Flow of metal in constrained plane-strain extrusion forging- Part II

With many innovations in process technology, forging is establishing itself as a precision manufacturing process: as forging is used to produce complex shapes in difficult materials, it requires dies of complex configuration of high strength and of wear-resistant materials. Extensive research and development work is being undertaken, internationally, to analyse the stresses in forging dies and the flow of material in forged components. Identification of the location, size and shape of dead-metal zones is required for component design. Further, knowledge of the strain distribution in the flowing metal indicates the degree to which the component is being work hardened. Such information is helpful in the selection of process parameters such as dimensional allowances and interface lubrication, as well as in the determination of post-forging operations such as heat treatment and machining. In the presently reported work the effect of aperture width and initial specimen height on the strain distribution in the plane-strain extrusion forging of machined lead billets is observed: the distortion of grids inscribed on the face of the specimen gives the strain distribution. The stress-equilibrium approach is used to optimise a model of flow in extrusion forging, which model is found to be effective in estimating the size of the dead-metal zone. The work carried out so far indicates that the methodology of using the stress-equilibrium approach to develop models of flow in closed-die forging can be a useful tool in component, process and die design.

Numerical simulations of void growth near a notch tip in ductile single crystals

The objective of this work is to study the growth of a cylindrical void ahead of a notch tip in ductile FCC single crystals under mode I, plane strain, small scale yielding (SSY) conditions. To this end, finite element simulations are performed within crystal plasticity framework neglecting elastic anisotropy. Attention is focussed on the effects of crystal hardening, ratio of void diameter to spacing from the notch and crystal orientation on plastic flow localization in the ligament connecting the notch and the void as well as their growth. The results show strong interaction between shear bands emanating from the notch and angular sectors of single slip forming around the void leading to intense plastic strain development in the ligament. Further, the ductile fracture processes are retarded by increase in hardening of the single crystal and decrease in ratio of void diameter to spacing from the notch. Also, a strong influence of crystal orientation on near-tip void growth and plastic slip band development is observed. Finally, the synergistic, cooperative growth of multiple voids ahead of the notch tip is examined.

On factors influencing the ductile-to-brittle transition in a bulk metallic glass

An experimental study to ascertain the ductile-to-brittle transition (DBT) in a bulk metallic glass (BMG) was conducted. Results of the impact toughness tests conducted at various temperatures on as-cast and structurally relaxed Zr-based BMG show a sharp DBT. The DBT temperature was found to be sensitive to the free-volume content in the alloy. Possible factors that result in the DBT were critically examined. It was found that the postulate of a critical free volume required for the amorphous alloy to exhibit good toughness cannot rationalize the experimental trends. Likewise, the Poisson's ratio-toughness correlations, which suggest a critical Poisson's ratio above which all glasses are tough, were found not to hold good. Viscoplasticity theories, developed using the concept of shear transformation zones and which describe the temperature and strain rate dependence of the crack-tip plasticity in BMGs, appear to be capable of capturing the essence of the experiments. Our results highlight the need for a more generalized theory to understand the origins of toughness in BMGs.

Effects of Isothermal and Adiabatic Thermal Loadings on Size and Strain Rate Dependence of Copper Nanowire

In the present paper, the size and strain rate effects on ultra-thin < 100 >/{100} Cu nanowires at an initial temperature of 10 K have been discussed. Extensive molecular dynamics (MD) simulations have been performed using Embedded atom method (EAM) to investigate the structural behaviours and properties under high strain rate. Velocity-Verlet algorithm has been used to solve the equation of motions. Two different thermal loading cases have been considered: (i) Isothermal loading, in which Nose-Hoover thermostat is used to maintain the constant system temperature, and (ii) Adiabatic loading, i.e., without any thermostat. Five different wire cross-sections were considered ranging from 0.723 x 0.723 nm(2) to 2.169 x 2.169 nm(2) The strain rates used in the present study were 1 x 10(9) s(-1), 1 x 10(8) s(-1), and 1 x 10(7) s(-1). The effect of strain rate on the mechanical properties of copper nanowires was analysed, which shows that elastic properties are independent of thermal loading for a given strain rate and cross-sectional dimension of nanowire. It showed a decreasing yield stress and yield strain with decreasing strain rate for a given cross- section. Also, a decreasing yield stress and increasing yield strain were observed for a given strain rate with increasing cross-sectional area. Elastic modulus was found to be similar to 100 GPa, which was independent of processing temperature, strain rate, and size for a given initial temperature. Reorientation of < 100 >/{100} square cross-sectional copper nanowire into a series of stable ultra-thin Pentagon copper nanobridge structures with dia of similar to 1 nm at 10 K was observed under high strain rate tensile loading. The effect of isothermal and adiabatic loading on the formation of such pentagonal nanobridge structure has been discussed.

Phase field study of precipitate growth: Effect of misfit strain and interface curvature

We have used phase field simulations to study the effect of misfit and interfacial curvature on diffusion-controlled growth of an isolated precipitate in a supersaturated matrix. Treating our simulations as computer experiments, we compare our simulation results with those based on the Zener–Frank and Laraia–Johnson–Voorhees theories for the growth of non-misfitting and misfitting precipitates, respectively. The agreement between simulations and the Zener–Frank theory is very good in one-dimensional systems. In two-dimensional systems with interfacial curvature (with and without misfit), we find good agreement between theory and simulations, but only at large supersaturations, where we find that the Gibbs–Thomson effect is less completely realized. At small supersaturations, the convergence of instantaneous growth coefficient in simulations towards its theoretical value could not be tracked to completion, because the diffusional field reached the system boundary. Also at small supersaturations, the elevation in precipitate composition matches well with the theoretically predicted Gibbs–Thomson effect in both misfitting and non-misfitting systems.

Strain hardening during constrained deformation of metal foams - Effect of shear displacement

The crush bands that form during plastic deformation of closed-cell metal foams are often inclined at 11-20 degrees to the loading axis, allowing for shear displacement of one part of the foam with respect to the other. Such displacement is prevented by the presence of a lateral constraint. This was analysed in this study, which shows that resistance against shear by the constraint leads to the strain-hardening effect in the foam that has been reported in a recent experimental study. (C) 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Dynamics of dense sheared granular flows. Part 1. Structure and diffusion

Shear flows of inelastic spheres in three dimensions in the Volume fraction range 0.4-0.64 are analysed using event-driven simulations.Particle interactions are considered to be due to instantaneous binary collisions, and the collision model has a normal coefficient of restitution e(n) (negative of the ratio of the post- and pre-collisional relative velocities of the particles along the line joining the centres) and a tangential coefficient of restitution e(t) (negative of the ratio of post- and pre-collisional velocities perpendicular to the line Joining the centres). Here, we have considered both e(t) = +1 and e(t) = e(n) (rough particles) and e(t) =-1 (smooth particles), and the normal coefficient of restitution e(n) was varied in the range 0.6-0.98. Care was taken to avoid inelastic collapse and ensure there are no particle overlaps during the simulation. First, we studied the ordering in the system by examining the icosahedral order parameter Q(6) in three dimensions and the planar order parameter q(6) in the plane perpendicular to the gradient direction. It was found that for shear flows of sufficiently large size, the system Continues to be in the random state, with Q(6) and q(6) close to 0, even for volume fractions between phi = 0.5 and phi = 0.6; in contrast, for a system of elastic particles in the absence of shear, the system orders (crystallizes) at phi = 0.49. This indicates that the shear flow prevents ordering in a system of sufficiently large size. In a shear flow of inelastic particles, the strain rate and the temperature are related through the energy balance equation, and all time scales can be non-dimensionalized by the inverse of the strain rate. Therefore, the dynamics of the system are determined only by the volume fraction and the coefficients of restitution. The variation of the collision frequency with volume fraction and coefficient of estitution was examined. It was found, by plotting the inverse of the collision frequency as a function of volume fraction, that the collision frequency at constant strain rate diverges at a volume fraction phi(ad) (volume fraction for arrested dynamics) which is lower than the random close-packing Volume fraction 0.64 in the absence of shear. The volume fraction phi(ad) decreases as the coefficient of restitution is decreased from e(n) = 1; phi(ad) has a minimum of about 0.585 for coefficient of restitution e(n) in the range 0.6-0.8 for rough particles and is slightly larger for smooth particles. It is found that the dissipation rate and all components of the stress diverge proportional to the collision frequency in the close-packing limit. The qualitative behaviour of the increase in the stress and dissipation rate are well Captured by results derived from kinetic theory, but the quantitative agreement is lacking even if the collision frequency obtained from simulations is used to calculate the pair correlation function used In the theory.

Stress and strain-driven algorithmic formulations for finite strain viscoplasticity for hybrid and standard finite elements

This work deals with the formulation and implementation of finite deformation viscoplasticity within the framework of stress-based hybrid finite element methods. Hybrid elements, which are based on a two-field variational formulation, are much less susceptible to locking than conventional displacement-based elements. The conventional return-mapping scheme cannot be used in the context of hybrid stress methods since the stress is known, and the strain and the internal plastic variables have to be recovered using this known stress field.We discuss the formulation and implementation of the consistent tangent tensor, and the return-mapping algorithm within the context of the hybrid method. We demonstrate the efficacy of the algorithm on a wide range of problems.

Similar solutions for the incompressible laminar boundary layer with pressure gradient in micropolar

This paper presents the similarity solution for the steady incompressible laminar boundary layer flow of a micropolar fluid past an infinite wedge. The governing equations have been solved numerically using fourth orderRunge-Kutta-Gill method. The results indicate the extent to which the velocity and microrotation profiles, and the surface shear stress are influenced by coupling, microrotation, and pressure gradient parameters. The important role played by the standard length of the micropolar fluid in determining the structure of the boundary layer has also been discussed.

Application of the Conjugate Gradient Method to a Problem on Minimum Time Orbit Transfer

This correspondence considers the problem of optimally controlling the thrust steering angle of an ion-propelled spaceship so as to effect a minimum time coplanar orbit transfer from the mean orbital distance of Earth to mean Martian and Venusian orbital distances. This problem has been modelled as a free terminal time-optimal control problem with unbounded control variable and with state variable equality constraints at the final time. The problem has been solved by the penalty function approach, using the conjugate gradient algorithm. In general, the optimal solution shows a significant departure from earlier work. In particular, the optimal control in the case of Earth-Mars orbit transfer, during the initial phase of the spaceship's flight, is found to be negative, resulting in the motion of the spaceship within the Earth's orbit for a significant fraction of the total optimized orbit transfer time. Such a feature exhibited by the optimal solution has not been reported at all by earlier investigators of this problem.

On plane-wave propagation in a uniform pipe in the presence of a mean flow and a temperature gradient

A theoretical study on the propagation of plane waves in the presence of a hot mean flow in a uniform pipe is presented. The temperature variation in the pipe is taken to be a linear temperature gradient along the axis. The theoretical studies include the formulation of a wave equation based on continuity, momentum, and state equation, and derivation of a general four-pole matrix, which is shown to yield the well-known transfer matrices for several other simpler cases.