Development of Low-cost Casting Titanium Alloys: An Integrated Computational
Materials Engineering (ICME) Guided Study
Dissertation
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy
in the Graduate School of The Ohio State University
By
Zhi Liang
Graduate Program in Materials Science and Engineering
The Ohio State University
2018
Dissertation Committee
Professor Alan A. Luo, Advisor
Professor Glenn Daehn
Professor Ji-cheng Zhao
Copyrighted by
Zhi Liang
2018
Abstract
Titanium alloys have proved to be important lightweight structural materials since
1960’s, due to their excellent intermediate temperature mechanical properties, corrosion resistance and weldability. Their good property-to-weight ratios make them ideal for many high-end and weight-sensitive applications. However, the application of titanium alloys is still limited due to the high costs in raw materials and manufacturing, indicating the importance of developing new cost-effective titanium alloys. Compared with other lightweight structural alloys (e.g. aluminum, magnesium), the raw material cost for titanium alloys is generally considered as expensive due to its expensive alloying elements such as vanadium, molybdenum, and tin. The cost issue is further amplified by the difficulties in using conventional machining methods for component-shaping due to the low thermal conductivity. Therefore, cost-effective titanium alloys should address either aspect. This work focuses on the goal of developing new cost-effective Ti-Al-Fe-
Mn titanium alloys for the casting process via Integrated Computational Materials
Engineering (ICME) approach by using cheaper alloying elements and net-shape manufacture process.
Calculation of Phase Diagram (CALPHAD) work on the Ti-Al-Mn ternary system was conducted to establish the reliable thermodynamic database to guide the alloy design.
ii
This investigation includes both experimental work and database programming.
Isothermal phase equilibria and differential scanning calorimetry (DSC) experiments were conducted to acquire the equilibrium information for the determination of phase boundaries. Based on the experimental results, an updated Ti-Al-Mn ternary thermodynamic database was built, which is beneficial for further multi-component titanium alloy development.
The other involved ternary titanium alloy system, Ti-Al-Fe ternary system, was investigated with CALPHAD method first to determine target compositions and desired phases, and then characterized experimentally with scanning electron microscopy (SEM) in order to establish the relationship between process parameters and microstructure.
Based on the combining results from CALPHAD and selected experiments, a new Ti-Al-
Fe casting titanium alloy was designed and produced with induction melting.
Microstructure characterization and mechanical property testing were conducted to examine the potent of this new alloy and establish the preliminary structure-property relationship in the as-cast condition. Besides regular scanning electron microscopy
(SEM), transmission electron microscopy (TEM) was also applied to investigate the effect of certain nano-size microstructural features linked to mechanical properties.
Finally, a laboratory-scale manufacture framework was constructed in OSU facility, including vacuum induction skull melting (ISM), gravity tilt-pour casting, and permanent metallic mold casting. This new framework was used to manufacture a prototype casting connecting rod with the new Ti-Al-Fe casting alloy served as iii
conceptual validation for further industrialization. A preliminary cost analysis was also
presented in this work to illustrate its commercialization potent compared with the current industry applications (e.g. alloy and process).
iv
Dedication
Dedicated to my parents, Fei Huang and Liming Liang, for their continuous and patient
support.
v
Acknowledgments
I shall firstly acknowledge my advisor, Prof. Alan Luo for his full support and
guidance on my PhD research period. With his significant industry experience and
courage, we successfully stepped into a brand new field, titanium alloy, for both of us.
Being pushed into this new and challenging area of research, he offered me a precious experience of handling and planning an entire research project. My achievements in OSU and my new career in NIST are mostly thanked to his backing and recommendations.
I also want to acknowledge the constant consultation from the other co-PI/advisor during my PhD research/project, Prof. James C. Williams. It is my honor to receive his suggestions and counseling in the titanium field, which is new for both me and Prof. Luo.
With his comprehensive experience of titanium in both academia and industry, he gave us many important hints in planning and conducting experiments, and giving us revisions and feedbacks for our publications.
I would like to thank Prof. Glenn Daehn and Prof. Ji-Cheng Zhao of OSU for their help and guidance for the completion of my degree, especially making time for my defense in a quite rushing timeframe during summer semester.
I specially acknowledge the support of all my colleagues in our research group.
Although most of us are all working towards different research directions, we established vi
a very strong collaboration and stimulating discussion across different fields. Among
them I thank especially Xuejun Huang, Scott Sutton and Emre Cinkilic for their constant
assistance in most of my critical experimentations, the titanium casting and testing. I
want to mention three of our group’s post-docs, Dr. Weihua Sun, Dr. Renhai Shi, and Dr.
Jiashi Miao, for providing me immense help in CALPHAD database-ing and microstructural characterizations. Also, as mentioned by our previous graduating colleague, Scott Sutton, I must thank to Janet Meier, Emre Cinkilic, and Scott Sutton for our routine “coffee caravan” with lots of “academia-bouts-exchanging” discussions that really gave me plenty of brand new (and sometimes weirdo) ideas to explore.
I acknowledge the MSE Department’s support staff for assisting us in accelerating
our research works. Especially, I would like to appraise Pete Gosser for helping me to
achieve a lot of casting mold machining and resolving the mechanical testing issues that
really saved me in a pressing need.
Finally, I think my family deserves the greatest thanks from me. My parents have
always stood with me through my entire college career in both China and the United
States, especially for their support and understandings for the path I chose during my
PhD period.
vii
Vita
Sep 2008……….B.S. China University of Mining and Technology, Xuzhou, China
Sep 2010……….B.S. University of Kentucky, Lexington, Kentucky, USA
Sep 2013……….Graduate Research Associate, Department of Materials Science and
Engineering, The Ohio State University
Publications
[1] Z. Liang, J. Miao, J.C. Williams, A.A. Luo, Phase transformation and
strengthening mechanisms investigation of a low-cost and high-strength Ti-Al-Fe-
based cast titanium alloy, in preparation.
[2] Z. Liang, J. Miao, R. Shi, J.C. Williams, A.A. Luo, CALPHAD modelling and
experimental assessment of Ti-Al-Mn ternary system, Calphad, Under Review.
[3] Z. Liang, J. Miao, T. Brown, A.K. Sachdev, J.C. Williams, A.A. Luo, A low-cost
and high-strength Ti-Al-Fe-based cast titanium alloy for structural applications,
Scr. Mater., 157 (2018) 124-128.
viii
[4] Z. Liang, W. Sun, A.A. Luo, J.C. Williams, A.K. Sachdev, CALPHAD modelling
and experimental validation of multi-component systems for cast titanium alloy
development, Proceedings of the 13th World Conference on Titanium, TMS, 2016
1937-1941.
Fields of Study
Major Field: Materials Science and Engineering
ix
Table of Contents
Abstract ...... ii
Dedication ...... v
Acknowledgments...... vi
Vita ...... viii
List of Tables ...... xv
List of Figures ...... xvi
Chapter 1 . Introduction ...... 1
1.1 Motivations ...... 1
1.1.1 Titanium alloys ...... 1
1.1.2 Overall concept of the dissertation and project ...... 3
1.2 Organization of the thesis ...... 7
1.3 References ...... 9
x
Chapter 2 . Titanium Alloying and Casting Technologies: State-of-art ...... 11
2.1.1 α stabilizers ...... 12
2.1.2 β stabilizers ...... 14
2.1.3 Neutral and tracing elements ...... 16
2.2 Casting of titanium alloys ...... 19
2.2.1 Melting technologies ...... 20
2.2.2 Casting and molding technologies ...... 24
2.3 References ...... 26
Chapter 3 . Thermodynamic Reassessment of Ti-Al-Mn Ternary System ...... 28
3.1 Introduction ...... 28
3.2 CALPHAD approach and design of experiments ...... 31
3.3 Sample preparation and microstructure characterization ...... 34
3.4 Differential scanning calorimetry ...... 35
3.5 Thermodynamic modelling and parameters optimization ...... 36
3.5.1 Unary phases ...... 36
3.5.2 Solution phases ...... 36
3.5.3 Intermetallic phases ...... 37
3.6 Experimental results...... 39
xi
3.6.1 Microstructure characterization and phase identification ...... 39
3.6.2 Differential scanning calorimetry ...... 46
3.7 Discussions ...... 46
3.7.1 Binary systems ...... 46
3.7.2 Ti-Al-Mn ternary system ...... 47
3.8 Conclusion ...... 59
3.9 References ...... 61
Chapter 4 . Development of Lightweight Casting Titanium Alloy, Ti-6Al-5Fe-0.05B-
0.05C ...... 66
4.1 Introduction ...... 66
4.2 CALPHAD approach and alloy determination ...... 68
4.3 Sample preparation and microstructure characterization ...... 78
4.4 Differential scanning calorimetry ...... 80
4.5 Mechanical property test ...... 80
4.6 Results and discussion ...... 81
4.6.1 Microstructure characterization ...... 81
4.6.2 As-cast tensile property ...... 85
4.6.3 (α + β) and β transus ...... 87
xii
4.7 Conclusion ...... 89
4.8 References ...... 89
Chapter 5 . Manufacture of Lab-scale Prototype Casting Automotive Connecting Rod .. 93
5.1 Introduction ...... 93
5.2 Lab-scale manufacture casting framework setup ...... 94
5.2.1 Basic concept of the framework ...... 94
5.2.2 Equipment and mold design...... 95
5.2.3 OSU facility setup ...... 97
5.3 Casting simulation ...... 100
5.4 Prototype casting in OSU facility ...... 101
5.4.1 Raw materials ...... 101
5.4.2 Melting operation ...... 103
5.4.3 Casting operation ...... 106
5.5 Casting results and post-assessments ...... 106
5.6 Manufacture cost analysis ...... 109
5.6.1 Raw Materials ...... 109
5.6.2 Energy and Labor ...... 111
5.6.3 Equipment ...... 111
xiii
5.6.4 Final Cost Analysis Comparison ...... 111
5.7 References ...... 116
Chapter 6 . Conclusions and Future Perspectives ...... 117
6.1 Conclusions ...... 117
6.2 Ongoing investigations and future perspectives ...... 119
6.2.1 Further investigation of thermodynamic and kinetics of Ti-Al-Fe system .... 119
6.2.2 Further development of the new alloy, T65-0.05BC ...... 122
6.2.3 Involvement of Mn in alloy design ...... 125
6.2.4 Mold coating investigation ...... 125
6.3 References ...... 128
Chapter 7 Supplementary Results ...... 129
Bibliography ...... 130
xiv
List of Tables
Table 3.1 The assessed thermodynamic parameters of Ti-Al-Mn ternary system in this
work. Only assessed parameters are included, the rest of parameters are inherited from
Ref. [3.25]...... 38
Table 3.2 Multiple phase transition temperatures from DSC and ThermoCalc based on assessed database. Temperature is in the unit of °C...... 58
Table 3.3 Design of experiments and measured EDX phase compositions (at.%) ...... 58
Table 4.1 Tensile properties of as-cast Ti-6Al-5Fe-0.05B-0.05C in comparison with as-
cast Ti-6Al-4V [4.16], Ti-6Al-4V-ELI [4.16] and Ti-5Al-2.5Fe [4.17, 4.18]...... 86
Table 5.1 Cost analysis of raw materials ...... 110
Table 5.2 Equipment, energy and labor cost analysis for cast T65-0.05BC ...... 113
Table 5.3 Equipment, energy and labor cost analysis for P/M steel ...... 114
Table 5.4 Cost analysis summary ...... 115
xv
List of Figures
Figure 1.1 Project/Thesis flowchart ...... 6
Figure 2.1 Calculated Ti-Al binary phase diagram. Database: PanTi_2017 ...... 13
Figure 2.2 Calculated (brown) Ti-V, (red) Ti-Fe, and (blue) Ti-Mn phase diagrams.
Database: PanTi_2017 ...... 15
Figure 2.3 Calculated (top to bottom) Ti-O, Ti-N, Ti-B, and Ti-C binary phase diagrams.
Database: PanTi_2017 ...... 17
Figure 2.4 (top) Schematic of a 50 kg VAR-casting setup with (1-5) VAR system, (6-10)
crucible and casting system, and (bottom) schematic of a 1000 kg semi-continuous VAR-
casting system with (1-5) VAR system, (6-11) crucible, casting, and mold controlling
system [2.9] ...... 21
Figure 3.1 Calculated 1000°C isothermal section of Ti-Al-Mn system based on starting
thermodynamic description [3.25] with design of experiments, including phase equilibria
and DSC experiments...... 33
Figure 3.2 Backscatter secondary electron (BSE) SEM image showing the microstructure of Sample 4...... 40
xvi
Figure 3.3 Backscatter secondary electron (BSE) SEM image showing the microstructure of Sample 6...... 41
Figure 3.4 TEM characterization of Sample 9: a) low magnification backscatter
secondary electron (BSE) SEM image, b) high magnification BSE-SEM with three
phases labeled, c) BF-STEM image with inserted selected area diffraction pattern from
Laves C14 phase (along [0001] zone axis) and L12 phase (along [001] zone axis), and d)
BF-STEM image with inserted diffraction patterns from L12 phase (along [001] zone axis
) and L10 phase (along [100] zone axis)...... 42
Figure 3.5 TEM characterization of Sample 11: a) BSE image, b) BF-STEM image of a
lift-out TEM specimen, c) selected area diffraction patterns of β-Ti (along [001] zone
axis), and d) selected area diffraction pattern of Laves C14 phase (along [[21 ̅1 ̅0] zone
axis)...... 43
Figure 3.6 DSC signal and derivative curves of Sample 12 through heating. The dashed lines are applied to determine the onset temperatures...... 45
Figure 3.7 Comparison between the calculated Ti-Al-Mn 1000°C isothermal sections
from (top) base thermodynamic description [3.25] and (bottom) this work with phase
equilibria data from this work, [3.20] and [3.21]...... 49
Figure 3.8 Calculated Ti-Al-Mn 1200°C isothermal section with phase equilibria data
from [3.20]...... 51
xvii
Figure 3.9 Calculated Ti-Al-Mn 1300°C isothermal section with phase equilibria data
from [3.20]...... 52
Figure 3.10 Calculated Ti-Al-Mn 1000°C isothermal section with XRD data from [3.22].
...... 54
Figure 3.11 Calculated Ti-Al-Mn 1000°C isothermal section with XRD data from [3.23].
...... 55
Figure 3.12 Calculated Ti-Al-Mn 1150°C isothermal section with XRD data from [3.24].
...... 56
Figure 3.13 Calculated Ti = 25 at.% isopleth with experimental data from [3.24]...... 57
Figure 4.1 Calculated Ti-(5, 6, 7)Al-xFe isopleths. Database: PanTi_2017 ...... 71
Figure 4.2 Calculated Ti-xAl-(4, 5, 6)Fe isopleths. Database: PanTi_2017 ...... 72
Figure 4.3 Calculated isopleth of Ti-6Al-5Fe-xB-xC. Database: PanTi_2017...... 75
Figure 4.4 Calculated Ti-6Al-5Fe-0.05B-0.05C-xO isopleth. Database: PanTi_2017. .... 76
Figure 4.5 Calculated Ti-6Al-5Fe-0.05B-0.05C equilibrium pathway. Database:
PanTi_2017...... 77
Figure 4.6 Machined ASTM E8 tensile specimen ...... 79
xviii
Figure 4.7 SEM images of as-cast Ti-6Al-5Fe-0.05B-0.05C under different
magnifications ...... 83
Figure 4.8 STEM characterization of the microstructure of Ti-6Al-5Fe-0.05B-0.05C: (a)
Bright field STEM image with a inserted selected area diffraction pattern showing the
Burgers orientation relationship between α and β phase, (b) HAADF-STEM image, (c)
STEM EDS maps, and (d) STEM EDS line...... 84
Figure 4.9 ASTM E8 tensile result of as-cast Ti-6Al-5Fe-0.05B-0.05C ...... 86
Figure 4.10 DSC signal curve of T65-0.05BC through heating. The dashed lines are applied to determine the onset and offset temperatures...... 88
Figure 5.1 (left column) Pre-casting mold with ZrO2 coating of (top to bottom) top half
and bottom half, and (right column) post-casting mold pictures of (top to bottom) top
half, bottom half, and core ...... 98
Figure 5.2 (top) OSU facility ISM-Casting furnace and (bottom) layout in the vacuum
chamber ...... 99
Figure 5.3 EKK simulation of (top row) final temperature/solidification and (bottom
row) filling time ...... 102
Figure 5.4 Schematics of charge material stacking in DI-water-cooled copper crucible
...... 105
xix
Figure 5.5 Prototype casting T65-0.05BC connecting rod ...... 108
Figure 5.6 The effect of P/M stainless steel powder price on final cost estimation ...... 115
Figure 6.1 Experimental 1000°C isothermal section of Ti-Al-Fe system [6.1]...... 121
Figure 6.2 SEM images of heat treated Ti-6Al-xFe: 1100°C/1hr + 800°C/1hr ...... 123
Figure 6.3 TTT experiments of Ti-6Al-5Fe-0.05B-0.05C: β-homogenization at
1100°C/1hr + (row 1) 750°C, (row 2) 800°C, (row 3) 850°C. The aging time is tagged.
...... 124
Figure 6.4 SEM images of Ti-6Al-xFe-yMn: β-homogenization at 1100°C/1hr +
800°C/1hr ...... 126
Figure 6.5 (a) The molten titanium – ceramic couple experiment setup in plasma arc melter, and SEM images of the ZrO2-titanium interfaces of (b) Ti-6Al-2Fe-2Mn and (c)
Ti-6Al-1Fe-3Mn ...... 127
Figure 7.1 SEM images of as-cast Ti-6Al-5Fe-xB-xC: (top) low magnification, and
(bottom) high magnification ...... 129
xx
Chapter 1 . Introduction
1.1 Motivations
1.1.1 Titanium alloys
The element titanium was firstly analyzed and named by a German chemist,
Martin Heinrich Klaproth, in 1795. However, the interest in titanium rose up much later around 1940’s to 1950’s. The investigation on titanium started from producing titanium sponge and then extended to titanium alloy design. The most important advance was the development of Ti-6Al-4V in the United States in 1954, one of the most successful and wide-applied α-β titanium alloys [1.1]. Since Ti-6Al-4V reaches a good combination between properties and manufacture capability, it still dominates the world titanium application field till today.
Due to its weight-savings, fatigue strength, and intermediate temperature performances [1.1-1.4], titanium and titanium alloys have attracted more attention as potential structural materials which require more ideal property-weight ratios. However, the application of titanium alloys is still limited compared with aluminum, magnesium alloys and steel because of its high cost in manufacture, especially for cost-sensitive civil applications. The cost of titanium alloys is generally composed of two aspects: the raw material and processing. The raw material aspect includes the sponge titanium production
1
and the alloying elements. The sponge titanium production is not related to the scope of
this work and therefore not illustrated. As for the alloying elements, the cost can be
further divided based on α, β stabilizers and neutral elements. For α stabilizers, Al is the
most common and economically reasonable, which does not induce the material cost issue. However, several other interstitial α stabilizer, such as oxygen, needs to be controlled to obtain the desired balance between strength and ductility levels, and thus introduces cost in purity control during manufacturing processes. For β stabilizer, the β
isomorphous category is the most widely used but also expensive, such as V, Mo and Ta.
On the other hand, the β eutectoid category is cheaper but introduces problem of segregation and intermetallic phases, which are detrimental to physical properties. For
neutral elements, they are generally expensive and mostly for morphological control,
which are not considered in this specific project but will be investigated in the future if
necessary.
The other important cost factor for titanium alloy is the manufacture process. For
intricate-shape component, machining is the conventional choice for final shaping.
However, titanium and titanium alloys are generally cost-inefficient in machining due to
their low thermal conductivity. The heat generated from machining process is hard to be
evacuated out of the tools, therefore greatly reduces the tool life and increases the
machining cost. Hence, instead of metal-removal shaping, the net-shape and near-net-
shape processes are more preferable for titanium alloys since they maximally avoid the
machining issues and minimize the metal waste during component realization.
2
This work is focused on addressing the cost issue in titanium alloy manufacture by applying appropriate alloy design and manufacture optimization strategies with a combination approach of simulation and experiments, which is explained in the following sub-section.
1.1.2 Overall concept of the dissertation and project
This work was initiated by the corresponding Department of Energy project targeting at reducing the cost of titanium alloy manufacture for automotive applications.
This dissertation covers multiple topics investigated within the scope of the DOE project, including Calculation of Phase Diagram (CALPHAD) for titanium alloy systems,
CALPHAD-assisted titanium alloy design and development for certain application, and design of correlated manufacture process with Integrated Computational Materials
Engineering (ICME) tools. In this 4-year project, we started from exploring new low-cost titanium alloy systems with the guidance of ICME-CALPHAD framework, and determined a promising alloy system, Ti-Al-Fe-Mn-B-C, that can allow further development (lab-scale and industry-scale) in the future. During the new alloy system exploration, considerable amount of scientific work was completed, including
CALPHAD modeling, microstructure morphology, mechanical properties, and processing of the new alloy systems. The relevant ternary titanium alloy systems, Ti-Al-Mn and Ti-
Al-Fe, were examined and reassessed both computationally and experimentally, leading to more comprehensive understanding of these alloy systems. 3
Based on this above study, a new low-cost casting titanium alloy was developed,
Ti-6Al-5Fe-0.05B-0.05C (designated as T65-0.05BC), which has competitive as-cast
strength level with current commercial titanium alloys but relatively low ductility.
However, in this project, since the target application, automotive engine connecting rod,
is a fatigue-limited component and does not require high ductility, this alloy shall suffice as the deliverable alloy in this project. It should be noted that in order to meet the field- test standard, this new alloy still needs to be thoroughly investigated in heat treatment,
which is a routine procedure for casting titanium alloys.
After designing and confirming the potent of the new alloy, we designed and built
a lab-scale manufacturing framework in OSU facility to conceptually prove that this alloy
can be manufactured with permanent mold casting, which is low-cost and potentially a
mass production process. We designed and produced a lab-scale prototype connecting rod
demonstrating the capability of permanent mold casting of this new alloy with ICME tools. Based on the results from lab-scale manufacturing, several recommendations are made for commercialization/industrialization of this process.
Also, in order to address that this alloy and the related manufacturing process we proposed are cost-competitive with the current alloy and manufacturing techniques, a cost analysis was conducted in this investigation. The results showed that compared with current conventional powder metallurgy steel and the Ti-6Al-4V, this new casting titanium alloy has the potent to replace them in actual manufacturing environment.
4
In addition to the major achievements listed above, there are a few issues that
need to be investigated about this new alloy and the manufacturing process. For example, the heat treatment of this new alloy needs to be further investigated to control the stable microstructure to enhance reliability of final components. The permanent mold casting process requires more precise design to reach maximum efficiency during operation.
These issues and challenges will be listed in Chapter 6. The flowchart of this project/thesis is shown in Figure 1.1.
5
Figure 1.1 Project/Thesis flowchart
6
1.2 Organization of the thesis
As briefly described above, the objective of this work is to develop new cost-
effective casting titanium alloys with the approach combining limited experiments and calculations, and to design the related manufacture process for industrial applications.
Several chapters are permitted to include/use of my own published/under-review journal articles by policies of Elsevier [1.5]. Their corresponding references are listed below accordingly. At first, a general review about titanium alloys is summarized in Chapter 2, focusing on alloying element effects, and the state-of-art manufacturing technologies as the background for the alloy and manufacture process design. Necessary details and literature reviews for different topics are expanded respectively in different chapters.
In Chapter 3, Ti-Al-Mn alloy system, one of the sub-systems studied in this project, is taken as an example for assessment of thermodynamic systems with
CALPHAD tool. This chapter involves the design of experiment for CALPHAD assessment, experimental evaluation, and thermodynamic database examination. The other sub-system, Ti-Al-Fe, is still under investigation and the current progress is illustrated. Its remaining issues are explained in Chapter 6. This chapter is a re-use of an under-review journal article that is expected to get published this year [1.6]
In Chapter 4, we propose a new low-cost casting titanium alloy, Ti-6Al-5Fe-
0.05B-0.05C. This chapter includes the design route of this new alloy starting with the determination of alloying elements, getting referential alloy composition by CALPHAD,
examining the new alloy for microstructure features and various properties with different 7
characterization tools. We also attempted to establish the structure-property relationship for this new titanium alloy. This chapter is a re-use of our published journal article [1.7].
In Chapter 5, a lab-scale permanent mold titanium casting framework was setup in OSU facility and casted with the new casting titanium alloy designed in Chapter 4, Ti-
6Al-5Fe-0.05B-0.05C. This chapter includes the concept of this casting framework, the installation of the equipment/accessories, the design of casting process with ICME tools, the detailed melting-casting operations, and finally presenting the conceptual prototype casting. In addition to the design of the manufacture process, a preliminary cost analysis is also conducted to illustrate the cost potent of this new alloy and manufacture process compared with current application in industry, and therefore proves them capable for further commercialization.
The conclusions and discussions on future works are presented in Chapter 6 for further development of the new alloy and manufacture process based on current work.
The investigations in this dissertation are sponsored by the U.S. Department of
Energy under project DE-FOA-0000988. This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States
Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to
8
any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof.
The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
1.3 References
[1.1] G. Lütjering, J.C. Williams, Titanium, second ed., Springer, 2007.
[1.2] D. Banerjee and J.C. Williams, “Perspectives on titanium science and
technology,” Acta Mater., 61 (2013) 844–879.
[1.3] J.T. Whittaker, Ductility and Use of Titanium Alloy and Stainless Steel
Aerospace Fasteners, Thesis, University of South Florida, Tampa FL, 2015.
[1.4] D. Eylon, F.H. Froes, R.W. Gardiner, J. Met., 35 (1983) 35–47; also, in:
Titanium Technology: Present Status and Future Trends, F.H. Froes, D. Eylon,
H.B. Bomberger (Eds.), Titanium Development Association, 1985, pp. 35–47.
[1.5] Elsevier. 2017. Copyright. [ONLINE] Available at:
https://www.elsevier.com/about/policies/copyright. [Accessed 15 August 2018].
[1.6] Z. Liang, J. Miao, R. Shi, J.C. Williams, A.A. Luo, CALPHAD Modeling and
Experimental Assessment of Ti-Al-Mn Ternary System, Calphad, under review. 9
[1.7] Z. Liang, J. Miao, T. Brown, A.K. Sachdev, J.C. Williams, A.A. Luo, A Low-
cost and High-strength Ti-Al-Fe-based Cast Titanium Alloy for Structural
Applications, Scr. Mater., 157 (2018) 124-128.
10
Chapter 2 . Titanium Alloying and Casting Technologies: State-of-art
2.1 Alloying effects on casting titanium alloys
In general, the effects of alloying elements on pure titanium are categorized based
on how they affect the phase stabilities of two essential phases in titanium alloys:
hexagonal close-packed (HCP) α and body-centered cubic (BCC) β phases. The phase
fractions and morphologies of these two phases directly determine the anticipated
properties (especially mechanical properties) of titanium alloys. The phase transformation
temperature between α and β phases, the β transus, is at 882°C in pure titanium. Different
alloying elements can either increase or decrease this signature temperature respectively,
and also introduce a (α + β) two phase region in the middle. The methodologies for
different alloying elements are α stabilizer (increase β transus), β stabilizer (decrease β
transus), and neutral element (no obvious effect on β transus). It should be noted that
within the neutral element type, though they do not significantly affect the β transus,
some elements do have other effects, such as microstructural morphology. These
elements will be specifically discussed in 2.1.3 with other neutral elements since they are
also important factors in alloying design. And since this work focuses on titanium
casting, the casting-related characteristics are also discussed.
11
2.1.1 α stabilizers
The most common α stabilizer is aluminum despite from several tracing elements
such as oxygen, nitrogen, and carbon. Aluminum exists in almost every titanium alloys as
the α stabilizer since it is the only element raising β transus and has large solubility in a large temperature-composition space in titanium as shown in Figure 2.1, the Ti-Al binary
phase diagram. There are other alloying elements that can serve as α stabilizers, but due to their low solubility in titanium, they are not discussed in this work. According to the
binary phase diagram in Figure 2.1, aluminum can raise the β transus by ~24°C/wt.%,
and the maximum solubility of aluminum in titanium is 31.11 wt.% at 1503.15°C.
However, for alloy design purpose, the aluminum composition needs to be controlled
below ~15 wt.% due to the increased stability of ordered β phase as shown in the
neighboring two-phase regions, which is experimentally proved in multiple high
aluminum content titanium alloys [2.1]. The increase stability of Ti3Al (α2) phase should also be concerned. This ordered HCP structure precipitates from disordered α phase, and
can potentially strengthen α phase but severely undermines alloy ductility at room
temperature with large volume fraction [2.2]. The strengthening effect from Ti3Al is
usually applied in γ-TiAl alloys but not common in α-β alloys [2.3].
12
T[C]
Figure 2.1 Calculated Ti-Al binary phase diagram. Database: PanTi_2017
13
2.1.2 β stabilizers
The β stabilizers are further categorized into isomorphous and eutectoid ones depending on whether a eutectoid reaction occurs in the binary phase diagram. In this
sub-section, the involved β stabilizers in this work are discussed: vanadium as the
baseline, iron and manganese as potential candidates.
As can be seen from the calculated binary phase diagrams in Figure 2.2,
compared with vanadium, iron and manganese are more effective in reducing β transus,
and allow β phase to be stable at room temperature. More importantly for casting, these
elements suppress melting temperatures (liquidus). For casting process, the potential
decrease in melting temperature for several hundred degrees can significantly lower the
reactivity issues and difficulty in handling the molten titanium [2.4]. However, the
enlarged liquidus-solidus gap is regarded as the cause of solute segregation during
solidification, which in titanium alloys is known as the “β fleck” [2.5]. The β fleck is a
common problem in the ingot production when the segregation leads to different
compositions of β stabilizers across different regions in macro-scale, and consecutively
leads to different post-heat-treatment behaviors since different β stabilizer compositions
have different β transuses. This segregation problem is possible to be suppressed with
faster cooling rate in the metallic mold casting process to prevent solute from diffusion
(compared with the cooling rate and diffusion distance of large ingot).
14
T /C
Figure 2.2 Calculated (brown) Ti-V, (red) Ti-Fe, and (blue) Ti-Mn phase diagrams.
Database: PanTi_2017
15
2.1.3 Neutral and tracing elements
Most neutral elements, such as Zr, Hf, and Sn, are heavy elements compared with
titanium and cost-ineffective. Since they do not meet the requirements in this
work/project, these elements are not discussed. For trace elements like oxygen and
nitrogen, they are usually inevitable to be included during the processing of titanium
alloys and need to be considered. As for boron and carbon, their involvement originates
from multiple literature investigations.
As shown the binary phase diagrams in Figure 2.3, oxygen and nitrogen are more
soluble in titanium compared with boron and carbon, and both are strong α stabilizers,
and they can significantly modify the strength level of the alloy with trace compositions
[2.6, 2.7]. On the contrary, boron and carbon have limited solubility in titanium (carbon has some extent of solubility and can be partially considered as solid solution strengtheners below certain amounts and intend to form high temperature compounds, titanium boride and carbide. There are a few investigations on boron and carbon effects on titanium alloys about the strengthening and grain refinements, which are reviewed in details in Chapter 4. Among these four elements, oxygen is conventionally considered as the most critical in titanium alloys in order to control the strength and ductility of the final component.
16
T /C
2000 Liquid + Liquid 1750
1500
1250
1000 + T /C
750
500
250
+ Ti2N 0 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 Ti wt.%(N) Continued
Figure 2.3 Calculated (top to bottom) Ti-O, Ti-N, Ti-B, and Ti-C binary phase diagrams.
Database: PanTi_2017
17
Figure 2.3 continued
1750 Liquid
b + Liquid 1500
1250 + TiB
1000 T /C 750 + TiB
500
250
0 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 Ti wt.%(B)
2000 Liquid
1750 TiC + Liquid
1500
1250 + TiC
1000 + T /C
750
TiC + 500
250
0 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 Ti wt.%(C)
18
2.2 Casting of titanium alloys
Because of the high price of titanium itself, the total cost of titanium alloys is largely dependent on the technique in processing and forming. Due to the fact that conventional machining of titanium alloys are hard as explained in Chapter 1, the requirement for titanium casting is growing rapidly. Traditional processing of titanium alloys makes small parts and incorporates into the final component. Casting, instead, makes net shape casting component, which reduces the cost of assembling and metal- removing. For example, with same weight, the cost of each casting part is usually 15-
35% lower than that of wrought part, but without great differences in mechanical properties [2.8]. Usually, titanium casting can be of final product after several heat and surface treatments. Titanium shape casting was firstly applied by U.S. Bureau of Mines with high density graphite molds in 1954, and is growing rapidly right now [2.3].
Between 1978 and 1997, the United States titanium casting shipments had a great increase. Then the decrease was due to golf club production, one of the main users of titanium casting alloy, moved to low-cost countries, and thus another increase in 2003 happened with an increasing need of industrial titanium castings. Titanium casting industry is new compared with other metal casting industries (ferrous, aluminum, and magnesium). With the possibilities of casting techniques improvement and cost reduction, titanium casting is expected to extend its application areas quickly, especially in automotive industries, which requires lighter and stronger components to reduce energy costs. Large-scale titanium casting component has already been widely used in
19
aerospace industry. The challenge addressed in this work is mainly the cost requirements
from massive production in civil areas, specifically in automotive industries in this correlated DOE project. These challenges in titanium casting technology are further discussed in the melting and casting/molding methods respectively.
2.2.1 Melting technologies
Currently, the most commonly used process for making titanium ingot is the vacuum arc remelting technique (VAR). This technique uses the cold-compacted target alloy as the electrode, triggers the electric arc onto the hanged electrode, and gradually melts the electrode to form the ingot at the bottom of the crucible. The ingot is usually reverted and remelted for several times to ensure homogeneity. Today, mature VAR processes can reach a relatively large ingot size and weight (100 cm diameter, 10000-
15000 kg). However, when applying this melting technique with casting process, the setup is complex and not spatially preferable for lab-scale, but should be energy-efficient
and applicable for industry-scale. Two typical large-capacity VAR-casting setup
schematics are shown in Figure 2.4.
20
Continued
Figure 2.4 (top) Schematic of a 50 kg VAR-casting setup with (1-5) VAR system, (6-10) crucible and casting system, and (bottom) schematic of a 1000 kg semi-continuous VAR- casting system with (1-5) VAR system, (6-11) crucible, casting, and mold controlling system [2.9]
21
Figure 2.4 Continued
22
The other new melting technique is the cold hearth melting (CHM). The heating source of CHM processes can be plasma arc, electron beam, or induction field. The
former two approaches are known as plasma cold hearth melting (PCHM) and electron
beam cold hearth melting (EBCHM), and the latter one is known as induction skull
melting (ISM). Different from VAR, during the melting process, the contact location
between the molten metal and cold hearth remains a thin solid layer called “skull”,
preventing any contamination or reaction from the hearth. There are a number of
advantages of CHM compared with VAR, including the purity of the molten metal,
charge material preparation, etc. The most important advantage in this work, specifically for casting process, is the easiness in setup of transferring the molten metal into casting mold. As shown in Figure 2.4, conventional VAR-casting setup needs to transfer melted electrodes into a ladle and then into the casting mold, while the CHM process applied in this work, ISM, can directly transfer the charge materials into the mold. This setup is illustrated in details in Chapter 5. The only disadvantage of CHM process on casting is the limited superheat. Due to the continuous fast heat loss from the cold hearth, the superheat that most cold hearth processes can achieve is 50-100 degrees. It significantly decreases the viscosity of the molten metal and thus limits the intricate cavity filling performance in casting. For EBCHM, similar to VAR, the complexity in casting setup is another limitation for specifically for this work/project. On the other hand, ISM-casting setup is more spatially reasonable for lab-scale experiments, which is applied in this work/project and described in Chapter 5.
23
2.2.2 Casting and molding technologies
Besides the high requirements for melting technique, the other big challenge for
titanium casting technology is the high affinity of titanium with impurities such as
oxygen, nitrogen and hydrogen, and the high melting point of titanium, which requires
that titanium casting must be conducted under vacuum or inert-gas-protected condition
and also within special mold. Titanium casting is developing because of three key factors:
improvement of net shape casting technology, improvement of fatigue properties, and
preservation in casting-mold reaction [1.1]. Currently, there are generally two techniques
for titanium casting: conventional casting with rammed graphite mold, and investment
casting.
Conventional gravity casting is a common technique in the family of casting, but
applying rammed graphite mold is specific for titanium casting (or other highly reactive
metals). The graphite mold is usually made from compacted graphite powder and
organic/inorganic binders. The purpose of rammed graphite mold, which is different from
sand mold for ferrous and bronze casting, is to maximally reduce the reaction between molten titanium casting and the mold. Thus, with this decrease in interfacial reactions, rammed graphite titanium casting can produce complex net shape components with good surface conditions (after regular tumble cleaning and chemical milling) [1.1].
Investment casting is another common technique in casting. Compared with
conventional gravity casting, the first difference is the method of making mold. It firstly makes a wax mold cavity pattern, and then applies a nonreactive coating on it in order to 24
prevent reaction between ceramic mold and molten castings (not necessary). After the
coating is finished, with applying mold materials (ceramics, etc.) and removal of inner
wax by heating, the mold is completed. The advantage of investment casting, comparing
with conventional casting, is that it can produce more complex shape while avoiding
over-extra machining. Since the cavity, i.e. shape of casting, is made by wax (or similar
materials), the pattern can be easily shaped into very complicated forms without heavy
machining. But its disadvantage is also originated from its complicated procedure:
relatively high labor cost. So it is vastly applied in aerospace fields for producing large,
complex, and non-massive production of structural components.
In order to combine the advantages of investment casting and conventional
graphite casting – complex casting infrastructure and reusable mold, permanent mold casting is one of those options. Permanent mold casting usually uses metallic mold, which can provide better thermal conductivity, i.e. heat exchange rate to gain faster cooling rate of casting, and thus, better as-cast microstructure. Permanent mold casting are usually applied for casting of relatively lower melting temperature metals, such as aluminum and magnesium, and also relatively less reactive high melting temperature materials, such as steel. And as stated at the very beginning, titanium has a high melting temperature and also highly reactive with regular metal mold materials, which is difficult in applying permanent metal mold casting. Therefore, the key point in applying permanent metal mold casting for titanium alloy is to prevent reactions between mold and
25
molten metal, which can be achieved via two approaches: specialized mold and modification of casting alloys, which are the main contents in this work.
2.3 References
[2.1] K. Das, S. Das, Order-disorder transformation of the body centered cubic phase
in the Ti-Al-X (X=Ta, Nb, or Mo) system, J MATER SCI, 38 (2003) 3995-4002.
[2.2] R. Boyer, E.W. Collings, G. Welsch, Materials Properties Handbook: Titanium
Alloys, ASM International, 1994.
[2.3] J.C. Chesnutt, Titanium Aluminides for Aerospace Applications, in Superalloys,
TMS, 1992.
[2.4] M. Guclu, Titanium and titanium alloy castings, ASM Handbook Volume 15
Casting, ASM International, 2008.
[2.5] A. Mitchell, A. Kawakami, S.L. Cockcroft, Beta fleck and segregation in
titanium alloy ingots, High Temp Mater Proc, 25 (2011) 337-349.
[2.6] I.I. Kornilov, Effect of oxygen on titanium and its alloys, Met Sci Heat Treat+,
15 (1973) 826-829.
[2.7] W.L. Finlay, J.A. Snyder, Effects of three interstitial solutes (nitrogen, oxygen,
and carbon) on the mechanical properties of high-purity, alpha titanium, JOM, 2
26
(1950) 277-286
[2.8] I.J. Polmear, Light Alloys – From Traditional Alloys to Nanocrystals, 4th
Edition, Elsevier, 2006.
[2.9] Vacuum Arc Remelting, ASM Handbook, 15 (2008) 132-138.
27
Chapter 3 . Thermodynamic Reassessment of Ti-Al-Mn Ternary System
3.1 Introduction
Titanium alloys are increasingly important engineering structural materials for weight-savings, fatigue strength, and intermediate temperature performances [1.1, 1.2,
3.1]. The relatively high costs of titanium alloys have limited their applications to critical components, the development of new cost-effective titanium alloys is necessary to extend their high-volume applications. In order to reduce the cost of titanium components, either the alloy composition or the process (or both) can be tailored to address this issue. The properties of engineering alloys are dependent on their phase constitution and microstructure, resulting from the alloy composition and processing conditions. The alloy constituents and their morphologies are dependent on the thermodynamic and kinetic conditions of the alloy system. Therefore, it is essential to acquire the accurate thermodynamic description of the phase equilibria in order to enable the alloy design in titanium alloy systems.
Compared with aluminum, magnesium and steel, titanium is more expensive due to its raw material cost. Naturally, replacing the current expensive alloying elements (V,
Mo, etc.) with inexpensive alternates is an important approach to reduce the alloy cost
28
[1.2]. Thus, it is necessary to design new low-cost titanium alloys with inexpensive
alloying elements.
In this investigation, manganese was chosen as a potential alloying element to reduce the alloy raw material cost. Manganese is a strong β stabilizer in titanium, but also will significantly lower the melting and β transus temperatures as shown in Figure 2.2.
This also reduces the manufacturing difficulties in melting and heat treatment processes in applications such as casting and additive manufacturing (AM). Also, due to its large solubility in β-Ti phase as shown in Figure 2.2, manganese is expected to be a strong solid solution strengthener in titanium alloys. As for the detailed effects of manganese in titanium alloy system, the potential strength and plasticity of Ti-Al-Mn alloys were investigated by Luzhnikov and Metallovedenie [3.1]. A few studies indicate that the
addition of manganese can potentially improve the ductility in γ-TiAl alloys [3.2, 3.3],
and several γ-TiAl alloys with dilute amount of manganese additions show good
manufacturability, high temperature strength, and fatigue properties [3.5, 3.6]. In
addition, according to a number of investigations [3.7-3.14], manganese also showed
good alloying effect in certain dilute α-β (Ti-2Al-1.5Mn, Ti-2.6Al-2.2Mn, Ti-2.5Al-
1.8Mn) and near α (Ti-0.75Al-0.75Mn-0.3Fe) Ti-Al-Mn alloys regarding tensile
properties, weldability, post-welding mechanical properties, and superplastic deformation behavior. A series of α-β and near-α Ti-Al-Mn alloys were reported by Moissev for
balanced mechanical properties during cold and hot deformation [3.15]. All these reports
suggested potential applications for Ti-Al-Mn titanium alloys. Therefore, Ti-Al-Mn
29
phase diagrams should be examined in order to develop potential new Ti-Al-Mn alloys.
Specifically for Ti-rich alloy design, the major phase regions regarding α, β, and Ti3Al are important since β phase normally serves as the matrix phase, α as strengthening phase for β, and Ti3Al phase as strengthening phase for α. Additionally, acquiring accurate
information about γ-TiAl and its neighboring phases can benefit the design for Mn-
containing γ-Ti alloys as well. Overall, the relationship between the phase equilibria and
alloying elements in this system is essential to design the proper alloy compositions for
specific applications.
Although some thermodynamic assessments have been reported for this ternary
system, most experimental results and assessments were focused on γ-TiAl, Ti3Al and
surrounding Laves phase [3.21, 3.25, 3.26, 3.27], including L12 and Laves C14 phases.
The experimental Ti-Al-Mn phase diagrams were reported in a few investigations [3.16-
3.24]. Chen et al. studied the phase equilibria of alloy composition Ti-42Al-10Mn (at.%) at 1000°C and 800°C [3.21]. Butler et al. investigated the phase transformation temperatures of several γ-TiAl based alloys experimentally and compared with computational results [3.17-3.19]. Kainuma et al. [3.20] studied the alloy composition Ti-
45Al-4Mn (at.%) at 1300°C, 1200°C, and 1000°C and constructed a few experimental isothermal sections. Mabuchi and Nakayama et al. investigated the ternary L12
compound, Ti25Mn9Al66, and neighboring phase regions experimentally [3.22-3.24].
Chakrabarti reported an experimental Mn-rich isothermal section at 1000°C [3.26], which
was later experimentally confirmed by Yan et al. [3.27]. It should be noted that some
30
experimental results may not be sufficiently accurate for alloy design and thermodynamic
assessment. For example, the equilibrated alloy experiments of Mabuchi and Nakayama
et al. [3.22-3.24] were conducted using a short time span that the specimens might not
reach full equilibrium conditions. Despite the most recent work by Chen et al. [3.25], the
assessments of Ti-rich regions (Ti > 80 wt.%) were scarce in either experiments or
modeling, which affect phase regions containing α, β, and Ti3Al phases. As illustrated
above, the formation of these phases are critical to the final alloy properties. Therefore, in
this paper, the equilibrated alloy method was used to obtain phase equilibria information
in Ti-Al-Mn ternary system, and its thermodynamic description was assessed, especially
for Ti-rich region based on the experimental results. These outcomes will provide an
important basis of assessing Ti-Al-Mn-based multi-component systems and assisting design of new cost-effective titanium alloys in the future. The content of this chapter has been under review in Calphad and expected to be published in 2018 [1.6].
3.2 CALPHAD approach and design of experiments
In recent years, CALPHAD proves to be a useful tool for the new alloy design and validation in the ICME framework [3.33]. As mentioned above, accurate thermodynamic databases are the essential input for CALPHAD simulation to predict the equilibrium phase stability, driving force for phase transformation etc. However, unlike existed well-established databases for steel, aluminum and magnesium, the current titanium-based commercial databases are lack of validations due to the scarce 31
experimental data. Therefore, the Ti-Al-Mn experimental data generated in this work is
highly beneficial to improve the current titanium databases.
In this work, the Ti-Al-Mn 1000°C isothermal section was selected to cover most
important phase regions in Ti-rich corner. The design of experiments was based on the
thermodynamic description from Chen et al. [3.25]. Multiple compositions were prepared
in the isotherm as shown in Figure 3.1 and listed in Table 3.3 to validate/reassess the
calculated phase equilibria. Since the focus of this investigation is the Ti-rich region, the
design of experiments is determined in the 2-phase and 3-phase regions neighbouring of the target single phase regions
32
Figure 3.1 Calculated 1000°C isothermal section of Ti-Al-Mn system based on starting thermodynamic description [3.25] with design of experiments, including phase equilibria and DSC experiments.
33
3.3 Sample preparation and microstructure characterization
The button specimens were prepared with plasma arc melter (Arc melter, SA-200,
Materials Research Furnaces, Inc.) from high purity elements: titanium (99.99%, Kamis
Inc.), aluminum (99.99%, SCI Engineering), and manganese (99.9%, Alfa Aesar). Each specimen was re-melted four times to ensure homogeneity, and then encapsulated in the quartz tubes back filled with ¼ atmospheric pressure of Ar for equilibrated annealing treatment. Each encapsulation included a small Ta-3W (wt.%) block to absorb remaining trace oxygen. The specimens were annealed in tube furnace for 720 hours at 1000°C to reach phase equilibria, and then water-quenched to room temperature. Samples for microstructure characterization were ground and polished following conventional metallographic specimen preparation procedures. General microstructure observation was conducted in a FEI Apreo Scanning Electron Microscopy (SEM) equipped with an
Energy-Dispersive X-ray Spectroscopy (EDAX) system. Cross-sectional Transmission
Electron Microscopy (TEM) specimens for phase identification were prepared in a FEI
Helios focused ion beam (FIB) microscope using lift-out method. All FIB TEM specimens were further cleaned using Fischione 1040 nanomill to reduce ion beam damage associated with FIB sample preparation. TEM characterization was carried out on a FEI Tecnai TF20 TEM/STEM microscope operating at an accelerating voltage of
200keV.
34
3.4 Differential scanning calorimetry
The differential scanning calorimetry (DSC) was conducted with the NETZSCH
DSC 404F1 Pegasus® in this investigation at University of Science & Technology
Beijing in order to evaluate the 3-phase region, (β-TiMn + β + Laves C14), which is hard
to pinpoint via equilibrated alloy method. The DSC specimen was prepared with the
equilibrated alloy method above. The specimen, Ti-2.24Al-48.94Mn (wt.%), was placed
in an alumina crucible with an empty alumina crucible as reference. The specimen
chamber is evacuated and backfilled with argon gas. The empty alumina crucible was
tested before the sample to obtain the baseline, which was deducted for the results of the sample. The DSC instrument, namely the thermocouple, has been calibrated regularly.
The calibration process includes both the temperature and sensitivity calibrations, which are specific to the crucible, the heating rate, and the protective gas. Five pure metals, i.e.
Au, Al, Zn, Bi, and In, were applied for the calibrations. The temperature calibration
eliminates the deviation between the temperature measured by the thermocouple and the
actual temperature of the sample. Sensitivity correction ensures the accurate conversion
between thermocouple signal and heat flow power. The chamber temperature was
increased to 1200°C at the rate of 20°C min.
35
3.5 Thermodynamic modelling and parameters optimization
3.5.1 Unary phases
The Gibbs free energy function for the element Ti, Al, Mn in all phases is described by Eq. (1) from SGTE compilation of Dinsdale [3.30]: