3‘ ,n( ‘ .p, ‘ mm .4.‘ a ‘r_ '. , 64%? ‘ 9-3 .36.: ‘ V m. am. a: 2: < 9‘32: a, 1g. . ,{i‘ifi‘fi’ ' in“! , . ‘ . : .C‘ . NH' ’.".'A'~ hi ‘1‘ . . a @w \ ‘yqfifl‘ ”l- .I' I" . '. Wu "gay ‘ my?! ,, “o'f‘» w A. - 4am; . . 25335334" ”4» mama: +7 ’ fl 2'?! “flak . 31%. n’ U '1 . v . madam:- . r” -a‘ «w . m4" llllllllllllllllllllllUIHIHIllllWIHIIHIIlllllllllllllilll 293 01411 0435 THESOS K...»- This is to certify that the thesis entitled High Temperature Creep Deformation of Gamma—Based Titanium Aluminide presented by Randy S. Beals has been accepted towards fulfillment of the requirements for Wdegree in Material Science fiesta Major professor Date 3/19/95 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution LlBRARY 5 Michigan Statei University PLACE N RETURN BOX to romovo this chockout from your rocord. TO AVOID FINES Mum on or bdoro duo duo. DATE DUE DATE DUE DATE DUE HIGH TEMPERATURE CREEP DEF ORMATION OF GAMMA-BASED TITANIUM ALUMINIDE By Randy S. Beals A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTERS OF SCIENCE Department of Materials Science and Mechanics 1995 r CSpon Complt ConCer Comb'u tion as [he Cre in Gide the allr ture. A temper 0n the ‘ Undem "HA1. ABSTRACT HIGH TEMPERATURE CREEP DEFORMATION OF GAMMA-BASED TITANIUM ALUMINIDE By Randy S. Beats As part of an ongoing research concerning creep deformation mechanism(s) responsible for the creep behavior of ingot investment cast near y—TrAl, a study has been completed which several creep studies where performed and some theoretical arguments concerning the behavior of TiAl where introduced. The theoretical arguments include the combining the composite rule-of-mixture and the power-law Mukerjee-Bird-Dom equa- tion as a mathematical creep deforrnation model. Also, a transitional interface between the gamma and alpha2 constituents is introduced. A literature review has been completed and the creep characteristics of different compositions was explored at different test conditions in order to list the trends that appear in the data. The creep experiments achieved where on the alloy Ti-48Al-2Cr-2Nb and the data obtained was compared to the data in the litera- ture. All the experimental data in the literature and from this study was normalized by the temperature dependence of the diffusively and the shear modulus. The temperature nor- ' malization of values allows the investigator a more accurate view of the stress dependence on the creep deformation. The creep characteristics where then analyzed to improve our understanding of the deformation mechanism(s) responsible for the creep behavior of TiAl. LIST T V1. 5.. F L C (L 5.. 2 «I. illll il‘l'il“ ll I NEN LIST OF FIGURES .............................................................................................. vi LIST OF TABLES ................................................................................................ xi CHAPTER ONE. INTRODUCTION ............................................................... 1 CHAPTER TWO. THEORY ............................................................................. 2 2.1. REVIEW OF CREEP .................................................................................... 2 2.1.1. The high temperature materials problem ........................................ 2 2.1.2. Stages of creep ................................................................................ 3 2.1.3. Temperature effects ......................................................................... 5 2.1.4. Stress effects .................................................................................... 7 2.1.5. Power law relation .......................................................................... 8 2.1.6. Transitions in stress exponent, n ..................................................... 8 2.1.7. Transitions in activation energy, Q ................................................. 9 2.2. CREEP DEFORMATION MECHANISMS .................................................. 11 2.2.1. Diffusion controlled ........................................................................ 12 (a) Nabarro-Hem'ng ...................................................................... 12 (b) Coble ...................................................................................... 13 2.2.2. Dislocation controlled .................................................................... 14 (a) Dislocation glide ..................................................................... 15 (b) Dislocation climb .................................................................... 15 (c) Dislocation glide limited by solute atmospheres ..................... 16 (d) Grain boundary sliding ............................................................ 16 (e) Deformation induced twinning ................................................ 17 2.3. CREEP EQUATIONS .................................................................................. 2.3.1. Power law equation ........................................................................ 2.3.2. Mukerjee-Dorn equation ................................................................ 2.3.3. Power law breakdown .................................................................... 2.3.4. Composite modeling............................... ....................................... CHAPTER THREE. TITANIUM ALUMINIDE TiAl ................................... 3.1 CRYSTAL LATTICE STURCI'URE ............................................................ 3.1.1. L10 ................................................................................................. 3.1.2. D019 .............................................................................................. 3.1.3. Differences between L10 and D019 .............................................. 3.2. MICROSTRUCTURE ................................................................................. 3.2.1. Lamellar structure ........................................................................ 3.2.2. Thermomechanical structure ....................................................... (a) Near-gamma (NG) ................................................................ (b) Duplex (DP) ......................................................................... (c) Nearly lamellar (NL) ............................................................ ((1) Fully lamellar (FL) ............................................................... 3.2.3. Alloying ........................................................................................ (a) Ti-48Al—2Cr-2Nb ................................................................... CHAPTER FOUR. LITERATURE SURVEY OF CREEP IN TiAl ............ 4.1. INTRODUCTION ........................................................................................ 4.1.1. Trade-off approach ........................................................................ 4.1.2. Comparison of creep resistance of different rnicrostructures ........ iii 18 19 19 2() 20 22 22 22 23 24 25 27 28 28 29 29 29 30 31 33 34 34 4.2. PROBLEMS IN UNDRSTANDING CREEP OF TiAl .............................. 4.2.1. Minimum creep rate ..................................................................... 4.2.2. No instantaneous strain ................................................................ 4.2.3. Dynamic recrystalization .............................................................. 4.3. DEFORMATION HISTORY INDEPENDENCE ....................................... 4.4. DIFFUSION CONTROLLED CREEP OF TIA] ........................................ 4.4.1. Self-diffusion of 'I'r-S4Al ............................................................. 4.4.2. Alloys containing Cr ..................................................................... 4.5. DISLOCATION CONTROLLED CREEP IN TrAl .................................... 4.5.1. Twinning ....................................................................................... 4.5.2. Dislocation glide-climb ................................................................. 4.6.3. Geometrical constant A ................................................................. 4.6. DEFORMATION MECHANISM TRANSITION ....................................... 4.6.1. Unique creep behavior of Ii-48A1-2Cr—2Nb ................................. 4.6.2. Aluminum content. ....................................................................... 4.7. COMPOSITE VIEW OF CREEP ............................................................... 4.8. SUMMARY OF CREEP RATES ............................................................... CHAPTER FIVE. CREEP EXPERIMENTS ON Ti-48Al-2Cr-2Nb .......... 5.1. INTRODUCTION ...................................................................................... 5.2. MATERIALS .............................................................................................. 5.3. EXPERIMENTAL PROCEDURE .............................................................. 5.3.1. Open-air ........................................................................................ 5.3.2. Vacuum ......................................................................................... iv 35 35 38 38 40 41 '41 46 47 49 52 55 58 58 59 60 60 5.3.3. Testing techniques ........................................................................ 5.4. EXPERIMENTAL RESULTS ..................................................................... CHAPTER SIX. ANALYSIS ........................................................................... 6.1. INTRODUCTION ....................................................................................... 6.2. THE VARIABILITY OF UNSTABLE MICROSTRUCTURE IN IIAI ..... 6.3. L10 and D019 TRANSITIONAL INTERFACE .......................................... 6.4. ANALYSIS OF SOBOYEJO COMPOSITE CREEP MODEL .................. 6.4.1. Application of the Soboyejo model .............................................. 6.4.2. Problems with the Soboyejo model .............................................. 6.4.3. Three constituent composite creep model .................................... 6.5. RULE-OF-MD(TURE-MUKERJEE-BIRD-DORN EQUATION .............. CHAPTER SEVEN. DISCUSSION ................................................................ 7.1. INTRODUCTION ....................................................................................... 7.2. COMPARISON OF MSU DATA TO LITERATURE ................................. 7.2.1. Experiment #4 ............................................................................... 7.2.2. Experiment #7 .............................................................................. 7.2.3. Investigation of deformation history independence ..................... 7.3. COMPARISON OF CREEP PLOTS OF T1Al ........................................... 7.3.1. Unique power-law behavior of 'Ii-48Al-2Cr-2Nb ....................... 7.3.2. Oikawa and multiple creep deformation regimes ......................... 7.3.3. Temperature compensated comparisons ....................................... 7.3.4. Mechanisms that soften the microstructure or restrict glide ......... CHAPTER EIGHT. CONCLUSION .............................................................. 61 85 85 86 87 92 93 94 96 96 104 104 104 107 109 109 114 114 120 123 138 140 APPENDIX 1. EXPERIMENTAL CREEP PROCEDURE .......................... A.1. INTRODUCTION ....................................................................................... A.2. LIST OF CREEP FRAME EQUIPMENT ................................................... A.3. OPEN-AIR CREEP EXPERIMENTAL PROCEDURE ............................. A.4. PROCEDURE TO SHUT DOWN OPEN-AIR ........................................... A.5. VACUUM EQUIPTMENT ........................................................................... A.6. VACUUM CREEP EXPERIMENTAL PROCEDURE ............................... A.7. VACUUM SHUT DOWN PROCEDURE ................................................... A.8. RECURRENT PROBLEMS ........................................................................ APPENDIX II. TABLE OF DATA ON CREEP OF TiAl ............................... REFERENCES ..................................................................................................... vi 151 153 156 157 159 165 2.1. Characteristic three stage creep curve .............................................................. 5 2.2. lncreasin g strain rate with increasing temperature ........................................... 6 2.3. Plot of Activation energy .................................................................................. 6 2.4. Increasing strain rate with increasing stress ..................................................... 7 2.5. Plot of stress exponential, after [1] .................................................................. 8 2.6. Transition of n with different stress conditions, after [2] ................................ 9 2.7. Transition of Q with different temperature conditions, after [3] ..................... 10 2.8. Schematic of Nabarro-Herring creep on an ideal grain, after [4] .................... 12 2.9. Schematic of Coble creep on an ideal grain, after [4] ...................................... 14 2.10. Schematic of the dislocation climb mechanism, after [5] .............................. 15 2.11. Definition of twinning, [10] ........................................................................... 17 2.12. Schematic of twinning plane, [11] ................................................................. 18 3.1. Lattice structure of L10, after [16] ................................................................... 23 3.2. Lattice structure of 0019, [16] ....................................................................... 24 3.3. TrAl phase diagram around the gamma phase, [18] ....................................... 26 3.4. Creep resistance comparison of different microstructures, [22] ..................... 29 4.1. Minimum creep rate of near gamma-TiAl, [24] .............................................. 36 4.2. Plot of self-diffusion of T1-54A1, [32] ............................................................. 39 4.3. Representation of twinning system, [34] ......................................................... 42 4.4. Twin orientations as viewed along the <110> direction, [15] ......................... 43 vii 4.5. Creep behavior of Ti-48Al-2Cr-2Nb (DP). [25] ............................................. 48 4.6. Transition of stress exponent of Ti-53.4A1 (NO), [26 - 30] ............................ 51 4.7. Transition of activation energy of Ti-53.4Al (NC), [26 - 30] ......................... 51 4.8. Idealized duplex grain, [8] .............................................................................. 53 5.1. Experiment #1 ................................................................................................ 65 5.2. Experiment #2 ................................................................................................ 67 5.3. Experiment #3 ................................................................................................ 69 5.4. Experiment #4 ....................................................... 71 5.5. Experiment #5 ................................................................................................ 73 5.6. Experiment #6 ................................................................................................ 75 5.7. Experiment #7 ................................................................................................ 77 5.8. Experiment #8 ................................................................................................ 79 5.9. Experiment #9 ................................................................................................ 81 5.10. Comparison plot of all MSU experiments ................................................... 83 5.11 Comparison plot of all MSU experiments temperature compensated .......... 84 6.1.(111)planeofthe L10 .................................................................................... 89 6.2.(0001) basel plane of the D019 ...................................................................... 89 6.3. Interface between the gamma and alpha2 .................................................... 89 6.4. Transitional interface of TiAl and T13A1 (a) .................................................. 90 6.5. Transitional interface of TiAl and T13Al (b) ................................................. 90 6.6. Representation of diffusion without transitional interface ............................ 91 6.7. Effect of T1 concentration on Diffusion ......................................................... 92 viii 6.8. T1 content vs. lamellar position ...................................................................... 92 6.9. Idealized highly anisotropic duplex grain ...................................................... 95 6.10. Rule-of-mixture-MBD plot of range of creep conditions ............................. 102 6.11. Temperature normalized rule-of-mixture-MBD plot. ................................... 103 7.1. Unique power-law behavior shared by Experiment #4 and Wheeler [25] ..... 108 7.2. Experiment #7 shares same creep rate as Soboyejo [8] ................................. 110 7.3. Comparison plot of experiments #3, 4 and 7 ................................................. 111 7.4. Temperature normalized plot of experiments #3, 4 and 7 .............................. 112 7.5. Unique power-law behavior reported by Wheeler [25] for Ii-48Al-2Cr-2Nb 115 7.6. Unique power-law behavior reported by Wheeler [25] for Ti-48Al-2Cr-2Nb 116 _ temperature compensated 7.7. Unique power-law behavior reported by Hayes [36] for Tr-48Al-2Cr-2Nb... 118 7.8.Unique power-law behavior reported by Hayes [36] for Ti-48Al-2Cr—2Nb.... 119 temperature compensated 7.9. Steady-state creep rates of 13-53.4A1 reported by Oikawa [26 - 30] .............. 121 7.10. Steady-state creep rates of Ti-53.4A1 reported by Oikawa [26 - 30] ............ 122 temperature compensated 7.11. Multiple deformation mechanism for different stress regimes ..................... 120 7.12. Hot tension test of '1'1-48Al-2Cr-2Nb at different temperatures reported by 124 Shih and Scarr [23] 7.13. Hot tension test of 1'1-48Al-2Cr—2Nb at different temperatures reported by 125 Shih and Scarr [23] temperature compensated 7.14. Global plot #1 comparing data from various authors [8,23,60] .................... 126 7.15. Global plot #1 comparing data from various authors [8,23,60] .................... 127 temperature compensated 7.16. Oikawa [26 - 30] for Ii-S3.4A1 temperature compensated ........................... 129 7.17. Wheeler [25] for Ti-48Al-2Cr-2Nb temperature compensated. .................... 130 7.18. A. Loiseau and A. Lasalrnonie [35] for 'I'r-54Al .......................................... 131 temperature compensated 7.19. H. Lipsitt [40] for Tr-50A1 temperature compensated ................................... 132 7.20. S.C. Huang [19] for ‘I'r-47A1-1Cr-1V—2.5Nb temperature compensated ...... 133 7.21. Martin [49] for T1-46Al-2V + 6.6 vol% T182 temperature compensated ..... 134 7.22. M. Bartholomeusz for TrAI and lamellar structure temperature compensated 135 7.23. This study for ‘I'r-48Al-2Cr-2Nb temperature compensated ......................... 136 7.24. Global plot #2 temperature compensated ...................................................... 137 7.25. Mechanisms that add to or interfere with climb ........................................... 139 W 3.1. Alloying effects observed in gamma-based alloys ........................................ 30 4.1. Mechanical twinning elements of the thin twin layer .................................... 42 4.2. Comparison of difl‘erent creep parameters and A [37] .................................. 45 4.3. Creep deformation Mechanisms at T > 0.4Tm [43] ....................................... 47 4.4. Relationship between aluminum content and creep parameters ................... 49 at low temperatures and low stresses [26] . 4.5. Relationship between different creep efiects [29] .......................................... 50 4.6. List of minimum steady-state creep rate and creep conditions............ .......... 55 5.1. Chemical composition of specimen [33] ....................................................... 59 5.2. Creep experiments on Ti-48Al-2Nb-2Cr at MSU ......................................... 63 6.1. Difl'erent creep parameter values used by Soboyejo [44] ............................. 94 6.2. List of various creep parameter values .......................................................... 99 6.3. List of predicted creep behavior using composite-MED equation ............... 101 7.1. List of creep data from MSU study ............................................................... 106 W INTRODUCTION Titanium aluminide TiAl based materials are promising candidates for high temperature service. This is due to their high specific strength, stiffness at elevated tem- peratures, and good oxidation and creep resistance. Also, their density is 2.5 times lower than current nickel-based superalloys. However, very little research of near y—TrAI based alloy creep behavior has been accomplished, and the creep deformation mechanisms are not clearly identified. The activation energies reported are much larger than those for self- diffusion and interdiffusion in TiAl, which implies that the creep rate may be controlled by processes other than the usual lattice diffusion mechanism. Also, the value of the stress exponent varies widely from about 2 to 8 in the literature. This suggests that several defor- mation mechanisms are involved in the creep of TiAl. The details of deformation mecha- nisms are not known and the limited results in the literature are not always consistent with the common creep theories. This work is concerned with studies of the high temperature creep behavior of gamma-based TrAl alloys having the duplex microstructure. A main emphasis was addressed toward the composition of 'I'1-48Al-ZCr-2Nb (at%). The creep characteristics of different compositions and microstructures was compared in order to find possible trends that appear in the data. The creep properties that where investigated were the activation energy for diffusion, Q, and the stress exponent, n, in order to determine what role they play in the creep behavior of the material. 4m W THEORY 2.1 REVIEW OF CREEP 2.1.1. The high-temperature materials problem It is well known to material scientists that the strength of mast metals decreases with increasing temperature. Since the mobility of atoms increases rapidly with temperature, it can be appreciated that diffusion-controlled processes can have a very sig— nificant effect an high-temperature mechanical properties. High temperature will also result in greater mobility of dislocations by the mechanism of climb. The equilibrium con- centration of vacancies likewise increases with temperature. New defamation mecha- nisms may come into play at elevated temperatures. In some metals the slip system changes, or additional slip systems are introduced with increasing temperature. Defama- tion at grain boundaries becomes an added possibility and grain boundary mation or recrystallization may occur during. the high-temperature defamation of metals. Another important factor to consider is the effect of prolonged exposure at elevated temperature on the metallurgical stability of metals and alloys. Thus, it should be apparent that the successful use of metals at high tem- peratures involves a number of problems. Aggressive allay-development programs have produced a number of materials with improved high-temperature properties, but the 3 ever increasing demands of modern technology require materials with even better high- temperature strength and oxidation resistance. Since the innoduction of the gas-turbine engine, materials must operate in critically stressed parts, such as turbine buckets, at tem- peratures around 765°C (1400 0F). An important characteristic of high-temperature strength is that it must always be considered with respect to some time scale. The tensile properties of most engi- neering metals at room temperature are independent of time, for practical purposes. It makes little difference in the result if the loading rate of a tension test is such that it requires 2 hours or 2 minutes to complete the test. However, at elevated temperatures the strength becomes very dependent on both strain rate and temperature. A number of metals under these conditions behave in many respects like viscoelastic materials. A metal sub- jected to a constant tensile load at an elevated temperature will creep and undergo a time- dependent increase in length. A strong time dependence of strength becomes important for different materials at different temperatures. What is high temperature for one material may not be so high for another. To compensate for this a high temperature is generally regarded as greater than one-half the melting temperature (0.5 Tm). 2.1.2. Stages of creep Creep is defined as “the resistance of materials to defamation and failure over long times, under load and at high temperatures”[1]. An example of a simple creep situation can be expressed as an copper wire that is loaded at one end by a large weight, and at the other end is attached to the ceiling. The wire is then heated and a time-depen- dent defomation occurs. 4 The time-dependent creep defamation is usually thought of as being divided into three stages: Primary, secondary and tertiary creep(See Figure 2.1). Stage one (primary, or transient) creep is actually divided into two stages. The first consists of an value of so which is the virtually instantaneous increase in length due to the elastic and plastic defamation which occurs on loading. The second consists of an value of 8c which is the time-dependent increase in length due to creep defamation. Materials subjected to transient creep shows that the structure changes with increasing strain in a manner somewhat analogous to that observed during work hardening; e.g., the dislocation density increases and, in many materials, a dislocation subgrain structure is famed with a cell size that decreases to a steady-state value with increasing strain. These structural changes are consistent with the creep rate decreasing with increasing time in stage I creep. In Great Britain, they divide stage one into the so and 8c components and combine them with the other two stages, and thus having four stages of creep. Stage two (secondary, or steady-state) creep is characterized by a constant- creep-rate. The amount of defamation strain divided by the time, (de/dt) known as the strain rate or the creep rate, is a constant for this creep region. The invariant microstruc- ture is indicative that recovery effects are concurrent with defamation during Stage II; that is, in the absence of recovery the dislocation density would increase and a subgrain structure, if present, would become progessively finer with increasing strain. Hence, hard- ing mechanisms effective at low temperatures are not so useful at higher temperatures, and stage II creep can be viewed as a regime in which the intrinsic work-hardening capacity of the material is balanced by recovery or “softening” effects allowed by the increased defor- mation temperature. Because of this relation between the material defamation and the Li 5 strain-rate being a constant, amost all of the mechanical modeling of creep defamation mechanisms is determined in the steady-state creep regime. Subsequent to stage II creep, stage III (tertiary) creep is observed. During tertiary creep, the creep rate is greater than stage II and increases continuously. This is shown further in a plot of strain vs. time (Figure 2.1), which also shows clearly that stage II is characterized by a constant, minimum creep rate. The accelerating creep defamation of stage III eventually leads to material fracture and is related to several factors. Some of these factors include the onset of recrystallization, the coarsening of second-phase parti- cles and/or the fomation of internal cracks or voids. time Figure 2.1 Characteristic three stage creep curve. 2.1.3. Temperature effects Earlier, creep was described as being a time-dependent defamation mech- anism; but it is also temperature-dependent. The “constant” steady-state strain rate increases exponentially with increasing temperature (Figure 2.2). T 1 T 1 >T2>T3>T4 T4 \ time Figure 2.2 Increasing strain rate with increasing temperature. By measuring the secondary creep rates recorded at the same stress, but at different temperatures, one can investigate the relationship In (dc/d0” a exp(-Q/RT) where (dc/dos is the steady-state strain rate, Q is the activation energy for creep (diffu- sion), R is the universal gas constant (8.31 .I/mol*l(), and T is the temperature. By plotting 1n (dc/dt) vs. (III) one can often obtain a good linear relationship, that yields the Q value (See Figure 2.3) ‘— increasing temp. 1n (dEIdt),s slope = -Q/R 1/T Figtue 2.3 Plot of Activation energy. 7 When procedures of this type have been used to study the creep behavior of pure metals at high temperatures, the values of Q have been found to be close to the activation energy for lattice self-diffusion. This emphasizes the importance of diffusion under the hi ghnemperature creep conditions. 2.1.4. Stress effects Another aspect of creep is the dependence on the applied stress. 80, the “constant” steady-state rate increases exponentially with increasing stress very similarly to it’s response to an increase in temperature(See Figure 2.4). 01>02>O3>C4 T = const. time Figure 2.4 Increasing strain rate with increasing stress. Similar to the last relationship discussed, by measuring the secondary creep rates recorded at the same temperature, but at different stresses, one can investigate the relationship: log (de/dt)SS at n log 0 where (dE/dt) is the steady-state strain rate, it is the stress sensitivity exponent and o is the applied stress(See Figure 2.5) log (dc/dt)SS ' slope = n log a Figure 2.5 Plot of stress exponential. 2.1.5. Power law relation This brings us to the discussion of the “power law” relationship which is widely used to describe high temperature creep. The power law representation of high temperature creep is defined by the equation below[2]: (dt—Z/dt)SS = Ao“exp(-Q/RT) (1) which is usually plotted in the form of log (de/dt)SS = log A + nlogo -Q/RT where (dr—t/dt)SS is the steady-state strain rate, A is an material constant, a is the applied stress, it is the stress sensitivity exponent, Q is the activation energy, R is the universal gas constant, T is the temperature. 2.1.6. Transition in the stress exponent However, the power law representation is accurate in limited temperature and stress regimes. That is, while it is approximately a linear constant over much of the 9 stress range, the plot curves upward at the higher stresses. So at very high stresses, the curvature of the line suggests that it increases continuously with increasing stress. This increase in the n value with increasing stress is referred to as power law breakdown. The steady-state is the most important condition for creep modeling. How- ever, our understanding of the creep behavior is obscured by the n value changing during creep. This has been discovered when the plot of log(de./dt)ss vs. logo have been found to curve with decreasing applied stress, such that a transition occurs from n = 4 at high stresses to n = 1 in the low stress regime(See Figure 2.6). log (dc/60,, low a very high a power-law breakdown I I I I I I I I I I I I I I I I I I I I I I g I I I . I g I ‘ a log a Figure 2.6 Transition of n with different stress conditions. 2.1.7. Transition in activation energy A similar transition occurs to the activation energy, Q, but instead of differ- ent stress regimes, this transitions occurs at different temperature regimes. Creep at high temperatures (0.7 Tm) frequently has the activation energy equal to that of self-diffusion. Creep properties studied at lower temperatures (0.4 Tm) have found that the activation energy equals about 1/2 that of self-diffusion. This transition from the activation energy 10 value equal to the self-diffusion to a value of 1/2 the self-diffusion activation energy has been found regardless if the test carried out at high stresses (n = 4 - 6) or low stresses (n = 1). The observation of the activation energy that suddenly changes from one value to another results from “preferential diffusion paths” to account for the change. [3] To explain further, the magnitude of the activation energy for diffusion depends on the bond energies between the moving atom and it’s neighbors. Because the surface (or interface, grain boundary) atoms have fewer neighbors and therefore, fewer bonds than the atoms in the crystal, surface paths offer an “easier path” for diflusion. Grain boundaries and the core of the lattice dislocations define regions where the atomic arrangements are less regular than in the crystal lattice, and should provide an “easier pa ” characterized by activation energies less than the value of lattice diffusion(See Fig- ure 2.7). increasing temp. log D (llRT) Figure 2.7 Transition of Q with different temperature conditions. 11 At high temperatures when lattice diffusion is rapid, diffusion along the easy paths makes a negligible contribution to the overall diffusion rate, because the volume of the grain boundaries is small when compared to the total volume of the crystalline sample. On the other hand, as bulk diffusion rates decrease, the diffusion along the easy paths becomes progressively more important since the rate of the process with the lower activa- tion energy changes less with decreasing temperature. Therefore, the process associated with the high activation energy value is dominant at high temperatures, but the process having the lower activation energy becomes dominant at lower temperatures. 2.2. CREEP DEFORMATION MECHANSIMS As mentioned, creep can be viewed phenomenologically as a process in which work hardening and recovery processes occur on the same time scale as the defor- mation process. In this section, several mechanisms of creep are discussed to illustrate the basis of the power law creep equation (Eqn. 1). Depending on temperature and applied stress, dislocation glide, dislocation recovery (for example, by processes involving dislo- cation climb), or other difi’usional-flow mechanisms may dominate creep deformation. Several of the mechanisms described, particularly those related to dislocation climb, are speculative in that they can not be (or at least have not yet been) verified by direct micro- structural examination. Nonetheless, processes similar to the ones investigated surely occur during creep defamation. Beyond that, a description of the processes allows the correlation of the power-law equation (Eqn. 1) with microstructure and the applied exter- nal “forces” of temperature and stress. [SJ 12 Generally, defamation mechanisms that occur during creep are usually divided into two main categories: diffusion controlled mechanisms and dislocation controlled mechanisms. 2.2.1. Diffusion controlled creep mechanisms There are two main types of diffusion conuolled creep mechanisms: Nabarro-Herring and Cable creep processes. (a) Nabarro-Herring Creep Nabarro-Herring creep is a process that involves diffusional transport of atoms through the grain. Consider the example of a grain of a polycrystalline deforming at high temperatures under stress(See Figure 2.8). If vancancies are generated at the boundaries experiencing the tensile stress I and these vacancies diffuse to the boundaries under compression. This results in a flow of vacancies and a counter flow of atoms. C/ Cami... D C to Figure 2.8 Schematic of Nabarro-Hening creep on an ideal grain, after [4]. 13 For Nabarro-Herring (N-H) creep, the creep rate is given by [5] (da/dt)NH=aNH(DSD/d2) QC we determine that Cable creep is the dominant creep mechanism at low temperatures (0.4 Tm) carried out at low stresses. 2.2.2. Dislocation controlled creep mechanisms Dislocation studies using the transmission electron microscope (TEM) have shown that the creep process leads to changes in the dislocation arrangements in crystals. The undefomed crystal will originally have a unifom (low) dislocation density. But after creep defamation the dislocations are converted into very homogeneous struc- tures. Some have a high density of dislocations (sub grain boundaries, etc.) and others are relatively dislocation free. There are four main types of dislocation controlled creep '23 15 mechanisms: dislocation glide, dislocation climb, glide limited by solute atoms, and grain boundary sliding. Defamation-induced twinning (due to coordinated dislocation move- ment) is rare in creep conditions, but it is observed in ordered materials. (a) Dislocation glide Dislocation glide is described as a dislocation moving on it’s glide plane under the influence of large stresses. The constitutive equation for creep by dislocation glide is given by [8] (OE/(1006 = (dc/dt)oexp(-Uo/kT)exp(tbas/kT) (5) where (deldt)DG is the strain rate due to dislocation glide, (dc/dt)o is a reference strain rate, U0 is the activation energy for dislocation glide, ‘t is the applied shear stress, b is the Burger’s vector, as is a fraction of the glide plane area, k is Boltzmann’s constant and T is the temperature. Note: has = V" is applied later. Also, it is important to note, in this mech- anism diffusion does not play a controlling role. (b) Dislocation climb During deformation a material is considered to contain a number of dislo- cation sources. During creep these sources emit dislocations which move across‘their glide plane until the leading dislocations eventually become held up at an obstacle, forming a pile up array. This is thought of as a hardening process. Finally the leading dislocation will climb out of it’s slip plane and continue on a parallel plane(See Figure 2.10). climb _L. __> . .L .1. .r. .L source obstacle Figure 2.10 Schematic of the dislocation climb mechanism, after [9]. 16 The constitutive equation for creep by dislocation climb is given by [4]: (dc/dong = (ammo/mom?) (6) where (dE/dI)DC is the strain rate due to dislocation climb, (Inc is a geometrical constant, DL is the lattice diffusion coefficient, k is Boltzmann’s constant and T is the temperature. (c) Dislocation glide limited by solute atmospheres When alloying a pure metal a solute atom is introduced into the host matrix. The solute atom improves the creep resistance of the host material by impeding dislocation glide and recovery processes. However, when the stress exponent, n, decreases and is accompanied by a change from nomal to inverse primary creep curve shapes, this is the symptoms of solute atoms drag. This behavior can be described as the solute atoms lattice strain field foms an atmosphere that encompasses the area around the dislocation. The solute/dislocation interaction is favored by large size differences between the solute and solvent atoms. The creep rate is then controlled by the rate at which the dislocations can move dragging their solute atom atmosphere. The creep rate is given by [5]: (dc/do = ttn<1-v)rra)/(6e2<:bSG)r*(o/o)3 (7) where e = (9‘7me - 1 and B = (char: + cab*)(1 + my mtg), D = Chemical diffusion of solute atom, D* = Chemical dependent diffusion coeff. 9* = effective atomic volume of solute atom. (d) Grain-boundary sliding At elevated temperatures the grains in polycrystalline metals are able to move relative to each other. Grain-boundary sliding is a shear process which occurs in the direction of the grain boundary. It is promoted by increasing the temperature and/or decreasing the strain rate. Although most investigations indicate that sliding occurs along the grain boundary as a bulk movement of the two grains. Other observations indicate that flow occurs in a softened area a finite distance away from the grain boundary. 17 Grain boundary sliding occurs discontinuously with time, and the amount of shear displacement is not unifom along the grain boundary. The amount of strain in the system is due to slip within the grains and grain boundary sliding. So, there is a close rela- tion between the crystallographic slip and grain-boundary sliding. Another way of accommodating grain-boundary strain at high-tempera- tures is by the fomation of folds at the end of a grain boundary. Another recovery process is grain-boundary migration, in which the grain boundary moves nomal to itself under the influence of shear stress and relieves the stress concentrations. (e) Deformation-induced twinning Mechanical twinning is a mode of plastic defamation that occurs by shear as the result of applied stresses. The shear associated with mechanical twinning is uni- formly distributed over an entire deformed volume rather than localized on the discrete slip planes. The movement of the atoms is only a fraction of an interatomic spacing relative to the atoms in the adjacent plane. There is no change in crystal structure but a reorientation of the crystal lattice. After mechanical twinning, the deformed portion of the crystal becomes mirror symmeuic with the undeformed matrix(See Figure 2.11). Figure 2.11 Definition of twinning, [10]. 18 A model used to describe a twin can be seen in Figure 2.12. K; plane before shear K 2 plane after shear / Plane of shear Figure 2.12 Schematic of twinning plane, [1 1]. Where Kl: twinning plane (the first undistorted plane). K2: conjugate twinning plane (the second undistorted plane). n1: twinning direction (the shear direction). n2: conjugate direction (the intersection of the plane of shear with the second undistorted plane). s: nomal to the plane of shear. 2.3. CREEP EQUATIONS During creep defamation several defamation mechanisms may be acting simultaneously, or difi'erent defamation mechanisms could be acting at difi'erent creep regimes. So, this may cause large differences in the values of the creep response. Most of the creep defamation equations describe the steady-state creep difl’usion controlled mech- anisms. However, some equations describe dislocation controlled mechanisms and power law breakdown, depending on the creep area of interest. 2.1.1 I squat tion I 23.2 bcn that Wilt size the fac vid CTCt Salt. 19 2.3.1 Power law equation One of the equations that is commonly used for creep is the power-law equation. The power law representation of high temperature creep is defined by the equa- tion below[2]: (dz/crass = Ao"exp(-Q/RT) (1) 2.3.2. Mukerjee-Dorn equation There are many adaptations to the power-law to “fine tune” the equation to be more specific and to have a greater accuracy. One of these power-law related equations that is used for creep behavior is the Mukerjee—Dorn (MD) equation[l2]: (dfildt)ss=(ADon/kTXO/G)“(b/d)peXP(-Q/RT) (8) where T is the temperature, k is Boltzmann’s constant, R is the gas constant, d is the grain size, p is the grain size exponent, b is the burgers vector and A is a geomeuic constant The MD equation has an obvious relation to the power-law equation, but it takes the grain size and the temperate dependence of the elastic modulus. Comparing the two equations the difierences are, a (b/d)p grain size ratio parameter, an inverse temperature factor and the temperature dependence of G is in the MBD equation. This refinement pro- vides a structure that is useful for exploring mechanistic details. i.e. when plotting the creep data at different strain rates and at different temperatures, the plot should fall on the same line if the same defamation mechanism is responsible. 20 2.3.3. Power law breakdown As mention previously, the steady-state creep condition is the most popular creep regime to determine experimental data. However, some research is involved in other creep conditions such as power law breakdown. During power law breakdown the Sellers- Teggart [12] equation is used to describe the creep behavior: (de/dt) = AD/anb2*(sinha(o/E))" (9) where a = (CS/E)"1 This equation describes the creep conditions when the stresses are very high, and power- law creep does not apply. 2.3.4. Composite modeling To model the creep behavior at intermediate temperatures and stresses, Raj and Langdon [13] have reported that mechanisms controlling the creep behavior at inter- mediate temperatures are non-diffusional. By exploring a number of different possibilities, they found that the most important type of defamation mechanism was the Obstacle-lim- ited glide of dislocations in the subgrain interior. Nix and Ilschner account for the smooth transition from power-law creep with increasing stress and decreasing temperature, by assuming that defamation mechanisms in the hard region occurs by diffusion controlled recovery and in the soft region by themally activated obstacle-limited dislocation glide, creep rate. The following equation was given[13]: e = as + an (10) Others have applied these ideas to specific materials, i.e. Soyboyeo [8] and Hazeldine [14]. The soft region (themally activated obstacle-limited dislocation glide) [12]: as = 0.5x1012(o/G)2exp[-(0.5kaob2doc - (o - ob)V*)]/RT (11) 21 where kf = obstacle strength, G0 = shear modulus at O K, V* = activation volume, d0c = stacking fault width at zero stress, ab = ave. long range back stress, The hard region is determined by diflusion controlled recovery[13]: ch = 3000(DSDGb/kT)(o/G)4 (12) where DSD = lattice diffusion coefficient The activation energy for obstacle-controlled glide, Qg[13]: Qg =O.5k,Gob2doc- (o- ob)V* (13) The magnitude of Q8 at zero stress is as predicted Qg = 290 kJ/mol at o = 0, kf = 0.2, d0C = 6b for a weak obstacle, assuming ab = 0.50 CHARIERIHREE TITANIUM ALUMINIDE TiAl 3.1. CRYSTAL LATTICE STRUCTURES In this section some basic understanding of the two crystal lattice structures of L10 (fct) for the gamma (TrAl) and the D019 (hcp) for the alpha2 (T13Al) was summa- rized. 3.1.1. L10 The gamma phase in TiAl has a L10 type lattice crystal structure where the titanium and aluminum atoms alternately stack in (002) planes (Figure 3.1). The L10 structure is a slightly tetragonally distorted, face-centered cubic with a temperature depen- dent composition range of 49 to 66 (at%) of Al. The ratio between the lattice parameters and in the direction of the tetragonal axis is c/a = 1.02. However, this value increases up to c/a = 1.03 with increasing Al content and decreases to c/a = 1.01 with decreasing Al con- tent [15]. The y-T'rAl phase remains ordered up to it’s melting point of about 1450°C. Because the c/a ratio is always close to unity, it is very close to the fcc crystal structure. However, there are more possibilities for complicated slip in L10 due to the anisotropic crystal structure. It is of interest to note that twinning deformation is relatively common in the gamma phase. 22 1.1 23 0 Ti atom ela I 1.03 0 Al atom a - 0.398 nm Figure 3.1 Lattice structure of L10, after [16] 3.1.2. D019 Because TrAl materials typically have 1-10 volume% of the alpha phase, which has a D019 type lattice crystal structure, it is of interest. The 0019 structure is based off the hexagonal closed-packed structure, but the a coordinate basel plane axis has been replaced by a value of twice as large (2a) to accommodate the lattice structure. lt’s relation to the hcp crystal lattice can be seen on the next page in Figure 3.2. The structure is based on the assurrrption of having a stoichiomeuic T13Al. However, the system is often off-stoichiometric with Al atoms in T1 sites. Therefore, this causes a slightly disordered lattice. Also, it is interesting to note that according to Yamaguchi [l6] defamation twin- ning is extremely rare in D019 structures. 24 [0001] 8 'AA ‘3' - I ' - C08: . 1i .{k. I E 1V1..°:1g9. Figure 3.2 Lattice structure of 0019, [16] 3.1.3. Differences between L10 and D019 The main difference between the L10 and the D019 is the stacking sequence. The stacking sequence for the 1.10 (gamma) is ABCABC, while the 0019 (alpha2) stacking sequence is ABABAB. So the interface between gamma and alpha2, as in the lamellae of TiAl has a stacking sequence that is ABCABCzABABAB. This inter- face corresponds to the (l l 1) plane of the L10 and the (0001) basel plane of the 0019. However, three <1 l20> directions on the (0001) basel plane of the hcp alpha phase are all equivalent while the [110] direction and other two <011] directions on the (l l 1) plane are not equivalent to each other. Thus, the gamma has six possible orientations of [110] on (111) in the gamma phase with respect to <1 l20> on (0001) in the alpha phase. 25 3.2. MICROSTRUCTURE Extensive progress and improvements in two-phase TrAl alloys have been made in the last five years. This is due to the fact that TrAl has become a candidate for high-temperature light-weight structural applications. The TrAl phase possesses a wide composition range and it extends primarily on the Al-rich side. While the TiAl compounds with Tr-rich compositions exhibit a two-phase microstructure are composed of the y ('I'rAl) phase and a small amount of a2 (Ti3Al) phase. The recent interest in TiAl compounds has been primarily devoted to the two-phase 7/02 alloys rather than the Al-rich TiAl com- pounds with a single-phase 7 structure. This is because the two-phase material is more ductile and tougher than the single phase compound. In the last few years, improvements in the mechanical properties of the two-phase alloys has been accomplished. Most of the work was directed toward improv- ing the tensile ductility; for example, two-phase alloys with tensile elongation as high as 4% [17] have been developed through alloying with ternary elements and controlling their microstructure by themomechanical processing. However, these improvements in room- temperature ductility have been naded for other mechanical properties such as toughness and high-temperature strength. This part of the paper will review recent advances in our understanding of microstructure and its relation to the physical properties of two-phase TiAl alloys. The phase equilibria and transfomations in the near-equiatomic region of the TiAl diagram have been investigated, and it has been concluded that the beta+gamma two-phase region does not exist but instead, the alpha-t-gamma two-phase field extends up 26 to the peritectic temperature, as seen in the phase diagram proposedby McCullough et al. [18](See Figure 3.3). So, the solidification in near-equiatomic compositions proceeds along the two peritectic reactions L + B -> a and L + at -> y, or the single peritectic L + at -> 7 depending on the cooling rate. The phase diagram of Figure 3.3 indicates that the a phase decomposes into the (IQ and 7 phases through a eutectoid reaction (at 1398 °C). However, some references[19] have suggested that it is impossible to observe the eutec- toid u'ansfomation due to the fact that there is a substantial difi'erence in the ease of nucle- ation between the (12 and yphases. The gamma precipitate is more Sluggish than the «la; transfomation and thus the gamma phase can precipitate out of either a or 0,2 phases depending on the cooling rate. I ' I ' I 1 I 1900 - — L 1800 - 4 g ‘. 9 1700— B 3 E 1600 i O. .2 1500— .. Y 1400 / \ "39° - (12 1300 _ 1 1 1 1 i1 1 1 _ 30 40 50 60 Atomic Percent Al Figure 3.3 TiAl phase diagram around the gamma phase, [18] t1 27 One of the most interesting features of the phase diagram of Figure 3.3, is the fact that the alpha single phase field extends all the way up to 1450°C in the near equi- atomic region. That is, alloys with nearly equiatomic compositions can be heated into the single phase field where aluminum is completely in solution in the disordered hexagonal close-packed (hcp) structure of titanium and thus may be heat treated under a number of different conditions to develop a wide variety of mircostructures. This is analogous to high-carbon steels which can be heated in the austenite single-phase field and subse- quently heat treated under appropriate conditions to develop the desired properties. Such a property has not been found in any other intemetallic compounds which have been stud- ied as possible candidate for high-temperature structural applications. This uniqueness together with the exceptional combination of light weight, superior strength and oxidation resistance make the near-equiatornic TrAl alloys extremely attractive for high-temperature service in the aerospace field. 3.2.1. Lamellar structure Most of the research covered in the literature discusses the lamellar struc- ture. The lamellar structure is produced from two-phase TrAl alloys with near-equiatomic compositions. They are prepared by the usual ingot-metallurgy methods, where the gamma phase precipitates from the alpha phase producing a lamellar structure. The lamel- lar structure is composed of the transfomed gamma and remaining alpha lamellae. Gamma lamellae are formed in such a way that closed-packed planes and directions in the gamma phase are parallel to the corresponding planes in directions in the alpha phase. In other words, the (0001) basel plane of the hop alpha phase interfaces with the (1 ll) plane 28 of the tetragonal Llo structure for the gamma phase. According to Yamaguchi [20] the gamma phase can be famed in six possible orientations corresponding to the six possible orientations of [110] on (111) in the gamma phase with respect to [1120] on (0001). The different crystal lattice structures will be discussed in a later section. 3.2.2. Thermomechanical structure Most of the newer literature discusses the rnicrostructures that are devel- oped through themomecharrical processing. Ingots of two-phase TrAl alloys prepared by ingot metallurgy methods are usually HIPed, hot-worked, heat treated and cooled at an appropriate rate to obtain a specific microstructure and desired resulting mechanical prop- erties. Such tlremomechanical processing can provide a wide variety of microstructures in comparison to simple heat treatments without hot—working. The hot-working that is most common is usually isothemal forging, and is typically conducted near the eutectoid tem- perature. Such hot-working generally results in the structure consisting mostly of fine par- tially recrystallized gamma grains. Hot-working is then subjected to a heat treatment for further microstructural control. The characteristics of these rnicrostructures have been cat- aloged by Kim and Dirniduk [21]. They classified the rnicrostructures into four groups: Near-gamma (NG), Duplex (DP), Nearly lamellar (NL) and Fully lamellar (FL). (11) The near-gamma (NG) structure is obtained by an annealing heat treat- ment at temperatures just above the eutectoid temperature and is characterized by coarse gamma grains and banded regions consisting of fine gamma and alpha2 grains. This type of microstructure is also known as equiaxed y. 29 (b) The Duplex (DP) microstructure has a microstructure composed of fine gamma grains, and fine lamellar grains. This is obtained only by combination of hot-work- ing and subsequent heat treatment at temperatures where the volume fractions of alpha and gamma phases are roughly equal. Competitive growth between the alpha and gamma phases din-ing heat treatment results in the fine duplex microstructure. (c) The nearly lamellar (NL) structure is composed of coarse lamellar grains and a small volume fraction of fine gamma grains. Nearly lamellar is usually obtained by heat treatment of as-cast ingots. (d) The fully lamellar (FL) is the same as that observed in as-cast condi- tions. They are obtained by heat treatments at temperatures a little below and above the alpha transus line. 1 A comparison of the creep resistance of duplex, single phase 7 and fully lamellar microstructures tested under the same stress and temperatures can be seen in Fig- 3-0 OOO‘C; 10 ksl m 14 «w; raoo°c H.T. ' 25 01.1910! .‘ 5210;1400'0 H.T. 23-2-0 SinglePhsey $15 § 48M;1400°CH.T. 0.5 Fully Lamellar o 1.1.1....11.-.I.Mal-...1...-l....l-.-.l....l 0 100 200 300 400 500 Tlme(hours) Figure3.4 Creep resistance comparison of different microstructures, [22]. 30 3.2.3. Alloying The effects of alloy element additions to the two-phase material is a very complicated issue. The literature on the subject of alloying is concerned with the effects alloying has on the rrricrostructure and consequently on the mechanical properties. These alloy elements additions and their reported effects are listed in the table below [19]: Al Er Fe Table 3.1 Alloying effects observed in gamma-based alloys mm It strongly afl’ects ductility by changing the microstructure. Best ductility occurs in the range of 46-50 at%. Additions of >0.5 at% refine grain size, and improve strength and workability. Doping with B generally increases castability. Carbon-doping increase creep resistance and reduces ductility. Additions of 1 - 3 at% increase the ductility of duplex alloys. Additions of >2 at% enhance the workability and superplasticity. Additions of >8 at% greatly improve the oxidation resistance. Its additions change the deformation subsu'uctures and increase the ductility of single-phase gamma. The addition of Fe increases fluidity, but also the susceptibility to hot cracking. The addition of 1 - 3 at% Mn increases the ductility of duplex alloys. The addition of Mo improves the ductility and strength of a fine- grained material. It also improves the oxidation resistance. Increases fluidity. The addition of Nb greatly improves the oxidation resistance. It slightly improves the creep resistance. lmn Si Ta 31 Table 3.1 (cont’d) Alloying effects observed in gamma-based alloys W Doping with P decreases the oxidation rate. An addition of 0.5 - l at% Si improves the creep resistance. The addition of Si also improves the oxidation resistance. The addition of Si increases fluidity, but reduces the susceptibility to hot cracking. The addition of Ta tends to improve the oxidation and creep resistance. It increases the susceptibility to hot cracking. The addition of l - 3 at% V increases the ductility of duplex alloys. Its addition generally reduces the oxidation resistance. The addition of W greatly improves the oxidation resistance. It improves the creep resistance. (a) 'I‘i-48Al-2Cr-2Nb alloy The duplex alloy, Tr-48Al-2Cr-2Nb (at%) is one of the two-phase alloys which have been a subject of many studies [8,15,19,23,24,25]. This alloy is reported to have attractively balanced mechanical properties. The addition of Cr in near-gamma two- phased alloys in duplex fom shows good ductility at room temperature because of an increased volume fraction of equiaxed soft gamma grains. This is obtained by the Cr depressing the alpha-transus, thereby raising the Al content of primary alpha phase and leading to a reduction in volume fraction and width in the alpha21amellae. The addition of Nb has been reported to improve the oxidation resistance of the two-phase alloys, but does not seem to be beneficial to the ductility of the two-phase alloys. The effect of the addition of Nb together with Cr on the mechanical properties of the two-phase alloys needs to be clarified. Of Nb or Cr, in particular, Nb is considerably enriched in the alpha2 phase, so 32 the mechanical properties of the alpha2 phase and therefore the lamellar grains would be changed [19]. However, further studies on this subject are needed. Another important aspect of the microstructure is the effect of the intersti- tial impurities. The nominal oxygen content in ‘y-based materials are typically 500 - 1000 ppm [19]. However, the actual content is lower in the y-phase of the duplex structure, since the a»; phase tends to absorb oxygen. The org also tends to absorb nitrogen and car- bon impurities. The impurities tend to increase strength and reduce ductility. Additionally, they may have beneficial effect of reducing the creep rate. LITERATURE SURVEY OF CREEP IN TiAI 4.1. INTRODUCTION For the last decade, intemetallic alloys based on 'y-TrAl have become promising candidates for high temperature service. Surprisingly, the issue of creep in near y-TrAl based alloys has been addressed only marginally and, in contrast to the large amount of literature on rrricrostructure and mechanical properties, a very limited number of publications have been concerned with the creep properties of these alloys. Studies of some of the microstructures and their resulting creep defamation mechanisms are still missing. The creep defamation mechanism(s) for T’iAl appear to be very compli- cated. The results obtained from this literature survey show the creep defamation is a function of the composition of the specimen, grain size, themomechanical processing (microstructure), as well as the applied stress and test temperature. Because there is so much various data to catalog, the conditions of the different tests and trends in the data are listed. However, these trends may be limited to a single composition, microstructure or test condition. Again, little is known about the creep behavior of this material. This is partially due to the fact that most of the creep experimental results are not exhaustively analyzed so the creep defamation mechanisms are only partially understood. Also, the values obtained to describe the creep characteristics for different test conditions have a 33 34 large variance, and these large differences in values are not well understood. These large differences in the creep parameters of gamma-based TiAl will be investigated in an attempt to understand which possible defamation mechanisms control creep. 4.1.1 Trade-off approach There are many different compositions and microstructures of titanium alu- rninides. Each composition affects mechanical properties and processability through microstructural control. The most important aspect of the composition is the amount of aluminum present. Duplex alloys containing 45-50 at% A1 are generally most desirable. Alloying additions that improve the ductility, oxidation, creep resistance, and fabricability have been identified in Table l, but those additions may adversely affect other properties at the same time. Therefore, it is important to empirically determine the trade-off of each alloying approach. The selection of the alloying approach also depends on the application, which defines the property requirements and the preferred processing route. Based on the progress and improvements, several engineering two-phase alloys in duplex microstruc- ture fom with 3 - 4% room-temperature ductility and improved strength have been devel- oped. Creep strength has also been markedly improved in the last few years. 4.1.2. Comparison of different microstructures creep resistance The creep resistance of each different composition and microstructure are different. The fully lamellar (FL) structure is not only tougher, but more resistant to creep than the single phase (NO) or the duplex (DP) structure. The fully lamellar dramatically reduces the initial transient creep and the rate of steady-state creep(See Figure 3.4). As a 35 result, the time to creep to 0.2% strain increases by two orders of magnitude. However, the fully lamellar structure is also the most brittle at room temperature. Therefore, it makes the fully lamellar structure hard to machine and the fabrication of useful high temperature components very expensive. The duplex structure has moderate creep resistance but is the best trade-off of creep resistance for ductility. The composition of T'1-48Al-2Cr-2Nb is the alloyed com— position that seems to have the best of both worlds. A good creep resistance with up to 3- 4% ductility. However, this composition also has a small grain size which effects the creep properties. 4.2. PROBLEMS IN UNDERSTANDING CREEP OF TiAl There are many problems in determining which creep defamation mecha- nisms are responsible for the steady-state creep behavior of TIA]. The following will sum- marize the most obvious problems which are: 1) minimum creep rate with no steady state defamation, 2) no instantaneous strain or primary creep in some compositions and 3) dynamic recrystallization. However, there are many more subtle problems in understand- ing of creep of TrAl that are not as apparent as the ones that will be discussed. 4.2.1. Minimum creep rate The most obvious problem is the fact that TrAl does not have a steady- state creep rate regime. The term steady-state assumes the strain rate to be a constant, i.e. when the recovery rate balances perfectly with the strain hardening rate for a significant fraction of the creep life. However, the strain rate reported for a polycrystalline TrAl in the 36 duplex condition exhibits a minimum strain rate followed by an increase. Hence no steady-state strain rate is truly observed, though the minimum provides a basis for com- parison. Some examples of experimental creep curves are given in Figure 4.1 [24]. 1o" Tl-lIJAI-ZNb-ZCI , 175 b‘.?.:.'.‘.;;,;g” ‘ ... g- 1 —--7src o . .. O 10 ”ar- 3' I I: s to" _ - 5 a go" --------------- l--.» 0 0.01 0.02 0.03 0.04 0.05 0.00 Streln Figure4.l Minimum creep rate of near gamma-TIA], [24] 4.2.2. No instantaneous strain Oikawa [26,27,28,29,30] reports that under low stresses. no instantaneous strain can be observed in equiaxed gamma (Ti-53M). The strain at the primary stage is very limited and an apparent steady state soon appears. After this low strain rate stage, the creep rate increases up to a high value which is more than one order of magnitude higher than the steady state creep rate. This type of creep behavior is unusual because there is shift in defamation from a slower one to a faster one, depending of the amount of strain in the system The mechanisms of this type of creep response have not yet been clarified. 37 4.2.3. Dynamic recrystallization Another problem that obscures our understanding of creep in T1A1 is the dynamic recrystallization (DRX) that occurs. The strain rate passes through a minimum and increases to a steady state value. The characteristic steady state associated with dynamic recovery exhibits a lower activation energy (269 kJ/mol) than the apparent steady-state stress during DRX (400 kJ/mol)[25]. The difference between the two activa— tion energies is about 15% higher for the DRX than the activation energy for the steady-state recovery. At larger strains the creep conditions are dominated by DRX. There is a tendency for the recrystallized grains to nucleate along prior grain boundaries of the original microstructures[25]. DRX has been reported to be important at higher-tempera; tures (approx. 760°C) and at strains of approximately 20% strain. The physical impact of the creep characteristics by DRX could be one reason why the values for the activation energy have such a large variance. 4.3. DEF ORMATION HISTORY INDEPENDENCE Some of the studies in the literature [8,15,19,22,23,24,25] assume the creep specimen is defamation history independent. That is, the creep defamation taking place at 0’3, is not influenced by prior creep defamation which occurred at 02 and 01 previously. In other words, a fresh creep specimen loaded initially at a stress level equal to 0'3 and a specimen that was initially loaded at a different stress then, after a stress change, was loaded to 03, at the same temperature, would creep at identical or nearly identical rates. Therefore, the same specimen is used to determine the creep behavior at different stress re gimes. This type of approach saves time and money. This technique is also known as the 38 stress increment technique. 4.4. DIFFUSION CONTROLLED CREEP IN TiAl As mentioned previously, diffusion controlled creep can be classified as either Nabarro-Herring creep, where Q = QSD» or Cable creep, where Q = 1/2 Q30. depending on the temperature and stress regime examined. However, both creep models are based on self-diffusion. 4.4.1. Self diffusion of Ti-54A1 The literature has shown a variety of values for the activation energy, rang- ing from 80 to 600 (kl/mol) [26,27,28,29,30,31] depending on the different conditions of each creep study. But a majority of the literature suggest a value near 291 kJ/mol, the value reported by Kroll, Mehrer for 11 diffusion[32]. The value of 291 kJ/mol was obtained by a concentration-depth profile of the radioisotope Ti44 in binary Ti-54Al using a serial sectioning technique. Although much work has been done on other intemetallic structures, such as the B2, little or no work has been reported on the diffusion in the Llo type crystal structure. Kroll and Mehrer where one of the first to investigate the self-diffu- sion of the intemetallic 'y-TiAl. The figure below shows the arrhenius relationship for y- TiAl for the self-diffusion of T1(See Figure 4.2). 39 10‘“ r Mo's" 10'“ [ "'1 3.4.—.- cue-0....- ~o un—‘.—.~o—-‘— . “od- 10" [ Lush-1--.... 4 S 1 I 1/YITI"I" ‘ cl Figure 4.2 Plot of self-diffusion of Ti-54Al, [32] Using the equation for diffusion one can obtain a value for the activation energy equation (3). a = Doexp(-Q/RT) [6] where a0 = 1.53 x 10" m2/s and Q = 291 kJ/mol Because the compound y-TiAl does not have a congruent melting point but instead decom- poses by a peritetic reaction into B—TrAl and a melt (See Figure 3.3), Kroll and Mehrer instead use the value of the peritetic reaction in place of the melting temperature, Tm. Fol- lowing this argument, Kroll and Mehrer estimate a value of 261 kJ/mol instead of the mea- sured value of 291 kJ/mol. However, since their specimen composition is on the Al-rich side (Ti-54Al) of the phase diagram, which may have a significant impact on the physical properties, it is not clear if the difiusion mechanism is the same in the near-y range. Also, Tr-S4Al (N G) has a microstructure that is gamma without much alpha2 present. Therefore, the value may not be directly applicable for the lamellar-based on microstructural con- straints. 40 The value reported for the self-diffusion is very important for the mathe- matical modeling of creep. Because, this value will help to pinpoint the rate-limitin g defamation mechanisms for different creep regimes. However, the defamation mecha- nism(s) are hard to determine due to the large variance in the values reported by the litera- ture for the activation energy. 4.4.2. Alloys containing chromium The activation energies determined from creep experiments on single phase alloys are much higher than the interdiffusian (of T1 and A1) activation energies of 80 and 168 kJ/mol determined by Ouchi from diffusion couples of a2 and y alloys, respectively [54]. This suggests that factors other than diffusion play a significant role in creep defor- mation of gamma alloys. These may include the dislocation/cell structures, and pipe diffu- sion phenomena. Alternatively, very high creep activation energies in the Cr-containing alloys may be due to the strong effects of Cr an the diffusion kinetics in gamma alloys. Cr has been shown to slow down the transfomation kinetics in duplex gamma alloys, but it’s effects on diffusion have not been studied. Nevertheless, it is clear from studies of phase transfomations in gamma alloys that Cr reduces the diffusion kinetics by 1-2 orders of magnitude [8]. The investigation of the phenomena of the lower diffusion rate associated with the creep defamation of Cr-containing gamma alloys, unfortunately must rely on data obtained for non-chromium containing gamma alloys. Nevertheless, although the available single and multi-phase gamma diffusion data are insufficient for rigorous analy- sis, they do provide the basis for preliminary analysis of the trends in creep behavior in the low stress regime. 41 4.5 DISLOCATION CONTROLLED CREEP IN TiAl It is well known that at higher stresses, dislocation motion will contribute more to defamation than diffusion. This has led to dislocation studies using the transmission electron microscope (TEM), that have shown that the creep process leads to changes in the dislocation arrangements in crystals. The two types of dislocation con- trolled creep mechanisms that will be discussed are twinning and dislocation glide-climb. 4.5.1. Twinning To most material scientists, mechanical twinning is considered to occur only in crystalline materials at high strain rates and for low temperature conditions. How- ever, recently several studies investigating T’rAl have reported that mechanical twinning occurs at creep conditions with low strain rates and at intemediate to high temperatures. Since the introduction of the twinning type of defamation mechanism in TIA], it’s role in the creep process has been largely overlooked. Jin and Bieler [15,33,34] have shown that twinning occurs in various ways, including pseudo-twinning in different parts of the microstructure. In equiaxed gamma grains, twins nucleate from grain bound- aries due to stress concentrations at grain boundaries and triple paints. While twinning is not supposed to occur in the alpha2, the lamellar structure also includes some gamma that have shown cross-twinning. Twinning occurs at certain temperatures, while twinning does not occur at other temperatures. This type of temperature sensitive behavior has been indi- cated in an analysis of the ductile to brittle transition [19]. It has been observed that twin- nin g has a significant role in the transition, by causing the material to be more brittle than before twinning. A description by Shih [23] found twinning in the lamellar (FL) type structure at a creep temperature of 760°C, while Loiseau [35] also found twinning in 42 Tr-54Al in single phase gamma (NG) type structure at a creep temperature of 800°C. However, Huang and Kim [36] did not find twinning in a two phase alloy at a creep tem- perature of 900°C. Clearly, twinning is an important defamation mechanism in the range of creep rates and temperature. A representation of the twinning system for the gamma- based TiAl can be seen in Figure 4.3. o in plane of figure 0 above plane of figure '1: '[112]=‘ 1 Figure 4.3 Representation of twinning system. [34] The twinning elements shown in Figure 4.3 are listed as relative orienta- tions as viewed along [110] direction. The dashed line in Figure 4.3 indicates the position of K2 after true-twiruring. Table 4.1 Mechanical twinning elements of the thin twin layer K1 K2 711 1I2 Shear (111) (III) [112] [112] 0.707 43 In order to better understand the relation between the twin elements, and their orientation to tensile axis of the specimen Figure 4.4 provides a reference. [115’] Twin plane trace (111) Figure 4.4 Twin orientations as viewed along the <110> direction, [15] The mechanical twinning mechanisms is based on the dissociation of nor- mal dislocation b = l/2[110] into two partial dislocations[33,34]: 1/2[110]->1/3[111]+ l/6[112] This leads to the glide of a/6[112] partials that cause deformation-induced twinning in ‘y alloys. However, there been no reports of models describing how creep by defamation- induced twinning contributes to creep defamation of y—based titanium alumirrides. Soboyejo and others [8] report that the simple twin model neglects additional strains that are induced by coordinated movements of the partials. The effects of shear strains that result from defamation-induced twinning have been neglected due to the complexity of the modeling efforts required for the assessment of such strain distributions. 4.5.2. Dislocation glide-climb At higher stresses, dislocation motion will contribute more to defamation than diffusion. However, a stress may be high enough for a dislocation to move but not sufficient to overcome obstacles. Diffusion assisted dislocation motion is achieved allows the dislocation to climb around obstacles so they can continue to slip on another plane, and thus permit continued defamation. Hayes and London [37] have reported an activa- tion energy of Q = 326.4 kJ/mol and a stress exponent n = 4.95 for the composition Tr-48Al-1Nb yTrAl. The value reported in the study for the stress exponent is in agree- ment with dislocation climb controlled power law creep. Hayes indicates twinning occurs at low SFE, while climb occurs at higher stresses and high SFE [38]. A study of the com- bination of these two types of dislocation mechanisms acting either simultaneously or independently is needed to understand their role in the creep process. According to the incoherent twin boundary structure the true-twin plane energy can be estimated to be about one-half of the intrinsic stacking fault energy or extrinsic stacking fault energy in TrAl, assuming that the intrinsic stacking fault energy and the extrinsic are equal to each other. Based on the intrinsic stacking fault energy reported in the literature [15], 70 mJ/mz, the true twin plane energy in TrAl is about 35 mJ/mz. 4.6.3. Geometrical constant A An investigation into the power-law equation (Eqn. 1)[2] has yielded many interesting questions. The meaning of the “A” term is considered next. (de/dt),.=Ao"cxp(-Q/RT) (1) For a vast majority of the creep data in the literature, “A” is ignored. However, Sherby and 45 Burke [39] reports that the A value is a structure dependent constant which reflects the influence of stacking fault energy (SFE). It is considered that low values of A correspond to materials having a low SFE [39]. The SFE is also believed to be a function of the alumi— num content, where the stacking fault energy decreases with increasing aluminum content. A minimum exists in the stacking fault energy within the 48 to 51 (at%) aluminium range [37]. Martin and Lipsitt [40] observed a significant reduction in the steady-state creep rate of the TiAl alloy Tr-48.7Al-2.2W when the W was held in solid solution as opposed to previous creep rates measured for the same alloy with the W precipitated out on internal surfaces in the fom of fine beta phase particles. The apparent stress exponents and activa— tion energies for creep deformation were found to be nearly identical for the two condi- tions. It was concluded that the significant differences in creep resistance could not be explained on the basis of the stress or temperature dependence leaving the pre-exponential constant A as the only remaining variable. Table 4.5 shows the values of A obtained from previous studies, along with the apparent stress exponents and activation energies used in the calculations of A. Table 4.2 Comparison of different creep parameters and A [37] Commence“ ' a 112m 11 Q A BEE (at%) (MPa) (°C) (kl/mal) ’I‘i-48.7Al-2.2W* r73 - 345 700 - 900 4.5 400 2.20 x 105 [13] 'I'i-48.7Al-2.2W 172.4 750 - 900 5.5 370 2.83 x 107 [13] Ti-50.3Al 206 - 241 700 - 850 4.0 300 1.78 x 107 [26] Ti—48Al-1Nb 103 - 241 704 - 800 4.95 326.4 6.34 x 107 [37] Ti-53Al-1Nb 69 - 103 832 - 900 6.0 560 3.00 x 1010 [37] where * = W in solid solution 46 Martin and Lipsitt pointed out that a difference in the pre-exponential constant A, could result in differing steady-state creep rates without influencing the stress or tem- perature dependence of the steady-state creep rate. Table 4.2 indicates that the basic defor- mation process remains unaltered, but occurs at different velocities. Therefore, it is indicated that lowering the SFE (lower A) reduces the climb velocity by making climb more difficult. If dislocation climb is the rate controlling mechanism, we expect an appar- ent creep activation energy close to that of self-diffusion and a stress exponent in the range of 4-5. Hayes indicates that the A value, obtained by his method, varies from one study to another. One possible reason for these large differences in the A parameter could be explained by the changes in microstructure from one composition to the next. For example, the fully lamellar (FL) and the duplex (DP) structure, would have different A values. However, the results are preliminary and more work needs to be completed to understand how this pre-exponential A value effects the creep defamation process. 4.6. DEFORMATION MECHANISM TRANSITION As mentioned previously, the creep defamation mechanism that is dominate in one temperature and stress regime is often replaced by another defamation mechanism at a different temperature and stress regime. To illustrate this defamation mechanism transi- tion a list of the potential creep defamation at temperatures of (T > 0.4Tm) for equiaxed gamma [43] is shown in table 4.3. 47 Table 4.3 Creep defamation Mechanisms at T > 0.4Tm [43] Immature stress a Q a medrmisnr Low Low 1 Q08 3 Cable 1 QSD 0 Harper-Dom Intemediate 7 Qp 0 Climb-recovery High non-linear QSD? 0 Power-law breakdown High Low 1 QSD 2 Nabarro-Herring 1 QSD O Harper—Dom Intemediate 5 QSD 0 Climb-recovery 3 Q1 0 Viscous glide High non-linear QSD? 0 Power-law breakdown where Q99 = activation energy for lattice self diffusion QGB = activation energy for grain boundary difiusion (approx. = 1/2 QSD) Qp = activation energy for pipe diffusion Q = activation energy for interdiffusian of solute atoms 4.6.1. Unique creep behavior of Ti-48Al-2Cr-2Nb A study of the steady-state creep properties by Wheeler and London [25] shows for the composition of T'1—48Al-2Nb-2Cr the steady-state strain rate has a unique power-law behavior, see equation 1. The results indicate the stress exponent, 11, increases from n = 3 at low stresses, to n = 7 at higher stresses. See Figure 4.5 on the next page. 48 10‘ to" Steady State Creep Rate 10‘ 1 (8") g -I 1 O 760'0 ‘ A 7os-c 10:... ‘ -1--- 1... Stress (MPa) Figure 4.5 Creep behavior of Tr-48Al-2Cr-2Nb (DP), [25] The stress exponents here are not characteristic of stress-assisted diffusion creep process, such as Nabarro-Herring or Cable creep, which typically have an exponent of n = l, or dislocation creep processes which have an exponent of n = 5. However, Ruano and Sherby [39] have reported the stress exponent can be increased by two when pipe dif- fusion is the rate-controlling mechanism of creep defamation at intemediate tempera- tures. The power-law here can possibly be explained by creep being controlled by pipe difiusion at low stresses and then changing control to dislocation creep at high stresses. The mechanism can be thought of as being controlled by difiusion via dislocation align- ment and subgrain fomation during the creep defamation. Wheeler [25] made an Arrhenius plot to indicate the activation energy and came up with a value of 300 kJ/mol which is in agreement with 291 kJ/mol found by Kroll. However, an increase in the activation energy greater than 400 kJ/mol appears at 49 high stress levels. This observation is consistent with the idea of a change in the control- ling creep mechanism at higher stress levels, and it was correlated with DRX. 4.6.2. Aluminium content As mentioned previously, the Al concentration is suggested to be related to the SFE. Therefore, the Al concentration is indicated to determine the steady-state creep rate. This report was confimed by a study of equiaxed gamma (NG) with different amounts of aluminum by Oikawa [26,27,28,29,30]. Using the (MD) equation to analyze the data, a trend based on the aluminum content of different specimens, is in the table 4.4. With decreasing aluminum, the stress exponent, n, and the activation energy, Q increases. The conditions of the creep test was a compressive creep test at a temperature of 677- 927 °C and at stresses between 80 - 400 MPa. Table 4.4 Relationship between aluminum content and creep parameters at low temperatures and low stresses [26] Qamnesitian a Q (at%) (kJ/mol) Ti-53.4Al (NG) 4.0 - 4.5 330 Ti-51.5Al (NG) 4.5 - 5.5 330 Ti-SOAI (NG) 5.0 - 5.7 380 This same change occurs in the other two compositions of lower aluminum content, Ti-51.1Al and Ti-50Al. Oikawa suggests that creep parameters such as the activa- tion energy and the stress exponent are insensitive to microstructural change. This would imply that changes in the creep parameters are caused by the changing of defamation mechanisms from one type of mechanism to another. Also, Oikawa reports that the minimum creep rate depends on the creep condition. This adds another factor to the 50 consideration of the creep rate. He notes the following trends associated with the alumi- num CODICIII. Table 4.5 Relationship between different creep eflects [29] 1. Concentration of Al decreases: Grain size effect increases, the microstructural effect increases. 2. The effects A] concentration has on the properties decreases with: Increasing stress and temperature, increasing grain size. 3. As the amount of strain increases: Amount of twinning increases, amount of recrystallization increases. Table 4.5 shows that the creep characteristics are changing due to the amount of aluminium in the specimen. Seertrnan [41] indicates a modification of the mathematical approach is needed to compensate for the effect. He states that in the steady- state condition the creep rate in two-phase alloys obeys the conventional power-law creep equation. The reported values of the apparent creep activation values are in the range of 300 - 600 kJ/mol and the stress exponent values are in the range of 4.0 - 6.0. The composi- tion and grain size dependence of the minimum creep rate can be described by the follow- ing equation [41]: det 8mm, = A(l+X)mdo‘p (13) where A is a constant, X = 2NAl-l, N A] is the mole fraction of Al, do is the initial grain size and m is in the range of 10 - 20. The grain size exponent p is 3.7 - 4.7 for T1 - 50 at% Al and 0.5 - 2.3 for Ti — 51 at% Al. Again, the grain size effect on creep is found to be sen- sitive to the Al concentration, although the reason for this has yet to be established. 51 From Oikawa, the figures 4.6 and 4.7 show the change in defamation behavior of T'r-53.4 Al (NG)at a different stresses and temperature. It is not clear whether the defamation mechanisms changes from one type to another, or if two or more defor- mation mechanisms act simultaneously. to" h-Iltu ’4 “21 3". .—. le/ Figure 4.6 Figure 4.7 Transition of activation energy of Ti-53.4Al (NG), [26,27,28,29,30] 52 4.7. COMPOSITE VIEW OF CREEP Soboyejo and Lederich [8,42] report that the creep behavior of gamma- based alloys with duplex alpha2 and gamma microstructure can be modeled by recogniz- ing that the two phase alloys are composites that consists of alpha2 and gamma phases. However, these two phases are grouped differently into alpha2-gamma lamellar colonies and single gamma grains. The creep mechanisms in the individual constituents of the composite are thus assumed to be similar to those that would occur in polycrystalline alpha2 or gamma subjected to the same stresses and temperatures. This assumption neglects the different geometrical constraints and stress states that can exists at the bound- aries between alpha2 and gamma grains. Nevertheless it does provide useful insights into the contributions of individual alpha2-gamma and gamma phases to the composite creep defamation process. The strain rate contributions from the alpha2-gamma and gamma phases are determined for the composite using a simple rule-of—mixtures approach, and constitutive equations for the assessment of diffusion-controlled and dislocation con- trolled creep. Assuming that the equiaxed grains and lamellar colonies are arranged in series, i.e., constant stress conditions (See Figure 4.8), the difiusion coefficient of the com- posite can be estimated from a simple rule-of-mixtures to be: Dc = FGZDGZ + FYDT (14) where Dc = Diffusion Coefficient, F = phase volume fraction of a2 and 'yphases respec- tively 53 0’ Figure 4.8 Idealized duplex grain, [8] The value of the difiusion rate, D, is usually equivalent to the activation energy for diffusion-controlled creep defamation. Also, the experimental conditions of 200 MPa and 800°C and an observed creep rate of 6.44 x 10’7 were used to evaluate their model. Using the interdiffusian data of Ouchi [31], they obtained difiusion coefficients for single phase alpha2, Do; is 5.1x10‘8 mzs'l and for single phase gamma, D7 is 1.2x10'° mzs‘l. This gives composite diffusivity that is close to that of the 1 phase. 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(l _s) on: num. 84 3835.58 3320an. 8:055qu DmZ =m we :ommBmEcU :.n 2:3". .32. 02-25 32.. 08.0 owood m qwo_ w . . _ . . mow m 98 B an: m 96 o o o .m- 3 o 98 4 m I H A: was. + o v93. x mo 1.123 m 98 o VWOO m axo n. m: or F 98 n. o H a. m . mufop 9.87.58. _ _ . . . :3 «.3: . :ms. 8.8:. __o newton—Eco 091.0 / (l .6) 9an mm: 85 W ANALYSIS 6.1. INTRODUCTION The majority of the literature on creep of TiAl [8,19,20,23,25 - 30,35] is directed at describing the creep behavior as utilizing a single deformation mechanism, based on the concepts of common creep theory. However, because'there are so many dif- ferent microstructures and each has it’s own unique properties, a single model for all gamma-based titanium aluminides is unrealistic. Therefore, instead of directing this study toward a single deformation mechanism to explain the creep behavior of TiAl, this study will examine the different creep parameters that surround each creep experiment in an attempt to analyze the trends that appear in the data. This chapter will consider the unstable microstructure of TIA] and explain why a composite model is useful for understanding the deformation characteristics of TIA]. Then an analysis of the interface between the L10 and the D019 will provide impor- tant implications on the criteria for choosing elements of a composite model. The compos- ite creep model presented by Soboyejo [8] will also be re-evaluated in the light of the interface, and a simplified model based on the application of the Mukerjee-Bird-Dom equation to the rule-of-mixtures will be presented. 86 6.2. THE VARIABILITY OF UNSTABLE MICROSTRUCTURE IN TiAI As mentioned previously, the creep behavior of TiAl is not understood. The creep rate values for specimens of nearly the same composition and microstructure, at the same creep conditions are often different. Furthermore, the values for the activation energy, Q, and the stress exponent, n, reported in the literature survey vary widely from study to another. This leads to confusion about which creep deformation mechanism(s) is responsible for the observed creep behavior of TlAl. The literature survey has shown that slight changes in A] content of TiAl has a very large effect on the creep behavior. However, slight changes in the heat treat- ment history, grain size, test temperature, test environment and prior deformation which the creep specimen has experienced also have a large effect on the creep behavior of TiAl. Therefore, the creep data reported in the literature is often incomplete and inconclusive. This illustrates the fact that EA] has a microstructure that can change very easily with slight changes in composition and/or test conditions. Furthermore, alloying elements added to TiAl increase the variability of the TiAl microstructure. This is due to the fact that the phases present do not correspond to the phase diagram proposed by McCullough [18](SeeFigure3.3). Because McCullough only considers binary “Al in the phase diagram, once alloying elements are added to TiAl the phase diagram is no longer valid, and new ternary phase diagrams are needed. For example adding Cr to TiAl causes the alpha-transus line to be depressed, thereby raising the Al content of primary alpha phase. This leads to a reduction in volume fraction and width in the alpha21amellae. How much of a reduction with a given concentration of Cr is also variable [8, 23, 25,54]. The creep behavior of these materials is not similar, and the 87 creep deformation mechanism(s) responsible are not consistent with common creep theo- ries. More work is necessary to understand the effect of alloying on the microstructure of TiAl. Throughout the literature, the constituents of the microstructure are often generalized without considering the variability of the microstructure. This is why a com- posite model is important tool for describing the creep behavior of TiAl. The composite model allows for modifications of the description of the creep behavior to account for the variability of the microstructure. While the previous accounts attempt to describe the creep behavior by applying the existing creep data to common creep theory formulas. This approach resulted in a limited success (many of the successful attempts are accomplished by adding fitting parameters, such as modifying the geometrical constant, A). The advan- tage of employing the composite approach to describe the creep behavior, is the ability to identify different heat treatment histories, grain sizes and test conditions within the con- stituents of the microstructure. Only the composite model can make a distinction between which constituent(s) is adding to, or subtracting from the instability of the microstructure. 6.3. THE L10 AND D019 TRANSITIONAL INTERFACE The lamellar part of the duplex structure has become an important topic of discussion when trying to understand the creep properties of TiAl. The values found in the literature [8,23,25 - 30] for the diffusion rate through the lamellar structure are varied and contradicting. Therefore, it is important to investigate the interface between the L10 and the D019 lamellar constituents. In the literature [8,22,23,25,31] the diffusion rate through the interface is 88 considered to be controlled by the diffusion along the interface by the two diffusion rates for both the L10 and the D019. However, consider the interface between the lamellae con- stituents consisting of a gradual change from the L10 (gamma) stacking sequence of ABCABC, to the D019 (alpha2) stacking sequence of ABABAB. Then the interface between gamma and alpha2 can not be considered to have an normal interface boundary. Therefore, the interface between the two lamellae constituents can be thought of as having a transitional interface. Because the chemical composition of the duplex structure is usually in the 45-50 at% Al region, the titanium rich side of the phase diagram, Figure 3.1, the chemical composition of each individual phase is often off-stoichiometric. Based on the phase dia- gram, the concentration of aluminum atoms to titanium atoms in T13Al is not always two to one. The chemical composition of the different constituents in the lamellar interface evolves in increments from one composition to another, and has a one-half L10 one-half D019 composition at the so called “interface”, thus the idea of a transitional interface. To further explain, it is well known that the stacking sequence of the gamma corresponds to the (111) plane of the L10 (Figure 6.1) and the stacking sequence of the alpha2 corre- sponds to the (0001) basel plane of the D019 (Figure 6.2). Then the interface between the gamma and alpha2 is depicted in Figure 6.3. .Vf'AVA‘W. ' ° 90 But allow the composition of the interface to be off-stoichiometn'c. Then a titanium atom oCcupies a aluminum atom site. Note, that the relative size of aluminum and titanium are nearly equal, so therefore very little lattice strain is involved. The transitional interface plane appears as below (Figure 6.4 and Figure 6.5). 0 TI atom 0 Al atom all-stolchlomotrlc Figure 6.4 Transitional interface of 'I'iAl and Ti3Al (a) (111) phn. Figure 6.5 Transitional interface of TiAl and Ti3Al (b) 91 Thus, the stacking of this transitional interface corresponds to the (111) plane of the L10 while in the D019 basel plane. This is considered a slightly disordered matrix. Where the amount of disorder is controlled by the location away from the transi- tional interface, which shares a nearly 50%-50% composition. Therefore, the diffusion rate through the interface is not two diffusion rates, for the L10 and the D019, controlled by the diffusion along the interface of the two (Figure 6.6). Instead there is a single diffu- sion rate throughout the lamellar due to the solid interface nominalizing the diffusion path through the lamellar structure (Figure 6.7). A description of the diffusion rate and T1 con- tent vs. lamellar position is shown in top graph of Figure 6.8. Effect of Ti concentration on Diffusion boundary Diffusion rate grain 1 grain 2 Figure 6.6 Representation of diffusion without transitional interface 92 Ti-75Al —-> Ti-65Al interface TI 3 Al TiAl \ alpha2 gamma Figure 6.7 Effect of T1 concentration on Diffusion Concentration of Ti atoms 113m "mm“ TiAl Diffusion rat. alpha2 gamma (atomic plane) Figure 6.8 Ti content vs. lamellar position 6.4. ANALYSIS OF SOBOYEJO COMPOSITE CREEP MODEL As mentioned earlier, Soboyejo [8] and others [14,42] report that gamma- based TIA] alloys with duplex (gamma-alpha2) microstructure can be modeled by recog- nizing that the two phase alloys are composites that consists of gamma and alpha2 constit- uents. Because creep deformation within two-phase y alloys may occur by any one of the 93 deformation mechanisms discussed previously, Soboyejo developed a method of deter- mining the creep rate by applying a simple rule-of-mixtures approach. Again, the equation Soboyejo used for the composite strain rate, (de/dt)c, is given by [8]: (d8/dt)c = fa2[(d8/dt)DCa.2 + (C's/(1000a + (d8/dt)ca2 + (dB/(IONHafl + “(dc/dupe, + (dc/dam7 + (dc/dam + (deldt)NH.,]+ (15) 6.4.1. Application of the Soboyejo model When executing the equation for the creep rate, Soboyejo would apply the theoretical values to each the individual creep deformation mechanisms (DC,DG,C,N-H) for both constituents (gamma, alpha2). Then he would compare the value obtained for - each deformation mechanisms to the observed creep rate, and the deformation. mechanism that was the closest to the observed value was named the dominate creep deformation mechanism. While the other deformation mechanisms that resulted in values that did not come close to the observed creep rate where labeled insignificant and removed from the above equation. The value for the observed creep rate was 6.44 x 10'7 s'1 at creep condi- tions of 800°C and 200 MPa. Application of the difiusion-controlled mechanisms showed that the value for Nabarro-Herring type creep was too large when compared to the actual creep rate. Obtaining a value of lZOaNH (3") for the temperature and stress conditions reported. Coble type creep was one order of magnitude faster than the observed creep rate. When the dislocation controlled mechanisms were applied, the values for the creep rate were much too slow compared to the observed creep rate. However, there was a severe lack of adequate information on the dislocation structures to make a justifiable approxima- tion. Therefore, Soboyejo indicates that Coble creep is the dominate deformation mecha- nism for the creep conditions reported. 94 6.4.2. Problems with the Soboyejo model There where several problems with the actual article published by Soboyejo [8], including leaving out certain characters out of corrunon creep theory formu- las (i.e. p, d and T in the Coble creep equation). However, this paper will only address cer- tain theoretical values used in the equations that formulate equation 15, and some basic assumptions that were made by Soboyejo. Soboyejo listed values for the atomic volume, 9, and thickness of the grain boundary, 8, listed on Table 6.1. An attempt to reproduce the values indicated in Table resulted in another value for the atomic volume of the D019 structure. This would have a definite impact on the creep rate calculated by Soboyejo. Table 6.1 Different creep parameter values used by Soboyejo [44] mum: a 9 9 fl L10 0.398 nm 0.408 nm 4.62 x 10'30 m3 0.001 pm 13019 0.462 nm 0.578 nm 2.67 x 10‘28 m3 0.001 um where aS = l um for a typical lath, and b = 0.398 nm note: the D019 structure has a hexagonal based atomic volume, also there are errors in atomic volume Also, here seams to be some confusion about the value for the grain size being determined by either the average individual lath size of 15m, or the average size of the lamellar col- ony which is approximately 200 pm. The correct value for the gram size would be esti- mated as the size of the colony approximately 200 um. Applying the wrong value in the dislocation controlled creep equation would also have a very large effect on the calculated creep rate by Soboyejo. Soboyejo does indicate that the differences between the predicted and the measured creep rate may be due to the use of Coble creep geometrical constant for materi- als with duplex microstructures. This leads to an investigation of the assumption that the 95 equiaxed grains and lamellar colonies are arranged in series as in Figure 4.8. This assumption neglects the highly anisotropic nature of the grain boundary orientation, See Figure 6.9. G Figure 6.9. Idealized highly anisotropic duplex grain Coble creep utilizes diffusion along grain boundaries. The original assump- tion indicates that grain boundaries are smooth and easy for a difiusing atom to transverse. However, the new idealized grain shows that the grain boundaries are highly misaligned due to the lamellar grain structure. 80, the length of the diffusional path along grain boundaries will be longer and harder for a diffusing atom to transverse. This would cause the diffusion along the grain boundaries to slow down. Furthermore, another important aspect of the new idealized grain to observe, is that no grain boundary sliding can occur due to the highly misaligned grains. As opposed to the original idealized grain where the grain boundaries where portrayed as smooth and grain boundary sliding easy to initiate. 96 6.4.3. Three constituent composite creep model Another way to view duplex TiAl as a composite model is to consider the structure as having three constituents. The three constituents being the equiaxed y grains, the (12 phase in the lamellae and the yphase in the lamellae. The reason for this type of arrangement is due to the fact that (12 tends to absorb oxygen and other impurities. Because these impurities tend to increase strength and reduce diffusion in the a2, both gamma phases can be thought of as being soft or diffusion is faster than the hard a2 phase. However, the impurity content is lower in the y—phase of the lamellar structure than in the equiaxed y grains because to its close proximity to the (12 phase. Therefore, the y-phase in the lamellae would experience the greatest reduction in the impurity content, and would be considered softer than the y in the equiaxed grains. Thus, there is a need for the division of the gamma phase into the gamma in the lamellae and the gamma in the equiaxed grains. Therefore, the three constituent composite rule-of—mixture equation would then be: DC = FyeDye + FaZIDazl + FwDyl ' (16) where D = Diffusion Coefficient, F = phase volume fraction of 7,, in the equiaxed, a2. lamellae and the y] lamellae. The phase volume fraction would be approximately Fr: = 0.50, 1:11.21 = 0.05 and F.” = 0.45. However, no information is available on the difference in diffusion rates in the equiaxed gamma phases and the lamellae 7. More work needs to be accomplished in this area. 6.5. RULE-OF-MIXTURE-MUKERJEE-BIRD-DORN EQUATION As mentioned earlier, Soboyejo [8] and Hazzledine [14] report that the creep behavior of gamma-based alloys with duplex microstructure can be modeled by 97 recognizing that the two phase alloys are composites that consists of alpha2 and gamma phases. However, instead of using the Soboyejo approach as described previously, an attempt to use more physically meaningful mechanisms and to simplify the mathematics has resulted in a new approach. Consider an approach which combines the composite rule- of-mixtures with the Mukerjee-Bird-Dom equation. Thus, the new approach yields the equation: (dB/(IOCMBD = fa2{ (ADoale/kT)(C/G)"CXp(-QSD/RT)} + f'Yl(ADOYGb/kT)(o/G)"exp(-QSD/RT)} (17) where f is the phase volume fraction for the (12 and yphases. This statement of the MBD equation has no grain size dependence (p = 0). By utilizing the equations D112 = Doazexp(-QSD/RT) and Dy = Do'yexp(-QSD/RT) for the diffusion rates of a2 and 7 respectively, the above equation becomes: (dE/dt)cMBD = fagl Da2(AGb/kT)(o/G)"} + fy] DY(AGb/kT)(G/G)"} (18) Then using values obtained for the diffusion coefficient reported by Ouchi[31], D612 = 5.057 x 10'8m25'1 and Dy: 1.241 x 10’6m28'1 But, recall that diffusion coefficients reported by Ouchi [31] where computed from non- chromium containing alloys. Thus, the values have to be scaled using ratios of phase transformations determined from previous studies. The ratio appears to be by a factor of 10 slower for chromium containing alloys [8,43]. Therefore, D62 = 5.057 x 10'9m2s;l and D7 = 1.241 x 10'7m2s'l A study by Schafrik [44] reported a value for the temperature dependent shear modulus. However, the aluminium concentration of the study was 36 (at%) Al in 98 TiAl, and as mentioned previously this has an effect on the properties of the material. Therefore, by an extrapolation, and the fact that we know the shear modulus at room temperature for Ti-48Al-2Cr-2Nb [34] is 69620 MPa, we can estimate a value using the following equation: G = 73494 -13T = 69620 MPa (T = 298) and 59545 MPa (T = 1073) The Burgers vector, b, is found by considering the different lattice parame- ters. The gamma (L10) structure has a c/a ratio of 1.03 with a = 0.398 nm. Thus, the [110] direction the Burgers vector is SQRT(2)/2 x (0.398 x 109) = 0.283 nm. While the alpha2 (D019) has a hexagonal structure with a = 0.462 nm. However, because the D019 is con- sidered a super lattice the hexagonal lattice is twice as large as a normal hexagonal closed pack (hcp) lattice. Thus, the burgers vector is b = 0.462 nm. Which implies super disloca-' tion controlled creep. The geometrical constant A is a fitting parameter based on the data reported by Howmet [25]. A number of geometrical factors are not identified, such as: the grain size and the sub grain size. A is often composed of the relationship between the stacking fault energy and the grain size. A = A’(y/Gb)3(b/d)p where y = stacking fault energy, G = shear modulus, b = Burgers vector, d = grain size, p = grain size parameter. A list of the values used in the rule-of-mix-MBD equation is shown in Table 6.2. 99 Table 6.2. List of various creep parameter values Gamma AlphaZ L10 D019 1)Y = 1.241 x 10'7 mzs'l Do,2 = 5.057 x 10") m25'1 b = 0.689 nm b = 0.462 nm G = 59545 MPa G = 59545 MPa 0 = 400 MPa 0 = 400 MPa 11 = 4.5 n = 4.5 11:1:110'll A=lx10'” T = 800°C T = 800°C Therefore, by applying values given we obtain: b For alpha2: (116/111),,2 = Daz(AGb/kT) * (o/G)" = (5.057 x 10% x 10‘“)(59545 x 106)(0.462 x 10'9)/(1.38 x 10'23)(1073) * (400 x 106/59545 x 106)“.5 = 1.57 x 10'8(s'1) For gamma: (de/dt)7 = DY(AGb/kT) * (tr/G)n = (1.241 x 10'7)(1 x 10'“)(59545 x 106)(0.689 x 10'9)/(1.38 x 10:23)(1073) * (400 x 106/59545 x 10")“-5 = 5.74 x 10‘7 (5") 100 Now employing the rule-of-mixture for the nominal volume fraction of 5% (12 present in the duplex microstructure yields: (de/dt)cMBD = (0.05)(1.57 x 10'“) + (0.95)(5.74 x 107) = 5.53 x 10'7 (5'1) When compared to the observed value of 6.0 x 10‘8 (s'l) at 800°C and 200 MPa [8], we find the experimental error is {(6.0 x 10'8- 5.5 x 10'7)/6.0 x 104‘} x 100 = 816.7% error. This is within an order of magnitude of the observed steady—state creep rate, and is approximately the value Soboyejo obtained using the composite creep approach, with Coble creep being the dominate creep mechanism. However, when compared to the Wheeler [25] observed rate 6.0 x 10’7 at 800°C and 200 MPa, we find the experimental error is {(6.0 x 10'7— 5.5 x 10'7)/6.0 X 107} x 100 = 8.3% error Most mathematical creep models that fall within one order of magnitude of the measured creep rate are considered a decent approximation. The A value was chosen to get a good approximation. The differences between the measured and predicted creep rates in the rule-of-mixture-Mukerjee-Bird-Dom equation may be due to significant errors in the diffusion coefficients used in the calculations. When comparing this new approach to the Soboyejo model it is important to mention that Soboyejo only examines a limited creep regime of one temperature and one stress for his creep model. Therefore, it represents a single point when plotted as log 101 steady-state strain-rate vs. log stress. So, in order to compare the new approach more accurately, a range of the predicted creep behavior using the composite-MBD equation is provided. The predicted creep behavior using the composite-MBD equation is shown in Table 6.3. Table 6.3. List of predicted creep behavior using composite-MBD equation limit. a 9 2,12 .27 mam (°C) (MPa) (MPa) (m2s“) (mzs'l) 6“) 700 100 60845 1.59 x 10’10 3.91 x 10'9 3.0 x 10'11 700 200 60845 1.59 x 10'10 3.91 x 10'9 3.0 x 10'10 700 300 60845 1.59 x 10'10 3.91 x 10‘9 2.0 x 10'9 700 400 60845 1.59 x 10‘10 3.91 x 10'9 2.0 x 10'8 800 100 59545 5.057 x 10'9 1.241 x 10'7 1.0x 10'9 800 200 59545 5.057 x 10'9 1.241 x 10‘7 3.0 x 10'8 800 300 59545 5.057 x 10'9 1.241 x 10'7 7.0 x 10'8 800 400 59545 5.057 x 10'9 1.241 x 10'7 6.0 x 10'7 900 100 58245 8.90 x 10‘8 2.19 x 10'6 2.0 x 10'“ 900 200 58245 8.90 x 10'8 2.19 x 10'6 3.0 x 10‘7 900 300 58245 8.90 x 10'8 2.19 x 106 1.0 x 10'6 900 400 58245 8.90 x 10'8 2.19 x 10'6 1.0 x 10'5 Figure 6.10 shows a comparison of different creep conditions on one plot of logarithmic strain-rate vs. logarithmic stress. While Figure 6.11 shows a comparison of the temperature compensated comparison plot of logarithmic strain-rate vs. logarithmic stress. The temperature compensation technique will be described in detail later in chapter 7. 102 :23an QQZQVSES ..8 8622.8 :88 328.5. ..o eomEnEoU 2 .6 use". .32. ...... ”fir... . «$3.. . 6.. 3 up. ’70—. Top Oooom + 5.0.. Ooomm x Queen 0 mb— Ooowh D G d d d d d d 1 ‘1! d d d d 1000-Oh. F0000 (l 3) our maria 103 388595“. 23225.8 cause—co ans—6.6388 05 .8 2.33:3 n85 .5..ch no cash—Eco e a 2:2... .32. ...... 83 8 85 oo :55 L: —-»-b.~ - p rpb... . . _:....L p — OF . ' m I ' ppOP m m. . m . . go? I ‘0 30—. ...uad . « _.-.d-a°w:. _:qq.d « - 9.358.352: Eco: .o 23.9. R VE DISCUSSION 7.1. INTRODUCTION In this chapter, the data from the experiments described in chapter 5 are compared to other studies in the literature [8,25 - 30]. An important issue resulting from this comparison is the assumption of the deformation history independence in multiple stress jump creep tests. The experimental data is nOrmalized by the temperature depen- dence of the self diffusivity [32] and the shear modulus [44] for most of the available stud- ies on creep of TiAl [8,19,23,25 - 30,35,40,49,60,62]. The data from several studies [19,25 - 30] is compared in plots of logarithmic strain rate vs. logarithmic stress in order to inves- tigate the stress exponent, 11. Finally, the mechanisms that soften the microstructure and restricts dislocation glide by lamellae are explored to improve our understanding of the deformation mechanism(s) responsible for the creep behavior of TiAl. 7.2. COMPARISON OF MSU DATA TO LITERATURE The comparison of the data from this study and the literature has shown that some creep specimens appear to creep faster than others, even-though the creep spec- imens had the same nominal composition and the same test conditions. The reasons behind this unusual creep behavior will be explored. Table 7.] lists the minimum steady-state creep rates obtained for a given stress and temperature condition for all the creep experiments of this study. The strain at 104 105 which the creep specimens achieved minimum steady-state is also given. This information is a useful tool to understand the creep condition of the specimen during deformation. From the data given in Table 7.1 a trend of increasing steady-state strain rate with increasing stress holds for all the experiments. However, there appears to be two groups of creep behavior. The first group of experiments (1, 2, 3, 4, 8, 9) have a steady- state creep rate that is a magnitude faster than the second group (6, 7). The steady-state creep rates of group one are approximately equal to the values obtained by Soboyejo [8] 6.4 x 10'7 s'1 for creep conditions of 800°C and 200 MPa and the values obtained for group two are approximately equal to the values obtained reported by Wheeler [25] 6.0 x 10'8 s’1 for the creep conditions of 815°C and 200 MPa. It is curious that both trends in this study have similar data existing in the literature. How- ever, due to the fact the other creep studies [8,25] had specimens of the same composition and similar microstructure, and were tested at similar creep conditions, the data seems contradictory. 106 Table 7.1 List of creep data from MSU study W 8 11°21 Ti-48Al-2Cr-2Nb 760 (DP) 760 760 760 760 760 760 760 760 760 760 760 760 760 760 760 760 760 760 760 760 760 760 760 760 760 \IO‘Ut-hUJN—e \IOUt-hU-JN— where # = data point number f = final strain * = reload of exp 2 added to exp 3 SLLMEal 160 183 315 225 180 150 175 320 215 245 170 125 145 154 186 186 105 145 155 I47 I77 155 205 180 180 190 M1111) 1.0 x 10'7 6.0 x 10'7 3.0 x 10'6 1.0 x 10’6 6.0 x 10’7 3.0 x 10'7 3.4 x 10'7 3.0 x 10'6 1.4 x 10’7 4.3 x 10'7 23 x 10'7 1.6 x 10'8 1.8 x 10'7 3.0 x 10'7 5.5 x 10'8 8.5 x 10’8 1.8 x 10‘8 2.0 x 10'8 2.4 x 10'8 2.2 x 10'8 4Jx103 2.8 x 10'8 5.1 x 10'8 2.8 x 10'7 3.8 x 10'7 1.0 x 10'7 L 0.05, 0.10, 0.022 0.05 0.076 0.095 1352f exp 1 exp 2 exp 3 0.107, (0.13,)* 0.045 0.065 0.073 0.108 0.1 15 0.133 0.15, 0.04 0.23, 0.033 0.042 0.053 0.068 0.086 0.105 0.17, 0.035 0.155, 0.08, exp 4 exp 6 exp 7 exp 8 exp 9 107 7.2.]. Experiment #4 Experiment #4 employed the stress decrement technique. However, the experiment also cycled the load up and down as the specimen deformed, to obtain a corn- bination of stress cycling and stress decrements during creep testing. The stress was cycled up and down, but a general stress decrease was the overall direction of the experi- ment(See Figure 5.4 and 7.1). Also, this experiment was performed in a rough vacuum, which has a small effect on the creep behavior (due to reduced oxide formation). Experiment #4 was of particular interest because it exhibits similar creep properties as found in the studies by Wheeler [25] and by Soboyejo [8] in the same speci- men. The trend in common with Wheeler [25] is a distinct change in the stress exponent from n = 1.7 at low stress to n = 7.7 at higher stresses(See Figure 7.1). But there is a large strain between the data points that indicate the n = 1.7 value. The stress exponents here are not characteristic of stress-assisted diffusion creep process, such as Nabarro-Herring or Coble creep, which typically have an exponent of n = 1, or dislocation creep processes which have an exponent of n = 5. However, the steady-state creep rate in experiment #4 was 2.3 x 10'7 s'1 at conditions of 760°C and 170 MPa which is approximately equal to the value found by Soboyejo [8] of approximately 6.4 x 10:7s‘1 at a creep conditions of 800°C and 200 MPa(See darken line in table 7.1). But the temperature difference between the two studies is large enough to cause significant differences in the data. Wheeler [25] reports to have a steady-state creep rate of 6.0 x 10'8 s’1 for creep conditions of 815°C and 200 MPa. There- fore, experiment #4 shares the unique stress exponent change behavior found in the inves- tigation by Wheeler (Wheeler’s report was categorized as group two), but had a 108 EN. 5.3.5? .8. I. .5858“... .3 58..» 83.5.. 32.532. 2.3.5 3 2.8.. A35 ...... 80. oo— . . 1 q q q u . 00°F .11. m0 .. n H m A w. 1m 0 ..o— . ~ nu I 'g l n no u m Nut: \ m ...... 1 obp ... PD 1 n a p p p p . p u p 1 MtOP 3.. 808.598 (13) our man. 109 steady—state creep rate of group one. 7.2.2. Experiment #7 Experiment #7 also employed the stress change technique, and the experi- ment also used an uncommon test technique of cycling the load up and down to obtain a combination of a stress cycling during creep testing. However, instead of the stress direc- tion being generally decreasing overall as in experiment #4, experiment #7 had a generally increasing stress condition(See Figure 7.2). Also, experiment #7 was performed in an open air atmosphere and not in a rough vacuum, as was the case in experiment #4. The results indicate that the steady-state creep rate obtained is similar to group one, 4.1 x 10'8 s'1 for creep conditions of 760°C and 177 MPa, which is near the creep rate reported by Wheeler [25], 6.0 x 10'8 s'1 for the creep condition of 800°C and 200 MPa(See darkened line in table 7 .1). However, the experiment did not show the unique power-law behavior shared with experiment #4 and the data from Wheeler [25](See Figures 4.5 and 7.5). A comparison plot of experiments #4 and #7 is provided in Figure 7.3. A temperature compensated plot of the same experiments is provided in Figure 7.4. 7.2.3. Investigation of deformation history independence Before experiment #4 began, the TiAl specimen has already experienced a complicated heat treatment history. The creep experiment started with loading to a high stress, which introduced dislocations and twinning into the material. This could be consid- ered as another therrnomechancial treatment. There can be two types of deformation 110 equxonom .3 5:05. sue me 2.... 508 083. 5.8.... 2» 808.595 2 65mm .35 8.3. coo. cc. q q a q q q q 1 - 90F — N O , .... . no r ml: oO . I no I t No a r 4 LL - b b n p . hOOF be 808598 (15) out man. 111 t. E... 3. 3:08:85 he 88 88:389.. < 2 28E Aizv 3.3. coop cop or «4.4. q a 8 -...d u . q . 00°F r ‘0. r m co m m. D .m 8.0— . 6m. . n D H .. .. r2 . #96 D . m 0 ~98 o H m...» p p h p —p-- p . b P m OF “I 3% am: .0 88.5888 (..8) an arms 112 5880.83 22.5.82 2. ...... 2. 5.5.8.5.... ..o 8.. :om_8.88 < E. as»... .5... o :8... .8... ..o S... Sod Seed dddld d 1 .111111 1 d ddddddq d d 1 “OP . ..‘u. ...: m. U a a ... . . D 20. 0 m. v.5 o .98 o 23 Phbbb b P —bbbhbtP b h t-Pnbbbbib - 23 am: 83.. .o 52.5.83 113 mechanisms operating at the same time. One of the mechanisms is the dislocation glide- climb type and the other is a twin softening type. The dislocation glide-climb type of deformation mechanism would exhibit dislocations that are climbing and annihilating each other. But the softening type of deformation mechanisms could result from the mechanical twins that propagated across the grain, and permanently changed the micro- structure. Therefore, the material creeps faster, and the assumption of the deformation his— tory independence does not hold. In the second case, the generally increasing stress experiment (experiment #7) starts off at a low stress and is increased to a high stress, the amount of mechanical twins propagating across the grain is smaller, and the dislocations that are climbing and annihilating remains the same. Therefore, the material creeps slower than the generally decreasing stress group, and the assumption of the deformation history independence holds. In conclusion, the assumption of the deformation history independence depends on the overall stress direction of the creep experiment. Furthermore, the effect of twinning deformation mechanisms prevents the assumption from being accurate in the generally increasing and decreasing stress directions. 114 7.3. COMPARISON OF CREEP DATA PLOTS of TiAl The experimental data has been normalized by the temperature dependence of the diffusively and the shear modulus for all the various creep experiments at different temperatures. The temperature normalization of values allows the investigator a more accurate comparative view of the stress dependence on the creep deformation. 7.3.1. Unique power-law behavior of Ti-48Al-2Cr-2Nb As mentioned previously, the steady state creep rates plotted in Figures 7.5 and. 7.6 reported by Wheeler [25] for Ti-48Al-2Cr-2Nb, reveal a unique power-law behavior within the stress regime tested. A distinct change in stress exponent from n = 3 at a low stress to n = 7 at higher stresses is observed, indicating a change in the controlling creep deformation mechanism. Again, the stress exponents measured here are not characteristic of stress-assisted diffusional creep processes, such as Nabarro-Herring or Coble creep where n = l, or dislocation creep processes, where n = 5. Recent work has shown that stress exponents can be increased by a factor of two when pipe diffusion is rate-controlling dtuing intermediate temperature creep deformation [25,43]. With this knowledge, the power-law behavior identified here could be explained by diffusional creep at low stresses with a change to dislocation creep at high stresses, both of which being controlled by diflusion via dislocation pipes. This hypothesis is supported by the observation of dislocation alignment and subgrain formation during the creep deformation of gamma alloys [25]. 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