53$: IIHHIHIWHIWIHIIHIIHIIIIIHHIIIHHINIIIIHIHIIHII THESE“) This is to certify that the thesis entitled EFFECT OF TEMPERATURE ON THE MECHANICAL PROPERTIES OF Cu-lONi—6Sn SPINODAL ALLOY presented by Apiohart Vilassakdanont has been accepted towards fulfillment of the requirements for M o S 0 degree in metallurgy ‘& lYXLJNOLA/vx MCOLM Major professor Date—MMO 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution TV1£31_] RETURNING MATERIALS: Place in book drop to mantles remove this checkout from ‘— your record. FINES will be charged if book is returned after the date stamped below. ‘1 1 M - 1 £1 0-} It... a,- fire? 9 C3 0,:3 EFFECT OF TEMPERATURE ON THE MECHANICAL PROPERTIES OF Cu-lONi-éSn SPINODAL ALLOY By Apichart Vilassakdanont A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Metallurgy, Mechanics and Materials Science 1983 ABSTRACT EFFECT OF TEMPERATURE ON THE MECHANICAL PROPERTIES OF Cu-1ONi-6Sn SPINODAL ALLOY By Apichart Vilassakdanont Tensile tests on Cu-1ONi-6Sn spinodal alloy were carried out on polycrystalline samples in as-quenched and aged condi- tionszrtvarious temperatures ranging from 770K to 3530K. Yield stress, work-hardening rate, and total elongation to fracture were measured. It was found that the temperature dependence of the yield stress could be explained by the solid solution hardening mechanism. The experimentally measured incremental yield stress of aged specimens is in good agreement with Kato- Mori-Schwartz's theory (1). The incremental yield stress due to spinodal decomposition is temperature independent and there is no marked difference in activation energy for plastic flow of as—quenched and aged specimens. The work—hardening rate and the total elongation are independent of the amplitude and wavelength of the composition modulation in the spinodally- modulated structure. Deformation of the aged specimens is accommodated by coarse slip, whereas the as-quenched specimens deform by fine slip. ACKNOWLEDGEMENTS The author wishes to express his deepest appreciation to his present advisor, Dr. K.N. Subramanian and his former advisor, Dr. M. Kato for their suggestions and guidance in this work. Also, to his friends and his colleagues, especially Mr. T. Lee, Mr. S. Shekhar, and Mr. N.B. Dahotre who gave their timely help and support when he needed them most. Finally, to his wife and daughter, the author expresses his deep gratitude for their patience and encouragement. This research was partially supported by the Department of Energy by Contract Number DE—ACOZ-81ER10942. TABLE OF CONTENTS LIST OF FIGURES......... .............. . ..... .......... LIST OF TABLES. ...................................... . 1. INTRODUCTION ................................. ..... 1.1 Spinodal Decomposition ....................... 1.2 The Theories of Age-Hardening of Spinodally- Modulated Structures .................... ..... 1.3 Thermal Activation of Dislocation ............ 2. EXPERIMENTAL PROCEDURE ............................ 2.1 Sample Preparation. ......................... . 2.2 Mechanical Pr0perties ........................ 2.3 Scanning Electron Microsc0py and Transmission Electron Microscopy Studies.. ................ 3. EXPERIMENTAL RESULTS .............................. 3.1 Mechanical Properties.. ...................... 3.2 Activation Energy ............................ 3.3 Scanning Electron Microscopy and Transmission Electron Microscopy .......................... 4. DISCUSSION. ......... ..... ......... . ...... ......... 4.1 The Role of Spinodally-Modulated Structure on the Yield Stress .......................... 4.2 The Effect of Temperature on the Yield Stress ....................................... 4.3 The Effect of Spinodally—Modulated Structure on the Work-Hardening Rate ................... iii Page vii 11 11 14 14 17 17 32 35 42 42 48 49 Page 4.4 The Effect of Spinodally-Modulated Structure on the Total Elongation. ..................... 50 4.5 Slip Distribution in Deformed Specimens...... 51 5. SUMMARY. ...................................... .... 52 LIST OF REFERENCES .................................... 54 SUGGESTION FOR FURTHER RESEARCH ..................... .. 58 iv Figure U 10 11 12 13 LIST OF FIGURES (a) The free energy versus composition at temperature T0 for a binary alloy that can undergo spinodal decomposition...... ............. (b) Binary alloy phase diagram indicating spinodal region and miscibility gap .............. Internal stress field encountered by a dislocation moving through the crystal lattice... Schematic of the tensile test specimen ........... Schematic drawing of the furnace used for heat treatment ................................... Test fixture for tensile prOperties .............. Stress—strain curves of specimens which were deformed until fracture at 770K...‘ ............... Stress-strain curves of specimens which were deformed until fracture at 2030K..... ............ Stress-strain curves of specimens which were deformed until fracture at 2980K ................. Stress-strain curves of specimens which were deformed until fracture at 3530K ................. Plot of yield stress versus aging time of specimens which were deformed at various temperatures ........................... .. ........ Plot of yield stress versus testing temperature of as-quenched and aged specimens ...... . ......... Plot of incremental yield stress (in aged specimens with respect to as—quenched specimens) versus testing temperature ....................... 1 Plot of true stress versus (true strain)2 for specimens which were deformed at 770K ............ Page 9 12 13 15 18 19 20 21 22 23 24 26 Figure Page 14 Plot of true stress versus (true strain)% for specimens which were deformed at 203°K.. ......... 27 15 Plot of true stress versus (true strain)% for specimens which were deformed at 2980K ........... 28 16 Plot of true stress versus (true strain)% for specimens which were deformed at 3530K... ........ 29 17 Plot of total elongation versus aging time of specimens which were deformed until fracture at various temperatures .......................... 31 18 Plot of yield stress versus testing temperature of as-quenched and aged specimens. ............... 33 19 Plot of activation energy versus testing temperature of as-quenched and aged specimens.... 34 20 Scanning electron micrographs of as-quenched specimens which were deformed by 20% at (a) 2980K and (b) 770K ..................................... 36 21 Scanning electron micrographs of 20 minutes aged specimens which were deformed by 20% at (a) 2980K and (b) 77°K ........................... 37 22 Scanning electron micrographs of 4 hours aged specimens which were deformed by 20% at (a) 2980K and (b) 77°K.. ......................... 38 23 Scanning electron micrographs of 24 hours aged specimens which were deformed by 20% at (a) 2980K and (b) 770K ............ . .............. 39 24 Transmission electron micrographs of specimens aged at 350°C for (a) 4 hours and (b) 24 hours... 40 25 Plot of incremental yield stress versus A, AZA, AZ/A, and A/A .............................. 44 vi LIST OF TABLES Table Page 1 Comparison of the experimental and theoretically predicted values of incremental yield stress ...... 43 2 The values of amplitude and wavelength of composition modulation in Cu-lONi-éSn alloy after aging at 350°C for various lengths of time .............................................. 45 3 The values of n, y, Y, b, (PO/ E)max, G .......... 46 vii 1. INTRODUCTION It has long been known that the modulated structure pro- duced by spinodal decomposition can cause age hardening. How- ever, the details of the mechanism of this hardening are far from being fully understood. The main purpose of the present study is to investigate the effects of temperature on the yield stress, work-hardening rate, and total elongation of the spinodally—modulated structure and to correlate measured values of these mechanical properties with proposed theoreti- cal models. The Cu—10Ni—6Sn alloy is chosen for the present study, since this system (Cu-Ni-Sn) has been well character- ized fbr spinodally-modulated structure (2,3,4). In this chapter, literature review relevant to the present study will be presented. 1.1 Spinodal Decomposition. Spinodal decomposition is interesting scientifically because it is an example of a homogeneous reaction which involves only one phase (from the crytallographic point of view). The essential characteristics of this transformation involve the special shape of the free-energy curve as shown in Figure 1(a). In this figure the Helmholtz free energy, f(C), varies with composition C at a temperature To. It must have a 2 central maximum, consequently BZf/BC must be negative within (a) Helmholtz free Energy, f(C) at T0 'I"-" \ I I I ,. | I I I g l 1 l ‘ 41_,. . i i .031 .082 I 1 ' l l ' I I ' (b) ' I l : l MiSCiPility a l l - I I 8 ' I 5 I l .p a ' ' ______ —--J 8. To E (1) 9+ ‘ , 1 Atomic concentration of second composition, C Figure 1 (a) The free energy versus composition at temperature T0 for a binary alloy that can undergo Spinodal decomposition. (b) Binary alloy phase diagram indicating spinodal region and miscibility gap. a certain range of composition. This range is known as the spinodal region and determined by the two inflection points, C81 and C52, defined by 2 (Ea—g) = o (1) 3C T,V where C is the atomic fraction of the secondary component, V is the volume of the material, and T is the temperature. The spinodal region in the phase diagram is indicated in Figure 1(b); it is defined by the area under the locus of points (dashed-line) satisfying equation (1). So spinodal decomposi— tion occurs when the alloy is aged at temperatures and the spinodal compositions which are given by the region bounded by the spinodal curve (dashed-line). The initial studies of spinodal decomposition were carried out in early 1940's. At that time, Daniel and Lipson (5,6) observed the sidebands around the Bragg peaks of the X-ray diffraction pattern of Cu-Ni-Fe alloys quenched and aged inside the spinodal region. Daniel and Lipson showed that these side- bands could be explained by a periodic modulation of composi- tion in the (100) directions with wavelengths of the order of 100 X. In the early 1960's Hillert (7) and Cahn (8,9) gave the explanation of this periodic composition modulation. Within a spinodal region (Figure 1(b)) aZfYWEZ is negative, and in this special case the decomposition of a solid solution is thermo— dynamically possible as far as the chemical free energy is concerned. This means that any random fluctuation in composi- tion produces a relatively stable mixture of two different compositions. In fact, diffusion now tends to occur up the gradient of concentration (called "Uphill diffusion") and tends to increase the magnitude of the difference in concentration. These are some of the general concepts of spinodal decom— position. 1.2 The Theories of Age—Hardening of Spinodally-Modulated Structures. a). Cahn's Theory (10)- Cahn assumed that the compositibn fluctuation in spinodally-modulated structure could be described as the sum of three perpendicular cosine waves. He calculated the hardening due to the coherency internal stress field, which develops as a consequence of spinodal decomposition, and solved the force- balance equation for screw and edge dislocations under applied stress and the action of coherency stress field. According to his theory 222 O = JLBLLJEL (for screw dislocation) 6/6 FY where 0C is the critical resolved shear stress, 3A and 1 are the amplitude and the wavelength of the three-dimensional composition modulation, b is the magnitude of the Burgers vector, Y is the self energy per unit length of dislocation, n is the variation in lattice parameters due to composition variation (= Eula] N3), and Y can be expressed in term of the elastic constants C For the case of the (100) modulation waves, ij' Y can be written as ( C11"CMZ) (Chl'tzciz) C11 Y According to Cahn's theory 0c is prOportional to AZA b). Ghista and Nix's Theory (11). Ghista and Nix considered the elastic interaction between dislocation and periodic fluctuation of the shear modulus. They assumed that the elastic constants vary periodically with composition. If so, the elastic energy of a dislocation in an inhomogeneous material could be treated as if the shear modulus varies radially from the axis of the dislocation. For simpli- city, the shear modulus is assumed to vary according to Bessel function of the first kind of order either 0 or 1. According to this theory where C is the average shear modulus, E = C—bz, P is the force intensity on the dislocation due to o the elastic heterogeneities, and (PO/ E§max is the maximum value of P0/ E} According to Ghista and Nix's theory 00 is prOportional to A/AJ A dependence arises from (P0/ E>max in the equation. 0). Dahlgren's Theory (12). Dahlgren developed his theory for the late stages of spinodal decomposition, where composition fluctuation can be represented by square waves. He considered a lamellar micro- structure, and set the critical resolved shear stress equal to the mean coherency stress acting on dislocation. In this way Dahlgren found that 1 2 CC = m-fijY = '—6-AnY where [Ia is the difference in the cubic lattice parameters of the modulated structure, a0 is the average of the cubic lattice parameters of the modulated structure, and A a/aO corresponds to 6An (1). According to this theory Cc is proportional to A and is independent of x, d). Hanai, Miyazaki, and Mori's Theory (13). Hanai, Miyazaki, and Mori assumed that an increment in yield stress was due to the effect of interfacial energy of the modulated structure. In this way Hanai, Miyazaki, and Mori found that 2 4/2 " ( 2U 011 + kunz) A (for screw dislocation) c 9 E S A where UE is the interchange energy of atom-pairs, nS is the number of atoms per unit area of the interface, V is the co-ordination number, U is the shear modulus, and k is a constant related to the shape of the solute rich region. According to this theory (fizis prOportional to AZ/A. e). Kato, Mori, and Schwartz's Theory (1). Kato, Mori, and Schwartz assumed that the composition fluctuation could be described as the sum of three perpendic- Lfleu? cosine waves. Then they calculated the hardening due to the coherency internal stress field which develops as a con- sequence of spinodal decomposition. They solved the force- balance equation for a mixed dislocation, having the minimum energy configuration and largest resistance from the internal stress field under applied stress and the action of coherency stress field. In this way Kato et al. found that o =LAnY. C /6 According to this theory <£ is proportional to A and independent of A. 1.3 Thermal Activation of Dislocation. According to Conrad and Wiedersich (14,15,16), the inter- nal stress field experienced by a moving dislocation can be considered to be of the form indicated in Figure 2, where in short—range and long—range stress fields are superimposed. The long-range internal stress field is considered to be inde- pendent of temperature and strain-rate (called "athermal component'al"). The short-range stress field is strongly dependent on temperature and strain-rate (called "thermal component 1*"). The rate controlling proCess will depend on overcoming the strongest short-range obstacle situated near the maxima of the Opposing long-range stress field. At absolute zero, where thermal fluctuations do not exist, the applied stress 1 would have to equal to a value To which is equivalent to the maximum of the spike in the curve to cause plastic flow. However, at some temperature greater than 00K, thermal fluctua- tions will assist the applied stress and plastic flow can occur at a stress I which is less than 10' The activation energy H that must be supplied by thermal fluctuation for plastic flow to occur is indicated by the shaded region in Figure 2. This can be determined experimentally by the following equation + T t _______ Short-range stress field To ...... .l. T U) 53 .E T Long-range stress field 11 '3 l fiC) - distance (D +9 2 H Wavelength of long-range stress field Figure 2 Internal stress field encountered by a dislocation moving through the crystal lattice. R = -kT2(——— 1' -kT where k is the Sis the Eris the change (21). is the 3T8 1O 3 ln___§ )T(5'-I‘e 2 (1n ::/€1)(3T (2) 3T6 Boltmann’s constant strain-rate, incremental resolved shear stress by the in strain-rate from 81 to e2 (ez>€1 ), and slope of T versus T plot. 2. EXPERIMENTAL PROCEDURE 2.1 Sample Preparation. Tensile specimens were cut from as-rolled Cu-10 wt.% Ni-6 wt.% .Sn alloy; The length of the specimens was 40 mm. and the cross section was 0.40 mm.x 5.00 mm. Schematic of the specimen is presented in Figure 3. The specimens were annealed in a vertical furnace shown in Figure 4, using argon atmos- phere at 800°C (1073OK) for 1 minute and then drop-quenched into water to produce a fully recrystallized homogeneous matrix. The drop-quenching was done by passing a large current through the electrical connections on tOp of the furnace as shown in Figure 4 and melting wires made of manganin. This results in the specimens drOpping into the water bath and getting quenched instantaneously. Specimens which received no further heat treatment are referred to as "as-quenched". Annealed specimens were then aged in argon at 3500C (6230K) for 5 minutes, 20 minutes, 1 hour, 4 hours, and 24 hours. These heat treatments provided various extents of spinodal decomposition as has been predicted in previous studies (4,18). After heat treatment, all specimens were chemically polished for 30 seconds in a solution of 40% nitric acid and 60% distilled water, and electrOpolished for 2 to 5 minutes in a solution of 80% methanal and 20% nitric acid at —3o°c with 8 volts of direct current. The electrOpolished specimens 11 12 ‘9 5mm.$- 14mm. 40mm. . AL k H IJ ”I 12mm. l .. k—JIMmL-—1 afikg. Figure 3 Schematic of the tensile test specimen. 13 Electrical connections for drop-quenching set-up Vacuum auge 4”” g Inert gas inlet ---*5 Eiyrl #5__g.To vacuum pump Thermocouple Cooling coils \\ ' Three-zone Specimen <———«-furnace heating elements / / Inert gas outlet fih—if Detachable lid for F’ yr/Iquenching Figure 4 Schematic drawing of the furnace used for heat treatment. 14 were etched for 10 seconds, in a solution consisting of 5 gm. ferric chloride, 50 ml. hydrochloric acid, and 100 ml. methanol. The above treatments produced a smooth clean surface suitable for mechanical testing and microscopic examination. 2.2 Mechanical Properties. Tensile tests were carried using an Instron testing machine. All specimens were deformed in tension at the following tem- peratures; -196°C (770K), —7o°c (2030K), 25°C (2980K), and 80°C (3530K). Liquid nitrogen, methanol saturated with dry ice, room temperature, and hot water respectively provided the above test temperatures. The test fixture used is shown in Figure 5. During deformation the strain-rate was instantaneously changed several times between él = 1.45 x lo-u/sec. and éz = 1.45 x 10-3/sec. so that the activation energy H could be obtained by using equation (2) as shown in section 1.3. A Taylor factor of three (18) was used in the present study, so that the resolved shear stress 1 is obtained from tension test data. 2.3 Scanning Electron MicrosCOpy and Transmission Electron MicrOSCOpy Studies. The slip bands of specimens deformed by 20% were observed directly from specimens' surfaces by using a HITACHI S - 415 A scanning electron microscope with an accelerating voltage of 25 KV. Screw for clamping specimen @@ (a) <——-Specimen holder (b) ‘——————————Specimen @@ Screw-hole for fastening micro—tensile device on to Instron machine Figure 5 Test fixture for tensile properties. (a) Photograph. (b) Schematic. 16 For transmission electron microscopic observations, the deformed specimens were thinned down chemically to 0.1 mm. using a solution of 40% nitric and 60% distilled water. Three mm. diameter disks were cut out from the thinned sheet, and these disks were jet polished one side at a time. The solution used for this electropolishing step consisted of 80% methanol and 20% nitric acid cooled to -30°C and the voltage used was 50 volts direct current. The jet polished disks were final polished in a solution of 80% methanol and 20% nitric acid cooled to ~300C with a voltage of 8 volts direct current. The specimens were observed in a HITACHI HU - 11A electron microsCOpe operated at an accelerating voltage of 100 KV. 3. EXPERIMENTAL RESULTS 3.1 Mechanical Properties. a). Stress-Strain Behavior. The tensile stress—strain curves of as-quenched and aged specimens which were deformed until fracture at the following temperatures 770K, 2030K, 2980K, and 3530K are shown in Figure 6,7,8,and 9 respectively. It can be seen from these results that for a specific strain and specific testing tem- perature, the flow stress increases as the aging time increases. This hardening is known to be due to spinodal decomposition (2,3,4,18). b). Yield Stress. The effect of aging time on the yield stress (0.2% offset) of specimens which were deformed in the temperature range from 770K to 3530K are presented in Figure 10. From this result it can be seen that for a fixed testing temperature, the yield stress is linearly related to the aging time. Figure 11 illustrates the effect of testing temperature on the yield stress (0.2% offset). It can be seen that for specimens that have recieved identical aging treatment, the yield stress increases as the testing temperature decreases. The effect of testing temperature on the incremental yield stress A0 in aged specimens compared to that of as— Y quenched specimens is shown in Figure 12. This result indicates 17 18 1600- 1400- 1200 - 1000 - 800 _ 600 - True stress (MPa) I 400 200 Figure 10 20 3o 40 5o 60 True strain x 100 Stress-strain curves of specimens which were deformed until fracture at 770K (B: as-quenched, C: 5 minutes aged, D: 20 minutes aged, E: 1 hour aged, F: 4 hours aged, and G: 24 hours aged). 1600t 1400» 1200. True stress (MPa) 200. 19 G 1000- D B 800- 600- 400” l l I l l Figure 7 10 20 50 40 5o 60 True strain x 100 Stress-strain curves of specimens which were deformed until fracture at 2030K (B: as-quenched, C: 5 minutes aged, D: 20 minutes aged, E: 1hour aged, F: 4 hours aged, and G: 24 hours aged). 1600 1400 1200 1000 800 600 True stress (MPa) 400 200_ Figure 8 '— I 1 P p U I I0 2b 30 4b 50 60 True strain x 100 Stress-strain curves of specimens which were deformed until fracture at 2980K (B: as-quenched, C: 5 minutes aged, D: 20 minutes aged, E: 1 hour aged, F: 4 hours aged, and G: 24 hours aged). 1600 1400 1200 1000 800 600 True stress (MPa) 400 200 21 I T p- p b (r 1 IO 4 20 3'0 4‘0 1 50 I 60 True strain x 100 Figure 9 Stress-strain curves of specimens which were deformed until fracture at 3530K (B: as-quenched, C: 5 minutes aged, D: 20 minutes aged, E: 1 hour aged, F: 4 hours aged, and G: 24 hours aged). 22 .Axommm ”Oven .xommm uo .Momom ”4 £02. an: megapmpmnsmp macapms pm. emspommc who; gown: mzmsfiowmm Ho meflp mcflwm msmnm> mmonpm vamwz Ho Foam 0H mpswflm oeflp wcflw< .mp2 .mps .n: .mcfle .mCHE .mcfle .cfla em a H om n m . o u q - q a . .lefio TA I. To 8 T. p 0. Doom w. 0 44 m S D S -00.: m we .. % O .86 U. S 9 A 1. -oow M B -oooH 23 .Acmwm meson em "0 ccm .cmwm meson : “no.6mmm p30: H ”D .comm mopscfle om ”a..emmm mopscfle m ”0 .cococmzwnmm “bv mecefloomm news can cmnocmsvumm mo ensemnmmsmp mcflpmmp msmno> mmmppm came» mo poam Ha mesmflm Axov endpmanEmp mcflpmme 00: 0mm oom omm oom omH ooH om o 1 q d d q i a - i TA T... m. -oom p S 1- . I 8 S .06: s m . a % .000 o I IV S .. 8 1. .oow \, N .d . mw 000H 1 24 .Auomm whee: 3N ”0 van .pwwm whacz 3 “0 .pmmm use: H ”U .vmmm mopscfle om “4 .vmmm mopscfls m ”0V ensemhmmEmp mcflpmmp mzmhm> Amcmsfloomm cmSoCoswumm op pomnmmp spa: memeflommm 66mm :Hv mmohpm caoflz HapcmEmpocfl mo poam NH madman Amov endpmpmmsmp wcflpmme 8: 6mm oom 6mm I com o? 63 on o — J a u q u u u q M» «V d 1 I U m «r. .4 n In nooa m II W. Lu T u - w 1. 0 e 9 0 0 I -oom r. I. . m. 9 Ilflll LP .IO .9 S oom n 8 I S S .8: m m. 25 that the incremental yield stress Aoy is essentially tempera- ture independent. 0). Work-Hardening Behavior. Experimentally obtained data plotted as stress versus square root of strain for as-quenched and aged specimens which were deformed at temperatures of 770K, 2030K, 2980K, and 3530K are presented:hiFigures113, 14, 15, and 16 respectively. These data were taken from specimens deformed by 5% to 25% elongation. It can be seen from these results that the data support a relation of the following form 2.. o = o(0)+he«2 where o is the applied stress, 6 is the strain, 6(0)is the extrapolated yield stress which is given by zero—strain intercept of 0 versus 5% plot, and h is the work-hardening coefficient which is given by slope of 0 versus eé plot. The above relationship between stress and strain obtained during present investigation is in good agreement with the theoretical relationship predicted by Taylor (19) and Mott (20). Their theories predicted that the work-hardening in face- centred-cubic crystals should have a parabolic relation between stress and strain, that is True stress (MPa) 1200. 1000' h=1150 MPa 800- E h = 1000 MPa 600- ,” l/ 400:’ ’,;Z:5:::ZI’ E13161” 200:” L l l 1 J 1 0 (L1. 0.2 CL3 . 0A: 0.5 0.6 i (True strain)2 Figure 13 Plot of true stress versus (true strain)% for specimens which were deformed at 770K (B: as- quenched, C: 5 minutes aged, D: 20 minutes aged, E: 1 hour aged, F: 4 hours aged, and G: 24 hours aged). 27 1200- 1000’ _ h=1000 MP8. "‘ 800- $ F E E V - h=9OO MP8. to m / 8000- ,’/: P ,I m ,’ I, Q) I. ’I’ 1” r a ’I’ 1” I”’ B “00:” ,” ,’:’::’ r”,/’,:::””” 2005’,,I” r’ O 0.1 0.2 0.3 0.4 0.5 0.6 A (True strain)2 Figure 14 Plot of true stress versus (true strain)% for specimens which were deformed at 2030K (B: as— quenched, C: 5 minutes aged, D: 20 minutes aged, E: 1 hour aged, F: 4 hours aged, and G: 24 hours aged). True stress (MPa) 28 1200- 1000- 800_ G h==925 MPa F - E D h=850ilea 600- ,,” B I- ,I’ , [+00_”” ’/::”:’ :::/:” ’:::’ 200:’ ’,;:3” :5:’ r 0 0.1 0.2 0.3 0.41 0.5 0.6 - (True strain)5 A Figure 15 Plot of true stress versus (true strain)2 for specimens which were deformed at 2980K (B: as- quenched, C: 5 minutes aged, D: 20 minutes aged, E: 1 hour aged, F: 4 hours aged, and G: 24 hours aged). True stress (MPa) Figure 16 29 1200 I 1000 I 800. 600. #00; 200 r h = 900 MP8. F \ /E D )h = 750 MPa C B D l l l 0.1 0.2 033 01.4 0.5 0.6 (True strain)% 1 Plot of true stress versus (true strain)? for specimens which were deformed at 3530K (B: as- quenched, C: 5 minutes aged, D: 20 minutes aged, E: 1 hour aged, F: 4 hours aged, and G: 24 hours aged). 30 where K is a constant, and Epis the plastic strain. From the 0 versus 6% plot in Figures 13,14,15,and 16 it can be seen that for a fixed testing temperature, there is no marked difference in the measured h values of as-quenched and aged specimens. However, significantly larger values of h, when compared to as-quenched or the other aged specimens (5 minutes 'to 4 hours aged), were obtained for the 24 hours aged specimens. This result indicates that the work-hardening rate for the 5 minutes to 4 hours aged specimens are the same as that of the as-quenched specimens and is independent of the amplitude and the wavelength of composition modulation. Furthermore, it has been observed that for the specimens with identical aging treatments, the 'h' value increases as the testing temperature decreases. This indicates that the work- hardening rate is inversely related to the testing temperature. d). Total Elongation. Experimental data obtained for specimens which were deformed to fracture at temperatures ranging from 770K to 3530K are plotted on a total elongation versus aging time graph are shown in Figure 17. From this result it can be seen that there is no marked difference of total elongation between as—quenched and specimens aged to produce spinodal decomposition. However, 31 02 £1104 . c> :f uorieBuoTe iueoaed .Qommm no use .xommm unv.xomom “a..xonm ”UV moHSPMmeEmH mSOHHm> Pm mHSHomHm HHPQS coshommc who; QOHAB mcmEHommm Ho mEHH mchm mamHo> COHPMmQOHm Hmpop Ho HOHm 5H mpzmHm mEHp wch< .mH: .mpn .H: .mcHE .mcHE .mcHE .CHE m H H i. . 0.. m Fl: DIG 32 specimens aged for 24 hours exhibited significantly lower total elongation as compared to as-quenched or the other aged spe- cimens (5 minutes to 4 hours aged). This result indicates that the total elongation is independent of amplitude and wavelength of composition modulation in the spinodally—modulated structure. Furthermore, it can be seen that for specimens that have undergone identical aging treatment, total elongation at dif- ferent: test temperatures ranging from 770K to 3530K is almost the same. This result indicates that total elongation of these specimens is almost temperature independent in the temperature range used in the present investigation. 3.2 Activation Energy. The activation energy H for plastic flow to occur was calculated by the use of equation (2) as shown in section 1.3, 8. O H = -kT2.{1“ ( 2/ 81 )} (33) AT 3T 6 where AT is the incremental resolved shear stress induced by the change in the strain rate from ii. to éz as shown in Figures 6,7,8,and 9. (3Tflfl3é is the slope of 1 versus T plot as shown in Figure 18. The results of such calculations of the activation energy H are shown in Figure 19 where the activation energies of as— quenched and aged specimens are plotted as a function of 33 .Aummm meso: 3N no use .mem meson : “0 .mem H50: H "n .womm mmpSCHE om "4 .cowm mopscHE m "o .ano:oswrmm "9v mCmEHoQO comm can 6030:05wnwm Ho enzymemQEwP wcHHmmv mzmpm> mmmppm vaHz mo HOHA Axov mHSHMHmQEop mchmwB om: omm 2.6m 0mm 2.6m omH ooH om wH opsmHm o 10.: now S U: 3 . m -omH w a 9 S I S -owH M E .ooN 34 .Avmmm WHSOS 3N u. .Ummm WHSOS d "O .Umww .HSOS H "D .wam mopssHs om "4 6me mmHSCHE m ”0 .meOCmsvumm "3 mcoeflommm comm pew U¢£0Cmsvnmm Mo mHSPMHmQEmH mcHHmmp msmpm> mmnmco COHHm>Hpom mo HOHm 0H mpstm Axov mHSPmHoQEmP mcHHmme co: own oom 0mm oom omH ooH om o .I d a q u «I d d E: v 0 flIT 1 TL. A m. w 0 Jim M. m . u W a u I m d NH 3 K - n O 90H ~./V O 1 M. n Tl. low M. 35 temperature. From this result, it can be seen that the activa— tion energy is a linearly increasing function of temperature and almost independent of aging time. Furthermore, data from Figure 19 satisfies a relationship of the form H = 24 kT. If each atom is considered as a harmonic oscillator, the thermal energy of each atom in solids can be written as 3 kT. Using this basis the number of atoms involved in single acti- vation process can be estimated as to be equal to 8 atoms. 3.3 Scanning Electron Microsc0py and Transmission Electron Microscopy. The scanning electron micrograph of the surfaces of as- quenched and aged specimens which were deformed by 20% at 770K and 2980K are shown in Figures 20, 21, 22,and 23. It can be seen that for the samples tested at the same temperature, as- quenched Specimens show fine slip bands, whereas aged specimens show coarse slip bands. Width of slip bands of samples that have received identical aging treatment and deformed at different temperatures do not show significant variations. The transmission electron micrographs of specimens aged for 4 and 24 hours are shown in Figure 24. It can be seen that the 24 hours aged specimen did show some precipitates, while the 4 hours aged specimen exhibited only spinodally-modulated 36 (a) (b) Figure 20 Scanning electron micrographs of as-quenched specimens which were deformed by 20% at (a) 2980K, and (b) 77°K showing fine slip bands. Figure 21 37 (a) (b) Scanning electron micrographs of 20 minutes aged specimens which were deformed by 20% at (a) 2980K, and (b) 77°K showing coarse slip bands. 38 (b) Figure 22 Scanning electron micrographs of 4 hours aged specimens which were deformed by 20% at (a) 2980K, and (b) 77°K showing coarse slip bands. (a) (b) Figure 23 Scanning electron micrographs of 24 hours aged specimens which were deformed by 20% at (a) 2980K, and (b) 77°K showing coarse slip bands. Figure 24 40 (a) (b) Transmission electron micrographs of specimens aged at 350°C for (a) 4 hours, and (b) 24 hours. Grain-boundary precipitates can be observed in the 24 hours aged specimens. 41 structure. According to Ditchek and Schwartz (23), these pre- cipitates may probably be NiBSn, which they believed precipi- tate after aging at 350°C for 8 hours or longer. 4. DISCUSSION 4.1 The Role of Spinodally-Modulated Structure on the Yield Stress. Many theoretical models of age hardening due to spinodal decomposition exist in literature (1,10,11,12,13) as mentioned earlier in section 1.2. In order to understand which mechanism is responsible for age hardening in spinodally-modulated structure, the experimentally obtained values of incremental yield stress were compared to the theoretically predicted values by the various mechanisms. Table 1 compares the experimental values of incremental yield stress mngith the theoretically predicted values accor- ding to various models. Figure 25 illustrates the relationship between the incremental yield stress, and the amplitude and the wavelength of the composition modulation. The experimentally obtained value of incremental yield stress is a linearly increasing function of the amplitude as shown in Figure 25. This indicates that the incremental yield stress is pr0por- tional to the amplitude and is independent of wavelength as has been predicted by Kato—Mori-Schwartz (1) and as well as by Dahlgren (12). Furthermore, the theoretical value of incre- mental yield stress calculated by Kato-Mori-Schwartz's theory (1) is in good agreement with the experimental values within a factor of two as shown in Table 1. Since Kato-Mori-Schwartz's 42 43 HOS 0km .m .ucmmmua um czocx : new 3 mm sosm .muamHmcoo mEom moch .ucmEoE mHsu um wmumHsono on uoccmo mmsHm> mmmSH * .m paw N oHan :H aaoam mum % .xms o o< mo o=Hm> HmoHumuomnu ecu ouwaaono cu won: mums 50H;3.m AM\ mv .> .4 .n .w .c .< mo mUSHm> 0:9 *« 0.0mm o.omH o.qu o.oHH o.om moaHm> HmuaoEHpmmxm HHS uuumanum paw mm s . . o.Hmm m.Hw~ o.HH~ m.an o.wm wc< m u 0< Hue: cuwM AMHvHuoz 6am .meumst IKI m m m % « « « z « ANb< Hobos :o comma mmH=EHom HonumuomsH «« S b< mmmuum vaH% HmuaosmuocH mo mmaHm> onUvaua HHHmoHumuomzu can Hmusmefiumnxm ecu mo aomHumano .H oHan 44 A-OI) Y/zv ON 0: vAuow (:- ow .HH\< "need .H\m< ”o; < flora "3 N H\< use .H\N< .HN< .< msmpm> mmmppm UHmHH HapcmEmHocH mo HOHH mm mpzmHm Ammsv mmmhpm pHmHz HMPCmsmHocH cam oom 00H ONH om o: o O H H 4 1 H H 0“) 0 J0 OH: I .ON V . <_\I\II\ . V // \\ who V\ n om. .3 n 0 O. - l CH 1 6w. (6 VOOMw D. lllll \N :00 WW0 . \ o .L x \ ( \ \ I. 4 H \ \ \ \\ 0:. \\ (x -m .ow \\\ . @\ . I L 45 Table 2. The values of amplitude and wavelength of composition modulation in Cu-10Ni-6Sn alloy after aging at 350°C for various lengths of time (2,23). Composition Aging time modulation 5 20 1 4 24 mins. mins. hr. hrs. hrs. Amplitude . —2 -2 -2 -2 -2 (atomic 0.5x10 1.6x10 1.8x10 2.4x10 3.0x10 fraction) Wavelength 53 68 80 90 100 o (A) Table 3. The Values of n, y, Y, b, (Po/Edmax, C Values Reference n = 0.25 (1) -9 Y = 5.0 x 10 N (1) Y = 11.48 x 1011 N/m2 (1) b = 2.57 x 10'10 m (1) —- 4 -1 (P /E) = 2.5 x 10 cm (11) 0 max 6’ = 7.56 x 1010 N/m2 (17) 47‘ theory is based on the assumption that the hardening is due to the coherency internal stress field as a consequence of spino- dal decomposition, the mixed dislocation having the minimum energy configuration and largest resistance from the internal stress field is responsible for macrosCOpic yielding. Present experimental results indicate that the hardening in spinodally- modulated structure is probably caused by the movement of mixed dislocation. which has the minimum energy configuration and largest resistance from the internal stress field as predicted by Kato et al. (1). As illustrated in Figure 25, the present experimental values of incremental yield stress are not pr0portional to ADM A/x, and AZ/A as predicted by Cahn (10), Ghista-Nix (11), and Hanai-Miyazaki-Mori (13) respectively. Furthermore, from Table 1 , it can be seen that the theoretical values of incre- mental yield stress calculated by Cahn's theory (10) is too low when compare to experimental values; they differ by a factor of 102. In contrast, the theoretical values of incremental yield stress calculated by Ghista—Nix's theory (11) is too high when compared with the experimental values; they differ by a factor of 10. The theoretical value of incremental yield stress can not be calculated by Hanai-Miyazaki—Mori's theory (13) at this moment, since some constants in the formula, such as k and n8, are not known at present. 48 From the above results, it can be seen that the present experimental results are not in good agreement with the theories of Cahn (10), Ghista-Nix (11), and Hanai-Miyazaki-Mori (13). 4.2 The Effect of Temperature on the Yield Stress. As shown in Figure 19, the activation energy for plastic flow to occur at various temperatures is related to each other in the following form: H = ka ; m = 24. The above experimentally measured value of m is in good agreement with the theoretical value calculated by Feltham and Butt (25,26). Their theory has predicted that the solid solution hardening of metal would satisfy the following equation H = ka ; m a 25. i The present experimental results indicate that the tem— perature dependence of yield stress of as—quenched and aged specimens as shown in Figure 11 are determined by the solid solution hardening effect. Furthermore, there is no marked difference in the activa- tion energy between as—quenched and aged specimens in the present experiments as shown in Figure 19. This result indi- cates that modulated structure does not produce any additional thermal barrier to dislocation motion as compared to homogeneous structure. Further, this indicates that the incremental yield stress Aoy in aged specimens with respect to as—quenched 49 specimens depends on the aging treatment of the specimens only. It does not depend on the testing temperature. This temperature independence of incremental yield stress Aoy is also observed in the present experiments as shown in Figure 12. 4.3 The Effect of Spinodally-Modulated Structure on the Work- Hardening Rate. As shown in Figures 13,14,15,and 16,in section 3.1 (c), the work-hardening rates for as-quenched and 5 minutes to 4 hours aged specimens are essentially'uuesame. But 24 hours aged specimens did show significantly larger work-hardening rate when compared to as-quenched or the other aged specimens (5 minutes to 4 hours aged). This large work—hardening rate of 24 hours aged specimens is believed to be due to the precip- itation cxf N138n as shown in Figure 24. The above results indicate that the work-hardening rate is independent of the amplitude and the wavelength of compo- sition modulation. This means that, during the deformation of aged specimens, when dislocations become mobile, they can cut through the pseudo-particles resulting from the composition fluctuation relatively easily, so that there is no accumulation of glide dislocation due to the modulated structure. This results in the same work-hardening rate as as-quenched speci- mens. In contrast, in the 24 hours aged specimens, the dislo- cations are unable to cut through the precipitates with relative 5O ease. As a result glide dislocations are blocked causing a pile-up, which results in a larger work-hardening rate (24) as compared to as-quenched or the other aged specimens which have no distinct precipitates. 4.4 The Effect of Spinodally-Modulated Structure on the Total Elongation. As shown in Figure 16, section 3.1 (d), the total elong- ation for as-quenched and 5 minutes to 4 hours aged specimens is almost the same. But 24 hours aged specimens did show a significantly lower elongation when compared to the other specimens. This lower elongation of 24 hours aged specimens may be due to the precipitation of NiBSn, especially the grain-boundary precipitation as shown in Figure 24. The above results indicate that the total elongation is independent of the amplitude and the wavelength of composition modulation. This can also be explained in a way similar to the role of spinodally-modulated structure on the work-hardening rate (section 4.3). Accordingly when dislocations become mobile in aged specimens, they can move through the pseudo-particles resulting from the composition modulation with relative ease. However; the movement ofIiislocations in the modulated structure will be more difficult compared to the as-quenched structure which does not have any modulation. This results in the same total elongation in the as—quenched and as well as the aged 51 Specimens. In contrast, for the 24 hours aged specimens, the dislocations are unable to cut through the precipitates, which act as obstacles against the motion of glide dislocations. The presence of the grain-boundary precipitates can cause disloca- tion pile-ups and cause crack initiation. This results in the lower elongation when compared to as-quenched or aged specimens which have no distinct precipitates. 4.5 Slip Distribution in Deformed Specimens. As shownifiFigure320,21,22,and 23, in section 3.3, the as-quenched specimens show fine slip bands, whereas aged— specimens show coarse slip bands. According to Quin and Schwartz (21,22), the movement of dislocations on a given slip plane in a homogeneous matrix leaves behind a path which is essentially unchanged. Subsequent dislocations have no preference for the same path and will move randomly (n1 many slip planes leading to the formation of fine slip bands. In the modulated matrix the motion of the first dislocations produces a local decrease in the coherency strains. The same path becomes energetically favorable for subsequent dislocations movement. This tendency for dislocation motion to be concentrated on certain initial slip planes leading to the formation of coarse slip bands. Results of the present investigation are in agreement with the above predictions. 5. SUMMARY The mechanical pr0perties of Cu-10Ni-6Sn alloy were studied at temperatures ranging from 770K to 3530K. The important results of the present investigation can be sum- marized as follows 1. The temperature dependence of the yield stress of as- quenched and aged Cu-10Ni-6Sn alloy can be explained by the solid solution hardening mechanism. The experimentally measured incremental yield stress of aged specimens is in good agreement with Kato-Mori- Schwartz's theory (1). This indicates that the hardening by spinodal decomposition is caused by the internal coherency stress field due to the composition modula- tion, and the yield stress of aged specimen is deter- mined by the movement of mixed dislocations having the minimum energy configuration and largest resistance from the internal stress field. The incremental yield stress due to spinodal decompo- sition is temperature independent. The work hardening of as-quenched and aged specimens support a relation of the following form a o = o (0) + h 82 52 10. 53 The work-hardening rate of aged and as-quenched specimens increases as the test temperature decreases. The work-hardening rate is independent of the amplitude and wavelength of the composition fluctuation in the spinodally-modulated structure. Deformation of specimens with modulated structure is by coarse slip, whereas the as-quenched specimens deform by fine slip. The total elongation to fracture is independent of the spinodally-modulated structure and is also almost inde- pendent of the test temperature (in the range of 770K to 3530K). Results obtained in the present study reveal that there is no marked difference in activation energy for plastic flow of as-quenched and aged specimens. The estimated number of atoms involved in a single activation process is about eight. REFERENCES Kato, M., Mori, T. and Schwartz, L.H., "Hardening by Spinodal Modulated Structure",Acta Metall., 22 (1980), 285 - 290. Schwartz, L.H., Mahajan, S. and Plewes, J.T., "Spinodal Decomposition in a Cu - 9 wt. % Ni — 6 wt. % Sn Alloy", Acta Metall., 22 (1974), 601 - 609. Schwartz, L.H. and Plewes, J.T., "Spinodal Decomposition in Cu — 9 wt. % Ni - 6 wt. % Sn — II", Acta Metall., 22 (1974). 911 —921. Ditchek, B. and Schwartz, L.H., "Application of Spinodal Alloys", Annual Review of Material Science, 9 (1979), 219 -253. Daniel, V. and Lipson, H., "An X-ray Study of the Disso- ciation of an Alloy of Copper, Iron and Nickel", Proc. Roy. Soc., A, 2Q; (1943), 368 - 378. Daniel, V. and Lipson, H., "The Dissociation of an Alloy of Copper, Iron and Nickel Further X-ray Work", Proc. Roy. Soc., A, 222 (1944), 378 — 387. Hillert, M., Cohen, M. and Averbach, B.L., "Formation of Modulated Structures in C0pper-Nickel-Iron Alloys", Acta Metall., 9 (1961). 536 - 546. 54 10. 11. 12. 13. 14. 15. 16. 55 Cahn, J.W., "0n Spinodal Decomposition", Acta Metall., 2 (1961). 795 - 801. Cahn, J.W., "0n Spinodal Decomposition in Cubic Crystals", Acta Metall., 10 (1962), 179 - 183. Cahn, J.W., "Hardening by Spinodal Decomposition", Acta Metall., ;; (1963), 1275 — 1282. Ghista, D.N. and Nix, W.D., "A Dislocation Model Pertaining to the Strength of Elastically Inhomogeneous Materials", Mater. Sci. Eng., 3 (1968/69), 293 - 298. Dahlgren, S.D., "Correlation of Yield Strength with Inter- nal Coherency Strain for Age-Hardened Cu-Ni-Fe Alloys", Met. Trans. A, § (1977), 347 - 351. Hanai, Y., Miyazaki, T. and Mori, M., "Theoretical Esti— mation of the Effect of Interfacial Energy on the Mecha- nical Strength of Spinodally Decomposed Alloys", J. Mater. 501-2 1% (1979). 599 - 606- Conrad, H. and Wiedersich, H., "Activation Energy for Deformation of Metal at Low Temperature", Acta Metall., 2 (1960), 128 - 130. Conrad, H., "Thermally Activated Deformation of Metals", J. Metals, 2Q (1964), 582 - 588. Conrad, H., "The Athermal Component of the Flow Stress in Crystalline Solids", Mater. Sci. Eng., Q (1970), 265 - 273. 17. 18. 19. 20. 21. 22. 23. 24. 56 Wert, C.A. and Thomson, R.M., "Elastic Modulus and Dislo- cation Energies for Various Materials", Physics of solids, Second Edition (1970), 113. Kato, M. and Schwartz, L.H., "The Temperature Dependence of Yield Stress and Work Hardening in Spinodally Decomposed Cu-10Ni-6Sn Alloy", Mater. Sci. Eng., 41 (1979). 137 - 142. Taylor, 0.1., "The Nature of Work Hardening in Face-Centred Cubic Crystals", Progress in Metal Physics, 8 (1959), 52 - 53- Mott, N.F., "The Nature of Work Hardening in Face-Centred Cubic Crystals", Progress in Metal Physics, 2 (1959), 54 - 55- Quin, M.P. and Schwartz, L.H., "Low Cycle Fatigue in Spinodal Cu — 10 wt. % Ni - 6 wt. % Sn", Mater. Sci. Eng., 19 (1980). 249 - 259. Quin, M.P. and Schwartz, L.H., "High Cycle Fatigue Behavior of Spinodal Cu - 10 wt. % Ni - 6 wt. % Sn", Mater. Sci. Eng., 54 (1982), 121 - 126. Ditchek, B. and Schwartz, L.H., "Diffraction Study of Spinodal Decomposition in Cu - 10 wt. % Ni - 6 wt. % Sn", Acta Metall., 2§_(1980), 807 - 822. Tanaka, K. and Mori, T., "The Hardening of Crystals by Non-Deforming Particles and Fibres", Acta Metall., 2 (1970). 931 - 941. 25. 26. 57 Feltham, P., "Solid Solution Hardening of Metal Crystals", Brit. J. Appl. Phys., 2 (1968), 303 - 308. Butt, M.Z. and Feltham, P., "Solid Solution Hardening", Acta Metall., 2Q (1978), 167 - 173. SUGGESTION FOR FURTHER RESEARCH From the experimental studies on spinodal alloys carried out so far, one can note that the spinodally-modulated struc- ture can produce higher yield stress values without sacrificing ductility. The decrease in ductility of the 24 hours aged Cu-10Ni-6Sn specimens is due to the formation of an embrittling equilibrium grain-boundary phase and not due to anything inherent to the spinodal microstructure. This observation can lead us to further research focused on the retardation of the formation of the grain-boundary phase without affecting the spinodally-modulated structure, leading to alloys processing high yield stress and as well as high ductility. Any research of this kind would be extremely interesting from both the theoretical and experimental points of view. 58 II'IIIIIIIIIIIIIIII' 03177 I E“ Vl Nil] U" E“ Tl! “III IHIHHIIIIH 7265 293