation (DNS) study that reveals the effects of polymers on statistically steady, forced, homogeneous, and isotropic fluid turbulence. We find clear manifestations of dissipation-reduction phenomena: on the addition of polymers to the turbulent fluid, we obtain a reduction in the energy dissipation rate; a significant modification of the fluid-energy spectrum, especially in the deep-dissipation range; and signatures of the suppression of small-scale structures, including a decrease in small-scale vorticity filaments. We also compare our results with recent experiments and earlier DNS studies of decaying fluid turbulence with polymer additives.

Numerical Electromagnetic Analysis of Current and Voltage Distribution along Down Conductors and Towers Hit by Direct Lightning

In order to answer the practically important question of whether the down conductors of lightning protection systems to tall towers and buildings can be electrically isolated from the structure itself, this work is conducted. As a first step in this regard, it is presumed that the down conductor placed on metallic tower will be a pessimistic representation of the actual problem. This opinion was based on the fact that the proximity of heavy metallic structure will have a large damping effect. The post-stroke current distributions along the down conductors and towers, which can be quite different from that in the lightning channel, govern the post-stroke near field and the resulting gradient in the soil. Also, for a reliable estimation of the actual stroke current from the measured down conductor currents, it is essential to know the current distribution characteristics along the down conductors. In view of these, the present work attempts to deduce the post-stroke current and voltage distribution along typical down conductors and towers. A solution of the governing field equations on an electromagnetic model of the system is sought for the investigation. Simulation results providing the spatio-temporal distribution of the post-stroke current and voltage has provided very interesting results. It is concluded that it is almost impossible to achieve electrical isolation between the structure and the down conductor. Furthermore, there will be significant induction into the steel matrix of the supporting structure.

A numerical investigation of ductile fracture initiation in a high-strength low-alloy steel

In this work, static and drop-weight impact experiments, which have been conducted using three-point bend fracture specimens of a high-strength low-alloy steel, are analysed by performing finite-element simulations. The Gurson constitutive model that accounts for the ductile failure mechanisms of microvoid nucleation, growth and is employed within the framework of a finite deformation plasticity theory. Two populations of second-phase particles are considered, including large inclusions which initiate voids at an early stage and small particles which require large strains to nucleate voids. The most important objective of the work is to assess quantitatively the effects of material inertia, strain rate sensitivity and local adiabatic temperature rise (due to conversion of plastic work into heat) on dynamic ductile crack initiation. This is accomplished by comparing the evolution histories of void volume fraction near the notch tip in the static analysis with the dynamic analyses. The results indicate that increased strain hardening caused by strain rate sensitivity, which becomes important under dynamic loading, plays a benign role in considerably slowing down the void growth rate near the notch tip. This is partially opposed by thermal softening caused by adiabatic heating near the notch tip.

A characteristic based numerical method with tracking for nonlinear wave equations

Many physical problems can be modeled by scalar, first-order, nonlinear, hyperbolic, partial differential equations (PDEs). The solutions to these PDEs often contain shock and rarefaction waves, where the solution becomes discontinuous or has a discontinuous derivative. One can encounter difficulties using traditional finite difference methods to solve these equations. In this paper, we introduce a numerical method for solving first-order scalar wave equations. The method involves solving ordinary differential equations (ODEs) to advance the solution along the characteristics and to propagate the characteristics in time. Shocks are created when characteristics cross, and the shocks are then propagated by applying analytical jump conditions. New characteristics are inserted in spreading rarefaction fans. New characteristics are also inserted when values on adjacent characteristics lie on opposite sides of an inflection point of a nonconvex flux function, Solutions along characteristics are propagated using a standard fourth-order Runge-Kutta ODE solver. Shocks waves are kept perfectly sharp. In addition, shock locations and velocities are determined without analyzing smeared profiles or taking numerical derivatives. In order to test the numerical method, we study analytically a particular class of nonlinear hyperbolic PDEs, deriving closed form solutions for certain special initial data. We also find bounded, smooth, self-similar solutions using group theoretic methods. The numerical method is validated against these analytical results. In addition, we compare the errors in our method with those using the Lax-Wendroff method for both convex and nonconvex flux functions. Finally, we apply the method to solve a PDE with a convex flux function describing the development of a thin liquid film on a horizontally rotating disk and a PDE with a nonconvex flux function, arising in a problem concerning flow in an underground reservoir.

A numerical study of division of flow in open channels

A two-dimensional numerical model which employs the depth-averaged forms of continuity and momentum equations along with k-e turbulence closure scheme is used to simulate the flow at the open channel divisions. The model is generalised to flows of arbitrary geometries and MacCormack finite volume method is used for solving governing equations. Application of cartesian version of the model to analyse the flow at right-angled junction is presented. The numerical predictions are compared with experimental data of earlier investigators and measurements made as part of the present study. Performance of the model in predicting discharge distribution, surface profiles, separation zone parameters and energy losses is evaluated and discussed in detail. To illustrate the application of the numerical model to analyse the flow in acute angled offtakes and streamlined branch entries, a few computational results are presented.

Evaluation of strain-rate effects in transitional round jets using direct numerical simulation

The coherent flame model uses the strain rate to predict reaction rate per unit flame surface area and some procedure that solves for the dynamics of flame surfaces to predict species distributions. The strainrate formula for the reaction rate is obtained from the analytical solution for a flame in a laminar, plane stagnation point flow. Here, the formula's effectiveness is examined by comparisons with data from a direct numerical simulation (DNS) of a round jetlike flow that undergoes transition to turbulence. Significant differences due to general flow features can be understood qualitatively: Model predictions are good in the braids between vortex rings, which are present in the near field of round jets, as the strain rate is extensional and reaction surfaces are isolated. In several other regions, the strain rate is compressive or flame surfaces are folded close together. There, the predictions are poor as the local flow no longer resembles the model flow. Quantitative comparisons showed some discrepancies. A modified, consistent application of the strain-rate solution did not show significant changes in the prediction of mean reaction rate distributions.

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.

Numerical simulations of fracture initiation in ductile solids under mode I, dynamic loading

In this paper, an overview of some recent computational studies by the authors on ductile crack initiation under mode I, dynamic loading is presented. In these studies, a large deformation finite element procedure is employed along with the viscoplastic version of the Gurson constitutive model that accounts for the micro-mechanical processes of void nucleation, growth and coalescence. A three-point bend fracture specimen subjected to impact, and a single edge notched specimen loaded by a tensile stress pulse are analysed. Several loading rates are simulated by varying the impact speed or the rise time and magnitude of the stress pulse. A simple model involving a semi-circular notch with a pre-nucleated circular hole situated ahead of it is considered. The growth of the hole and its interaction with the notch tip, which leads to plastic strain and porosity localization in the ligament connecting them, is simulated. The role of strain-rate dependence on ductile crack initiation at high loading rates, and the specimen geometry effect on the variation of dynamic fracture toughness with loading rate are Investigated.

Numerical modeling of heat and mass transfer in laser surface alloying: Non-equilibrium solidification effects

A transient macroscopic model is developed for studying heat and mass transfer in a single-pass laser surface alloying process, with particular emphasis on non-equilibrium solidification considerations. The solution for species concentration distribution requires suitable treatment of non-equilibrium mass transfer conditions. In this context, microscopic features pertaining to non-equilibrium effects on account of solutal undercooling are incorporated through the formulation of a modified partition-coefficient. The effective partition-coefficient is numerically modeled by Means of a number of macroscopically observable parameters related to the solidifying domain. The numerical model is so developed that the modifications on account of non-equilibrium solidification considerations can be conveniently implemented in existing numerical codes based on equilibrium solidification considerations.

An economical method for direct numerical simulation studies of transitional round jets

A pseudo-spectral method based on Fourier expansions in a Cartesian coordinate system is shown to be an economical method for direct numerical simulation studies of transitional round jets, Several characteristics of the solutions are presented to establish the validity of the solutions in spite of the unnatural choices. We show that neither periodicity, nor the use of a Cartesian system have adversely affected the simulations, Instead, there are benefits in terms of ease of computing and lack of the usual restrictions due to grid structure near the jet axis. By computing the simultaneous evolution of passive scalers, the process of reaction in round jet burners, between a fuel-laden jet and an ambient oxidizer, was also simulated. Some typical solutions are shown and then the results of analysis of these data are summarized. (C) 2001 Elsevier Science Ltd, All rights reserved.

Direct numerical simulation of turbulent spots

A group of high-order finite-difference schemes for incompressible flow was implemented to simulate the evolution of turbulent spots in channel flows. The long-time accuracy of these schemes was tested by comparing the evolution of small disturbances to a plane channel flow against the growth rate predicted by linear theory. When the perturbation is the unstable eigenfunction at a Reynolds number of 7500, the solution grows only if there are a comparatively large number of (equispaced) grid points across the channel. Fifth-order upwind biasing of convection terms is found to be worse than second-order central differencing. But, for a decaying mode at a Reynolds number of 1000, about a fourth of the points suffice to obtain the correct decay rate. We show that this is due to the comparatively high gradients in the unstable eigenfunction near the walls. So, high-wave-number dissipation of the high-order upwind biasing degrades the solution especially. But for a well-resolved calculation, the weak dissipation does not degrade solutions even over the very long times (O(100)) computed in these tests. Some new solutions of spot evolution in Couette flows with pressure gradients are presented. The approach to self-similarity at long times can be seen readily in contour plots.

Grain Floatation During Equiaxed Solidification of an Al-Cu Alloy in a Side-Cooled Cavity: Part II-Numerical Studies

In this article, a single-phase, one-domain macroscopic model is developed for studying binary alloy solidification with moving equiaxed solid phase, along with the associated transport phenomena. In this model, issues such as thermosolutal convection, motion of solid phase relative to liquid and viscosity variations of the solid-liquid mixture with solid fraction in the mobile zone are taken into account. Using the model, the associated transport phenomena during solidification of Al-Cu alloys in a rectangular cavity are predicted. The results for temperature variation, segregation patterns, and eutectic fraction distribution are compared with data from in-house experiments. The model predictions compare well with the experimental results. To highlight the influence of solid phase movement on convection and final macrosegregation, the results of the current model are also compared with those obtained from the conventional solidification model with stationary solid phase. By including the independent movement of the solid phase into the fluid transport model, better predictions of macrosegregation, microstructure, and even shrinkage locations were obtained. Mechanical property prediction models based on microstructure will benefit from the improved accuracy of this model.

A numerical model of a liquid-feed solid polymer electrolyte DMFC and its experimental validation

A one-dimensional, biphasic, multicomponent steady-state model based on phenomenological transport equations for the catalyst layer, diffusion layer, and polymeric electrolyte membrane has been developed for a liquid-feed solid polymer electrolyte direct methanol fuel cell (SPE- DMFC). The model employs three important requisites: (i) implementation of analytical treatment of nonlinear terms to obtain a faster numerical solution as also to render the iterative scheme easier to converge, (ii) an appropriate description of two-phase transport phenomena in the diffusive region of the cell to account for flooding and water condensation/evaporation effects, and (iii) treatment of polarization effects due to methanol crossover. An improved numerical solution has been achieved by coupling analytical integration of kinetics and transport equations in the reaction layer, which explicitly include the effect of concentration and pressure gradient on cell polarization within the bulk catalyst layer. In particular, the integrated kinetic treatment explicitly accounts for the nonhomogeneous porous structure of the catalyst layer and the diffusion of reactants within and between the pores in the cathode. At the anode, the analytical integration of electrode kinetics has been obtained within the assumption of macrohomogeneous electrode porous structure, because methanol transport in a liquid-feed SPE- DMFC is essentially a single-phase process because of the high miscibility of methanol with water and its higher concentration in relation to gaseous reactants. A simple empirical model accounts for the effect of capillary forces on liquid-phase saturation in the diffusion layer. Consequently, diffusive and convective flow equations, comprising Nernst-Plank relation for solutes, Darcy law for liquid water, and Stefan-Maxwell equation for gaseous species, have been modified to include the capillary flow contribution to transport. To understand fully the role of model parameters in simulating the performance of the DMCF, we have carried out its parametric study. An experimental validation of model has also been carried out. (C) 2003 The Electrochemical Society.