Analytical models for the internal oxidation of a binary alloy that forms oxide precipitates of high stability

2013 ◽  
Vol 73 ◽  
pp. 89-98 ◽  
Author(s):  
Amitesh Madeshia
Keyword(s):  
Internal Oxidation ◽  
Binary Alloy ◽  
High Stability ◽  
Analytical Models

Predicting Internal Oxidation: Building on the Wagner Model

2011 ◽  
Vol 696 ◽  
pp. 1-11 ◽  
Author(s):  
David J. Young
Keyword(s):  
Internal Oxidation ◽  
Binary Alloy ◽  
Reactive Component ◽  
Internal Interface ◽  
Parabolic Kinetics ◽  
Internal Precipitation ◽  
Diffusion Effects ◽  
Multiple Oxidants ◽  
Low Solubility ◽  
Dilute Alloy

Wagner’s 1959 diffusion model of the internal oxidation process provided a method of predicting the rate at which a binary alloy was penetrated by dissolved oxygen as it precipitated the more reactive (but dilute) alloy component. Parabolic kinetics were predicted to depend on oxygen permeability in the unreacted alloy solvent and also, in cases where the reactive component was sufficiently mobile, the diffusion coefficient of the latter. The model has proven very successful, but is restricted to single oxidant-binary alloy systems, in which the precipitated oxide has extremely low solubility. This paper reviews recent results on a number of internal precipitation processes which cannot be described with the Wagner theory. These include formation of low stability carbides and nitrades; internal precipitation driven by multiple oxidants; the templating effects of prior precipitates on subsequently formed corrosion products; cellular precipitation morphologies; internal interface diffusion effects; volume changes in the reaction zone and the effects upon them of simultaneous external scaling.

Numerical Model to Describe the Growth of the Internal Oxidation Layer in Binary Alloys

2006 ◽  
Vol 258-260 ◽  
pp. 282-287
Author(s):  
Gabriel Plascencia ◽  
Torstein A. Utigard ◽  
Juliana Gutiérrez ◽  
David Jaramillo ◽  
Fernando Martínez
Keyword(s):  
Internal Oxidation ◽  
Oxidation Process ◽  
Binary Alloys ◽  
Numerical Approach ◽  
Analytical Models ◽  
Oxidation Layer ◽  
Different Temperatures ◽  
Set Up ◽  
High Degree ◽  
Good Agreement

Several analytical models have been developed through the years to describe the formation and growth of the internal oxidation layer in binary alloys. Such models are often complex and their validity strongly rely on precise measurements of molar fluxes of the different species involved in the oxidation process. The main disadvantage of such measurements is that they are difficult to made and present a high degree of uncertainties, thus some assumptions are needed to ease understanding and the applicability of them. In this paper we set up a numerical scheme (finite differences) to describe the growth of the internal oxidation layer in binary Cu-Al alloys oxidized in air at different temperatures. There is good agreement between the experimental results and the values calculated with the aid of our numerical approach.

Approximate Analytical Models for Microsegregation Considering the Effect of Dendrite Arm Coarsening

2006 ◽  
Vol 508 ◽  
pp. 449-454 ◽  
Author(s):  
Altan Turkeli
Keyword(s):  
Binary Alloy ◽  
Analytical Models ◽  
Back Diffusion ◽  
Parabolic Growth ◽  
Exact Model ◽  
Simple Models

In this study, simple analytical microsegregation models for constant cooling and parabolic growth are proposed considering dendrite arm coarsening effect with and without back diffusion. These simple models are compared with the Mortensen exact model and Voller’s models. It is shown that these analytical models can be used to predict approximately microsegregation in a binary alloy.

Mechanism of irregular crack-propagation in thermal controlled fracture of ceramics induced by microwave

2020 ◽  
Vol 21 (6) ◽  
pp. 610
Author(s):  
Xiaoliang Cheng ◽  
Chunyang Zhao ◽  
Hailong Wang ◽  
Yang Wang ◽  
Zhenlong Wang
Keyword(s):  
Crack Propagation ◽  
Industrial Application ◽  
Ceramic Materials ◽  
Advanced Technology ◽  
Analytical Models ◽  
Propagation Mechanism ◽  
Unstable Crack ◽  
Fracture Simulation ◽  
Initial Stage ◽  
Controlled Fracture

Microwave cutting glass and ceramics based on thermal controlled fracture method has gained much attention recently for its advantages in lower energy-consumption and higher efficiency than conventional processing method. However, the irregular crack-propagation is problematic in this procedure, which hinders the industrial application of this advanced technology. In this study, the irregular crack-propagation is summarized as the unstable propagation in the initial stage, the deviated propagation in the middle stage, and the non-penetrating propagation in the end segment based on experimental work. Method for predicting the unstable propagation in the initial stage has been developed by combining analytical models with thermal-fracture simulation. Experimental results show good agreement with the prediction results, and the relative deviation between them can be <5% in cutting of some ceramics. The mechanism of deviated propagation and the non-penetrating propagation have been revealed by simulation and theoretical analysis. Since this study provides effective methods to predict unstable crack-propagation in the initial stage and understand the irregular propagation mechanism in the whole crack-propagation stage in microwave cutting ceramics, it is of great significance to the industrial application of thermal controlled fracture method for cutting ceramic materials using microwave.

Classifying the Past: Discriminant Analysis and its Application to Medieval Farming Systems

1996 ◽  
Vol 8 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Ken Bartley
Keyword(s):  
Cluster Analysis ◽  
Discriminant Analysis ◽  
Processing Time ◽  
Farming Systems ◽  
Frame Of Reference ◽  
Analytical Models ◽  
Successful Implementation ◽  
Medieval Period ◽  
The Past ◽  
Livestock Management

This paper discusses the need for nationally based analytical models of the medieval period. The use of cluster analysis as a method for classifying demesne farms, by the crops they grew and their livestock management, is explained. Successful implementation of cluster analysis requires both the existence of a large base sample, to permit isolation of specific groupings within the data, and access to considerable processing time. The paper concludes by demonstrating how discriminant analysis can provide an efficient and systematic way of classifying even a single manor within a national frame of reference.

Validation of a Belt Model for Prediction of Hub Forces from a Rolling Tire4

2009 ◽  
Vol 37 (2) ◽  
pp. 62-102 ◽  
Author(s):  
C. Lecomte ◽  
W. R. Graham ◽  
D. J. O’Boy
Keyword(s):  
Internal Pressure ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Prediction Method ◽  
Analytical Models ◽  
Beam Model ◽  
Impedance Boundary ◽  
Bending Waves ◽  
Tire Rotation ◽  
Three Dimensional Models

Abstract An integrated model is under development which will be able to predict the interior noise due to the vibrations of a rolling tire structurally transmitted to the hub of a vehicle. Here, the tire belt model used as part of this prediction method is first briefly presented and discussed, and it is then compared to other models available in the literature. This component will be linked to the tread blocks through normal and tangential forces and to the sidewalls through impedance boundary conditions. The tire belt is modeled as an orthotropic cylindrical ring of negligible thickness with rotational effects, internal pressure, and prestresses included. The associated equations of motion are derived by a variational approach and are investigated for both unforced and forced motions. The model supports extensional and bending waves, which are believed to be the important features to correctly predict the hub forces in the midfrequency (50–500 Hz) range of interest. The predicted waves and forced responses of a benchmark structure are compared to the predictions of several alternative analytical models: two three dimensional models that can support multiple isotropic layers, one of these models include curvature and the other one is flat; a one-dimensional beam model which does not consider axial variations; and several shell models. Finally, the effects of internal pressure, prestress, curvature, and tire rotation on free waves are discussed.

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