Austenite grain growth prediction coupling with drag and pinning effects in low carbon Nb microalloyed steels

Abstract

A metallurgical model has been developed to predict the austenite grain growth in Nb microalloyed steels. The mutual effects of Nb(CN) particle pinning and Nb solute drag on grain growth kinetics are studied. The particle dissolution, the undissolved particle coarsening and the changes in Nb solute in solution during reheating or isothermal heat treatment process are taken into account in the model. It is shown that, besides the pinning exerted by the NbC precipitates, the solute drag of Nb in solid solution plays an important role in the inhibition of austenite grain growth in Nb microalloyed steels. The Nb solute drag effect on grain growth decreases with increasing temperature because the grain boundary can gradually break away from the solute atmosphere in the higher velocity region at high temperature. The mean austenite grain size sluggishly increases with temperature in the low temperature region, while it significantly increases in the relative high temperature region. The predicted austenite grain size concerning the combined effect of Nb drag and Nb(CN) pinning is in good agreement with the experimental results from the literature.     

Lüders elongation in AI-Mg alloy AA5182

Abstract

Aluminium-magnesium alloys such as AA5182 exhibit a yield point elongation, or Lüders strain, when deformed in the annealed O temper, and the extent of the Lüders strain is a function of processing history and the deformation conditions. The yield point effect is usually attributed to Mg solute pinning, but is has been appreciated for some time that factors such as grain size, and cooling rate from the annealing temperature, affect the Lüders strain, and it has not been clear how this behaviour is consistent with solute pinning. In this paper it is shown that the presence, or absence of Lüders effect (Lüdering) is related to the grain boundary structure, and processing which results in a high concentration of grain boundary dislocations removes the yield point effect, whereas fabrication routes which produce defect free bondaries result in a Lüders strain. The extent of the Lüders strain, and its dependence on grain size and deformation conditions, is reasonably consistent with some recent models of propagative plastic instabilities.     

A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method

The Element free Galerkin method, which is based on the Moving Least Squares approximation, requires only nodal data and no element connectivity, and therefore is more flexible than the conventional finite element method. Direct imposition of essential boundary conditions for the element free Galerkin (EFG) method is always difficult because the shape functions from the Moving Least Squares approximation do not have the delta function property. In the prior literature, a direct collocation of the fictitious nodal values & u circ; used as undetermined coefficients in the MLS approximation, u ^h (x) [u ^h (x)=Φ·& u circ;], was used to enforce the essential boundary conditions. A modified collocation method using the actual nodal values of the trial function u ^h (x) is presented here, to enforce the essential boundary conditions. This modified collocation method is more consistent with the variational basis of the EFG method. Alternatively, a penalty formulation for easily imposing the essential boundary conditions in the EFG method with the MLS approximation is also presented. The present penalty formulation yields a symmetric positive definite system stiffness matrix. Numerical examples show that the present penalty method does not exhibit any volumetric locking and retains high rates of convergence for both displacements and strain energy. The penalty method is easy to implement as compared to the Lagrange multiplier method, which increases the number of degrees of freedom and yields a non-positive definite system matrix.     

Austenite grain growth simulation considering the solute-drag effect and pinning effect

Abstract

The pinning effect is useful for restraining austenite grain growth in low alloy steel and improving heat affected zone toughness in welded joints. We propose a new calculation model for predicting austenite grain growth behavior. The model is mainly comprised of two theories: the solute-drag effect and the pinning effect of TiN precipitates. The calculation of the solute-drag effect is based on the hypothesis that the width of each austenite grain boundary is constant and that the element content maintains equilibrium segregation at the austenite grain boundaries. We used Hillert’s law under the assumption that the austenite grain boundary phase is a liquid so that we could estimate the equilibrium solute concentration at the austenite grain boundaries. The equilibrium solute concentration was calculated using the Thermo-Calc software. Pinning effect was estimated by Nishizawa’s equation. The calculated austenite grain growth at 1473–1673 K showed excellent correspondence with the experimental results.     

Modeling of non-equilibrium solute diffusion upon rapid solidification: effective mobility versus kinetic energy

Abstract

The effective mobility approach is compared with the kinetic energy approach in terms of sharp interface modeling and phase-field modelling of non-equilibrium solute diffusion upon rapid solidification of binary alloys. The two approaches are equivalent for modelling of long range solute diffusion in bulk phases, but only the effective mobility approach can introduce the non-equilibrium solute diffusion effect to short range solute diffusion at a sharp interface or within a diffuse interface. Addition of the kinetic energy terms results in an unreasonable non-bilinear expression of the flux and thermodynamic driving force in the free energy production of interface migration or phase field propagation, whereas the effective mobility approach allows the thermodynamic extremal principle workable.     

Kinetic equations for non-equilibrium grain boundary segregation induced by applied tensile stress

Abstract

Based on an earlier model, a set of kinetic equations is derived to formulate the process of non-equilibrium grain boundary segregation induced by a low tensile stress. These kinetic equations allow excellent simulation of the grain boundary segregation of phosphorus and sulphur observed in steels subjected to low tensile stresses. The simulation results justify both the earlier model and the present kinetic equations. They also show that an applied tensile stress can increase the diffusion rate of solute-vacancy complexes and decrease that of isolated solute atoms significantly, and can also bring forward the critical time of non-equilibrium segregation for phosphorus and delay that for sulphur.     

Simulation of constrained dendrite growth of multicomponent alloys using a Calphad method

Abstract

The conventional theory of constrained dendrite growth for binary alloys has been extended to multicomponent alloys based on the Calphad method by consideration of solute interactions in each phase. The variable solute partition coefficients and liquidus slopes under different tip undercooling were calculated in detail for a series of Al-Si-Mg alloys. Their influence on the kinetics of dendrite growth was demonstrated quantitatively. The most important microstructure scale, the primary dendrite spacing, was predicted in several Al-Si-Mg alloys. By comparing with the experimental results of former researchers, it is found that the present method coupled with Calphad is a satisfactory way for the prediction of primary dendrite arm spacing.     

Welding of rapidly solidified Alloy 8009 (Al–8·5Fe–1·7Si–1·3V): preliminary study

Abstract

Alloy 8009 is a rapidly solidified, dispersion strengthened Al–8·5Fe (wt-%) alloy designed for high temperature (up to 400°C) aerospace applications. Both fusion and solid state joining techniques were shown to produce bonds. Fusion techniques destroyed the base metal microstructure with primary Fe₃Al, loss of solute, formation of larger aluminium grains, and the formation of grain boundary FeAl₃ and intermetallics enriched with silicon and vanadium. Solid state friction stir welding did not cause a significant modification to the dispersoid population but there was a loss of solute to dispersoid/matrix interfaces.

MST/3500     

Free‐surface effects on an oblique towing flat plate

Abstract

This paper applies a finite difference method in calculating the free surface profiles, the lateral hydrodynamic forces as well as the moments acting on a plate during the oblique towing of a flat plate on the free surface. The 3‐D fluid motion in the infinite region is approximated by the unsteady 2‐D flow in the finite region with an artificial open boundary on which a more relaxed Sommerfeld's radiation condition is imposed. The free surface profiles, nondimensional side forces and yawing moments are calculated by the present method and are compared satisfactorily with the experimental results [15], Chapman's results [4], and Yamasaki's computational results [16].     

Post-yield deformation characteristics in Al–Li alloys

Abstract

The post-yield deformation characteristics of Al–Li–Cu–Mg–Zr alloys in the solution treated and naturally aged conditions have been investigated. Two essential features were observed: the existence of a region with no work hardening and pronounced serrations superimposed on the flow curve. The no work hardening regime is associated with the activation of a single slip system in unrecrystallised and textured material; activation of further slip systems and consequent hardening is assisted by natural aging. Serrated post-yield flow is attributed to the production of free dislocations from those pinned by lithium atom atmospheres; this form of serrated yielding is suppressed as the concentration of lithium solute falls during natural aging.

MST/816     

Role of vacancies in coprecipitation of δ′ – and S–phasesin Al–Li–Cu–Mg alloys

Abstract

Precipitation reactions in a series of Al–Li–Cu–Mg alloys, encompassing the composition ranges of the commercial Lital A and Lital B materials, have been studied to determine the role of solute and vacancy concentrations on homogeneous S-phase (Al₂CuMg) precipitation. Homogeneous precipitation of S-phase only occurs when a critical combination of free vacancy and copper and magnesium supersaturation is achieved. Lithium reduces the free-vacancy concentration by strong binding between vacancies and lithium atoms or atom clusters. Precipitation of δ′ (Al₃ Li) releases the bound vacancies and thereby promotes S-phase formation and, in extreme cases, vacancy condensation, producing dislocation loops.

MST/350     

Forced convection flow channel defects in castings

Abstract

Slow filling of castings may lead to remelting of the partially solidified casting thereby forming channels through the structure. The channels are analogous to the channel defects formed by the segregation of solute in the pasty zone leading to the A and V segregates in ingots and large castings. Flow convection channels, however, are characterised externally by a rougher surface finish on the casting and internally by almost zero segregation. The internal structure comprises an edge region of crushed dendrites (leading to the only significant segregation); an intermediate region of refined equiaxed grain structure, coarse dendrite arm spacing, and coarse porosity; and a central region of large grains and large dendrite arm spacing. Some gas pores tend to float to the top of the channel, where they decorate its upper boundary. It is concluded that the channels are not severe defects per se, but are undesirable in castings where good control over quality is required. In particular, because of the delayed solidification, they allow the growth and alignment of porosity in sections which would otherwise freeze rapidly and be sound, or at worst, have fine distributed porosity.

MST/1655     

Partitioning of titanium during solidification of aluminium alloys

Abstract

The purpose of the present work is to compare the segregation behaviour of Ti solute in low solute alloys, such as nominally pure Al, and high solute alloys typical of Al–Si casting alloys. Microprobe measurements of Ti segregation within grains show that, under the solidification conditions employed, the measured partition coefficient of Ti in pure Al is 6.7 compared with the phase diagram prediction of ～7.5. Similar measurements in an Al–7Si–0.3Mg alloy resulted in a partition coefficient of 3.2. Based on the measured partition coefficients, this translates into a reduction in the growth restriction factor (a measure of the segregating power of solute elements) from 8.75 K in pure Al to 3.36 K in Al–7Si–0.3Mg with an addition of 0.05 wt-%Ti. This may explain why Ti in solution is a less effective grain refiner in casting alloys than in low solute content wrought alloys. In addition, the measured Ti segregation profiles were compared with predicted profiles based on the Scheil or similar solidification relationships. It was found that the predictions of the Scheil equation produced a good fit with the measured Ti segregation profiles once it was adapted for the geometrical nature of dendritic solidification.     

Role of dislocation density and structure in grain boundary segregation of phosphorus and carbon in model Fe-P-C alloy

Abstract

The present study has investigated the effects of dislocation density, produced by tensile prestraining, on the grain boundary segregation of phosphorus and carbon in a Fe-0.06P-0.002C (wt-%) alloy during stress free isothermal annealing at 500°C for periods up to 1800 h. Changes in grain boundary segregation were followed using Auger spectroscopy, while changes in dislocation density and structure were observed using transmission electron microscopy techniques. The segregation of phosphorus (but not carbon) was enhanced, compared with unstrained specimens, during initial aging. Analysis of diffusion rates required to cause the observed increase in phosphorus segregation suggested that the kinetics of phosphorus segregation was enhanced by pipe diffusion. At intermediate aging times, desegregation of phosphorus was observed, an effect attributed to a reduction in intragranular solute levels resulting from phosphorus precipitation on dislocations. In the case of carbon this process continued to the longest aging times examined and, essentially, complete desegregation ensued. In contrast, at these long aging times, phosphorus segregation resumed, and this was associated with an increase in the binding energy of phosphorus to the carbon denuded grain boundary.     

Kinetic analysis of daily hemofiltration

Background: Daily hemofiltration (D‐HF) is a new treatment modality that shows unique solute removal characteristics and possibly provides a high quality of life for patients with end‐stage renal disease. We evaluated solute removal characteristics of D‐HF for five patients by kinetic modeling analysis. Methods: Five patients treated with normal 3 × 4 hr/week hemodialysis (HD) were switched to D‐HF (6 × 2 hr/week). Ultrafiltration rates (Q_F) or small‐solute clearances ranged from 63 to 106 mL/min. All the necessary kinetic parameters were determined from patients' physical data and HD portion of the clinical measurements. The two‐compartment kinetic model predicted the concentration changes after switching from normal HD to D‐HF. Results: Concentrations of small solutes such as urea nitrogen (UN) increased, whereas that of β₂‐microglobulin (β₂‐MG) decreased after switching from normal HD to D‐HF in all five patients. Predicted solute concentrations and clinical measurements for UN and β₂‐MG were in good agreement with mean error less than 10%. The model predicted that Q_F = 155 mL/min may be necessary for time‐averaged concentration (TAC) of UN to be unchanged. The model also predicted that the 7 times/week D‐HF should not increase the pretreatment concentration of UN, expecting even much lower β₂‐MG concentration after switching from normal HD to D‐HF. Conclusion: D‐HF is superior to normal HD for removing larger solutes but may increase the TAC of small solutes. Seven‐day (7 times/week) D‐HF may improve the solute removal capacity of small solutes.     

Twin growth and its interaction with precipitates

New models for twin growth and its interaction with precipitate in Inconel-718 are proposed in this paper. The measured accumulated XRD intensities to represent the quantity of the Ni₃Nb(δ) phase are in agreement with its dissolution in twin/grain interior and precipitation again in twin/grain boundary. Present result shows that twin growth is associated with and similar to a “wave front” movement of twin boundary mainly resulting from the assistance of sufficient vacancies and solute atoms from dissolved Ni₃Nb(δ) phase diffusing from the twin interior toward the twin boundary to build up the existed twin. This leads to the overall free energy reduction and results in twin growth. Furthermore, possible interaction of twin growth meeting NbC particle is also discussed.     

Oxidation behaviour and kinetics of α-SiAlON ceramics

Abstract

In this study, the oxidation behaviours of Y, Sm and Y/Sm doped α-SiAlON ceramics are investigated to examine the oxidation kinetics. The oxidation tests are carried out at 1300–1450°C for different holding times (6–72 hours). Measurements of weight gain and observations of oxidized surfaces were made. The results show that up to 1400°C, oxidation resistance of Sm-doped samples is better than dual cations (Y/Sm) doped compositions even though the former has the higher amount of grain boundary phase. Results are discussed based on grain boundary phase, oxidation morphology and thickness.     

Internal oxidation: does the classical model contradict local equilibrium conditions?

Abstract

Previously, Morral and Li have published an anomalous behaviour of the classical model of internal oxidation with respect to their local-equilibrium conditions/rules. The local-equilibrium conditions were interpreted from the local-equilibrium expression derived from the flux balance at the inter-region boundary – the boundary between a two-phase region and a single-phase region – under the local-equilibrium assumption. These local-equilibrium conditions predict a continuous average composition profile for the system where the two-phase region is growing at the expense of the single-phase region. In contrast, the classical model of internal oxidation shows a composition jump at the boundary of the growing two-phase region and the shrinking single-phase region.

Here, a complete interpretation of the local-equilibrium expression is delineated including the case of zero solubility-product. The relative behaviour of two of the composition-vectors in the local-equilibrium expression undergoes an abrupt change at zero solubility-product. This change in behaviour predicts a composition jump at the inter-region boundary for the growing two-phase region. Consequently, the classical model of internal oxidation is shown to follow the local equilibrium on all counts and thereby eliminating all contradictions.     

Effect of Colloidal Carriers on the Disposition and Tissue Uptake of Doxorubicin: I. Conjugation with Oxidized Dextran Particles

Abstract

Dextrans are water soluble polymers of glucose, with varying molecular weights. The free hydroxyl groups offer attractive sites for conjugation of drugs with the potential for altering the pharmacokinetic profile of the drug. Doxorubicin is a useful anticancer drug with cardiotoxicity as its most serious side effect. This drug was conjugated to dextran in the following manner. A Schiffs base was formed by incubating oxidized dextran (generated using sodium periodate) with doxorubicin. This mixture was then reduced using sodium borohydride. The conjugates, in the size range of 20 nm, were studied in vitro for the maximum uptake and the release of the drug. In vivo, the conjugates showed a markedly altered disposition profile from the control group. The total body clearance of the drug associated with the conjugate decreased. Additionally, lower concentrations of the drug were found in the heart of animals treated with the conjugates indicating the possibility of reduced cardiotoxicity.     

Predicting recrystallised volume fraction in aluminium alloy 7050 hot rolled plate

Abstract

An investigation into the partial recrystallisation that occurs during solution treatment of hot rolled thick aluminum alloy 7050 plate has been performed for three alloy variants with different zirconium concentrations. Electron backscattered diffraction has been used to study the grain and subgrain structure in the as rolled condition and after solution treatment. Localised recrystallisation in the grain boundary regions during solution treatment has been largely attributed to the stimulating effect of large intermetallic particles on the boundaries, combined with the low number density of pinning dispersoids close to the grain edges. A model that predicts the dispersoid distribution across a grain has been applied to predict the fraction of recrystallisation after solution treatment. It has been demonstrated that the recrystallised fractions predicted by the model show good agreement with those measured experimentally. Example calculations are presented showing the predicted effect of the zirconium level, homogenisation conditions, and subgrain size on the recrystallised fraction.