Finite Element Analysis ::
Numerical Analyses for Treating Diffusion in Single-, Two-, and Three Phase Binary Alloy Systems
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This package consists of a series of three computer programs for treating
one-dimensional transient diffusion problems in single and multiple
phase binary alloy systems. An accurate understanding of the diffusion
process is important in the development and production of binary alloys.
Previous solutions of the diffusion equations were highly restricted in
their scope and application. The finite-difference solutions developed
for this package are applicable for planar, cylindrical, and spherical geometries
with any diffusion-zone size and any continuous variation of the
diffusion coefficient with concentration. Special techniques were included
to account for differences in modal volumes, initiation and growth
of an intermediate phase, disappearance of a phase, and the presence of an
initial composition profile in the specimen. In each analysis, an effort
was made to achieve good accuracy while minimizing computation time.
The solutions to the diffusion equations for single-, two-, and threephase
binary alloy systems are numerically calculated by the three programs
NAD1, NAD2, and NAD3.
NAD1 treats the diffusion between pure metals which
belong to a single-phase system. Diffusion in this system is described by a
one-dimensional Fick's second law and will result in a continuous composition
variation. For computational purposes, Fick's second law is expressed
as an explicit second-order finite difference equation. Finite difference
calculations are made by choosing the grid spacing small enough to give convergent
solutions of acceptable accuracy.
NAD2 treats diffusion between
pure metals which form a two-phase system. Diffusion in the twophase system
is described by two partial differential equations (a Fick's second law
for each phase) and an interface-flux-balance equation which describes the
location of the interface. Actual interface motion is obtained by a mass
conservation procedure. To account for changes in the thicknesses of the
two phases as diffusion progresses, a variable grid technique developed by
Murray and Landis is employed. These equations are expressed in finite difference
form and solved numerically.
Program NAD3 treats diffusion between
pure metals which form a two-phase system with an intermediate third phase.
Diffusion in the three-phase system is described by three partial differential
expressions of Fick's second law and two interface-flux-balance
equations. As with the two-phase case, a variable grid finite difference
is used to numerically solve the diffusion equations. Computation time is
minimized without sacrificing solution accuracy by treating the threephase
problem as a two-phase problem when the thickness of the intermediate
phase is less than a preset value. Comparisons between these programs and
other solutions have shown excellent agreement.
NAD Programs carries the NASA case number LAR-12381. They were originally released as part of the NASA COSMIC collection.
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