Initial Transient Stage Research Articles

Finite element modelling and analysis of crack shape evolution in mode-I fatigue Middle Cracked Tension specimens

A numerical procedure was employed to study the shape evolution of fatigue cracks in Middle Cracked Tension specimens. This iterative procedure consists of a 3D finite element analysis to obtain the displacement field in the cracked body, calculation of stress intensity factors along crack front and definition of local crack advances considering the Paris law. Numerical predictions were compared with experimental crack shapes with a good agreement. The evolution of crack shape was analysed for different propagation conditions considering robust dependent parameters. Two main propagation stages were identified: an initial transient stage highly dependent on initial crack shape and a stable stage where the crack follows preferred paths. Mathematical models were proposed for transient and stable stages consisting of exponential and polynomial functions, respectively. The transition between both stages was defined considering two criteria: the rate of shape variation and the distance to stable shape. Finally, the crack shape change was linked with the distribution of stress intensity factor along crack front.

Steady-state diffusion regime in solid-phase microextraction kinetics

The temporal evolution of diffusion-controlled analyte accumulation in solid-phase microextraction (SPME) is critically discussed in terms of the various aspects of steady-state diffusion in the two phases under conditions of fast exchange of the analyte at the solid phase film/water interface. For partition coefficients ( K sw) much larger than unity and a sufficiently thin polymer film, the concentration gradient of the analyte in the polymer phase is largely insignificant. The growth of the accumulated amount of analyte is then adequately described by the well-known exponential expression for steady-state diffusion under non-depletive conditions, provided the initial transient stage is properly taken into account. In case of fiber-type solid phases, the cylindrical nature of the diffusion complicates the nature of the transient stage as well as the magnitude of the steady-state flux.

Single-crystal growth of NiMnGa magnetic shape memory alloys

The crystal growth of NiMnGa magnetic shape memory alloys was investigated by the optical zone melting method. Slightly macroscopic convex and planar solid–liquid interfaces were achieved by controlling the molten zone morphologies. Single crystals were successfully prepared in three typical series of NiMnGa magnetic shape memory alloys, including stoichiometric Ni 50Mn 25Ga 25, Ni-rich NiMnGa and Mn-rich NiMnGa alloys. Studies on the solute partition during crystal growth revealed the enrichment of Mn and deficiency of both Ni and Ga in front of the solid–liquid interface for both stoichiometric and Mn-rich NiMnGa alloys, while a slight enrichment of Ni for Ni-rich NiMnGa alloys. An initial transient stage was determined to be about 20 mm, and a uniform composition distribution existed along the axis of the crystals in the stable growth parts, which matches well with the proposed mathematic model.

Thermal Management of Biomaterials in a Rectangular Cavity Surrounded by a Phase Change Material

The shipping of live biological materials requires very close monitoring and perhaps active control of the temperature of the materials. This paper presents the results of a numerical study of 2-D transient natural convection inside a rectangular cavity. The cavity is intended to simulate a typical biological shipping container in which the biomaterials are encased in a chamber surrounded by a phase change material. The rectangular cavity is filled with air (Pr ap 0.69). Initially, the air is at uniform temperature and zero velocity. The top and side walls of the rectangular cavity are fixed at a low temperature and the bottom wall is coupled to the top wall of the heated solid block. For the lower solid block, the side and bottom wall are assumed adiabatic and filled with solid biomaterials. The biomaterial is subjected to a step heat input at time zero. A finite volume approach is used to solve the generic transport equations with the Boussinesq approximation. The flow inside the rectangular cavity is divided into three transient regimes: 1) initial transient stage; 2) quasi-steady stage; and 3) late quasi-steady stage. The results of the parametric study are included for shallow cavities, Ar = 0.5, Ar = 0.25, Ar = 0.125. The transient regimes and fluid flow structure were found to be functions of Rayleigh number, aspect ratio, Prandtl number, thermal capacity parameter (Q*), and nondimensional time (t*).

Kinetics of solute driven melting and solidification

Following previous investigations of [Rettenmayr M, Warkentin O, Rappaz M, Exner HE. Acta Mater 2001;49:2499–510] on solute driven melting in the Al–Mg-system, a recently developed thermodynamic model [Svoboda J, Gamsjäger E, Fischer FD, Fratzl P. Acta Mater 2004;52:959–67] has been applied to describe the kinetics of the melting process. By means of this sharp interface model, which is based on the principle of maximum Gibbs energy dissipation, additional insight into the underlying physics is provided. The characteristics of the melting and resolidification process can be described by considering both diffusion processes in the bulk and interfacial reactions. It is shown that, except for a short initial transient stage when the kinetics of melting is controlled by interfacial reactions, the process is diffusion and convection controlled.

Mechanisms of pressure filtration of liquid aluminum alloys

The Prefil Footprinter, a portable pressure filtration instrument, is usually used to detect the quality of liquid aluminum alloys. However, no investigations have ever been done to calculate the cake resistance to date. Based on the identification and classification of flow behavior using the first derivative method for filtrate mass vs filtration time curves, conventional filtration equations are successfully employed to understand the filtration behaviors. From the analyses of the variations of cake resistance with filtration time, the filtration mechanisms are discussed in detail over the different filtration stages. During the steady stage, either incompressible or compressible cake mode is the main mechanism. At the initial and terminal transient stages, however, deep-bed filtration, complete straining, and solidification clogging may appear. Solid inclusions in liquid metal have significant influence on the cake structures and properties. Some important issues related to the heterogeneity of filter media and test methodology are highlighted in this work.

Reaching the statistical steady state regime in two-fluid simulation of risers

Two-fluid simulation of gas–solid flows in risers is very time-consuming and highly bounded by computational resources. Actual simulations are mostly performed applying either coarse meshes in small scale columns, or finer meshes in partial very small domains. In any case, simulations go through an initial transient stage and finally reach a statistical steady state regime over which analyses are performed. Despite the early transient stage is not of higher interest, its transient computation accounts for a very significant share of the total computing time in a simulation. In this work it is proposed to replace such transient computation by a steady state run. It is shown that such procedure allows to quickly overcome the early transient stage of a simulation so that a transient run may start straightly inside the statistical steady state regime. For an ordinary particular case, it is shown that the procedure can save as much as 8 calendar months of computing.

A new indirect method of measuring the contents of solid inclusions in liquid aluminium alloys

The introduction of derivative methods and the classification of three flow states (i.e. initial transient, steady and terminal transient stages) provide new approaches to understand the filtration behaviors of liquid aluminum alloys during the Prefil Footprinter tests. The effective-ness of the filtration equations of incompressible cake mode can be well identified over some steady stages during the course of the filtration tests. Based on these new findings a new indirect method of measuring the contents of solid inclusions in liquid aluminum alloys is devel-oped using the Prefil Footprinter tests. However, the benchmarks of specific cake resistance should be made for commercial aluminum alloy melts before this method becomes feasible in laboratories and industries. It is found that for a given volume concentration of solid inclusions, lighter inclusions usually lead to higher specific cake resistance, and the heavier solid inclusions reduce the specific cake resistance. For higher quality liquid metal, usually with lower lumped parameter (σ α), the types of solid inclusions have less influence on specific cake resistance.

Numerical simulations of frictional melting: Small dependence of shear stress drop on viscosity parameters

Frictional melting during coseismic slipping strongly affects dynamic sliding. An idealized numerical simulation of shear stress drop due to lubrication of fault surfaces by frictional melting is performed to investigate dynamical adjustment of melt thickness and its dependence on material properties. We numerically solved one‐dimensional heat conduction equations coupled with hydrodynamic equations of motion of the melt layer. We adopt a simple Arrhenius‐type temperature dependence of melt viscosity with a parametric factor η0. After the initial transient stage, the evolution of the melt layer asymptotes to the late stage, where the melt thickness increases as and the generated shear stress drops as 1/. An analytic self‐similar solution of the temperature profile for the late stage is obtained. The balance between the viscous heat generation and conductive heat loss characterizes the late stage. For small η0, the melt thickness is proportional to η0, whereas it will saturate for a larger η0. This is because the strong temperature dependence of viscosity enables an automatic adjustment of viscosity, which drops through the temperature increase due to the viscous heating even if a large η0 is chosen. Numerical results and the thickness data of natural pseudotachylyte layers were compared. A maximum ratio X/ (X is thickness, D is sliding distance) exists above which no solution is found. The effective thermal conductivity of the melt layer should be large, probably due to the sliding surface roughness. Comparison with laboratory experimental results showed that the normal stress applied to the sample is an important parameter for stress drop.

The unsteady drag force on a cylinder immersed in a dilute granular flow

This paper presents results from hard-particle discrete element simulations of a two-dimensional dilute stream of particles accelerating past an immersed fixed cylinder. Simulation measurements of the drag force Fd are expressed in terms of a dimensionless drag coefficient, Cd=Fd∕[12ρνU2(D+d)], where ρ is the particle density, ν is the upstream solid fraction, U is the upstream instantaneous velocity, and D and d are the cylinder and particle diameters, respectively. Measurements indicate that the cylinder’s unsteady drag coefficient does not vary significantly from its steady (nonaccelerating) drag coefficient for both frictionless and frictional particles implying that the added mass for the flow is negligible. However, the drag coefficient is larger than its nominal value during an initial transient stage, during which a shock wave develops in front of the cylinder. Once the shock has developed, the drag coefficient remains constant despite the stream’s acceleration. The duration of the shock development transient stage is a function of the number of particle/cylinder collisions.

Ultraviolet cascade in the thermalization of the classicalϕ4theory in3+1dimensions

We investigate the dynamics of thermalization and the approach to equilibrium in the classical phi^4 theory in 3+1 spacetime dimensions. The non-equilibrium dynamics is studied by numerically solving the equations of motion in a light- cone-like discretization of the model for a broad range of initial conditions and energy densities.A smooth cascade of energy towards the ultraviolet is found to be the basic mechanism of thermalization.After an initial transient stage,at a time scale of several hundreds inverse masses,the squared of the field gradient becomes larger than the nonlinear term and a stage of universal cascade emerges. As the cascade progresses, the modes with higher wavenumbers exhibit weaker and weaker nonlinearities well described by the Hartree approximation while the infrared modes retain strong selfinteractions. Two timescales for equilibration appears.For k^2><phi^2>(t) we observe an effective thermalization with a time scale in the thousands of inverse masses and the Hartree approximation holds. By effective thermalization we mean that the observable acquires the equilibrium functional form with an effective time dependent temperature Teff, which slowly decreases with time. Infrared modes with k^2 < <phi^2>(t) equilibrate only by time scales in the millions of inverse masses. Infrared modes with k^2 < <phi^2>(t) equilibrate only by time scales in the millions.Virialization and the equation of state start to set much earlier than effective thermalization.The applicability of these results in quantum field theory for large occupation numbers and small coupling is analyzed.

Examination and verification of the filtration mechanism of cake mode during the pressure filtration tests of liquid Al–Si cast alloys

The filtration equations at constant pressure were used to examine and verify the filtration mechanism of cake mode during the Prefil Footprinter ® tests of liquid Al–Si cast alloys. Although cake mode is the dominant mechanism, the conventional equations have not well described the Prefil curves. The inverse mass flow rate deviates from the linearity with filtrate weight at the initial and terminal transient stages. The deviation at the initial transient stage is probably due to the lack of well-formed cakes. In the terminal transient stage the occurrences of partial and/or complete clogging may cause the deviation. If both the initial and terminal transient stages disappear, the linear relationship tends to hold true over the whole course. For some low filtrate weight melts, however, the deviations from the linearity occur at the steady stage probably due to the compressibility of the formed cake caused by oxide films and non-uniform cake thickness.

Aluminium anodising in low acidity sulphate baths: growth mechanism and nanostructure of porous anodic films

Overall kinetic and chronopotentiometric studies were performed during Al anodising in H2SO4, 0–5% w/v, bath solutions pure and saturated by Al2(SO4)3. Peculiarities in film growth mechanism and nanostructure in these cases appeared, like significant differences of porosity and its dependence on film thickness, different critical current density above which pitting appears, salt deposition on pitted surface regions in saturated bath, etc. The different conditions inside pores are responsible for this behaviour like almost depletion of H+ during a long initial transient stage in the first case, supersaturation and formation of Al2(SO4)3 nanoparticle micelles on pore surface in the second case, etc. Differences in film growth mechanism also appeared between these and alike baths at higher acidity. Anodising in low acidity saturated baths shows superiority for growing low porosity films at specific conditions. New technologies may be suggested to produce optimal films of desired structure.

HIV–1 dynamics at different time scales under antiretroviral therapy

We exploit a model that considers three compartments: blood plasma (BP), lymphoid tissue-interstitial spaces (LT-IS), and follicular dendritic cells (FDC), for the HIV-1 dynamics under the application of highly active antiretroviral therapy (HAART) which allowed us to unravel distinct viral dynamics occurring in short- (2 days), middle- (21 days), and long-term (183 days) time scales. The different time scales are determined by the viral clearance rate, the ratio of productively infected CD4 + T cells to chronically infected cells, and the dissociation rate of HIV-1 complexes from FDC. This generates a scenario in which, after an initial transient stage, the viral BP dynamics decouples and becomes governed by the lymphoid tissue (LT) dynamics; in a later stage, a new decoupling occurs in which the LT-IS dynamics is slaved to that of the FDC dynamics. We observed an initial increase in the viremia after HAART in a patient who did not receive protease inhibitors (PI). By means of the above-mentioned model we were able to highlight the relevant parameters which need to be estimated at three different time scales after HAART.

Determination of the Minority Carrier Surface Thermogeneration Rate in Metal-Oxide-Semiconductor Structures

A metal-oxide-semiconductor (MOS) structure with the common field electrode insulated from the semiconductor by oxide layers h of different thicknesses allows the surface generation rate of minority charge carriers from current I(t) of nonequilibrium depletion state relaxation to be found. At the same time, it is possible in similar structures to observe the kinematics of electron-hole pair generation at the periphery of the field electrode (the edge generation effect). Measurements performed on an n-Si MOS structure with a stepwise change in oxide layer thickness (h1 = 100 A and h2 = 3200 A) allowed the generation rate at both the initial transient (t ∼ 10−5 s) stage of surface generation (4.34 × 1010 cm−2 s−1) and at the basic extremely slow stage (10.4 cm−2 s−1) to be reliably determined for the first time. The estimated peripheral generation rate of minority charge carriers (holes) was 7.8 × 1011 cm−2 s−1.

Pressure filtration tests of liquid Al–Si cast alloys: I. Flow behaviour

The flow behaviour during the Prifil Footprinter ® tests of liquid Al–Si cast alloys has been investigated for the first time using the first and second derivative methods. The first derivative approach is recommended as the preferred method to determine the transitional points. At the initial transient stage flow rate decreases with filtration time. Higher quality liquid metal usually exhibits a shorter, or even no observable transient period. However, there remains some uncertainty of this conclusion, probably due to the variable waiting periods for the attainment of a designated temperature requirement prior to starting the filtration tests. During the steady state flow rate decreases linearly with filtration time and the second derivative values are around zero. At the initial and terminal transient states a periodic flow mode was also observed. The primary intermetallics possibly precipitated and sedimented prior to or during the tests may significantly influence the filtration behaviour.

Yttrium addition effect on isothermal and cyclic high temperature oxidation behaviour of 304 stainless steel

The aim of the present study is to investigate the beneficial influence of an yttrium sol–gel coating on a chromia forming alloy (304 stainless steel), in air, at 1000°C. Thermal cyclic experiments were carried out in order to study the influence of the addition of yttriumon the scale adherence. The yttrium sol–gel coating plays a significant role in enhancing oxidation resistance during isothermal oxidation tests, decreasing specimen weight gain and suppressing the initial transient oxidation stage. Yttrium addition appears to promote silicon segregationat the metal/oxide interface. It is then observed that iron containing oxides are not formed. Under thermal cycling conditions, the addition of yttrium also remarkably improves oxide scale adherence.

In situX-ray diffraction contribution to the study of reactive element oxide coating effect on the high temperature oxidation behaviour of FeCrAl alloys

The influence of yttrium oxide coating (processed by sol-gel method) on the oxidation behaviour of a commercial FeCrAl alloy (Kanthal Al) has been investigated during isothermal exposures in air at 1373K. The scale growth kinetic of the uncoated alloy obeys a parabolic rate law during the whole oxidation test whereas the kinetic curve of the Y-coated specimen exhibits an initial transient stage during the first hours, followed by a parabolic regime. The yttrium sol-gel coating deposited on the bare alloy does not conduct to the beneficial effect usually ascribed to the reactive elements. No oxidation rate improvement of the coated alloy is observed, the parabolic rate constants values are strictly identical for the both specimens. In situ X-ray diffraction reveals a marked influence of the reactive element on the composition of the oxide scale. The oxide layer formed on the yttrium-coated specimen revealed, in addition to α-alumina which is the main oxide also identified on the bare specimen, the presence of yttrium aluminates (YAlO 3 , Y 3 Al 5 O 12 ) located in the outermost part of the layer.

STOCHASTIC PHASE-FIELD SIMULATIONS OF SYMMETRIC ALLOY SOLIDIFICATION

We study initial transient stages in directional solidification by means of a non-variational phase field model with fluctuations. This model applies for the symmetric solidification of dilute binary solutions and does not invoke fluctuation-dissipation theorem to account for the fluctuation statistics. We devote our attention to the transient regime during which concentration gradients are building up and fluctuations act to destabilize the interface. To this end, we calculate both the temporally dependent growth rate of each mode and the power spectrum of the interface evolving under the effect of fluctuations. Quantitative agreement is found when comparing the phase-field simulations with theoretical predictions.

Effect of reactive element oxide coating on the high temperature oxidation behaviour of FeCrAl alloys

The influence of yttrium oxide coating (processed by the sol–gel method) on the oxidation behaviour of a commercial FeCrAl alloy (Kanthal A1) has been investigated during isothermal exposures in air at 1373K. The scale growth kinetics of the uncoated alloy obey a parabolic rate law during the whole oxidation test, whereas the kinetic curves of the Y-coated specimen exhibit an initial transient stage for the first few hours, followed by a parabolic regime. The yttrium sol–gel coating deposited on the bare alloy does not provide the beneficial effect usually ascribed to reactive elements. No oxidation rate improvement of the coated alloy is observed, the parabolic rate constant values are strictly identical for both specimens. In situ X-ray diffraction reveals a marked influence of the reactive element on the composition of the oxide scale. The oxide layer formed on the yttrium-coated specimen comprised, in addition to α-alumina which is the main oxide also identified on the bare specimen, the presence of yttrium aluminates (YAlO3, Y3Al5O12) located in the outermost part of the layer.