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Transformation elasticity in polycrystaline Cu-Zn-Sn alloy Dvorak, Ilja 1973

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TRANSFORMATION ELASTICITY IN POLYCRYSTALLINE Cu-Zn-Sn ALLOY by I. DVORAK B.A.Sc, University of Brno, 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 t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1973 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood t h a t c o p y i n g or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed w ithout my w r i t t e n p e r m i s s i o n . Department o f ' i t The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada Date - i i -ABSTRACT A study has been made of the ela s t i c i t y associated with the marten-site transformation in the polycrystalline B-phase alloy of composition Cu-33.6 wt. % Zn-4 wt. % Sn tested at room temperature. The mechanical properties of the material undergoing the stress induced martensite transformation have been examined. These properties are influenced by the elastic anisotropy of the bcc 3-phase, the development, preferential distribution and morphology and the mechanical properties of the trans-formation product. The elastic shape change associated with the elast i c a l l y accommo-dated, stress-induced martensitic transformation was always found to be accompanied by some plastic deformation. A relationship between the B-grain size, the sample thickness and the deformation response was observed. Specimens with grains extending through the sample thickness exhibited large reversible strains (^2.5%), whereas specimens with a much smaller grain size/thickness ratio (<1) exhibited only limited transformation e l a s t i c i t y . The morphology of the thermal martensite and the Mg temperature was also found to be influenced by the ratio grain size/thickness (g.s./t). A lower Mg temperature was associated with a decreasing g.s./t ratio; only self-accommodating burst martensite was observed i n very fine grained material. The A^ temperature increased with a decreasing g.s./t ratio. Repeated loading (cycling) reduced the hysteresis of the stress strain curve for a l l g.s./t ratios tested, but was always accompanied by plastic deformation of the matrix and the development of non-reversible deformation martensite. - i i i -The experimentally determined habit plane for the thermal and the stress induced martensite were in moderate agreement with the planes predicted by the phenomenological martensite theory (W.L.R.) assuming a {110} <110> microscopic shear. - i v -TABLE OF CONTENTS Page 1. INTRODUCTION 1 1.1 The S t r u c t u r a l S t a b i l i t y of the g-Phase i n Cu-Zn-Sn Al l o y s 1 1.2 C h a r a c t e r i s t i c s of the Mar t e n s i t i c Transformation.. 1 1.3 The Morphology and C r y s t a l Structure of Thermal Martensite 6 1.4 The Morphology and C r y s t a l Structure of Mechanically Induced Martensite 7 1.5 The Relationship of S t r e s s - S t r a i n Curve to Stress-Induced Shear Transformations 8 1.5.1 Single C r y s t a l 8 1.5.2 Pol y c r y s t a l s 1 2 1.6 Purpose of the Present Study 14 2. EXPERIMENTAL PROCEDURE 1 5 2.1 Selection of Composition 1^ 2.2 A l l o y Preparation 1 5 2.3 Preparation of Tensile Specimens 1? 2.4 L i m i t a t i o n of Specimen's Dimensions 1? 2.5 Metallography I 8 2.6 Tensile Tests 1 8 2.7 Measurement of Transformation Temperatures 19 2.8 Phase Analysis 2 0 2.9 Habit Plane Analysis 2 0 3. EXPERIMENTAL RESULTS AND DISCUSSION 1 1 3.1 Deformation and Transformation E l a s t i c i t y of the Polycrystalline,Metastable 8-Phase 2 1 - v -Page 3.1.1 General Observations 21 3.1.2 Discussion 29 3.1.3 The E f f e c t of Grain Size and Specimen Dimensions on the St r e s s - S t r a i n Relationship. 31 3.1.4 The E f f e c t of g.s./t Ratio on the Magnitude of Reversible S t r a i n 38 3.1.5 The E f f e c t of Tot a l S t r a i n on R e v e r s i b i l i t y of S t r a i n 41 3.1.6 The E f f e c t of Cycling on R e v e r s i b i l i t y of Str a i n 46 (i ) E f f e c t s Associated with I n i t i a l Cycling 46 ( i i ) The E f f e c t of Extended Cycling 51 3.2 The E f f e c t of g.s./t Ratio on Martensite Transforma-t i o n Temperatures 62 3.3 Phase Analysis 66 3.3.1 The Ef f e c t of S t r a i n Magnitude 66 3.3.2 The E f f e c t of Cycling 70 3.3.3 Summary 70 3.4 Determination of Habit Plane of the Martensite Plate 70 4. CONCLUSIONS 74 REFERENCES 76 - v i -LIST OF FIGURES Figure 1 Cu-Zn phase diagram 2 Typical stress-strain curve for a ternary Cu-Zn based alloy deformed in tension at room temperature 3 Portion of tensile curve for a ternary Cu-Zn-Sn alloy deformed at room temperature 4 Stress-strain curve for Cu-Zn-Sn single crystal specimen strained close to [100] direction 5 Transformation temperature,Ms,of ternary alloys based upon Cu-Zn g-phase 6 Dimensions of the tensile specimens 7 Typical stress-strain curve for polycrystalline Cu-33.6 wt. % Zn-4 wt.% Sn alloy strained at room temperature 8 The surface shape distrotion revealing the strain concentrations in the true elastic region 9 The surface shape distortion associated with the formation of stress-induced martensite 10 The surface shape distortion of the specimen strained into the yielding region 11 The surface of the unloaded specimen prestrained to the yielding region 12 The surface topography adjacent to a grain boundary after unloading a specimen prestrained to yielding region 13 Retained martensite product observed on an abraded, polished and etched surface of a sample i n i t i a l l y prestrained to yielding, then unloaded 14 Loading portions of the stress-strain curves for specimens of the same thickness with various grain size 15 Loading portions of the stress-strain curves for specimens having constant grain size and various thickness - v i i -- v i i i -Figure 31 The effect of g.s./t ratio on c r i t i c a l martensite transformation temperatures 32 Habit planes for thermoelastic martensite plates ... 33 Habit planes for stress-induced martensite plates .. 34 Habit planes for thermoelastic martensite and stress induced martensite in Cu-Zn-Sn alloy 35 Habit planes for thermoelastic martensite and stress induced martensite i n Ag-Cd alloys (13) - i x -LIST OF TABLES Table Page I Temperature i n t e r v a l s between the c r i t i c a l martensite temperatures 64 II X-Ray d i f f r a c t i o n peaks of strained specimens 67 III Comparison of X-ray d i f f r a c t i o n peaks of strained specimens with the d i f f r a c t i o n traces from f i l i n g s . . 68 TV X-Ray d i f f r a c t i o n peaks associated with cycled product 69 - x -ACKNOWLEDGEMENT The author wishes to express h i s sincere gratitude to Dr. E.B. Hawbolt, f o r h i s advice and assistance during the course of th i s i n v e s t i g a t i o n . I t i s a pleasure to thank Dr. L.C. Brown f o r h i s h e l p f u l comments and c r i t i c i s m . Thanks are also extended to the members of the f a c u l t y , fellow graduate students and technical s t a f f f o r t h e i r assistance. The graduate fellowship awarded by the Univ e r s i t y of B r i t i s h Columbia i s g r a t e f u l l y acknowledged. - 1 -1. INTRODUCTION 1.1 The Structural Stability of the g-Phase in Cu-Zn-Sn Alloys The g-phase of Cu-Zn-Sn alloys belongs to that group of body centered compounds which tend to become unstable at low temperatures (1). The Cu-Zn phase diagram is shown in Figure 1. The disordered g-phase stable at high temperature, can be retained to room temperature by rapid quenching. However, the rate of ordering in these alloys is very rapid and a high degree of order i s found immediately after quenching. Several authors have suggested that the ordering reaction in Cu-Zn alloys i s a second-order transformation (2). The ordered structure,g', is a caesium chloride type structure. Although the presence of a third alloying element would likely affect the rate of the ordering reaction, no quantitative data is available for the Cu-Zn-Sn system. The retained g' phase is metastable and may undergo a martensitic transformation on further cooling (3). Recent work (4) indicates that a very fine precipitate may be already present in the quenched g phase as a product of the premartensitic ins t a b i l i t y . 1.2 Characteristics of the Martensitic Transformation The martensitic transformation is diffusionless the product being produced by a coordinated movement of atoms (5). This type of reaction Figure 1. Cu-Zn phase diagram. - 3 -gives r i s e to a change of shape which i s evident on a prepolished surface following the transformation. The p r i n c i p a l d i r e c t i o n s and planes i n both phases are rela t e d by a s p e c i f i c o r i e n t a t i o n r e l a t i o n s h i p ( 6 ) . Most martensitic transformations are athermal. The transformation on cooling begins at a c r i t i c a l temperature Mg, and progresses only with further decrease i n temperature u n t i l the reaction i s complete at M^. The corresponding temperatures f o r the reverse transformations are A s and Af r e s p e c t i v e l y . From a thermodynamic viewpoint the temperature f o r spontaneous transformation to martensite, Mg, must be below the temperature, T Q . Where T q i s the temperature at which the chemical free energies of the parent and the martensitic phase are equal. The difference,(.T^-M), i s then a measure of the d r i v i n g force necessary for the i n i t i a t i o n of the transformation. An applied stress has a marked influence on most martensitic transformations (7). The martensitic product can often be formed by the ap p l i c a t i o n of stress at temperatures above the c r i t i c a l M g temperature. The formation of a martensite plate i s governed by the energy balance between d r i v i n g forces and the opposing forces (8) and can be written as follows (9): (F -F M)dV + (Y T + e a )dV > (Y T + e a )dV + S dA + Y MS dV A M M a M a Mo M a M M eqn. (1) Where F = s p e c i f i c volume free energy of the parent phase. F^j = s p e c i f i c volume free energy of the martensite phase. v., = t o t a l shear associated with the formation of a martensite 'M phase. - 4 -volume change normal to the habit plane associated with the formation of a martensite plate. applied shear stress resolved along the habit plane and in the shear direction of a martensite plate. applied tensile stress normal to the habit plane of a martensite plate. int r i n s i c shear resistance of the material against Y„. M intrinsic tensile resistance of the material against e... specific surface free energy of the matric-martensite interface. energy term associated with deformation process occurring around the growing martensite plate, incremental volume expansion of a martensite plate, surface increment of martensite-matrix interface. The work done by the driving forces is written in the left-hand side of eqn. (1). The right-hand side is composed of three terms: the work of internal f r i c t i o n stresses opposing the deformation associated with the martensite plate growth, a surface energy term, and an energy term associated with the accommodation process around the growing martensite plate. This energy balance can be externally affected by either undercooling below the T q temperature or by the application of an external stress. Although the applied stress may exhibit a measurable influence on the onset of the martensite transformation as a result of the volume change term, i t is primarily the shear component of the applied stress that T = a = T = a = S w = M 5 = dV dA - 5 -affects the mode of the transformation. Those martensite plates form for which the resolved shear stress can provide the largest work. Therefore martensite formation induced by the application of external stress exhibits a preferential orientation with a limited number of martensite plate variants operative. The maximum number of possible martensite plate variants that can form in one grain depends on the crystal symmetry of the parent phase. For a cubic parent phase, 24 martensite plate variants can form. Frequently the martensite formation is either partially or fu l l y s e l f -accommodating (11). Such formations are characterized by a mimimum or zero-resulting microscopic shape deformation. Consequently, in the absence of external stresses and when the volume change i s negligible, martensite formation w i l l proceed without an external shape change. On the contrary, i f an external stress f i e l d aids the martensite formation, either a limited number of martensite plate variants are expected to grow or, in the case of self-accommodating formations, certain martensite plate variants w i l l become dominant in the different groups and this w i l l lead to an external shape change. The influence of external stresses on the martensite transformation is expressed by a temperature, M^ , defined as the highest temperature at which mechanically induced martensite formation is possible. When the temperature is higher than and i f a specific situation arises at which the martensite formed under applied stress in this^^-A^) temperature interval i s elastically accommodated in the surrounding matrix, i t w i l l disappear on removal of the external stress giving rise to a phenomenon termed superelasticity. - 6 -This e f f e c t has been observed i n the following systems (Cu-Zn-Sn) (CU-Zn-Si), 1 0 ( C u - A l - N i ) , 1 2 (Ag-Cd), 1 3 and (Au-Cd). 1 4 When the i n t e r a c t i o n of the applied stress with the accommodation stress exceeds the flow stress of the parent phase, the p l a s t i c deformation may r e s u l t i n the formation of non-reversible, strain-induced martensite. The transformation to s t r a i n induced martensite during p l a s t i c deformation i s believed to account f o r the r e l a t i v e l y small degree of p l a s t i c flow (9). 1.3 The Morphology and C r y s t a l Structure of Thermal Martensite Observations of the morphology of thermal martensite i n ternary Cu-Zn based B-phase a l l o y s (16) has revealed that two types of martensite can form on cooling. Just below the c r i t i c a l temperature, Mg, a needle-like thermoelastic martensite forms. This type of martensite i s i n thermoelastic equilibrium with the parent phase. The amount formed i s dependent on the temperature. Thermoelastic martensite has a banded appearance forming as p a r a l l e l - s i d e d , long pla t e s . At temperatures below the c r i t i c a l Mg temperature, burst martensite forms i n sudden growth increments. The i n d i v i d u a l regions of burst martensite once formed, usually do not grow. Di f f e r e n t areas transform on decreasing the temperature. On heating, i n d i v i d u a l areas of burst martensite disappear suddenly This reverse reaction exhibits a larger temperature hysteresis than that associated with the reversion of thermoelastic martensite. The c r y s t a l structures of the ternary Cu-Zn based thermal martensites have been determined using transmission electron microscopy. For a l l o y s - 7 -containing the trivalent elements Ga and Al (17-19) and tetravalent Si (20) both thermoelastic and burst thermal martensites were found to contain a faulted structure. The structures could be interpreted as a lamellar mixture of the two close packed structures, orthorhombic (ABCBCACAB) and fee (ABC). It is generally agreed that the habit plane for both thermoelastic and burst martensite in Cu-Zn alloys is (2 11 12) while for ternary Cu-Zn based both (2 11 12) (16) and (110) (22) have been reported. 1.4 The Morphology and Crystal Structure of Mechanically Induced  Martensite The morphology and structure of mechanically induced martensite in Cu-Zn and ternary Cu-Zn based alloys have been examined by several investigators (21,22,23). Ahlers and Pops (23) investigated two types of mechanically induced martensite in a Cu-Zn alloy, one appearing as broad bands with a habit plane close to (110) and one appearing as very narrow straight bands with either a (112) or (110) habit plane. The habit plane of the broad martensite band changed continuously from (110) to (2,11,12) with increasing amounts of strain. This type of martensite formed only i f slip occurred within the 6 phase matrix on planes nearly parallel to the habit plane. Straining of single crystal specimens oriented with the [001] direction parallel to the tensile axis, produced a form of burst martensite with a habit plane close to (2,11,12) (21). The Wechsler-Lieberman-Read theory (6) for thermal martensite was applied to stress induced martensite and gave a habit plane in moderate agreement with the experimentally observed (22,35). The crystal - 8 -structure of deformation martensite in Cu-Zn alloys has been determined as fct (29). 1.5 The Relationship of Stress-Strain Curve to Stress Induced Shear  Transformations 1.5.1 Single Crystal . Typical stress-strain curve of single crystal specimens of Cu-Zn-Sn alloys strained at temperatures above the temperature are shown in Figures 2, 3, and 4 (10,21). Figure 2 shows four distinctive regions which have been interpreted as follows. Region a_ on i n i t i a l loading, represents the true linear elastic response of the 3 phase. As the stress increases beyond the elastic yield point E, the stain increases rapidly with a small increase of stress until a new linear region, b_, is observed. Region b_ is characterized by a very low slope and reflects the strain associated with the transformation of the matrix to the stress induced martensite. Beyond the region b_, the slope increases corresponding to the completion of the transformation and subsequent elastic straining of the martensitic phase. Point P corresponds to the start of plastic deformation of the martensite. A similar stress-strain relationship is shown in Figure 3 for loading up to the elastic region of the martensite followed by removal of the applied load. Upon unloading, the stress-strain curve exhibits some stress hysteresis but almost complete reversibility of the applied strain. The effect of crystal orientation with respect to the tensile axis has also been reported (21). The stress-strain curves were T - 1 I 1 I I stress ( 1 0 0 0 psi ) 20 -strain (%) Figure 2. Typical stress-strain curve for a ternary Cu-Zn based alloy deformed in tension at room temperature. - 10 -stress I lOOOpsi) strain (%) F i g u r e 3. P o r t i o n o f t e n s i l e c u r v e f o r a t e r n a r y C u - Z n - S n a l l o y d e f o r m e d a t room t e m p e r a t u r e s h o w i n g c h a r a c t e r i s t i c h y s t e r e s i s l o o p a f t e r u n l o a d i n g . S e r r a t i o n s a r e a s s o c i a t e d w i t h t h e f o r m a t i o n o f e l a s t i c m a r t e n s i t e (10). - 11 -stress ( 1000 psi)20 strain (%) Figure 4. S t r e s s - s t r a i n curve f o r Cu-Zn-Sn single c r y s t a l specimen strained close to [100] d i r e c t i o n (21). - 12 -comparable to that shown in Figure 3. Moreover, specimens strained along their [001] direction produced a stress-strain curve similar to that shown in Figure 4. A large strain was retained on unloading. The reversible strain represents only a small fraction of the total applied strain. A high elastic anisotropy i s also a characteristic feature of the 6 phase in Cu-Zn alloys (25). A measure of the degree of anisotropy is introduced as an anisotropy factor - a ratio of the elastic constants ^[111]^[001] t b e ^ U - Z n ^ phase approximately ^ 8.9 (25). The elastic anisotropy when expressed as a ratio of the shear coefficients 2 Cii^cn~ci2 i s a P P r o x i m a t e l y 18 (25). C ^ and ( C 1 1 - C 1 2 ^ 2 3 r e r i g i d i t y moduli for shear on the (100) plane in an arbitrary direction and on the (110) plane in the [110] direction respectively. 1.5.2 Polycrystals On straining, the anisotropy of individual grains in the poly-crystalline matrix gives rise to the development of strain concentrations at specific sites in the matrix. In particular, grain boundaries and multigrain intersections can become regions of high localized strain. An analysis of the energy associated with the deformation of poly-crystalline metal has shown that the highest deformation is localized at the grain boundary of grains which exhibit a maximum difference in their stress-strain behaviour (28,29). Assuming that the width of the grain is proportional to the strain difference between adjacent grains, Abe (28,29) has shown that the deformation of polycrystals changes it s mode from constant stress to constant strain with increasing total strain and decreasing grain size. - 13 -For a randomly oriented polycrystalline specimen the structure may be regarded as a multiphase material consisting of an i n f i n i t e number of anisotropic phases. Therefore, a prediction of mechanical properties of the polycrystalline material in terms of the mechanical properties observed on the single crystal requires a s t a t i s t i c a l formulation of the physical constants appearing as a random space function (27). The stress-strain relationships of the polycrystalline, metastable phase in Cu-Zn-Sn alloys at temperatures above the temperature are similar to the stress-strain relationship exhibited by single crystal specimens (10,21) although the magnitude of the recoverable strains i s considerably less for the polycrystalline material. In polycrystals, only certain grains are favourably oriented for the formation of stress induced martensite. Strain concentrations at grain boundaries causes martensite to form at low externally applied stresses. Repeated loading and unloading (cycling) of the specimens for 10 cycles does not affect the stress strain relationship (21). Brown (26) has shown that decreasing the grain size in specimens of constant thickness reduces the magnitude of the reversible strain. Specimens having a smaller grain size require a larger applied stress to produce a comparable strain magnitude. The associated high stress concentrations a t the grain boundaries give rise to local plastic deformation. The magnitude of the i n i t i a l linear elastic region at the beginning of loading and the near-linear region corresponding to martensite formation diminishes with decreasing grain size. - 14 -1.6 Purpose of the Present Study The present study was undertaken to: (1) determine the effect of grain size and specimen geometry on the magnitude of transformational ela s t i c i t y (2) determine which bulk constraints affect the tendency to form superelastic conditions (3) examine the influence of tensile cycling at high strain magnitudes (strains corresponding to transformational elasticity) on stress-strain relationships and on the structure of the poly-crystalline metastable 8 phase. - 15 -2. EXPERIMENTAL PROCEDURE 2.1 Selection of Composition An alloy composition was chosen to yield transformation temperatures just below room temperature. The relationship between Mg temperature and the composition is shown in Figure 5. A composition containing A wt. % Sn was selected and the Cu and Zn concentrations were experimentally determined (33.6 wt. % Zn,62.4wt. % Cu, 4 wt. % Sn) to provide an alloy having i t s A^ temperature at 15°C. 2.2 Alloy Preparation A 700 g ingot of the desired composition was obtained by melting a mixture of 60-40 commercial brass with Cu (99.98%) and Sn (99.999%). Melting was carried out in air using an induction heated graphite crucible. The molten alloy was well mixed and directionally cooled to obtain a sound ingot of approximately 35 mm diameter. The ingot was hot rolled 20% and annealed at 820°C in a stainless-steel bag (Sen-Pak) for 36 hours. After annealing, the ingot was heated to 810°C and subsequently hot rolled in 6 passes down to <v 2.5 mm thick strip. This strip was heated to the 8 phase (820°C) and rapidly quenched in a 10% caustic soda solution cooled to 5°C to retain the 8 phase. The transformation temperatures were measured to determine the composition losses related to the preparation procedures. - 16 -o O 0> k. 3 2 C L E 4> 0 - 5 0 -100 -150 -200 -250 -Sn —j& J Figure 5. I 2 3 atomic % solute Transformation temperature M of ternary a l l o y s based upon the Cn-Zn B'-phase, e/a = 1.395 (10). CM 85" Figure 6. Dimensions of the t e n s i l e specimens. - 17 -2.3 Preparation of Tensile Specimens Polycrystalline specimens for tensile tests were prepared from 0.3 to 2 mm thick cold rolled strip. A reduced section gauge length was prepared by either punching or spark machining the strip. Final dimensions are shown in Figure 6. The tensile specimens were heated to the g-phase f i e l d either in air or a molten salt bath and quenched in iced 10% caustic soda solution to retain the g-phase. A range of grain sizes were obtained by varying both the % cold deformation (5-80%) prior to the f i n a l heat treatment and the holding time in the g-phase f i e l d (3 sec to 1.5 min). Following the heat-treatment, a thin surface layer of the specimens was either mechanically abraded or chemically removed using a solution of 50 parts ^PO^, 40 parts MN03 and 10 parts HCl. The specimens were polished either mechanically using 0.05 Alumina or electropolished in a solution of 25 cc chromic oxide, 133 cc acetic acid and 7 cc water. 2.4 Limitation of Specimen's Dimensions Prediction of the mechanical properties of a polycrystalline material can only be made when the specimens are in a quasi isotropic state. This condition requires the specimen to have a sufficient number of crystals such that these, although individually anisotropic, create a bulk specimen which can be s t a t i s t i c a l l y considered as quasi isotropic. This conditions was not satisfied during this investigation. - 18 -The specimen preparation procedures placed a limitation on their dimensions; the 6-phase could only be successfully retained by rapidly quenching samples whose thickness did not exceed approximately 3 mm. Thicker samples exhibited either a transformation to the stress-induced martensite apparently initiated by residual quenching stresses or a precipitation of the a-phase due to the reduced cooling rate. Grain growth occurred rapidly in the single phase region. The smallest grain size achieved in these specimens was 0.075 mm. 2.5 Metallography Metallography was carried out on either the tensile specimens or specimens selectively cut from the rolled strip. The specimens were polished and etched in a solution containing 10 g FeCl 3 20 cc HCl 100 cc H20 The average grain size was estimated by optically measuring the largest average grain diameter. Most of the specimens investigated were polycrystalline with the grain size extending from the top surface to the bottom surface of the sample. Thermal and stress-induced martensite were visible on prepolished surfaces without etching while martensite retained after deformation was revealed by removing, polishing, and etching the surface. 2.6 Tensile Tests A l l tensile tests were carried out at room temperature using a floor model Instron testing machine. An Instron extensometer was used to - 19 -obtain an accurate measurement of s t r a i n . Cycling i n tension, either between two load l i m i t s or between a small load and a chosen s t r a i n magnitude was c a r r i e d out. Load c y c l i n g , using the automatic c y c l i n g p o t e n t i a l of the Instron was conducted for 3 up to ^7 x 10 cycles, whereas l o a d - s t r a i n c y c l i n g was conducted 2 manually for np to 3 x 10 cycles. A crosshead speed of O.Olin/min was used i n most of the experiments; some c y c l i n g between two load l i m i t s was employed and used a crosshead speed of 0.05 in/min. A microscope mounted on the crosshead of the Instron was used to observe and record (35 mm photographs) the surface a f f e c t s associated with the t e n s i l e and c y c l i n g t e s t s . A t e n s i l e j i g (21) was used f o r s t r a i n i n g the specimens to determine the habit planes of the martensite plates and for obtaining X-ray d i f f r a c t i o n traces from specimens subjected to t e n s i l e loading. 2.7 Measurement of Transformation Temperatures The Mg, and A^ temperatures were determined by o p t i c a l microscopy. Specimens were mounted on a copper block and immersed i n an ethanol bath contained i n a pyrex dewar. The pyrex dewar was placed i n a large double walled dewar, the space between the dewars being p a r t i a l l y f i l l e d with ethanol. Both baths were well s t i r r e d . Specimen temperatures below room temperature were obtained by pouring l i q u i d nitrogen into the double walled dewar. This procedure insured a very uniform cooling rate for the specimens. The temperature was measured using e i t h e r a chromel-alumeLthermocouple or a glass thermometer. The immersed specimens were examined during cooling using a microscope f i t t e d with a long f o c a l - 20 -length lens. The onset of surface t i l t i n g associated with the martensite formation could be easily noted. 2.8 Phase Analysis X-ray diffraction investigations at room temperature were performed using a Norelco diffractometer operating at a scanning speed of l°-2°/min. A copper target was used either with or without Ni f i l t e r . A special mounting device for the tensile j i g was designed to obtain X-ray diffraction traces from the strained tensile specimens. 2.9 Habit Plane Analysis Habit plane poles were determined using a two surface trace analysis (30). The orientation of individual grains in large grained material was determined using the Back Reflection Laue method. The traces of the martensite within those grains were then obtained on two perpendicular surfaces using the tensile j i g . The pole of the habit plane of thermal martensite was determined by the same procedure using the cooling apparatus. - 21 -3. EXPERIMENTAL RESULTS AND DISCUSSION 3.1 Deformation and Transformation Elasticity of the Polycrystalline  Metastable g-Phase 3.1.1 General Observations A series of polycrystalline specimens of selected composition were tested in tension at room temperature. The typical stress-strain relationship observed i s shown in Figure 7. The shape of the stress strain curve generally included three specific regions. A portion, a., on i n i t i a l loading exhibited a modulus of E = 8 x 10 psi and corresponds to the e l a s t i c i t y of the g-phase. The anisotropy exhibited by the individual crystals gave rise to some surface shape distortion v i s i b l e at grain boundaries (Figure 8). The surface shape distortion revealed the presence of strain concentrations. A portion, _b, the transition region i s characterized by a gradual decrease of modulus. The local regions of stress concentrations acted as centers.for the i n i t i a t i o n of the martensite transformation. Thus martensite developed heterogeneously. A portion, the yielding region corresponds to non-reversible plastic flow, recoverable transformation ela s t i c i t y or a combination of both and is characterized by a low value of modulus (E = 1-1.7 x 10^ psi ) . - 22 -strain Figure 7. Typical stress-strain curve for polycrystalline Cu-33.6 wt. % Zn-4 wt. % Sn alloy strained at room temperature. Inter-polated stress associated with the transition between the i n i t i a l loading region (a) and the yielding region (c) is shown with a corresponding magnitude of strain. Figure 8. The surface shape d i s t o r t i o n revealing the s t r a i n concentrations in the true e l a s t i c region (50X). - 24 -Figure 9. The surface shape d i s t o r t i o n associated with the formation of stress-induced marrensite (50X). - 25 -Figure 10. The surface shape d i s t o r t i o n of the specimen strained into y i e l d i n g region c (50X). Figure 11. The surface of the unloaded specimen p r e s t r a i n e d i n t o y i e l d i n g region (SOX). - 27 -Figure 13. Retained martensite product observed on an abraded, polished and etched surface of a sample i n i t i a l l y prestrained into region c then unloaded (140X). - 29 -In t h i s region some l o c a l p l a s t i c deformation accompanied any increase i n the applied stress. Some grains exhibited a high density of martensite plates while other grains contained r e l a t i v e l y unaffected regions. Some grains deformed p l a s t i c a l l y e x h i b i t i n g a high density of s l i p - l i n e s (Figure 10). The unloading portion of the s t r e s s - s t r a i n curve exhibited some stress hysteresis. In some regions deformation produced s t r a i n induced non-reversible martensite. Some permanent set always remained as evidenced by surface d i s t o r t i o n retained on the unloaded specimen i n Figure 11. The surface d i s t o r t i o n was most severe i n the v i c i n i t y of the grain boundary, Figure 12, and gradually decreased toward the center of the grains. An abraded, polished and etched surface from a prestrained and unloaded specimen demonstrating the presence and inhomogeneous d i s t r i b u t i o n of retained martensite i s shown i n Figure 13. 3.1.2 Discussion The experimental r e s u l t s suggest that transformation e l a s t i c i t y doesnot occur homogeneously throughout p o l y c r y s t a l l i n e Cu-Zn base B-phase a l l o y s . Instead, the transformation i s l o c a l i z e d to s p e c i f i c s i t e s the choice of which i s dependent on the l o c a l stress f i e l d . The l o c a l stress condition i s affected by several f a c t o r s : (a) The anisotropy of the B-phase, E [ H Q ] ^ [ 1 00] ^ ° r 2 C44^ C12- C22 ^ 1 8 f ° r t h e e _ P h a s e o f C u _ Z n a l l o y s (25) and would be expected to be s i m i l a r for Cu-Zn-Sn a l l o y s . (b) The martensite product has mechanical properties which are believed to be d i f f e r e n t from those of the parent B-phase and i s - 30 -inhomogeneously distributed in the bulk specimen. (c) The properties of the material during the transformation correspond neither to those of the parent nor to-those of the newly-formed phase. The stress-strain characteristics of the material undergoing the stress-induced martensitic transformation are such that the applied stress corresponding to the elastic point E (Figure 2) which must be exceeded in order to set the transformation in motion, is lowered briefly just for the duration of the transformation and no increase in stress i s required to maintain flow of the transformation process. The stress can remain constant or even decrease and s t i l l cause a considerable degree of deformation associated with the martensitic transformation. During the reverse transformation,on unloading a similar phenomenon takes place but at different stresses giving rise to the typical hysterisis effect (Figure 3). The combined effect of those phenomena creates an anisotropic stress f i e l d throughout the polycrystalline material. The effect is most pronounced at grain boundaries (25). Hence, when a uniaxial stress is applied to polycrystalline material the individual grains encounter a three dimensional stress condition which necessitates that a high number of favorable martensite plate variants be operative. Eisenwasser (21) investigated the relationship between the crystal orientation and the tensile axis and showed that large elastic strains (transformational elasticity) were realized by straining the crystal along [110] and [111] directions. The crystals transformed with a single martensite plate variant operative. Whereas single crystals strained along the [100] direction exhibited very limited transformation el a s t i c i t y . - 31 -The following reasons could explain the non-reversibility of strain and are consistent with observed deformation behaviour of the poly-crystalline g-phase. (1) Transformation ela s t i c i t y does not occur along a l l possible crystallographic directions under uniaxial tension in single crystals. These crystallographic directions may become operative in polycrystalline material and so participate in non-reversibility of bulk strains. (2) The greater number of martensite plate variants formed on loading do not have to satisfy the energy balance created on unloading -different stress-strain conditions exist on unloading. Accommodation between the plates of different variants can occur on loading and need not be reversible on unloading. (3) Stress concentrations at specific grain boundary sites may exceed the flow stress of the parent phase causing : (a) non-reversible plastic flow of the g-phase. This w i l l also result in the retention of stress in adjacent areas after unloading. In such areas martensite..although elastically accommodated.will be retained as a result of incomplete unloading. (b) plastic deformation which alters the structure to an irreversible strain induced martensite (deformation martensite). 3.1.3 The Effect of Grain Size and Specimen Dimensions on the  Stress-Strain Relationship Specimens exhibiting a variety of thicknesses and grain sizes were tested. The gauge length and sample width were kept constant for a l l specimens tested. The stress-strain curves appearing in Figure 14 were - 32 -Figure 14. Loading portions of the s t r e s s - s t r a i n curves for specimens of the same thickness with various grain s i z e s . - 33 -Figure 15. Loading portions of the s t r e s s - s t r a i n curves f or specimens hav-ing a constant grain size and various thicknesses. - 34 -Figure 16. The effect of the g.s./t ratio on interpolated yield stress. - 35 -A 1 1 1 A A A A -_ A A - A A A A A A -A • A A A i 0 l 2 3 4 g.s-5 t. 17. The e f f e c t of the g.s./t r a t i o on the magnitude of the accommodated s t r a i n corresponding to the interpolated y i e l d stress. - 36 -obtained by testing a number of specimens, each having a different grain size but a constant thickness. A decrease in the grain size gives rise to an increase in the applied stress for a given strain magnitude. When specimens of various thicknesses each having the same grain size were tested a similar effect was observed (Figure 15). The thicker specimens yielded at a higher applied stress for the same strain magnitude. An examination of Figures 14 and 15 suggests that a relation-ship exists between the grain size and the sample thickness in terms of their effect on the stress-strain behaviour. A plot of the interpolated stress associated with the transition between the loading and the yielding region (as shown in Figure 7) vs. the grain size/thickness (g.s./t) ratio is shown in Figure 16. The strain associated with the yielding stress is plotted i n Figure 17. Specimens with a small g.s./t ratio yielded at significantly higher stresses and after accumulating a large magnitude of applied strains. A high value of the g.s./t ratio represents a specimen in which the grains extend throughout the thickness of the specimen. Such grains have relatively small grain boundary areas, and could be idealized as a single row of grains whose grain boundaries are essentially perpendicular to the sample surface. Because these samples contain only limited grain boundary constraints they can adjust to the shape changes associated with the heterogeneous character of the deformation and the accompanying martensite transformation. In these samples a small stress is associated with a given strain and within the yielding range a significant fraction of grain area transforms to martensite. Specimens with a small g.s./t ratio have more than a single layer of grains. Some grains are completely contained within the sample - 37 -18b (50X) Figure 18. The surface shape distortion of two samples strained 1.5% having the g.s./t ratio of 3 (18a) and 0.7 (18b). - 38 -thickness and are completely enclosed by grain boundaries. The larger grain boundary enclosure makes the shape changes associated with the martensite transformation more d i f f i c u l t to accommodate f o r a given s t r a i n magnitude. A given s t r a i n magnitude requires a higher applied s t r e s s . Within the y i e l d i n g range, specimens exhibited a large amount of p l a s t i c deformation for a given s t r a i n . Figure 18 shows the nature of y i e l d i n g associated with a g.s./t r a t i o of 3 (Figure 18a) compared to one with a g.s./t r a t i o of 0.8 (Eigure 18b). There i s a greater amount of p l a s t i c deformation associated with deformation of specimens having the smaller g.s./t r a t i o . Poor r e p r o d u c i b i l i t y of the t e n s i l e test r e s u l t s was c h a r a c t e r i s t i c of specimens having a large grain s i z e , the samples deformed over a small p o r t i o n of the gauge length with only a few favorably oriented grains p a r t i c i p a t i n g . Those specimens having a small grain s i z e proved to e x h i b i t a more reproducible response to t e n s i l e t e s t i n g . Therefore the s t r e s s - s t r a i n observations i n t h i s work are meaningfull only when interpreted together with geometrical conditions under which they were obtained. 3.1.4 The E f f e c t of g.s./t Ratio on the Magnitude of Reversible  S t r a i n Specimens of constant thickness with a varying grain s i z e were strained to 1 % extension and unloaded. The s t r e s s - s t r a i n r e l a t i o n s h i p s obtained are shown i n Figure 19. Specimens with the smallest g.s./t r a t i o 0.18) exhibited the smallest r e v e r s i b l e s t r a i n . The s t r e s s - s t r a i n curve t y p i c a l of - 39 -stress I i i i | (lOOOpsi) strain (%) Figure 19. The stress-strain curves for specimens with various values of the g.s./t ratio. - 40 -ft 1 1 1 o f tS .4 -c O Brown (26) 0 w. V) 0 A present total .3 - A -42 •—1 a> menl .2 -E 0) Q. A <*-O tude .1 O -m agni 0 1 , O A 0 1 2 3 4 5 g.s. Figure 20. The e f f e c t of the g.s./t r a t i o on the magnitude of the permanent set for t o t a l s t r a i n of 1%. - 41 -specimens having a g.s./t ratio of approximately 2, on unloading, exhibited some hysteresis and the amount of plastic strain was markedly smaller than that obtained from specimens with the g.s./t ratio of 0.18. On unloading the coarse grained specimens (g.s./t <v 4) the stress-strain curve exhibited a stress hysteresis similar to that observed on single crystals (Figure 3), and produced a high magnitude of reversible strain. These results show that on i n i t i a l straining of the polycrystals, although large reversible strains can be achieved, there is always some plastic deformation. The magnitude of the permanent set reflects the degree of grain boundary constraint. The constraints are small for a coarse grained specimen and large for fine grained specimens. These results are in good agreement with those reported by Brown (26). Figure 20 shows a plot of the magnitude of the permanent set, e^, for a total strain of 1% for a range of g.s./t. The reversibility of strain approaches 100% at a g.s./t ratio of approximately 4. 3.1.5 The Effect of Total Strain on Reversibility of Strain Several specimens, approximately 0.5 mm thick and having a range of grain sizes were repeatedly strained and unloaded (cycled). A constant increment of strain was added in each subsequent cycle u n t i l a maximum strain of 2.5% was attained. The resulting stress-strain diagrams are shown in Figures 21a,b,c. From these diagrams i t is apparent that the magnitude of transformation ela s t i c i t y (recoverable strain) i s very dependent on both the g.s./t ratio and on the amount of the prestrain. Specimens with a small g.s./t ratio exhibited limited strain (%) Figure 21b. The e f f e c t of the t o t a l s t r a i n on the magnitude of r e v e r s i b l e s t r a i n for various g.s./t r a t i o . - 45 -T 1 1 — r accommodative applied strain (%) Figure 22. A plot of the accommodated vs. re v e r s i b l e s t r a i n . - 46 -r e v e r s i b l e s t r a i n . Increasing the g.s./t r a t i o increased the magnitude of the transformation e l a s t i c i t y . The e f f e c t of the p r e s t r a i n i s shown i n Figure 22 by p l o t t i n g the magnitude of the recoverable s t r a i n versus the cummulative s t r a i n from Figures 21a,b,c. Only specimens with a large g.s./t r a t i o show a high degree of r e v e r s i b i l i t y a f t e r p r e s t r a i n i n g . Those specimens with the smallest g.s./t r a t i o exhibited non-reversible p l a s t i c flow a f t e r only 1.5% p r e s t r a i n . Thus the constraints imposed at grain boundaries give r i s e to high l o c a l stresses and subsequently prevents the r e a l i z a t i o n of r e v e r s i b l e s t r a i n s . 3.1.6 The Ef f e c t of Cycling on R e v e r s i b i l i t y of S t r a i n A series of tests were conducted to examine the influence of cyc l i n g on the r e v e r s i b i l i t y of s t r a i n . As has already been shown, a f t e r s t r a i n i n g and unloading a p o l y c r y s t a l l i n e specimen, only a f r a c t i o n of the applied s t r a i n i s r e v e r s i b l e , the remainder being associated with p l a s t i c flow of the matrix or the development of non-reversible martensite (deformation martensite or strain-induced martensite). The shape of the s t r e s s - s t r a i n curve was investigated during c y c l i n g specimens ei t h e r between a zero load and an upper s t r a i n l i m i t or between two load values. (i ) E f f e c t s Associated with I n i t i a l Cycling The stress s t r a i n curve appeared to s t a b i l i z e a f t e r a small number of cycles. Figure 23 shows the stress s t r a i n diagram of a specimen 3 cycled between a s t r a i n of 1.25% and a stress of 1 x 10 p s i . The loading portion of the second cycle d i f f e r s s i g n i f i c a n t l y from the i n i t i a l - 47 -Figure 23. S t r e s s - s t r a i n curve development during i n i t i a l c y c l i n g between a lower load l i m i t and an upper s t r a i n l i m i t . - 48 -loading. The difference between cycles decreases on continued cycling. The unloading portion of these curves does not change markedly during cycling. Only a slight decrease in stress hysteresis i s observed between the 1st and 2nd cycles. Figure 23 also shows that i n i t i a l cycling produces an additional increment of permanent deformation, although the magnitude of the non-reversible strain decreases on increased cycling. In these tests i t was necessary to cycle the specimens 4 times to achieve a relatively stabilized shape for the stress-strain curve. The effect of prestrain on the number of cycles necessary to obtain a stabilized stress-strain curve was also investigated. Specimens were strained producing a stress-strain curve similar to that shown in Figure 24. After each strain increment the specimens were cycled un t i l the stress-strain curve showed no significant change. An additional increment of strain was then added and cycling was repeated, the process being continued up to a total strain magnitude of 2%. Prestrain using constant increments did not markedly influence the number of cycles required to produce a stable stress-strain condition. The number of cycles for stabilization varied from 1 to 2 for small strain increments (0.20%) and from 2 to 4 for large strain increments (1%). Figure 25 shows the stress-strain curve of a specimen strained and cycled between load values. Cycling resulted in the change in shape and position of the stress-strain curve - compare the stress-strain curve for the 1st and the 10th cycle. The changes were similar to those observed when cycling to an upper limit set at a given strain magnitude. However, the decrease in the hysteresis of the curve on cycling produced a small s t ress ( l O O O p s i ) 0 2 5 .5 75 Figure 24. The effect of prestrain on i n i t i a l cycling. 1.25 1.5 2 stra in (%) - 50 -Figure 25. The stress-strain diagrams for i n i t i a l cycling between load limits. - 51 -increment of total strain. The stress-strain curves were reproducible in shape and position when cycled in excess of ten times. The stress-strain behaviour during i n i t i a l cycling reflects the following changes in the structure of the sample. After the sample has been strained beyond the true elastic region and unloaded, some martensite may be retained or some plastic deformation may have occurred with the result that some localized stress (either tensile or compresile) may be retained. Hence, subsequent loading of the sample may not follow the path ascribed by i n i t i a l loading, i.e., that path characterized by the three stages a, b, c. The presence of any retained tensile load in the unloaded state encourages a localized deformation response (stress-induced martensite, plastic deformation) to occur at a lower applied stress on reloading. During i n i t i a l cycling the g.s./t value had l i t t l e or no effect on the number of cycles required to obtain a relatively stable shape for the stress-strain curve. However, a very small stress hysteresis was evident after the 1st cycle for specimens having a small g.s./t ratio and thus hysteresis changes on cycling were more d i f f i c u l t to assess in these samples. ( i i ) The Effect of Extended Cycling The stress-strain curves obtained after i n i t i a l cycling appeared to become relatively reproducible in shape and position. However extended cycling did result in some additional modification in the stress-strain behaviour. Figure 26 shows the stress-strain response obtained by cycling between 3 a lower stress limit (1.7 x 10 psi) and an upper strain limit of - 52 -0 25 .5 .75 I 1.25 strain (%) Figure 26. The development of the stress-strain curve on extended cycling between a lower load limit and an upper strain limit. - 53 -1%. The results show that although the magnitude of the non-reversible stress-strain i s small after two cycles, some does exist, and this progressively shifts the curve to the right after an extended number of cycles (N^ to N^). The hysteresis between loading and unloading also decreases with increasing number of cycles. Tests using this particular type of cycling were not continued beyond 350 cycles as the cycling was done manually on the Instron and took a excessive length of time. Cycling the specimens between two load limits produced the stress-strain curves shown in Figures 27a,b. Cycling resulted in the development of a substantial amount of non-reverisble strain (0.8 and 0.65%). The strain increase associated with cycling to the upper load limit (N.. = 1 to N = 1 o 3 7260 at 20 x 10. psi) was only 50% of the increased non-recoverable 3 strain (N^ = 1 to Nfi = 7260 at 2.5 x 10 psi) experienced at the lower limit for both g.s./t ratios examined. The hysteresis evident during the i n i t i a l cycles decreased in magnitude on increased cycling. Although Figures 27 a and b were obtained from specimens with different 3 g.s./t ratios, the same number of cycles = 10 produced approximately the same irreversible strain. The transformational ela s t i c i t y obtained 3 at approximately 10 occurred with very l i t t l e hysteresis. The development of the surface shape distortion during cycling between load limits is demonstrated in Figures 29 a,b,c,d. Extended cycling results i n an increasing amount of non-reversible martensitic product. The abraded, polished and etched surface area after cycling is shown in Figure 30. A number of martensite plate variants are visible. This suggests that a mutual interaction of the martensite plates may have occurred and produced a stable condition thereby contributing to the non-reversible strain. Figure 27a. The development of the stress s t r a i n curve on extended c y c l i n g between load l i m i t s f o r specimens with a g.s./t r a t i o equal to 2.5. Figure 27b. The development of the stress s t r a i n curve on extended c y c l i n g between load l i m i t s specimens with a g.s./t r a t i o equal to 0.8. - 56 -I I I I 11111 | | | i |||[ 1 1 I I i i m l I I I I I I . I I I I i i i i 111 10 10* I0 J 10 number of c y c l e s Figure 28. The effect of extended cycling on the magnitude of the reversible strain. - 57 -a ( i i ) F i g u r e 29. T h e d e v e l o p m e n t o f t h e s u r f a c e s h a p e d i s t o r t i o n ~ o n e x t e n d e d c y c l i n g b e t w e e n l o a d l i m i t s - 2.5 x 10 p s i a n d s t r e s s c o r r e s p o n d i n g t o 1.25% o f i n i t i a l l y a p p l i e d s t r a i n a f t e r 1 0 ( a ) , 85 ( b ) , 425 ( c ) , 2870(d) c y c l e s ; ( i ) u n l o a d e d , ( i i ) l o a d e d ; g . s . / t \ 2.5 (35X). - 58 -b (ii) c ( i i ) - 60 -d ( i i ) - 61 -Figure 30. The abraded, p o l i s h e d and etched surface of sample a f t e r 3150 c y c l e s showing r e t a i n e d martensite product (180X). - 62 -3.2 The Effect of g.s./t on Martensite Transformation Temperature The transformation temperatures of polycrystalline specimens were found to be dependent on the g.s./t ratio for constant cooling rates of approximately l°C/min as shown in. Figure 31. The coarse grained specimens having a g.s../t ratio ^ 5 exhibited higher Mg temperature than specimens with a small g.s./t ratio. On cooling below the Mg temperature a large amount of thermoelastic martensite formed before the development of burst martensite. Burst martensite appeared at approximately 40°C below Mg and nucleated primarily at the sample edges although some surface nucleation was observed remote from the edges. The fine-grained specimens (g.s./t ^ 0.5-1) exhibited l i t t l e or no thermoelastic martensite plates before the i n i t i a t i o n of burst martensite. The burst martensite nucleated at the edges of the specimen and slowly progressed inward until the whole surface was transformed. This transformation extended over a much larger temperature interval than that observed for the coarse grained specimens. The M^  temperatures varied from specimen to specimen and were apparently affected by properties other than the g.s./t ratio. No attempt was made to investigate this observation. The published observations on the c r i t i c a l martensite temperatures (1,31-33,21) are shown in Table I. Pops (1), using an el e c t r i c a l r e s i s t i v i t y technique, found that the martensite transformation was generally complete on cooling and heating over a temperature range of 10°C. However, the electrical r e s i s t i v i t y results corresponded to the formation of the burst martensite for the polycrystalline, 1-5 mm grain size 10 -1.0 - 2 0 -30 - 4 0 -50 A i A A A A • " • -• --• A -O O • Ms -O M B -— O -O Figure 31. t. The effect of g.s./t ratio on c r i t i c a l martensite transformation temperatures. - 64 -MB-Mf M -Mr s f Present 0-40 1 2^ Pops-Massalski ' 16 10 26 33 Titchener-Bauer 50 Eisenwasser ! 1 t 7-13 ! i TAB I. Temperature i n t e r v a l s between the c r i t i c a l martensite temperatures. examined. Pops and Massalski (32) o p t i c a l l y determined the(M -M ) s ij temperature i n t e r v a l to be 16°C f o r p o l y c r y s t a l l i n e 5 mm diameter were of grain s i z e 1-2 mm i n a 61.45 Cu-38.55 Zn a l l o y . Titchener a n d Bauer (33) reported an(M -M_)temperature i n t e r v a l of ^ 50°C using e l e c t r i c a l r e s i s t i v i t y measurements on a 61.46 Cu-38.54 Zn a l l o y . Eisenwasser (21) o p t i c a l l y determined the^M -M f/temperature i n t e r v a l to be ,v7-130C for p o l y c r y s t a l l i n e specimens of 33.41 Zn-3.34 Sn-Cu having a grain s i z e of 0.05-0.1 inch; only selected regions of the specimen were examined. H u l l (31) reported a spontaneous martensitic transformation i n t h i n Cu-Zn 3-phase f o i l s w e l l above the Mg temperature of the bulk specimen. No cooling rates were reported. The present r e s u l t s show that thermoelastic martensite does not form i n a fine-grained material (g.s./t < 0.5). This can be interpreted i n terms of the shape changes associated with the martensite transforma-t i o n . The formation of the non-self accommodating thermoelastic, needle-like martensite i s accompanied by shape changes at the grain boundary. Such shape changes are r e s t r i c t e d by the grain boundary enclosure encountered by i n d i v i d u a l grains i n samples having a g.s./t r a t i o l e s s than 0.5. In such specimens only self-accommodating burst martensite can form. The observed increase i n the temperature with decreasing g.s./t r a t i o can be understood i n terms of the i n t e r n a l stress r e s u l t i n g from the grain boundary r e s t r i c t i o n s . The r e v e r s a l to the parent phase i s r e s t r i c t e d to those martensite plates which are favourably oriented and a complete transformation i s more d i f f i c u l t . The a p p l i c a t i o n of external stress has been found to r a i s e the Af temperature (35). - 66 -3.3 Phase Analysis X-Ray i n v e s t i g a t i o n (34) showed that the thermal martensite product had an orthorhombic structure while deformation martensite was reported to have a face centered tetragonal structure (24). A more recent transmission e l e c t r o n microscopy study (20) reported the structure of thermal martensite for Cu-Zn-Si as being a lamellar mixture of two close packed structures with a high density of stacking f a u l t s . The d i f f r a c t i o n l i n e s associated with the orthorhombic, the face centered tetragonal and the as-quenched bcc structure have been used to i d e n t i f y the transformation products that develop i n the samples tested i n the present study. 3.3.1 The E f f e c t of S t r a i n Magnitude X-Ray d i f f r a c t i o n r e s u l t s obtained from specimens strained to 0.8% and 2.5% s t r a i n are shown i n Table I I . St r a i n gives r i s e to broadening of the peaks corresponding to the bcc structure and some ad d i t i o n a l peaks appear. A comparison with the orthorhombic and the face centered tetragonal structure indicates that the product phase produced a f t e r 0.8% s t r a i n more cl o s e l y resembles the orthorhombic structure. However, the peaks apparent a f t e r 2.5% s t r a i n are consistent with the presence of both the orthorhombic and the f c t structures. The d i f f r a c t i o n r e s u l t s f or 0.8% and 2.5% s t r a i n are also compared with the r e s u l t s obtained from heavy deformed f i l i n g s i n Table I I I . Fewer peaks are v i s i b l e a f t e r heavy deformation. Those peaks agree well with the interplanar spacings reported f o r the f c t structure (35). - 67 -Lines corresponding to e = g.s. • 0. It .8% = 2 e = 2.5% g.s./t = 0. 7 beet orthorhombic f c t hkl dA h k l dA hk l dA dA I r dA Ir 200 2.135 111 2.136 2.13 w 2.14 u . 110 2.08 2.09-2. 02 vs 2.09-2.02 vs 120 1.997 1.96 w 1.96 u 200 1.887 1.87 u 111 1.7 1.69 vw 1.7 vw 121 1.589 1.6 vw 1.59 vw 200 1.97 1.49-1. 47 m 1.49-1.46 m 200 1.335 1.34 vw 210 1.31 1.32 211 1.2 1.21 m 1.21 u/m bec, a = 2.94 A (34) orthorhombic, a = 2.67 A, b = 9.27 A, c = 4.46 A (34) f c t , a = 3.775 A, c/a = 0.943 A (24) vs = very strong, m = medium, wm = weak medium, vw = very weak, Ir = r e l a t i v e v i s u a l i n t e n s i t i e s , tbec - calculated for a = 2.94. TAB. I I . X-ray d i f f r a c t i o n peaks of strained specimens. - 68 -Lines corres- e = 0.8% e = 2. 5% fi l i n g s ponding to fct g.s./t = 2 g.s./t = 0.7 hkl dA dA Ir dA Ir dA Ir 111 2.136 2.13 w 2.14 w 2.14 vw 2. 09-2.02 vs 2 .09-2.02 vs 1.96 vw 1.96 vw 200 1.887 1.87 w 1.87 m 1.69 vw 1.7 vw 1.6 vw 1.59 vw 1. 49-1.47 in 1 .49-1.46 m 220 1.335 1.39 vw 1.34 wm 1.32 vw 202 1.295 1.304 w 1.21 m 1.21 wm fct, a = 3.775 A, c/a = 0.943 A (24) vs = very strong, m = medium, wm = weak medium, vw = very weak, Ir = relative visual intensities. TAB. H i ; Comparison of X-ray diffraction peaks of strained specimens with the diffraction traces from f i l i n g s . - 69 -* f i l i n g s cycled e = 0.8% e = 2. 5% bcc^ N - 3x103 cycles g.s. It = 2 g.s./t = 0.7 h k l dA dA Ir o dA Ir dA Ir dA Ir 2.135 vs 2.13 w 2.19 w 2.14 w 110 2.08 2.09-2. 02 vs 2. 09-2.02 vs 2.09 vw 1.98 m 1.96 vw 1.96 vw 1.87 w 1.87 w 1.87 m 111 1.7 1.7 vw 1.69 vw 1.7 vw 1.6 vw 1.59 vw 200 1.47 1.49-1. 47 m 1. 49-1.46 m 1.34 vw 1.34 wm 1.32 vw 210 1.31 1.3 m 1.304 vw 211 1.2 1.2 vw 1.21 m 1.21 vw specimen with g.s./t = 2 cycled between low load limit corresponding 3 to 5 x 10 psi and upper limit set by load corresponding to 1% of i n i t i a l strain. vs = very strong, m = medium, wm = weak medium, w = weak, vw = very weak. IR = relative visual intensities, t bcc - calculated for a = 2.94. TAB. IV. X-ray diffraction peaks associated with cycled product. - 70 -3.3.2 The Effect of Cycling The X-ray diffraction peaks associated with a product cycled 3000 times are shown in Table IV; comparison data from Tables II and III is also included. Cycling reduces the intensity of the bcc peaks and gives rise to peaks comparable to those observed after 2.5% strain and heavy deformation ( f i l i n g s ) . 3.3.3 Summary It is observed that the interplanar spacings and the relative intensities agree, f a i r l y well, with the experimental results reported by (24,34). This suggests that thermal martensite and stress-induced martensite may have the same crystal structures. The .diffraction lines associated with large strains and extended cycling are comparable and suggest that both effects give rise to the development of the fct structure. However, as the specimen grain size was quite large, not a l l of the X-ray diffraction peaks were visible making a more quantitative treatment impossible. 3.4 Determination of Habit Plane of the Martensite Plate Angular measurements associated with the thermoelastic martensite traces were made at approximately 20°C below the Mg temperature. The traces on two perpendicular surfaces were matched and the habit plane was determined by two surface analysis. The back reflection Laue procedure was used to orient each of the coarse grains examined. The resulting poles of the thermoelastic martensite are shown in Figure 32 and are clustered close to the (2 11 12) plane of the bcc structure. Figure 33. Habit planes for stress-induced martensite plates. - 72 -present A - thermoelastic martensite (OOI) Figure 34. Habit planes for thermoelastic martensite and stress-induced martensite in Cu-Zn-Sn alloys. The latice parameters used in the calculation were a = 2.678 A, b = 4.283 A, c = 4.474 A for the orthorhombic martensite. The Bain relationship [100]gll[010] and [010]gll[110] o was employed with a microscopic sfiear (110)[110] (22). Figure 35. Habit planes for thermoelastic martensite and stress-induced martensite in Ag-Cd alloys (13). - 73 -The habit planes for the stress-induced martensite plates was determined for several grains using a strained,coarse grained specimen. The results obtained are shown in Figure 33. A l l habit planes are located close to the (110) plane of the bcc structure. Although there is some scatter in the results, which could be accounted for by experimental errors, there is an indication that the habit plane of the stress-induced martensite plate is different from that of the thermoelastic martensite plate as shown in Figure 34. The present results are similar to observations reported by Krishnan (13,26) for Ag-Cd alloy, where habit planes for thermoelastic martensite and stress-induced martensite were found clustered close to (331) and (110) respectively (Figure 35). - 74 -4. CONCLUSIONS (1) The metastable g-phase of a Cu-33.6 wt.% Zn-4 wt. % Sn alloy does not exhibit transformation e l a s t i c i t y throughout the poly-crystalline material when subjected to tensile deformation. The anisotropy of the g-phase, the presence of the preferentially distributed martensite phase and the mechanical properties of the material undergoing the martensitic transformation lead to the activation of other non-reversible deformation modes along or in the v i c i n i t y of the grain boundaries. (2) A relationship between the sample dimensions and the size of the g-grains effects the fraction of the reversible strain associated with the transformation ela s t i c i t y and the accompanying non-reversible strain. (3) Reversible strains of ^ 2.5% can be obtained from polycrystalline specimens with the g-grains extending through the sample thickness (g.s./t > 2). (4) Limited transformation e l a s t i c i t y i s exhibited by specimens with a g.s./t ratio < 0.5. Less than 1% of reversible strain is obtained following 2.5% of prestrain. - 75 -(5) I n i t i a l cycling either between two load limits or between a lower limit set by load and an upper limit set by strain produces a relatively stable stress-strain curve after 2 and 10 cycles respectively. 3 (6) Extended cycling (up to 1-7 x 10 cycles) reduces the hysteresis of the stress-strain curve, decreases the magnitude of the reversible strain, produces some additional plastic deformation and increases the amount of the retained non-reversible martensitic product. (7) C r i t i c a l martensitic temperatures on cooling are influenced by the g.s./t ratio. Thermoelastic martensite is not observed on the specimen when the g.s./t ratio is less than 0.5. Only self-accommodating "burst" martensite forms in these specimens. The temperature is lowered by increasing the g.s./t ratio. (8) X-ray diffraction experiments indicate the stress-induced martensite to have an orthorhombic structure the same as thermal martensite. (9) X*-Ray diffraction analysis showed that large strains and extended cycling produce fct3deformation martensite. (10) The habit planecfa thermoelastic plate was experimentally determined as (2 11 12) while the habit plane of the stress-induced martensite plate was determined to be (110). - 76 -REFERENCES 1. H. Pops, Trans. AIME, 236 (1966) 1532. 2. Hume Rothery, Elements of Structure Metallurgy, London 1961, 151. 3. A.B. Greninger, V.G. Mooradian, Trans. AIME, 128 (1938) 337. 4. L. Delaey, A.J. Parkins, T.B. Massalski, J. Mat. S c i . , 7 (1972) 1197. 5. D.S. Lieberman, Phase Transformation, A.S.M. Seminar (1970) 1-58. 6. M.S. Wachsler, D.S. Lieberman, T.A. Read, J. of Metals (1953) 1503. 7. C h r i s t i a n , Basic crystallography and k i n e t i c s of martensite, edited by E.R. Petty, Longman, 1970. 8. R.H. Richnan, G.F. B o i l i n g , Metal. Trans., 2 (1971) 2451. 9. H. Tas, L. Delaey, A. Deruyttere, J. Less-Common Metals, 28 (1972) 141. 10. H. Pops, Met. Trans., 1 (1970) 251. 11. H. Tas. L. Delaey, A. Deruyttere, Scr i p t a Met., 51 (1971) 1117. 12. W.A. Rachinger, J. Aus. Inst. Metals, 51 (I960) 118. 13. R.V. Krishnan, Ph.D. Thesis, U.B.C. (1971). 14. J. Intraker, L.C. Chang, P.A. Read, Phys. Rev., 86 (1952) 598. 15. E. Hornbogen, G. Wassermann, Z.' Ket a l l k . , 47 (1956) 427. 16. H. Pops, Trans. AIME, 239 (1967) 756. 17. L. Delaey, M. Warlimont, Z. Metallk., 56 (1965) 437. 18. L. Delaey, H. Warlimont, Z. Metallk., 57 (1966) 793. 19. L. Delaey, Z. Metallk., 58 (1967) 388. 20. L. Delaey, M. Pops, Trans. AIME, 242 (1968) 1849. 21. J.D. Eisenwasser, M.A.Sc. Thesis, U.B.C. (1971). 22. J.D. Eisenwasser, L.C. Brown, Metal. Trans., 3 (1972) 1359. 23. M. Ahlers, H. Pops, Trans. AIME, 242 (1968) 1267. 24. E. Hornbogen, A. Segmuller, G. Wassermann, Z. Metallk. 48 (1957) 379. -Il-ls. C. Zener, Phys. Rev., 71 (1947) 846. 26. L.C. Brown, S u p e r e l a s t i c i t y and the s t r a i n memory e f f e c t . Report on DRB Grant, UBC, 1972. 27. Z. Hashin, Ap. Mech. Rev., 17 (1964) 1. 28. T. Abe, B u l l . JSME, 14 (1971) 1263. 29. T. Abe, B u l l . JSME, 12 (1969) 165. 30. B.D. C u l l i t y , Elements of X-ray D i f f r a c t i o n , Addison Wesley Co., (1967) 25. 31. D. H u l l , P h i l . Mag., 7 (1962) 537. 32. M. Pops, T.B. Massalski, Trans. AIME, 230 (1964) 1662. 33. A.L. Titchener, M.B. Dever, Trans. AIME, 200 (1954) 303. 34. W. J o l l e y , D. H u l l , J. Inst. Metals, 92 (1963) 129. 35. L.C. Chang, T.A. Read, Trans. AIME, 191 (1951) 47. 36. R.V. Krishnan, L.C. Brown, Met. Trans., 4 (1973) 423. 

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