Viscous Zone Research Articles

Effect of Reflow Time on Wetting Behavior, Microstructure Evolution, and Joint Strength of Sn-2.5Ag-0.5Cu Solder on Bare and Nickel-Coated Copper Substrates

The effect of reflow time on wetting behavior of Sn-2.5Ag-0.5Cu lead-free solder on bare and nickel-coated copper substrates has been investigated. The solder alloy was reflowed at 270°C for various reflow times of 10 s, 100 s, 300 s, and 500 s. On bare copper substrate, the intermetallic compound (IMC) thickness increased with increase in reflow time, whereas on Ni-coated Cu substrate, the IMC thickness increased up to 300 s followed by a drop for solder alloy reflowed for 500 s. The spreading behavior of the solder alloy was categorized into capillary, gravity (diffusion), and viscous zones. Gravity zone was obtained from 3.8 ± 0.43 s to 38.97 ± 3.38 s and from 5.99 ± 0.5 s to 77.82 ± 8.84 s for the Sn-2.5Ag-0.5Cu/Cu and Sn-2.5Ag-0.5Cu/Ni/Cu system, respectively. Sn-2.5Ag-0.5Cu solder alloy was also reflowed for the period corresponding to the end of the gravity zone (40 s and 80 s on bare and Ni-coated Cu, respectively). The joint strength was maximum at reflow time of 40 s and 80 s for the Sn-2.5Ag-0.5Cu/Cu and Sn-2.5Ag-0.5Cu/Ni/Cu system, respectively. The dynamic contact angle at the end of the gravity (diffusion) zone (θgz) was found to be a better parameter compared with the stabilized contact angle (θf) to assess the effect of the wettability of the liquid solder on the microstructure and joint strength. The present investigation reveals the significance of the gravity zone in assessment of optimum reflow time for lead-free solder alloys.

A diffusion-regulated scheme for the compressible Navier–Stokes equations using a boundary-layer sensor

A new formulation to regulate the numerical diffusion of the Local Lax–Friedrichs (LLF) scheme for the accurate computation of high-speed viscous flows is proposed. This is achieved by modifying the diffusion regulation (DR) parameter of the DRLLF scheme originally proposed by Jaisankar and Raghurama Rao for the Euler equations. The modified version of the DR parameter operates based on a boundary layer sensor in such a way that the numerical diffusion is further reduced inside the viscous zone only and in the outer inviscid zone the parameter reverts back to the original inviscid formulation. This new scheme is named as the DRLLF-Viscous (DRLLFV) scheme. Test cases of viscous supersonic flow over a flat plate and hypersonic flow over a ramped surface are computed using the new scheme and compared with the AUSM scheme, DRLLF scheme and van Leer's Flux Vector Splitting (FVS) scheme. Comparisons with the literature show that the DRLLFV scheme resolves the boundary layer including flow separation more accurately than van Leer's FVS and DRLLF schemes and nearly as accurately as the AUSM scheme. In the inviscid zone, the DRLLFV scheme captures the leading-edge shock better than the rest of the schemes. If the overall results in both the viscous and inviscid regions are considered, the new scheme is seen to perform better than the AUSM scheme.

Modeling the evolution of microstructures in finite plasticity

AbstractKochmann and Hackl introduced in [1] a micromechanical model for finite single crystal plasticity. Based on thermodynamic variational principles this model leads to a non‐convex variational problem. Employing the Lagrange functional, an incremental strategy was outlined to model the time‐continuous evolution of a first order laminate microstructure. Although this model provides interesting results on the material point level, due to the global minimization in the evolution equations, the calculation time and numerical instabilities may cause problems when applying this model to macroscopic specimens.In order to avoid these problems, a smooth transition zone between the laminates is introduced to avoid global minimization, which makes the numerical calculations cumbersome compared to the model in [1]. By introducing a smooth viscous transition zone, the dissipation potential and its numerical treatment have to be adapted. We obtain rate‐dependent time‐evolution equations for the internal variables based on variational techniques and show as an example single slip shear. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A variational viscosity-limit approach to the evolution of microstructures in finite crystal plasticity

A micromechanical model for finite single crystal plasticity was introduced by Kochmann & Hackl (2011 Contin. Mech. Thermodyn. 23, 63–85 ( doi:10.1007/s00161-010-0714-5 )). This model is based on thermodynamic variational principles and leads to a non-convex variational problem. Based on the Lagrange functional, an incremental strategy was outlined to model the time-continuous evolution of a first-order laminate microstructure. Although this model provides interesting results on the material point level, owing to the global minimization in the evolution equations, the calculation time and numerical instabilities may cause problems when applying this model to macroscopic specimens. In this paper, a smooth transition zone between the laminates is introduced to avoid global minimization, which makes the numerical calculations cumbersome compared with the model in Kochmann & Hackl. By introducing a smooth viscous transition zone, the dissipation potential and its numerical treatment have to be adapted. We outline rate-dependent time-evolution equations for the internal variables based on variational techniques and show as first examples single-slip shear and tension/compression tests.

Planar Rayleigh–Taylor instabilities: outflows from a binary line-source system

Rayleigh–Taylor instabilities occur when a light fluid lies beneath a heavier one, with an interface separating them. Under the influence of gravity, the two fluid layers attempt to exchange positions, and as a result, the interface between them is unstable, forming fingers and plumes. Here, an analogous problem is considered, but in cylindrical geometry. Two line sources are present within an inner region of lighter fluid, and each of them has an inwardly directed gravity field. The surrounding fluid is heavier and is pushed outward by the light inner fluid ejected from the two sources. Nonlinear inviscid solutions are calculated and compared with the results of a linearized inviscid theory. In addition, the problem is formulated as a weakly compressible viscous outflow and modeled with Boussinesq theory. It is found that vorticity is generated in the viscous interfacial zone but that overturning plumes do not develop. However, the solution growth is highly sensitive to initial conditions.

Dynamic threshold pressure gradient in tight gas reservoir

Experimental approach was performed in this paper to study the threshold pressure gradient (TPG) in tight gas reservoir. The nonlinear flow behavior of tight gas reservoir was investigated at first, three zones of flow curve are divided to describe the nonlinear behavior of gas flow in tight formation: solid–gas viscous force zone, slippage zone and low-speed turbulent zone. On this basis, experiments using modified procedure were made in order to clarify the influence of pore pressure on TPG, results show that TPG of tight gas reservoir is highly effected by pore pressure and conventional experimental methods will lead to a significant error. And then, TPG during the development of tight gas reservoir was tested. The results we obtained demonstrated that there exists ‘Dynamic TPG Effect’ during the development process of tight gas reservoir: TPG is increasing along with the decrease of reservoir pressure (pore pressure). New concepts of ‘TPG Rising Cone’ and ‘TPG Sensitivity Coefficient’ are defined to characterize the dynamic TPG of tight gas reservoir. Finally, experiments were carried out to investigate the influence of permeability and water saturation on dynamic TPG. Results indicate that ‘TPG Rising Cone’ is more significant in reservoir with low-permeability or high water saturation.

The gravo-magneto disc instability with a viscous dead zone

We consider the evolution of accretion discs that contain some turbulence within a disc dead zone, a region about the disc midplane of a disc that is not sufficiently ionised for the magneto-rotational instability (MRI) to drive turbulence. In particular, we determine whether additional sources of turbulence within a dead zone are capable of suppressing gravo-magneto (GM) disc outbursts that arise from a rapid transition from gravitationally produced to MRI produced turbulence. With viscous $\alpha$ disc models we consider two mechanisms that may drive turbulence within the dead zone. First, we examine a constant $\alpha$ parameter within the dead zone. This may be applicable to hydrodynamical instability, such as baroclinic instability, where the turbulence level is independent of the MRI active surface layer properties. In this case, we find that the disc will not become stable to the outbursts unless the dead zone turbulent viscosity is comparable to that in the MRI active surface layers. Under such conditions, the accretion rate through the dead zone must be larger than that through the MRI active layers. In a second model, we assume that the accretion flow though the dead zone is a constant fraction (less than unity) of that through the active layers. This may be applicable to turbulence driven by hydrodynamic waves that are excited by the MRI active surface layers. We find that the instability is hardly affected by the viscous dead zone. In both cases however, we find that the triggering of the MRI during the outburst may be due to the heating from the viscosity in the dead zone, rather than self-gravity. Thus, neither mechanism for generating turbulence within the dead zone can significantly stabilise a disc or the resulting outburst behaviour.

Elastic–viscous transition in tear fracture of rubbers

There is a widely reported transition in the relationship between the critical strain energy release rate and a critical crack growth rate during the tearing of rubber materials. This transition is explained here for the first time in terms of an elastic–viscous transition phenomenon. The transition thus characterized depends on the balance of elasticity and viscosity of the material and hence the proximity of the test to the materials' glass transition temperature. Therefore two factors dominate the transition behavior, the cross-link density and the visco-elastic energy dissipation. A new elastic–viscous transition diagram is introduced to elucidate the mechanism of this phenomenon, where the diagram consists of three zones, each with a different fracture mode. These are an elastic–brittle fracture zone, a viscous–ductile fracture zone and an intermediate transition zone between the elastic and viscous zones. The transition zone characterized by stick–slip motion is caused in mechanics as results from unstable fluctuations of crack growth rate due to the energy dissipation near the glass transition temperature. The mechanism for the transition to be generated at the crack front is investigated both theoretically and experimentally with a consideration of surface roughness formation and stick–slip tear motion together with frictional sliding of the rubber at the crack tip.

Study on Hot Stamping Process of Cannonball Body Semiproduct Based on Numerical Simulation

Using the finite element simulation software Deform-3D , the forming characteristics of pressing, cupping and shell ironing of the thick-walled cannonball body semiproduct were analyzed, and the parameters of shell ironing was optimized. The results show that the load increases sharply at the end of the pressing, while the bottom corner of the billet and the boss are not well formed, which can be finished at the end of cupping; Due to friction, the metal closed to the end face of the punch dose not deform during the cupping process, but rigidly moves with the punch. This part without deformation of the billet is called deformation viscous zone. As the cylinder wall of the billet bears axial tensile stress during the shell ironing, deformation at the bottom and necking would occur easily undercondition of bad lubrication and large deformation. When die-entrance taper is 15º, the workpiece have homogeneous deformation, low axial tension stress and forming load. The forming load of shell ironing can be effectively reduced by good lubrication for die.

Physicochemical studies on the catanionics of alkyltrimethylammonium bromides and bile salts in aqueous media

Phase manifestation and aggregation behavior of long chain alkyltrimethylammonium bromides (CnTABr, n=12, 14 and 16) in combination with sodium cholate (NaC) and sodium deoxycholate (NaDC), were studied in aqueous medium. CnTABr–NaDC mixed systems exhibited different phases, viz., micelles, vesicles and precipitates while only clear isotropic phase was formed with NaC. With increasing chain length of CnTABr, both the area under precipitate and viscous zones increased. Micellization behavior of mixed surfactant systems at different compositions were studied by conductance, viscosity, fluorescence spectroscopy, dynamic light scattering, zeta potential and small angle X-Ray scattering measurements. Mixed micelles, at all combinations, were basically comprised of larger proportion (∼50–60%) of cationic surfactant, which were independent of the bulk composition. Interaction parameter, activity coefficient and micellar composition were evaluated in the light of Rubinigh's model for Regular Solution Theory (RST). Strong synergistic interaction occurred between CnTABr and bile salts where NaC behaved differently from NaDC due to its higher hydrophilicity. Complexity of the different systems increased with the increasing chain length of CnTABr. Such catanionic systems are considered to have prospects in drug delivery systems, nanoparticle synthesis, etc.

The deformation units in metallic glasses revealed by stress-induced localized glass transition

We report that even in quasi-static cyclic compressions in the apparent elastic regimes of the bulk metallic glasses, the precisely measured stress-strain curve presents a mechanical hysteresis loop, which is commonly perceived to occur only in high-frequency dynamic tests. A phenomenological viscoelastic model is established to explain the hysteresis loop and demonstrate the evolutions of the viscous zones in metallic glasses during the cyclic compression. The declining of the viscosity of the viscous zones to at least 1 × 1012 Pa s when stress applied indicates that stress-induced localized glass to supercooled liquid transition occurs. We show that the deformation units of metallic glasses are evolved from the intrinsic heterogeneous defects in metallic glasses under stress and the evolution is a manifestation of the stress-induced localized glass transition. Our study might provide a new insight into the atomic-scale mechanisms of plastic deformation of metallic glasses.

Subsurface shear instability and nanostructuring of metals in sliding

Dry sliding wear conditions were used to obtain a 500 μm-thick layer of nanosize grains on copper samples. As shown, this layer reveals a flow behavior pattern similar to that of a viscous non-Newtonian fluid. Four structurally different zones were found in the longitudinal cross-sections of samples below the worn surface. Upper two of them are nanocrystalline and consist of many ∼1 μm-thick sublayers, which show either laminar or turbulent flow behavior. These sublayers demonstrate different levels of elasticity as compared to each other and may be related to an interplay between work-hardening and thermal softening. Lower two zones undergo usual plastic deformation and severe fragmentation without viscous mass transfer. High level of Young's modulus in the fragmentation zone is evidence of insufficient thermal softening at that depth. We believe that viscous flow zones are the result of shear instability and subsequent shear deformation developed in subsurface layers due to thermal softening. Numerical study has been carried out to simulate friction-induced deformation and shear instability under conditions close to the experiment. As shown, such a situation is possible when deformation-generated heat is taken into account. Another interesting result relates to the sublayers’ strain rate distribution. It was found that 1 μm-thick sublayers may show either high strain rate gradient or zero strain rate as a function of depth below the worn surface. The latter case means that a pack of layers may exist and behave like an elastic body in ductile medium.

A Case Study in Using Compositional Grading to Improve Reservoir Characterization

Abstract This paper presents a case study of how compositional grading was used as a tool to greatly affect the subsurface interpretation of a deepwater field. Originally, the main reservoir at the field was viewed as being compartmentalized. There were also two viscous low API gravity oil reservoirs that were of little economic interest. A new interpretation based on compositional grading suggests that the main reservoir is, in fact, much better connected. There is also a risk of a viscous asphaltene-enriched zone at the oil-water contact that was not previously considered. Fortunately, if it exists, it would likely only delay aquifer drive. The two low API gravity oil reservoirs of little economic interest likely have much better quality oil updip making them good appraisal candidates. The different interpretation improves the overall view of the field and has implications for optimal development well locations, initial production rates and facility gas capacity. Compositional grading is particularly useful in aiding subsurface characterization in areas where grading is strong, and in deepwater offshore developments where uncertainty is great and development and appraisal costs are high. Fundamental geology and geochemistry are critical to being able to recognize a priori areas where compositional grading is strong. Introduction Compositional grading of hydrocarbons within a reservoir refers to the gradual and continuous change in fluid chemistry and physical properties such as density, gas-oil ratio and viscosity within the reservoir as a function of spatial location; in particular changes in elevation. Experience has shown that compositional grading is a common phenomenon(1–3). This paper demonstrates how compositional grading was used at a deepwater field as a valuable tool to aid in subsurface characterization. Such a tool is particularly useful in deepwater where development costs can be on the order of a billion dollars, uncertainty is great and appraisal costs are high. Yet, despite its common occurrence and potential use in subsurface characterization, compositional grading is poorly recognized in general and little used in practice to aid in characterization. For example, in the recent past, often only a single fluid sample would be taken in a reservoir. The fluid properties from this single sample would then be applied uniformly throughout a reservoir. Even when grading is recognized, there is often a belief among many practicing reservoir engineers that grading can be easily predicted using commercially available thermodynamic software. We discuss below how this can be misleading. Whilst grading occurs in both gas condensate and oil fields, in this paper we focus on grading in black oil columns; in particular in gas-oil ratio and in situ density. We first present background information on the theory of compositional grading and its practical manifestation including one of its by-products; namely asphaltene-enriched zones. We then discuss the case history. We feel that one of the keys to understanding compositional grading and using it in subsurface characterization is in the integration of a wide range of information, particularly from reservoir engineering, geochemistry and geology.

Glacial isostasy and plate motion

Abstract The influence of glacial-isostatic adjustment (GIA) on the motion of tectonic plates is usually neglected. Employing a recently developed numerical approach, we examine the effect of glacial loading on the motion of the Earth’s tectonic plates where we consider an elastic lithosphere of laterally variable strength and the plates losely connected by low viscous zones. The aim of this paper is to elucidate the physical processes which control the GIA-induced horizontal motion and to assess the impact of finite plate-boundary zones. We show that the present-day motion of tectonic plates induced by GIA is at, or above, the order of accuracy of the plate motions determined by very precise GPS observations. Therefore, its contribution should be considered when interpreting the mechanism controlling plate motion.

On the asymptotic layering of turbulent flows

The asymptotic structure of a turbulent boundary layer on a plate with a boundary-layer distributed suction, consisting of a suction zone, a viscous zone, a buffer zone, a velocity-defect zone, a Corrsin superlayer, and a irrotational-flow zone, has been determined. The analysis was carried out within the framework of the Reynolds equations with the use of the combined method of different scales and joined of asymptotic expansions. The Corrsin superlayer was interpreted as a discontinuity of turbulent stresses.

Hot macro-hardness of Zr52.5Al10Ni10Cu15Be12.5 bulk metallic glass

The hot hardness behavior of Zr52.5Al10Ni10Cu15Be12.5 bulk metallic glass is studied from ambient temperature to the temperature over Tx (the onset crystallization temperature) using a hot macro-hardness tester and scanning electron microscopy (SEM). The results show that the hot hardness behavior of Zr52.5Al10Ni10Cu15Be12.5 bulk metallic glass can be classified into 4 zones: the glassy zone in which the hardness almost linearly decreases with the increase of temperature, the viscoelastic zone in which the hardness is nearly unchanged, the viscous flow zone in which the hardness quickly tends towards near zero with temperature, and the crystallization zone in which the hardness sharply increases. The high temperature deformation behavior and the easy processable deformation region for bulk metallic glasses are also discussed on the basis of the hot marco-hardness.

Finite element analysis of crustal deformation in the Ou Backbone Range, northeastern Japan, with non-linear visco-elasticity and plasticity: effects of non-uniform thermal structure

AbstractA finite element analysis with non-linear visco-elasticity and plasticity was carried out with the aim of constructing a model of the slip and deformation processes in the deeper parts of the seismogenic zones of inland earthquakes. Our finite element code is based on the GeoFEM parallel finite element code and was developed using plug-ins to adopt several non-linear functions. We consider the effects of geothermal structures in the crust in a compressional tectonic setting to model the deformation and faulting that occur around the Ou Backbone Range in northeastern Japan. We set an area of high geothermal gradient in the center of the model. The numerical results show that shortening deformation due to non-linear viscous flow occurs in the high-temperature area in the lower part of the crust, which results in shear faulting in the upper part of the crust. In the case where the crust comprises two layers—the upper crust (quartz diorite) and the lower crust (wet diabase)—a weak viscous zone appears in the lower part of the upper crust and a strong viscous or plastic zone appears at the upper part of the lower crust. Our numerical results are able to explain the deformation and faulting that occur around the Ou Backbone Range in northeastern Japan.

Interfacial conditions between a pure fluid and a porous medium: implications for binary alloy solidification

The single-domain Darcy–Brinkman model is applied to some analytically tractable flows through adjacent porous and pure-fluid domains and is compared systematically with the multiple-domain Stokes–Darcy model. In particular, we focus on the interaction between flow and solidification within the mushy layer during binary alloy solidification in a corner flow and on the effects of the chosen mathematical description on the resulting macrosegregation patterns. Large-scale results provided by the multiple-domain formulation depend strongly on the microscopic interfacial conditions. No satisfactory agreement between the single- and multiple-domain approaches is obtained when using previously suggested conditions written directly at the interface between the liquid and the porous medium. Rather, we define a viscous transition zone inside the porous domain, where the Stokes equation still applies, and we impose continuity of pressure and velocities across it. This new condition provides good agreement between the two formulations of solidification problems when there is a continuous variation of porosity across the interface between a partially solidified region (mushy zone) and the melt.

Viscoelastic earthquake cycle models with deep stress‐driven creep along the San Andreas fault system

We develop a two‐dimensional boundary element earthquake cycle model including deep interseismic creep on vertical strike‐slip faults in an elastic lithosphere coupled to a viscoelastic asthenosphere. Uniform slip on the upper part of the fault is prescribed periodically to represent great strike‐slip earthquakes. Below the coseismic rupture the fault creeps in response to lithospheric shear stresses within a narrow linear viscous fault zone. The model is applied to the GPS contemporary velocity field across the Carrizo Plain and northern San Francisco Bay segments of the San Andreas fault, as well as triangulation measurements of postseismic strain following the 1906 San Francisco earthquake. Previous analysis of these data, using conventional viscoelastic coupling models without stress‐driven creep [Segall, 2002], shows that it is necessary to invoke different lithosphere‐asthenosphere rheology in northern and southern California in order to explain the data. We show that with deep stress‐driven interseismic creep on the San Andreas fault, the data can be explained with the same rheology for northern and southern California. We estimate elastic thickness in the range 44–100 km (95% confidence level), fault zone viscosity per unit width of 0.5–8.2 × 1017Pa s/m, and asthenosphere relaxation time of 24–622 years (0.1–2.9 × 1020Pa s) for northern and southern California. We estimate a slip rate of 21–27 mm/yr and recurrence time of 188–315 years for the northern San Francisco Bay San Andreas fault and slip rate of 32–42 mm/yr with recurrence time of 247–536 years for the Carrizo Plain.

The effects of gravity on the features of the interfacial waves in annular two-phase flow

A physical model of interfacial waves in annular two-phase flow was studied in both microgravity and normal gravity. The wave structure was obtained for local film thickness and velocity measurements using a conductance probe technique. It was found that the wave height, and not its width, is strongly affected by changing the gravity level. In fact, the wave height in normal gravity is more than twice that in microgravity. Using an analogous approach to a turbulent, single-phase flow in a rough tube, a preliminary mathematical model was proposed to calculate the wave amplitude. The model fits well with the experimental data and shows that the wave height in normal gravity is approximately 1.7 times the combined thickness of the viscous sublayer and transition zones in the turbulent gas stream. The wave height in microgravity was estimated to be approximately 80% of the total thickness.