Studies on two-phase co-current air/non-Newtonian shear-thinning fluid flows in inclined smooth pipes

In this work. co-current flow characteristics of air/non-Newtonian liquid systems in inclined smooth pipes are studied experimentally and theoretically using transparent tubes of 20, 40 and 60 turn in diameter. Each tube includes two 10 m lone pipe branches connected by a U-bend that is capable of being inclined to any angle, from a completely horizontal to a fully vertical position. The flow rate of each phase is varied over a wide range. The studied flow phenomena are bubbly, plug flow, slug flow, churn flow and annular flow. These are observed and recorded by a high flow. stratified flow. -speed camera over a wide range of operating conditions. The effects of the liquid phase properties, the inclination angle and the pipe diameter on two-phase flow characteristics are systematically studied. The Heywood-Charles model for horizontal flow was modified to accommodate stratified flow in inclined pipes, taking into account the average void fraction and pressure drop of the mixture flow of a gas/non-Newtonian liquid. The pressure drop gradient model of Taitel and Barnea for a gas/Newtonian liquid slug flow was extended to include liquids possessing shear-thinning flow behaviour in inclined pipes. The comparison of the predicted values with the experimental data shows that the models presented here provide a reasonable estimate of the average void fraction and the corresponding pressure drop for the mixture flow of a gas/ non-Newtonian liquid. (C) 2007 Elsevier Ltd. All rights reserved.

Effect of a laser pre-quenched steel substrate surface on the crack driving force in a coating-steel substrate system

A mechanical model of a coating/laser pre-quenched steel substrate specimen with a crack oriented perpendicular to the interface between the coating and the hardened layer is developed to quantify the effects of the residual stress and hardness gradient on the crack driving force in terms of the J-integral. It is assumed that the crack tip is in the middle of the hardened layer of the pre-quenched steel substrate. Using a composite double cantilever beam model, analytical solutions can be derived, and these can be used to quantify the effects of the residual stress and the hardness gradient resulting from the pre-quenched steel substrate surface on the crack driving force. A numerical example is presented to investigate how the residual compressive stress, the coefficient linking microhardness and yield strength and the Young's modulus ratio of the hardened layer to the coating influence the crack driving force for a given crack length. (C) 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Nonlinear dynamics of atomic force microscopy with intermittent contact

When the atomic force microscopy (AFM) in tapping mode is in intermittent contact with a soft substrate, the contact time can be a significant portion of a cycle, resulting in invalidity of the impact oscillator model, where the contact time is assumed to be infinitely small. Furthermore, we demonstrate that the AFM intermittent contact with soft substrate can induce the motion of higher modes in the AFM dynamic response. Traditional ways of modeling AFM (one degree of freedom (DOF) system or single mode analysis) are shown to have serious mistakes when applied to this kind of problem. A more reasonable displacement criterion on contact is proposed, where the contact time is a function of the mechanical properties of AFM and substrate, driving frequencies/amplitude, initial conditions, etc. Multi-modal analysis is presented and mode coupling is also shown. (c) 2006 Published by Elsevier Ltd.

Formation, microstructure and development of the localized shear deformation in low-carbon steels

An investigation has been made into the effect of microstructural parameters on the propensity for forming shear localization produced during high speed torsional testing by split Hopkinson bar with different average rates of 610, 650 and 1500 s(-1) in low carbon steels. These steels received the quenched, quenched and tempered as well as normalized treatments that provide wide microstructural parameters and mechanical properties. The results indicate that the occurrence of the shear localization is susceptible to the strength of the steels. In other words, the tendency of the quenched steel to form a shear band is higher than that of the other two steels. It is also found that there is a critical strain at which the shear localization occurs in the steels. The critical strain value is strongly dependent on the strength of the steels. Before arriving at this point, the material undergoes a slow work-hardening. After this point, the material suffers work-softening, corresponding to a process during which the deformation is gradually localized and eventually becomes spatially correlated to form a macroscopic shear band. Examinations by SEM reveal that the shear localization within the band involves a series of sequential crystallographic and non-crystallographic events including the change in crystal orientation, misorientation, generation and even perhaps damage in microstructures such as the initiation, growth and coalescence of the microcracks. It is expected that the sharp drop in the load-carrying capacity is associated with the growth and coalescence of the microcracks rather than the occurrence of the shear localization, but the shear localization is seen to accelerate the growth and coalescence of the microcracks. The thin foil observations by TEM reveal that the density of dislocations in the band is extremely high and the tangled arrangement and cell structure of dislocations tends to align along the shear direction. The multiplication and interaction of dislocations seems to be responsible for work-hardening of the steels. The avalanche of the dislocation cells corresponds to the sharp drop in shear stress at which the deformed specimen is broken. Double shear bands and kink bands are also observed in the present study. The principal band develops first and its width is narrower than that of the secondary band.

A modified split hopkinson torsional bar in studying shear localization

A modified split Hopkinson torsional bar (SHTB) is introduced to eliminate the effect of the loading reverberation of the standard SHTB on the study of evolution of shear localization. The effect, the cause and the method by which to eliminate loading wave reverberation are carefully analysed and discussed. By means of the modified apparatus, the post-mortem observation of tested specimens can provide data on actual evolution of micro-structure and micro-damage during shear localization. Some test results of shear banding conducted with this apparatus support the use of the modified design. Moreover, the modification makes possible the correlation of evolving micro-structures to the transient shear stress-strain recording.

Formation of shear bands in plane sheet

The formation of shear bands in plane sheet is studied, both analytically and experimentally, to enhance the fundamental understanding of this phenomenon and to develop a capability for predicting material failure. The evolution of voids is measured and its interaction with the process of shear banding is examined. The evolving dilatancy in plasticity is shown to have a vital role in analysing the shear-band type of bifurcation, and tremendously reduces the theoretical value of critical stresses. The analyses, referring to both localized and diffuse modes of bifurcation, fairly explain the corresponding observations obtained through testing a dual-phase steer sheet and provide a justification of the constitutive model used.

Influence of 2 secondary effects on shear failure of cantilever with attached mass block under impulsive loading

The influence of two secondary effects, rotatory inertia and presence of a crack, on the dynamic plastic shear failure of a cantilever with an attached mass block at its tip subjected to impulsive loading is investigated. It is illustrated that the consideration of the rotatory inertia of the cantilever and the presence of a crack at the upper root of the beam both increase the initial kinetic energy of the block required to cause shear failure at the interface between the beam tip and the tip mass, where the initial velocity has discontinuity Therefore, the influence of these two secondary effects on the dynamic shear failure is not negligible.

Unloading characteristics of anti-plane shear crack in softening materials

The local characteristics of the anti-plane shear stress and strain field are determined for a material where the stress increases linearly with strain up to a limit and then softens nonlinearly. Two unloading models are considered such that the unloading path always returns to the origin while the other assumes the unloading modulus to be that of the initial shear modulus. As the applied shear increases, an unloading zone is found to prevail between a zone in which the material softens and another zone in which the material is linear-elastic even though the crack does not propagate. The divisions of these zones are displayed graphically.

Characteristics and microstructure in the evolution of shear localization in ti-6al-4v alloy

A new interrupting method was proposed and the split Hopkinson torsional bar (SHTB) was modified in order to eliminate the effect of loading reverberation on post-mortem observations. This makes the comparative study of macro- and microscopic observations on tested materials and relevant transient measurement of tau - gamma curve possible. The experimental results of the evolution of shear localization in in Ti-6Al-4V alloy studied with the modified SHTB are reported in the paper. The collapse of shear stress seems to be closely related to the appearance of a certain critical coalescence of microcracks. The voids may form within the localized shear zone at a quite early stage. Finally, void coalescence results in elongated cavities and their extension leads to fracture along the shear band.

Bending solution of high-order refined shear deformation-theory for rectangular composite plates

A new high-order refined shear deformation theory based on Reissner's mixed variational principle in conjunction with the state- space concept is used to determine the deflections and stresses for rectangular cross-ply composite plates. A zig-zag shaped function and Legendre polynomials are introduced to approximate the in-plane displacement distributions across the plate thickness. Numerical results are presented with different edge conditions, aspect ratios, lamination schemes and loadings. A comparison with the exact solutions obtained by Pagano and the results by Khdeir indicates that the present theory accurately estimates the in-plane responses.

Vibration analysis of laminated plates using a refined shear deformation-theory

A previously published discrete-layer shear deformation theory is used to analyze free vibration of laminated plates. The theory includes the assumption that the transverse shear strains across any two layers are linearly dependent on each other. The theory has the same dependent variables as first order shear deformation theory, but the set of governing differential equations is of twelfth order. No shear correction factors are required. Free vibration of simply supported symmetric and antisymmetric cross-ply plates is calculated. The numerical results are in good agreement with those from three-dimensional elasticity theory.

Inhomogeneous behavior of antiplane shear crack in softening material with local unloading

Examined in this work is the anti-plane stress and strain near a crack in a material that softens beyond the elastic peak and unloads on a linear path through the initial state. The discontinuity in the constitutive relation is carried into the analysis such that one portion of the local solution is elliptic in character and the other hyperbolic. Material elements in one region may cross over to another as the loading is increased. Local unloading can thus prevail. Presented are the inhomogeneous character of the asymptotic stress and strain in the elliptic and hyperbolic region, in addition to the region in which the material elements had experienced unloading. No one single stress or strain coefficient would be adequate for describing crack instability.

Growth of zero-mean-shear turbulent-mixed layer with suspended particles in a 2-layer fluid system

The growth behaviour of zero-mean-shear turbulent-mixed layer containing suspended solid particles has been studied experimentally and analysed theoretically in a two-layer fluid system. The potential model for estimating the turbulent entrainment rate of the mixed layer has also been suggested, including the results of the turbulent entrainment for pure two-layer fluid. The experimental results show that the entrainment behaviour of a mixed layer with the suspended particles is well described by the model. The relationship between the entrainment distance and the time, and the variation of the dimensionless entrainment rate E with the local Richardson number Ri1 for the suspended particles differ from that for the pure two-layer fluid by the factors-eta-1/5 and eta-1, respectively, where eta = 1 + sigma-0-DELTA-rho/DELTA-rho-0.

On post-instability processes in adiabatic shear in hot rolled steel

EXPERIMENTS carried out using a split Hopkinson torsional bar have shown that only one shear band develops in specimens of hot rolled steel which break during testing. We observed, however, that in specimens which were not deformed to failure, several fine shear bands appeared. We believe that these formed during the loading cycle before the appearance of the final shear band and were not due to the effect of unloading. So we developed a numerical model to study the evolution of shear banding from several finite amplitude disturbances (FADs) in both temperature and strain rate. This numerical model reveals the detailed processes by which the FADs evolve into a fully developed shear band and suggests that beyond instability, the so-called shear banding process consists of two stages: inhomogeneous shearing and true shear-banding. The latter is characterized by the collapse of the stress and an abrupt increase of the local shear strain rate.