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Pseudoelasticity and the strain memory effect in Cu-Zn-Sn Eisenwasser, Jacob David 1971

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PSEUDOELASTICITY AND THE STRAIN MEMORY EFFECT IN Cu-Zn-Sn by J. D. EISENWASSER B.Eng., McGj.ll University, 1968 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of METALLURGY We accept this thesis as conforming to the standard required for candidates for the degree of MASTER OF APPLIED SCIENCE Members of the Department of Metallurgy THE UNIVERSITY OF BRITISH COLUMBIA January, 1971 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree tha permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Metallurgy  The University of British Columbia Vancouver 8, Canada Date February 1, 1971 A B S T R A C T An i n v e s t i g a t i o n of pseudoelasticity and the s t r a i n memory ef f e c t was ca r r i e d out on the g'-bcc phase of a l l o y of composition Cu-33Zn-3.4Sn. Pseudoelasticity was found to occur by a stress-induced, martensite transformation. Maximum pseudoelasticity occurred at ~the A^ temperature and was ~8% for sing l e c r y s t a l specimens and ~4% for p o l y c r y s t a l l i n e specimens. Calculations indicated that the large str a i n s were due to a transformation from a bcc to a f c t martensite structure. The s t r a i n memory e f f e c t was studied by deforming specimens below Aj and then heating above A^. At temperatures between Mg and A^, the deformation i s accommodated by the stress-induced martensite forma-t i o n . At temperatures below M^, deformation of the martensite takes place and i t i s suggested that there i s a change i n the martensite structure with an increase i n the amount of orthorhombic martensite present. The pseudoelastic and s t r a i n memory e f f e c t s have very s i m i l a r o r i g i n s and over a wide temperature range from well below M^ to well above A g the combined pseudoelastic and s t r a i n memory recovery i s e s s e n t i a l l y 100%. i i TABLE OF CONTENTS Page LIST OF FIGURES v 1. INTRODUCTION 1 2. EXPERIMENTAL 10 2.1. ALLOY PREPARATION 10 2.2. TENSILE TESTS 10 2.3. METALLOGRAPHY 12 2.4. PHOTOGRAPHY 12 2.5. MEASUREMENT OF TRANSFORMATION TEMPERATURES . . . . 15 2.6. X-RAY DIFFRACTION 15 2.7. HABIT PLANE ANALYSIS 15 2.8. STRAIN MEMORY EFFECT .15 3. RESULTS AND DISCUSSION 20 3.1. SINGLE CRYSTALS 20 3.1.1. TRANSFORMATION TEMPERATURES . . . .20 3.1.2. STRESS VS. STRAIN CURVES 22 3.1.3. DISCUSSION OF STRESS VS. STRAIN CURVES 24 3.1.4. EFFECT OF CYCLING 27 3.1.5. EFFECT OF STRAIN 27 3.1.6. EFFECT OF TEMPERATURE 27 3.1.7. VISUAL OBSERVATION OF SIM 43 3.2. POLYCRYSTALLINE SPECIMENS 50 3.2.1. TRANSFORMATION TEMPERATURES 50 3.2.2. STRESS VS. STRAIN CURVES 51 3.2.3. EFFECT OF TEMPERATURE 51 3.2.4. VISUAL OBSERVATION OF SIM 60 3.2.5. COMPARISON OF SINGLE CRYSTAL AND POLYCRYSTAL STRESS VS. STRAIN CURVES 64 i i i . i v Page 3.3. EFFECT OF CRYSTAL ORIENTATION 65 3.3.1. HABIT PLANE ANALYSIS 65 3.3.2. EFFECT OF ORIENTATION ON PSEUDOELASTICITY . . . . 68 3.4. X-RAY ANALYSIS 72 3.5. STRAIN MEMORY EFFECT 74 3.5.1. SINGLE CRYSTALS 74 3.5.2. POLYCRYSTALS 80 3.6. DISCUSSION OF MECHANISMS 87 3.6.1. PSEUDOELASTICITY . 87 3.6.2. STRAIN MEMORY EFFECT 93 4. CONCLUSIONS 96 4.1. COMPARISON WITH K. OISHI THESIS 97 REFERENCES 100 APPENDIX 1 v 102 APPENDIX 2 102 LIST OF FIGURES Figure Page 1. Cu-Zn Phase Diagram 6b 2. Stress vs. Strain Curve for a Cu-32.9%Zn - 2.2%Si Alloy Deformed i n Tension at Room Temperature 8 3. Transformation Temperature (M ) of Ternary Alloys Based Upon the Cu-Zn 3' Phase S 10 4. The Error i n Apparent Elongation, 6, (obtained by sub-tracting true elongation from apparent elongation) Plotted as a Function of Stress 13 5. Tensile Apparatus Used1 to Observe Martensitic Structure . 14 6. Apparatus Used to Measure Transformation Temperatures . . . 16 7. Apparatus Used to Stu4y the Strain Memory Effect During Bending Tests .17 8. Martensitic Structures Obtained on Cooling Cu-33Zn-4Sn Below M (-52°C) 21 s 9. Single Crystal Stress vs. Strain Curve Demonstrating Pseudoelasticity 23 10. Effect of Temperature on the S t a b i l i t y of the Austensite and Martensite Phases 24 11. Effect of Strain on E l a s t i c i t y Showing Complete Recovery Up to 9% Strain 28 12. Effect of Temperature on Stress vs. Strain Curves of ; Cu-34.7Zn-2.95Sn Single Crystal Specimens 31 13. Effect of Deforming a Single Crystal Specimen of Cu-Zn-Sn Below M^  and then Removing the Stress 33 14. Effect of Temperature on E l a s t i c Recovery of ; Cu-Zn-Sn 9,in<r']<> Cry.sf.-jl Specimen . 35 15. Effect of Temperature on Range of I n i t i a l Linear Portion of the Stress vs. Strain Curves of Cu-Zn-Sn Single Crystal Specimens 37 v v i Figure Page 16. Schematic Drawing of a Stress vs. Strain Curve for a Cu-Zn-Sn Single Crystal Above A Showing the Four Stress Values at Which Deviation from S i n e a r i t y Occurs — a , V V ctD • • • 3 8 17. Curves of a , a , a , a vs. Temperature Extrapolated to Zero Stress . 40 18. Stress vs. Strain Curve for Cu-Zn-Sn Single Crystal With Numbers Corresponding to Photographs i n Figure 19 42 19. Direct Observation of SIM Taken While Stressing a Single Crystal of Cu-Zn-Sn i n Instron 43 20. Stress vs. Strain Curve for Cu-Zn-Sn Single Crystal Specimen With Numbers Corresponding to Photographs i n Figure 21 45 21. Direct Observation of SIM Taken While Stressing a Single Crystal of Cu-Zn-Sn i n Instron 46 22. Burst Martensite Obtained by Stressing a Single Crystal Specimen of Cu-Zn-Sn i n the [001] Orientation 48 23. Effect of Strain on E l a s t i c i t y Showing Complete Recovery Up to 4.5% Strain 52 24. Effect of Temperature on Stress vs. Strain Curves of Cu-33.3Zn-3.17Sn Po l y c r y s t a l l i n e Specimens 53 25. Effect of Temperature on Range of I n i t i a l Linear Portion of the Stress vs. Strain Curves of Cu-Zn-Sn P o l y c r y s t a l l i n e Specimens 55 26(a) Effect of Temperature on E l a s t i c Recovery of Cu-Zn-Sn Pol y c r y s t a l l i n e Specimens With Stress vs. Strain Curves Shown i n Figure 24 . 57 26(b) Effect of Temperature on E l a s t i c Recovery of Cu-34.55Zn-3.37Sn Po l y c r y s t a l l i n e Specimens 58 27. Curves of a , a , a , a vs. Temperature Extrapolated to Zero Stress to Yield M,, M , A , A^ 59 f s s f 28. Stress vs. Strain Curve for Cu-32.8Zn-3.13Sn Pol y c r y s t a l l i n e Specimen With the Numbers Corresponding to the Photographs i n Figure 29 . . . 61 v i i Figure Page 29. Direct Observation of SIM Taken While Stressing a Poly c r y s t a l l i n e Specimen of Cu-Zn-Sn i n Instron 62 30. Stereographic Representation of Martensite Habit Plane . 66 31. Stress vs. Strain Curves for the Cu-34.72Zn-2.95Sn Single Crystal Specimens Whose Orientations are Shown i n Figure 29 69 32. Stress vs. Strain Curve for Cu-31.94Zn-3.75Sn Single Crystal Specimen Which Formed Irreversible Burst Marten-s i t e when Strained at an Orientation Close to [100] . . 71 33. X-Ray Diffractometer Traces Showing: (a) bcc matrix (b) low temperature martensite (c) powder f i l e d at room temperature 73 34. Effect of Temperature on Recovery of Strain i n Cu-Zn-Sn Single Crystal Specimens Due to the Strain Memory Effect 75 35. Effect of Temperature on E l a s t i c and Strain Memory Recovery i n Cu-Zn-Sn Single Crystal Specimens, Showing Almost Complete Recovery of the Strain 77 36. Demonstration of Strain Memory Effect for Cu-Zn-Sn Single C r y s t a l l i n e Specimen Strained at -69 C 79 37. Effect of Deformation Temperature on Strain Memory Recovery i n Po l y c r y s t a l l i n e Cu-33.3Zn-3.17Sn Specimens . 81 38. Effect of Temperature on E l a s t i c and Strain Memory Recovery i n Cu-Zn-Sn Po l y c r y s t a l l i n e Specimens Showing Almost Complete Recovery of the Strain 82 39. Effect of Temperature on Stress vs. Strain Curves for Cu-Zn-Sn Pol y c r y s t a l l i n e Specimens 83 40. Demonstration of Strain Memory Effect for Cu-Zn-Sn Pol y c r y s t a l l i n e Specimen Strained at -50°C 84 41. Effect of Deformation Temperature on Strain Memory Recovery i n Cu-33.5Zn-4.4Sn Po l y c r y s t a l l i n e Specimens Deformed by Bending • 85 42. Demonstration of Strain Memory Effect for Cu-33.4Zn-3.34Sn Pol y c r y s t a l l i n e Specimen Deformed by Bending at -70 C . . 86 v i i i Figure Page 43(a) 8 bcc Unit C e l l s Together With 2 f c t Unit C e l l s of the Ordered y' Martensite . . 89 43(b) 8 bcc Unit C e l l s Together With 1/8 of the Orthorhombic Unit C e l l of the Ordered y' Martensite 90 44(a) Normal Stacking Sequence (ABC) for a Close-packed fee Structure Showing the (111)^ Planes 95 44(b) Stacking Sequence of the (110) '//(111) f Planes (ABA) Showing the Positions to Which Atoms Must Move to Form a Close-packed Structure 95 A C K N O W L E D G E M E N T I am greatly indebted to my supervisor, Dr. L. C. Brown, for his advice and assistance i n wr i t i n g t h i s t h e s i s . I would also l i k e to thank Dr. Bruce Hawbolt for h i s advice and c r i t i c i s m . Thanks are also extended to my fellow graduate students, i n p a r t i c u l a r , R. V. Krishnan and K. O i s h i , for t h e i r assistance. F i n a n c i a l assistance provided by the National Research Council under grant number A-2459 i s g r a t e f u l l y acknowledged. ix 1. . INTRODUCTION In the a l l o y systems Cu-Zn, Cu-Al, Cu-Sn and others with s i m i l a r phase diagrams, the bcc phase (3) occurs at a composition corresponding to a valence electron: atom r a t i o of 3/2.^ The 3 phase i s usually stable only at high temperatures. However, i t can generally be retained to room temperature by rapid quenching. The structure i s generally ordered at low temperatures with the ordering reaction proceeding too r a p i d l y to be suppressed. The retained 3' phase i s metastable and i s subject to a martensitic transformation on further cooling. In most a l l o y s the 2 transformation occurs i n two stages. At j u s t below the Mg temperature a needle-like structure, referred to as thermoelastic martensite, appears and grows mainly i n the lengthwise d i r e c t i o n on cooling. This type of martensite exhibits an e l a s t i c response to temperature changes, growing as the temperature i s lowered and shrinking upon heating with a small temperature h y s t e r e s i s . On further cooling a second burst type martensite forms with plates having c h a r a c t e r i s t i c p a r a l l e l e p i p e d shapes. 3 Zener has a t t r i b u t e d the i n s t a b i l i t y of the 3' phases on cooling as due to the low shear modulus i n {110}(110). The measure of i n s t a b i l i t y i s termed the "anisotropy factor'/, and i s the r a t i o of the shear moduli i n the {100}<010> and {110} <110> d i r e c t i o n s . The 3-bcc phases have high anisotropy factors and the l a t t i c exerts l i t t l e 1 2 resistance to a {110}<110> shear. The resistance to such a shear also decreases with decreasing temperature. These two factors lead to i n -s t a b i l i t y on cooling and also on deformation. Above M , martensite has been observed to grow on the applica-4 tion of stress and to shrink on removal of the stress. Scheil observed that the application of stress to a 70Fe-30Ni all o y affected the Mg temp-erature. He postulated that at temperatures not too far above Mg (where the volume free energy of martensite i s lower than austensite) a c r i t i c a l shear stress i s required to promote the transformation to martensite, this stress increasing as the temperature increases. Patel and Cohen"' showed that although the transformation i n Fe-Ni alloys i s aided by shear stresses, i t may also be aided or opposed by the normal component of the applied stress, depending on whether the.latter i s tensile or compressive i n nature. Stress-induced martensite (SIM) was f i r s t observed i n non-ferrous alloys by Greninger f iin Cu-39.2Zn. For this a l l o y , thermal martensite forms between -30°C and -40°C. However, Greninger was able to induce mar-tensite formation at room temperature by straining. The habit plane was determined to be {155} or {166} . Additional investigations by Reynolds p p and Bever showed that SIM i n this alloy i s reversible on removal of the applied stress. They observed "long narrow plates" of martensite i n a compressed specimen. Upon release of the stress many of the plates d i s -appeared, while others decreased i n size. The martensite reappeared at the same location on cycling. Some wide bands, made up of clusters of 3 p a r a l l e l t h i n p l a t e s , formed on s t r e s s i n g . The metallographic appearance of the SIM was s i m i l a r to thermal martensite and the habit plane was the same (155) . ; Pseudoelastic behaviour has been found i n many 3 phase a l l o y s which undergo a martensite transformation, e.g., I n - T l , ^ Au-Cd, 9 C u - A l - N i , ^ 11 12 Cu-Zn-Sn, and Ag-Cd. In most cases the e l a s t i c behaviour i s a t t r i b u t e d to the formation of r e v e r s i b l e SIM on loading at temperatures above M . s Pseudoelasticity has been studied extensively i n the Cu-Al-Ni 10 system. Rachinger found that e l a s t i c s t r a i n s of up to 4% could be attained i n s i n g l e c r y s t a l specimens of composition Cu-14.5 A l - 3 Ni. Maximum e l a s t i c i t y was obtained by o i l quenching from the 3—phase f i e l d rather than by water quenching, the o i l quench allowing p r e c i p i t a t i o n of the 6 phase to occur and so giving a dispersion strengthening e f f e c t to the matrix. 13 Busch using the same a l l o y obtained e l a s t i c s t r a i n s as high as 24%. 14 O i s h i found that e l a s t i c s t r a i n s of up to 6% could be achieved i n s i n g l e c r y s t a l s of Cu-Al-Ni a l l o y of s i m i l a r composition,which had. been heat .treated to obtain a homogeneous g' phase. Maximum e l a s t i c i t y occurred close to A . s Q The martensite transformation i n In-20.7 TI i s fee -»- f c t (M = 65°C) and may be stress induced. Magnitudes of the e l a s t i c s t r a i n s have not been studied. However, rubber-like behaviour of the cubic phase has been noted. Pseudoelasticity may also occur on s t r a i n i n g the f u l l y martensitic phase. The martensite structure consists of fin e banded twins. Between -5°C and dry i c e temperature the twin boundaries are stable. The a p p l i c a t i o n of stress causes the movement of the twin boundaries which revert to t h e i r 4 o r i g i n a l positions on removal of the s t r e s s . The Au-50% Cd"'""' a l l o y i s only pseudoelastic below M . The mecha-nism described by Chang and Read i s s i m i l a r to that for In-Tl although twinning i s not s p e c i f i c a l l y mentioned. Stressing the orthorhombic mar-t e n s i t i c phase displaces the i n t e r f a c e s between d i f f e r e n t l y oriented regions. Releasing the stress allows the regions to assume t h e i r o r i g i n a l p o s i t i o n s . The d r i v i n g force f o r this return i s described as a "relaxation process" which occurs at or near the interfaces between d i f f e r e n t l y oriented regions. A s t r a i n memory e f f e c t has been found i n several of the a l l o y s men-tioned above and again i s related to the martensite transformation i n these systems. Two d i f f e r e n t s t r a i n memory e f f e c t s occur i n Au-50% Cd. A s p e c i -men cooled through the martensitic transformation while under a bending stress w i l l acquire a permanent set. The specimen straightens when reheated to the cubic phase. This indicates that the martensite formed by s t r e s s i n g i s s t a b i l i z e d on cooling but reverts back to the 3''phase on heating above A . s The rubber-like behaviour of the orthorhombic phase i n Au-50 Cd has been a t t r i b u t e d to a relaxation e f f e c t . It has also been observed that immediately a f t e r the transformation to the orthorhombic phase, i . e . , before the s t a r t of the r e l a x a t i o n process, Au-Cd i s very d u c t i l e and takes a permanent set which can be recovered by reheating to the cubic ; phase. The term "mechanical -memory" was f i r s t used with reference to the 16 behaviour of 3-NiTi of near stoichiometric composition. The memory effect occurs when a specimen deformed below A (~100°C) i s heated above s A g. The effect occurs i n a temperature range of 60°C below A.^ . This i s the martensitic " t r a n s i t i o n band" i n which martensite can be induced either thermally or by deformation. Heating above A g causes the struc-ture to revert to bcc resulting i n recovery of s t r a i n . Recent work has indicated that thermal martensite formation i s incomplete i n the t r a n s i t i o n region and the transformation can be advanced by deformation.''"'7 The stress-induced transformation takes place i n a pre-ferred orientation which depends on the direction and sign of the applied stress. The differences i n orientation on compression and tension are re-vealed i n a change of texture of the martensite. The Cu-Al-Ni a l l o y , when deformed just below M , retains i t s shape unless eitherthe load i s reversed or the temperature i s increased 13 above M , at which point the st r a i n i s recovered, s 14 Oishi has demonstrated that the memory effect i n pr e c i p i t a t e -free Cu-Al-Ni alloy occurs at temperatures between A g and M^  as well as below M . A st r a i n of 5.6% was recoverable at 10°C above M . In the s - s temperature range between Mg and To the effect was attributed to the formation of stable SIM for small strains and a reorientation of this martensite for strains beyond 3 to 4%. A l l the martensites showing the st r a i n memory effe c t , so far, have a fine twinned structure. It has been suggested that the mechanism for The temperature at which the 3 ' and martensite phases are i n equilibrium. 6 the effect i s the growth of favourably oriented twins and the shrinkage or disappearance of unfavourably oriented ones. Some evidence of this 18 has been found by electron microscopy. The object of this research was to examine pseudoelasticity and the s t r a i n memory effect i n the 3-Cu-Zn-Sn system. The al l o y used i s essentially Cu-Zn with the Sn added to vary the transformation tempera-ture. The Cu-Zn phase diagram i s shown i n Figure 1. The 3 phase ex-tends from 37 to 57wt%Zn at temperatures close to the solidus where the structure i s disordered bcc. Alloys with up to 39wt%Zn w i l l generally 30 undergo a massive transformation on quenching to room temperature. Above this composition, the 3 phase may be retained although a spontan-eous ordering to the CsCl structure occurs. The martensite transforma-tion of the quenched 3' phase can be induced, by cooling or by cold work. The thermal transformation has been studied by several work-2, 6, 19, 20 ers . 2 Pops and Massalski calculated the habit plane for Cu-Zn marten-s i t e on the basis of a $' -»- f c t transformation, with c/a = 1.165, giving good agreement with experimental results (close to {2, 11, 12}). 19 Garwood and Hull suggested that the structure of Cu-Zn marten-s i t e was i d e n t i c a l to that i n the Cu-Al system and had an orthorhombic 20 structure. This result was supported by J o l l e y and H u l l . ?1 The most recent study has shown that thermal martensite i n Cu-33.5Zn-l.8Si i s composed of orthorhombic and fee structures. The mar-tensite phases are composed of a lamellar mixture of the two phases. The orthorhombic phase can be considered to be an fee structure with a stack-ing fault density of about 1/3. •, 6 ( b ) Atomic Percentage Zinc 10 20 30 40 50 60 70 80 90 200 •={2000 -\I800 Boiling Point 1600 - 1400 - 1200 - 1000 800 419.5 • 600 Cu 10 20 30 40 50 60 70 80 90 Zn Weight Percentage Zinc 400 Figure 1 Cu-Zn Phase Diagram 7 Simpler structures appear to r e s u l t from deformation-induced transformations. 22 Hornbogen found that s t r a i n i n g s i n g l e c r y s t a l wires of compo-s i t i o n 39.5wt%Zn produced a f c t structure a f t e r 30% s t r a i n . This struc-ture was not r e v e r s i b l e on unloading. On r o l l i n g up to 80% reduction i n area, a s i m i l a r f c t structure was obtained; however beyond 80% the struc-23 ture became fee. Massalski and Barret found the martensite structures obtained a f t e r severely cold working a series of Cu-Zn a l l o y s . The.pro-duct structure changes gradually from fee to hep with increasing Zn con-tent up to 50% Zn. This agrees with Hornbogen's r e s u l t s . At higher Zn contents the structure i s completely hep. 24 Pops has carried out a det a i l e d i n v e s t i g a t i o n of the c r y s t a l l o -graphy of deformation-induced martensite i n Cu-Zn a l l o y s . Two types of non-reversible martensite were found i n single c r y s t a l s containing 43, 45 and 48% Zn; (a) martensite appearing as broad p a r a l l e l bands i n a l l o y s containing 45 and 48% Zn with habit plane close to {110}; (b) martensite appearing as very narrow straight bands (si m i l a r to thermoelastic marten-si t e ) with either a {112} or {110} habit plane. Homogeneous l a t t i c e de-formation was assumed to be bcc -> f c t with c/a equal to either 0.75 or 0.95 for the f c t phase depending on the amount of d i s t o r t i o n . Deformation i u s t above M causes formation of r e v e r s i b l e marten-J s s i t e . Pops obtained e l a s t i c s t r a i n s of 15% in coarse p o l y c r y s t a l l i n e specimens of Cu-Zn-Si a l l o y containing ~2% S i . Strains of the same order were obtained for Cu-33Zn-2Sn. (See Figure 2). The apparent y i e l d i 20 9 point i s associated with the onset of SIM formation. P l a s t i c deformation only occurs beyond the second l i n e a r segment of the curve. The stress at which martensite formation begins increases with temperature reaching a maximum at some c r i t i c a l temperature above which the matrix i s p l a s t i c a l l y deformed on s t r e s s i n g . Pseudoelasticity only occurs between Mg and th i s c r i t i c a l temperature (approximately 90°C above M ). s This present study was intended as a follow-up to the research of Pops i n order to obtain a more complete understanding of pseudoelasticity and the mechanism involved. The p o s s i b i l i t y of finding a s t r a i n memory ef f e c t was also examined. Experiments were c a r r i e d out over a range of temperature and com-po s i t i o n s . Both p o l y c r y s t a l l i n e and sing l e c r y s t a l specimens were tested, mainly i n u n i a x i a l tension. The e f f e c t of temperature on e l a s t i c recovery and the temperature l i m i t s of pseudoelasticity were examined. Also, the habit planes of both thermal and stress-induced martensite were determined for s i n g l e c r y s t a l specimens tested i n various o r i e n t a t i o n s . Some bending tests were also c a r r i e d out on p o l y c r y s t a l l i n e specimens to study the ef f e c t of deformation mode. 2. EXPERIMENTAL 2.1 ALLOY PREPARATION Alloy compositions were chosen to y i e l d transformation tempera-tures close to room temperature. Figure 3 indicates the r e l a t i o n s h i p of M to composition. 0 I 2 ATOMIC % SOLUTE Figure 3 Transformation Temperature (M ) of Ternary A l l o y s S 11 Based Upon the Cu-Zn B' Phase, e/a = 1.395. 10 A t o t a l of 11 a l l o y s were prepared, each weighing approximately 100 gms, using high p u r i t y Cu (99.98%), Zn (99.999%) and Sn (99.99%). The constituents were melted i n sealed, evacuated quartz tubes. The a l l o y s were kept molten at 960°C for three hours to ensure o 25 complete mixing, homogenized i n the 8 ' phase (810 C) for 24 hours and quenched from t h i s temperature into water at room temperature. P o l y c r y s t a l l i n e specimens were produced by hot r o l l i n g at 810°C to a thickness of 0.045 i n . and then cold r o l l i n g to a thickness of 0.040 i n . Some material was hot r o l l e d to 0.025 i n . and cold r o l l e d down to 0.020 i n . Specimens were s o l u t i o n heat treated by heating i n a s a l t pot for 60 sec. and quenching r a p i d l y into i ced-caustic s o l u t i o n . Chemical analysis showed that some zinc was l o s t from the o r i g i n a l cast composition during r o l l i n g . T e n s i l e specimens with one inch gauge length were cut from .040 i n . material on a spark machine, whilst specimens f or bend tests were 3 prepared by shearing the .020 i n . a l l o y i n t o s t r i p s of dimension 2 in.x y g i n . Single c r y s t a l s were grown by the standard Bridgman method. The previously cast b i l l e t s were swaged to approximately 0.5 i n . diameter and resealed i n quartz tubes under vacuum. The s o l i d i f i c a t i o n rate was 5 cm./hr. with the maximum temperature kept at 970°C. S o l i d i f i c a t i o n was i n i t i a t e d from a point giving a s i n g l e c r y s t a l of random o r i e n t a t i o n . S t r i p s of s i n g l e c r y s t a l were cut on a spark machine p r i o r to s o l u t i o n heat-treatment to avoid heating the whole b i l l e t at once. This reduced the p o s s i b i l i t y of r e c r y s t a l l i z a t i o n . Single c r y s t a l s were s o l u t i o n treated i n the same manner as the p o l y c r y s t a l l i n e m a t e r i a l . Laue back-reflec-t i o n photographs and metallographic observation revealed the presence of low angle grain boundaries (misorientation <2%) but these did not i n t e r f e r e with the progress of any phase transformations during experiments that followed. 12 Chemical analyses of phe completed specimens was car r i e d out by Can-Test Ltd. 2.2. TENSILE TESTS. An Instron machine was used for a l l t e n s i l e t e s t s . The cross-head speed was 0.005 in./min and the chart speed was kept at 1 in./min. Tests were ca r r i e d out either i n a i r or water f o r temperatures above room temperature or i n ethyl alcohol cooled by l i q u i d nitrogen f o r tests at lower temperatures. , A l l s t r a i n s were corrected f o r machine compliance using Figure 4. 2.3. METALLOGRAPHY. Specimens were polished mechanically, either with alumina or diamond powder. Some i n i t i a l tests showed e l e c t r o p o l i s h i n g to be slow and not r e l i a b l e . Polished specimens were etched i n a solu t i o n of 5 gms. FeCl^ j 10 c c . HCl, and 100 c c H 20. In single c r y s t a l s , deformation martensite was observed without etching, appearing as black l i n e s at low magnification and pink at higher magnification. 2.4. PHOTOGRAPHY. The martensitic transformation during t e n s i l e • loading was observed through a low power microscope with a long distance objective lens. A 35 mm. camera attached to the microscope was used to photograph any stress or thermally induced changes i n microstructure. In some cases, a s p e c i a l l y constructed t e n s i l e j i g (see Figure 5) was used for photography of the deformation induced transformations. Low tempera-ture photomicrographs were obtained using the apparatus i n Figure 6. Figure 4 The Error i n Apparent Elongation, 6, (obtained by subtracting true elongation from apparent elongation) Plotted as a Function of Stress 14 Figure 5 Tensile Apparatus Used to Observe Martensitic Structure 15 2.5. MEASUREMENT OF TRANSFORMATION TEMPERATURES. M , M,, A and s f s A^ were measured using the apparatus shown i n Figure 6. Temperatures were recorded with a chromel-alumel thermocouple. The appearance of f i n e traces of martensite at a s p e c i f i c a l l y chosen area of the specimen indicated the Mg temperature. Care was taken to avoid measurements close to edges or cracks. 2.6. X-RAY DIFFRACTION. Diffractometer traces were taken on poly-c r y s t a l l i n e specimens under the following conditions: (1) 3 ' phase at room temperature; (2) 6' phase cooled below M^; (3) F i l i n g s at room temperature. A Norelco diffractometer was used operating at a scanning speed of l°-26/min. with Fe-Ka r a d i a t i o n . 2.7. HABIT PLANE ANALYSIS. Habit planes were determined by the 29 standard two surface method. Specimens were strained i n the j i g (Figure 5) and martensite traces were photographed on two surfaces at r i g h t angles to each other. Thermal martensite was also photographed using the same specimens and the habit planes determined. 2.8. STRAIN MEMORY EFFECT. The s t r a i n memory phenomenon was ob-served i n both t e n s i l e and bending t e s t s . Bending tests were ca r r i e d out by bending specimens to a radius of 0.5 i n . at various temperatures and photographing them as they warmed up. The apparatus used i s shown i n Figure 7. The s t r a i n s were calculated by measuring the angles of bend from the photographs and s u b s t i t u t i n g these into the c a l c u l a t i o n shown on page l g # : 16 SPECIMEN Apparatus Used to Figure 6 Measure Transformation Temperatures (a) Figure 7 Apparatus Used to Study the Strain Memory Ef f e c t During Bending Tests Figure 7 (b) h - thickness of specimen r - radius of curvature of specimen neutral axis a - length of specimen through neutral'axis a = ar Aa on tension side = a (r + |) - a r h Aa = a "2 Aa a a = 1 8 0 - 6 e % = IQOh (180 - 9) = 50h (180 - 6) 2a a 19 The memory e f f e c t was o b s e r v e d under u n i a x i a l t e n s i l e l o a d i n g w i t h t h e I n s t r o n machine. Specimens were deformed i s o t h e r m a l l y a t v a r -i o u s t e m p e r a t u r e s below and the permanent s e t was r e c o r d e d . The specimens were t h e n h e a t e d above A^ w i t h the c r o s s - h e a d p o s i t i o n o f t h e I n s t r o n h e l d f i x e d t o p r e v e n t any l e n g t h changes i n the specimens d u r i n g h e a t i n g . S i n c e a c o n t r a c t i o n o c c u r s s i m u l t a n e o u s l y w i t h a m a r t e n s i t e t o bcc t r a n s f o r m a t i o n i n t h i s a l l o y , t h i s caused t h e s t r e s s t o r i s e f o r specimens u n d e r g o i n g a t r a n s f o r m a t i o n on h e a t i n g above A^. The v a l u e of t h i s s t r e s s i s p r o p o r t i o n a l t o t h e l e n g t h change a s s o c i a t e d w i t h the s t r a i n memory e f f e c t . T h e r e f o r e , t h e s t r a i n memory r e c o v e r y c o u l d be measured by removing t h e s t r e s s and r e a d i n g t h e r e s u l t i n g l e n g t h change from t h e I n s t r o n c h a r t . I n t h e e x p e r i m e n t s where the f r a c t i o n o f t o t a l memory r e c o v e r y was measured as a f u n c t i o n o f r i s i n g t e m p e r a t u r e , t h e s t r e s s was r e l e a s e d a t each r e c o r d e d t e m p e r a t u r e i n c r e m e n t and the r e s u l t -i n g l e n g t h change f o r t h i s i n c r e m e n t r e c o r d e d . T h i s p r e v e n t e d the s t r e s s from r i s i n g enough t o a f f e c t t he M g w h i c h , as w i l l be d i s c u s s e d s h o r t l y , v a r i e s w i t h a p p l i e d s t r e s s . T e s t s were c a r r i e d o ut t o en s u r e t h a t t h e r -mal c o n t r a c t i o n s o r e x p a n s i o n s d i d not a f f e e t " t h e s e r e s u l t s . 3. RESULTS AND DISCUSSION 3.1. SINGLE CRYSTALS 3.1.1. TRANSFORMATION TEMPERATURES. The transformation tempera-tures measured o p t i c a l l y are l i s t e d i n Table I. TABLE I ALLOY NO. COMP M f °C M°C s A f t 34 72 Zn 1 2. 95 Sn -65 -52 -50 -38 33 82 Zn 2 3 06 Sn -62 -48 -45 -31 31 94 Zn 3 3 75 Sn -22 Two types of martensite were observed (see Figure 8). On cooling j u s t below M , t h i n p a r a l l e l sets of martensite p l a t e l e t s appeared with varying orientations, within i n d i v i d u a l grains. • This type of martensite grew or shrank with changing temperature and i s . known as thermoelastic martensite. On further cooling, a d i f f e r e n t martensite structure began to grow. This i s burst martensite and consisted of wide p a r a l l e l e p i p e d shaped plates which, caused pronounced t i l t s on the specimen surface. In some cases t h i s martensite was d i f f i c u l t to resolve and appeared as dark patches caused 'by a more dense array of plates with narrow ledges. The burst martensite i n i t i a l l y appeared as short p l a t e l e t s nucleating simultaneously at several s i t e s . With cooling, more plates nucleated or 20 21 (a) X35 Figure 8 Martensitic Structures Obtained on Cooling Cu-33Zn-4Sn Below Mg (-52°C) (a) Thermoelastic martensite (b) Burst martensite 22 "burst" to gradually produce a uniform structure. On heating above A g the thermoelastic martensite f i r s t shrank and gradually disappeared. Burst martensite began to revert back to marten-s i t e at random s i t e s , several plates transforming a u t o c a t a l y t i c a l l y . The number of martensite plates disappearing increased with temperature u n t i l at A^, the transformation was complete. 3.1.2. STRESS VS. STRAIN CURVES. A t y p i c a l stress vs. s t r a i n curve for a si n g l e c r y s t a l deformed above Mg i s shown i n Figure 9. ! This curve can be divided into s i x regions. From 0 to .8% s t r a i n 6 6 the curve i s l i n e a r with a modulus of 1.6 x 10 p s i compared to 15 x 10 p s i f or 65 - 35 brass. At about 1% s t r a i n the curve l e v e l s to a plateau region with a slope approaching zero. The major portion of the s t r a i n occurs during t h i s stage. In some cases, serrations appear i n the curve i n t his plateau region. At about 6% s t r a i n , the stress begins to increase again and a second l i n e a r region begins with a modulus of 5500 p s i . Be-yond 9% s t r a i n the curve again deviates from l i n e a r i t y , becoming f l a t t e r . Pops'''"'" terms this f i n a l deviation from l i n e a r i t y the p l a s t i c y i e l d point. Strains beyond t h i s value r e s u l t i n permanent deformation and ultimately i n f a i l u r e . The unloading curve varies somewhat from speciment to specimen, but i n general drops almost v e r t i c a l l y at f i r s t and then becomes nearly horizon-t a l at a stress lower than the plateau stress on loading, thus producing a hysteresis loop. Serrations again appear i n the plateau p o r t i o n of the unloading curve i n some specimens; i n general the loading and unloading 23 50 Figure 9 Single Crystal Stress vs. Strain Curve Demonstrating Pseudoelasticity 24 plateau sections are very s i m i l a r . Almost a l l the observed e l a s t i c r e -covery occurs i n the plateau stage. The curve f i n a l l y becomes l i n e a r , changing i n shape at approximately the same s t r a i n as the loading curve. In most specimens, the f i n a l stage of the curve has some curvature, p a r t i c -u l a r l y close to zero s t r e s s . Also, the slope i n t h i s stage i s not equal to the slope of the i n i t i a l l i n e a r section. In some specimens, the stress i n -creases sharply j u s t p r i o r to the onset of the f i n a l l i n e a r segment. 3.1.3. DISCUSSION OF STRESS VS. STRAIN CURVES. The large e l a s t i c s t r a i n s obtained i n Cu-Zn-Sn and other a l l o y systems are pseudoelastic i n nature. They can be accounted for by a stress-induced martensitic phase transformation. At a c r i t i c a l temperature T , the unstressed g ' l a t t i c e i s i n equi-lib r i u m with the martensite phase, i . e . , t h e i r free energies are equal. As the temperature decreases below T^ the change i n chemical free energies r e -s u l t s i n a net d r i v i n g force for the martensite reaction, the decrease i n volume free energy counterbalancing the increase i n s t r a i n and i n t e r f a c i a l energy associated with formation of the new structure. Figure 10 E f f e c t of Temperature on tne S t a b i l i t y of the Austenite (a) and Martensite (m) phases 25 At the M G temperature, the difference i n volume free energies w i l l be s u f f i c i e n t for the reaction to proceed. In al l o y systems with Mg close to A g the driving force necessary for the martensite reaction i s s l i g h t . An applied stress may provide this driving force even at temperatures above T . The t o t a l energy required to produce the transformation remains constant, but some of this energy i s supplied mechanically. In e f f e c t , for any value of applied stress, the M temperature i s raised by the stress to M , . The transformation w i l l s • d proceed u n t i l a temperature i s reached at which the sum of the applied stress and the internal stresses caused by the transformation exceeds the e l a s t i c l i m i t of the matrix. The difference between M. and M may d s be as large as 300°C. Releasing the load removes the driving force for the forward reaction causing the martensite to revert to 3*. The unusual shape of the stress vs. s t r a i n curve and the large e l a s t i c i t i e s observed experimentally are due to SIM formation. On load-, ing, the stress increases l i n e a r l y with s t r a i n . Before the p l a s t i c y i e l d point i s reached SIM begins to form. This transformation i s accompanied by a drop i n stress giving r i s e to the plateau region. A l l the SIM i s formed i n this stage of the loading curve. The continuity of SIM forma-tion determines the presence and size of serrations. In p o l y c r y s t a l l i n e material serrations would be expected because the growth of SIM may be interrupted by the presence of grain boundaries or SIM formation may be more d i f f i c u l t i n particular orientations because of differences i n re-24 solved stress on the operating s l i p systems. ; Once the specimen i s completely transformed stress again becomes d i r e c t l y proportional to s t r a i n . This stage of the curve corresponds to 26 e l a s t i c s t r a i n of the martensipe. Further s t r e s s i n g r e s u l t s i n p l a s t i c deformation. On unloading there i s an i n i t i a l drop i n stress due p a r t l y to removal of e l a s t i c s t r a i n from the martensite. The differences i n slope between the i n i t i a l unloading stage and the part of the curve corresponding to e l a s t i c s t r a i n i n g of martensite implies that there are other constraints to the reverse transformation which are not understood at present. Reversion to the B*phase occurs at a lower stress than f o r the formation of martensite on loading. The reason f o r th i s i s that when the martensite i s forming i t may be e l a s t i c a l l y strained to some extent and does not revert u n t i l t h i s e l a s t i c s t r a i n i s removed. As w i l l be explained l a t e r , t h i s d i f f e r e n c e i n stress l e v e l s i s equivalent to the temperature diff e r e n c e between Mg and A g. The transformation from SIM to 3' proceeds at almost constant stress u n t i l the end of the unloading plateau. The f i n a l stage of the curve begins at the completion of the transformation. At th i s point the stress vs. s t r a i n curve would be expected to be l i n e a r and p a r a l l e l to the i n i t i a l loading curve, since the stress l e v e l i s within the e l a s t i c range of the matrix. The fact that the curve i s not p e r f e c t l y l i n e a r or p a r a l l e l to the loading curve indicates that some i n t e r n a l s t r u c t u r a l changes are occurring at this stage of unloading. No attempt has been made to v e r i f y t h i s i n th i s t h e s i s . Single c r y s t a l specimens were tested to observe the e f f e c t of the following parameters: (a) number of stress cycles (b) s t r a i n 27 (c) temperature. 3.1.4. EFFECT QF CYCLING. Specimen 1 was strained 8% and after 5 cycles had the same e l a s t i c i t y and stress vs. s t r a i n curve. This indicates that no p l a s t i c deformation occurred, that very l i t t l e of the SIM was re-tained on unloading and also that the martensite nucleates and grows i n the same manner i n each cycle. 3.1.5. EFFECT OF STRAIN, Crystal 1 was tested with s t r a i n increas-ing from 2% to 9.5%. The resulting stress vs. s t r a i n curves are shown i n Figure 11. The specimen recovered almost completely up to 9% s t r a i n ; fracture occurred at 9.5% s t r a i n . No p l a s t i c deformation occurred up to the end of the second linear portion of the stress vs. s t r a i n curve. The SIM which formed on loading transformed completely to 3' when the applied stress was released, producing the observed e l a s t i c i t y . 3.1.6. EFFECT OF TEMPERATURE. Single c r y s t a l 1 was strained over the temperature range -196°C to 77°C to observe the effect of temperature on e l a s t i c i t y and on the shape of the stress vs. s t r a i n curves. The re s u l t -ing curves are shown i n Figure 12. Four char a c t e r i s t i c shapes are observed, depending on the temperature range: (a) T < M F ( T = -196°C) The applied stress produces a very smooth curve, the slope de-creases slowly and then increases again resulting i n a f i n a l linear por-tion. The unloading curve decreases i n slope very gradually. E l a s t i c recovery increases s l i g h t l y at temperatures below M^  going from 10% at -68°C to 30% at -196°C. This could be due to a relaxation effect similar 25 to that postulated for the Au-Cd system. Figure 11 (Continued) 12 STRAIN, % Figure 11 (Continued) ° 40f S T R A I N , % Figure 12 Effect of Temperature on Stress vs. Strain Curves of Cu-34.7 ZN - 2.95 Sn Single Crystal Specimens 32 This temperature range corresponds to deformation of the f u l l y martensitic structure. The amount of recovery on release of the stress i s quite small. As discussed i n section 3.4.1, heating above A^ causes the specimen to recover i t s i n i t i a l length. Thus p l a s t i c deformation could not have occurred and the s t r a i n i s due to a rearrangement i n the martensite plates. Figure 13 shows photographs of an unetched specimen deformed and unloaded below M^ . Although the surface of the specimen has a different appearance after deformation the location of the mar-tensite plates i s not altered. Hence the s t r a i n i s accommodated by an internal rearrangement inside the martensite plates. The d e t a i l s of this internal rearrangement are discussed i n section -3.5.2. (b) Mf < T < Ms (T = -51°C) There i s no linear portion i n the stress vs. s t r a i n curve on loading; the curve gradually decreases i n slope to reach a plateau. No pronounced change i n the slope occurs prior to f a i l u r e . The unload-ing curve i s linear and the permanent set i s almost constant and a max-imum i n this temperature range. SIM starts forming at about zero stress and martensite formation i s complete at the end of the plateau region. The martensite i s retained on unloading, therefore no s i g n i f i c a n t pseudoelasticity r e s u l t s . (c) Mg < T < A f (T = -42°C, -39°C) At temperatures close to Mg, the curves a l l have an i n i t i a l linear section. The stress at which departure from l i n e a r i t y occurs increases with increasing temperature. The unloading curve drops quickly, then gradually decreases i n slope u n t i l the load i s completely removed. There 33 F i g u r e 13 Effect of Deforming a Single C r y s t a l Specimen of Cu-Zn-Sn Below M and then Removing the Stress 34 i s no f i n a l stage increase i n slope as discussed on page 24. Close to Mg the e l a s t i c recovery i s small but i t increases sharply with test temp-erature as can be seen by comparing the curves at -42°C and -39°C. This increase i n recovery i s due to the martensite s t a r t i n g to revert back on unloading, due to i t s i n s t a b i l i t y at zero s t r e s s . (d) T > A f (T = -37°C, -29°C, 24°C, 77°C) Just above A^, e l a s t i c recovery reaches a maximum, 100% i n many cases, 96% for c r y s t a l 1. The shapes of the stress vs. s t r a i n curves are as discussed i n section 3.1.2. With increasing temperature, the l i n e a r portion p r i o r to martensite formation increases and the e l a s t i c i t y s t a r t s to decrease. Maximum e l a s t i c i t y occurs because the martensite reverts completely to 3 ' on removal of the applied s t r e s s . At lower temperatures (<A^) some martensite i s retained even at zero s t r e s s . At higher temperatures the 3 ' matrix becomes increasingly s t a b l e . The volume free energy difference be-tween the bcc and martensitic phases increases with temperature and the stress to overcome the difference must therefore increase. A l l strains, are borne by a combination of the e l a s t i c i t y of the metal and SIM formation, provided that the stress required to form martensite i s below the y i e l d stress of the matrix. At some c r i t i c a l temperature, the free energy for SIM formation i s s u f f i c i e n t l y large that the stress to overcome i t ex-: ceeds the y i e l d stress of the 3 ' phase and some p l a s t i c deformation begins. The amount of SIM formed decreases as the temperature i s raised above the c r i t i c a l temperature while p l a s t i c deformation and permanent set increase. (See Figure 14). 70 -50 -30 -10 10 30 50 DEFORMATION TEMPERATURE, °C 70 90 Figure 14 Eff e c t of Temperature on E l a s t i c Recovery of Cu-Zn-Sn Single C r y s t a l Specimen 36 The i n i t i a l linear portion of the stress vs. s t r a i n curve i n -creased from .25% s t r a i n at -51°C to 1.55% s t r a i n at 77°C (Figure 15). The values for the proportional l i m i t are very large for a normal metal but can probably be explained as due to the very low strength of the bcc l a t t i c e i n {110}<110>. The Young's Modulus of the 3' phase also increases with temperature from 1 x 10 6 at -29°C to 1.3 x 10 6 at 77°C. This effect has been discussed 3 in d e t a i l by Zener and i s due to the metastability of the 3' phase to shear stresses. A schematic drawing of the stress vs. s t r a i n curve i n the temperature range above A^ i s shown i n Figure 16. As w i l l be discussed i n section 3.1.7, the i n i t i a l formation of deformation martensite coincides with the f i r s t stage of deviation from l i n e a r i t y of the stress vs. s t r a i n curve (a ). Below the Mg temperature martensite forms spontaneously and above Mg,the 3' phase becomes increasingly stable, requiring higher applied stresses to form SIM. P l o t t i n g as a function of temperature and extrapolating to zero stress should thus give the M^  temperature. Once the specimen has completely transformed to martensite, the stress begins to increase again since now the SIM i s being deformed. Hence, the stress at which the curve begins to deviate from the plateau (o D) corresponds to complete transformation to martensite. Using the same arguments as before, a should equal zero at Mc and a plot of a vs. T B r B should extrapolate to Mf at zero stress. Similar arguments apply on un-CO S CL 0 I I I I I I i i "60 - 40 -20 0 20 4 0 60 80 100 TEMPERATURE, °C Figure 15 Effect of Temperature on Range of I n i t i a l Linear Portion of the of Cu-Zn-Sn Single Crystal Specimens Stress vs. Strain Curves 38 Figure 16 Schematic Drawing of a Stress vs. Strain Curve for a Cu-Zn-Sn Single Crystal Above A g Showing the Four Stress Values at Which Deviation from Linearity Occurs — a., a . a . a . A B C D loading and plots of cr^ vs. T and vs. T should extrapolate to A g and A., re s p e c t i v e l y at zero s t r e s s . Plots of cr. , a„, a_ and cr_ V S . T for f A B C D the specimen with stress s t r a i n curves shown i n Figure 12 are given i n Figure 17. Table II shows a comparison of the values taken from Figure 17 and those from Table I. TABLE II FROM DIRECT EXTRAPOLATION OBSERVATION OF STRESS T VALUES M °C -50 -52 s M f ° C . -63 -65 A : ° C -50 -50 s A f °C -37 -38 Pops, using- the same method, plotted a and cr as a function of temperature f o r coarse grained p o l y c r y s t a l l i n e specimens. He concluded that the curve of a - vs. T extrapolates to A at zero stress rather than D s to A^. No reason i s , given for th i s conclusion and i t appears that Pops neglected to consider the p o s s i b i l i t y that the above curve y i e l d s I f a extrapolates to zero stress at A then t h i s would imply that SIM can revertcompletelyto 8'at T < A^. The conclusion reached i n th i s thesis seems to be more l o g i c a l . 5 Or 40-ro 3.1.7. VISUAL OBSERVATION OF SIM. Observations were made of the microstructure obtained on deforming c r y s t a l s 1 and 2 i n u n i a x i a l tension. The stress vs. s t r a i n curves are shown i n Figure 18 and Figure 20 respec-t i v e l y , with the numbers on the curves corresponding to the photographs shown i n Figure 19 and Figure 21. Using c r y s t a l 1 as an example, SIM formation can be characterized as follows: * 1. Martensite needles i n i t i a l l y appear when the stress vs. s t r a i n curve f i r s t deviates from l i n e a r i t y . 2. Martensite s t a r t s to form at one end of the specimen and moves progressively along the specimen length as the stress i s increased. 3. Needles of martensite nucleate at one edge and grow across the specimen at a d e f i n i t e angle to the t e n s i l e axis depending on the specimen o r i e n t a t i o n . 4. Several variants may appear i n any specimen (four i n t his example) but martensite plates of any one variant are always p a r a l l e l to each other. 5. The f i r s t martensite needles aire r e l a t i v e l y widely spaced. The density of needles increases with applied s t r e s s , d e n s i f i c a t i o n f i r s t occurring closer to the end of the specimen at which martensite growth, begins. This refers to the trace of a martensite plate on one surface. 42 25 2 3 4 STRAIN , % Figure 18 Stress vs. Strain Curve for Cu-Zn-Sn Single Crystal With Numbers Corresponding to Photographs i n Figure 19 Figure 19 (Continued) 4> 10 Figure 19 (Continued) 50 Figure 20 Stress vs. Strain Curve for Cu-Zn-Sn Single C r y s t a l Specimen With Numbers Corresponding to Photographs i n Figure 21 Figure 21 Direct Observation of SIM Taken While Stressing a Single Crystal of Cu-Zn-Sn i n Instron. (x35) ON Figure 21 (Continued) Figure 22 Burst Martensite Obtained by Stressing a Single C r y s t a l Specimen of Cu-Zn-Sn i n the [001] Orientation. This structure appeared at the s t a r t of the loading plateau of the stress vs. s t r a i n curve. 49 6. At some point, the density of martensite needles becomes high enough to give the impression that the specimen surface i s one s o l i d sheet of martensite. The surface becomes very shiny and the martensite traces appear as white rather than dark l i n e s and are more d i f f i c u l t to resolve. This can be seen i n photo 5 of Figure 19. I n i t i a l l y t h i s e f f e c t pro-duces a band covering part of the specimen; t h i s band grows with stress u n t i l the e n t i r e gauge length has a uniform shiny appearance. 7. On release of the applied s t r e s s , hysteresis of the martensite growth i s observed. This i s observed i n the set of photographs of Figure 19. No change occurs between photos 6 and 7 although the stress drop between them i s 1500 p s i . 8. The martensite reverts to 3'by reversing the sequence described for the forward transformation. 9. Martensite transforms completely to 31 at the end of the unloading plateau segment of the stress vs. s t r a i n curve. Specimen 2 was strained beyond the pseudoelastic l i m i t and demonstrates the e f f e c t of p l a s t i c deformation on SIM. An i n t e r e s t i n g feature of the set of photographs shown i n Figure 21 i s the appearance of v e r t i c a l bands, at the end of SIM formation, whose cause has not been determined. These bands are p a r a l l e l to the t e n s i l e axis and do not d i s -appear completely on release of the applied s t r e s s , although t h e i r appear-ance changes from s o l i d bands to f i n e traces. As discussed i n the Intro-duction, the 3' phase of Cu-Zn transforms to an f c t structure on severe 50 deformation and th i s i s not r e v e r s i b l e on removal of the s t r e s s . Since the bands form under conditions of f a i r l y severe deformation and are not r e v e r s i b l e i t seems l i k e l y that they are due to this de-formation martensite. However, no d i r e c t confirmation of t h i s has been made. Photo 10 demonstrates that most of the martensite i s retained af t e r the specimen i s unloaded. This i s due to p l a s t i c deformation which occurred with the formation of cracks shown i n photo 8. The p l a s -t i c deformation occurs at the s t a r t of the second plateau. 3.2. POLYCRYSTALLINE SPECIMENS 3.2.1. TRANSFORMATION TEMPERATURES. Table I II l i s t s the composi-tions and the transformation temperatures of the p o l y c r y s t a l l i n e specimens studied. Grain sizes varied between 0.05 and 0.1 inch. TABLE I I I ALLOY NO. COMPOSITION Wt. % M °C s M °c A s ° C A f°C 1 33.5 Zn, 4.4 Sn -15 -10 9 2 33.41 Zn,3.34 Sn -53 -67 -48 -20 3 35.03 Zn,3.36 Sn -70 -56 -20 4 34.55 Zn,3.37 Sn -20 -10 8 5 32.8 Zn, 3.13 Sn -29 -38 -24 1 6 33.31 Zn,3.17 Sn -27 -34 -25 -14 7 32.85 Zn,3.15 Sn -31 -27 -10 51 On cooling below M , thermoelastic and burst martensite are formed with a mode of transformation i d e n t i c a l to that described for s i n g l e crys-t a l s i n section 3.1.1. 3.2.2. STRESS VS. STRAIN CURVES. The' experiments carried out with sin g l e c r y s t a l s were repeated with p o l y c r y s t a l l i n e material. In general the r e s u l t s were very s i m i l a r . P o l y c r y s t a l l i n e metal exhibited the a b i l i t y to recover large s t r a i n s e l a s t i c a l l y , although the magnitude of the s t r a i n s was considerably less than f o r s i n g l e c r y s t a l s . Strain values seldom ex-ceeded 3%. A specimen of each a l l o y was strained and unloaded up to 10 times and i t was confirmed that the stress vs. s t r a i n curves were not affected by this c y c l i n g e f f e c t . This test was necessary since some specimens were used repeatedly f o r a serie s of te s t s . * In another preliminary experiment, p o l y c r y s t a l l i n e specimens were strained increasing amounts to v e r i f y that pseudoelasticity was not affected by s t r a i n . A l l o y 7 was strained over the range 1.5% to 5%. As can be seen i n Figure 23, the specimen recovered a l -most completely up to str a i n s of 4.5%, with f a i l u r e occurring at 5.3% s t r a i n s . The comparable fra c t u r e s t r a i n for the s i n g l e c r y s t a l specimen was 9.5%. 3.2.3. EFFECT OF TEMPERATURE. The stress vs. s t r a i n curves can be grouped into 3 temperature regions Csee Figure 24): Ca) T < M 0? = -29°C) s Very l i t t l e stress i s required to form SIM. The stress i n i t i a l l y increases l i n e a r l y with s t r a i n with a modulus of 1 x 10 p s i . In some of the experiments at higher temperatures, specimens which did not recover f u l l y were replaced. 2 5 Figure 23 E f f e c t of Str a i n on E l a s t i c i t y , Showing Complete Recovery Up to 4.5% S t r a i n .5 1.5 10 .5 0 .5 STRAIN, % .5 Ln U> 1.5 Figure 24 E f f e c t ofTemperature on Stress vs. S t r a i n Curves of Cu- 33.3 Zn-3.17 Sn P o l y c r y s t a l l i n e Specimens 54 At 1200 p s i SIM s t a r t s to form causing a decrease i n modulus which gives r i s e to a plateau section. Some serrations appear during t h i s stage. A second l i n e a r part of the curve begins at 1% € with an apparent modulus of approximately 6.7 x 10^ p s i . Releasing the load leaves a very large permanent set. Maximum set f o r a given s t r a i n i s observed i n this temp-erature i n t e r v a l . ' ( b ) M < T < A £ (T = - 26°C to -17°C) s f Increasing the temperature gives r i s e to several changes i n the nature of the stress vs. s t r a i n curves: (1) Between -26°C and -17°C, e l a s t i c recovery increases by approximately 80%. (2) The i n i t i a l l i n e a r portion of the stress vs. s t r a i n curve increases from .2% C a t -26°C to .4%£ at -8°C. (Figure 25). This e f f e c t was much more pronounced i n s i n g l e c r y s t a l s . This d i f f e r e n c e i s due presumably to the stress concentration e f f e c t s caused by the presence of the grain boundaries. (3) The stress f o r formation of SIM increases from 2000 p s i at -26°C to 7500 p s i at -17°C. (4) On unloading, the f i n a l ' l i n e a r ' part of the curve, observed at higher temperatures i n s i n g l e c r y s t a l s , does not occur u n t i l -19°C. For t h i s a l l o y A f = -14°C. This r e s u l t i s i n s l i g h t disagreement with the s i n g l e c r y s t a l work i n which o D, associated with the end of the unloading plateau, f i r s t appeared at A^. ^0.6 I °- ol I . I -30 -20 i 0 a 0 TEMPERATURE, C Figure 25 Ef f e c t of Temperature on Range of I n i t i a l Linear Portion of the Stress vs. Str a i n Curves of Cu-Zn-Sn P o l y c r y s t a l l i n e Specimens 56 (c) T > A f (T = -8°C) The stress vs. s t r a i n curves i n th i s temperature range are s i m i l a r i n shape to the single c r y s t a l curves. As i n s i n g l e c r y s t a l s , the stress to form martensite Co.) increases with temperature and the A amount of pseudoelasticity remains constant u n t i l cr exceeds the stress to cause y i e l d i n g of the 3 matrix. At this point, e l a s t i c i t y begins to decrease. This i s demonstrated i n Figure 26(b). In Figure 27, o^, a^, a^, for a l l o y 6 are plo t t e d as a function of temperature and extrapolated to zero s t r e s s . As explained previously for s i n g l e c r y s t a l s , these curves should extrapolate to the Mg, M^ , A g, A^ temperatures. Table IV shows a comparison of transformation temperatures measured previously and those taken from Figure 27. TABLE IV T FROM EXTRAPOLATION OF STRESS VALUES DIRECT OBSERVATION M °C s -34 -34 Mf °C -28 -27 °C A L -27 -25 s °r A A f -19 -14 The f i r s t three values are i n excellent agreement. The value of A f from Figure 27 i s lower than the measured value. This discrepancy This a l l o y was studied to temperatures well above A Figure 26(a) E f f e c t of Temperature on E l a s t i c Recovery of Cu-Zn-Sn P o l y c r y s t a l l i n e Specimens With Stress vs. St r a i n Curves Shown i n Figure 24 100 20 h 0J 1 I l l I -40 -20 0 20 40 60 DEFORMATION TEMPERATURE , °C Figure 26(b) E f f e c t of Temperature on E l a s t i c Recovery of Cu-34.55 Zn-3.37 Sn P o l y c r y s t a l l i n e Specimens 60 could be due to several f a c t o r s : (a) The end point of the plateau i s not d e f i n i t e i n the unloading p o s i t i o n of the stress vs. s t r a i n curves i n poly-c r y s t a l l i n e specimens. This makes i t d i f f i c u l t to measure cr^. (b) There i s some error involved i n measuring t r a n s f o r -mation temperatures. This i s a consequence of the v i s u a l method used. There i s never an abrupt change i n structure at which the temperature can be pinpointed. D i f f e r e n t areas i n a specimen may transform at s l i g h t l y d i f f e r e n t temperatures. (c) With most p o l y c r y s t a l l i n e specimens some SIM was s t i l l present beyond the unloading plateau. . . 3.2.4. VISUAL OBSERVATION OF SIM. P o l y c r y s t a l l i n e specimen 5 was strained u n i a x i a l l y and photographs were taken of SIM formation. The stress vs. s t r a i n curve i s shown i n Figure 28 with the corresponding photo-micrographs i n Figure 29. The specimen contained a very l i t t l e martensite p r i o r to s t r e s s i n g . The main features of the p o l y c r y s t a l l i n e SIM formation are as follows: (1) Martensite begins to form during the i n i t i a l l i n e a r loading stage of the stress vs. s t r a i n curve. In t h i s s p e c i -men, photo 2 shows that S;IM began at 3000 p s i , much below the departure from l i n e a r i t y at 5000 p s i . This e f f e c t was also 14 observed by Oish i i n Cu-Al-Ni a l l o y s . 61 \25 I 2 3 STRAIN, % Figure 28 Stress vs. Strain.Curve for Cu-32.8 Zn-3.13 Sn P o l y c r y s t a l l i n e Specimen With the Numbers Corresponding to the Photographs i n Figure 29 (2) Martensite begins to grow at grain boundaries as p a r a l l e l needles. These needles grow in t o the grain u n t i l they reach a grain boundary which hinders growth. (3) Increasing the applied stress causes an increase i n the number of martensite needles but not as much as i n sin g l e c r y s t a l s . Some needles darken and broaden but transformation to martensite i s not complete. Increasing the stress causes nucleation of SIM i n new grains rather than an increase i n density i n any p a r t i c u l a r grain. (4) Several martensite variants may be seen i n any one grain.:. Some needles can be seen to cross one another. (5) SIM fQrmation stops at approximately the end of the plateau stage of the loading curve. (6) Martensite reverts completely close to the end of the plateau segment of the unloading curve. In s p e c i -men 5, the end of the plateau region was very i n d e f i n i t e and the slope changed gradually to that c h a r a c t e r i s t i c of the f i n a l stage of unloading. As seen i n Figure 29, how-ever, most.of the martensite had reverted back above a stress of 2500 p s i . (7) Upon releasing the load, no change was observed u n t i l the stress dropped from 9000 p s i to 6500 p s i . Mar-te n s i t e does n o t begin to disappear u n t i l the beginning of the plateau region on the unloading stress vs. s t r a i n curve. 64 3.2.5. COMPARISON OF SINGLE CRYSTAL AND POLYCRYSTAL STRESS VS. STRAIN CURVES: (1) E l a s t i c s t r a i n s are much greater i n s i n g l e c r y s t a l s . In p o l y c r y s t a l s , only c e r t a i n grains are favorably oriented for SIM fo rmation. Also, martensite growth ends at grain boundaries. This r e s t r i c t i o n of martensite growth l i m i t s the amount of s t r a i n which can be accomodated by the trans-formation. (2) The proportional l i m i t increases with temperature to a greater extent i n sin g l e c r y s t a l s . Because of stress concentration e f f e c t s at grain boundaries, martensite forms at lower applied stresses and temperature e f f e c t s are less s i g n i f i c a n t . (3) The stress during the loading and unloading plateau stage remains almost constant f o r sin g l e c r y s t a l s . In poly-c r y s t a l s ,. the slope during the plateau stages i s usually greater. This again i s due to greater hindrance to martensite growth i n p o l y c r y s t a l s . In sin g l e c r y s t a l s , once martensite formation begins, i t continues to nucleate and grow s t e a d i l y u n t i l the specimen has completely transformed. In p o l y c r y s t a l s , once one grain has transformed, a d d i t i o n a l stress i s required to bring about the transformation i n less favourably oriented grains. In many p o l y c r y s t a l l i n e t e s t s , large serrations were observed during the plateau segment of s t r a i n , caused by a delayed nucleation i n some grains of the specimen. 65 This was observed i n larger grained specimens i n which i n d i -v i d u al grains contribute a larger e f f e c t . (4) In s i n g l e c r y s t a l s , SIM begins to form at the point of departure from l i n e a r i t y of the stress s t r a i n curve, but i n p o l y c r y s t a l s SIM forms at stresses below t h i s (see F i g -ure 29). Again this i s due to stress concentration at grain boundaries causing martensite formation i n i s o l a t e d grains. Also, the resolved shear stresses i n c e r t a i n very favorable grains may cause SIM to s t a r t forming at low stresses. S i g -n i f i c a n t SIM formation does not occur u n t i l the departure from l i n e a r i t y . (5) Single c r y s t a l specimens con s i s t e n t l y displayed almost complete e l a s t i c recovery for s t r a i n s beyond the pro-p o r t i o n a l l i m i t . P o l y c r y s t a l l i n e specimens often did not recover f u l l y . Certain grains must have been strained s u f f i -c i e n t l y to cause some p l a s t i c deformation. 3.3. EFFECT OF CRYSTAL ORIENTATION 3.3.1. HABIT PLANE ANALYSIS. The habit planes of s t r e s s -induced martensite were obtained f o r single c r y s t a l s having a wide range of o r i e n t a t i o n s . The habit planes of thermal martensite for most of the specimens were also determined. The r e s u l t s are shown i n Figure 30. In most specimens several variants of the habit plane were ob-served. In a l l cases, however, the habit plane was found to be close D CRYSTAL ORIENTATION Figure 30 X (2,11,12) HABIT PLANE 0 THERMOELASTIC SIM HABIT PLANE THERMAL MARTENSITE HABIT PLANE . BURST MARTENSITE HABIT PLANE Stereographic representation of martensite habit plane. Triangles 1-8 show the habit plane of thermal and stress-induced thermoelastic martensite along with the (2,11,12) habit plane found previously by Pops. Triangles 9-10 show the orientation of c r y s t a l s i n which burst martensite was obtained. A c i r c l e of 4° representing experimental error i s drawn around the (2,11,12) habit plane. 67 to the {110} corner of the stereographlc t r i a n g l e both, f o r thermal and for deformation induced martensite. Considerable s c a t t e r i s observed although much of t h i s can be a t t r i b u t e d to the experimental erro r . This i s approximately 4° and a c i r c l e of t h i s diameter i s shown i n the r e s u l t s i n Figure 30. A d d i t i o n a l sc a t t e r i s due to imperfections i n the c r y s t a l s used, most of which contained subgrains and so sharp spots were seldom obtained i n the back r e f l e c t i o n photographs. The present r e s u l t s are i n good agreement with observations of 2 6 thermal and deformation-induced thermoelastic martensite i n Cu-Zn. ' It appears that thermal and deformation-induced martensite have exactly the same structure. They have the same habit plane and i n several of the specimens examined the variants of SIM appeared at exactly the same angles and locations as i n thermal martensite. It i s l i k e l y that the i n i t i a l formation of thermal martensite made c e r t a i n s i t e s i n the 3*matrix more favourable for SIM nucleation of s i m i l a r o r i e n t a t i o n . Varying the o r i e n t a t i o n of the stress axis had no e f f e c t on the habit plane which was always close to {110}. However, i n orientations close to {100} a non-reversible burst type martensite was obtained as shown i n Figure 22. The traces of t h i s martensite were bent so that an exact habit plane determination was not possible. However, approxi-mate measurements indicated that the habit plane lay i n the same section of the stereographic t r i a n g l e as i n the r e v e r s i b l e thermoelastic marten-s i t e found i n other specimens. 68 3.3.2. EFFECT OF ORIENTATION ON PSEUDOELASTICITY. Single c r y s t a l specimens were strained at various orientations of the stress axis to study the e f f e c t on p s e u d o e l a s t i c i t y . Several problems were encountered i n these experiments, p a r t i c u l a r l y with specimen preparation. Single c r y s t a l s grown by the Bridgman method from a point tended to grow with orientations close to <lt0>. The largest c r y s t a l s grown had a diameter of 1/2". Specimens cut with orientations close to <100> and <111> were thus very small and d i f f i c u l t to form into proper t e n s i l e specimens and to g r i p . A l l tests were ca r r i e d out at 70°C above M and the stress vs. s s t r a i n curves obtained are shown i n Figures 31 and 32. There are s i g n i -f i c a n t differences between the stress vs. s t r a i n curves. However, except for specimens 9 and 10, which had orientations near [100] , the specimens had almost 100% e l a s t i c i t y . No stress vs. s t r a i n curve was obtained for specimen 8 with an o r i e n t a t i o n near [111] although the SIM i n t h i s s p e c i -men was found to be completely r e v e r s i b l e using the t e n s i l e device of Figure 5 and i t i s l i k e l y that the specimen would have had a stress vs. s t r a i n curve s i m i l a r to those shown i n Figure 31. Specimens 9 and 10 were strained i n an o r i e n t a t i o n close to [100]. The stress vs. s t r a i n curve for specimen 10 i s shown i n Figure 32, A large s t r a i n was achieved with this specimen although very l i t t l e of i t was recovered on unloading. The large s t r a i n i s associated with the formation of burst martensite on s t r e s s i n g . The i r r e v e r s i b i l i t y of the martensite even a f t e r heating to 200°C indicates that the material was p l a s t i c a l l y deformed to some extent during the transformation. 50 STRAIN , % gure 31. Stress v.s. s t r a i n curves f o r the Cu- 34.72 Zn- 2.95 Sn single c r y s t a l specimens whose orientations are shown i n Figure 29. A l l tests were car r i e d out at 70°C above M . 7( STRAIN , % Figure 31 (Continued) 71 10 STRAIN, % Figure 32 Stress vs. Str a i n Curve for Cu-31.94Zn-3.75Sn Single C r y s t a l Specimen which Formed I r r e v e r s i b l e Burst Martensite when Strained at an Orientation Close to [100] 72 3.4. X-RAY ANALYSIS The X-ray diffTactometer traces are shown i n Figure 33. Figure 33(a) shows the most intense peak of the 3' phase trace, corresponding to (110)^,. The trace of thermal martensite [Figure 33(b)] was obtained by cooling the specimen to l i q u i d nitrogen temperature. Table V l i s t s the 26 angles, i n t e n s i t i e s and calculated d-spacings for t h i s trace. 20 Also l i s t e d are the values obtained by J o l l e y and H u l l f or thermal martensite i n Cu-39 wt.% Zn. The agreement i s only moderate, although o the addition of a correction term of 0.09A to the d-spacings of the pre-sent work bring the r e s u l t s somewhat closer. J o l l e y and H u l l calculated the d-spacings for an orthorhombic l a t t i c e and obtained good agreement 21 with t h e i r experimental r e s u l t s . The work of Pops and Delaey with Cu-33.5 Zn - 1.8 S i has shown that thermal martensite more l i k e l y con-s i s t s of a mixture of fee and orthorhombic and t h i s could explain the discrepancy between the present r e s u l t s and those of J o l l e y and H u l l . No d e t a i l e d analysis was possible with the traces obtained on t h i s work. Figure 33(c) shows the trace obtained f o r powder f i l i n g s at room 22 temperature. Hornbogen determined the structure of heavily deformed Cu-Zn to be f c t with a = 3.77, c = 3.56. The X-ray trace obtained i n the present work gives excellent agreement with Hornbogen's r e s u l t s as can be seen from Table V. ro O O Figure 33 X-Ray Diffractometer Traces Showing: a) bcc matrix b) low temperature martensite c) powder f i l e d at room temperature TABLE V X-RAY ANALYSIS RESULTS AND COMPARISON WITH LITERATURE THERMAL MARTENSITE SOURCE 26 d I h k l A Present Work, 51 2.25 23 011 54.2 2.12 20 020 56.5 2.04 100 200 59.1 1.94 24 111 J o l l e y & H u l l , 2.23 20 020 2.13 100 200 2.03 60 111 DEFORMATION MARTENSITE Present Work, 53.8 2.14 100 111 F i l i n g s 62.8 1.86 20 200 Calculated for 2.14 111 f c t with c/a = .943 1.88 200 a = 3.77 Cu-34.5 Zn - 3.37 Sn, a = 2.94 3.5. STRAIN MEMORY EFFECT 3.5.1. SINGLE CRYSTALS. The s t r a i n memory e f f e c t was studied i n c r y s t a l 1 by deforming i n the temperature range - 69°C to 77°C, releasing the stress and heating the specimen up to room temperature. The recovery was measured and i s plo t t e d as a function of the deformation temperature i n Figure 34. Maximum memory recovery occurs on deformation below M . Cn DEFORMATION TEMPERATURE, C Figure 34 E f f e c t of Temperature on Recovery of S t r a i n i n Cu-Zn-Sh, Single C r y s t a l Specimens Due to the S t r a i n Memory E f f e c t 76 Between Mg and A^, the recovery drops very r a p i d l y and at temperatures above A^ there i s very l i t t l e recovery. In th i s graph, recovery i s never 1Q3%, even on deformation below M . The specimen always has some e l a s t i c i t y accounting f o r some of the recovery. Figure 35 shows Figure 13 and Figure 34 superimposed. This graph c l e a r l y demonstrates the r e -lati o n s h i p between the shape memory e f f e c t and pseu d o e l a s t i c i t y . When the s t r a i n memory i s a maximum, the e l a s t i c i t y i s a minimum and v i c e versa. Total recovery i s approximately 96% at a l l temperatures up to A^. Above A^ the t o t a l recovery slowly decreases due to p l a s t i c de-formation i n the martensite. Two mechanisms are responsible f o r the s t r a i n memory phenomenon, depending on the temperature: (a) T < M The e f f e c t of stress on thermal martensite was discussed i n section 3.1.6. In a completely martensitic material s t r a i n i s accomo-dated by a change i n the i n t e r n a l structure of the martensite rather than by s l i p . This modified martensite i s unstable above A and on heat-s ing i t reverts to the o r i g i n a l martensitic structure which then disappears completely above A^. This e f f e c t was observed o p t i c a l l y . The reverse transformation r e s u l t s i n complete reve r s a l of the events during s t r a i n -ing and no permanent set occurs unless the martensite i s deformed p l a s t i -c a l l y . Figure 35 Ef f e c t of Temperature on E l a s t i c and S t r a i n Memory Recovery i n Cu-Zn-Sn Single C r y s t a l Specimens, Showing Almost Complete Recovery of the S t r a i n (b) M s < T < A f The a p p l i c a t i o n of stress causes SIM formation which only p a r t i a l l y reverts on release of the load. The martensite w i l l completely reverse when heated above giving r i s e to t o t a l recovery of the s t r a i n . In thi s temperature range, the memory recovery decreases sharply with i n -creasing temperature since a large proportion of the s t r a i n i s recovered by pseudoelasticity at higher temperatures. (c) M c < T < M f s This i s a t r a n s i t i o n region. Both e f f e c t s described above are occurring, with change i n structure i n e x i s t i n g plates more dominant at temperatures close to M^. The s t r a i n memory recovery i s p l o t t e d as a function of temperature as the specimen warms up a f t e r deformation at -69°C (see Figure 36) . In thi s graph, the v e r t i c a l axis represents the f r a c t i o n of t o t a l memory recovery. Approximately 90% of the s t r a i n memory e f f e c t occurs between the measured A g and A^ temperatures. 14 O i s h i found that i n Cu-Al-Ni, a si n g l e c r y s t a l specimen strained 5.6% at 15°C below M^  began recovery around 10°C above A g upon heating and recovery was not complete u n t i l 16°C above A^. This was a t t r i b u t e d to the i n t e r n a l stresses caused by the presence of unfavorably oriented martensite plates on deformation at temperatures below M^ with these stresses opposing the transformation back to bcc. No s i m i l a r e f f e c t was observed i n the Cu-Zn-Sn system. 79 0 I -Q 1 I | 1 1 -55 "50 "45 -40 o "35 "30 T E M P E R A T U R E , ° C Figure 36 Cu-Zn-Demonstration of Str a i n Memory E f f e c t for Sn Single C r y s t a l l i n e Specimen Strained at -69°C. 80 3.5.2. POLYCRYSTALS. The tests on si n g l e c r y s t a l s were repeated on p o l y c r y s t a l l i n e specimens with e s s e n t i a l l y s i m i l a r r e s u l t s . Figure 37 shows the e f f e c t of deformation at various temperatures on the s t r a i n mem-ory e f f e c t , whilst Figure 38 shows the r e l a t i o n s h i p between the s t r a i n memory e f f e c t and pseu d o e l a s t i c i t y . As with si n g l e c r y s t a l s , maximum s t r a i n memory e f f e c t occurs below M g and i n t h i s temperature range the pseudoelasticity i s a minimum. At any temperature, the combined s t r a i n memory e f f e c t and pseudoelasticity gives a t o t a l recovery close to 100% The stress vs. s t r a i n curves of Figure 24 are repeated i n Figure 39, t h i s time showing the e f f e c t of heating the specimens above A^ at constant s t r a i n and then re l e a s i n g the s t r e s s . Heating the material com-p l e t e l y transforms any SIM present to B1 which normally would cause the specimen to shrink. Since the specimen i s being restrained, the 8 matrix i s now strained by an amount equal to the low temperature permanent set. The stress value i s proportional to t h i s s t r a i n . The value of the stresses caused by heating the specimens i s greater at lower temperatures, corres-ponding to the increased permanent set. In the case when the i n i t i a l per-manent set i s s u f f i c i e n t l y large, the stress to form martensite i n the 8' matrix w i l l be exceeded causing SIM to form. This w i l l give r i s e to a non-l i n e a r i t y i n the s t r a i n memory unloading curve such as occurred at -29°C i n Figure 39. , . The s t r a i n memory e f f e c t was observed i n an a l l o y deformed below M^ and allowed to warm up under zero stress (Figure 40). As expected, recovery of the s t r a i n begins at A g and i s complete at A^. Some bend tests were made on p o l y c r y s t a l l i n e specimens using the experimental procedure described i n section 2.8. As seen i n Figure 41, 100 -30 -25 -20 -15 -10 DEFORMATION TEMPERATURE,0C Figure 37 Eff e c t of Deformation Temperature on Strain Memory Recovery i n P o l y c r y s t a l l i n e Cu-33.3 Zn-3.17 Sn Specimens -30 -25 -20 -15 -10 DEFORMATION TEMPERATURE °C Figure 38 Eff e c t of Temperature on E l a s t i c and St r a i n Memory Recovery i n Cu-Zn-Sn P o l y c r y s t a l l i n e Specimens Showing Almost Complete Recovery of the St r a i n 15 Figure 39 E f f e c t o f Temperature on S t r e s s v s . S t r a i n Curves f o r Cu-Zn-Sn P o l y c r y s t a l l i n e Specimens. The e f f e c t o f h e a t i n g the specimen to room temperature at c o n s t a n t s t r a i n and then r e l e a s i n g t h e load i s a l s o shown. 84 -20 TEMPERATURE, "C Figure 40 Demonstration of S t r a i n Memory E f f e c t for Cu-Zn-Sn P o l y c r y s t a l l i n e Specimen Strained at -50 C. i Figure 41 E f f e c t of Deformation Temperature on St r a i n Memory Recovery i n Cu-33.5Zn-4.4Sn P o l y c r y s t a l l i n e Specimens Deformed by Bending -50 -40 -30 o -20 TEMPERATURE , °C -10 Figure 42 Demonstration of Strain Memory E f f e c t for Cu-33.4 Zn-3.34 Sn P o l y c r y s t a l l i n e Specimen Deformed by Bending at -70°C. 87 the curve for the recovery as a function of bending temperature i s exactly the same as for t e n s i l e t e s t i n g , as i s the graph of recovery vs. temperature for a specimen deformed below and allowed gradually to heat up to room temperature (Figure 42). The r e s u l t s i n d i c a t e that the mode of deformation does not a l t e r the nature of the s t r a i n memory e f f e c t . 3.6. DISCUSSION OF MECHANISMS 3.6.1. PSEUDOELASTICITY. The r e s u l t s obtained i n the present work have shown that ps e u d o e l a s t i c i t y i n the Cu-Zn-Sn a l l o y s occurs by SIM formation. Thermoelastic type SIM alone i s responsible for t h i s phe-nomenon. In almost a l l orientations of the t e n s i l e axis, thermoelastic martensite was obtained on s t r e s s i n g and was found to be r e v e r s i b l e on removing the s t r e s s . No burst martensite was observed within the pseudo-e l a s t i c l i m i t of the material. Burst SIM was observed, however, when stressing specimens with the stress axis oriented close to <100> and t h i s did not revert to 8* even af t e r heating to 200°C. An understanding of t h i s r e s u l t required further experimental i n v e s t i g a t i o n and w i l l not be discussed further here. Thermal and stress-induced thermoelastic martensite have been 6 21 shown to have s i m i l a r c r y s t a l structures. ' Observations of t h i s mar-21 tens i t e i n d i c a t e that i t i s single phase with no f i n e scale structure. 27 The phenomenological theory of martensite formation provides for two types of s t r a i n s : (a) an invariant plane s t r a i n , which i s homogeneous and 88 produces a macroscopic shape change; and (b) an inhomogeneous d i s t o r t i o n which can induce e i t h e r s l i p or twinning. This d i s t o r t i o n must be invoked to s a t i s f y the c r i t e r i o n of a s t r a i n - f r e e habit plane. The absence of a f i n e scale structure i n thermoelastic martensite as ob-21 served by Pops implies one of two things: 1. That the habit plane i s not a plane of zero net d i s t o r t i o n ( i n disagreement with the above theory), i . e . , i t i s i n a state of high s t r a i n ; 2. That the f i n e structure i s one of d i s -locations at the i n t e r f a c e , although t h i s i s not observed i n burst martensite, which has a s i m i l a r habit plane and thus would be expected to have a s i m i l a r f i n e structure. E l a s t i c s t r a i n s up to 12% have been obtained i n 3-Cu-Zn-Sn. Two possible transformations have been considered, i . e . , bcc -> f c t and bcc ->-orthorhombic. Figure 43 i l l u s t r a t e s the r e l a t i o n s h i p between the parent bcc l a t t i c e and the f c t and orthorhombic martensite structures. The l a t t i c e parameters of the three unit c e l l s are l i s t e d i n Table VI together with the o r i e n t a t i o n r e l a t i o n s h i p s between the l a t t i c e s . Figure 43(a) bcc Unit C e l l s Together With 2 f c t Unit C e l l s of the Ordered y' Martensite 91 TABLE VI STRUCTURE a b c bcc 2.94 f c t 3.77 3.56 Ortho 2.67 4.27 36.29 bcc // f c t // Ortho [001] [001] [101] [010] [110] [010] [100] [110] [101] Based on the l a t t i c e parameters, d i r e c t i o n a l changes have been calculated for the two transformations and are tabulated i n Appendix 1. In the case of the bcc ->• orthorhombic transformation, a maximum ex-pansion of 5.9% occurs i n the [100] o d i r e c t i o n . A gradual decrease P occurs moving away from [001]^. At [011]^ and [111]^, contractions of 1.4% and 1.1% occur. Table VII shows the poles of c r y s t a l axes of specimens which were examined and the corresponding s t r a i n values. TABLE VII VARIATION OF STRAIN* WITH ORIENTATION OF TENSILE AXIS SPECIMEN ORIENTATION e % 1 [1 5 20] 6.7 2 [1 10 15] 7 3 [1 6 8] 5.2 4 [0 3 4] 7.6 5 [13 14 18] 6.1 10 [118] 16 S t r a i n values taken at end of plateau stage of stress vs. s t r a i n curves. A comparison with the calculated values for s i m i l a r o r i e n t a t i o n s shows c l e a r l y that the transformation cannot be simply bcc •+ ortho. A s i m i l a r comparison for the bcc -> f c t transformation shows that the ex-perimental s t r a i n s agree well with the t h e o r e t i c a l values. At [001]. , a 8 t h e o r e t i c a l expansion of 21% i s possible. As the o r i e n t a t i o n moves to-ward [011]^ the expansion decreases although an expansion of 7% i s s t i l l p o ssible at [011]^. The observed s t r a i n s are thus adequately explained by a bcc -*• f c t transformation. According to Pops, the thermal thermo-e l a s t i c martensite has a completely fee structure. However, he does not give a l a t t i c e parameter for the structure. The f c t structure determined by Hornbogen has c/a = 0..943 and so i s very s i m i l a r to fee and i s used for the present c a l c u l a t i o n s . 3.6.2. STRAIN MEMORY EFFECT. In the previous discussion of the memory effect i t was pointed out that two mechanisms are involved, one in the temperature range between Mg and A^ and a second mechanism below M£. Both mechanisms are active between M,. and M . Above Mr, SIM forms f f s f on straining and only partly reverts when the stress on the specimen is removed. The specimen takes a permanent set which can be recovered by heating above A^ at zero applied stress. The strain is recovered be-cause SIM is unstable above A^ and reverts to the 3 ' phase. The mechanism is identical to that occurring during pseudoelasticity with.the strain being accomodated by a bcc to fct martensite transformation. The only difference is that the reversion to 3 ' is delayed in a specific tempera-ture range. Below M^  the material is fully martensitic prior to stressing. The present experiments have shown that single crystals of Cu-Zn-Sn can be strained at least 4% at temperatures below M^  without undergoing any plastic deformation. Figure 13 shows photomicrographs of a specimen be-fore and after straining below M^ . There is no indication that a reorien-14 tation of the martensite occurred, as has been hypothesized for Cu-Al-Ni 28 and Ti-Nb. Another mechanism must therefore be considered. Striations in Cu-Zn-Si burst martensite have been studied by Pops 21 and Delaey. By means of selected area diffraction experiments they have shown that striations in burst martensite are due to the presence of two close-packed structures with different stacking sequences. The marten-site platelets are made up of successive lamellae of fee and orthorhombic structures with stacking sequences ABC and ABC BCA CAB respectively. The 94 boundaries of the lamellae are p a r a l l e l to the (100) plane of the orthor-hombic and to the {111} planes of the fee. The orthorhombic structure i s an fee structure containing a regular sequence of stacking f a u l t s with stacking f a u l t p r o b a b i l i t y close to 1/3. The d i f f e r e n c e between the two structures i s i n the amount of s l i p occurring i n the secondary inhomogeneous shear along <110> . If t h i s shear occurs on a l l successive planes, the r e -ft s u i t i n g l a t t i c e w i l l be f a u l t free fee or f c t with c/a of .943. If i t occurs on alternate planes the structure becomes HCP and on every t h i r d plane, the structure i s orthorhombic. This i s i l l u s t r a t e d i n Figure 44. In appendix 2 the expansions which occur i n an f c t to orthorhombic transformation have been calculated f or d i f f e r e n t l a t t i c e o r i e n t a t i o n s . A l l orientations give an expansion of at l e a s t 10% for s p e c i f i c v a r i a n t s . I t . i s therefore proposed that the a p p l i c a t i o n of stress at T < Mg gives r i s e to stacking f a u l t s producing an orthorhombic structure with changes i n the related fee l a t t i c e parameters. R e l a t i v e l y large s t r a i n s can be accomodated by changes i n the proportions of f c t and orthorhombic s t r u c -tures. This involves very small atomic displacements i n the secondary shear planes of the martensite. This can be achieved by d i s p l a c i n g atoms on every t h i r d plane along ^r[121],. or ^[izil],. d i r e c t i o n s i n the {111} o rec o rec planes. 95 ° • O o • o O o n 0 0 O • O O • O ( I I I ) fee O o • o o Q _ A ° • O o • O 0-B 0 - 0 Q o o D " ~ c ® x o y ® o \ m o Figure 44(a) — Normal stacking sequence (ABC) for a close-packed fee structure showing the (111) planes. Figure 44(b) — Stacking sequence of the (110) ,//(111),, planes (ABA), showing the positions to which atoms must move to form a close-packed structure. To form an orthorhombic l a t -t i c e , this shear must take place on every t h i r d plane. O — A 0-B (110) bee ( M i l f e e 96 4. CONCLUSIONS 1. Very large e l a s t i c s t r a i n s can be obtained i n the 6' phase of Cu-33Zn-4Sn a l l o y s . These s t r a i n s are a r e s u l t of formation of stress-induced martensite which i s completely r e v e r s i b l e above A^. 2. Reversible s t r a i n s of ~8% and ~4% were obtained i n sin g l e c r y s t a l and small grained p o l y c r y s t a l l i n e specimens r e s p e c t i v e l y . The magnitude of these s t r a i n s i s the only major differ e n c e between sing l e and p o l y c r y s t a l l i n e material. 3. SIM formation begins at the i n i t i a l d eviation from l i n e a r i t y of the stress vs. s t r a i n curve i n sing l e c r y s t a l s and. at lower stresses i n p o l y c r y s t a l l i n e specimens. The stress at which deviation from,linearity occurs, o^, increases l i n e a r i l y with temperature. 4. The four stresses at which deviation from l i n e a r i t y occurs i n the stress vs. s t r a i n curves, a., o_, a „ and cr extrapolate A B C D to M,., M , A and A. respectively at zero stress, f s s . f 5. Pseudoelasticity occurs between A^ and some upper c r i -t i c a l temperature, at which applied stress i s s u f f i c i e n t l y large to de-form the 6' matrix. Maximum pseudoelasticity occurs at close to A^. 6. A-. s t r a i n memory e f f e c t i s found on deformation at temperatures close to M . Above M i t i s due to SIM formation; below s s M to a change i n the i n t e r n a l structure of the martensite (probably from 97 fct-ortho) on deformation. No permanent deformation r e s u l t s during t h i s transformation. 7. At any temperature, the sum of the pseudoelastic and s t r a i n memory recovery i s very close to 100%. Below i t i s mainly s t r a i n memory recovery, above A g i t i s e n t i r e l y pseudoelastic recovery. Between A and i t i s a combination of the two e f f e c t s , s f 8. X-ray d i f f r a c t i o n observation of thermal martensite tended to confirm the orthorhombic structure found by J o l l e y and H u l l . The structure of deformation martensite was found to be f c t with l a t t i c e parameters i d e n t i c a l to those of Hornbogen. 9. The habit planes of r e v e r s i b l e SIM and thermal martensite were found to be the same, close to {110} for a l l orie n t a t i o n s of the ten-s i l e a x i s. When the or i e n t a t i o n of the t e n s i l e axis was close to [100] non-reversible burst SIM was formed. 4.1. COMPARISON WITH K. OISHI THESIS. The objectives and program of experiments c a r r i e d out for th i s thesis are very s i m i l a r to those of K. Oi s h i who worked with Cu-14Al-2Ni and Cu-14Al-6Ni a l l o y s . A compari-son of the r e s u l t s obtained i n the two theses i s presented below. 1. Pseudoelasticity i s caused by stress-induced martensite i n both systems. This only applies for r e l a t i v e l y small s t r a i n s i n Cu-Al-Ni. At larger s t r a i n s , a twinning mechanism has been proposed. In both cases, the magnitude of the e f f e c t was greater i n single c r y s t a l s than i n p o l y c r y s t a l s . 98 Maximum pseudoelasticity occurred close to A i n Cu-Al-Ni s and close to A^ i n Cu-Zn-Sn. 2. SIM formed at the deviation from l i n e a r i t y of the stress vs. s t r a i n curve i n single c r y s t a l s of both systems and at an e a r l i e r stage i n p o l y c r y s t a l s . 3. ' The stress at which i n i t i a l deviation from l i n e a r i t y occurred, a , extrapolated to M, at zero stress i n Cu-Al-Ni and to M i n A 3- S Cu-Zn-Sn. The stresses a , a and a were not plotted i n Oishi's t h e s i s . 4. O i s h i found that burst martensite formed on deformation at a l l orientations examined. The burst martensite coincided with the appearance of serrations i n the stress vs. s t r a i n curve. Burst SIM i n p o l y c r y s t a l l i n e specimens had the appearance of burst martensite formed on cooling. In single c r y s t a l s , burst martensite was either wedge shaped or consisted of s o l i d bands crossing the specimen. In Cu-Zn-Sn, burst SIM only formed i n specimens near the [001] t e n s i l e axis o r i e n t a t i o n . The martensite had the appearance of burst martensite formed on cooling but was not r e v e r s i b l e even a f t e r heating well above A^. No burst SIM was observed i n p o l y c r y s t a l l i n e s p e c i -mens. An i n t e r e s t i n g feature of SIM formation i n Cu-Zn-Sn i s the d e n s i f i -cation process i n single c r y s t a l s ;which formed bands of martensite s i m i l a r i n appearance to the bands of burst martensite which were observed by Oi s h i . However, i n Cu-Zn-Sn these bands formed gradually with no sudden drop i n stress during t h e i r formation. 99 5. A s t r a i n memory e f f e c t was found i n b o t h s y s t e m s . I n C u - A l - N i , specimens began t o r e c o v e r a t d i f f e r e n t t e m p e r a t u r e s d e p e n d i n g on whether the bcc o r the m a r t e n s i t e was deformed. For t e n s i l e t e s t s , r e c o v e r y o c c u r r e d a t ~A g when t h e b c c phase was deformed and ~10°C above M when m a r t e n s i t e was deformed. I n Cu-Zn-Sn r e c o v e r y s t a r t e d a t ~A f o r s . J s a l l d e f o r m a t i o n t e m p e r a t u r e s . I n C u - A l - N i , t h e memory e f f e c t , above M g, i s due t o t h e f o r m a t i o n o f s t a b l e SIM w i t h d e f o r m a t i o n of i n d i v i d u a l m a r t e n s i t e p l a t e s o c c u r r i n g a t s t r a i n s >4%. Below M^, d e f o r m a t i o n o f a c o m p l e t e l y m a r t e n -s i t i c s t r u c t u r e i s t a k i n g p l a c e . Thus, t h e a p p l i e d s t r e s s c a u s e s t h e growth o f f a v o r a b l y o r i e n t e d m a r t e n s i t e a t t h e expense o f l e s s f a v o r a b l y o r i e n t e d p l a t e s . No such e f f e c t has been o b s e r v e d i n Cu-Zn-Sn. The memory e f f e c t i s due o n l y t o the f o r m a t i o n o f s t a b l e SIM above M . De'formation s of the m a r t e n s i t e c a u s i n g e i t h e r t w i n n i n g o r s t r u c t u r a l changes does n o t o c c u r . Below M^, d e f o r m a t i o n o f a f u l l y m a r t e n s i t i c s t r u c t u r e p o s s i b l y c auses f o r m a t i o n of s t a c k i n g f a u l t s t r a n s f o r m i n g some f c t m a r t e n s i t e t o o r t h o r h o m b i c . 6. O i s h i d i d not f i n d a u n i q u e h a b i t p l a n e f o r e i t h e r b u r s t o r n e e d l e - l i k e m a r t e n s i t e . Both had d i f f e r e n t h a b i t p l a n e s . The h a b i t p l a n e d e t e r m i n a t i o n s i n t h i s t h e s i s a l s o r e -s u l t e d i n c o n s i d e r a b l e s c a t t e r a l t h o u g h the h a b i t p l a n e was c o n s i s t e n t l y near [110] of the s t e r e o g r a p h i c t r i a n g l e . I n s e v e r a l c a s e s t h e r m a l and s t r e s s - i n d u c e d m a r t e n s i t e had t h e same h a b i t p l a n e . REFERENCES 1. Hume-Rothery, Elements of S t r u c t u r a l Metallurgy, p. 151, Chaucer Press, London, 1966. 2. Pops, H., Massalski, T.B., Trans. AIME, 230 (1964), 1662. 3. Zener, C , Phys. Rev., 71 (1947) 946. 4. S c h e i l , E., Ztsch. anorg. allgem. Chemie, 20J7 (1932) 21. 5. P a t e l , J.R., Cohen, M., Acta. Met 1 (1953) 531. 6. Greninger, A.B., Mooradian, V.G., Trans. AIME, 128 (1938) 337. 7. Reynolds, J.E., Bever, M.B., Trans. AIME, 194 (1952) 1065, 8. Burkart, N.W., Read, T.A., Trans. AIME, 197 (1953) 1516-1524. 9. Olander, A., Ztsch. K r i s t . , 83A, (1932) 145. 10. Rachinger, W.A., J . Aust. Inst, of Met., _5 (1960) 114-117. 11. Pops, H., Met. Trans. 1 (1970) 251. 12. Brown, L.C., Krlshnan, R.V., Private Communication (1970). 13. Busch, R.E., Lenderman, R.T., Gross, P.M., Rep. U.S. Army Materials Research Agency, ARMA, Cr 65-02/1, Feb. (1966). 14. Brown, L.C:, O i s h i , K., Submitted to M e t a l l u r g i c a l Trans., Sept. (1970). 15. Chang, L.C.', Read, T.A., Trans. AIME, 191 (1951) 47. 100 101 16. Buehler, W.J., Wang, F.E., Ocean Eng., 1_ (1968) 105. 17. Lange, R.G., Zijderveld, J.A., J. Appl. Phys., 39 (1968) 2195. 18. Otsuka, K., Shimizu, K. , Scripta Met., h_ June (1970) 469. 19. H u l l , D., Garwood, R.D., J. Inst, of Metals, 86 (1957-8) 485. 20. J o l l e y , W., H u l l , D., J. Inst, of Metals, 92 (1964) 129. 21. Pops, H., Delaey, L., Trans. AIME, 242 (1968) 1849. 22. Hornbogen, E., Segmuller, A., Wasserman, G., Z. Metallk, ^8 (1957) 379. 23. Massalskl, T.B., Barret, C.S., Trans. AIME,209 (1957) 455. 24. Ahlers, M., Pops, H. , Trans. AIME, 24_2 (1968) 1267. 25. Pops, H., Trans. AIME,230 (1964) 813. 26. Kulin, S.A., Cohen, M., Averbach, B.L., J. Met., 4 (1952) 661. 27. Wechsler, M.S., Lieberman, D.S., Read, T.A., Trans. AIME, .197 (1953) 1503. 28. Baker, C, Submitted to Acta. Met., (1970) 29. C u l l i t y , B.D., Elements of X-Ray D i f f r a c t i o n . Addison-Wesley Co., Inc., Reading, 1967. 30. H u l l , D., Garwood, R.D., The Mechanism of Phase Transformation i n Metals. The Institute of Metals, London, 1965, p. 219. 102 APPENDIX 1 For f c t , the d spacing of a plane (hkl) with l a t t i c e parameters a nd c i s given by the formula: 2 2 2 1_ h + k 1_ si 2 2 d a c For an orthorhombic l a t t i c e : 2 2 2 „2 2 ,2 2 d a b c APPENDIX 2 The expansions and contractions due to the transformations bcc •> ct, bcc ->• orthorhombic and f c t ->• orthorhombic along the p r i n c i p a l poles f a cubic c r y s t a l are l i s t e d i n Tables VIII, IX, and X. Expansions are hown by a plus sign. 103 TABLE VIII bcc fct d(bcc) d ( f c t ) %/bcc <001> [001] ' [001] 2.94 3.56 21.1 [020] [110] 5.88 5.33 -9.3 [200] [110] 5.88 5.33 -9.3 <015> [0 2 10] [110] 29.98 36 20.1 [0 10 2] [552] 29.98 27.59 -8 [5 1 0] [320] 14.99 13.59 -9.3 [10 0 2] [552] 29.98 27.59 -8 [1 5 0] [320] 14.99 13.59 -9.3 [2 0 10] [110] 29.98 36 20.1 <013> [026] [116] 18.59 • 22.01 18.4 [062] [332] 18.59 17.51 -5.8 [206] [116] 18.59 22.01 18.4 [130] [210] 9.29 8.43 -9.3 [310] [210] 9.29 8.45 -9.3 [602] [332] 18.59 17.51 -5.8 <115> [115] [105] 15.28 18.20 19.1 [151] [321] 15.28 14.05 -8.0 [511] [321] 15.28 14.05 -8.0 <012> [420] [310] 13.15 11.92 -9.3 [240] [310] 13.15 11.92 -9.3 [024] [114] 13.15 15.21 15.6 [201] [111] 6.58 6.41 -2.5 [204] [114] 13.15 15.21 15.6 [042] [222] 13.15 12.82 -2.5 <124> [248] [318] 26.95 30.87 14.6 [284] [534] 26.95 26.19 -2.8 [428] [318] 26.95 30.87 14.6 [241] [311] 13.48 12.44 -7.7 [421] [311] 13.48 12.44 -7.7 [824] [534] 26.95 26.19 -2.8 <135> [135J [215] 17.4 19.69 13.2 [153] [323] 17.4 14.29 - .6 [315] [215] 17.5 19.69 13.2 [351] [411] 17.4 15.95 -8.3 [531] [411] 17.4 15.95 -8.3 [513] [323] 17.4 14.29 -0.6 104 TABLE VIII (Continued) bcc f c t d(bcc) d ( f c t ) %/bcc <113> [113] [103] 9.75 11.33 16.15 [131] [211] 9.75 9.15 -6.2 [311] [211] 9.75 9.15 -6.2 <123> [246] [316] 22.0 24.46 11.2 [132] [212] 11.0 11.04 0.3 [426] [31C] 22.0 24.46 11.2 [462] [512] 22.0 20.5 -6.8 [643] [512] 22.0 20.5 -6.8 [312] [212] 11.0 11.04 0.3 <112> [112] [102] 7.2 8.06 11.9 [242] [3121 14.4 13.36 -7.2 [422] [312] 14.4 13.36 -7.2 <011> [022] [112] 8.32 8.89 6.9 [202] [112] 8.32 8.89 6.9 [110] [100] 4.16 4.45 -9.4 <122> [244] [314] 17.64 18.71 6.0 [221] [201] 8.82 8.34 -5.5 [42 4] [314] 17.64 18.71 6.0 <111> [111] [101] 5.09 5.19 1.9 105 TABLE IX bcc ORTHORHOMBIC d(bcc) d(ORTHOR) %/bcc <001> [002] [1 0 1/8] [010] [0 1 0] [200] [1 0 1/8] <015> [0 2 10] [5 2 5/8] [0 10 2] [1 10 1/8] [10 2 0] [5 2 5/8] [10 0 2] [6 0 1/2] [2 0 10] [6 0 1/2] <013> [026] [3 2 3/8] [062] [1 6 1/8] [206] [4 0 1/4] [260] [1 6 1/8] [620] [2 2 3/8] [602] [4 0 1/4] <115> [2 2 10] [6 2 1/2] [2 10 2] [2 10 0] [10 2 2] [6 2 1/2] <012> [420] [2 2 1/4] [240] [1 4 1/8] [042] [1 4 1/8] [024] [2 2 1/4] [402] [3 0 1/8] [204] [2 0 1/8] <124> [248] [5 4 3/8] [284] [3 8 1/8] [428] [6 2 1/4] [482] [3 8 1/8] [842] [5 4 3/8] [824] [6 2 1/4] <135> [2 6 10] [6 6 1/2] [2 10 6] [4 10 1/4] [6 2 10] [8 2 1/4] [6 10 2] [4 10 1/4] [10 6 2] [6 6 1/2] [10 2 6] [8 2 1/4] 5.88 6.23 5.9 2.94 2.67 -9.2 5.88 6.23 5.9 29.98 31.60 5.4 29.98 27.42 -8.5 29.98 31.60 5.4 29.98 27.42 -8.5 29.98 31.39 4.7 18.59 19.44 4.6 18.59 17.19 -7.5 18.59 19.34 4.0 18.59 17.19 -7.5 19.94 19.44 4.6 18.59 19.34 4.0 30.55 31.85 4.2 30.55 28.03 -8.2 30.55 31.85 4.2 13.15 13.55 3.1 13.15 12.36 -6.0 13.15 12.36 -6.0 13.15 13.55 3.1 13.15 13.59 3.3 13.15 13.59 3.3 26.95 27.48 2.0 26.95 25.32 -6.1 26.95 27.7 2.8 26.95 25.37 -6.1 26.95 27.48 2.0 26.95 27.7 2.8 34.79 35.25 1.3 34.79 32.97 -5.2 34.79 35.75 2.7 34.79 32.79 -5.2 34.79 35.25 1.3 34.79 35.75 2.7 107 TABLE IX (Continued) bcc ORTHORHOMBIC d(bcc) d(ORTHOR) %/bcc <113> [226] [6 6 1/2] 19.5 20.06 2.9 [262] [2 6 0] 19.5 18.5 -6.9 [622] [4 2 1/4] 19.5 20.06 2.9 <123> [246] [4 4 1/4] 22.0 22.09 0.4 [264] [3 6 1/8] 22.0 21.01 -4.5 [426] [5 2 1/8] 22.0 22.47 2.1 [462] [3 6 1/8] 22.0 21.01 -4.5 [642] [4 4 1/4] 22.0 22.08 0.4 [624] [5 2 1/8] 22.0 22.47 2.1 <112> [224] [3 2 1/8] 14.4 14.60 1.4 [242] [2 4 0] 14.4 13.67 -5.0 [422] [3 2 1/8] 14.4 14.6 1.4 <011> [022] [1 2 1/8] 8.32 8.21 -1.4 [202] [2 0 0] 8.32 8.54 2.6 [220] [1 2 1/8] 8.32 8.21 -1.4 <122> [244] [3 4 1/8] 17.64 17.28 -2.0 [442] [3 4 1/8] 17.64 17.28 -2.0 [424] [4 2 0] 17.64 17.9 1.5 <111> [222] [2 2 0] 10.18 10.07 -1.1 108 TABLE X f c t ORTHORHOMBIC d( f c t ) d(ORTHOR) % / f c t <001> [002] [1 0 1/8] 7.12 6.23 -12.5 [020] [1 2 1/8] 7.54 8.21 8.9 [200] [1 2 1/8] 7.54 8.21 8.9 <015> [015] [2 1 3/8] 18.2 16.29 -10.5 [051] [2 5 3/8] 19.18 20.89 8.9 [510] [2 6 1/4] 19.22 20.29 5.6 [501] [3 5 1/4] 19.18 20.60 7.4 [150] [2 6 1/4] 19.22 20.29 5.6 [105] [3 1 1/4] 18.2 16.29 -10.5 [150] [3 4 3/8] 19.22 21.53 12.02 [015] [3 1 1/4] 18.22 17.62 -3.3 [051] [3 5 1/4] 19.18 20.61 7.5 <013> [013] [1 1 1/4] 11.32 10.37 [031] [1 3 1/4] 11.86 12.83 8.2 [103] [2 1 1/8] 11.36 10.03 -11.7 [130] [1 4 1/8] 11.92 12.36 3.7 [310] [1 4 1/8] 11.92 12.36 3.7 [301] [2 3 1/8] 11.86 12.56 5.9 [130] [2 2 1/4] 11.92 13.56 13.7 <115> [2 2 10] [5 4 5/8] 37.16 32.93 -11.4 [2 10 2] [3 12 5/8] 39.1 41.29 5.6 [10 2 2] [5 12 3/8] 39.1 40.84 4.4 [2 2 10] [7 0 3/8] 37.16 32.84 -11.6 [10 2 2] 7 8 5/8] 39.1 43.18 10.4 <120> [420] [1 6 1/8] 16.86 17.19 1.9 [240] [1 6 1/8] 16.86 17.19 1.9 [042] [1 4 3/8] 16.68 17.82 6.8 [024] [1 2 3/8] 16.11 15.23 -5.5 [402] [3 4 1/8] 16.68 17.28 3.6 [204] [3 2 1/8] 16.11 14.60 -9.4 [240] [3 2 3/8] 16.86 19.44 15.3 <124> [248] [3 6 5/8] 33.1 30.58 -7.6 [284] [1 10 5/8] 34.19 35.29 3.2 [428] [5 6 3/8] 33.1 29.96 -9.5 [482] [1 12 3/8] 34.46 35.07 1.8 [842] [3 12 1/8] 34.46 34.81 1.0 [824] [5 10 1/8] 34.19 34.49 0.9 [428] [7 2 1/8] 33.1 30.7 -7.2 [824] [7 6 3/8] 34.19 36.54 6.9 [482] [7 4 5/8] 34.46 39.01 13.2 109 TABLE X (Continued) f c t ORTHORHOMBIC d ( f c t ) d(ORTHOR) % / f c t <135> [2 6 10] [3 8 7/8] 42.85 40.36 -5.8 [2 10 6] [1 12 7/8] 43.98 45.31 3.0 [6 2 10] [7 8 3/8] 42.85 39.18 -8.6 [6 10 2] [1 16 3/8] 44.54 45.04 1.3 [10 6 2] [3 16 1/8] 44.54 44.83 0.7 [10 2 6] [7 -12 1/8] 43.98 44.05 .17 [6 2 10] [9 4 1/8] 42.85 40.14 -6.3 [10 2 6] [9 8 3/8] 43.98 46.03 4.6 [10 6 2] [9 4 7/8] 44.54 50.98 14.5 <113> [226] [3 4 3/8] 23.87 21.53 -9.8 [262] [1 8 3/8] 24.88 25.68 3.2 [622] [3 8 1/8] 24.88 25.32 1.8 [226] [5 0 1/8] . 23.87 21.83 -8.6 [622] [5 4 3/8] 24.88 27.48 10.4 <123> [123] [1 3 1/4] 13.60 12.83 -5.7 [132] [0 4 1/4] 13.89 14.01 0.9 [213] [2 3 1/8] 13.60 12.56 -7.7 [231] [0 5 1/8] 14.05 14.10 0.4 [321] [1 5 0] 14.05 14.02 -0.2 [312] [2 4 0] 13.89 13.67 -1.6 [213] [ 3 1 0 ] 13.60 13.09 -3.8 [312] [3 2 1/8] 13.89 14.6 5.1 [321] [3 1 1/4] 14.05 15.92 13.3 <112> [112] [1 2 1/8] 8.89 8.21 -7.7 [121] [0 3 1/8] 9.15 9.21 0.6 [211] [ 1 3 0 ] ' 9.15 9.08 -0.8 [112] [2 0 0] 8.89 8.54 -3.9 [211] [2 1 1/8] 9.15 10.03 9.6 <011> [Oil] [0 1 1/8] 5.18 5.26 1.6 [101] [1 1 0] 5.18 5.04 -2.8 [110] [0 2 0] 5.33 6.23 16.9 <122> [244] [1 6 3/8] 22.07 21.45 -2.8 [442] [1 8 1/8] 22.48 22.25 -1.0 [424] [3 6 1/8] 22.07 20.58 -6.8 [424] [5 2 1/8] 22.07 22.47 1.8 [442] [5 0 3/8] 22.48 25.31 12.6 <111> [222] [1 4 1/8] 12.82 12.36 -3.6 [222] [3 0 1/8] 12.82 13.59 6.0 [222] [1 0 3/8] 12.82 13.68 6.7 

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