TRIP Titanium.pdf

7/30/2019 TRIP Titanium.pdf

1/50

1

Ti51111: TRIP Titanium

Entry based on a design project in the Northwestern University,

Materials Science and Engineering undergraduate capstone

course: MatSci 390

Clients: Office of Naval Research and General Motors

Group Members:

Pitichon Klomjit, Frank Lin, Kelsey Stoerzinger,

Wenhao Sun, Allison Weil, Tian Zhou

Graduate Advisor:

Jamie Tran

Instructor:

Dr. Gregory Olson

Correspondence address: 2220 Campus Drive Evanston, IL 60208

A.U. Navy Photo from Austrailian Defence Jobs Website


2/50

2

Executive Summary

Motivated by the prospect of lower cost Ti production processes, new directions in Tialloy design are explored for naval and automotive applications. Using the near-Ti5111 alloy as a reference alloy, the feasibility is assessed for application of

transformation toughening to maintain the high toughness of Ti5111 at the higher 120ksi(827MPa) yield strength of Ti-6Al-4V. Principles established in steels are used tooptimize the phase transformation stability for toughening. First principles quantummechanical calculations are combined with available atomic volume data to model thecomposition dependence of the transformation volume change. Experimentalmeasurement of the mechanical transformation stability of the phase in Ti5111 providesa calibration of transformation models. Combined with models of solution and grainrefinement strengthening, a modification of the 5111 composition is designed meeting thetransformation stability requirement while increasing the transformation volume changeby a factor of 3 for efficient toughening.


3/50

3

Table of Contents

EXECUTIVE SUMMARY.......................................................................................2

1 MOTIVATION AND BACKGROUND ...............................................................51.1 Motivation ........................................................................................................................................5

1.2 Alternatives ......................................................................................................................................51.2.1 Steel and Aluminum .....................................................................................................................51.2.2 Titanium alloys .............................................................................................................................6

1.3 Limitations of Current Titanium Alloys........................................................................................6

1.4 Titanium Phase Relations ...............................................................................................................6

1.5 Ti5111................................................................................................................................................7

1.5.1 Ti5111 Processing/Structure/Properties........................................................................................7

2 PROPERTY OBJECTIVES FOR TRIP TITANIUM ........................................8

2.1 Application Requirements ..............................................................................................................8

2.2 Property Objectives.........................................................................................................................82.2.1 Specific Strength and Toughness..................................................................................................82.2.2 Corrosion Resistance ..................................................................................................................102.2.3 Weldability..................................................................................................................................102.2.4 Alloying Cost ..............................................................................................................................10

3 TEAM ORGANIZATION...............................................................................11

4 SYSTEM STRUCTURE................................................................................12

5 DESIGN APPROACH ..................................................................................13

5.1 Strength Model...............................................................................................................................135.1.1 Hall-Petch Strengthening............................................................................................................135.1.2 Solid Solution Strengthening......................................................................................................14

5.2 Transformation Toughening.........................................................................................................155.2.1 TRIP Steels and Ceramics ..........................................................................................................155.2.2 Martensitic Transformation in Titanium Alloys .........................................................................165.2.3 Modeling the Martensitic Transformation in Titanium ..............................................................175.2.4 Ab-initio Calculations of Molar Volume for Control of Transformation Volume Change........195.2.5 Transformation Stability Measurements.....................................................................................21

5.3 Cost Model......................................................................................................................................21

6 DESIGN MODELING....................................................................................22


4/50

4

6.1 Hall-Petch Grain Size Refinement ...............................................................................................226.1.1 Lineal Intercept Measurement ....................................................................................................236.1.2 Grain Size Modeling ...................................................................................................................24

6.2 Solid Solution Strengthening ........................................................................................................25

6.3 Martensitic Transformation Toughening....................................................................................276.3.1 Volume Change of Martensitic Transformation in Titanium .....................................................276.3.2 DFT Atomic Volume Calculations .............................................................................................276.3.3 Redlich-Kister Fitting to Atomic Volume Data..........................................................................306.3.4 Interfacial Friction of the Martensitic Transformation in Titanium ...........................................336.3.5 Ms calculations and Measurement.............................................................................................346.3.6 Ms calculations for Ti5111 and Model Calibration...................................................................37

7 DESIGN INTEGRATION ..............................................................................40

7.1 Design Constraints.........................................................................................................................407.1.1 Composition constraints..............................................................................................................407.1.2 -phase fraction constraints ........................................................................................................427.1.3 Annealing temperature constraints .............................................................................................427.1.4 Mo partitioning interaction with Fe ............................................................................................43

7.2 Final Alloy Composition................................................................................................................447.2.1 Composition Refinement ............................................................................................................447.2.2 Final Composition.......................................................................................................................447.2.3 Annealing Temperature and Ms.................................................................................................457.2.4 phase composition....................................................................................................................45

7.3 Processing .......................................................................................................................................46

7.4 Strengthening Results....................................................................................................................467.4.1 Solid Solution Strengthening......................................................................................................46

7.4.2 Hall-Petch Grain Refinement......................................................................................................46

7.5 Toughening Results .......................................................................................................................47

8 CONCLUSION AND RECOMMENDATIONS ..............................................47

9 ACKNOWLEDGEMENTS ............................................................................48

10 REFERENCES..........................................................................................49


5/50

5

1 Motivation and Background

1.1 MotivationRecent innovations have led to low cost production methods such as the FFC/Cambridgeand the Armstrong/ITP methods which may reduce the cost of titanium by amounts on

the order of 30% to 50%.1 Spurred by the prospect of more affordable Ti alloys, theUnited States Navy and the automotive industry are re-examining titanium alloys in thesearch for reliable structural materials that are lightweight, strong, tough, and corrosion-resistant. Titanium alloys are well known for their high strength-to-weight ratio. Thisproperty first rendered them ideal for aerospace applications, but their use has since beenextended to other realms where high strength and low density are desired. In fact,titanium alloys may achieve the high strength of certain steels at a fraction of the weight.Titanium is also very corrosion-resistant, forming a very thin, stable layer of titaniumoxide that serves to chemically protect the base metal underneath. The principaldrawback of titanium has been high cost.

Realizing the potential for low cost titanium in military, naval, and aerospaceapplications, the United States Office of Naval Research (ONR) has supported researchinto tailoring alloy properties to a variety of needs. The Navy in collaboration withTitanium Metals Corporation (Timet) has recently developed an alloy, Ti5111 (TitaniumFive Triple One), for structural marine applications. This alloy has a composition of5wt%Al, 1wt%V, 1wt%Sn, 1wt%Zr, 0.8wt%Mo, and 0.1wt%Si. It possessesintermediate strength, high toughness, excellent stress-corrosion cracking resistance, andweldability.

In addition to support from ONR2, General Motors (GM) has awarded a grant toNorthwestern3 in response to recent government regulations that require an automobile to

run at 35 miles per gallon by the year 2020.4 Many high performance components of anautomobile engine require the use of heavy steel. The high strength-to-weight ratio oftitanium has the potential to reduce the energy consumption of an automobile by 25%when replacing steel products.5

A new alloy combining the strength of commercial alloy Ti-6Al-4V with the toughnessof Ti5111 will be designed by exploiting transformation toughening. Grain sizerefinement and solid solution strengthening models are used to obtain the increase instrength. Building on principles established in high-performance steel design, a newmodel for transformation toughening of titanium is developed to compensate for theconcomitant decrease of toughness with increase in strength; resulting in a

TRansformation Induced Plasticity (TRIP) titanium alloy design.

1.2 Alternatives1.2.1 Steel and Aluminum

High-strength alloyed steel is the primary material currently used for submarine hulls andother shipbuilding applications. However, the low corrosion resistance and strength-to-weight ratios of steel limit its use from many marine applications.6


6/50

6

The low density, non magnetic nature and lower cost of aluminum (Al) compared totitanium (Ti) make it desirable for a wide variety of applications. However, the lowabsolute strength and low corrosion resistance of Al alloys make them unsuitable formany structural applications in naval applications.

1.2.2 Titanium alloysThe commercial titanium alloy Ti-6Al-4V (Ti64) accounts for more than 50% of total Tialloy tonnage worldwide: the aerospace industry accounting for 80% of this usage, andthe automotive, marine, and chemical industries also use small amounts.7 Although thestrength of Ti64 (Table 1) is high, the fracture toughness and stress corrosion crackingresistance of the material are insufficient for structural naval applications.

The alloy Ti100 with a composition of Ti-6Al-2Nb-1Ta-0.8Mo (values in wt%) wasoriginally developed by the Navy for high toughness and moderate strength applications.While the properties of the alloy met the Navys strength requirements (Table 1), theexpensive alloying elements and manufacturing difficulties prevented its use.

Table 1: Mechanical and physical properties of Ti, Al, and steel alloys8

Ti5111 Ti100 Ti64 Al 7075-T6 HSLA1009

Yield Strength (ksi) 100 100 120 73 100

Density (lb/in3) 0.160 0.162 0.160 0.102 0.284

Elongation at Break 15% 11% 14% 11% 11-13%

Strength/Density 625 617 813 716 352Kic Fracture Toughness

(ksi in1/2)10107-11311 100-11012 74.6-91 27.3-30 -

Salt Water Corrosion

Resistance

10

Very good11 Very good12 Very good Good Average

1.3 Limitations of Current Titanium AlloysWhile the excellent corrosion resistance and strength-to-weight ratio of current Ti alloysmake them particularly desirable for Navy applications, there are still several drawbacks.In addition to relative cost, the high affinity of Ti for oxygen dictates that Ti alloyscannot be produced and welded in atmosphere. Production and fabrication steps requirethe use of vacuum or inert gas atmospheres which is difficult when large sections of Tiare needed. Furthermore, available fundamental data and research on Ti and its alloys arelimited compared to other materials such as steel with a longer history as a structuralmaterial.

1.4 Titanium Phase RelationsThere are two different crystal structures of pure titanium, a low temperature HCP alpha() phase, and a high-temperature BCC beta () phase. The transition between thesephases occurs at 882oC, termed the -transus temperature. This temperature can bemodified by alloy composition, which can be used to engineer combinations of and titanium phases tailored to desired microstructures.


7/50

7

Titanium alloys fall into two main categories, -Ti and -Ti alloys, denoting thedominant phase. Notable mechanical properties of alpha alloys include high resistance tofracture, as well as fatigue. They also tend to be easier to weld than other titanium alloys,and are highly resistant to corrosion. Beta alloys can achieve higher strengths than alphaalloys, but are also less tough. In general, specific properties can be attained by tuning the

different fractions of alpha and beta phases. These alloys are called + alloys, generallywith beta phase concentrations over 10%, featuring properties between the -Ti alloy and-Ti alloy extremes.

Alpha phase stabilizers include aluminum and tin, which replaces titaniumsubstitutionally, and oxygen, which occupies the titanium lattice interstitially. Beta phasestabilizers include substitutional molybdenum (Mo), vanadium (V), silicon (Si), iron (Fe),and interstitial hydrogen (H). There are also neutral alloying elements, such as zirconium(Zr), that affect the properties of the material without significantly changing the betatransition temperature.

Titanium can transform into a martensite phase through a Bain transformation of theBCC -Ti lattice to the HCP '-Ti lattice. There is also an orthorhombic ''-Timartensitic phase, which can be described by an incomplete BCCHCP Baintransformation associated with high alloying.13

1.5 Ti5111The U.S. Naval Research Laboratory worked in conjunction with the Titanium MetalsCorporation (Timet) to develop an improved structural alloy as an alternative to Ti100 foruse primarily in ship hulls. Requirements of the material include high strength(especially a high strength-to-weight ratio), high fracture toughness, and superior marineenvironment corrosion resistance. Ti5111, met all of these requirements set by the Navy

(Table 1) and is more cost efficient and easier to manufacture than Ti100.

1.5.1 Ti5111 Processing/Structure/Properties

The microstructure and properties of an alloy are controlled though optimized processing.Hot rolling of Ti5111 above the transus temperature (1093C) followed by a two-stepduplex annealing treatment in the phase field (1010C) and + field (954C) is usedto obtain a lamellar microstructure with a limited retained phase content (termed anear- alloy). During both annealing steps the material is held for 1 hour per 25 mm ofthickness with an air cooling of ~15-20C/min after each stage.

The optimized microstructure of Ti5111 is characterized by a basket weave or

Widmansttten microstructure (Figure 1). When the high temperature phase is cooled atslow rates below the transus, the low temperature incoherent phase begins to nucleateat grain boundaries. Further cooling leads to the nucleation of additional phase atboth and grain boundaries that grow into the grains as parallel plates11.


8/50

8

Figure 1: Widmansttten Microstructure of Ti511111

The average yield strength of Ti5111 in the longitudinal direction is 100ksi, withminimum yield strength of 85ksi. The fracture toughness values are also excellent, as arestress corrosion resistance properties14. Tests show that Ti5111 had no visible crevicecorrosion after a full year of exposure to seawater15. This alloy also costs less to producethan other Ti alloys of comparable properties.

2 Property Objectives for TRIP Titanium

2.1 Application RequirementsThe first step in determining the property objectives of TRIP Titanium is to understandthe requirements of the application it will be used for. A structural alloy must havesufficient strength and toughness to withstand the physical forces acting upon it. Thealloy must also have a high corrosion resistance for use in corrosive environments. Theability of components to be welded in air would also be desirable for ship building.

2.2 Property Objectives2.2.1 Specific Strength and ToughnessIn this project, we seek to design an alloy with the toughness of Ti5111 (110ksi in1/2) andthe strength of Ti64 (120ksi). A large toughness protects against projectiles, explosions,and general usage and a high strength allows the use of the design alloy as a structuralhull material. Furthermore, using high specific strength and specific toughness (valuesnormalized by density) criteria allows for the design of strong and fracture resistantmaterials that enable lightweight structures. As previously seen in Table 1, titaniumalloys can provide higher specific strength and specific toughness than the other highperformance engineering alloys.

Cambridge Engineering/Materials Selector (CES/CMS) is used to plot and compareproperty objectives to currently available materials. As lightweight structures areimportant to the Navy, material properties normalized by density are plotted. To limit theCES plots to relevant materials, restrictions/minimum criteria were applied. A minimumelongation of 10% is placed on the materials as this is a criterion of weldable metals inthe Navy. Also the mechanical property constraint of a minimum fracture toughness of50ksi in is placed to eliminate materials that would not be appropriate for structuralapplications for the Navy. Additional constraints of a material having average, good,


9/50

9

or very good freshwater properties are included. Most importantly the plot wasobtained with the restriction that all materials had to perform very well in seawater.These five criteria were entered into the CES software and the following plot wasproduced:

Figure 2: CES Plot of Specific Toughness vs Specific Strength

Figure 2 cross plots the specific fracture toughness and specific strength of all materialsthat have passed the aforementioned selection parameters. The main materialcompetitors in this plot are titanium (purple), nickel (red), and stainless steels (teal). Ti

alloys offer good specific fracture toughness to specific strength values, evidenced bytheir location in the upper right hand corner of the plot. This makes Ti alloys a goodstarting point for the development of a material that best meets our applications needs.The two Ti alloys previously mentioned, Ti5111 and Ti-6Al-4V, are detailed in the CESplot. As the project goal location shows, the property goals for the alloy being developedare in a range that no current alloy achieves.


10/50

10

The lines in Figure 2 represent values for the critical flaw size (acrit) at the yield stress,(YS), which can be defined as:

Equation 1

The minimum fracture toughness to yield strength (KIC/YS) ratio allowed by the Navy is0.5, while a value of 1 is ideal. The minimum and ideal ratios correspond to critical flawsizes of 0.08 and 0.32 respectively. Ti5111 surpasses the minimum ratio and closelyapproaches the ideal ratio.

2.2.2 Corrosion ResistanceNaval materials have continuous exposure to seawater, and therefore corrosion resistanceis very important. Elemental Ti and Ti alloys form a layer of TiO2 upon exposure tooxygen, which acts as a native oxide passivation layer that provides corrosion resistance.This property gives Ti alloys an advantage over other alloys that do not form such a

layer, for example nonstainless Fe alloys, which need additional protective coatings priorto use in marine applications. Relevant to many current real-world industrial and navalapplications, Ti alloys resist both unpolluted and polluted seawater corrosion up to 80C,in atmospheric corrosion and microbiologically induced corrosion.16

Crack tips resulting from material deformation are plagued by a lack of sufficient TiO2buildup, threatening the material integrity. For this reason it is important to restrictcertain alloying elements which increase the susceptibility of Ti alloys to stress corrosioncracking, including Al, Zr, oxygen (O), and tin (Sn). Other alloying elements, Mo and V,increase resistance to stress corrosion cracking. Part of the stress corrosion resistance ofTi5111 is due to the low weight percentages of Al (5 wt%) and O (0.09wt%). 17,18,19

2.2.3 WeldabilityTitanium alloys can be welded by gas tungsten arc welding, plasma arc welding, or anumber of other techniques. Due to the high temperatures during welding, the weld sitemust be isolated from oxygen and nitrogen gas that can embrittle the area if theseelements are dissolved into the metal. In addition, stresses from welding must be relievedto increase fatigue resistance in the weld area. Adding yttrium (Y) to the alloy and theweld filler helps to getter the oxygen introduced during the weld process by formingY2O3precipitates. These precipitates, formed in lieu of more brittle metal oxides, alsohelp strengthen the welding point by pinning -phase grain boundaries duringrecrystallization to reduce the grain size.20

2.2.4 Alloying Cost

Although titanium alloys exhibit many exceptional properties that make them desirablefor a wide range of applications, cost remains a primary limitation. Alloy cost iscontrolled by both raw material costs and processing costs. Assuming the processingcosts are similar for other Ti plate material, the cost of Ti alloys then is driven by theamount and type of alloying elements used. The most commonly used Ti alloy, Ti64, willserve as a relative alloying cost constraint for the project.


11/50

11

3 Team OrganizationPitichon Klomjit will assess strengthening mechanisms for Ti5111 type alloys. He isparticularly interested in working with metals, and is currently working with the Olsongroup to improve the mechanical properties of alloys. The course MSE 332 Mechanical

Properties of Materials, taught by Professor Panico, introduced him to manystrengthening mechanisms, such as solid solution strengthening, precipitate hardening,and grain size refining. He is excited to apply this knowledge quantitatively to real worldapplications.

Currently in her junior year, Kelsey Stoerzinger has worked for over a year in theresearch group of Prof. Teri Odom, researching the fabrication, self assembly, and opticalproperties of nanoparticles. The many classes she has taken at Northwestern Universityhave prepared her for work in many other areas as well. She was introduced to thesubject of solid solution strengthening in Professor Seidmans 316 course sequence onMicrostructural Dynamics. She is very interested in material behavior at interfaces and is

excited to investigate strengthening mechanisms and microstructure control.

To control the volume change of martensite transformation, Wenhao Sun, a joint major inmaterials and applied mathematics, will focus on using Density Functional Theory topredict molar volumes of primary titanium phases, as well as their relative formationenergies. Wenhao has considerable experience using DFT and other first-principlesquantum mechanical simulations in his research in the research group of Prof. ChrisWolverton, and has also taken Professor Wolvertons MSE 510 graduate-levelComputational Materials Science course. Wenhao has always been interested inpredicting the behavior of novel high-performance materials through first-principles,which is why he is particularly interested in predicting the properties of this new high-

toughness titanium alloy.

Allison Weil, currently a pre-senior, is a co-op at Federal-Mogul who has worked onmaterials development and failure analysis for metallic gaskets, including research inhigh temperature materials for exhaust gasket applications. This experience has furtherfamiliarized her with metallic mechanical properties. Several courses have prepared herfor this project, and she gained an interest in toughening mechanisms due to ProfessorDunands MSE 332 Mechanical Properties of Materials course, and in this project will befocusing on this aspect.

Currently a senior, Tian Zhou has worked for the past year in the Shull group researching

strengthening mechanisms in polymeric materials. In this project, he will explore theconcept of transformation toughening, applying the mechanism of TRIP steels to Tialloys. Professor Dunands Mechanical Properties of Materials course has prepared himwell for analyzing this particular system.

Senior Project student Frank Lin is currently working with the Olson group to measurethe mechanical properties of titanium alloys. Frank has coordinated his experimentalresearch with the TRIP titanium design project, building on his experience as a member


12/50

12

of last years MatSci 390 Materials Design titanium project. He will perform Bolling-Richman tensile tests to measure the Ms

temperature of the reference Ti5111 alloy toprovide an experimental calibration point for toughening models.

Table 2: Responsibility Allocation Matrix (X = primary, O = secondary)

Responsibilities Klomjit Stoerzinger Sun Weil Zhou Lin

Strength

Hall Petch Strengthening X OSolid Solution O X

SCC Constraints X OToughening

Frictional work O XVolume change X O

Density Functional Theory X phase stability X O

Ti5111 stabilitymeasurement X

Cost O X

4 System Structure

Figure 3: System Chart


13/50

13

Systems engineering has had great success in materials design21. This method ofengineering works by optimizing a hierarchy of subsystems where the requirements areset at the highest level: property priorities are optimized by materials structure, which iscontrolled by processing, see Figure 3. For the design of this particular alloy, the primaryperformance requirements are a high strength (equivalent to that of Ti64), high fracture

toughness (equivalent to Ti5111), and resistance to stress corrosion cracking. Alloystrength and corrosion resistance is provided by grain refinement and the solid solutionstrengthening of the phase. Toughness is increased by optimized martensitictransformation of the phase during deformation. A balance of both properties ismaintained with the prevention of the formation of embrittling phases such as Ti3Al. Asequence of processing steps is used to control microstructure. The initial cooling rateand annealing provide grain refinement and solution strengthening for the phase, whilethe secondary anneal and subsequent cooling affect the final composition determininghow effectively strain induced martensitic transformations will act as a source oftoughening.

5 Design Approach5.1 Strength ModelThere are several approaches to strengthening a titanium alloy: grain size refinement(Hall-Petch strengthening), interstitial solid solution strengthening, substitutional solidsolution strengthening, precipitation, and the control of crystallographic texture. Basedon the Ti5111 type of alloy as our starting point, our initial approach will emphasizegrain size refinement and solid solution strengthening.

5.1.1 Hall-Petch StrengtheningThe strength of a crystalline material is determined by the force required to movedislocations through the lattice, resulting in macroscopic deformation. Creating moreobstacles for dislocation movement thus improves strength. One such obstacle is grainboundaries.

In their two classic papers, Hall and Petch studied two different material behaviors, butarrived at the same conclusion. Hall published three papers about the influence of grainsize on mechanical properties, while Petch focused on the brittle failure of steels bymeasuring cleavage strength with respect to grain size. The relationship that the twoscientists developed is:22

Equation 2

where D is the average grain diameter, y is the yield stress, 0 is a material constant forthe base stress for dislocation movement, and k is the strengthening coefficient.

It is noted that the Hall-Petch relationship holds true only for grain sizes between 1millimeter and 1 micrometer. Studies on many nanocrystalline materials with grain sizesless than 100 nanometers have shown that the yield strength either remains constant or


14/50

14

decreases with further decrease of grain size. This phenomenon has been termed reverseor inverse Hall-Petch behavior as shown in Figure 4:

Figure 4: Schematic of the variation of hardness H with grain size D23

5.1.2 Solid Solution Strengthening

The solid solution of atoms within the matrix can also act as obstacles to dislocationpropagation. When solid solution atoms are dissolved into the lattice, local stress fieldsare formed that interact with the dislocations. The behavior can differ for the two typesof solid solution alloying: substitutional and interstitial.

The strengthening increment, , arising from solid solution strengthening can beestimated as:

Equation 3

where G is the shear modulus, c is the concentration of the solute atoms, b is the

magnitude of the dislocation Burgers vector, and is the atomic misfit strain. The G, b,and values are material dependent terms and can be grouped into a constant K. Thisallows an estimate of the strengthening effectiveness of a solute from its atomic sizemisfit, and the relationship has been experimentally verified for interstitial-elementadditions in titanium systems.24

Experimentally measured solution strengthening coefficients by Collings24 andHammond25 show a more accurate description of strengthening increment due tosubstitutional metal additions can be made using a linear relationship of strengtheningincrement, , to concentration:

Equation 4

These solid-solution relationships, experimentally determined, are summarized in Table 3for transition elements and in Table 4 for common substitutional and interstitial-elementadditions to titanium alloys. While Table 4 provides coefficients for hardness, Collingsnotes that hardness values in Ti alloys are linearly related to the strength values26, the


15/50

15

experimental relationship between which is determined for the solid-solutionstrengthening model in Section 6.2.

Table 3: Solid-Solution Strengthening of Titanium by Transition Elements(Recreated from Collings, Table 5-4)25

Solute ElementSolid-solutionstrengthening rate, MPa V Cr Mn Fe Co Ni Cu Mo

Per wt. % 19 21 34 46 48 35 14 27Per at. % 20 23 39 54 59 43 18 54

Table 4: Solid-Solution Hardening of Titanium by Substitutional and Interstitial Elements(Recreated from Collings Table 5-3)24

Hardening rate,dHv/dc,

kg mm-2 at. %-1Concrange,at%

Condition* Law**

Slope, b,kg mm-2

at. %-1/2 orkg mm-2

at. %-1

Intercept,a,

kg mm-1/2

Correlationcoefficient,

% At 0.1at. %

At 1.0at%

(a) Substitutional additionsAl 0-10 100h/850C/I

c 15 102 99.6 - 15

Ga 0-5 As-cast c 24 108 99 - 24Si 0-2 1h/100C/IB

c 39 125 83 - 39

Ge 0-5 1h/100C/IB

c 33 120 98 - 33Sn 0-7 As-cast c 24 112 99 - 24

(b) Interstitial-element additionsB 0-0.2 120h/800C/I

c

1/2 218 110 92 344 109C 0-0.5 120h/800C/I

c1/2 170 104 99.9 269 85

N 0-5 120h/800C/Ic

1/2

239 98 99.8 678 120O 0-3 120h/800C/I

c1/2 194 100 99.9 307 97

* IBQ=Ice Brine Quenched**Data fitted to eitherHv = a + bc orHv = a + bc

1/2

5.2 Transformation Toughening5.2.1 TRIP Steels and CeramicsTRansformation-induced plasticity (TRIP) steels have demonstrated great promise byoffering good ductility and toughness at high strength. Transformation plasticity resultsfrom mechanical transformation of a metastable austenite phase at operating

temperatures. Strain at a crack tip triggers the austenite to martensite transformation,enhancing strain hardening to stabilize flow against localization. Overall toughness canbe greatly improved by this mechanism.

Utilized for ceramics as well as metals, transformation toughening is also effective inbrittle fracture, but not to the same extent as ductile fracture. In brittle fracture,transformation shear and dilation greatly increases the fracture process zone volume and


16/50

16

subsequently the toughening interaction. The transformation toughening in brittle solidsscales with the square of the transformation dilation.29

In ductile solids, transformation toughening occurs on three structural scales. At thelargest scale, the transformation zone is enlarged because transformation hardening near

the crack tip delays shear localization in this region. At a smaller scale, thetransformation also delays microvoid-softening. These microvoids assist in crackpropagation, so in limiting their growth, the fracture is restricted. This is the largesttoughening effect on the ductile material. Finally, the inhibited shear localization in thetransformation zone can promote crack branching, which in turn increases the fractureprocess zone size. The combination of these factors leads to a greater toughening effect inductile versus brittle solids, with JIC toughness increment scaling with volume change tothe third power.29

5.2.2 Martensitic Transformation in Titanium AlloysThe concept of transformation-induced plasticity may be extended to titanium alloys,

exploiting martensitic transformation of the parent phase. Although this process mayoccur spontaneously on cooling, it is desirable to induce the transformation via plasticstrain to enhance toughness.27 Beta-stabilizers, such as Mo and V, may be added tocontrol the stability of a metastable parent phase at operating temperatures.

Figure 5 shows the dependence of stress-assisted and strain-induced martensitictransformations on stress and temperature. Ms is the temperature at which martensitictransformation begins upon cooling; Ms

is the temperature at which stress-assistedtransformation occurs at a stress level equal to the yield stress of the parent phase, and Mdthe temperature above which no deformation-induced transformation occurs.29 A stress-assisted martensitic transformation may occur when the temperature lies between Ms andM

s

where transformation controls yielding. In addition to lowering the yieldingstrength, large martensitic plates form in this region which can reduce toughness. Incontrast, formation of fine strain-induced transformation increases toughness, and willoccur at a temperature between Ms

and Md. The largest increase in toughness occurs atjust above Ms

. These two regimes of transformation are delineated in Figure 5.

Due to the interaction of hydrostatic stress with the transformation volume change, thecharacteristic mechanical transformation temperature, Ms

, strongly depends on stressstate. According to the equivalent stress plot of Figure 6, Ms

under uniaxial tensiondiffers from that for the triaxial stress at a crack tip. Since uniaxial tension determinesuniform ductility and the crack tip stress state dictates fracture toughness, it is difficult to

optimize transformation stability for both uniform ductility and toughness at the sametemperature. Because improving fracture toughness is a primary goal of this project, Ms

will be optimized for the crack-tip stress state.


17/50

17

Figure 5: Stress and temperature relations for stress-assisted and strain-induced martensitictransformations.28

Figure 6: Martensitic transformation temperature for uniaxial tension and crack-tip .29,30

5.2.3 Modeling the Martensitic Transformation in Titanium

A quantitative model of martensitic transformation in titanium may be derived byadapting principles established in steels. The general Olson-Cohen model describes theheterogeneous nucleation of martensite. The driving force for transformation of theparent phase to martensite is composed of mechanical and chemical components.31


18/50

18

Equation 5

Here Gtot is the total free energy change of the martensitic transformation, Gchem is thechemical free energy difference between parent and martensite phases at a giventemperature in units J/mol. Gchem values are computed by ThermoCalc using thelicensed Thermotech Ti-DATA-v3 thermodynamic database. Gmech is given by thefollowing equation:34

Equation 6

The three terms in Equation 6 have been developed over many years from steel research.Patel and Cohen32 derived the first term in Equation 6 from the known transformation

shear strain for martensitic transformations in steel alloys where is the equivalentstress. Since the transformation strains in steels are ~20% and those in Ti are ~14%,33 thecoefficient in the first term is reduced by a factor of 0.7 to accommodate the reduction intransformation strain in Ti. The second term describes the effect of hydrostatic stress, h,and parent to martensite volume change V/V on the driving force. The h term is

described by for a crack tip stress state and for a uniaxial

tension stress state; all stress units in Equation 6 in MPa. The volume change may befound by fitting lattice parameter measurements of parent and martensite phases in Tiwith changes in composition. This composition dependence can be described by thesame Redlich-Kister polynomials employed in the ThermoCalc database. The third termin the equation is based on analysis of the Cech-Turnbull small particle experiments,defining a potency distribution of the heterogeneous nucleation sites controllingmartensitic transformations. Cohen et al. extended this exponential nucleation sitedistribution, adding the effect of applied stress to the effective potency distribution.34 Bycombining the statistical model of structural potency distribution with a driving-forcedistribution for random orientation distribution of nucleation sites, relations wereobtained for stress-assisted transformation plasticity, and the nonlinear expression forGmech()was determined.

The Olson-Cohen model31 further predicts that martensitic nucleation occurs at a criticalfree energy change:

Equation 7

Equation 8


19/50

19

Here Gn is a function of nucleation site potency, G0, particle volume Vpof the

transforming phase, a reference V0 and a proportionality factor K. The ln term inEquation 8 reflects the increased stability of the parent phase when small particle volumereduces the characteristic potency of available nucleation sites. The boundary betweenmicroscopic and macroscopic behaviors is determined by the reference volume, defined

as the volume of a sphere of diameter 100m.

34

As the particle volume increases stabilityof the phase decreases.

Wf is the frictional work opposing glide of the martensitic interface in the solid solution.As discussed in Section 6.3.4, analysis of transformation data in Ti alloys suggests thisfriction is a linear function of composition:

Equation 9

Ki serves as the proportionality constant andXi is the atomic fraction of alloying element

i. This linear relationship is equivalent to the linear relationship of solid solutionstrengthening for slip measured by Collings.24

When the testing or use temperature is T= Ms and the stress applied =ys, the total free

energy change may be set equal to Gcrit, yielding:

Equation 10

as the basis for predicting Ms. The desired Ms

for this design project is roomtemperature (300K or 27C) and the target yield strength is 120ksi or 827MPa.

5.2.4 Ab-initio Calculations of Molar Volume for Control of TransformationVolume Change

Application of transformation toughening principles established in steels to Ti alloys hasalready been demonstrated in a system consisting of-Ti-Al-V particles in a -Ti-Alintermetallic alloy by Grujicic.35 He assumed that toughening follows the samedependence on thermodynamic stability of the parent phase and volume change duringthe martensitic transformation as in steels. Applying these same concepts to our design,the phase should be well-stabilized to promote a strain-induced transformation. Thetransformation itself should generate as large a volume change as possible.

One of the many computational methods now used by materials engineers is DensityFunctional Theory (DFT), a quantum mechanical method that has proven extremelysuccessful in describing a wide range of solid-state systems. The foundation of DFT isformed by the two Hohnberg-Kohn theorems, developed in 1964. The first theorem statesthat the ground-state properties of a many-electron system can be uniquely described byits three-dimensional electron density. Finding the total electronic-energy of acomplicated system using this approach is significantly cheaper computationally thansolving for the energy of a many-body wave function. The second theorem states that the


20/50

20

correct ground-state electron density will effectively minimize the energy functional ofthe system.

One of the most elementary tasks in DFT is determining the molar volume of a material.However, this is hindered by one of the fundamental difficulties in DFT - that is,

determining a suitable exchange-correlation for approximation of the energycontributions from the electron density. Two most prominent methods are the LocalDensity Approximation (LDA) and the Generalized Gradient Approximation (GGA)exchange correlations. LDA approximates the contribution to electronic energy byassuming that a volume element constitutes a uniform homogeneous electron gas,whereas GGA also considers the gradient of the electron density within that element.GGA tends to give results more consistent with experiment, and so we will performmolar volume calculations of different binary titanium phases using the GGA exchangecorrelation. Because there are many calculations, we will reduce time by usingpseudopotentials by Perdew and Wang36 instead of full-potential LAPW calculations.These DFT calculations will first be applied to cases where experimental data are

available to assess model accuracy. The technique will then be applied to assemble amolar volume database for all components of interest for this project. As mentionedearlier, the database will employ the same Redlich-Kister polynomial format employedby the ThermoCalc software.

In addition, DFT can be utilized to map relative energies at 0K of the phases of interestfor comparison with ThermoCalc database predictions. Because the electronic total-energy of a material is a direct function of its volume and lattice parameters, it is possibleto determine energetic minima and metastable diffusionless phases by relaxing aninherently unstable structure to a ground state minimum, where lattice parameters can bedetermined.

The martensitic lattice transformation of titanium is described by the Bain distortion,whereby BCC titanium deforms uniformly into an HCP structure. Although highlyalloyed titanium is observed to exhibit an orthorhombic structure (termed ), whichcorresponds to an incomplete BCCHCP transformation13, the volume change in amartensitic transformation can be well-approximated by modeling the HCP cell.* Theprimitive-cell to be run in DFT is generated by placing titanium and its alloying atoms ona HCP lattice. DFT relaxation of this transformed cell should allow prediction of thecomposition dependence of the axial ratios as well as the molar volumes of thesestructures, pictured below in Figure 7.

* Originally the orthorhombic cell was modeled by applying a transformation to the unit BCC cell, althoughit was found to naturally relax back to either the BCC or HCP cell energetically.


21/50

21

Figure 7: DFT will model the volume change of a Bain deformation of a BCC phase of binary Ti-Xalloys (left) to an orthorhombic structure (right), approximated by an HCP lattice.

5.2.5 Transformation Stability MeasurementsAs represented in Figure 5, a reversal in the temperature of yield strength defines the Ms

temperature in uniaxial tension. The test for MS temperature is done following theBolling-Richman test method.37 Tensile tests were performed on a single flat dogbonespecimen in an enclosed thermal temperature controlling device. The temperature of thechamber is set to 180C with a loading rate of 0.5mm/min. When the stress-strain curveextends into the plastic region where the slope decreases, the sample is unloaded. Aftereach loading and unloading sequence, the temperature is reduced by 20C and thesequence is repeated. Cooling is achieved either by air injection or nitrogen gas injectionto the lowest attainable temperature of -90C is reached.

5.3 Cost ModelAs discussed earlier in Section 2.2.4 the cost of producing Ti alloys is dictated by thealloying elements once the processing costs are assumed to be similar to current Ti platealloys. The cost of elements generally used in Ti alloys is listed in Table 5, along withtheir price ranges and average prices. These values were obtained from the CES 2008database10. A second case for cost of Ti is also listed, corresponding to projected costreduction of the new Ti production processes.

It is readily apparent that the cost of Ti alloys tends to be high by virtue of the fact thatthe majority of the composition is Ti, a relatively expensive metal. Final alloy cost willtherefore be sensitive to the effectiveness of the new Ti production processes. The use ofexpensive alloying elements, such as vanadium, can also dramatically increase the cost ofthe alloys. The calculated raw material cost of Ti alloys of interest for marine andautomotive applications is listed in Table 6. These costs are calculated directly from thecompositions by weight:

Equation 11


22/50

22

where Wi and Ci are the weight fractions and costs per weight of alloying element i,respectively. As expected, Ti64, with high V content, is the most expensive alloy,whereas Ti5111 is 30-40% lower in cost. In order to design a cost-efficient Ti alloy thiscost model will be applied.

Table 5: Costs of elements in Titanium Alloys10

ElementPrice Range

(USD/lb) AverageTi (1) $36.60 $40.20 $38.40Ti (2) $24.40 $26.80 $25.60

V $527.00 $658.00 $592.50Ta $188.00 $254.00 $221.00Nb $84.70 $122.00 $103.35Ni $19.20 $21.10 $20.15Mo $12.00 $15.00 $13.50

Zr $12.40 $13.60 $13.00Sn $6.02 $6.62 $6.32Si $4.14 $6.87 $5.51Cr $3.49 $3.84 $3.67Cu $3.05 $3.36 $3.21Al $1.14 $1.25 $1.20Fe $0.35 $0.38 $0.37

Table 6: Costs of Titanium Alloys

Cost (USD/lb)Titanium Alloys With Ti(1) With Ti(2)Ti5111 (Ti-5Al-1Sn-1V-1Zr-0.8Mo) $41.26 $29.59Ti64 (Ti-6Al-4V-0.25Fe) $58.24 $46.75

6 Design Modeling

6.1 Hall-Petch Grain Size RefinementThe Hall-Petch relationship was used to first assess if the yield strength of a Ti alloycould be increased by reducing the grain size to meet the desired final yield strength of120ksi (827MPa) through an adjustment of the processing. To quantify the relationship

between grain size and yield strength in the system of interest, the values for thereference alloy Ti5111 processed with different schemes (slow cooled, fast quenched ofwrought Ti and SPS Ti), resulting in different microstructures, are used (Table 7). Thewrought material was provided by the Navy and the SPS Ti5111 alloys were powderprocessed in the doctoral research of Jamie Tran. The slow cooled alloys are firstbrought to 30C above the -transus for 30minutes and cooled at 15C/min to roomtemperature. The alloy is then held at 30C below the -transus for another 30min andcooled to room temperature at 15C/min. For fast quenched alloys, the alloy is first


23/50

23

brought to 30C above the -transus for 30minutes and rapidly quenched to roomtemperature with helium jets, before being held at 30C below the -transus for another30min and cooled to room temperature at 15C/min. The fastest quenching rate for theproduction of Ti plates is estimated around 1000C/min.38

Because the spark plasma sintered (SPS) alloys are powder processed, there is excessoxygen when compared to the wrought alloys. The excess oxygen increases the hardnessdue to solid solution hardening. To compare wrought data with SPS data, the increase inhardness due to excess oxygen is calculated knowing the coefficient for oxygen solidsolution strengthening is 194 kg mm-2 at%-1/2 (Table 4) and the amount of oxygen in theSPS and wrought alloys. The hardness from oxygen is calculated and subtracted from theoverall hardness. The hardness (HVN) is converted to yield strength (Y.S.) with modelspresented in section 6.2.

Table 7: Strength and Average Lineal Intercept Measurements for Different Processing Routes

Ti5111 (m) HVN O at%

Hardnessreduction to

compensatefor excess

oxygen

Strength(MPa)

wrought slow cooled 4.10 249 0.245 0 583wrought quenched 3.45 297 0.245 0 695SPS slow cooled* 5.12 365 1.014 99.33 622SPS quenched* 2.72 405 1.014 99.33 715

*Spark Plasma Sintered

6.1.1 Lineal Intercept Measurement

The average lineal intercept length ( ) of plates in these structures was determined in

the doctoral research of Jamie Tran.11

Following ASTM E 112 9639

, Standard TestMethods for Determining Average Grain Size, a circular intercept procedure was used tomeasure the average lineal intercept length of plates. As stated in the standard, the useof circular test lines rather than straight test lines automatically compensates fordepartures from equiaxed grain shapes, without biasing any direction. For this project theHilliard Single-Circle Procedure is used.

Several digital optical micrographs of processing route are obtained at 50X magnificationwhere is the light phase and is the dark phase (Figure 8 left). Imaging software isthen used to threshold the image to clearly distinguish phase boundaries (Figure 8 right).In this case, the phases are converted to red and phases are converted to white. A

circle is randomly applied to the microscope image at 50X magnification, making surethe circle diameter is not smaller than the largest observed grains to ensure arepresentative distribution of sizes. Every point on the circle intersecting the phase isdeleted leaving an image similar to Figure 9. Each lineal intercept length is calculated bycounting the intercepts on the test line and tabulated to calculate an average. Themeasurement is taken as our measure of grain size in these microstructures.


24/50

24

Figure 8: (Left) Optical micrograph Ti5111 wrought fast quenched 50x magnification. (Right)Threshold image with phase colored red and phase colored white.

Figure 9: Example of circle with i ntercept region erased

6.1.2 Grain Size Modeling

With the data from Table 7, yield strength (MPa) can be plotted versus average linealintercept value -1/2 in m-1/2 (Figure 10) to determine the Hall-Petch coefficients.

Figure 10: Graph of yield strength versus average linear intercept of the plates-1/2 for Ti5111


25/50

25

These four data points give the following constants for the Hall-Petch relations:

Equation 12

Rearranging the variables

Equation 13

From the above equation, in order to increase yield strength of Ti5111 to 120 ksi or 827MPa using only the mechanism of grain size refinement, the value would have to bereduced to 1.72 m.

The Hall-Petch coefficients are calculated from plots of stresses in commercially pure

(CP) Ti with grain size measurement .40 However, to compare data from this report tothese values, the is converted to an value. According to ASTM E3112-9639, the

conversion is . The measured 0 for CP Ti ranges from 424-715 MPa, while

the value for wrought Ti5111 is lower at 281 MPa. For CP Ti the Hall-Petch coefficientkranges from 0.136-0.233 MPa m1/2, while the calculated strengthening coefficient kforTi5111is 0.716 MPa m1/2. The difference in results may be due to the differingmicrostructures where Ti5111 has a basket weave widmanstatten microstructure and CPTi has equaixed grains.

6.2 Solid Solution Strengthening

A contribution to the 20 ksi, or138 MPa, strength increase desired of this alloy can alsobe provided by increased solution strengthening of the phase. Levels of stabilizingelements such as V, Fe, and Mo, will be highly constrained by composition control of the-phase for transformation toughening, subsequently.24 Another option is increasing thecontent of phase substitutional elements, such as Al, Sn, and Si by a fraction of apercent, but with the consequence of reducing the corrosion resistance of the alloy.

Values are available for the hardness coefficient per atomic percent of elements Al, Si,and Sn and strength coefficient per atomic percent of elements Mo, V, and Fe in Tialloys as shown in Section 5.1.2..24 A linear proportionality between microhardness andstrength was determined using Vickers hardness and yield strength measurements from

the doctoral research of Jamie Tran (Figure 11). This relationship was used to convertbetween hardness and strength in obtaining the strength coefficients of Table 8. Theeffect of Zr was assumed negligible. Table 8 lists the hardness and strength coefficientsfor all alloying elements in Ti5111.


26/50

26

Figure 11: Yield Strength vs. MicroHardness for Ti5111

Table 8: Slopes of Solid Solution Effects of Alloying Elements in Ti24,26

ElementSSH slope

(kg at%-1mm-2)

SSS slope(*106N at%-1m-2)

MPa/at%Al 15* 35Fe 23* 54

Mo 23* 54Si 39 91*Sn 24 56*V 9 20*

* Coefficient was converted with the empirical relationship of Figure 11

Using the above values from the literature, a model was created to estimate the hardnessand strength of near Ti alloys, from solid solution hardening, from the content of V, Fe,Mo, Al, Sn, and Si approximating the alloy as 100% phase. Linear relationships andlinear superposition of element effects were assumed. A spreadsheet to calculate the

solid solution strength is created with the overall composition in at% as an input, shownbelow in Figure 12.


27/50

27

Figure 12: Model Predicting Solid Solution Strengthening

The total strength of the design alloy will be a superposition of the Hall-Petchstrengthening effects with the solid solution strengthening effects41:

Equation 14

6.3 Martensitic Transformation Toughening6.3.1 Volume Change of Martensitic Transformation in Titanium

The composition dependence of the martensitic transformation volume change can bedescribed via a Redlich-Kister equation as employed in the ThermoCalc databasestructure. Coefficients for the Redlich-Kister fit have been calculated using availableliterature data35, 42,434445,46, and calculated DFT data, described in Section 5.2.4. Becauseliterature values of the atomic volume are only available for Ti-Mo, Ti-V, and Ti-V-Al

alloys, DFT calculations are performed to estimate the atomic volumes of other elementsfor the binary interaction parameters with Ti.

6.3.2 DFT Atomic Volume CalculationsDFT calculations are used to make first-principles predictions of the volume change.After these atomic volumes are found, the Redlich-Kister model can be fit to the data tointerpolate between points. As proof of concept, preliminary DFT modeling on thevolume change in the Ti-V system was shown to confirm good trend fits between DFTcalculations and experimental values, albeit with a displacement (Figure 17). Thisdisplacement is not unexpected, as the DFT calculations are carried out at T=0Kwhilethe data represents 300K. In addition, there is expected to be some element of tight-

binding between atoms in DFT calculations, leading to lower bulk volume. However,because the curve shape of the DFT data has strong correlation to experiment, acalibration increment can be applied to volumes uniformly to approximate the thermalexpansion from 0 to 300K. The systematic increment employed is 0.62083/atom and0.57343/atom for the and martensite phase, respectively.


28/50

28

Figure 13: Redlich-Kister Curve Fit to the Beta Phase of Experimental and DFT values for Ti-V

Table 9 and Figure 14 show values of phase atomic volume calculations for binary Ti-X alloys, where X is Al, Fe, Mo, Si, Sn, Ti, V, and Zr. Alloy solutions at the 25% and50% concentrations are represented by ordered BCC structures corresponding to the A3BL21, (Heusler) and AB B2 (CsCl) structures, respectively. The heusler phase for Mo wasfound to be energetically unstable, and so that point was removed. Table 10 and Figure15 show the calculations for the martensitic volume approximations with HCP phase. ForHCP, only the equiatomic mixed phase was modeled. Also, calculations for pure Feended up being extremely unstable energetically, and so the volume data was taken fromempirical measurements.

Table 9: Atomic Volume Calculations (Angstroms3/Atom)

Heusler (Ti3X)xi=25%

BCC-B2 (TiX)xi=50%

Pure BCC Phasexi=100%

Al 17.14 16.73 17.74Fe 15.12 13.35 10.87Mo - 16.28 16.28Si 16.04 15.69 15.39Sn 18.36 20.39 28.43Ti - - 17.47

V 16.32 15.65 13.81Zr 18.89 20.39 23.52


29/50

29

Figure 14: DFT atomic volume values for Phase

Table 10: Martensite Atomic Volume Calculations (Angstroms3/Atom)

HCP (TiX)xi=50%

Pure HCP Phasexi=100%

Al 17.12 17.33Fe 13.67Mo 16.78 14.14Si 15.54 15.11Sn 20.56 28.42V 15.81 14.29Zr 20.89 23.88

Ti - 17.65


30/50

30

Figure 15: DFT atomic volume values for Martensite Phase

6.3.3 Redlich-Kister Fitting to Atomic Volume Data

All volume data used in fitting is available in the Error! Reference source not found..Equation 15 and Equation 16 below both show the Redlich-Kister equation used to modelthe molar volume of both phases for Ti-V. In the equation, Vi is the molar volume of thealloy with pure component i, Xi is the atomic fraction, and is a an interaction

parameter equivalent to a regular solution form. Similar equations were used for the otheralloying components.

Equation 15

Equation 16

The solver function in excel is used to iterate through possible values of to find the

coefficient for the least squared fit to the experimental data. The values of theseparameters are given in Table 11 and Table 12.

1

0

12

1

4

1

6

1

8

2

0

2

2

2

4

2

6

2

8

3

0

0 0.2

0.

40.

60.

81

X

i

Atomic

Volume

Fe

A

Zr

S

MV

S


31/50

31

Table 11: Fitting Constants for Ti-Mo.

Ti-Mo Atomic Volume Parameters (3)

VTi 17.45 VTi

17.66

VMo 15.58 VMo

14.14

-1.76 -2.97

Table 12: Fitting Constants for Ti-V.

Ti-V Atomic Volume Parameters (3)

VTi 17.45 VTi

17.66

VV 13.84 VV

14.29

0.37 -0.069

The available experimental data points and appropriate DFT calculations of the atomic

volume of Ti-V and Ti-Mo binary alloys in both and martensitic phases are shown inFigure 16andFigure 17 respectively. The Redlich-Kister fit for each phase is shown tocompare with the data. Binary interaction parameters for all other elements with Ti arecomputed from DFT values.

Figure 16: Dependence of Atomic Volume in Ti-V on Composition for and Martensite Phases45


32/50

32

Figure 17: Dependence of Atomic Volume in Ti-Mo on Composition for and Martensite Phases46

Through the research of Grujicic,35 there is available ternary, Ti-Al-V, atomic volumedata. This data is used to compute the binary interaction parameter and ternary

interaction parameter . The form of the Redlich-Kister equation used for ternary

Ti-V-Al atomic volume data is as follows:

Equation 17

where the binary interactions of Ti-V and Ti-Al are fixed from calculations with the

respective binary data. This approach is taken rather than first combining all data tocalculate all interaction parameters at once, as the ternary data is heavily weightedtowards Ti lean sections of the Ti-Al-V ternary diagram.

Table 13: Fitting Constants for Ti-V-Al

Ti-V-Al Atomic Volume Parameters

17.45 17.66

13.84 14.29

17.74 17.34

0.37 -0.07-2.96 -1.50

-4.59 -3.82

-12.29 -22.83


33/50

33

6.3.4 Interfacial Friction of the Martensitic Transformation in TitaniumFollowing Equation 8 and Equation 9 discussed in Section 5.2.3, the critical free energychange for martensitic transformation can be expressed as:

Equation 18

Compiling data for the composition dependence of Ms in binary Ti alloys, the Wfinterfacial friction term for martensitic transformation in Ti is found to show a lineardependence on the atomic fraction of most alloying elements agreeing with the linearrelationship found for solid solution strengthening. The following graphical method isused to solve for the proportionality constantKi (for Wfcalculations) and G0.ThermoCalc is first used to generate values forGchem. at Ms. A plot of -Gchem versusatomic fractionXi results in a line for every element with the exception of tin (Figure 18),which follows the x0.5 parabolic behavior observed for martensitic transformation inferrous alloys.

The value ofG0 is determined by averaging the y-intercepts of all two-componentsystems.Ki is then estimated to be the slope of a line constructed between G0 and thecenter of each data set. Having found G0 andKi for each binary system, it is possible topredict the critical chemical driving force for martensitic transformation at a given atomicfraction of each alloying element.

Figure 18: Chemical driving force of transformation at Ms as a function of atomic fraction

G0was determined to be 48 J/mol, and a table ofKi values is given in Table 14. Note thatthe proportionality constant for Sn satisfies Equation 19, where the work of friction


34/50

34

depends on atomic fraction to the power. The full model for the work of friction isgiven in Equation 20.

Equation 19

Equation 20

Table 14: Ki values of alloying elements in Ti5111

AlloyingElement

Ki (J/mol)

Zr 405V 2530Fe 4260Al 7640Mo 9557Si 13000Sn 3360

All Ms values for relevant binary Ti-X alloys are available except for binary Ti-Si. TheKi value for Si is estimated using an alternative method. As the mechanism of solidsolution strengthening and work of friction are the same, a correlation between the knownsolid solution strengthening parameter to the measured Ki values is found and applied toestimate a KSi value.

6.3.5 Mscalculations and Measurement

Figure 19 shows a flow chart of the design process proposed to optimize the composition, volume fraction, and dispersion for the design alloy. The optimization ofthe phase parameters is important in order to obtain an increase in toughness as a resultof volume change upon martensitic transformation. The iterative nature of this processstems from determining an initial composition and annealing temperature, yielding phase parameters and inputs of the Olson-Cohen model, from which Ms

is determined,and the process is continued until a final composition is obtained from the highlightedresults shown below.

To provide an important calibration point for the current Ti5111 alloy, flat dog bonetensile samples with cross section 5mm x 1mm and gauge length of 10mm weremachined and tensile tested. The Bolling-Richman tensile tests for the reference Ti5111alloy is shown in Figure 20 where the Ms

temperature is estimated to be -67C. Inaddition this data can be used to obtain a YS vs T trendline. The Ms

value for a materialis dependent upon its yield strength, which is itself dependent on temperature. Thereversal of the temperature dependence of the yield strength defines the Ms

temperatureof the phase in Ti5111 denoted by the vertical arrow in Figure 20 and Figure 21. The


35/50

35

yield stress vs temperature dependence is depicted in Figure 21 for data measured onTi5111 1 thick plate giving a d/dT of -1.101 MPa K-1. For the design alloy with adesired strength value of 120ksi or 827 MPa at 300K, this relationship is shifted upwardsto use for Ms

calculations as shown in Figure 21.

Figure 19: Iterative Flow Chart for Alloy Design, Highlighted Sections Lead to Final Composition


36/50


37/50

37

6.3.6 Mscalculations for Ti5111 and Model Calibration

For Ms calculations, the composition of the phase in Ti5111 is needed and can be

calculated and validated by LEAP microanalysis. The nonequilibrium and phasecompositions formed during nonisothermal processing can be modeled using theDIffusion Controlled TRAnsformation (DICTRA) software. DICTRA with a proper

mobility database for the titanium system can solve the flux balance equations of an alloysystem during various processing phases such as cooling from an annealing temperature.

Using DICTRA with a mobility database previously validated by diffusion coupleexperiments in the senior project of Eric Simpson,48 a 1-D simulation oftransformation in Ti5111 by plate thickening during the cooling process is modeled.Figure 22 compares the retained phase fraction upon cooling between DICTRA coolingsimulations and equilibrium predictions of the Thermotech Ti-DATA-v3 database. Theretained phase fraction from the DICTRA simulations correspond well with the 10-20%measured in conventionally processed Ti5111. An estimate of the amount of elementpartitioning that takes place during cooling is also modeled and compared to

experimental data from the Local Electrode Atom Probe (LEAP) (Figure 23).

A three dimensional image of individual atoms is obtained as the LEAP removes atomsfrom an atomically sharp tip. The atom probe microscope uses time-of-flight massspectrometry to identify individual atoms, and uses point-projection microscopy toidentify original atom locations in three dimensions. This technique was used in thedoctoral research of Jamie Tran to analyze a Ti5111 specimen, shown in Figure 23.11

Figure 22: phase fraction with temperature from DICTRA simulations compared to equilbriumpredictions


38/50

38

From composition profiles simulated by DICTRA (Figure 24 left) it is confirmed that Mois a very strong partitioning element and can be used to define the and regions in theLEAP analysis. A proximity histogram (proxigram), a function in the IVAS atom-probeanalysis software used to find the composition profiles in LEAP tomographicreconstructions, is then created (Figure 24 right).

Figure 23: Reconstruction of Ti5111 LEAP sample showing thin platelet in retained region11

Figure 24: Positional composition of Ti5111 alloy from DICTRA simulations (left) and LEAPmicroanalysis (right)11


39/50

39

The composition of the phase of conventionally processed Ti5111 material (Table 15)is used as an input to our transformation model to predict the Ms temperature of thealloy in uniaxial tension.

Table 15: composition measured from LEAP microanalysis in decreasing concentration

Element composition(Xi: at fract)

V 0.0642

Mo 0.0482

Al 0.0315

Fe 0.0111

Sn 0.0071

Zr 0.0058

Si 0.0019

Assuming a macroscopic particle size where Vp > Vo: Gn=Go=48J/mol, the Ms

(ut) ofTi5111 was predicted to be 74C. As presented in section 6.3.5 Bolling-Richman49tensile testing was preformed to measure the Ms

temperature of Ti5111 with a singletensile specimen. The tensile specimen is taken into a chamber at 180C, tension isapplied to create a stress-strain curve until a yield strength can be measured. Thechamber temperature is then lowered 20 degrees to 160C and strained to measure theyield strength at that temperature. This process is continued to -90C. The measuredMs temperature is the temperature where the drop in yield stress with temperature ismeasured. As shown in Figure 21, the Ms

(ut) of Ti5111 is measured to be -67C; 141C

lower than that of the predicted model due to the assumption of a macroscopic particlesize. This data was used as a calibration for the transformation toughening model insection 6.3.5 for the proportionality constant, K, in Equation 8 reproduced here:

Equation 21

For the model to predict an Ms temperature of -67C for Ti5111, a Gn value of 778 J/mol

is needed. Since G0 remains 48, the second term in the equation is equal to 730J/mol.

The reference volume V0 is 5.24x10

5

m

3

which is the volume of a 100 m diametersphere. Vp,is estimated from micrographs of Ti5111. The phase is modeled as a squareplate with lengths of 40m, and thickness of 1m for a Vp of 1600 m

3. To calibrate themodel to Ti5111, Gn=778J/mol,Kis equal to -4230 J/mol. This value is comparable tothat evaluated for steels, when normalized by the shear modulus.34


40/50

40

Figure 25: Ti 5111 Ms as a function of annealing temperature for crack tip and uniaxial tension

stress states

Figure 25 shows Ms calculations using the calibrated transformation model for both

crack tip and uniaxial tension stress states vs. annealing temperatures. To achieve a roomtemperature Ms

(300K or 27C), the Ti5111 must be annealed at 737C and 740C for

crack-tip and uniaxial tension stress states respectively, until equilibrium composition isachieved and subsequent quenching will retain the appropriate -phase composition. Thelower Ms

temperature of the conventionally processed Ti5111 material reflects the slowcool of the alloy from a temperature of 954C at 15C/min. The conventionallyprocessed (slow cool) Ti5111 composition is equivalent to an equilibrium composition707C corresponding to the uniaxial tension stress state measured Ms

.

7 Design IntegrationThe project objective, to design a Ti alloy with 120 ksi yield strength (comparable to thatof Ti64), high fracture toughness and stress corrosion resistance (comparable to that ofTi5111), at a cost lower than that of Ti64, can be achieved using the models developed

over a range of compositions.

7.1 Design Constraints7.1.1 Composition constraints

Initial designs employ the same alloying components as our reference alloy Ti5111.Ti5111 has seven alloying elements and the models for strengthening and transformationtoughening are developed for these elements. In Table 16 a summary of the relative


41/50

41

effects of each element on , volume fraction, SCC resistance and cost is

presented where the + and symbols indicate the affect on the alloy if the element isincreased. Increases in all values except cost are desired.

Table 16: Summary of Alloying Element Effects

Element V/V volumefraction

SCCresistance

Cost ($/lb)

Al ++ --

(


42/50

42

Figure 26: Effect of atomic fraction on volume change

7.1.2 -phase fraction constraintsAdditionally, the goal of this design is for the -phase fraction to be similar to that inTi5111; 10-20%. The phase provides our principal mechanism to promote highertoughness in the alloy. It is also important to limit the amount of phase because as the phase fraction increases into the + alloy region, the segregation from stabilizers isharder to control during heating processes such as welding. This is why near- alloys areconsidered weldable. As a result, in determining the -phase fraction in our final alloy,the goal is 15% phase.

7.1.3 Annealing temperature constraints

Another constraint to the design is that Ms

(ct) is set at room temperature (300K) to allowfor optimal martensitic transformation at use temperature. This constraint determines theannealing temperature associated with each alloy composition. In other words, eachoverall design composition will have one associated annealing temperature to obtain thedesired room temperature Ms

(ct) value of 300K. To allow for practical designs, the

annealing temperature is constrained to >600C due to the slow kinetics of alloypartitioning at low temperatures. In addition annealing temperatures


43/50

43

under consideration should have a rate constant higher than that of Ti5111, whereprecipitation rate constants increase with increasing temperature.

7.1.4 Mo partitioning interaction with Fe

Analysis of the change in volume provided from each component give the direction of

chemical change necessary to increase toughness. The two components with the largesteffect on this parameter are Fe and Mo. To maximize volume change, the Fe content ofthe phase should be increased, while Mo of the phase should be decreased.As expected, ThermoCalc calculations showed that increasing the amount of Fe in theoverall composition increased the amount of Fe in the phase. Unexpectedly, theseThermoCalc calculations also showed that increasing Fe content cause Mo to stronglypartition out to the phase thereby decreasing the Mo content in the phase as shown inFigure 27. This is desirable, as decreasing the overall Mo content was previously shownto decrease the total volume fraction of the phase, moving away from the target 15% phase by volume. If this interplay between components was not present, the Mo contentwould have to be decreased to reduce the composition in the phase in order to increase

the volume change, consequentially decreasing the volume fraction of and SCCresistance of the alloy. To compensate, V content would have been increased to achievethe 15% volume fraction of and maintain the SCC resistance of the alloy, therebyincreasing the cost of the alloy. Fortunately, because of the partitioning of Mo with Fecontent, changes to Mo and V content can be avoided and an efficient optimization canbe achieved with an increase in Fe content.

Figure 27: phase partitioning of elements with Fe in alloy content

T=730C


44/50

44

7.2 Final Alloy Composition7.2.1 Composition Refinement

Figure 28: Effect of Fe in atomic percent on volume fraction of beta

Because iron has been identified as having the most significant effect on the volumefraction beta, we varied Fe in order to determine the composition that would provide a15% volume. The data is collected by varying atomic composition of iron while

holding all other alloying components constant (Figure 28). We fit a third order curve tothe resulting beta volume compositions, and interpolated the point where beta volume is15%. This value is 0.858 at% Fe.

7.2.2 Final CompositionThe final overall composition of the proposed design alloy is listed in Table 17. Theamount of Fe in the design is about 1wt%, suggesting the design alloy name should beTi51111 (Titanium five quadruple one).

Table 17: Final Composition of Design Alloy

Element at% wt%Al 8.67 4.99Fe 0.86 1.02Mo 0.44 0.90Si 0.17 0.10Sn 0.39 1.00V 0.92 1.00Zr 0.51 1.00Ti 88.04 89.98

T=730C


45/50

45

7.2.3 Annealing Temperature and Ms

To find the annealing temperature for our desired Ms, we generated three different

phase compositions at different annealing temperatures. Figure 29 shows Ms as a

function of annealing temperature for the two stress states of interest. Since our goal is

transformation toughening, the crack tip stress state is of primary interest. For a roomtemperature transformation, corresponding to an Ms

(ct) of 27C, the annealingtemperature must be 717C or 990K. This corresponds to an Ms

(ut) of -5C which can be

easily validated experimentally.

Figure 29: Final composition Ms as a function of annealing temperature for crack tip and uniaxial

tension stress states

7.2.4 phase composition

The phase composition at an annealing temperature of 717C is found usingThermoCalc. The alloy is ~14 at% phase, and the compositions of alloying elementswithin the phase are shown in Table 18.

crack tip

uniaxial tension


46/50

46

Table 18: phase composition of the design alloy at 717C

Element at% wt%Al 6.35 3.54Fe 5.77 6.66Mo 2.04 4.05

Si 0.22 0.13Sn 0.11 0.28V 2.89 3.04Zr 0.60 1.14Ti 82.02 81.16

The rate constant for coarsening of the designed alloy, determined using CMD at itsannealing temperature of 717C, was found to be 5.45E-19 m2mol/Js. This KLee isgreater than that of Ti5111 at its minimum annealing temperature, where KLee is 4.04E-20m2mol/Js. This verifies increased precipitation rate for the newly designed alloy in

comparison to Ti5111.

7.3 ProcessingThe proposed processing treatment of the design alloy is similar Ti5111. Afterhomogenization of the alloy and hot rolling deformation, there is two-step annealing. InTi5111 the first annealing temperature is 30C above the transus temperature for 30min. Ti alloys annealed above the transus can fully recrystallize in the phase field toproduce a Widmansttten microstructure upon cooling. This annealing temperature mustnot be too high as the grains will rapidly coarsen which leads to lower yield strengths.

The transus is calculated using ThermoCalc and found to be 1212K (939oC) for the

current alloy design compared to 1253K (980C) for Ti5111. Therefore the design alloyTi51111 (Ti5111 + 1wt%Fe) is brought to 969oC, 30oC above the transition temperature,for 30 minutes. Unlike conventionally processed Ti5111, the Ti51111 design alloy willbe quenched after the first annealing step to produce refined martensitic plates andbrought to the second annealing step at 731C to develop the desired 15% phasefraction and composition for the fracture toughness model. After the second annealingstep the alloy is cooled at 15oC/min to room temperature similar to conventionallyprocessed Ti5111.

7.4 Strengthening Results7.4.1 Solid Solution Strengthening

The final alloy composition with Fe content of 0.86at% is input into the solid solutionstrengthening model, detailed in section 6.2, to determine the change in strengthcompared to the reference composition of Ti5111 as a result of a change in the alloyingelements. Using this model the strength is found to increase by 41.83MPa.

7.4.2 Hall-Petch Grain RefinementHall-Petch strengthening supplements SSS to achieve the end strength goal. Thedifference of strength between the goal of 827MPa and the strengthening obtained from


47/50

47

SSS (41.83MPa) is 785.17 MPa, the strength which must be achieved as a result of grainrefinement. Using Equation 13, the lineal intercept length corresponding to this strengthwas found to be 2.02 m which should be achievable by fast cooling. Thismicrostructure, along with the composition and processing previously mentioned, willachieve the desired strength of 120ksi.

7.5 Toughening ResultsHaving determined the design composition of the alloy and the annealing temperatureneeded for Ms

(ct) at 300K, the Gmech, Gchem, Gn, and Wfvalues of the martensitic

transformation model are reported here. Gmech is given by Equation 6, where is our

target yield strength of 120 ksi (827 MPa). Furthermore, h= 3 for the crack tip stressstate, and V/V based on our composition is 1.21%. This volume change compares to0.4% in Ti5111, corresponding to a factor of 3 increase. These values result in a Gmech=-359 J/mol. ThermoCalc is used to determine Gchem, which is -1562 J/mol. Gn,calibrated to experimental results, is 778 J/mol. The total Wfcan be found using thecomposition andKi values calculated in section 6.3.4, and is 1143 J/mol. These values ofGmech, Gchem, Gn, and Wfsum to zero when Ms is at room temperature for that specificstress state. A similar procedure can be used to calculate Gmech for uniaxial tension.Table 19 shows values for both uniaxial tension and crack tip stress states. Note that thetotal does not sum to zero for the uniaxial stress state as the Ms

temperature cannot bethe same for both crack tip and uniaxial stress states.

Table 19: Martensitic Transformation Model for Uniaxial Tension and Crack Tip Stress States

Crack Tip Uniaxial TensionGmech (J/mol) -359 -219Gchem. (J/mol) -1562 -1645

Gn (J/mol) 778 778Wf(J/mol) 1143 1143Total 0 57

8 Conclusion and RecommendationsA new alloy, Ti51111(Ti5111+1wt%Fe) was designed, capable of a high strength of120ksi, an increase in volume change upon martensitic transformation of the phase withoptimized stability for transformation toughening, a lower cost of $29.34 to $40.86,without sacrificing corrosion resistance. This alloy was designed with the constraint of

having a volume fraction of ~15%, enough to utilize the toughness provided by phasevolume change, but not high enough to exceed the weldable near- phase regime. Table20 compares important values predicted for Ti5111 and the design alloy, Ti51111.


48/50

48

Table 20: Comparison of Ti5111 and design alloy

Ti5111 Ti51111 designMs

(ct) -59C 27C

Ms

(ut) -67C -5C phase fraction 10-20% 14%

V/V 0.4% 1.2%

Several models were generated and used in this design, including one of volume change,utilizing Redlich-Kister curve fits of density functional theory calculations, work offriction models employing both thermodynamic and experimental data, -partitioningmodels utilizing atom probe tomography data, solid solution strengthening models, Hall-Petch and grain size predictions, and a cost model. The use of all of these design toolsallowed for all aspects of current titanium alloys to be improved: Ti51111(Ti5111+1wt%Fe) promises greater strength, improved toughness, and lower cost,making it an attractive candidate to evaluate for naval and automotive applications.

Next step recommendations include testing the prediction of Figure 25 that an optimumstability of can be achieved with higher temperature annealing. The corresponding Ms

in uniaxial tension can be tested experimentally as further validation of thetransformation models. The new composition can be made first as small arc meltedbuttons to test phase relations and predicted Ms

(ut) with the single tensile test technique.

Validated stability can be followed by larger scale melts for toughness tests.Arrangements are being made to conduct experiments this summer.

9 AcknowledgementsDoctoral candidate Jamie Tran provided significant data, discussion, and guidance for

this work, without which such a well-explored solution would not have been possible.Professor Olson also provided significant insight and interpretation, for which we arevery grateful. Also the senior project of Eric Simpson gave useful experimental insightinto the microstructure and properties of the reference alloy Ti5111, and the contributionsof previous 390 teams provided a solid foundation upon which this work was built.


49/50

49

10References

1EHKTechnologies; Summary of Emerging Titanium Cost Reduction Technologies. US Department ofEnergy Oak Ridge National Laboratory (2004).2

Cyberalloys 2020: Naval Materials by Design Award #: N00014-07-1-02793 GM High Toughness, High Strength Titanium Wrought Alloys Made by Powder Consolidation;Contract #: P.O. TCS142334 U.S. Congress. P.L. 110-140: Clean Energy Act of 2007. (2007).5 C. Kim and M.L. Holly. Low Cost Titanium for Automobiles. GM Research and Development Center10 (2006) 618.6 Brickey, J.; Chen, C.; Chastain, M.; Lin, F. MSE 390 Report: Ti120 Marine Titanium. NorthwesternUniversity: Evanston, IL (2008).7 Henry, S.D.; Dragolich, K.S.; DiMatteo, N.D. Fatigue Data Book: light structural alloysASMInternational(1995) 264.8

Delmedico, R., J. Fakonas, K. Peter, G. Scott and E. Simpson

Date post:	14-Apr-2018
Category:	Documents
Upload:	ahmadreza-aminian
View:	221 times
Download:	0 times

TRIP Titanium.pdf

Documents