Modeling the Survival of HardAlpha Inclusions in Titanium
Ernesto Gutierrez-Miravete, Rensselaer at Hartford
Tony Giamei, Belcan
Indresh Padmonkar, Rensselaer Hartford
Srikanth Bandlamudi, Rensselaer Hartford
Mas Hongoh, Pratt & Whitney
Brice Cassenti, UTRC and Pratt&Whitney
Outline
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•
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Introduction
Model Description
Description of Code
Preliminary Results
Summary
Introduction
• Undetected N- and/or O-containing particles in
Ti alloys (hard-alpha) can result in catastrophic
failure of aircraft engine components.
• The process metallurgy of Ti alloys provides
many potential sources of N and/or O.
• Better understanding of the dissolution
behavior of N- and/or O containing Ti
inclusions in Ti alloys during thermal
processing is required.
Model Description
• When N and/or O come in contact with Ti
several different phases can form depending
on composition and temperature.
– The Ti-N phase diagram (Fig 1a).
– The Ti-O phase diagram (Fig 1b).
• If an isolated N-rich or O-rich seed particle
is embedded in a Ti matrix, the various
phases appear as concentric layers on the
original particle.
Fig 1a
Fig 1b
Model Description (contd.)
• The concentration of impurity decreases
with distance from the center of the seed
particle.
• Dissolution of the resulting layers involves
mass transport of N and/or O away from the
seed particle.
• See Figure 2.
C
Flux of N (or O)



L
x
Fig 2 Concentration profile around a dissolving inclusion.
Model Description (contd.)
• Assumptions and Limitations
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–
–
–
Binary Systems (Ti-N or Ti-O)
Chemical Equilibrium at all Interfaces
All Phases form Ideal Solutions
Temperatures restricted to within beta transus of
pure Ti and first peritectic
• 882 - 2020 C for Ti-N
• 882- 1720 C for Ti-O
– Necessary Diffusivity Data Available
– Porosity Neglected
Model Description (contd.)
• Governing Equation
c/t = div ( D grad a)
c/t = div ( grad a*)
where
c = concentration of N (or O)
D = diffusivity of N (or O)
a = activity of N (or O) (Fig 3)
da* = D da (Fig. 4)
a



L
C
Fig 3
a*



L
a
Fig 4
Model Description (contd.)
• Solution Methodology:
– Finite Difference, Fixed Domain Method
– Fixed Mesh
– Explicit Scheme
• Physico-Chemical Data:
– Phase Diagrams
– Diffusivities
Description of the Code
• Derived from earlier code MICRO developed at UTRC.
• FORTRAN program embedded in a UNIX wrapper.
• Code can be used from a computer anywhere anytime via
the internet.
• Inputs:
– Inclusion size and geometry
– Inclusion and matrix concentration
– Thermal history
– Mesh
The GROW Code (contd.)
• Outputs
– Concentration profiles around inclusion at
selected times during specified temperature
history
– Extent of the various layers as functions of
time.
– Extent of the diffusion zone surrounding the
inclusion as function of time.
Preliminary Results (Ti-N)
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•
•
•
250 micron inclusion with 32 a/o N
Isothermal Hold at 1200 C (Figs. 5a and 5b)
Isothermal Hold at 1600 C (Figs. 6a and 6b)
Isothermal Hold at 2020 C (Figs. 7a and 7b)
• Sample Thermal History (Figs. 8a and 8b)
t (min) 0
T(C)
1
5
10
2000 1670 1000 1000
12
13
15
1300 1500 1000
Fig 5a
Fig 5b
Fig 6a
Fig 6b
Fig 7a
Fig 7b
Fig 8a
Fig 8b
Preliminary Results (Ti-N)
(contd.)
• Two-dimensional system (250 by 1000
micron inclusion). Figs. 9a and 9b.
• Three-dimensional system (250 by 500 by
1000 micron inclusion). Figs. 10a and 10b.
Fig 9a
Fig 9b
Fig 10a
Fig 10b
Preliminary Results (Ti-O)
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•
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250 micron inclusion with 50 a/o O
Isothermal Hold at 1200 C (Figs. 11a and 11b)
Isothermal Hold at 1600 C (Figs. 12a and 12b)
Isothermal Hold at 1720 C (Figs. 13a and 13b)
Sample Thermal History (Figs. 14a and 14b)
t (min) 0
1
5
10
12
13 15
T(C) 2000 1670 1000 1000 1300 1500 1000
Fig 11a
Fig 11b
Fig 12a
Fig 12b
Fig 13a
Fig 13b
Fig 14a
Fig 14b
Example Runs (Ti-N) (contd.)
• Two alternative calculation methods of
phase thickness under thermal history (Figs.
15 and 16)
• Two alternative calculation methods of
phase thickness under isothermal hold at
2020 C (Fig. 17).
Fig 15
Fig 16
Fig 17
Web Enabled Simulation
• The code is now being made available for
execution within a web browser.
• Users can execute the program using their
own inputs from anywhere anytime while a
single version of the code is maintained in
our local server.
• See Figs. 18 and 19.
Screen Navigation Process
Home Page
Select Files for Display
Select and Execute Program
Results
Page
Fig. 18
Fig. 19a
Fig. 19b
Fig. 19c
Fig. 19d
Parametric and Sensitivity
Studies
• Effect of Initial Seed Particle Size on Extent
of Diffusion Zone under Specified Thermal
History (Triple Melt VAR).
• Effect of Initial Seed Particle Concentration
on Extent of Diffusion Zone under
Specified Thermal History (Triple Melt
VAR).
Summary (contd.)
• A mathematical model and associated
computer code are now available to
investigate the spread of diffusion zones
around N- or O-rich inclusion particles in Ti
as a function of thermal history, inclusion
geometry and composition.
Summary (contd.)
• Once fully validated, the code can help
process engineers, designers, NDT and
quality assurance personnel to achieve their
goal of producing hard-alpha free aircraft
engine components.
Summary (contd.)
• Although the results of calculation are in
reasonably good agreement with at least
some of the existing empirical data on
dissolution rates, full validation of the
model still requires comparison against
results of carefully conducted experiments
on selected systems.