Wm!“ M This is to certify that the thesis entitled ROLE OF PHASE BOUNDARY 0N DEFORMATION 0F POLYCRYSTALLINE ALPHA—BETA BRASS presented by Sagar Prabhakar Naik has been accepted towards fulfillment of the requirements for M.S. degree in Material Science “SQ-[‘1' MCWWCM’ Major professor - ATV __ /‘<~4 MSU LIBRARIES RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES will be charged if book Is returned after the date stamped below. c.- o.-. . ROLE OF PHASE BOUNDARY ON DEFORMATION OF POLYCRYSTALLINE ALPHA-BETA BRASS By Sagar Prabhakar Naik A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Metallurgy. Mechanics and Material Science 1985 ABSTRACT ROLE OF PHASE BOUNDARY ON DEFORMATION OF POLYCRYSTALLINE ALPHA-BETA BRASS By Sagar Prabhakar Naik The deformation structure near equiaxed phase boundary in polycrystalline specimens of two-phase alpha-beta brass was studied by Transmission Electron Microsc0py after deforming the specimens up to a 27 percent strain level. Although dislocation pile-ups in alpha region were observed, no evidence of dislocation activity occurred as a result of this pile-up in beta phase near alpha-beta phase boundary. Dislocations observed in beta phase tended to be screw in character. The Finite Element Method was used to study stress- strain relationship and stress-strain distribution in the region near the alpha-beta phase boundary. Increasing the number of elements incorporated in the chosen mesh increased the accuracy of the results obtained. ACKNOWLEDGMENTS I would like to take this opportunity to sincerely thank my advisor, Dr. K. N. Subramanian, but for whose guidance and encouragement this endeavor would not have ended successfully. A special thanks to my colleagues, Tong C. Lee, Narendra Dahotre, N. Krishnan, S. Sircar, S. Shekhar and Sanjeev Deshpande, for having helped me during this work. This work could not have been completed without the help of all the aforementioned. TABLE OF CONTENTS List of Figures . . . . . . . . . . . . . List of Tables . . . . . . . . . . . . . . . . H 0 INTRODUCTION . . . . . . . . . . II HISTORICAL BACKGROUND . . . II-A. Copper-Zinc System . . . . . . . . II-B. Deformation Behavior of Single Crystals ,of Alpha and Beta Brasses . . . . . . . II-C. Deformation of Bicrystals of Alpha and Beta Brasses . . . . . . . . . . . . . II-D. Deformation Behavior of Polycrystals of Alpha and Beta Brasses . . . . . . . . II-E. Deformation of Two-Phase Materials . . a) Deformation of Bicrystals of Two- Phase Materials b) Deformation of Polycrystals of Alpha-Beta Brass II-F. Theoretical Models for Interaction of Slip with Boundaries . . . . . . . . . II-G. Finite Element Method . . . . . . . . . III. EXPERIMENTAL PROCEDURE . . . . . . . . . . III-A. Procedures Used for Transmission Electron Microsc0pic Study of the Deformation Structure in the Phase Boundary Region . . . . . . . . . III-B. Finite Element Analysis . . . . . . . . IV. RESULTS AND DISCUSSION . . . . . . . . . . IV-A. Transmission Electron Microscopic Analysis of the Deformation Structure in Alpha-Beta Brass . . . . . . . . iii VI. a) Analysis of Dislocations Present Near Phase Boundary b) Interaction of Dislocations with Equiaxed Phase Boundary IV-B. FEM Analysis of Stress-Strain Behavior of Alpha- Beta Brass . . . . 73 a) Stress- Strain Relationship for Alpha- Beta Brass Containing 25. 50, and 75 Volume Percent of Beta Phase b) Stress-Strain Relationship for Small, Medium, and Coarse Grain Sizes of Alpha and Beta Phases c) Stress-Strain Distribution Across Alpha-Beta Interface d) Stress-Strain Curve for Two-Phase Region e) Comparison of Experimental Stress- Strain Curve with the FEM-Calculated Curves (Two Different Meshes) CONCLUSIONS . . . . . . . . . . . . . . . . . . 94 V-A. Transmission Electron Microsc0pic Studies . . . . . . . . . . . . . . . . . 94 V-B. FEM Analysis . . . . . . . . . . . . . . 94 REFERENCES . . . . . . . 95 iv Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure N o b (A o 0 LIST OF FIGURES The copper-zinc phase diagram (Ref: 16) . . . . . . . . . . . . . . . Unit cell of ordered beta brass (A-Cu, B-ZHIIREf: 19) o o o o o o o o o o 0 Schematic of “jet-polishing" unit Schematic of the final electropolishing unit . . . . . . . . . . . . . . . . . . FEM mesh for alpha-beta brass containing 25 volume percent beta phase (beta phase is shaded dark): . . . . . . . . . . . A) Fine grain distribution B) Medium grain distribution C) Coarse grain distribution FEM mesh for alpha-beta brass containing 50 volume percent beta phase (beta phase is shaded dark): . . . . . . . . . . . . . A) Fine grain distribution B) Medium grain distribution C) Coarse grain distribution FEM mesh for alpha-beta brass containing 75 volume percent beta phase (beta phase is shaded dark): . . . . . . . . A) Fine grain distribution B) Medium grain distribution C) Coarse grain distribution FEM input stress-strain curve of "Alpha" and "Beta" brasses (Ref: 48) . . . . . . FEM mesh, for alpha-beta brass containing 25 volume percent beta phase (shaded dark), used for calculation of the stress- strain distributions, across the alpha- beta interface . . . . . . . . . . . . . . FEM mesh for alpha-beta brass containing 50 volume percent beta and 50 volume percent alpha . . . . . . . . . . . . . A) Phase boundary parallel to tensile axis B) Phase boundary perpendicular to tensile axis 24 25 27 29 31 33 35 36 Figure Figure Figure Figure Figure Figure ll. 12. 13. 14. 15. 16. Dislocations near grain boundary in alpha phase of alpha-beta brass specimen deformed to 12 percent strain evel . A) t = [200] B) = [290] c) = [220] D) = [220] E) = [020] Dislocations near grain boundary in alpha phase of alpha-beta brass. Location of grain boundary: upper right corner 60° to X-aXIS '0 o o o o o o o o o o o o A) g = [1T1] B) = EIZ1] c) = 220] D) = [042] Specimen deformed to l2 percent strain level Dislocations near grain boundary in alpha phase of alpha-beta brass. Specimen deformed to 12 percent strain level . . A) * = [TiT] B) g = [002] C) = [T11] Dislocations in alpha region near alpha- beta phase boundary. Specimen deformed to l2 percent strain level. Location of phase boundary: lower left corner 50° to X-axis . . . . . . . . . . . . . . A) g = [002] B) = [T11] c) b = [1T1] Dislocations in alpha region near alpha- beta phase boundary. Specimen deformed to 15 percent strain level . A) = [1T1] B) = [T11] C) = [002] Dislocations in alpha region near alpha- beta phase boundary. Specimen deformed to l5 percent strain level. Location of phase boundary: vertical, left . . . A) = [T11] B) = [002] c) g = [1T1] vi 39 45 47 49 53 57 Figure 11. Figure Figure Figure Figure Figure 12. 13. 14. 15. 16. Dislocations near grain boundary in alpha phase of alpha-beta brass spec1men deformed to 12 percent strain evel . A) 15 = [200] B) l] = [290] C) = [220] 0) = [2’20] E) = [020] Dislocations near grain boundary in alpha phase of alpha-beta brass. Location of grain boundary: upper right corner 60° to X-axis a. . . . . . . . . . . . . a; 1": [1:1] C) 3 ; E2201 D) = [042] Specimen deformed to 12 percent strain level Dislocations near grain boundary in alpha phase of alpha-beta brass. Specimen deformed to 12 percent strain level A) " = [T1T] B) é = [002'] C) = [T11] Dislocations in alpha region near alpha- beta phase boundary. Specimen deformed to 12 percent strain level. Location of phase boundary: lower left corner 50° to X-axis . . . . . . . . . . . . . A) g = [007] B) = [T11] C) a = [1T1] Dislocations in alpha region near alpha- beta phase boundary. Specimen deformed to 15 percent strain level . . . A) g [1T1] B) c) [Tll] [002'] Dislocations in alpha region near alpha— beta phase boundary. Specimen deformed to 15 percent strain level. Location of phase boundary: vertical, left . . . A) = [T11] B) = [002] c) g= [1T1] vi 39 45 47 49 53 57 Figure 17. Dislocations in alpha region near alpha- beta phase boundary. Specimen deformed to 18 percent strain level. Location of phase boundary: vertical, left . . . . 60 A) = [1T1] B) = [002] C) = [T11] Figure 18. Dislocations in beta region near alpha- beta phase boundary. Specimen strained to 18 percent strain level. Location of phase boundary: lower left corner 65° to X-axis . . . . . . . . . . . . . . 64 A) g = [200] B) 3 = [110] C) 9 = [Tle D) 9 = [T10] Figure 19. Deformation structure near phase boundary of alpha-beta brass . . . . . . . . . 67 A and B: Specimen deformed to 12 percen strain level C and D: Specimen deformed to 15 percent strain level E) Specimen deformed to 18 percent strain level F) Specimen deformed to 20 percent strain level G) Specimen deformed to 27 percent strain level Figure 20. Antiphase boundaries in beta region of alpha-beta brass . . . . . . . . . . . . . 71 Figure 21. FEM-calculated stress-strain curves for alpha-beta brass containing 25, 50, and 75 volume percents of beta phase. Grain size: small . . . . . . . . . . . . . . . 75 I. % VB - 25% II. % VB - 50% III. % VB - 75% Figure 22. FEM-calculated stress-strain curves of alpha-beta brass containing 25 volume percent beta phase for fine (I) and coarse (II) grain size distribution . . . 77 Figure 23. FEM-calculated stress-strain curves of alpha-beta brass containing 50 volume percent beta phase for fine (I) and coarse (II) grain size distribution . . . 78 vii Figure 17. Dislocations in alpha region near alpha- beta phase boundary. Specimen deformed to 18 percent strain level. Location of phase boundary: vertical, left . . . . 60 A) = [1T1] B) = [002] C) = [T11] Figure 18. Dislocations in beta region near alpha- beta phase boundary. Specimen strained to 18 percent strain level. Location of phase boundary: lower left corner 65° to x-axis . . . . . . . . . . . . . . 64 A) g = [200] B) 9 = [110] C) 9 = [TET] D) 9 = [T10] Figure 19. Deformation structure near phase boundary of alpha-beta brass . . . . . . . . . . . 67 A and B: Specimen deformed to 12 percent strain level C and D: Specimen deformed to 15 percent strain level E) Specimen deformed to 18 percent strain level F) Specimen deformed to 20 percent strain level G) Specimen deformed to 27 percent strain level Figure 20. Antiphase boundaries in beta region of aIPha-beta brass o o o o o o o o o o o o o 71 Figure 21. FEM-calculated stress-strain curves for alpha-beta brass containing 25, 50, and 75 volume percents of beta phase. Grain size: small . . . . . . . . . . . . . . . 75 I. % VB - 25% II. % VB - 50% III. % vB - 75% Figure 22. FEM-calculated stress-strain curves of alpha-beta brass containing 25 volume percent beta phase for fine (I) and coarse (II) grain size distribution . . . 77 Figure 23. FEM-calculated stress-strain curves of alpha-beta brass containing 50 volume percent beta phase for fine (I) and coarse (II) grain size distribution . . . 78 vii Figure Figure Figure Figure Figure Figure Figure Figure 24. 25. 26. 27. 28. 29. 30. 31. FEM-calculated stress-strain curves of alpha-beta brass containing 75 volume percent beta phase for fine (I) and coarse (II) grain size distribution . . FEM-calculated stress distribution plot in alpha and beta region of alpha-beta brass containing 25 volume percent beta phase in the Y-direction (gyy) . . . . . FEM-calculated stress distribution plot in alpha and beta region of alpha-beta brass containing 25 volume percent beta phase, in the X-direction (oxx) . . . . FEM-calculated strain distribution plot in alpha and beta region of alpha-beta brass containing 25 volume percent beta phase . . . . . . . . . . . . . . . . . 'FEM-calculated stress distribution plot in alpha-beta region of alpha-beta brass containing 20 volume percent beta phase, in Y-direction (0 ) . . . . . . . . A) Stress distribdtion with 60-element mesh (Ref: 47) 8) Stress distribution with 128-element mesh FEM-calculated stress distribution plot in alpha and beta region of alpha-beta brass containing 20 volume percent beta phase, in X-direction (OXX) . . . . . A) Stress distribution with 60-element mesh (Ref: 47) 8) Stress distribution with lZB-element mesh FEM-calculated strain distribution plot in alpha and beta region of alpha-beta brass containing 20 volume percent beta phase . . . . . . . . . . . . . . . . . A) Strain distribution with 60-element mesh (Ref: 47) B) Strain distribution with 128-element mesh FEM-generated stress contour distribution plot in the 128-element mesh for alpha- beta brass containing 25 volume percent beta phase in the loading Y-direction (ow) viii 79 81 82 84 85 86 87 88 Figure Figure Figure Figure 32. 33. 34. 35. FEM-generated stress contour distribution plot in the lZB-element mesh for alpha- beta brass containing 25 volume percent beta phase, in the x-direction (oxx) . . . 89 FEM-calculated stress-strain curves of alpha-beta brass containing 50 volume percent of alpha and 50 volume percent beta 0 O O O O O O O O O O O O 0 I O O 0 O 90 I. .Phase boundary parallel to tensile axis II. Phase boundary perpendicular to tensile axis FEM-calculated stress-strain curve of alpha-beta brass containing 80 volume percent of alpha and 20 volume percent beta . . . . . . . . . . . . . . . . ... 91 1. Phase boundary parallel to tensile axis 11. Experimental III. Phase boundary perpendicular to the tensile axis Comparison between the eXperimentally determined stress-strain curve of 60 Cu- 40 Zn brass and the FEM-calculated curves of alpha-beta brass containing 20 volume percent beta phase . . . . . . . . . . . . 93 I. FEM curve with 60-element mesh (Ref: 47) II. FEM curve with 128-element mesh III. Experimental ix Table 1. LIST OF TABLES Yield Stress Values Obtained by Using 0.2% Offset Method . . . . . . . . . . . . . 76 I. INTRODUCTION Many of the engineering materials used in practical applications are two-phase alloys. Alpha-beta brass, alpha- beta titanium, micro-duplex stainless steels, and copper-tin alloys are typical examples of such alloys that are of commercial and engineering importance. The mechanical pr0perties of these materials are dependent on the characteristics of individual phases, the distribution and volume fraction of each phase, phase boundaries, and on grain boundaries. Mechanical properties are also affected by crystallography, strain-hardening, dislocation behavior, and slip systems in each of the phases. Single-phase polycrystalline materials consist of individual grains that possess the same crystal structure and composition. In such single-phase materials, different regions with different crystallographic orientations are separated by grain boundaries. 0n the other hand, each phase in a two-phase material will possess different crystal structures and different Chemical compositions. Because of their different compositions and crystal structures, the mechanical properties of the various phases will be different. Such two-phase materials will possess inter- phase boundaries in addition to grain boundaries. To study the mechanical behavior of two-phase material, several models can be simulated. One of the models incorporates a phase boundary separating two single crystals 1 2 of individual phases formed by diffusion bonding (1). In another approach, a single crystal is joined to several large grains of another phase, so that there exists only one grain of this phase at the phase boundary in contact with the single crystal of the other phase (2). This model system is produced by melting the interface region, and is considered to produce a phase boundary that might correSpond closer to those present in actual two-phase materials. A third model would comprise of duplex crystal (Nidmanstatten platelets) with definite crystallographic orientation relationships between the two phases. Studies on the mechanical pr0perties of two-phase model systems have been conducted, in the past, by Hingwe 35 31. (2,3,4) and Nilsen gt El: (5,6,7). They studied the room temperature mechanical pr0perties of bicrystals of alpha- beta brass under uniaxial tension at various strain rates. Khezri-Yazdan £3 31, (8) conducted similar investigations at higher temperatures. Izumi St 21‘ (9-15) have also studied mechanical pr0perties of alpha-beta brass bicrystals produced by the diffusion bonding method. These studies on bicrystals of alpha-beta brasses have been aimed at understanding the basic deformation mechanisms of two-phase materials. The engineering materials in use are polycrystalline, and to understand their mechanical behavior one needs to study the deformation behavior of polycrystalline two-phase materials. None of the above studies has dealt with the direct observations of detailed dislocation behavior in the phase boundary region. In the present investigation, the dislocation behavior in the phase boundary region of polycrystalline two-phase alpha-beta brass was studied by transmission electron microscopy. In addition, a finite element method (FEM) was used to study stress-strain behavior of alpha-beta brass. study the deformation behavior of polycrystalline two-phase materials. None of the above studies has dealt with the direct observations of detailed dislocation behavior in the phase boundary region. In the present investigation, the dislocation behavior in the phase boundary region of polycrystalline two-phase alpha-beta brass was studied by transmission electron microscopy. In addition, a finite element method (FEM) was used to study stress-strain behavior of alpha-beta brass. II. HISTORICAL BACKGROUND II—A. Copper-Zinc System Brass is a class of commercial alloys which is comprised of copper and zinc with useful mechanical pr0perties and corrosion resistance. A phase diagram of this system is presented in Figure 1. The alpha phase has a face-centered cubic (FCC) structure. This phase has a maximum solubility of about 38 weight percent zinc, as shown in this diagram. The alpha phase is fairly strong and possesses excellent ductility and formability. A secondary phase termed the beta phase forms above 38 weight percent zinc concentration. The beta phase has quite different pr0perties as compared to the alpha phase. It has a cesium- chloride structure and is harder and stronger, but much less ductile than the alpha phase. Above approximately 454°C to 468°C (depending on composition). the beta phase has a disordered, body-centered cubic structure. In brasses with zinc composition of 38 to 46 weight percent, both alpha and beta phases are present. These brasses are known as alpha- beta brasses. Brass containing 40 weight percent of zinc and 60 weight percent of copper is representative of this class, and is known as "MUNTZ METAL." Muntz metal is used for the present investigation, so as to understand the role of an inter-phase boundary on the deformation behavior. 3'- u—c-m Figure l. The c0pper-zinc phase diagram (Ref. 16). IEIGNT PEI CEIT ZINC 10 20 no so so to so so 1100 y ‘ I 1’ I l I \ 1 1000 I ' 900 c" 1 I 31.9 03“ 132.31 M a 000 \ / [ 9 70° N L I 70? I ‘5 B l g an (5;) 1 2600 Y 3 0' ‘ o __._. C ” ‘ ’ A '\ e 550' x I .‘L‘ 500 1 ass- I . . O D 01 :33 «191 u, ‘2‘, 619' ‘°° ‘ 1723 v / V I9 J, q«(101 300 I . 34.0 ‘ ' ' I ’13:.2) , , 1 1 l I 1 1 I 1 1 1' 200 I 1 I 1 " 1 I o I I I I ’ . 1 ' ”.09 100 l l A 1 199.11 0 10 20 30 40 so so 70 no so 100 c- aromc Pu cur mac 2: 6 II-B. Deformation Behavior of Single Crystals of Alpha and Beta Brasses Alpha brass single crystal has an FCC structure with zinc atoms occupying random positions in the copper lattice. Deformation of alpha brass occurs along close- packed {111} planes and along <110> directions. It has been suggested by Heidenreich and Shockley (17) that dislocations in FCC crystals, such as alpha brass, can split into two partial dislocations according to the reaction .3. [110] = g. [211] + 2‘} [12T] , and thereby lower the energy of the system. Alpha brass single crystals undergo three stages of work-hardening during uniaxial tensile deformation. The first stage is characterized by a low work-hardening rate which is influenced by crystal orientation, temperature, and purity. The second stage is characterized by a high work- hardening rate and is independent of crystal orientation and test variables. The third stage of hardening has a decreasing work-hardening rate due to dislocation climb and cross-slip of screw dislocations. Ordered beta brass has cesium chloride (CsCl) structure below the critical temperature (Tc). The CsCl structure is comprised of two interpenetrating simple cubes, one of c0pper atoms and the other of zinc, termed as 8-2 type superlattice. This structure is illustrated in Figure 2. Figure 2. Unit cell of ordered beta brass (A-Cu, B-Zn) (Ref. 19) 8 The slip system in the ordered beta structure is of {110} type. In 8-2 type structures, when a dislocation, whose Burger's vector is a unit lattice vector, moves through an ordered lattice, there is a local rearrangement of atoms leading to the creation of an antiphase boundary. The high energy antiphase boundary can only be dissociated when another single unit dislocation passes through the plane of disorder. This pair of dislocations is termed as superlattice dislocation. Brown (18) has observed that a high stress is required for movement of such dislocations. Disordered beta brass exhibits a decreasing strain-hardening rate over its entire range of deformation. 0r0wan (20) has made observations on the factors influencing the strain-rate sensitivity of materials and has given the formula for strain rate 1;) as, d 3% = g = pbv , where p is dislocation density 5 is strain rate b is Burger's vector of mobile dislocations v is average velocity of dislocations. It was suggested by Johnson and Gilman (21) that the total strain is related to the density of mobile dislocations. It has been observed that the deformation of beta brass is highly strain-rate sensitive. With increasing strain rate, ease of movement of mobile dislocations decreases because of 9 the more frequent dislocation intractions. After the mobile dislocations are tangled, a higher stress is required to activate new dislocation sources. At this stage, rate of deformation corresponds to the rate of dislocation multiplication. Titchener and Ferguson (22) investigated the dynamic compressive behavior of beta single crystals, and have observed upper and lower yield points. The upper and lower yield stresses were found to depend on both strain-rate and temperature. The yield stress increases significantly with increasing strain rate and with decreasing temperature. At strains greater than 4 percent, dynamically deformed material was found to be softer than that deformed statically. The dynamic work-hardening rate was less than the static work-hardening rate. Deformation bands were observed in Titchener and Ferguson's studies, although no twinning or jerky flow was apparent. II-C. Deformation of Bicrystals of Alpha and Beta Brasses Bicrystals of single-phase materials are comprised of two grains of same phase. Grain boundaries are an impediment for the motion of dislocations during plastic deformation of a bicrystal. When bicrystals are deformed, interaction of slip with the boundary occurs and sometimes slip propagates from one grain to another. A grain boundary is often referred to as a forest of dislocations. 10 McLean (23) studied some of the mechanical behaviors of grain boundaries in Cu-Zn alloys. The grain boundaries in alpha bicrystals have been observed to slide with respect to each other. A grain boundary with an orientation of 45° with respect to tensile axis was observed to undergo a continuous deformation, and necking took place at this grain boundary. Chuang and Margolin (24) studied the stress-strain relationship of beta brass crystals. Three isoaxial bicrystals and one nonisoaxial bicrystal of beta brass, oriented to have the grain boundaries parallel to the axis of loading, were used in their studies to investigate the stress-strain relationships. It was found that grain boundary strengthening was greater in nonisoaxial bicrystals of beta brass. II-D. Deformation Behavior of Polycrystals of Alpha and Beta Brasses Deformation behavior in polycrystalline materials differ from that of a single crystal. The presence of grain boundaries impose added constraints when deformation of individual grains takes place. Grain boundaries have no repetitive pattern in their structures and hence it is difficult to clearly understand their deformation behavior. Karashima (25,26) studied the deformation behavior of alpha brass polycrystals. He observed pile-up of dislocations against grain boundaries and sub-grain boundaries at low strains (1-5 percent). With increasing 11 degrees of deformation (5-10 percent). dislocations from two or three slip systems interacted and formed dislocation tangles and kinks. The dislocation sub-structure varied according to the degree of deformation and was correlated with work-hardening mechanisms in various stages. Work- hardening in the initial stages was mainly attributed to the back stresses caused by dislocations piling up against grain boundaries. Formation of Lomer-Cottrell sessile dislocations (27), and development of jogs due to interaction of dislocations with vacancies, become important as deformation progressed. A prominent feature in alpha brass is that most of the dislocations introduced during cold-working are confined to the primary slip planes (6). Karashima's (25, 26) studies on alpha brass showed that slip progresses through grain boundaries at above 8 percent strain with clear indications that slip was continuous across the boundary into the neighboring grain. This observation supports the view that some dislocations can apparently pass through the boundary (47) if adjacent grains possess favorable relative crystallographic orientations. Greninger (28) has studied the plastic deformation of beta brass and found that parallel markings that appear on the surface of a crystal after slight deformation represent lattice transformation. The polished surface revealed two distinct structural characteristics: 12 1) fine hair-like lines referred to as slip bands, and 2) a relief which is corrugated. Neither slip lines nor deformation bands were observed to continue through a grain boundary without changing direction, and both must have been related in some way to the beta lattice. According to Head _£’_l. (30), a[lll], a[lOO], and a/2[lll] are types of dislocations that exist in the deformation structure of beta brass. Head gt _1. computed the theoretical image profiles of dislocations in beta brass using two-beam dynamical theory, and considering the full anisotropic strain fields of the dislocations. Comparing the theoretical and experimental images, it was concluded that the majority of dislocations in beta brass were screw dislocations of type <1ll> gliding on {T10}. Some of these a<1ll> dislocations split into two a/2 dislocations. Other dislocations observed were of the <010> type that were glissile on 001 . II-E. Deformation of Two-Phase Materials So far, this review has dealt with deformation of single-phase materials. A more complicated deformation behavior is observed in two-phase materials. a) Deformation of Bicrystals of Two-Phase Materials: Different models such as bicrystal and duplex crystals have been used to understand the deformation of two-phase materials. Hingwe and Subramanian (3) deformed bicrystals 13 of alpha-beta brass in uniaxial tension to study the initiation of plastic deformation and its pr0pagation across the phase boundary. Observations were made with the phase boundary perpendicular to the tensile axis. The effectiveness of the phase boundary as a barrier for slip pr0pagation depends upon the relative crystallographic orientation of the two phases. This may be due to i) the difference in shear moduli of alpha and beta, ii) the difference in Burger's vector of slip dislocations in the two phases, and iii) the difference in the number of available slip systems. Nilsen and Subramanian (6) carried out investigations on bicrystals of alpha-beta brass consisting of oriented and equiaxed duplex boundaries. Equiaxed boundaries were found to be more effective in blocking the propagation of deformation from alpha to beta phase than the oriented boundary. They concluded that wider slip bands formed in alpha phase produced more effective stress concentration so as to activate slip in beta phase across the boundary. Fine or multiple slip formed in alpha phase at high strain rates did not produce effective stress concentrations to cause slip across the phase boundary. High strain rates tend to form fine slip in alpha phase by activating many dislocation sources. Interaction of fine slip with the boundary caused multiple slip immobilizing a large fraction of the dislocations. Nilsen and Subramanian (5) have also carried 14 out tensile tests on bicrystals of alpha-beta brass at various strain-rates, and for specimens having two different types of boundary geometries, corrugated and flat. They found out that corrugated boundary was more effective in blocking the pr0pagation of slip from alpha to beta phase. All specimens tested were found to be strain-rate sensitive. At low strain rates, both boundary types were found to be ineffective barriers to the pr0pagation of slip, and coarse slip was observed in the alpha phase. At higher strain rates, fine slip was observed in alpha phase. Slip pr0pagation in the beta phase requires the movements and multiplication of superlattice dislocations. Motion of superlattice dislocation is difficult and requires a high stress. As any slip line crosses from the alpha phase into the beta phase, it will proceed only to a limited extent. This extent depends upon the level of stress concentration created in alpha phase near the phase boundary. The effect of this stress concentration in beta phase diminishes in direct proportion to the distance from the phase boundary. When slip line in beta reaches a position at which the stress concentration is insufficient to continue slip propagation, it will st0p. Khezri-Yazdan (8) investigated the role of phase boundary orientation relative to the tensile axis in bicrystals of alpha-beta brass. In such a geometry the phase boundary experiences both shear and normal stresses 15 under uniaxial loading. In bicrystals with inclined boundaries, the pile-up stress due to interaction of slip in the alpha phase with the phase boundary was not the motivating force for creating deformation in beta phase. In these specimens, slip in beta phase normally occurred on its own. This may be due to the shear stress acting on the inclined boundaries. Takasugi, Izumi and Fat-Halla (12-15) tested diffusion-bonded alpha-beta bicrystals at specific strain-rates at various temperatures. They studied the specimens with the phase boundary parallel to the tensile axis. Under such loading conditions, the strain in alpha and beta phases are the same, and the boundary does not experience any stress. Interface studies by Takasugi and Izumi (11) on bicrystals of alpha-beta brass led them to believe that the phenomenon of interface sliding was strongly dependent on the nature of the interface; i.e., the crystallographic orientation relationship, shear direction, and microstructure of the interface. Izumi 33 El! (9) have studied operative slip systems in diffusion-bonded alpha- beta brass two-phase bicrystals at 150°K. They found out that the primary (111)“ [TOlJa system, in the alpha phase, and the primary PB [lll]B, in the beta phase, were operative (PB being the actual observed slip plane in the beta phase lying between [T01] and [TT2]). H. Kawazoe gt 1. (10) have performed fatigue tests on diffusion-bonded two-phase 16 bicrystals of alpha-beta brass. Fatigue testing at room temperature was performed at 30 Hz in tension-compression under constant stress amplitude of about 1 100 MPa. Predominant slip in the alpha phase occurred on the primary (111) plane, while those in the beta phase occurred on the planes apart from the (T01) plane rather close to the (211) plane. b) Deformation of Polycrystals of Alpha-Beta Brass: Honeycomb and Boas (31) conducted metallographic studies of deformed alpha-beta brass containing 40 percent zinc. Initial deformation started in alpha phase and after heavy deformation in alpha, slip was observed in beta grains. When deformed specimens of alpha-beta brass were repolished and strained further, slip lines were found to appear again in alpha grains. Slip traces occasionally crossed the alpha-beta phase boundaries and the grains that deformed had parallel slip traces. The orientation relationships required between the alpha and beta brass, for slip pr0pagation through the boundary to occur, was {110}B 1| {lllla and B ll <110>a. Grains satisfying these orientation conditions are called contiguous grains. Substantial deformation in beta was observed in the vicinity of alpha-beta phase boundary more than in the interior of beta grains. 17 II-F. Theoretical Models for Interaction of Slip with Boundaries Grain boundaries are one of the most important barrier to dislocation motion during plastic deformation of polycrystalline solids. During plastic deformation, the dislocations tend to pile up at grain boundaries. Because of this pile-up, a back stress is created which eventually may st0p the dislocation source from operating (7). When stress concentration at a grain boundary is high enough, slip proceeds across the boundary and moves into a coherent slip plane in the adjacent region (7). Various theories have been proposed to eXplain the continuation of slip through the boundary into the adjacent grain. A pr0position of Hall (32) and Petch (33) is that a dislocation pile-up can "burst" through a grain boundary due to stress concentrations at the head of the pile-up. If Ta is the applied resolved shear stress on the slip plane, then stress acting on the head of the pile-up containing n dislocations is (n13). The number of dislocations in a pile-up depends on the length of the pile- up, which in turn, is proportional to the grain diameter. Cottrell (34) used a somewhat similar approach. He suggested that it is virtually impossible for dislocations to "burst" through boundaries. Instead, he assumed that the stress concentration produced by a pile-up in one grain can activate dislocation sources in the adjacent grain. 18 Li (36) has pointed out that grain boundary can be a source of dislocations. According to him, irregularities at a grain boundary (steps, or ledges) could be responsible for emission of dislocations into the adjacent grains. Li has suggested that the grain boundary ledges can generate dislocations, "pumping" them into the adjacent grain. Murr (37), among others, has shown that the grain boundaries could actually emit dislocations. He observed the emission of dislocations from a grain boundary source. In his study, dislocations were observed to be generated at the grain boundary ledge. There have also been further evidences in transmission electron microscopic studies indicating that grain boundaries can be a source of dislocations (38). It is presently thought that dislocation emission from grain boundaries is an important source of dislocations in the early stages of plastic deformation of a polycrystal (35.37.38). II-G. Finite Element Method To conduct an investigation of the stress-strain response in alpha-beta brass, the finite element method (FEM) was adapted. FEM is a numerical technique used for solving various problems in stress analysis (39). With this technique, the stress distribution in individual phases and stress-strain behavior of two-phase region can be ascertained. 19 Fishmeister and Sundstrom (40) used the FEM technique to calculate the stress-strain curves for different hardness ratios between different phases present in plain carbon steels (0.11 and 0.21 weight percent carbon) and aluminum bronzes (8 to 12 percent aluminum). They also studied deformation of individual phase regions in case of plain carbon steel by using two-dimensional ("plate“) model of the ferrite-martensite microstructure. Karlsson and Sundstrom (41) have also studied plastic deformation in ferritic- martensitic steels. They used FEM to study inhomogeneity in correSponding two-phase model. They found that strain field is very inhomogeneous in two-phase structure and inhomogeneity increases substantially with increasing yield . stress ratio. Sundstrom (42) has used FEM to study the ,elastic-plastic behavior of WC-CO alloys. He showed that continuum mechanics can be applied to a two-dimensional model of real microstructure. His results indicated that the plastic strain distribution calculated using FEM is very inhomogeneous on the microscale, and that FEM cannot give a high resolution on the microscale of stress and strain fields in the phases. This is because of computational limitations leading to coarser sub-division of the model into elements. Jinoch st 31. (39) used FEM to study stress- strain curves of an alpha-beta Ti-8Mn alloy. In their investigation, they used a uniform mesh of 392 triangular two-dimensional (plane stress) plate elements.) The volume 20 fraction, particle size, and shape could be varied by designating each triangle as either alpha or beta. The shapes of the particle used in the meshes were not the same as those in actual specimens but were idealized to make calculations simpler while maintaining the volume fraction constant at 17 percent. Their studies showed that an FEM- calculated stress-strain curve attained lower stress levels for similar strain levels as compared to an experimentally calculated stress-strain curve. This difference may be due to the finer grain sizes in the Ti-8Mn alloy and the contribution of the interface phase, which were not considered. Margolin st 21. (43,44) studied the influence of particle size, matrix, and volume fraction of the phases on the stress-strain relationship of alpha-beta Ti alloys. They found that for a given volume fraction of second phase, the calCulated stress-strain curve was higher for specimens with a finer particle size as compared to that of specimens with coarser particle size. For the stronger beta phase, the stress-strain curve reached higher stress values. There were discrepancies between the experimental values and calculated values in general, because the anisotr0py of alpha and beta phase was not considered and no distinctions were made between the slip behavior for equiaxed and Widmanstatten alpha. It was also observed that average strain in alpha phase was higher than average strain in beta phase. Maximum strain in alpha occurred at the center of 21 the alpha particle, away from the constraints imposed by beta. 0n the other hand, maximum strain in beta phase occurred at the alpha-beta interface, because of the need for beta to maintain compatibility with the alpha particle. III. EXPERIMENTAL PROCEDURE III-A. Procedures Used for Transmission Electron MTCroscopjc Study of theFDefbrmatTon Structure in the Phase’Boundary Region Stock of Muntz metal (60 percent Cu, 40 percent Zn) was rolled down to a thickness of about 0.45 to 0.50 millimeters using a cold rolling mill. Tensile samples with a gauge length of 18 millimeters and a width of 7 millimeters were cut out. These samples were annealed for one hour at 425°C in evacuated quartz tubes to relieve prior stresses in the material. These specimens were then imparted a critical strain of 8 percent plastic strain and heat-treated for 18 hours at 825°C in evacuated quartz tubes to obtain large grain sizes. These heat-treated samples were strained to 12-27 percent plastic strains at 0.2 cm/min strain rate. A microtensile fixture fitted onto an Instron testing machine was used to strain the samples. These deformed specimens were thinned down chemically to 0.10 millimeters using 45 percent nitric acid and 55 percent distilled water solution and washed with methanol. A disc of 3 millimeters' diameter was cut out of the gauge length of the specimen. Two-step polishing techniques were used to produce electron transparent regions. It is difficult to thin samples so as to have transparent areas at the interface region consisting of both alpha and beta phases, owing to the possibility of selective polishing of one of the two phases and etching of the phase boundary (45). Although several conditions and 22 23 chemicals have been tried, the best results were obtained using the following conditions and electrolyte. Jet polishing was carried out to achieve a concave surface on one side of the sample using the set-up shown in Figure 3. Conditions and chemicals used were as follows: Electrolyte: 12 volume percent nitric acid, 88 percent methyl alcohol Voltage: 60 volts (DC) Temperature: 243°K Time: 2 minutes. Final polishing was used to obtain a small hole at the center of the specimen. This hole was produced by using a cylindrical cathode immersed in the elctrolyte mentioned below. The specimen was held between two platinum loops as shown in Figure 4. A light source was used to detect the hole as soon as it was formed. Subsequently, the specimen was washed thoroughly with methanol. Electrolyte: 12 volume percent nitric acid, 88 percent methyl alcohol Voltage: 7.5 volts (DC) Temperature: 243°K Time: 1-2 minutes. These specimens were observed in an EM-300 Transmission Electron Microscope Operated at 100 Kv. "A Fl'9ure 3. Schematic of 3. Shekhar, "jet- MMM, M 24 POITShing" ichigan Sta unit (by courtes te University). ygf p01 lShIn1_.__‘-____ solution esy of TC DOwer Suppl) ..___ Stand 859’ i r'ryv ~——vTc power Supply Platinum \ T7" .../‘11 L.__._.". 4fi_‘ Petridish with a h01€ ) A Reservoir -_--—--o~ I I I I I I I A —-_—_—-————1 25 Figure 4- Schematic of courtesy of 3 University), the final electro polishing unit (by ° Shakhar. MMM, Michigan State InlI{N To cathode.— )te ‘\ a . __ _J ...... ... ........ _ . Electrolyte '-—-rlo anode ‘3 Stainless steel sheet .-—‘-' T d with slots [1' cut out , w ,,——-Platinun wire : ’,,,_«*""' loops Specimen g J 26 III-B Finite Element Analysis FEM analysis was carried out using a Prime 750 computer system analysis computer program, which is used for the tion of several classes of engineering problems and The ANSYS Element solu which was utilized for the present study. Library (46) offers 95 different element types to carry out a wide range of engineering analyses. Element type STIF (42) was used for analysis of alpha-beta brass. In order to generate a nonlinear stress-strain relationship, the Young's modulus, Poisson's ratio, and five strains in the nonlinear region of the stress-strain curve with correSponding stress have to be defined (46). A mesh of 128 elements was prepared for the ANSYS, and FEM analysis was carried out with various volume percent of beta phase and grain sizes. In a prior study, Kulkarni (47) used a mesh of 60 elements Dividing the area into more number of a 128- for FEM analysis. elements increases the degree of accuracy; hence, element mesh was prepared for this analysis. Comparison of the results obtained by using these two different meshes is presented in detail in the next section. Node "J“ was fixed in the meshes shown in Figures 5, 6 and 7, and all other nodes along AB could move in both X- and Y-directions. Node along CU had the same "Y“ displacement. Input stress-strain curves used are shown in Figure 8. The stress-strain curve for alpha brass was based on the stress-strain curve of brass containing 70 weight Figure 5. 27 A) Fine grain distribution. Medium grain distribution. shaded in! a ll nunnnr in q n‘n 28 Figure 5 (continued) C) Coarse grain distribution. Figure 6. FEM mesh f or alpha-be volume percent beta p dark): 29 ta brass containing 50 hase (beta phase is shaded A) Fine grain distribution. 8) Medium grain distribution. 3O Figure 6 (continued) C) Coarse grain distribution. Figure 7. FEM mes volume dark): h for alpha-b percent beta 31 eta brass containing 75 Phase (beta phase is shaded A) Fine grain distribution. B) Medium grain distribution. 32 Figure 7 (continued) C) Coarse grain distribution. 33 Figure 8. FEM input streSS-strain curve of Alpha and 391:3 brasses (Ref. 48). cm...‘_-_,._ __¢ 1 fiBFDSS 1 Beta 400 / i / / _STRESS(MPa) : // // Q 'Bros1 1 ’- 1 : \ g / / 1 1 / / i 200 / / J Youwcs AA004ULUS (MPa) 1 E:I '1 o .10 1 1 E_ .‘ s - '3” 1 1 YIELD Sreess 1 a ‘10 MPa 1 B :52 MP. 0 I I I 1 I T T. f O l ‘5 3 a ’1 STRAIN PERCENT 34 percent copper and 30 weight percent zinc. The stress- strain curve for beta brass was obtained from the available values of Young's modulus, yield stress, and the correSponding strain value at the yield stress level (48). To obtain the stress-strain curves, the applied stresses were known for each loading condition. The corresponding strains were calculated from the common displacements of the nodes on the line CD and the initial length AC. Stress- strain distribution plots were obtained by using the mesh shown in Figure 9. Stresses at neighboring triangular elements were averaged to deduce stress at the center of each square on line EU. Displacement in the "Y"-direction of two successive nodes were used for calculation of strains. Stress-strain curves were plotted for the two-phase region (alpha, beta) for two different loading configurations. In the first case tensile axis was normal to the phase boundary, and in the second case tensile axis was parallel to the phase boundary. The above two cases are illustrated in Figure 10. Similarly, stress-strain curves were plotted for 25, 50, and 75 volume percent of beta phase. For each volume percent of beta phase, three different grain sizes were analyzed. Figure 9. 35 FEM mesh, for alpha-beta brass containing 25 volume percent beta phase (shaded dark). used for calculation of the stress-strain distributions. across the alpha-beta interface. Figure 10. 36 FEM mesh for alpha-beta brass containing 50 volume A) 8) Percent beta and 50 volume percent alpha. Phase boundary parallel to tensile axis. Phase boundary perpendicular to tensile axis. C W W IA AU B IV. RESULTS AND DISCUSSION IV-A. TRANSMISSION ELECTRON MICROSCOPE ANALYSIS OF THE D - This study is divided into the following parts: a) Burger's vector analysis of dislocations present near grain and phase boundaries, and b) analysis of interaction of dislocations with equiaxed phase boundary. a) ANALYSIS OF DISLOCATIONS PRESENT NEAR GRAIN AND PHASE BOUNDARIES This study mainly focused on the Burger's vector analysis of the dislocations present in the deformation structure of the two-phase alpha-beta brass near a) alpha- alpha grain boundary, and b) alpha-beta phase boundary. Burger's vector analysis of dislocations near the boundary was performed to determine the character of dislocations. Two parameters are needed in the dislocation analysis to determine the character of dislocations. These two parameters are the Burger's vector of dislocation and the orientation of dislocation line. Burger's vector can be determined by using "§.6 = 0" criterion and orientation of dislocation line can be determined with the help of stereographic projection. A total of eight analyses are presented in this thesis. They are divided as follows: i) Three Burger's vector analyses of dislocations present near alpha-alpha grain boundary, 37 IV. RESULTS AND DISCUSSION IV-A. TRANSMISSION ELECTRON MICROSCOPE ANALYSIS OF THE D - This study is divided into the following parts: a) Burger's vector analysis of dislocations present near grain and phase boundaries, and b) analysis of interaction of dislocations with equiaxed phase boundary. ANALYSIS OF DISLOCATIONS PRESENT NEAR GRAIN AND PHASE BOUNDARIES This study mainly focused on the Burger's vector a) analysis of the dislocations present in the deformation structure of the two-phase alpha-beta brass near a) alpha- alpha grain boundary, and b) alpha-beta phase boundary. Burger's vector analysis of dislocations near the boundary was performed to determine the character of dislocations. Two parameters are needed in the dislocation analysis to determine the character of dislocations. These two parameters are the Burger's vector of dislocation and the orientation of dislocation line. Burger‘s vector can be determined by using "§.B = 0" criterion and orientation of dislocation line can be determined with the help of stereographic projection. A total of eight analyses are presented in this thesis. They are divided as follows: i) Three Burger‘s vector analyses of dislocations present near alpha-alpha grain boundary, 37 38 ii) Four Burger's vector analyses of dislocations present in alpha region near alpha-beta phase boundary, and iii) one Burger's vector analysis of dislocations present in beta region near alpha-beta phase boundary. In all these tables, "9" represents the angle between the Burger‘s vector and the dislocation line direction. 1) Burger‘s Vector Analyses of Dislocations Present Near (ATpha-ATphaT GraTn BOundary*T#T;#3] Analysis #1 Dislocations which are present in slip traces marked "a" and "b" in Figure 11 were analyzed. A set of five micrographs with three different 5 vectors was obtained with different tilting conditions. Possible Burger's vector of these dislocations can be determined by using the following table where "X" represents cases for which the "5-3 = O criterion" is satisfied and L.“ represents cases for which the "3-6 = 0 criterion" is not satisfied. Possible Bugger's Vector [110] [1T0] [101] [lOT] [011] [OlT] Figure 3 Number 11A. B [200] - - - 11C, 0 [220] x - - 11E [020] - - X Dislocation trace analysis was carried out as shown in the following table: 39 Figure 11. Dislocations near grain boundary in alpha phase of alpha-beta brass specimen deformed to 12 percent strain level. + A) g = [200]. ‘(110) Figure 11 (continued) B) §= [200]. 40 Figure 11 (continued) C) §= [220]. 41 W :33 - .....x _ A. . ..Am/ . m . ._ . l 4 H .W... .1 s $00 . n \.x I... .0 . ..V11. Jwv. s. H C.N mta Figure 11 (continued) 01 3= [220]. 42 (110) Figure 11 (continued) E) 3= [0’20]. 43 "T (110) ll 1 A ‘17 . 0’ . (‘1 1 r . - I, ‘14 I, I. q ’ '1 . I109! 1’. 111.1 "x i /I 1 1’ 1 \I I . I -.. 1. . 1 C . 11 f1 / ' 10 V \ I I I A I. . \ ' 0.250m :44 L , 44 Dislocations Dislocation Present in Burger's Slip Line Dislocation Slip Traces Vector Plane Direction Character a [101] (111) [011] Mixed (111) N-P e = 60°-85° [101'] (111) [0T1] Mixed [1T1] N-P e = 120°-l45° [1T0] (111) [0T1] Mixed e = 60°-85° (HT) [011] Mixed e = 120°-l45° b [101] (llT) N-P (111) [0T7] Mixed e = 60°-80° [101'] (111) N-P (1T1) [011] Mixed e = 120°-l40° N-P in the above table represents that the particular slip plane is not a possible one. Analysis #2 Dislocations present in slip trace "a" in Figure 12 were analyzed. A set of four micrographs was obtained with different tilting conditions. Possible Burger's vector can be determined from the following table: 45 Figure 12. Dislocations near grain boundary in alpha phase of alpha-beta brass. Location of grain boundary: upper right corner 60° to X-axis. A) 'g’ [1T1]. B) §= [131]. C) §= [2'20]. 13) 3= [012]. Specimen deformed to 12 percent strain level. 46 Figure 3 Possible Burger's Vector Number [110] [1T0] [101] [10T] [011] [01T] 12A [1T1] X - - x x - 128 [T3‘1] - - x — . - - 12C [220] - x - - .. - 120 [042] - - - - - - Dislocation trace analysis was carried out as shown below: Dislocations Dislocation Present in Burger's Slip Line Dislocation Slip Traces Vector Plane Direction Character a [011] (111) [011] Screw (Tll)ILP Analysis #3 Dislocations present in slip trace marked "a" in Figure 13 were analyzed. A set of three micrographs was obtained with different tilting conditions. Possible Burger's vector of these dislocations can be determined from the following table: 47 Figure 13. Dislocations near grain boundary in alpha phase of alpha-beta brass. Specimen deformed to 12 percent strain level. A) 3 = [T1T]. B) 3 = [002]. C) 5 = [T11]. C 48 Figure g Possible Burger's Vector Number [110] [1T0] [101] [10T] [011] [MT] 13A [T1T] X - _ X X _ 13B [002] x x - - - - 130 [T11] X - x - - x Dislocation trace analysis was carried out as shown below: Dislocations Dislocation Present in Burger's Slip Line Dislocation Slip Traces Vector Plane Direction Character a [1T0] (lll) [TWO] Screw ( 1 11') [T10] Screw 11) Burger's Vector Analyses of Dislocations Present in ATpha Region Near ATpha-Béta Phase Boundary (#4-#7l Analysis #4 Dislocations present in slip traces marked "a," "b," and “c" in Figure 14 were analyzed. A set of three micrographs was obtained with different tilting conditions. Possible Burger's vector of these dislocations can be determined from the following table: 48 Figure 5 Possible Burger's Vector Number [110] [1T0] [101] [10T] [011] [OlT] 133 [002] x x - - - - 13C [T11] X - x _ _ X Dislocation trace analysis was carried out as shown below: Dislocations Dislocation Present in Burger's Slip Line Dislocation Slip Traces Vector Plane Direction Character a [1T0] (lll) [T10] Screw (11T) [T10] Screw ll) Burger's Vector Analyses of Dislocations Present in Alpha Region Near ATpha-Beta Phase Boundary (#4-#7) Analysis #4 ll llb ’ll Dislocations present in slip traces marked "a, and "c" in Figure 14 were analyzed. A set of three micrographs was obtained with different tilting conditions. Possible Burger's vector of these dislocations can be determined from the following table: 49 Figure 14. Dislocations in alpha region near alpha-beta phase boundary. Specimen deformed to 12 percent strain level. Location of phase boundary: lower left corner 50° to X-axis. A) 3 = [002]. = [Tll']. 0+ 8) Figure 14 (continued) C) ‘5: [1T1]. 50 51 + Figure 9 Possible Burger's Vector Number [110] [1T0] [101] HOT] [011] [01T] 14A [002] X X - - - - 148 lel] X - X - - x 14C [1T1] x - — x x - Dislocation trace analysis was carried as shown below: Dislocations Dislocation Present in Burger's Slip Line Dislocation Slip Traces Vector Plane Direction Character a [101] (111) N-P (111) [1T2] Mixed e = 30°-45° [011] (111) N-P (T11) [1T2] Mixed e = 150°-l65° b [1T0] (111) [017] Mixed e = 120°-155° (llT) [101] Mixed e = 60°-95° c [lOT] (lll) N-P (111) [1T2] Mixed e = 30°-50° [011] 11m 11- P (111) [1T2] Mixed e = 150°-l70° 52 Analysis #5 Dislocations present in the slip trace marked "a," "b" and c" in Figure 15 were analyzed. A set of three micrographs was obtained with different tilting conditions. Possible Burger's vectors of these dislocations can be determined from the following table: 4' Figure 9 Possible Burger's Vector Number [110] [1T0] [101] [10T] [011] [01T] 15A [1T1] X - - x x - 158 [Tll] x - X - - x 150 [002] X X - - - - Dislocation trace analysis was carried out as shown on page 56: 53 Figure 15. Dislocations in alpha region near alpha-beta phase boundary. Specimen deformed to 15 percent strain level. A) 5: [1T1]. Figure 15 (continued) 8) 25: [T11]. 54 Figure 15 (continued) 0) Ej= [002']. 55 56 Dislocations Dislocation Present in Burger's Slip Line Dislocation Slip Traces Vector Plane Direction Character a [10T] (111) N-P (117) [1T2] Mixed e = 30°-55° [011] (llT) N.P (111) [1123 Mixed e = 150°-l75° b [101] (T11) [1T2] Mixed (llT) N-P e = 30°-45° [01T] (111) N-P (111) [1T2] Mixed e = 150°-l65° c [101] (T11) N.P (111) [101] Screw [011] (111) [01T] Screw (llT) N.P Analysis #6 Dislocations present in the slip traces marked "a," and "b" in Figure 16 were analyzed. A set of three micrographs was obtained with different tilting conditions. Possible Burger's vector of these dislocations can be determined from the following table: 57 Figure 16. Dislocations in alpha region near alpha-beta phase boundary. Specimen deformed to 15 percent strain level. Location of phase boundary: vertical, left. A) 11 [T11]. B) a [002]. Figure 16 (continued) C) ‘5: [1T1]. 58 59 Figure 3 Possible Burger‘s Vector Number [110] [1T0] [101] [10T] [011] [01T] 168 [002] X X - - - - 16A [T11] X - X - - X 160 [1T1] x - - x x - Dislocation trace analysis was carried out as shown below: Dislocations Dislocation Present in Burger's Slip Line Dislocation Slip Traces Vector Plane Direction .Character a [101] (llT) [1T0] Mixed (111) N-P e = 60°-100° [OTT] (111) [1T0] Mixed [T11] N-P e = 120°-160° b [101] (llT) N°P (Tll) [101] Screw [01T] (111) N-P (111) [101] Mixed 0 = 120°-135° Analysis #7 Dislocations present in slip trace marked "a" in Figure 17 were analyzed. A set of three micrographs was obtained 60 Figure 17. Dislocation in alpha region near alpha-beta phase boundary. Specimen deformed to 18 percent strain level. Location of phase boundary: vertical, left. A) g [1T1]. B) a [002]. Figure 17 (continued) c) §= [T11]. 61 62 with different tilting conditions. Possible Burger's vectors of these dislocations can be determined from the following table: Figure 3 Possible Burger's Vector Number [110] [1T0] [101] [10T] [011] [01T] 17A [1T1] X - - X X - 17B [002] X X - - I - - 17C [T11] X - X - - X Dislocation trace analysis was carried out as shown below. Dislocations Dislocation . . Present in Burger's Slip .Line. Dislocation Slip Traces Vector Plane Direction Character a [1T0] (111) [011] Mixed e = 120°-l70° (lTT) [101] Mixed e = 60°-110° 63 iii) Burger's Vector Analysis of Dislocations Present in Beta RegiOn Near Alpha-Beta Phase Boundary (#8) Analysis #8 Dislocations present in slip trace marked "a" in Figure 18 were analyzed. A set of four micrographs was obtained with different tilting conditions. Possible Burger's vector of these dislocations can be determined from the following table: Figure 3 Possible Burger's Vector Number [111] [111] [1T1] [llT] 18A [200] - - - - 188 [110] - X X - 13 C [121'] - x - x 180 [T10] X - - X Dislocation trace analysis was carried out as shown below: Dislocations Dislocation . Present in Burger's Slip Line Dislocation Slip Traces Vector Plane Direction Character a [111] (110) [111] Screw (lOT) [111] Screw (OTT)N°P Figure 18. 64 Dislocations in beta region near alpha-beta phase boundary. Specimen strained to 18 percent strain level. Location of phase boundary: lower left corner, 65° to X-axis. [200]. [110]. A) 1.0+ (0+ 11 B) Figure 18. 64 Dislocations in beta region near alpha-beta phase boundary. Specimen strained to 18 percent strain level. Location of phase boundary: lower left corner, 65° to X-axis. [200]. [110]. A) 10+ {04' II B) "T (001) .‘3. Figure 18 (continued) [Tfl’] . [T10] . C) (0+ «3+ 11 D) 65 66 Individual dislocations present in beta phase were observed at regions away from the phase boundary. These slip dislocations were screw in character and of the type §<1ll> gliding on {T10}. Such an observation is consistent with studies of Head £5 31. (30). b) INTERACTION 0F DISLOCATIONS WITH EQUIAXED PHASE BOUNDARY The micrographs which are presented in Figure 19 reveal dislocation pile-up at the equiaxed phase boundary in alpha region, and some slip dislocations in beta region. Three models have been proposed to explain the initiation of deformation in the adjacent grain due to interaction of slip in one grain with the boundary. Accofiding to Hall (32) and Petch (33) a dislocation pile-up can "burst" through a boundary due to stress concentration at the head of the pile-up. Cottrell (34) suggested that the stress- concentration produced by a pile-up in one grain can activate dislocation sources in the adjacent grain. According to Li (36). stress concentration created due to the pile-up at the boundary forces the boundary dislocation sources into the adjacent grain. According to Nabarro (34), a slip band cannot cross from one grain to another without irregularity unless slip direction is the same in both the grains and the choice of the crystal plane for slip is not critical in the adjoining grain. Which one of the above models is applicable to alpha-beta phase boundary cannot be verified during the present study since dislocation pile-up 67 Figure 19. Deformatidn structure near phase boundary of alpha-beta brass. A and B: Specimen deformed to 12 percent strain level. C and D: Specimen deformed to 15 percent strain level. 0.2511111 " .. ' A ALPHA P ~ 1 ' 68 Figure 19 (continued) E) Specimen deformed to 18 percent strain level. 68 Figure 19 (continued) E) Specimen deformed to 18 percent strain level. 69 Figure 19 (continued) F) Specimen deformed to 20 percent strain level. 69 Figure 19 (continued) F) Specimen deformed to 20 percent strain level. 70 Figure 19 (continued) G) Specimen deformed to 27 percent strain level. 1 0-25uml 71 Figure 20. Antiphase boundaries in beta region of alpha- beta brass. 72 in alpha at an equiaxed boundary never initiated slip in beta near the phase boundary in the range of strain levels studied. In this study, the dislocation pile-ups in alpha region were observed at the phase boundary for Specimens that were deformed to strain levels of more than 12 percent. This observation is consistent with the results of Karashima (25) and Kulkarni (47). Karashima observed complex tangled dislocation structures in 70 Cu-30 Zn alpha brass at strain levels higher than 5 percent. Similar observations were made by Kulkarni (47) in alpha phase of 60 Cu-40 Zn brass. Since beta brass has higher yield stress than alpha brass, plastic deformation starts earlier in alpha phase than in beta phase. At strain levels of 12 to 27 percent, the alpha phase exhibits dislocation pile-up at the phase boundary. There is no evidence of dislocation activity in beta phase near alpha-beta phase boundary as a result of this pile- gup. A probable reason is that the adjacent alpha and beta grains did not possess the specific orientation relationship as has been mentioned by Honeycombe and Boas (31). They have stated that such slip pr0pagation from alpha to beta can occur when both the grains are contiguous. Slip planes and slip directions in both phases will match with each other under such conditions. There are other reasons for not observing dislocation activity in beta near the phase boundary. According to 73 Khezri-Yazdan (8). the pile-up stress in the alpha phase is not the motivating force for creating deformation in beta phase when phase boundary is inclined to tensile axis. Under such conditions, slip in beta phase normally occurs on its own. This may be due to the shear stresses acting on the inclined boundaries due to applied tensile loading. In two-phase bicrystal studies with the phase boundary oriented either parallel or perpendicular to the tensile axis (2-6,9-l5), the special constraints imposed by the loading geometry may facilitate activation of slip in beta phase as a result of dislocation pile-up in the alpha region at the boundary. Such constraints will be absent during deformation of polycrystals. In the present study, slip initiation in beta as a result of dislocation pile-up in alpha did not occur. This may be due to the absence of specific relative crystallographic orientations of alpha and beta, and due to the presence of shear stresses (inclined boundary) in the phase boundary due to applied tensile loading. IV-B. ‘géM ANALYSIS OF STRESS-STRAIN BEHAVIOR OF ALPHA-BETA ASS The result of present FEM analysis is divided as follows: a) Stress-strain relationship for alpha-beta brass containing 25, 50, and 75 volume percent of beta phase. 74 b) Stress-strain relationship for small, medium, and coarse grain sizes of alpha and beta phases. c) Stress-strain distribution across alpha-beta interface. d) Stress-strain curve for two-phase region. e) Comparison of experimental and FEM calculated stress-strain curves. a) Stress-Strain Relationship for Alpha-Beta Brass ”Containing 25, 50} and775 Volume Percent ofiBeta Bless The FEM-calculated stress-strain curves for alpha-beta brass containing 25, 50, and 75 volume percent of beta phase are presented in Figure 21. It can be observed that the stress level increases with increasing beta volume for identical strain levels. Phase distribution and grain sizes used for calculation are shown in Figures 5A, 6A, and 7A. Yield stress values are determined using 0.2 percent offset method. These yield stress values are tabulated in Table l. b) Stress-Strain Relationship for Small, Medium, and COarse GrainiSizes OT Alpha and Beta Phases Stress-strain curves of alpha-beta brass with two different grain sizes are presented in Figures 22, 23, and 24 for 25, 50, and 75 volume percent of beta phase respectively. It can be seen from the figures that as the grain size gets smaller, a stress-strain curve tends to shift upwards; i.e., for equal strain levels, the stress- strain curve for finer grain size attains higher stress values than the stress-strain curve for a coarser grain 74 b) Stress-strain relationship for small, medium, and coarse grain sizes of alpha and beta phases. c) Stress-strain distribution across alpha-beta interface. d) Stress-strain curve for two-phase region. e) Comparison of experimental and FEM calculated stress-strain curves. a) Stress-Strain Relationship for Alpha-Beta Brass [Containing 25, 50, andT75 VBTDme PErcent ofiBeta Phase The FEM-calculated stress-strain curves for alpha-beta brass containing 25, 50, and 75 volume percent of beta phase are presented in Figure 21. It can be observed that the stress level increases with increasing beta volume for identical strain levels. Phase distribution and grain sizes used for calculation are shown in Figures 5A, 6A, and 7A. Yield stress values are determined using 0.2 percent offset method. These yield stress values are tabulated in Table l. b) Stress-Strain Relationship for Small, Medium, and Coarse Grain STzes of Alpha and Beta Phases Stress-strain curves of alpha-beta brass with two different grain sizes are presented in Figures 22, 23, and 24 for 25, 50, and 75 volume percent of beta phase respectively. It can be seen from the figures that as the grain size gets smaller, a stress-strain curve tends to shift upwards; i.e., for equal strain levels, the stress- strain curve for finer grain size attains higher stress values than the stress-strain curve for a coarser grain 75 Figure 21. FEM-calculated stress-strain curves for alpha- beta brass containing 25, 50, and 75 volume percent of beta phase. Grain size: small. I. % VB - 25%. 5 III. % VB - 75%. II. % V - 50%. hzmomma z. Q A A B . Figure 33. 90 FEM-calculated stress-strain curves of alpha- beta brass containing 50 volume percent of alpha and 50 volume percent beta. I. Phase boundary parallel to tensile axis. II. Phase boundary perpendicular to tensile axis. ..- till. I #200000 2. <0...m 0.0 0.0 ed «.0 0.0 _ 00 oo. 00' com 33.3050 000 000 000 Figure 34. 91 FEM-calculated stress-strain curve of alpha-beta brass containing 80 volume percent of alpha and 20 volume percent beta. I. Phase boundary parallel to tensile axis. II. Experimental. III. Phase boundary perpendicular to the tensile axis. 400 ~-beta 200 and STRESS (MPa) m . /m ‘ A // / d 3 4 STRAIN PERCENT 92 the degree of accuracy has increased with more divisions in the given area. These curves are presented in Figure 35. '.' dawn-h 8 1 _ ' 93 Figure 35. Comparison between the experimentally determined stress-strain curve of 60 Cu-4O Zn brass and the FEM-calculated curves of alpha-beta brass containing 20 volume percent beta phase. I. FEM curve with 60-element mesh (Ref. 47)- II. FEM curve with 128-element mesh. III. Experimental. 11.161 1 the 400 \\\. )1) \ srness( MPa) 200 — i. o o STRAIN PERCENT V. CONCLUSIONS V-A. Transmission Electron Microscope Studies 1. Extensive dislocation pile-ups were observed in alpha region near equiaxed phase boundary, but there was not evidence of dislocation activity due to these pile-ups in beta region for specimens that were strained up to 27 percent. 2. Slip dislocations observed in beta brass at regions away from the phase boundary were screw in Character and were of type §<1ll> gliding on {T10}. V-B. FEM Analysis 1. At a specific strain it was observed that the stress level for specimens with tensile axis, parallel to the phase boundary, was higher than that for specimens with tensile axis perpendicular to the phase boundary. The experimentally obtained stress-strain curve was observed to , be in between the two extremes. 2. 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