THE UNIVERSITY OF MICHIGAN COLLEGE OF ENGINEERING Department of Chemical and Metallurgical Engineering Technical Report THE PLASTIC DEFORMATION OF MAGNESIUM E. W. KIlley W. Fo Hosford, Jr., Project Director ORA'Proje.ct 07164 under eo~ttr4qt.with: Uo So ARMY RESEARCH OFFICE-DURHAM CONTRACT NO. DA-51-124-ARO-D-321 DURHAM, NORTH CAROLINA administered through: OFFICE OF RESEARCH ADMINISTRATION February 1967 ANN ARBOR Distribution of this document is unlimited

This report was also a dissertation submitted by the first author in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan, 1967.

TABLE OF COENENTS ACKNOWLEDGEMENTS. *.. *.. * * TABLE OF CONTENTS..... ~... LIST OF TABLES..... *. LIST OF FIGURESo.... ~.... ABSTRACT o ~ ~ ~... a.. INTRODUCTION. o......... EXPERIMENTAL PROCEDURE......... Single crystal production....... Preparation of specimens for testing, Specimen testing........... Determination of pole figures..... Evaluation of frictional effects.... Analysis of the data........ RESULTS AND DISCUSSION........ Pure magnesium single crystal deformation Compression along the c-axis.. o Compression perpendicular to the. unconstrained c-axis..... Compression perpendicular to the constrained c-axis.,..... Basal slip o......... {101} Twinning..a....... Alloy single crystal deformationo. Magnesium plus.5% thorium * *.. Magnesium plus 4% lithium. * *. page.. g.. ii e * o o o i.. o *. vi *,.. Viii..... 17 o e ~ ~ Vlll ~ o o~ ~ o~ * 0 0 6. 10 O* r * 0 I0 1* 0. o.e 103 ~.... 13... 14 ~.~* *. 15. o o. *.15 *.... 15.) 0 0 o.. 19 ~ *. 0 0 23 ~.... 0 31 ~.. ~.32..... 34.... * 34..... 41 iii

Deformation of textured polycrystalline magnesium..47 Textured polycrystalline pure magnesium *.. o ~48 Textured polycrystalline Mg-.5%Th..o.,.54 Textured polycrystalline Mg-4%Li.. e to.,57 Yield loci of textured materials, o..,. o 58 Pure magnesium yield locus. o. o o o o o.62 Mg-.5%Th yield locus, o.. o o. o o o. 0 66 Mg-4%Li yield locus, o. o o o. o a a o o o67 CONCLUSIONS o o o o. o. o... o.. 68 APPENDICES Ao The Production of Single Crystals, o,.. o.70 Bo Plane-Strain Compression Testing Procedure *. 74 CO Analysis of the Frictional Effects in Compression Tests. o o ~ o ~ o o 77 D, Yield Stresses for 1011 Banding in Orientations C and D o. o * o *.. a o.82 BIBLIOGRAPHY. o o 8, o t. o. *.. 86 DATA.o o o o........... o.. 89 iv

LIST OF TABLES page 1. Magnesium Alloy Compositions 7 2. Single Crystal Orientations used in Plane-strain 9 Compression Testing 3. Experimentally Determined Yield Stresses for 1% 65 Strain in Textured Magnesium Sheets v

LIST OF FIGURES page 1. Plane-strain compression fixture 2. Stress vs. Strain in Pure Magnesium Single Crystals compressed along the c-axis 3o Fractures in Pure Magnesium Single Crystals 4. Stress vs. Strain in Pure Magnesium Single Crystals compressed perpendicular to the unconstrained c-axis, and compressed to activate easy basal glide 5, Stress vso Strain in Pure Magnesium Single Crystals compressed perpendicular to the constrained c-axis 6. Simultaneous {1012} Twinning and {101)} Banding in a C-oriented Single Crystal 7. (1010) compression surface of C-oriented pure magnesium single crystal 8. (1210) compression surface of D-oriented pure magnesium single crystal 11 16 18 21 24 25 30 30 9o Stress vs. Strain in A-oriented Single of magnesium and magnesium alloys 10o Stress vso Strain in B-oriented Single of magnesium and magnesium alloys 11. Stress vs Strain in E-oriented Single of magnesium and magnesium alloys 12. Stress vs Strain in F-oriented Single of magnesium and magnesium alloys 13. Stress vs. Strain in C-oriented Single of magnesium and magnesium alloys 14. Stress vs. Strain in D-oriented Single of magnesium and magnesium alloys Crystals Crystals Crystals Crystals Crystals Crystals 35 36 37 38 39 40 43 15. {1010}(1210) Prism Slip in a C-oriented Single Crystal of Mg-4%Li 16. l1010}(1210) Prism Slip Systems in Magnesium vi

17. [0001o Pole Figure for Textured Pure Magnesium 49 18. Stress vs. Strain in Pure Magnesium 51 19. [0001 Pole Figure for Textured Mg-.5oTh 55 20. Stress vs. Strain in Mg-.5%Th 56 21. [0001J Pole Figure for Textured Mg-4LLi 59 22. Stress vs. Strain in Mg-4%Li 60 23. Plane-stress (o' = O) Yield Locus (schematic) 63 z 24. 1% Strain Yield Loci for Biaxial Stresses in 64 Textured Polycrystalline Magnesium and Magnesium Alloys with Thorium and with Lithium vii

The Plastic Deformation of Magnesium by Eugene Wallace Kelley ABSTRACT Deformation studies have been conducted at room temperature on single crystals and textured polycrystals of magnesium and magnesium alloys with thorium and with lithium. Single crystals oriented to suppress shear on the easily activated basal slip systems were deformed by planestrain compression. Compression along the c-axis was accommodated by {1011 banding. Compression perpendicular to the unconstrained c-axis activated t1012} twinning, and, after virtually complete twinning, deformation continued by 41011} banding in the twinned material. Compression perpendicular to the constrained c-axis was accommodated by the simultaneous operation of {1012} twinning against the constraint and 1011 banding. Although this orientation was favorable for {1010}(1210) prism and 1011o}<1210) pyramidal slip, these modes were not observed in pure magnesium or in Mg-.5%Th. However, {1010(<1210) prism slip was active in crystals of Mg-4%Li during compression perpendicular to the constrained c-axis. Fracture in all materials occurred parallel to {1124} or &1011} depending on the orientation and composition of the specimen. Anisotropy of strength in textured polycrystals was determined in uniaxial compression and tension as well as plane-strain compression. The results are correlated with the orientation texture and the deformation modes observed in single crystals, and have been used to establish yield loci for the materials. viii

INTRODUCTION Metals which crystallize in the hexagonal close packed (HCP) structure are becoming more and more important as engineering performance requirements increase with the growing technology. The various combinations of strength, density and high temperature properties that can be attained in these metals make them extremely useful in many applications. The mechanical behavior of the HCP metals is strongly influenced by the inherent anisotropy that results from the HCP crystallographic structure0 Although a variety of slip systems have been reported the slip is commonly in the directions of closest packing, the (1210)(1) Because (1210> slip directions are confined to the basal plane the slip modes do not produce strains parallel to the c-axis. Hence the inherent anisotropy. Magnesium, a HCP metal, has been structurally important for many years because of its high strength-to-weight characteristics0 At room temperature the deformation mode most easily activated is (0001) (1210> basal slip. {1010} <1210> prism slip and {10ll} (1210> pyramidal slip have also been reported in magnesium, primarily at elevated temperatures. (2,3,4) However, at room temperature the resolved shear stresses to activate the prism and pyramidal modes are in excess of a hundred-fold greater than that required to initiate basal slip. Thus prism and pyramidal 1

2 slip may be expected to occur only under special conditions of loading. Because all three of these deformation modes have (1210) slip directions, none of them, either singly or in combination with the others, can produce strains out of the basal plane. Strains normal to the basal plane can be produced by twinning, however. (5) Magnesium twinning modes which have been reported include {1011}, {112, 1013, j103} 14}, l10Ol5, {1121} and {1124Io (1) Of these, {10121 twinning is by far the most common and is relatively easily activated by tension parallel, or compression perpendicular, to the c-axis. Twinning, of course, is dependent upon the sign of the shear stress, If a shear in one direction can activate a given twinning mode a shear in the opposite direction cannot. Thus magnesium can deform by {1012} twinning when stressed by tension along the c-axis but cannot deform by this mode when compressed along the c-axiso {10l11 twinning on the other hand is activated in magnesium by compression along the c-axis and not by tension. In addition to primary twinning it is possible for secondary twinning or slip to occur within the reoriented material of primary twins. (6) For this reason many combined deformation systems are theoretically possible although the only systems that become active are those that require the least resolved shear stresses for the loading and constraint conditions imposed.

3 Plastic deformation within the individual grains of a polycrystalline aggregate must occur by the activation of crystallographic deformation modes. Because the individual grains are constrained by their neighbors it is seldom that a grain is able to plastically deform by basal slip alone. In general at least five independent shear systems must be available to bring about an arbitrary shape change such as that which must be accommodated in the individual grains of a deforming polycrystalline material~ (7) In magnesium this requirement means that in some grains, depending upon their crygtallographic6, orientation with respect to the load, deformation modes other than basal slip and primary {10121 twinning must be brought into playo If the complete deformation characteristics of a magnesium polycrystalline aggregate are to be properly understood, all of the possible deformation modes must be identified and investigated. Researchers in the past have made observations upon the less common deformation modes through the examination and crystallographic analysis of either deformed polycrystalline aggregates or oriented single crystals. Much of the work in such investigations has involved deformation resulting from uniaxial tension or, in fewer instances, from uniaxial compressiono These two methods of loading can initiate all of the possible deformation modes in polycrystalline aggregates but the identification of the less common modes becomes extremely arduous and the direct

4 evaluation of the resolved shear stresses to activate them is not feasible. In oriented single crystals, however, some of the possible deformation modes are not activated by uniaxial tension or compression. This is because the easily activated basal slip and -1012} twinning modes cannot both be suppressed simultaneously, under uniaxial loading in most of the many orientations which can occur in a polycrystalline material. The only two exceptions are tension perpendicular to the c-axis and compression along the c-axis. By deforming oriented single crystals under conditions of plane-strain compression it should be possible to activate all possible deformation modeso Single crystal specimens carefully prepared should also make the identification of active deformation systems relatively easy and should permit direct evaluation of the resolved shear stresses required to activate such systems. Wonsiewicz and Backofen (8) have recently completed an investigation of pure magnesium at various temperatures utilizing planestrain compression of single crystals. Through the selective crystallographic orientation of the monocrystals they were able to suppress both basal slip and t1012} twinning and thereby force other deformation modes that require higher shear stresses for activationo In planning the present work it was thought that by loading single crystals under plane-strain compression in various specific crystallographic orientations it would be

5 possible to initiate, identify and evaluate all of the possible modes that can participate in the deformation of the materials of interest. Thus, plane-strain compression along the c-axis should activate some deformation mode other than basal, prism or pyramidal slip, or {1012} twinning. This is because compressive stress along the c-axis is perpendicular to the (1210) slip direction of basal, prism or pyramidal slip and is in the opposite direction of that necessary for {1012} twinning. In another crystal orientation where the material is compressed perpendicular to the c-axis while c-axis elongation is constrained, prism or pyramidal slip would be expected to take placeo In this orientation basal slip is suppressed because the load is applied parallel to the basal plane with no possibility for shear strain and {101i2 twinning is suppressed by the c-axis constraint of the plane-strain condition, In a third crystal orientation where the compressive load is applied perpendicular to an unconstrained c-axis the three slip modes would be suppressed but not {1012} twinningo The primary objectives of the present investigation were to study the various deformation modes in magnesium with special emphasis on those that are less easily activated, to investigate the effects of certain alloying elements upon the deformation of magnesium, and to relate the plastic deformation characteristics of textured poly crystalline magnesium to the deformation modes that are

6 found to be active in single crystals. The two alloying elements, thorium and lithium, both commercially important, were to be used in that part of the work involving the study of alloying effects. In view of the foregoing an experimental program was initiated to deform by plane-strain compression various orientations of single crystal specimens of pure magnesium as well as thorium and lithium alloys of magnesiumo The active deformation modes were to be identified by examination of the specimens after compression, and the stressstrain relationships for the various modes were to be evaluated from the load-deformation data taken during compression. In addition, similar plane-strain compression tests plus uniaxial tension and compression tests were to be conducted upon textured polycrystalline specimens of the same alloys. Because of the scope of the experimental program only room temperature testing was plannedo

EXPERIMENTAL PROCEDURE Single crystal production The initial requirement in the experimental program was to produce single crystals of a suitable sizes shape and crystallographic orientation for subsequent testing under conditions of plane-strain compression. The raw materials were three textured sheets provided by Dow Chemical Companyo These had received approximately 80% reduction in the process of being hot-rolled to their final 1/4 ino thicknesses. The nominal compositions of the sheets were pure magnesium, Mg-.5%Th and Mg -4Lio Analyses, also furnished by Dow, for the textured sheets and for single crystals grown from the alloy sheets, are given in Table 1o Al Ca Cu Fe Mn Ni Pb Si Sn Zn Th Li Mg Table 1. Magnesium Alloy Compositions Pure Mg Mg-Th Sheet Sheet Xtals Si <.0005% <.0005% < 03 <.o o.01 <.01 <. 01. <.001 <.001 < 001 < o.001.002.004 <.0006 <.0006 <.01 < o <.001 <.001 ( 001 <. <.003 <.003 <.01 <o. <.001 <.001 <.01 <. <.001.o001 <o01 <. (<01 <.o01.02 <..49.30-.50 ~~- - 3 >99.97 >99.48 >99.4 >96 heet 000O 01 001 014 oooE 0006 001 003 001 001 01 084.11 Mg-Li Xtals')% <.03. <.01 <.001.015 ) <.01 <.001 <.01 <.01 <o01 <.02 3.2-3~8 )96.1 7

8 For each of these compositions single crystals approximately 1/4 in. by 1/2 in. by 6 in. were grown to furnish specimens of specific crystallographic orientations. The seven desired orientations and the code letters which have been assigned to facilitate their identification are indicated in Table 2, The single crystals were grown from the melt in graphite molds by a modified Bridgeman method utilizing oriented seed crystals. A flowing helium atmosphere was used in the crystal furnace. Seeds were aligned and the orientations of single crystals were checked by the Laue back reflection x-ray methodo The details of the crystal growing procedure are presented in Appendix Ao Preparation of specimens for testing Single crystals were carefully removed from the graphite mold and lightly cleaned with 10% HC1. Those determined by x-ray to be within 2~ of the desired orientation were sectioned with an acid saw into compression test specimens roughly 3/8 ino in length. Because the surfaces of the crystals were considered to be too rough in the as-grown condition to permit satisfactory results in the compression tests the specimens were carefully polished successively on wet 400 and 600 grit silicon carbide papers. This was followed by a light chemical polish with 10% HNO3 to remove the markings and minute surface twins that were produced by the mechanical

9 Table 2. Single Crystal Orientations used in Plane-strain Compression Testing Assigned Identification Orientation Compression Direction Constraint Direction LOAD A ] -EXTEN. <OOOI> KoTo> CONSTRAINT B XoTo <ooo00> <21 C <I010> KOOO> D, <o 1> <0ooo> E | _ < oTo<> <o210> ~F <,- <210> <oTo> G _\_ <O000P@450 o<OTo>

10 polishingo The resulting test specimens, with a nominal size of 1/4 in. thick by 3/8 ino long by 1/2 in. wide, were smooth to within an estimated.0002 in. with sides parallel to within.0002 in. and with all six surfaces polished for metallographic examination. Textured polycrystalline specimens were prepared for testing in a manner similar to that used for single crystals. They were cut from the 1/4 in. sheet material with a silicon carbide wheel and sized, shaped and mechanically polished on wet 400 and 600 grit papers. The specimens were prepared in the six orientations of interest, these being the six combinations of rolling, transverse and thickness directions serving as loading, extension and constraint directions in the plane-strain compression testo All polycrystalline specimens were stress-relieved at 550~F for one-half hour as the final step in their preparation for testing. Specimen testing Test specimens were plastically deformed under conditions of plane-strain compression in a hardened steel fixture incorporating an adjustable-width channel (Figo 1). Five interchangeable steel indentors with slightly varying widths were used so that specimens o480 in. to.500 in. wide could be tested under width constrainto The indentors, which were.450 in. long, extended beyond both. ends of most specimens. A few specimens longer than the indentors were

11 O' Fig. 1. Plane-strain compression fixture. (a) Deflectometer actuator, (b) Instron crosshead, (c) deflectometer, (d) indentor, (e) specimen, (f) adjustable-width fixture, (g) die holder, (h) compression load cell.

12 tested without appreciably different results. During compression testing a 2-mil teflon film between the specimen and the test fixture acted as a lubricant and also served to cushion the specimen surfaces and protect them from smearing as deformation occurredo This protection was sufficient to permit direct microscopic observation of the deformed surfaces. To insure reproducibility, at least four duplicate monocrystal specimens of each of the six crystallographic orientations A through F were tested in each of the three compositions under study. Crystals of the G (or easy basal glide) orientation were prepared and tested only for pure magnesium. At least three duplicate polycrystalline specimens were tested for each of the six orientations for each of the three compositions. The textured materials were also tested in uniaxial compression in the rolling, transverse and thickness directions, and in uniaxial tension in the rolling and transverse directions, The uniaxial tests supplemented those in plane-strain compression to provide data for the construction of yield loci for each of the three textured materials. In addition to the textured specimens one set of randomly oriented polycrystalline specimens of pure magnesium was prepared and tested in plane-strain compression. The experimental details of the testing procedure are given in Appendix Bo

13 Determination of pole figures Basal pole figures of the three textured polycrystalline materials were determined by x-ray diffractometer reflection. The resulting pole figures are presented in Figs. 17, 19 and 21. Evaluation of frictional effects Uniaxial compression test results are inherently in error owing to the frictional resistance to sliding that occurs between the specimen and the loading platens. For plane-strain compression in a channel these effects are even greater because of the added frictional resistance imposed by the channel walls. The friction was reduced and made reasonably consistent in this investigation by the use of the teflon film, but its rble:could, not' be negleetedo The magnitude of the frictional effect was evaluated by comparing the results obtained from compressive and tensile tests made on aluminum, an essentially isotropic material. The frictional contribution in the compression tests was taken to be that compressive true stress in excess of the tensile true stress for a corresponding true strain. From these experiments correction factors, f, were determined which have been used to convert all observed values of compressive stress to frictionless valueso These factors are: plane-strain = 489 funiaxial 91

14 An analysis of the frictional effects involved in compression testing is presented in Appendix Co Analysis of the data The plane-strain compression tests, as well as the uniaxial compression and tension tests, provided load vs. plastic deformation data which were converted to true stress vs. true strain using the relationships: (1) true = ln (L/L) true strain (2) =rue f P/ A e- true true stress where: L = specimen height in loading direction A = specimen original area normal to the loading direction P = applied load f = correction factor for friction The specimens were examined microscopically prior to compression testing and again after testing. Direct postcompression observation of the as-deformed surfaces was possible because of the protection to those surfaces provided by the teflon film, Active deformation modes were identified in the specimens by three-surface trace analysisO A few specimens were sectioned with an acid saw, mechanically polished, chemically polished and etched, and metallographically examined to check the interior structureo

RESULTS AND DISCUSSION Pure magnesium single crystal deformation The plane-strain compression stress-strain curves for the pure magnesium crystals are given in Figs. 2, 4 and 5. Fig. 2 shows the results of the compression along the c-axis (orientations A and B). The results of compression perpendicular to the unconstrained c-axis (orientations E and F) where 1012} twinning is not suppressed are presented in Fig, 4. Fig. 5 gives the results of compression perpendicular to the constrained c-axis (orientations C and D) where {1012} twinning is resisted. Easy basal glide results obtained from the compression of orientation G are presented in Fig. 4. Compression along the c-axis: The curves for orientations A and B (Fig. 2) differ significantly only in the values of fracture stress. Both orientations work hardened rapidly up to about 4% strain at a loading stress of 43 to 45 ksi. A decreasing slope at this point led to abrupt failure within a fraction of a percent additional strain. The dominant modes responsible for each of the three portions of the curves are discussed below, The initial 4% strain is attributed to (0001)(1210> basal slip since traces on this system were the only ones observed. Although c-axis compression would not activate basal slip if the alignment of the compression axis with the 15

16 vy c() 0) LU HnU LLJ D H -0 2 4 6 8 10 12 TRUE STRAIN (PERCENT) Stress vs. Strain in Pure Magnesium Single Crystals compressed Fig. 2. along the c-axis.

17 c-axis were ideal, only a very slight misalignment would be required for the basal slip systems to operate. Using values of Z= 70-psi for the critical resolved shear stress (2,9,14) and aC= 10 ks:i as the compressive stress to produce the first plastic strain (see Fig. 2), Schmid's law, f= @ cos C cos A, is satisfied when q (the angle between the compression and c axes) is only.40 or larger. Since a misalignment of this magnitude is not at all unreasonable, basal slip should not be unexpected. Although the slight misalignment that is involved can not account for 4% strain by itself, surface asperities..and imperfect constraint in conjunction with a small misalignment may well account for the initial strain in the curves of Fig. 2. At stresses above s40 ksi, sharp bands parallel to {10l1} were observed in both orientations. The decreased work hardening just prior to fracture undoubtedly resulted from the deformation associated with these bands. Such bands have been explained by Couling, Pashak and Sturkey (10) and by Reed-Hill (11) as resulting from {l0ll} twins followed almost immediately by {l1022} retwinning and -then by basal slip within the doubly twinned material. Fracture occurred along {1124} planes as can be observed in the specimen shown in Fig. 3. No evidence was found to indicate that {1124} slip or:I1124}'.twinning occurred as a prelude to {114} fracture. The fracture stress for orientation B, where constraint was imposed

18 (Iota) (1124) (2114) ii'ii (I To I) (1210)?:~:i'::*,'~ii~::I:::::. iii:-:i:i~ ~:: ii:iiiilii::i:i-il::.:.i:ii~:,iiiiii::iij~i~ i:-: (1210) (1101) 61101)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~':~1!i~1 (0001) Fig. 3. Fractures in Pure Magnesium Single Crystals. Top: The (0001) compression surface showing (l1241~ fracture in a B-oriented-specimen.. Bottom: The (161010 compression surface in a C-oriented specimen showing (10113 fracture. The sharp lines on the'top surface of the specimen are (101-13 traces. Note: In both specimens the small portion on the right has been tipped 9Q0 to better see the fracture surface.:iii':i:i-~iiiiii~ii~i'il.i::ii:-:;_:ii;::i:l~ ( ~ e J o }???~,,,,iii'?~!'~?:iii','~ii',,'!ii;::'~':'i::':'':~i~::iYii.: -i~l~-lii::iii::i~iii:i?:i':i?:i~iiii i::-':::::'i:ii~-~-~;::!:i~iii,:.::;:-......ii:::i:::i:i:. _::..:.....i...:~::~:,:j::-z:~:::i;-:::!-:~i::'~':.-iii!::il',':i: %:::::.::,i1!::~i:.:r::1iiiiiiiii~:::::::::;i:,~',i (o o, i:-i:::-~r::-:::::.::?.::::::::::~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i iiiiii.::~,,! ii-iii:i ~ ~:i-::ii::i_::iiii iiiii:iii!~;:!,:ah:i~:-::i:,:~:;j::::i:::.:.: jiiljii:i::i I;,:;;;iiiii -iiai?~ il~-i~iiii i::!:::-i::ii:~iii:~l:"::.i::::;:::i:.':::::..'i~: iiiii~~~~~~~~~~~,i~~~~~izi::i —i:;ili~~~~~~~~~~~~~~~~~~~~~~~~~ii'';:ilii,-l:::i::::::~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~~~~~::?y ~:~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ii~id:-ig~ ~ ~. }. ~rseti_-res:.?r::es:i.u. m S;:i.-Ie C:~-t's o: ~h 00' [1011] frac~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-i::-~tur. Tesarp~::~:::::line o teto srace of the ~speimenar [10~ t races. Note' In both specimens the small portion on the right~~~~~~_itiiiiiiiii~~i~ii~:_l:ii::::i::iil;'iiii:;~iiiiii'-:'ii~::l-ii has been t~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ii~pped:-:'i::i:'::i- 9 0~:: tobetr seethefraturesurace

19 along a l210) direction, was significantly greater than that for orientation A where constraint was imposed along a (010) direction. This is consistent with the fact that shear on active {1124} planes is resisted in orientation B by a component of the constraint stress, whereas in orientation A this is not the case. Couling (12) has reported {1124} fracture under compression in an environment of high hydrostatic pressure, and this fracture habit has also been observed by Reed Hill and Robertson (13) for magnesium under tension at -190~C. Wonsi-ewicz and Backofen (8), on the other hand, did not observe {1124} fracture under conditions of plane-strain compression similar to those of this investigation. Instead, in the limited number of specimens which they strained to fracture they reported the fracture surface orientation to be "variable", Magnesium compressed along the c-axis should not undergo {1012} twinning because this mode produces an extension in the c-axis direction, In spite of this numerous {1012- twins were found in specimens which had been compressed in orientations A and B. Wonsiewicz and Backofen (8) also observed this twinning mode under similar circumstances and experimentally determined that the {1012) twins which occur in compression along the c-axis are actually generated by residual stresses during the unloading of the compressive force. Compression perpendicular to the unconstrained c-axis:~ In plane-strain orientations E and F (10121 twinning is not

20 suppressed. Deformation by this mode was therefore expected to proceed until the crystals were completely twinned at about 6% strain and other deformation modes were then expected to come into play in the reoriented material to accommodate further strain. These expectations were borne out by the results that are presented in Figo 4. {lo12} twinning was initiated in orientation E at a loading stress of perhaps 1,000 psi, with the two equally favored twinning systems producing lattice rotations of the opposite sense. After the +86o30 reorientation due to twinning the crystal was only ~3o7O away from a B orientation. At'6% strain, twinning was complete (the theoretical strain for complete {1012} twinning in pure magnesium is 604%) and the stress then rose sharply to a maximum of slightly over 50 ksi at a total strain of 9%f {1011} banding within the essentially B-oriented material was evident during the final fraction of a percent strain and fracture occurred primarily along {1124} planes, with some fracture segments along {lOll}. Thus the deformation of the fully twinned crystals was almost identical to that of B-oriented specimens as described previously, Crystals of E orientation exhibited a fracture strength 8 to 10% greater than that of B-oriented crystals and this is attributed to the strengthening of the E-oriented crystals by the twin boundaries generated during the initial {1012} twinning process.

21 60 50 40 U) w IU) LLJ D H 30 20 100 0 2 4 6 TRUE STRAIN 8 (PERCENT) 10 12 Fig. 4. Stress vs. Strain in Pure Magnesium Single Crystals compressed perpendicular to the unconstrained c-axis, and compressed to activate easy basal glide.

22 F-oriented single crystals deformed in general very much like those of E orientation in that jl012} twinning produced an initial strain of about 6% (because of the orientation the theoretical strain in the compression direction for complete {1012} twinning of F-oriented crystals is 5.6%). This was followed by other deformation modes which produced additional strain within the twinned material, With the F orientation a greater loading stress is necessary to produce a given shear stress on the active {1012} twin planes than with the E orientationo This explains the higher level of loading stress for the initial^6% strain (Fig, 4). The four equally favored twinning systems reoriented the lattice so that the basal plane normal formed an angle of -310 with the loading stress direction rather than the'3.7~ of the twinned E orientation, Because of the realignment the twinned F was favorable for basal slip although such slip was resisted by the side constraint imposed by the plane-strain fixtureo Actually this constraint was relieved somewhat during the twinning because in this orientation the active 410121 systems produce a slight contraction in the constraint directionu A small amount of basal slip was therefore able to operate within the twins0 As the strain continued beyond the -6% to cause complete {1012} twinning the stress increased moderately to a maximum of about 32 ksi at a strain of approximately 10% where {1011} banding was activated within the reoriented lattice. When the strain was increased beyond this point

23 the crystal became so disrupted by the l1012} twinning, basal slip, 101O} banding, lattice rotation, kinking and cracking that the stress decreased again as the crystal continued to deform. It was not possible in the disrupted structure to identify a crystallographic fracture planeo Compression perpendicular to the constrained c-axis: The plane-strain compression curves for orientations C and D (Fig. 5) differ markedly from those for compression along the c-axis. Since these are the most favorable orientations for {1010(}1210) prism slip and {10ol}<(1210) pyramidal slip, it was anticipated that one or both of these modes would be active. However, no traces of slip on these systems could be, faund. Instead, deformation occurred primarily by a combination of {1012} twinning and {O1l} banding as shown in Fig. 6. Although compression perpendicular to the c-axis tends to activate {1012V twinning, this mode was not expected to operate since the lateral constraint in orientations C and D resisted the c-axis extension accompanying {1012} twinningo However, constraint was not perfect because of the elasticity of the lubricating film, the test channel walls and the specimen itself, so a limited amount of {1012} twinning could therefore occur. The resulting expansion against the constraint induced a lateral compressive stress which increased with the imposed load. When this lateral constraining stress reached a sufficiently high value, it caused {1011} twinning. The c-axis contraction caused by

24 60 50 O) -0 () LUr) 40 30 20 10 O 2 4 6 8 10 12 TRUE STRAIN (PERCENT) Fig. 5. Stress vs. Strain in Pure Magnesium Single Crystals compressed perpendicular to the constrained c-axis.

25 [000l]' CONSTRAINT S o0001] V CON!TI ['010] [iLOAD] LOAD.. 4 — 121o] ELONG. X50 X (a)Top (b) End [iloo] + LOAD 50 b21 o ELONG lOlo] LOAD I 77 TOP 4 i. ELONG (c)Side t X50,T (d) Schematic Fig. 6. Simultaneous {1012} Twinning and (1011) Banding in a C-oriented Single Crystal. Polished surfaces protected during deformation by teflon. (a) (1010) compression surface showing {1011) bands with band-widening and horizontal (1012} twins. (b) Unconstrained (1210) surface. Heavy traces are {1011} bands. (c) Constrained (0001) surface showing {1Oll0 bands and horizontal (1012) twins. (d) Schematic. Only one each of two active {1012) and four active (1011 systems are depicted. The load causes (1012) twinning with extension against constraint, building up a constraining stress. This then causes (1011} twinning which leads to banding, and elongation in the unconstrained direction.

26 the -1011} twins compensated for the simultaneous c-axis extension of the {1012} twins. The {1011} twinning initiated the {1011} banding described earliero In view of the foregoing it is evident that the resolved shear stresses to activate prism and pyramidal slip at room temperature in magnesium are both greater than that to activate the combination of {1012} twinning against constraint plus {1011 banding. The experimental data shows that the loading stress for activating -1011} banding for crystals of orientations C and D was about 20 ksio For a stress of this magnitude, Schmid's law gives values of -8.7 ksi for the resolved shear stress on operable prism planes and ~'7.6 ksi on pyramidal planes. Since these modes were not observed, the shear stresses to initiate prism and pyramidal slip must be greater than -8.7 ksi and -706 ksi respectively in pure magnesium at room temperature. These results are in significant disagreement with those of previous investigators who have reported ioom temperature prism slip in magnesium in tensiono (2, 4,15) ReedHill and Robertson (2) reported a CRSS of -5o7 ksi for prism slip and Flynn, Mote and Dorn ( 4) reported ^7.5 ksi. Both values were based upon a very few specimens and Flynn, Mote and Dorn further reported that only extremely limited strain by prism slip occurred before fracture, In an attempt to duplicate the experimental results of these investigators a monocrystal tensile specimen was

27 prepared with a {1010} tensile axis and strained at a rate of.00005 sec. This specimen underwent a limited amount of {1012} twinning owing to inadvertant bending stresses during testing and then deformed by {1011} banding at a loading stress of -20 ksi (i.e., a resolved shear stress of'8.7 ksi), which is identical to the value found by plane-strain compression. After a very small strain, fracture occurred on {1011} planes. Again, no evidence of prism slip could be observed. If prism slip can be activated at room temperature by shear stresses less than 8o7 ksi as reported by Reed-Hill and the others, it must have been suppressed in this investigation by the duplex loading of the plane-strain conditions and/or the occurrence of {1012} twinning. The stress-strain curve for orientation C is significantly steeper than that for orientation D in the region of initial strain. The initial deformation in both cases was due to basal slip that occurred as a result of surface asperities and minor misalignment of the specimen with respect to the loading direction. {1012} twinning activated against constraint also contributed to the initial strain. In the C orientation the two active {1012} twinning systems reoriented the twinned material -86o3~ to a new crystallographic orientation where the twinned basal planes were almost normal to the loading direction, and basal slip within the twinned material was therefore suppressed.

28 In the D orientation however, the resolving factor was such that the resolved shear stress on the four active {10ol2 twin planes was about 1/3 less than that in the C orientation for a given loading stress. Once the 1012-O twinning systems were activated in the D crystals though, the twinned material was realigned so that the twinned basal plane was -59~ out of the loading direction, making basal slip very favorable within the twins (see Figo 8). Thus, under the initial loading stresses, orientation D could accommodate plastic deformation by basal slip within the twinned material whereas orientation C could not, This accounts for the difference in the slopes of the initial portions of the stress-strain curves. In both orientations C and D, {101} banding was active at a loading stress of about 20 ksi after which the stress-strain curves were much less steep. Although the crystallographic resolution of stresses involved is different for the two orientations, the loading stresses for {1011} banding were essentially the same in both C and D. Theoretically these loading stresses should be identical as is demonstrated in Appendix D. Microscopic examination of C-oriented crystals showed that once the (1011 bands were formed, additional deformation occurred by a widening of the bands as indicated in Fig. 6. Furthermore, it was apparent that the bulk of the deformation strain occurred within the 1011} bands. The incremental steps that appeared on the surfaces of the

29 specimens could be associated with deformation in the 41011} bands, and the material within the bands was almost entirely recrystallized at room temperature soon after the deformation occurred (see Fig. 7). This is indicative of a high degree of local strain within these deformation areas. The evidence strongly suggests that deformation within the {1011} bands contributed directly to the further contraction of the crystal along the loading direction, rather than in conjunction with {1012} twinning, once the bands were initiated. If this were not the case and all of the contraction did occur by {1012} twinning, the loading stress would have been expected to increase sharply after the crystal had undergone complete {1012} twinning (at no more than 6.4L strain). An increase in loading stress of this nature was not observed. In the D orientation a different situation existed in that the {1Oil1 bands could not contribute directly to contraction in the loading direction because the bands formed principally along those 10il1} planes containing the loading direction, Post-deformation examination revealed little widening of the {1011 bands in this orientation. Rather, basal slip within the {1012} twins produced extensive deformation (see Fig. 8)o Single crystals of orientations C and D tended to undergo large strains before failure. Failures did occur, though not on {1124} planes as was the case in orientations A and B. Instead, cracks appeared in C-oriented crystals

30 (1101) O Io ) 77 (1012) 4-~ X50 Fig. 7. (1010) compression surface of a c-oriented pure magnesium single crystal showing horizontal (1012} twins and recrystallization within (1011} bands. Polished and etched after deformation. [o001] a. (101o ) (Io1 1) (0112) \ /(1102) (0001) l[ioo] ELONG. X 50 Fig. 8. (1210) compression surface of a D-oriented pure magnesium single crystal showing (1011} bands, horizontal basal slip, and basal slip in (1012) twins. Polished surface protected by teflon during deformation.

31 along {1011 bands after perhaps 10% strain and cracking became more widespread with additional strain. In some specimens fractures occurred rather abruptly on surfaces parallel to klOll}o A typical C-oriented specimen that fractured in this manner is shown in Fig. 3o Cracking was not as prevalent in the D orientation as in the C, but where it did occur it generally followed a 41'io1 trace. More often 102}1 twinning, (1011} banding, basal slip within (10o12 twins, lattice rotations and kinking so disrupted the structure after some 15% strain that the specimens lost much of their single crystal character and the crystallographic orientation of fractures could not be determinedo Basal slip: Orientation G is favorable for (0001) (1210) easy basal glide; that is, the single crystal is so aligned that all of the plastic strain can be accommodated by a single active basal slip system. Furthermore, in orientation G the basal pole lies,45~ from the loading direction, minimizing the load necessary to initiate basal slip0 Fig. 4 gives the stress-strain results for basal slip as obtained by plane-strain compression of G-oriented crystalso The critical resolved shear stress in pure magnesium was measured to be approximately 140 psi. That this is twice the value generally reported for basal slip in pure magnesium is understandable because in the plane-strain compression test a slight misalignment of the crystal with respect to the constraint direction creates additional resistance to basal slip. Furthermore, measurements are

32 affected by friction within the experimental apparatus and this is difficult to correct for at the low stresses involved. Despite this the results of the compression of Goriented specimens provided an order-of-magnitude check upon the operation of the plane-strain compression apparatus and also clearly demonstrated the extreme crystalloi graphic anisotropy to plastic deformation that exists in magnesium l011y Twinning: {101i twinning is the initial and key step to (101l} banding, and the activation stress for the twinning mode is also the stress to initiate (101l banding. Other investigators (8,16) have concluded that a simple critical resolved shear stress law does not exist for {1011} twinning It has been postulated by these investigators that stress concentrations produced by the intersection of various non-basal slip systems may be necessary for the activation of this twinning mode. The results obtained in this work tend to support this concept in that those orientations most favorable for non-basal slip exhibited the lowest shear stress to activate {1011} bandingo Thus, the C and D orientations, most favorable for non-basal slip, had resolved shear stresses of only -7 ksi when banding was activated, whereas orientations A, B and -1012}-twinned-E, in which it is theoretically impossible to generate the non-basal systems of -10O1O}1210) prism or 1{O1l} (1210) pyramidal slip, had high shear stresses (-19 ksi) when lOll} banding was initiated.

33 Reed-Hill and Robertson (17) reported minute amounts of {1122} slip out of the basal plane at -190~C and this mode could be a factor in the initiation of banding in orientations A, B and E. Orientation F, reoriented by {1012} twinning, is only moderately favorable for non-basal slip and exhibited a resolved shear stress of -10:ksi at the time that 1{01l} banding was activated. lOilY banding is a combined system of deformation consisting of {lO1i} twinning followed immediately by {1012} retwinning at a reduced activation shear stress, with this being followed by basal slip in the retwinned band at a still lower critical resolved shear stress. Thus, once a small volume of material has undergone {101) twinning as a result of a compressive stress, an extended strain within the twin should occur, and the stress required to continue strain in a band should be considerably less than that to initiate the band. The stress-strain curve would therefore be expected to have a marked yield point at the initiation of 441Ol} twinning. Yield points were not observed, however, (see Figs. 2, 4 and 5) and this might be explained by the extremely small volume of material in a 10O1l} twin as compared to the total volume of the specimen. High stresses in very localized regions of the crystal could be generated owing to surface asperities or to the interaction of various deformation systems. These stresses, high enough to activate local 1011) twinning, would be virtually impossible to measure because of their extremely localized

34 nature, and the apparent stress measured over the entire crystal would be significantly less than the activation stresso Since the stresses to actuate {1012} retwinning and subsequent basal slip in a band must be much less than those for the initial {1011 twinning, and because a yield point is not observed, it is reasoned that the stress indicated by the stress-strain curve at the beginning of {10ol} banding more nearly represents the stress to continue rather than to activate the bandingo This leads to the conclusion that the stress to initiate {0lOl- twinning would be very difficult to isolate and measure. Alloy single crystal deformation The results of plane-strain compression testing of single crystals of the two magnesium alloys, Mg-o.5Th and Mg-4%Li, are compared with the pure magnesium results in Figs, 9 through 14. Each figure presents a comparison of the two alloys with pure magnesium for a particular orientation. Magnesium plus 05 thorium: Single crystals of the.5 wt% thorium alloy exhibited initial strain hardening rates in orientations A, B, C and D roughly 70 greater than those encountered in pure magnesium crystals of the same orientations. As indicated earlier the initial shape of the stress-strain curve in these orientations is attributable to strain hardening of basal slip systems that were activated despite efforts to suppress this mode. Sheely et alo (18) has shown that thorium in magnesium greatly

35 60 50 (1210) ELONG <1010> CONSTRAINT 40/1*,)__,_ U 30 4 -- PURE MG. 3- /0 in 1' < —----- MG -.5 % TH w I:::0 M MG - 4% LI 20 10 0 _ I I I I 0 2 4 6 8 10 12 TRUE STRAIN (PERCENT) Fig. 9. Stress vs. Strain in A-oriented Single Crystals of magnesium and magnesium alloys.

36 61 (f) en (0) lLJ Ur Ch H 12 TRUE STRAIN (PERCENT) Fig. 10. Stress vs. Strain in B-oriented Single Crystals of magnesium and magnesium alloys.

37 6 - 40 Be I (1), 30 LU 20 MG -4% LI i MG -.5%TH PURE MG 0 2 4 6 8 10 12 TRUE STRAIN (PERCENT) Fig. 11. Stress vs. Strain in E-oriented Single Crystals of magnesium and magnesium alloys.

38 60 50,- 40 u) cLJ r 30 LJ cr -20 MG -4% LI MG -.5%TH I0 PURE MG O0 2 4 TRUE Fig. 12. Stress vs. Strain in and magnesium alloys. 6 8 STRAIN (PERCENT) 12 F-oriented Single Crystals of magnesium

39 60 50 - 40,) y f-01 U),U) w U) rr LJ 30 20 10 0o1 0 2 4 6 8 10 12 TRUE STRAIN (PERCENT) Fig. 13. Stress vs. Strain in C-oriented Single Crystals of magnesium and magnesium alloys.

40 U) Un UJ crt FD Hl 0 2 4 6 8 10 12 TRUE STRAIN (PERCENT) Fig. 14. Stress vs. Strain in D-oriented Single Crystals and magnesium alloys. of magnesium

41 increases the rate of strain hardening of the basal slip systems, which would account for the steeper stress-strain curves in the alloy crystals. In orientations E and F a hardening against 41012} twinning was encountered as is evident in Figs, 11 and 12, This too was considered to be a manifestation of the solution strengthening of the thorium, although the substructure present in the alloy single crystals may have contributed to the effect, All other deformation characteristics of the Mg-,55Th alloy single crystals were essentially the same as those of pure magnesium crystals. The fracture strengths and the modes of fracture were identical for the two materials and l10l1 banding was activated in the alloy in an equivalent manner and under loading stresses similar to those encountered in pure magnesium. Magnesium plus 4: lithium: Like the thorium alloy crystals, single crystals of the 4 wt% lithium alloy of magnesium exhibited initial strain hardening rates some 70 to 80% greater than those of pure magnesium crystals. This strengthening effect was also attributed to the solution strengthening of the alloying element on the basal slip and {1012} twinning systems. The somewhat greater hardening effect evident in the lithium alloy crystals is credited to the much greater fraction of solute element in the magnesiumlithium alloy (12 at% lithium vs..05 at% thorium).

42 In orientations C and D the magnesium-lithium crystals deformed by {10103 (1i210) prism slip, a mode not observed in either the pure magnesium or in Mg-.5%Th. However this mode was not unexpected as it had been previously reported (19,20) for o solid solution alloys of lithium in magnesium at room temperature. The typical prism slip lines that appeared on the surfaces of a deformed Mg-4%Li crystal of C orientation are shown in Fig, 15. The room-temperature critical resolved shear stress for this mode was found to be about 3.5 ksi, which compares favorably with the results of Yoshinaga and Horiuchi (20) Crystals of the D orientation strain hardened at a much faster rate than those of the C orientation. This is explained by the lattice rotation produced by the prism slipo Lattice rotation incident to slip deformation in compression reduces y, the angle between the normal to the slip plane and the loading direction. At the same time A, the angle between the slip direction and the loading direction, is increased toward a maximum of 900. For prism slip in the D orientation 4 is initially 300 and A is 600 (see Fig. 16a). Lattice rotation caused by prism slip on system 3 of Fig. 16a tends to reduce 3 and increase A3 thus "hardening" that system. However, lattice rotation due to slip on system 3 rotates system 3' to a more favorable crystallographic orientation and slip should then operate on system 31 causing an opposite rotation, As deformation continues the two systems should operate

43 [00oo1]' CONSTRAINT (0111) (1101) [ 121 ELON OlLOAD m X200 (b TpX250 (b)Top (a)End [10io] V LOAD [I210] ELONG, + X150 (c) Side Fig. 15. {1010) <1210> Prism Slip in a C-oriented Single Crystal of Mg-4fLi. (a) (1210) unconstrained surface, (b) (1010) compression surface showing prism slip. (c) (0001) constrained surface. Prism slip in material that has twinned by (1012) is shown plus (1011) bands. Polished surface protected by teflon during deformation.

44 C.\ \ a) D ORIENTATION C9 <y~ b) C ORIENTATION,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Fig. 16. {1010) <1210> Prism Slip Systems in Magnesium. (a) D orientation: Systems 3 and 3' active, System 4 inactive. (b) C orientation: Systems2 or 2' active, System 1 initially inactive but active after lattice rotation of 30~.

45 together, For this reason orientation D is stable with regard to lattice rotation and deformation will proceed with no net rotation. On the other hand orientation C is unstable (see Fig. 16b). Initially prism slip on either system 2 or 2' is equally likely, but once one system operates more than the other, it becomes the favored system. If, for example, slightly more slip were to occur on system 2, the lattice would then rotate so as to reduce bZ and to increase XK toward values of 45~, the orientation of easiest slip. Slip on system 2 would become more favorable, while the same rotation would make system 2' less favorable for slip. System 2 should therefore continue to operate. Because of this, orientation C is unstable with regard to lattice rotation under prism slip and once the slip has begun on a particular system it will continue on the same system. The lattice will be rotated toward the 450 orientation of easiest slip and on through this optimum toward the stable D orientation. Thus the C orientation can be expected to undergo as much as 300 of lattice rotation. During the first 15~ of this, a crystallographic "work softening" will be produced which tempers the basic strain hardening of the slip system, X-rays of deformed crystals have confirmed the stability of the D orientation and the tendency of the C orientation to rotate toward the D orientation during prism slip. The "softening" due to rotation in the C orientation

46 accounts for the difference between the strain hardening rates of the Mg-4%Li stress-strain curves of Figs. 13 and 14o Although crystals of D orientation strain hardened faster during prism slip than those of C, specimens of both orientations hardened at a sufficiently rapid rate so that after some initial deformation the stress necessary to produce additional strain had increased to a value great enough to activate (1011} banding, preceded as before by {1012} twinning. Fig. 15 shows the three surfaces of a C-oriented specimen in which this has occurred. Both l10111 bands and prism slip markings (within {1012} twins in this instance) are readily identified in the (0001) surface. Single crystals of the Mg-4%Li alloy under planestrain compression along the c-axis exhibited fracture stresses roughly 25% lower than those of either pure magnesium or Mg-.5%Th crystals. These results are indicated in Figs. 9, 10 and 11o Furthermore, fracture occurred along {101} planes instead of along L1124} planes as observed in both pure magnesium and Mg-.5%Th crystals of similar orientations. Apparently the 4% lithium in magnesium reduces the stress necessary for failure along j1011O planes to a value well below that required to initiate fracture along {1124}. The fracture stress of specimens of orientation A in

47 the Mg-4%Li alloy was about 5% greater than in B-oriented specimens. This is consistent with the fact that lateral constraint would offer a resistance to shear on active O101 planes in orientation A but not in orientation B. Deformation of textured polycrystalline magnesium Two major factors are responsible for the stress-strain characteristics of textured polycrystalline materials. These are the single crystal deformation characteristics of the material and the crystallographic texture of the polycrystalline aggregate. The single crystal deformation studies have demonstrated that the individual grains within a magnesium polycrystalline aggregate must deform by basal slip, prism slip (in the lithium alloy), {1012 twinning, o101l} banding or combinations of these. Because the critical resolved shear stress for basal slip is very low compared to the activation stresses for other plastic deformation modes in magnesium, basal slip accounts for much of the deformation in the polycrystalline aggregateo However, since there are only three basal slip systems (and only two of these are independent) in a single grain of magnesium, and because five independent deformation modes are required for an arbitrary shape change in any material (7), it is reasonable that modes other than basal slip must account for some of the deformation, Texture plays an extremely significant role in the

48 deformation of polycrystalline magnesium. because of the orientation dependence of strength in the individual grainso If the texture is very strong the polycrystalline material can be expected to exhibit deformation characteristics quite similar to those of single crystals of the same composition. If the polycrystalline material has a weak texture its deformation characteristics should not differ markedly from those of a randomly oriented polycrystalline aggregateo To assist in the identification of, and reference to, the polycrystalline specimens, each of the six orientations has been assigned a two letter identifying code. These are combinations of the letters Z (thickness direction), R (rolling direction) and T (transverse direction) with the first letter signifying the loading direction and the second letter the extension direction. Thus ZR specimens were compressed in the thickness direction while extension was permitted to operate in the rolling direction of the textured material, Polycrystalline specimens ZR and ZT have textures which resemble the orientations of single crystal specimens A and B, while TR and RT are most nearly like specimens C and D, and TZ and RZ resemble E and F. Textured polycrystalline pure magnesium: The texture of the polycrystalline pure magnesium under investigation was found to be that represented by the pole figure in Figo 17, This is a strong texture with the basal pole aligned predominantly in the thickness direction, and with considerably more rotation of the basal pole about the

49 TRANSVERSE DIRECTION 30 V _I__ 100 ROLLING DIRECTION Fig. 17. [0001] Pole Figure for Textured Pure Magnesium.

50 transverse direction than about the rolling direction. The stress-strain results of plane-strain compression of the textured pure magnesium specimens are presented in Fig. 18. The single crystal curves for pure magnesium are also presented for comparison. The similarity of the results of textured polycrystals and single crystals is apparent. The differences that do exist are attributable to the fact that the texture does not completely match a single crystal orientation. Orientation ZT (compression in the thickness direction and constraint along the rolling direction) most nearly approximates single crystal orientations A and B (compression along the c-axis), differing only in that the misalignment of many of the grains of the polycrystalline specimen allows a significant amount of basal slip. This difference leads to a greatly reduced maximum stress in the polycrystalline specimens. Nevertheless, orientation ZT was found to require the largest stress to bring about a given amount of initial strain of any of the polycrystalline orientations. Thi s is consistent with the resemblance of the ZT orientation to orientations A and B which are the strongest of the single crystal orientations. Orientation ZR (compression also in the thickness direction but with constraint along the transverse direction) is considerably softer than orientation ZTo This is because the basal pole is more widely distributed about the

51 _ e f = ruInF_ IVIl.UIl I UIVI U) LU TEXTURED PURE MAGNESIUM. 09: T q.' Z D f /~ 0 2 4 6 8 10 12 TRUE STRAIN (PERCENT) Fig. 18. Stress vs. Strain in Pure Magnesium. Top: For each of the single crystalline plane-strain orientations A, B, C, D, E, and F. Bottom: For each of the textured polycrystalline plane-strain orientations ZT, RT, ZR, TZ, TR and RZ, and for randomly oriented polycrystalline material. ~. crystalline material.

52 transverse direction and basal slip in the ZR-oriented specimens is therefore favorable in a greater percent of the grains. Orientations RT and TR bear a similarity to single crystal orientations C and D although, like the other polycrystalline orientations, they too contain many grains which are favorably oriented for basal slip. Since basal slip was favorable in some of the grains, the RT and TR polycrystalline specimens were deformed during the early stages of loading more easily than were the single crystals. In both the RT and TR textured specimens the deformation produced by the 1011} banding and band widening was augmented in numerous grains by basal slip and/or {1012} twinning where the orientations were favorable for these modes. Due to the activation of different modes in the various grains of the polycrystalline specimens the texture became more and more random as deformation progressed, The relatively widespread operation of a single mode, such as the {1011 band widening in single crystal orientation C, was not possible and the stress to continue deformation increased steadily with strain, At approximately 6% strain the stress in the polycrystalline specimens rose above the maximum values observed for single crystal orientation C and D. Values as high as 35 ksi were attained in polycrystalline orientation TR, some 20% higher than the maximum values observed in the single crystals, Orientations TZ and RZ of the textured pure magnesium

53 exhibited extensive 1012} twinning during the first 5 to 7% strain. After this initial deformation the stress-strain curves rose more steeply as the twinning approached completion and other deformation modes were required. In these specimens the crystallographic texture resembled single crystal orientations E and F (c-axis unconstrained). The fact that the polycrystalline strengths during {1012} twinning were much greater than those of the single crystal orientations is attributable to two factors. First, the polycrystalline specimens were not able, because of the diversity of the grain orientations, to accommodate all of the strain by {1012} twinning as was possible in the single crystals. Instead, other modes were forced to participate in some of the grains, requiring a higher stress. In addition, the polycrystalline material was more resistant to {10121 twinning owing to a grain-size effect. In a single crystal, once a 10i2} twin system is activated, strain can be extended relatively easily by the operation of the twinning system through the full dimension of the specimeno In a polycrystal, however, a system can operate only within the small volume of a grain, and other systems must be activated in other grains to extend the strain. This causes a hardening that varies with grain size, and this is credited in this instance for much of the difference between the polycrystalline and single crystal resultso Randomly oriented specimen results are also presented in Fig. 18 by a curve for specimens of cast cell magnesium

54 (99.96% Mg). Since three orthogonal specimen orientations of the cell magnesium were tested and found to be very similar, it was concluded that the material was essentially random in orientation. As might be expected, the curve for these randomly oriented specimens is a rather general average of the curves for the textured materialso Textured polycrystalline Mg-.5%Th: The single crystal deformation results showed that the solution hardening of magnesium by.5 wt% thorium is very significant for both basal slip and ~1012} twinning. The differences between deformation characteristics of polycrystalline specimens of the Mg-.5%Th alloy and those of pure magnesium are explained by this solution hardening as well as by the differences in the pole figures for the two materials (FigSo 19 and 17), The Mg-o5%Th alloy has a much weaker crystallographic texture than that of the pure magnesium, the peak intensity being about one-half as great. Furthermore, the pole figure is more nearly symmetrical about the thickness direction. The stress-strain relationships found for the textured Mg-.5oTh specimens are presented in Fig, 20 together with those for single crystals of the same alloy. The effect of the texture symmetry about the thickness direction is readily apparent as orientations ZTTh and ZRTh produced almost identical stress-strain curves. In a like manner pairs of similar curves resulted from TRTh and RTTh and from TZTh and RZTh

55 Fig. 19. [0001] Pole Figure for Textured Mg-.5%Th.

56 _ I D U) ZRThlow'-m -W LL^ 30 - ZTS> ^::Z TTh SN'' 30 F.* s'o TRUE STRAIN (PERCENT) Fig. 20. Stress vs. Str n in M. RZ5 Th single crystalline plane-strain orientations A, B, C, D, E, and F. Bottom: For each of the textured polycrystalline plane-strain orientations ZT, RT, ZR, TZ, TR, and RZ.

57 The strengthening of the.5 thorium influenced the stress-strain relationships in all polycrystalline orientations in the form of a very steep rise in the stress to cause the first ~.2% strain. This is consistent with the high critical resolved shear stresses for basal slip and for t1012} twinning in the alloy. The fact that the ZTTh and ZRTh specimens (compression in the thickness direction) were only 3 to 4 ksi stronger than the TRTh and RTTh specimens (compression perpendicular to the constrained thickness direction) is attributed to the relatively weaker texture of the alloy as compared to that for pure magnesium. The markedly greater activation stresses for {1012} twinning in orientations RZTh and TZTh (compression perpendicular to the unconstrained thickness direction) were due to the hardening of the {1012} twinning systems by the alloying element, to the diversity of grain orientations associated with the much less intense texture than that for the pure metal, and to the grain size effect that was described earlier, Textured polycrystalline Mg-4%Li: The single crystal results demonstrated that the solution hardening of magnesium by 4 wt% lithium is slightly greater than that by.5 wt% thorium. The solution strengthening affects the deformation characteristics of the textured material in a similar manner. It accounts for the very steep initial portion of the stress-strain curves that are presented in Fig. 22. The pole figure of the magnesium-lithium polycrystalline

58 material (Fig. 21) indicates a relatively weak texture with a peak intensity about one-third of that of the pure magnesium and less than that of the thorium alloyo The texture is almost symmetrical about the thickness direction with a slightly greater divergence about the rolling direction than about the transverse. The weakness of the texture explains the low strengths of the ZRLi and the ZTLi specimens (compression in the thickness direction) relative to pure magnesium and magnesium-thorium alloy specimens of similar orientations. The high activation stresses for {1012} twinning in TZLi and RZLi specimens (compression perpendicular to the unconstrained thickness direction) is a consequence of the weak texture of the lithium. alloy and the effect of the grain size. The symmetry of the pole figure about the thickness direction accounts for the virtually identical behavior of the ZTLi and ZRLi specimens, of the TRLi and RTLi specimens, and of the TZLi and RZLi specimens. Specimens of TRLi and RTLi orientations (compression perpendicular to the thickness direction) exhibited strengths about 30 below those of the ZRLi and ZTLi orientations. This is in significant contrast to the behavior of the thorium alloy and is a direct result of the prism slip that is active in the lithium alloyo Yield loci of textured materials One of the more useful characteristics of crystallographically textured metals is the strengthening that can

59 TRANSVERSE DIRECTION ROLLING DIRECTION 100 Fig. 21. [0001] Pole Figure for Textured Mg-4%Li.

60 C-eM / -.t SINGLE CRYST/ MG 4-%Li w I C) LL 30 ZRLI w= 20 Zf ^^ RTLLI^ ^ 0~1~~ O ~..OL O0 TRUE STRAIN (PERCENT ttO~ns ZTY of the textu d PolycA P Ba^ C tqe For eT re' P l, cryst ill Paane^.sT. nd r. Botto m. and RZ Ine Plane-st.Al ain Orien_

61 occur under combined stresses. Especially significant in this regard are the HCP metals with their inherent anisotropy as they often exhibit a pronounced increase in resistance to yielding under conditions of biaxial tension as compared to that under uniaxial loading. Both Tresca and von Mises postulated criteria for yielding of isotropic materials under conditions of combined stresses. Hill (21) has generalized the von Mises criterion in formulating a yield criterion for anisotropic materials. The Hill criterion, however, predicts loci which are centered about the origin, a restriction which is unsatisfactory for materials such as the HCP metals which deform extensively by twinning (22). At present there is no simple mathematical yield criterion for such materials, and considerable experimental data is required to establish the yielding behavior for a given material of this type (23). It is convenient to represent yield criteria graphically by assuming conditions of plane stress, i.e. the stress in one of the three orthogonal directions is taken to be zero. This representation of yield criteria is not severely restrictive since yielding is virtually insensitive to the level of hydrostatic stress, and any state of triaxial stress can therefore be represented by a hydrostatic stress plus a plane-stress state. The yLeld locus represents all of the various combinations of biaxial stress that will produce yielding,

62 In the experimental determination of a yield locus by mechanical testing, two types of data are useful; the values of the stresses at yielding serve to fix points on the locus, and measurements of the plastic strains accompanying yielding can be used to establish the slopes of the locus at these points. The significance of the plastic strain measurements follows from the principle of normality of the plastic strain vector to the yield locus (24), so that the slope of the plane-stress locus, tanE (io.e dO//dcx ), y x equals -d x/dy Measureemements of the lateral strains as well as the yield stresses were made in two uniaxial tension and three uniaxial compression tests to fix five points on the locus (a, c, e, f and i in Fig. 23) and the slopes at these points. A sixth test, tension in the thickness direction, was considered impractical. The- yield stresses observed in the plane-strain compression tests presented earlier were used to fix the stresses at which tane = 0 00, and 1 (lines d and h, b and g, and k and j in Fig. 23). The resulting yield loci, at 1% strain, are shown in Fig. 24 and the data used to construct them are listed in Table 3. Pure magnesium yield locus: The yield locus for the textured pure magnesium (Fig. 24) is extremely interesting because of its highly non-symmetrical shape. Fundamentally, the non-symmetry consists of two distinct factors: the greater strength in tension than'.in compression,:and the greater tensile strength in the transverse direction than

63 Tensile tTensiled b k 4 — a --- Tensile a Anisotropy with Rotational__ Symmetry about Z (Hill) Compressive Fig. 23. Plane-stress (cz = 0) Yield Locus (schematic). Points and slopes are determined as follows: a and f, x-direction uniaxial tension and compression; e and i, y-direction uniaxial tension and compression; c, z-direction uniaxial compression; b and d, z-direction plane-strain compression; g and k, x-direction plane-strain compression; h and j, y-direction plane-strain compression. The loci predicted by von Mises and Hill criteria are shown for comparison. Adapted from Hosford.23

64 0-TRANSV. DIR. 30H () U) U) Ld wI(n 0 UT tr Hi > nr cr I 20 MG -.5%TH PURE MG / iMG -/4%/L ) /1 lO i OF I t / O-ROLL, DIR. 101-.0 20 -10 ROLLING 0 10 20 DIRECTION STRESS (KSI) Fig. 24. %o Strain Yield Loci for Biaxial Stresses in Textured Polycrystalline Magnesium and Magnesium Alloys with Thorium and with Lithium.

Table 3. Experimentally Determined Yield Stresses for 1% Strain in Textured Magnesium Sheets Pure Mg Mg-.5%Th Mg-4%Li Locus Specimen Stress Slope Stress Slope Stress Slope Point orient, (ksi) (ksi) (ksi) a tens 10.5 6.5 26.7 4.6 13.9 2.5 7b ZR 10.9 oo 27,0 o 16.7 o omp 10.3 -2,5 27.5 -.7 14,3 -.7 comp d ZT 19.5 0 26.6 0 159 0 e Ttens 18,8.37 24.5 *37 11,6.50 Rcomp 3.7 9.5 14.2 17.0 10.0 4.5 g RZ 3.8 oo 143 oo 10.1 oo h TZ 4.4 0 14.7 0 100 0 i Tcom 4,1.18 14.6 07 9.4.14 i TR 10.8 1.0 24.6 1.0 10.7 1.0 k RT 15.0 1.0 24.4 1.0 11,2 1.0 65

66 in the rolling direction. The low strengths in compression are due to yielding by 1012} twinning since this mode is active in compression but not in tension along the c-axis. The texture, with strong alignment of the basal pole in the thickness direction (Fig. 17), is such that {1012} twinning is readily activated by compression perpendicular to this direction. The tensile strength in the rolling direction is significantly lower than in the transverse direction owing to the greater spread of the texture about the transverse direction, thus permitting more widespread operation of basal slip under conditions of rolling direction stress. Mg-o5.Th yield locus: The yield locus for the textured magnesium-thorium alloy (Fig. 24) is much more elliptical than is the locus for pure magnesium, In the thorium-bearing alloy the yield strengths for the transverse and rolling directions are essentially identical, and also are markedly greater than those of the pure metal. These observations are explained by the relatively symmetrical pole figure (Fig. 19) and the solution hardening effect of the thorium. In addition, the compressive yield strengths of the alloy are from 60 to 65% of the values for the tensile yield strengths, whereas in the pure metal the compressive yield strengths are only 20 to 40 of the tensile values. This reflects the greater effect of solution hardening on {1012} twinning than on P10o11 banding that was observed in the single crystal tests, in addition to the weaker texture.

67 Mg-4%Li yield locus: The yield locus for the textured magnesium-lithium material is similar in shape to that for the thorium-bearing alloy (see Fig. 24), but with greatly reduced yield stress values even though solute strengthening is slightly greater in the Mg-4Li. These reduced values are the result of the occurrence of prism slip and of the weaker crystallographic texture. The prism slip is considered to have a greater influence in reducing the strengths in the second and fourth quadrants of the yield locus because the biaxial stress states (orthogonal combi — nations of tension and compression) in these quadrants are the most favorable for the prism slip mode. The reduction of yield strengths in the first arnd third quadrants, on the other hand, is attributed primarily to the weak texture of the alloy which allows the activation of basal slip in a greater fraction of the grains. The compressive yield strengths more nearly approach the tensile values in the lithium-bearing alloy also because of the weakness of the texture.

CONCLUSIONS As a result of this investigation the following conclusions have been drawn: 1. {10ll} banding, consisting of lo0ll} twinning followed by {1012} retwinning and basal slip within the doubly twinned band, is a significant deformation mechanism, along with basal slip and {1012} twinning, in pure magnesium at room temperature. Neither 1010} (1210) prism slip nor {1011} (1210) pyramidal slip, both previously reported, are confirmed at room temperature Instead, in crystals ideally oriented for these modes, deformation occurs by 10lOll bandi-ng operating simultaneously with {1012} twinningo It is concluded that activation. shear stresses for prism and pyramidal slip are greater at room temperature than ^8.7 ksi and -7.6 ksi respectivelyo 2o Fracture in pure magnesium occurs on {1124} under compression along the c-axis, and on {10l1 by compression perpendicular to the c-axis0 3. Thorium of.5 wt% in magnesium raises the activation stresses for basal slip and {1012} twinning, but not for {1011} banding or for fractureo 4, Lithium of 4 wt% in magnesium reduces the resistance to {1010} (1210) prism slip so that it becomes active at room temperature, while the basal slip and {1012} twinning systems are hardened Under compression along the 68

69 c-axis, 4 wt% lithium lowers the fracture strength and changes the fracture habit from l1124} to [1Oll. 5. Yielding in polycrystalline aggregates of magnesium is extremely dependent on the texture of the material and the shear stresses required to activate the various deformation modes.

APPENDIX A THE PRODUCTION OF SINGLE CRYSTALS The single crystals necessary for plane-strain compression specimens were grown from seed crystals by a modified Bridgeman technique,. The seed crystals were grown under helium in a solid graphite channel in a horizontal resistance furnace moving at a speed of approximately 1 cm/hro Seed crystals thus produced were checked for crystallographic orientation by the Laue back-reflection x-ray method. Each of those with an orientation suitable for use in seeding was then clamped into a fixture which allowed accurate orientation adjustment by three rotations, The fixture was designed to hold both a seed and the polycrystalline blank from which the single crystal was to be grown. By x-raying the seed in the fixture it was accurately oriented with respect to the polycrystalline blank, and then heliarc welded to one end of the 1/4 in. by 1/2 ino by 6 in. blanko Each polycrystalline blank was converted into a single crystal of a desired orientation in a graphite mold utilized to hold the blank and seedo The mold was placed in the furnace which was now positioned nearly vertically to facilitate the gravity feeding of the molten metal to the solidifying crystal during the growing process0 The furnace was brought up to temperature while centered about the 70

71 upper end of the mold, melting the upper portion of the polycrystalline blank. The furnace was then lowered slowly until the blank was entirely molten and the liquid-solid interface was stabilized in the single crystal seed, At this point an electric motor was used to move the furnace upward at about 1 cm/hr, allowing the molten metal to solidify with';the liquid-solid interface moving upward from the seed. A helium atmosphere was employed in the furnace during the crystal growing operation, The center of the furnace was maintained at approximately 60~C above the melting point of magnesium with an appropriate fixed setting of the power inputs For the two compositions, pure magnesium and Mg-o5%Th, a cylindrical split:-mold of solid graphite was employed that incorporated a channel of rectangular cross section (1/4 in. by 1/2 ino) running the length of the mold. The channel was enlarged at the bottom of the mold for a length of about three.inches to permit the seed to be tightly packed in powdered graphite. The mold was held together with graphite caps at both ends. The upper cap had a small hole to vent the mold to the helium atmosphere of the furnace tube and the lower cap was equipped with a thermocouple so that the seed temperature might be monitored during the crystal growing process, Because molten magnesium-lithium alloys react with graphite a modified mold was developed for growing crystals of the 4% lithium alloy, Instead of a solid split-mold,

72 a graphite hollow tube split-mold was used in which the entire blank and its attached seed could be packed in powdered MgO. A large opening through the MgO packing at the upper end served to accommodate the expansion and contraction of the metal during the: crystal growing operation. Except for the modified mold, the technique for growing single crystals of Mg-4%Li was identical to that used with the other materialse Although pure magnesium crystals could be grown at furnace speeds of up to at least 3 cm/hr, furnace speeds of more than about 1 cm/hr resulted in the nucleation of random grains in alloy crystals~ Furthermore, the alloy compositions were prone to the development of randomly oriented grains at the seed-to-blank junction unless a generous taper was provided at that point. Microscopically, the pure magnesium crystals appeared to be relatively free from defects and substructure. The alloy crystals, however, exhibited well developed substructure which was readily discernible under the microscope. Representative single crystals of the two allo-y compositions were analyzed by Dow Chemical Company for endto-end segregation of the alloying elements. Spectrographic analyses of the Mg-o5%Th alloy disclosed that endto-end segregation was significant with the thorium concentration increasing from approximately.3 wt% at midlength to about.5 wt% at the last-to-freeze end of the crystal. Chemical analyses indicated that end-to-end

73 segregation was less severe in the Mg-4%Li alloy with the lithium concentration ranging from 3.2% at mid-length to 3.8% at the last-to-freeze end. In view of these:results all alloy single crystal specimens were taken from locations in the crystals between mid-length and the last-to-freeze end

APPENDIX B PLANE-STRAIN COMPRESSION TESTING PROCEDURE Plane-strain compression tests were made in a hardened steel fixture on an Instron testing machine, The test fixture consisted of a channel with provision for width adjustment and an indentor designed to fit down into the channel, The indentor was mounted on the end of a supporting shaft which also served to actuate a cantilever beam deflectometer bolted to the top of the steel channel (see Fig, 1)o The deflectometer utilized two SR-4 strain gauges as sensing elements permanently affixed to the cantilever beam. The channel portion of the test fixture was bolted to the base of a steel die holder and the indentor support shaft was affixed to the movable top piece of the die holder (see Fig, 1). The die holder provided accurate and reproducible alignment of the indentor in the channel and also insured precise vertical movement of the indentor during compressiono The specimens were placed in the test fixture with 2-mil teflon film between the specimen-and the contacting surfaces of the channel, The adjustable side of the fixture was then tightened with finger pressure on the adjusting screw to provide width constraint of the specimen during the testo The indentor was placed on the top -.of the specimen with teflon film between the indentor and the 74

75 specimen, For testing, the die holder was positioned on the platform of the compression load cell of the Instron and the load was applied to the top of the die holder by the Instron crosshead. The specimen was compressed at a rate of.01 in/min (a strain rate of.00o67 sec-1 for the 1/4 in. specimens). Load data was taken directly from the Instron recorder while deformation data was obtained from three independent sources which were used to check one another, The first of these was the crosshead displacement which was recorded automatically by the Instron recorder. This was corrected to account for the elasticity of the Instron and test fixture by running calibrating tests on a hardened steel specimen. A second system utilized to measure deformation was the SR-4 deflectometer connected to a strain indicator. The third source of deformation data was micrometer measurements of the specimen before and after compression. In some instances compression tests were halted at selected increments of load and the specimen removed from the fixture so that it could be measured with the micrometer to insure positive plastic deformation data in critical regions of the stress-strain curve. A dial indicator actuated by the movable jaw of the test fixture served to insure that the width constraint that existed before removal of the specimen was accurately reapplied when the specimen was reinserted into the fixture for further deformation. This

76 technique was most helpful in the low strain region of the curve where plastic strain was just beginning.

APPENDIX C ANALYSIS OF THE FRICTIONAL EFFECTS IN COMPRESSION TESTS The stress relationships in plane-strain compression can be represented as indicated below. The y direction has been taken as the axis of compression, z the lateral (constraint) direction, and x the direction of extension. The coefficient of friction is indicated by A; and L, h and w are the dimensions of the specimen in the respective directions, x, y and z. aL-y W rU a~, —-----'x- do'x / OLZ Uxt -xd — Ax - dx - L Consider the forces acting on an element of the specimen under the applied stress, o. A force balance in the x y direction gives: (hw)o + 2(hdx) oZ + 2(wdx)pa = (hw)(x + da ) (1) xA. z-i y x2\. xy 77

78 In plane-strain, the lateral constraining stress, Cz, may be approximated by assuming that the Hencky-Mises flow rules apply even though the material is anisotropic, This gives: Ez = / - (%x + %y7 (2) In plane-strain, where Ez = 0 (2) leads to: z C - 2 (x + ) (3) For plane-strain yielding (where 0o = yield stress): aCT ~~ -rO~~~~ =~ ~(4) y -:x o cY =o~ - T (5) x y o d = dy' (6) Substituting (3) and (5) into (1) and simplifying: dcrx = dx 2(h+w)o - ho (7) x hw y 0 Substituting (6) into (7): dy =' dx 2(h+w) - ho (8) y hw ~ y 04 2h~w h 2 Mdx d= y / (o - 2 ) (9) Integrating: 2wfx %= f d'y 2-(h+w) A dx do /3 ( - h - 0 hw 0 T y / 20w o~~~~~s 2'hw0o)

79 2 (hlw)n hw t4=n h ~ [ 1' h )] o lff"- 2(h+w)] (10) Rewriting, and letting k = h/2(h+w): -kw Ty = k + (Co o- k ) e The average compressive stress in plane-strain, at yielding is: p Yrs C dx fdx T-, y ps ps L/2 -L/2 f0 [kc + (0% - kar)e'w j dx 2 dx o 0 (11) Y5s' (12) (13) (14) = kO + 2 (T - ky) o L o o ) "k r ML 1 [e 2kw - 2L of Q 2kw: By series expansion TYps Ypsx 2 kw AL A2 + k- + ( - k ) 2k + ( 0 0 bA7 2k-w + (2Nkw} ~ - (:5 k~CY + (ly - k G' 0 0 (16) Substituting for k: ps ps 0 1 + AL (2W+h)1 L C jur (17)

80 In this work, wz2h for all specimens. Therefore: OT = ~o [0+^ 8h- (18) Yps For frictionless plane-strain: y = 1.15Cr (19) From the aluminum data (where L = 18h): 0 = 1.33o (20) Yps Ytensile Substituting (20) into (19): Go = 1.15(yPs / 1.33) (21) yps Substituting for ao from (18): aY / 1 + (1.85/8)(5/8) =.86T (22) Yps Yps A =.147 (23) Let f be a frictional factor such that: = f" (24) o y Substituting (18) into (24) and using the average L/h of 103: plane-strain = l/1 + (L/h)(5/8)A, = 1/[ + (1.3)(5/8)(.147) fplane-strain =.89 for plane strain loading

81 For uniaxial compression, a =O, and a similar mathematical analysis will produce: C - = l [l + (L/h) (/2)4 (25) "ua -J Substituting (25) into (24): funiaxial = 1/P1 + (L/h) (l/2) ] funiaxial = *91 for uniaxial loading

APPENDIX D YIELD STRESSES FOR t101- BANDING IN ORIENTATIONS C AND D The {lOll banding mechanism in orientations C and D involves the simultaneous operation of 010121 twinning against c-axis constraint and {lOl1 twinning as a result of the constraint stress, The shear stress to activate the {1011} twinning is generated by the constraining stress built up through the operation of {1012} twinning. Although the {1011} twinning probably has an activation shear stress greater than the average stress on the crystal at the time banding begins, the latter is taken to be representative of the yield stress for banding in this analysis. Furthermore, because orientations C and D are equally favorable for non-basal slip, any orientation factor in the activation stress for {1Oll twinning is assumed to be identical for the two orientations. Therefore, for C and D-oriented crystals, one activation shear stress is assumed to exist for {1011} banding and another for {1012} twinning. The compressive stress to cause yielding in each orientation, then, is that loading stress that raises the constraint stress sufficiently to activate {1011 banding on an appropriate system. The analysis developed here is only assumed to hold for the beginning of banding where {1012} twinning against c-axis constraint operates simultaneously with {1011} twinning. 82

83 To show that the compressive stress for yielding is the same in orientation C as it is in orientation D, identical expressions are derived below for both. Let: = shear stress to activate {1012} twins p = shear stress to activate {1011} bands =compressive load stress at yielding Sy T = constraint stress at yielding m = Schmid's law factor (cos OcosA) Orientation C At yielding, {1012} twinning on systems 1 is activated by CG y 2 with 71 = 47~ and O = 43~.1011 banding is activated by Cz on systems 2 with <2 = 620 and A2 = (180-28)~. Therefore: my 1 = cos470cos43~ mZ1 = cos430cos(180-47) mz32 = cos62~cos(180-28)~ = m 2 = cos28~cos62~cos260 = Resolution of stresses at yielding gives:' = ymy/l + zmzl 13 = (y-myy2 + zmzA2.499 -.499 -.414.414cos260~ (1) (2) Rewriting (1): rz -.1 (c -.499(y) yT (3)

84 Substituting (3) into (2):.414 fi = y.414cos2600 + (o-.499) (C = (3 -.83so)/[-.414(1-cos260)]: = (p -.83o)/ [.i44cos230~] Orientation D At yielding, {1012} twinning is activated by cr on systems 3 y and {10l1} banding is activated 4 by OV on systems 4. Then: / i~~~~~~ (4) (5) (6) my3 = cos47~cos43~cos230 =.499cos230~ mz,3 = cos43~cos(180-47) = -.499 mz4 = cos62cos(180-28)0 = -.414 my/04 = cos280cos620cos290 = 0 Resolution of stresses at yielding gives: o(=' V yo + TM ( 3 ymJTs^ t CT zmz 3 = ymy34 + GzmZ94 Rewriting (7): z = — T49 ( - (y.499cos 30 ) Substituting (9) into (8): +.414 2 0)99cos23 yo + (o- r. 499cos30) Y (7) (8) (9) (10)

85 CT = (p -.83o0)/[ l44cos2o] y 3 (11) Equations (6) and (11) are identical and therefore: YC YDD Thus, the loading stresses for {1011} banding are identical in orientations C and D.

BIBLIOGRAPHY 1. Co S. Roberts, Magnesium and its Alloys, Chapt. 4, Wiley and Sons (1960). 2. R, E. Reed-Hill and W. D. Robertson, "Deformation of Magnesium Single Crystals by Non-basal Slip", AIME Trans., 209, p 496 (1957)o 30 F. Eo Hauser, PO R. Landon and J. Eo Dorn, "Deformation and Fracture Mechanisms of Polycrystalline Magnesium at Low Temperatures", Transo ASM, 48, p 986 (1955). 4, PO W. Flynn, Jo Mote and J. E. Dorn, "On Thermally Activated Mechanism of Prismatic Slip in Magnesium Single Crystals", AIME Trans., 221, p 1148 (1961). 5, Co S. Barrett and C, T. Haller, "Twinning in Polycrystalline Magnesium", AIME Transo, 171, p 246 (1947)0 6. R. E. Reed-Hill and W. D. Robertson, "Additional Modes of Deformation Twinning in Magnesium", Acta Met, 5, P 717 (1957). 7. Go I. Taylor, "Plastic Strain in Metals", J. Inst. Metals, 62, p 307 (1938). 8. B. C. Wonsiewicz and W. A, Backofen, to be published (Wonsiewicz' Ph.. DoThesis, MIT, 1966) 9, E. CO Burke and W. R. Hibbard, "Plastic Deformation of Magnesium Single Crystals", AIME Trans., 194, P 295 (1952)o 10, S. Lo Couling, J. Fo Pashak and Lo Sturkey, "Unique Deformation and Aging Characteristics of Certain Mg-based Alloys", Trans. ASM, 51, p 94 (1959)o 11. Ro E. Reed-Hill, "A Study of the {10o1l and 1013}1 Twinning Modes in Magnesium", AIME Trans., 218, p 554 (1.960). - 12, S, L. Couling, Dow Chemical Company, private communication, 13o Ro E. Reed-Hill and W. D. Robertson, "Crystallographic Characteristics of Fracture in Magnesium Single Crystals"t, Acta Met, 5, p 728 (1957) 140 W. Fo Sheely and Ro Ro Nash, "Mechanical Properties of Magnesium Monocrystals", AIME Transo, 218, p 417 (1960). 86

87 15. H. Yoshinaga and R. Horiuchi, "On the Nonbasal Slip in Magnesium Crystals", Trans. Jap. Inst. of Metals, 5, p 14 (1963). 16. R. L. Bell and R. W. Cahn, "The Dynamics of Twinning and the Interrelation of Slip and Twinning in Zinc Crystals", Proc. Roy. Soc., A239, p 494 (1957). 17o Ro E. Reed-Hill and W. D. Robertson, "Pyramidal Slip in Magnesium", AIME Trans,, 212, p 256 (1958)o 18. W. F. Sheely, E. D, Levine and Ro R. Nash, "Temperature Dependence of the Critical Stress for Slip in Magnesium Alloy Monocrystals", AIME Trans,, 215, p 693 (1959). 19. Fo Eo Hauser, P. R. Landon and J, Eo Dorn, "Deformation and Fracture of o4 Solid Solution of Lithium in Magnesium't Trans. ASM, 50, p 856 (1958), 20o H. Yoshinaga and R. Horiuchi, "On the Flow Stress of Q(Solid Solution Mg-Li Alloy Single Crystals", Trans. Japo Insto of Metals, _4, p 134 (1963). 21. R. Hill, Mathematical Theory of Plasticity, Chapto XII~ Oxford Univo Press (1960). 22, W. F. Hosford, Jr. and W. A. Backofen, "Strength and Plasticity of Textured Metals", Fundamentals of Deformation Processing, Syracuse Univ. Press, p 259 (1964) o 23. W. F. Hosford, Jr., "Texture Strengthening", ASM Metals Engr. Qtrlyo, 6, No. 4, p 13 (1966) 24, D. Co Drucker, "A More Fundamental Approach to Plastic Stress-Strain Relations", Proc, 1st U.S. Nato Cong. of Appl. Mech., p 487 (1951).

89 DATA PLaIN-STRAIN COMPdESSION Plain-strain compression data is presented in four columns for each specimen as follows: lst column - applied load (thousands of pounds) 2nd column - height of specimen in load direction (inches) 3rd column - calculated true stress (ksi) 4th column - calculated true strain (percent) Specimen original width and length is given in parentheses following the specimen identification. *denotes specimen fracture $ indicates that the test was halted after each incrernnt of load, the specimen removed and measured with micrometers, and the specimen then reinserted and the load reapplied. The specimen heights given are micrometer data. PURE MAGNESIUM SINGLE CHYSTALS (in plane-strain compression): All (.485"x.450") 0.0.2516 0.0 0.00 3.0.2509 13.7 0.28 4.0.2504 18.3 0.47 5.0.2497 22.9 0.76 6.0.2490 27.5 1.04 7.0.2481 32.1 1.40 8.0.2471 38.6 1.80 9.0.2459 41.2 2.28 A21 (.490"x.450") 0.0.2508 0.0 0.00 3.0.2502 13.6 0.24 4.0.2497 18.2 0.44 5.0.2487 22.7 0.84 6.0.2475 27.2 1.33 70.2465 31.7 1.72 8.0.2453 36.3 2.21 A22 (.490"x.450") 0.0.2519 0.0 0.00 3.0.2513 15.6 0.24 4.0.2507 18.2 0.47 5.0.2499 22.7 0.80 6.0.2489 27.2 1.19 7.0.2478 31.7 1.64 8.0.2467 36.3 2.08 9.0.2452 40.9 2.70 A23 (.480"x.450") 0.0.2453 0.0 0.00 3.0.2445 13.9 0.32 4.0.2439 18.5 0.57 5.0.2432 23.2 0.86 6.0.2422 27.8 1.26 7.0.2412 32,4 1.68 8.0.2398 37.0 2.28 9.0.2382 41.7 2.94 9.4.2370 43.6 3.45 A24 (.480"x.450") 0.0.2438 0.0 0.00 3.0.2435 13.9 0.21 4.0.2428 18.5 0.41 5.0.2423 23.2 0.62 6.0.2416 27.8 0.91 7.0.2409 32.4 1.19 8.0.2399 37.0 1.61 9.0.2385 41.7 2.20 9.9.2371 46.3 2.82 A25 (.480"X.4297") 0.0.2419 0.0 0.00 2.0.2409 9.7 0.42 3.0.2403 14.4 0.67 4.0.2398 19.1 0.87 5.0.2392 23,9 1.12 6.0.2383 28.6 1.50 7.0.2373 33.3 1.92 8.0.2359 37.9 2.51 9.0 2342 42.5 3.24 9.9.2320 46.9 4.17 A26 (.480"x.4065") 0.0.2432 0.0 0.00 4.0.2413 20.3 0.78 5.0.2405 25.3 1.11 6.0.2399 30.3 1.35 7.0.2387 35.2 1.86 8.0.274 40.0 2.41 9.0.2355 44.7 3.21 9.8*.2334 48.2 4.11 A27 (.480"x. 4101") 0.0.2457 0.0 0.00 3.0.2448 15.2 0.36 4.0.2443 20.2 0.57 5.0.2439 25.2 0.72.0.2430 30.1 1.10 7.0.2421 35.0 1.45 8.0.2408 39.8 2.01 9.0.2390 44.5 2.76 9.4.2382 46.3 3.10 B12 (.485"x.450") 0.0.2548 0.0 0.00 2.0.2541 9.2 0.27 3.0.2436 13.8 0.47 4.0.2531 18.3 0.67 5.0.2526 22.9 0.87 6.0.2521 27.5 1.07 7.0.2515 32.1 1.30 8.0.2508 36.6 1.58 9.0.2497 41.2 2.02 9.5.2483 43.5 2.57 B14 (.480"x.3922") 0.0.2450 0.0 0.00 2.0.2441 10.6 0.36 3.0.2436 15.8 0.57 4.0.2430 21.1 0.82 5.0.2422 26.2 1.15 6.0.2414 31.4 1.48 7.0.2405 36.5 1.85 8.0.2395 41.5 2.27 9.0.2381 46.5 2.85 9.1*.2370 46.8 3.33 B15 (.480"x.3963" ) 0.0.2488 0.0 0.00 2.0.2478 10.5 0.40 3.0.2472 15.7 0.64 4.0.2465 20.8 0.93 5.0.2457 26.0 1.25 6.0.2448 31.1 1.62 7.0.2439 36.1 1.98 8.0.2424 41.0 2.60 8.4.2406 42.8 3.35 B19 (.480"x.3122") $ 0.0.2462 0.0 0.00 1.0.2461 6.7 0.04 2,0.2458 13.4 0.16 4.0.2450 26.6 0.48 6.0.2431 39.5 1.26 B21 (.480"x.450") 0.0.2471 0.0 0.00 2.0.2465 9.3 0.24 3.0.2460 13.9 0.45 4.0.2455 18.5 0.65 5.0.2450 23.2 0.85 6.0.2445 27.8 1.06 7.0.2439 32.4 1.30 8.0.2429 37.0 1.70 9.0.2420 41.7 2.08 9.9*.2401 46.3 2,90 B22 (.480"x.450") 0.0.2470 0.0 0.00 2.0.2461 9.3 0.36 5.0,2446 23.2 0.98 8.0.2422 37.0 1.95 9.9.2401 46.3 2.85 0 *0*0*0 G15 (.485"x.450").00.2397.00 0.00.02.2386.09 0.46.04.2375.18 0.92.06.2362.27 1.46.08.2345.36 2.18.20.2285.46 4.78.15.2040.69 16.1.20.1990.92 18.6.30.1832 1;4 21.6.40.1882 1.8 24.1.50.1837 2.3 26.5.60.1814 2.7 27.8 G18 (.485"x.450").00.2394.00 0.00.04.2382.18 0.58.06.2375.27 0.80.08.2367.36 1.12.10.2337.46 2.40.15.2110.69 12.4.20.2075.92 14.2.30.2022 1.4 16.7.40.1975 1.8 19.2.50.1932 2.3 21.4 017 (.485"x.450").00.2398.00 0.00.04.2378.18 0.84.06.2360.27 1.59.08.2325.36 3,09.10.2242.46 6.72.15.1960.69 20.1.20.1798.92 28.7 C11 (.485"x.450") 0.0.2495 0.0 0.00 1.0.2488 4.6 0.28 2.0.2481 9.2 0.56 3.0.2472 13.7 0.93 4.0.2465 18.3 1.21 5.0.2456 22.9 1.57 5.5.2446 25.2 1.98 6.0.2422 27.5 2.97 6.4.2382 29.3 4.63 012 (.485"x.450") 0.0.2497 0.0 0.00 1.0.2489 4.6 0.32 2.0.2481 9.2 0.64 3.0.2475 13.7 0.88 4.0.2466 18.3 1.24 5.0.2456 22.9 1.65 6.0.2447 27.5 2.02 6.5.2439 29.8 2.35 7.0.2406 32.1 3.71 7.1.2357 32.6 5.75 7.0.2319 32.1 7.40 6.9.2306 31.6 7.95 013 (.485"X.450") 0.0.2505 0.0 0.00 1.0.2498 4.6 0.28 2.0.2491 9.2 0.56 3.0.2485 13.7 0.80 4.0.2479 18.3 1.03 5.0.2472 22.9 1.31 6.0.2466 27.5 1.56 6.5.2458 29,.8 1.89 6.9.2415 31.6 3.66 018 (.480"x.2750") 0.0.2390 0.0 0.00 0.5.2385 3.7 0.20 1.0.2381 7.6 0.37 1.5.2377 11.3 0.54 2.0.2372 15.0 0.75 2.5.2367 18.8 0.97 3.0.2362 22.5 1.18 3.8.2348 28.7 1.76 4.0.2323 29.5 2.84 4.2.2260 29.9 5.60 4.1.2225 28.6 7.16 C19 (.480"x.2467") 0.0.2346 0.0 0.00 0.5.2340 4.2 0.25 1.0.2334 8.4 0.51 1.5.2328 12.8 0.77 2.0.2321 16.7 1..06 2.5.2317 20.8 1.24 3.0.2306 24.9 1.71 3.3.2291 26.8 2.37 3.5.2259 28.5 3.78 3.6.2227 28.9 5.20 3.1.2198 24.6 6.51 C31 (.480"X.4300") 0.0.2319 0.0 0.00 1.0.2310 4.8 0.39 2.0.2300 9.6 0.82 3.0.2290 14.4 1.25 4.0.2281 19.1 1.65 5.0.2270 23.7 2.13 5.5.2261 26.0 2.55 6.0.2228 28.0 4.00 6.1.2207 28.0 4.94 6.0.2182 27.4 6.07 5.9.2177 26.9 8.31 034 (.480"X.3791") 0.0.2346 0.0 0.00 2.0.2326 11.0 0.94 3.0.2316 16.3 1.19 4.0.2306 21.6 1.70 5.0.2282 26.8 2.78 5.5.2236 28.9 4.80 6.0.2156 30.5 8.45 6.1.2136 30.4 9.36 6.0.2116 29.8 10.3 5.0.2003 23.8 15.8 3.7.1874 16.9 22.4 4.0.1771 18.5 28.1 5.0.1555 23.2 41.0 6.0.1086 27.8 77.0 D21 (.490"x.450") 0.0.2508 0.0 0.00 1.0.2496 4.5 0.48 2.0.2485 9.1 0.92 3.0.2474 13.6 1.36 4.0.2463 18.2 1.81 5.0.2450 22.7 2.33 5.5.2440 25.0 2.74 6.0.2421 27.2 3.53 6.3.2363 28.6 5.95 D22 (.490"x.450") 0.0.2512 0.0 0.00 1.0.2502 4.5 0.40 2.0.2492 9.1 0.80 3.0.2482 13.6 1.20 4.0.2472 18.2 1.60 5.0.2460 22.7 2.08 5.5.2453 25.0 2.37 6.0.2432 27.2 3.24 6.2.2390 27.9 4.97 D23 (.490"x.450") 0.0.2512 0.0 0.00 1.0.2504 4.5 0.32 2.0.2496 9.1 0.64 3.0.2488 13.6 0.96 4.0.2480 18.2 1.28 5.0.2467 22.7 1.80 5.5.2456 25.0 2.25 6;0.2438 27.2 3.00 6.2.2413 28.1 4.04 D26 (.480"x.450") 0.0.2415 0.0 0.00 1.0.2404 4.6 0.46 2.0.2396 9.3 0.79 3.0.2388 13.9 1.12 4.0.2379 18.5 1.50 5.0.2368 23.2 1.97 6.0.2349 27.8 2.76 6.2.2320 28.7 4.00 6.3.2270 29.2 6.19 6.5.2175 30.1 10.6 6.7.2127 31.0 12.7 6.9.2060 31.9 15.8 6.7.2000 31.0 18.9 6.5.1970 30.1 20.4 6.2.3941 28.7 21.9 D27 (.485"x.3865") 0.0.2321 0.0 0.00 1.0.2311 5.4 0.43 2.0.2303 10.6 0.78 3.0.2295 15.9 1.12 4.0.2285 21.0 1.55 5.0.2271 26.2 2.18 5.3.2258 27.6 2.76 5.5.2205 28.0 5.12 5.7.2090 27.6 10.5 6.0.2034 28.4 13.2 6.5.1955 29.8 17.2 7.0.1845 32.1 22.9 6.5.1757 29.8 27.8 4.0.1610 18.7 36.6 D28 (.480"x.3190") $ 0.0.2346 0.0 0.00 0.6.2342 3.9 0.17 1.4.2340 9.1 0.25 2.5.2337 16.3 0.38 3.6.2313 23.2 1.42 4.1.2230 25.3 5.07 4.8.1998 26.8 15.9 11 (.485"x.450") F14 (.480"x.450") 0.0.2507 0.0 0.00 0.0.2402 0.0 0.00 0.5.2461 2.3 1.86 0.2.2392 0.9 0.41 1.0.2390 4.6 4.78 0.5.2379 23 0.96 2.0.2365 9.2 5.83 0.7.2355 3.5 1.97 3.0.2357 13.7 6.17 1.0.2829 4.6 2.85 4.0.2351 18.3 6.42 1.3.2305 8.0 4.03 5.0.2346 22.9 6.55 1.6.2288 7.4 4.86 6.0.2341 27.5 6.85 2.0.2270 9.3 5.66 7.0.2334 32.1 7.16 3.0.2253 13.9 6.40 8.0.2329 36.6 7.36 4.0.2245 18.5 6.76 5.0.2240 23.2 6.98 E12 (.490"x.450") 6.0.2233 27.8 7.30 6.5.2227 30.1 7.56 0.0.2508 0.0 0.00 6.9.2195 1.9 9.01 0.3.2478 1.4 1.20 6.5.2155 30.1 10.8 0.5.2433 2.3 3.04 8.0.2103 27.8 12.2 1.0.2371 4.5 5.60 5.0.1970 23.2 19.8 8.0.2334 27.2 7.19 0 8 2 7.0.2330 31.7 7.36 F15 (.480X.450") 8.0.2324 36.3 7.61 0.0.2307 0.0 0.00 9.0.2317 40.8 7.91 0.2.2297 0.9 0.44 9.9.2307 45.4 8.38 0.5.2285 2.3 0.95 0.7.2269 3.5 1.66 E24 (.480"6x.285") 10.224 4.6 2.77 1.2.2215 8.0 4.07 0.0.2250 0.0 0.00 1 6 2197 7.4 4.89 0.2.2223 1.3 1.20 2:0:2181 9.3 5.62 0.3.2190 1.9 2.70 3:0 2168 13.9 6.21 0.5.2150 3.1 4*.5 4:0.2162 18.5 6.50 1.0.2127 6.0 5.62 5.0.2155 23.2 6.82 2.0.2117 12.0 86.10 6.0.2149 27.8 7.10 3.0.2113 17.9 6.27.6.2144 30.1 7.33 4.0.21098 23.9 6.47 69.2118 31.9 8.55 5.0.2103 29.8 6.76 6.5.2053 30.1 12.4 8.0.2095 35.8 7.14 6.0.2007 27.8 13.9 7.0.2086 41.4 7.57 5.0.1890 23.2 19.9 8.0.2077 47.1 7.98 4.5.1787 20.8 25.5 9.0.2068 52.8 8.^4 4.3.1725 19.9 29.0 9.9.2080 58.4 8.83 25 (.485"x.3452") F23 (80".3557"). 0.0.2433 0.0 0.00 0.0.2412 0.0 0~00 0.3.2402 2.0 1.29 0.2.2380 1.2 1.32 0.52375 2.9 2.40 0.3.2357 1.8 2.30 0.9.2358 5.3 4.40 0.5.2312 2.9 4.23 1.0.2287 5.7 5.31 2.0.2276 11.3 5.80 3.0.2271 16.9 6.02 4.0.2267 22.6 8.20 5.0.2268 28.2 6.32 6.0.2256 33.7 6.70 7.0.2248 39.2 7.05 8.0.2239 44.6 7.45 9.0.2230 50.0 7.84 9.9.2212 55.1 8.66 B27 (.485"x.2620") 0.0.2271 0.0 0.00 0.5.2198 3.8 3.27 1.0.2161 7.5 4.96 1.5.2151 11.2 5.42 2.0.2148 14.9 5.57 3.0.2141 22.3 5.90 4.0.2134 29.6 6.22 5.0.2127 36.9 6.56 6.0.2117 44.1 7.04 7.0.2104 51.2 7.65 8.0.2088 58.0 8.51 8.4*.2079 60.7 8.91 28 (.485"x.2730") 0.0.2406 0.0 0.00 0.5.2323 3.6 3.50 1.0.2272 7.1 5.73 1.5.2261 10.7 6.22 2.0.2256 14.2 6.44 3.0.2250 21.2 6.70 4.0.2242 28.2 7.07 5.0.2233 35.1 7.46 6.0.2222 42.0 7.95 7.0.2210 48.7 8.50 8.0.2191 55.2 9.35 8.7*.2169 59.6 10.3 E29 (.480"x.3015") $ 0.0.2412 0.0 0.00 0.1.2410 0.8 0.08 0.2.2404 1.4 0.33 0.3.2391 2.1 0.87 0.4.2371 2.7 1.71 0.5.2352 3.4 2.52 1.0.2301 6.6 4.70 3.5.2263 22.8 6.33 F31 (.485"x.450") 0.0.2519 0.0 0.00 0.5.2488 2.3 1.32 1.0.2430 4.6 3.60 1.5.2379 6.9 5.72 2.0.2356 9.2 6.68 3.0.2337 13.7 7.50 4.0.2327 18.3 7.92 5.0.2320 22.9 8.22 6.0.2310 27.5 8.64 6.9.2275 31.6 10.4 F32 (.490"x.450") 0.0.2523 0.0 0.00 0.5.2487 2.3 1.16 1.0.2436 4.5 3.50 1.5.2384 6.8 5.66 2.0.2362 9.1 6.59 3.0.2341 13.6 7.50 4.0.2333 18.2 7.82 5.0.2327 22.7 8.09 6.0.2315 27.2 8.60 6.9.2295 31.3 9.37 F33 (.490"x.450") 0.0.2522 0.0 0.00 0.5.2480 2.3 1.67 1.0.2421 4.5 4.08 1.5.2375 6.8 6.00 2.0.2352 9.1 6.96 3.0.2334 13.6 7.74 4.0.2325 18.2 8.13 5.0.2317 22.7 8.46 6.0.2309 27.2 8.82 6.7.2286 30.4 9.80

90 Mg-.5%Th SINGLE CRYSTALS (in plane-strain compression): TAll (.480"X.450") 0.0.2410 0.0 0.00 3.0.2406 13.9 0.17 4.0.2404 18.5 0.25 5.0.2402 2352 0.33 6.0.2400 27.8 0.41 7.0.2395 32.4 0.62 8.0.2388 37.0 0.91 9.0.2381 41.7 1.20 9.9.2371 46.3 1.61 TA12 (.480"x.450") 0.0.2440 0.0 0.00 3.0.2438 13.9 0.16 4.0.2434 18.5 0.25 5.0.2431 23.2 0.37 6.0.2427 27.8 0.53 7.0.2421 32.4 0.78 8.0.2413 37.0 1.10 9.0.2405 41.7 1.43 9.9.2396 46.3 1.80 TA14 (.485"X.2220") 0.0.2400 0.0 0.00 1.0.2393 9.3 0.29 2.0.2384 18b6 0.67 3.0.2370 27.8 1.25 4.0.2355 36.8 1.88 5.0.2338 45.7 2.61 5.5*.2329 50.0 3.00 TA15 (.480"x.2220") 0.0.2495 0.0 0.00 1.0.2487 9.4 0.32 2.0.2478 18.6 0.68 3.0.2465 27.8 1;20 4.0.2451 36.9 1.78 5.0.2432 45.7 2.56 5.8*.2405 52.7 3.68 TA17 (.485"x.3070") $ 0.0.2446 0.0 0.00 1.0.2447 6.7 0.00 2.0.2447 13.4 0.00 5.0.2432 44.2 0.57 6.7.2401 1.86 TB12 (.480"x. 450") 0.0.2430 0.0 0.00 3.0.2424 13.9 0.24 5.0.2416 23.2 0.57 7.0.2409 32.4 0.87 8.0.2403 37.0 1.11 9.0.2394 41.7 1.48 TB14 (.480"x.450") 0.0.2421 0.0 0.00 3.0.2415 13.9 0.24 4.0.2410 18.5 0.45 5.0.2406 23.2 0.62 6.0.2401 27.8 0.83 7.0.2393 32.4 1.16 8.0.2384 37.0 1.54 9.0.2372 41.7 2.04 9.9.2358 46.3 2.64 TB22 (.490"x.2437") 0.0.2210 0.0 0.00 1.0.2205 8.4 0.22 2.0.2200 16.7 0.45 3.0.2193 24.9 0.77 4.0.2184 33.1 1.18 5.0.2174 41.2 1.63 6.0.2165 49.2 2.04 6.9*.2149 56.2 2.79 TB21 (.490"x.2110") 0.0.2410 0.0 0.00 1.0.2400 9.6 0.41 2.0.2390 19.2 0.83 3.0.2379 28.6 1.30 4.0.2368 38.0 1.75 5.0.2356 47.3 2.26 6.0.2340 56.4 2.96 6.1*.2337 57.2 3.08 TB24 (.490"x.3801") $ 0.0.2415 0.0 0.00 1.0.2412 5.4 0.12 2.0.2412 10.7 0.12 3.5.2409 18.8 0.24 5.0.2399 26.7 0.62 8.0.2389 42.5 1.08 TC13 (.480"x.450") 0.0.2450 0.0 0.00 1.0.2443 4.6 0.28 2.0.2436 9.3 0.57 3.0.2430 13.9 0.82 4.0.2424 18.5 1.07 5.0.2403 23.2 1.93 5.5.2366 25.5 3.49 6.0.2314 27.8 5.61 6.4.2283 29.7 7.06 TC21 (.485"x.2180") 0.0.2400 0.0 0.00 1.0.2385 9.3 0.62 2.0.2370 18.7 1.25 2.5.2360 23.3 1.68 3.0.2338 27.7 2.60 3.5.2298 31.7 4.35 3.8.2210 32.8 8.24 4.0.2125 33.7 12.2 4.1.2100 33.8 13.3 4.0.2075 33.0 14.5 3.5.1995 27.9 18.5 3.1.1929 23.7 21.8 TC23 (.480"x.2634") 0.0.2404 0.0 0.00 1.0.2394 7.9 0.41 2.0.2383 15.7 0.88 3.0.2371 23.4 1.38 3.5.2348 27.0 2.35 4.0.2276 30.0 5.47 4.5.2178 32.4 9.87 4.6.2145 32.7 11.4 4.0.2032 27.1 16.6 3.6.1961 23.3 20.4 TC24 (.480"x.2565") 0.0.2397 0.0 0.00 1.0.2386 8.1 0.46 2.0.2376 16.1 0.88 3.0.2364 24.0 1.38 3.5.2351 28.0 1.68 4.0.2273 30.9 5.06 4.6.2187 34.3 8.91 TD43 (.485"x.2869") 0.0.1748 0.0 0.00 1.0.1740 8.2 0.46 2.0.1727 16.2 1.21 3.0.1705 24.0 2.48 4.0.1664 31.3 4.90 4.5.1622 34.4 7.50 5.0.1483 35.2 16.5 5.5.1299 34.8 29.6 5.7.1220 34.4 36.0 5.5.1180 32.4 39.2 TD44 (.485"x.2410") 0.0.1751 0.0 0.00 1.0.1741 8.5 0.57 2.0.1727 16.9 1.37 3.0.1702 25.0 2.84 4.0.1634 32.0 6.92 4.5.1417 31.8 21.1 4.8.1303 31.4 29.5 4.5.1239 28.7 34.6 4.1.1191 25.3 38.5 TD45 (.485"x.2460") 0.0.1780 0.0 0.00 1.0.1770 8.3 0.56 2.0.1755 16.5 1.41 3.0.1733 24.5 2.67 4.0.1694 31.9 4.94 4.2.1658 33.3 7.10 4.5.1493 32.1 17.5 5.1.1320 32.9 30.0 4.5.1220 27.4 37.7 TD46 (.490"x.2491") 0.0.1970 0.0 0.00 1.0.1959 8.1 0.56 2.0.1947 16.2 1.17 3.0.1927 24.0 2.20 4.0.1876 31.2 4.90 4.5.1756 33.1 11.4 4.8.1634 32.8 18.6 5.2.1390 31.4 34.8 5.0.1330 29.4 39.3 TD21 (.485"x.2869") $ 0.0.2432 0.0 0.00 1.0.2432 7.2 0.00 2.0.2425 14.3 0.28 3.0.2419 21.4 0.53 4.5.2375 31.5 2.36 5.0.2177 32.0 11.0 TE14(.480"x.2120") 0.0.2413 0.0 0.00 0.3.2386 2.9 1.13 0.5.2338 4.8 3.15 0.7.2302 8.6 4.71 1.0.2290 9.3 5.22 1.5.2281 14.0 5.62 2.0.2276 18.6 5.85 4.0.2255 36.8 6.76 5.0.2242 45.8 7.34 5.6*.2812 50.6 8.70 T15 (.485"x.1980") 0.0.2478 0.0 0.00 0.3.2452 3.0 1.06 0.5.2410 5.0 2.78 0.7.2365 7.0 4.66 1.0.2345 9.9 5.52 1.5.2335 14.7 5.95 2.0.2329 19.6 6.21 3.0.2319 29.3 6.63 5.0.2292 48.2 7.83 6.0*.2261 57.2 9.15 TE23 (.480"x.450") 0.0.2480 0.0 0.00 0.3.2464 1.4 0.65 0.5.2452 2.3 1.13 0.7.2435 3.2 1.83 1.0.2398 4.6 3.35 1.5.2355 6.9 5.27 2.0.2342 9.3 5.72 4.0.2330 18.5 6.24 6.0.2320 27.8 6.66 8.0.2309 37.0 7.15 9.9.2297 46.3 7.69 TS26 (.485"x.2835") $ 0.0.2502 0.0 0.00 0.2.2492 1.4 0.40 0.3.2472 2.2 1.21 0.4.2440 2.8 2.50 0.5;2399 3.6 4.20 1.0.2360 6.9 5.85 3.0.2348 20.5 6.35 5.0.2342 34.1 6.60 TFll (.480"x.450") 0.0.2511 0.0 0.00 0.5.2503 2.5 0.32 1.0.2489 4.6 0.88 1.5.2469 6.9 1.70 2.0.2437 9.3 3.00 3.0.2365 13.9 5.98 4.0.2341 18.5 7.02 5.0.2331 23.2 7.45 6.0.2322 27.8 7.82 7.0.2311 32.4 8.30 8.3.2262 38.4 10.4 TF12 (.480"x.450") 0.0.2543 0.0 0.00 1.0.2513 4.6 1.18 1.5.2486 6.9 2.26 2.0.2440 9.3 4.12 3.0.2395 13.9 6.00 4.0.2382 18.5 6.55 5.0.2373 23.2 6.92 6.0.2367 27.8 7.18 7.0.2361 32.4 7.41 8.0.2350 37.0 7.90 8.5.2332 39.4 8.65 TF13 (.480"x.2130") 0.0.2524 0.0 0.00 0.2.2515 1.9 0.35 0.5.2491 4.8 1.32 1.0.2437 9.4 3.50 1.5.2389 13.9 5.50 2.0.2371 18.4 6.26 2.5.2360 22.9 6.72 3.0.2351 27.4 7.20 3.5.2340 31.8 7.56 4.1.2310 36.4 8.85 3.6.2275 31.4 10.4 F15 (.490"x.2888") $ 0.0.2556 0.0 0.00 0.2.2553 1.4 0.11 0.4.2540 2.8 0.62 0.6.2519 4.2 1.46 1.0.2488 6.8 3.50 2.0.2408 13.3 5.96 Mg-4%6Li SINGLE CRYSTALS (in plane-strain compression): LA21 (.495'x.3000") 0.0.1675 0.0 0.00 1.0.673 6.7 0.12 2.0.1670 13.4 0.29 3.0.1667 20.1 0.47 4.0.1663 26.7 0.12 5.0.1656 33.3 1.14 6.0.1646 39.7 1.75 6.6.1638 43.5 2.22 LA23 (.490"x.2790") 0.0.1760 0.0 0.00 1.0.1757 7.3 0.17 2.0.1754 14.6 0.34 3.0.1750 21.8 0.57 4.0.1744 29.0 0.91 5.0.1734 36.0 1.48 5.8.1724 41.2 2.06 LA25 (.490"x.3260") 0.0.1817 0.0 0.00 1.0.1814 6.3 0.16 2.0.1811 12.5 0.33 3.0 1807 18.7 0.55 4;0.1802 24.8 0.85 5.0.1794 30.9 1.27 6.0 1780 36.8 2.04 6.6*.1758 40.0 3.30 LA28 (.500"x.3836") _ 0.0.2010 0.0 0.00 1.0;2010 5.2 0.00 2.0.2010 10.4 0.00 3.5.2008 18.2 0.10 5.0.2003 26.0 0.35 7.5.1980 38.5 1.50 7.7* - - - LB21 (.495"x.2296") 0.0.2025 0.0 0.00 1.0.2022 8.8 0.14 2.0.2015 17.5 0.49 3.0;2009 26.2 0.79 3.5;2005 30.5 0.99 4.0.2000 34.8 1.25 4.3.1985 37.4 2.00 LB23 (.495"x.2470") 0.0.2050 0.0 0.00 1.0.2047 8.1 0.14 2.0.2043 16.3 0.34 3.0.2038 24.4 0.58 4.0.2032 32.4 0.88 4.5.2025 36.4 1.23 4.7.2019 37.7 1.53 LB25 (.495"X.2170") 0.0.2136 0.0 0.00 1.0.2133 9.3 0.14 2.0.2128 18.6 0.37 3.0.2120 27.7 0.75 3.5.2114 32.2 1.04 4.0.2107 36.7 1.36 4.1.2104 34.3 1.52 LB27 (.490"x.3241") $ 0.0.2412 0.0 0.00 1.0.2412 6.3 0.00 2.0.2412 12.6 0.00 3.5.2412 22.0 0.00 5.0.2408 31.5 0.16 5.9*.2400 37.0 0.50 LC21 (.490"x.3080") 0.0.1957 0.0 0.00 0.5.1954 3.3 0.15 1.0.1951 6.6 0.30 1.5.1946 9.9 0.56 2.0.1936 15.1 1.08 2.5.1915 16.3 2.16 3.0.1878 19.1 4.11 4.0.1768 24.1 10.2 5.0.1673 28.7 15.7 5.7.1601 31.6 18.4 LG23 (.495"x.2690") 0.0.2035 0.0 0.00 0.5.2033 3.7 0.10 1.0.2026 7.5 0.44 1.5.2013 11,1 1.09 2.0.1992 14.7 2.12 3.0.1900 21.1 6.87 4.0.1800 26.8 12.2 5.0.1627 30.7 22.4 5.5.1502 31.7 30.4 6.0.1367 32.2 39.8 6.5.1260 33.2 47.0 7.0.1180 34.2 54.5 LC25 (.485"x.8610") 0.0.1899 0.0 0.00 0.5.1896 3.9 0.15 1.0.1893 7.9 0.31 1.5.1881 11.7 0.95 2.0.1844 15.3 2.94 2.5.1780 18.6 6.48 3.0.1710 21.5 10.4 3.5.1649 24.2 14.1 4.2.1564 27.5 19.4 LC27 (.495"x.2579") $ 0.0.2230 0.0 0.00 1.0.2229 7.8 0.04 1.5.8211 11.8 0.B5 2.3.2155 17.0 3.42 ID42 (.490"x.2030') 0.0.1689 0.0 0.00 0.5.1678 5.0 0.65 1.0.1666 9.9 1.37 1.5.1652 14.7 2.20 2.0.1626.914 3.80 2.5.1582 23.6 6.55 3.0.1500 26.9 11.9 3.5.1409 29.8 18.2 3.8.1361 31.1 21.6 LD44 (.490"x.2050") 0.0.1587 0.0 0.00 0.5.1578 4,9 0.57 1.0.1565 9.9 1.40 1.5.1549 1468 2.41 2.0.1523 19.1 4.12 2.5.1494 23.5 6.04 3.0.1448 27.4 9.15 3.5.1380 30.6 14.0 4.0.1270 32.6 22.2 LD46 (.490"x.1940*) 0,0.2122 0.0 0.00 0.5.2113 5.0 0.42 1.0 2097 10.4 1.19 1.5.2074 15.4 2.27 2.0.2038 20.2 4o02 2.5.1990 24,7 6.41 3.0.1903 29.8 10,9 3.5.1790 31.5 17.1 LD48 (.495"x.2312") $ 0.0.2607 0.0 0.00 0.5.2604 4.4 0.11 1.0.2590 8.7 0.65 1.6.2564 13.6 1.66 2.0.2527 17.0 3.10 2.8.2388 22.2 8.80 IE42 (.495"x.2130") 0.0.2379 0.0 0.00 0.2.2373 2.0 0.25 0.5.2334 4.7 1.90 0.8.2285 6.8 4.01 1.0.2254 9.0 5.38 1.5.2238 13.4 6.10 2.0.2231 17.8 6.42 3.0.2223 26.6 6.87 4.0.2215 35.4 7.12 4.1.2208 36.2 7.45 L144 (.495"x.2160") 0.0.2261 0.0 0.00 0.3.2240 2.8 0.93 0.5.2190 4.5 3.18 0.8.2152 6.7 4.93 1.0,2133 8.8 5.8X 1.5.2124 13.2 6.25 2.0.2119 17;6 8.50 3.0.2113 26.3 6.76 4.0.2104 34.9 7.20 4.2.2100 36.1 7.40 L246 (.495"x.2150") 0.0.2049 0.0 0.00 0.3.2030 2.8 0.93 0.5.1990 4.6 2.92 0.8.1952 6.7 4,85 1.0.1938 8.9 5.56 1.5.1927 13.3 6.14 2.0.1923 17.7 6.36 3.0.1916 26.4 6.70 3.5.1911 30.8 6.97 3.9.1896 33.8 7.75 L.48 (.500"'x.481") 3 0.0.2751 0.0 0.00 0.5.2732 3.6 0.69 0.8.2646 6.5 3.88 2.0,2584 15.2 6.27 4.7.2562 35.1 7.11 UL42 (.495"x.1790") 60..2440 0.0 0.00 0.2.2431 2.2 0.37 0.5.2403 5.6 1.52 0.8.2370 8.2 2.90 1.0.2328 10.8 4.70 1.5.2284 15.9 6.60 2.0.2266 21.0 7.40 3.0.2235 31.1 8.80 4.0.2122 40.0 14.0 4.1.2080 39.4 16.0 LF44 (.495"x.2090") 0.0.2057 0.0 0.00 0.4.2048 3.9 0.43 0.7.2030 6.7 1.33 1.0;2003 9.4 2.65 1.5.1962 13.9 4.72 2.0.1938 18.3 5.96 3.0.1919 27.1 8.94 3.5.1910 31.5 7.40 4.0.1893 35.7 8.30 4.7.1784 39.4 14.3 LF46 (.495"x.2210") 0.0.2611 0.0 0.00 0.5.2597 4.6 0.53 0.8.2581 6.8 1.16 1.0.2554 8.9 2.20 1.5.2484 13.1 4.98 2.0.2452 17.2 6.28 2.5.2437 21.4 6.90 3.0.2430 25.6 7.17 4.0.2401 33.7 8.38 4.5.2341 37.1 10.9 LF47 (.495"x.2185") ) 0.0.2753 0.0 0.00 0.2.2750 1.9 0.10 0.4.2730 3.7 0.84 0.8.2687 7.2 2.42 1.5.2811 13.1 5.28 2.0.2587 17.4 6.20

91 TEXTURED PUtAE MiGNESIUM POLYGCYSTALS (in plane-strain compression): ZT1 (.495"x.3953") ZR1 (.495"X.2300") 0.0.2430 0.0 0.00 0.0.2470 0.0 0.00 1.0.2422 5.1 0.33 0.5.2462 4.4 0.32 2.0.2413 10.1 0.70 1.0.2453 8.7 0.69 3.0.2402 15.2 1.16 1.5.2433 13.0 1.51 4.0.2388 20.1 1.74 2.0.2408 17.1 2.54 5.0.2369 24.9 2.54 2.5.2382 21.2 3.60 5.5.2358 27.3 3.00 3.0.2341 25.0 5.35 6.0.2341 29.6 3.73 3.2.2286 26.3 7.73 6.5.2318 31.7 4.72 3.1.2250 24.9 9.33 6.8.2270 32.5 6.81 ZR3 (.495"x.2280" ) ZT3 (.495"x.2760") —------ ZT3 (.495".2760) 0.0.2452 0.0 0.00 0.0.2460 0.0 0.00 0.5.2447 4.4 0.20.10.2455 7.3 0.20 1.0.2442 8.8 0.41 2.0.2446 14.5 0.57 1.5.2431 13.2 0.86 3.0.2427 21.7 1.35 2.0.2404 17.4 1.98 4.0.2396 28.5 2.63 2.5.2376 21.5 3.15 4.5.2375 31.8 3.52 3.0.2332 25.3 5.02 4.7.2352 33.3 4.50 3.2.2277 26.8 7.40 4.9.2310 33.7 6.30 3.3.2250 26.9 8.61 4.7.2258 31.7 8.56 3.2.2232 26.3 9.40 ZT6 (.495"x.2537") $ ZR6 (.490"x.2454") $ 0.0.2487 0.0 0.00 0.0.2490 0.0 0.00 0.8.2484 6.4 0.12 1.0 2484 8.3 0.24 1.5.2479 11.9 0.32 2.0.2446 16.3 1.78 2.0.2473 15.8 0.56 3.0.2387 23.9 4.22 3.0.2460 23.8 1.09 4.4.2410 33.6 3.15 TH1 (.500"X.2231") 0.0.2533 0.0 0.00 1.0.2519 8.9 0.55 2.0.2486 17.6 1.87 3.0.2437 25.9 3.85 4.0.2368 33.6 6.71 4.5.2321 37.1 9.73 5.0.2261 40.2 11.4 5.2.2228 41.4 12.5 TR2 (.500"X.2520") 0.0.1682 0.0 0.00 1.0.1676 7.9 0.35 2.0.1659 15.7 1.37 3.0.1630 23.1 3.14 4.0.1589 30.1 5.68 5.0.1536 36.4 9.07 5.5.1502 39.2 1.3 6.0.1430 41.0 16.2 5.9.1405 40.0 18o0 TR3 (.500"X.2090") 0.0.1757 0.0 0.00 1.0.1743 9.5 0.80 2.0.1717 18.7 2.30 3.0.1680 27.5 4.48 4.0.1620 35.4 8.12 4.5.1583 39.0 10.4 5.0.1505 41.4 15.5 4.9.1490 40.6 16.6 TZ1 (.495"x. 2483") 0.0.2451 0.0 0.00 0.5.2436 4.0 0.61 1.0.2378 7.9 3.62 1.5.2327 11.6 5.19 2.0.2301 15.3 6.30 4.0.2250 30.0 8.55 5.0.2213 36.9 10.2 5.3.2181 38.6 11.7 5.0.2141 35.9 13.5 TZ2 (.495"x.2471") 0.0.2381 0.0 0.00 0.5.2353 4.0 1.18 1.0.2309 7.9 3.07 1.5.2254 11.6 5.48 2.0.2225 15.3 6.77 4.0.2165 29.9 9.52 5.0.2130 36.8 11.1 5.4.2095 39.2 12.8 5.3.2079 38.2 13.6 TZ3 (.495"x.2487") 0.0.2591 0.0 0.00 0.5.2580 4.0 0.42 1.0.2515 7.9 3.16 1.5.2462 11.6 5.10 2.0.2437 15.3 6.13 4.0.2383 30.0 8.37 5.0.2348 37.0 9.86 5.5.2305 40.0 11.7 5.3.2283 38.2 12.7 R21 (.495"x.2480") 0.0.2171 0.0 0.00 0.5.2157 4.0 0.64 1.0.2092 7.9 3.70 1.5.2044 11.5 6.02 2.0.2018 15.2 7.30 3.0.1986 22.5 8.90 3.5.1965 25.9 9.96 4.0.1934 29.2 11.6 4.2.1913 30.4 12.6 RZ2 (.495"x.2480") 0.0.2249 0.0 0.00 0.5.2223 4.0 1.16 1.0.2158 7.8 4.12 1.5.2115 11.5 6.15 2.0.2086 15.2 7.52 3.0.2051 22.5 9.20 3.5.2032 25.9 10.1 4.0.2001 29.2 11.7 4.3.1971 30.6 13.2 RZ3 (.500"x.2485") 0.0.2179 0.0 0.00 0.5.2160 4.0 0.87 1.0.2096 7.7 3.94 1.5.2052 11.4 6.01 2.0.2026 15.0 7.28 3.0.1998 22.2 8.66 3.5.1981 25.7 9.55 4.0.1957 29.1 10.7 4.3.1901 30.1 13.6 RT1 (.500"x.2320") 0.0.2167 0.0 0.00 1.0.2156 8.6 0.51 2.0.2137 17.0 1.40 3.0.2107 25.2 2.80 4.0.2044 32.6 5.83 4.5.1986 35.7 8.70 5.0.1894 38.0 13.5 5.2.1828 38.2 17.0 5.1.1788 36.8 19.3 RT2 (.500"x.2675") 0.0.2183 0.0 0.00 1.0.2175 7.4 0.36 2.0.2161 14.8 1.00 3.0.2138 22.0 2.08 4.0.2098 28.8 3.96 5.0.2006 34.5 8.45 5.5.1926 36.6 12.5 5.7.1840 36.7 17.2 5.6.1805 35.5 19.1 RT3 (.500"x.2700") 0.0.1929 0.0 0.00 1.0.1920 7.4 0.46 2.0.1908 14.7 1.10 3.0.1886 21.7 2.23 4.0.1850 28.5 4.18 5.0.1770 34.1 8.60 5.5.1707 36.3 12.2 6.0.1570 36.9 20.6 5.9.1546 36.1 22.1 TETUBED Mg-.5%Th POLYGAYSTALS (in plane-strain compression): Tb-ZT1 (.495"x.279") 0.0.2525 0.0 0.00 1.0.2521 7.2 0.16 2.0.2516 14.4 0.35 3.0.2507 21.6 0.71 4.0.2484 28.5 1.65 5.0.2446 35.0 3.16 5.7.2402 39.3 5.00 Th-ZT2 (.495"x.251") 0.0.2528 0.0 0.00 1.0.2521 8.0 0.27 2.0.2513 16.0 0.59 3.0.2494 23.8 1.36 4.0.2459 31.3 2.76 4.5.2425 34.8 4.20 4.9.2362 37.1 6.84 Th-ZT3 (.490"x.233") 0.0.2510 0.0 0.00 1.0.2503 8.7 0.27 2.0.2495 17.4 0.60 3.0.2470 25.8 1.60 4.0.2423 33.8 3.53 4.6.2360 37.9 6.16 Th-ZT6 (.490"x.2382) $ 0.0.2541 0.0 0.00 1.0;2540 8.6 0.03 2.0.2539 16.1 0.07 3.0.2530 25.6 0.43 3.8;2508 32.1 1.31 4.2.2479 35.1 2.47 4.7.2402 38.1 5.65 Th-ZR1 (.495"x.250") 0.0.2526 0.0 0.00 1.0.2523: 8.1 0.12 2.0.2518 16.1 0.32 3.0.2507 24.0 0.75 4.0.2477 31.7 1.96 4.8.2415 36.8 4.50 Th-ZR2 (.495"x.233") 0.0.2513 0.0 0.00 1.0.2509 8.7 0.16 2.0.2504 17.3 0.36 3.0;2488 25.8 1.00 4.0.2454 33.9 2.37 4.5.2398 37.3 4.70 Th-ZR3 (.500"x.246") 0.0.2538 0.0 0.00 1.0;2535 8.1 0.11 2.0.2531 16.2 0.27 3.0.2524 24.3 0.55 4.0.2502 32.0 1.42 4.8.2413 37.4 5.05 Th-ZR6 (.495"x.2750) $ 0.0.2530 0.0 0.00 1.0.2429 7.4 0.03 2.0.2528 14.7 0.07 3.0 2525 22.0 0.19 3.9;2512 28.5 0.71 4.3.2498 30.9 1.28 Th-TRI (.500"x.217") 0.0.2463 0.0 0.00 1.0.2457 9.3 0.24 2.0.2448 18.6 0.63 3.0.2438 27.7 1.10 4.0.2377 35.8 3.61 4.4.2330 38.4 5.62 Th-TR2 (.495"x.219") 0.0.2148 0.0 0.00 1.0.2137 9.2 0.51 2.0.2122 18.2 1.22 3.0.2098 27.0 2.35 3.5.2075 31.2 3.45 4.0.2031 34.9 5.60 4.5.1966 38.1 8.85 4.9.1880 40.1 13.3 Th-TR3 (.500"x.213") 0.0.2219 0.0 0.00 1.0.2212 9.3 0.31 2.0.2201 18.6 0.81 3.0.2181 27.7 1.73 3.5.2153 31.9 3.01 4.0.2095 35.5 5.75 4.5.2023 38.7 9.25 4.9.1928 40.2 14.1 Th-TR6 (.500"x.2971) $ 0.0.2320 0.0 0.00 1.0.2320 6.7 0.00 2.0.2319 13.5 0.04 3.1.2314 20.5 0.25 4.0.2303 26.7 0.73 4.9.2280 32.1 1.74 Th-TZ1 (.495"x.253") 0.0.2635 0.0 0.00 1.0.2629 7.9 0.22 1.5.2623 11.9 0.45 2.0.2589 15.7 1.76 2.5.2515 19.1 4.66 3.0.2480 22.6 6.07 4.0.2434 29.6 7.92 5.0.2390 36.4 9.77 6.0.2316 42.4 12.9 Th-TZ2 (.490"x.252") 0.0.2431 0.0 0.00 1.0.2426 8.1 0.20 1.5.2418 12.1 0.53 2.0.2383 15.9 1.98 2.5.2308 19.3 5.20 3.0;2276 22.8 6.60 4.0.2232 29.8 8.55 5.0.2187 36.7 10.5 5.9.2100 41.7 14.6 Th-TZ3 (.495"x.253") 0.0.2508 0.0 0.00 1.0.2504 7.9 0.15 1.5.2500 11.9 0.32 2.0.2468 15.7 1.62 2.5.2397 19.1 4.53 3.0.2363 22.6 5.95 4.0.2323 29.6 7.67 5.3.2272 38.5 9.90 Th-TZ6 (.490"x.2523) $ 0.0.1952 0.0 0.00 1.0.1951 8.1 0.05 1.5.1950 12.1 0.10 1.9.1949 15.5 0.41 2.1.1934 16.8 0.93 2.4.1886 -18.8 3.43 3.5.1826 26.5 6.70 Th-RZl (.490"x.253") 0.0.1957 0.0 0.00 1.0.1951 8.0 0.30 1.5.1945 12.0 0.61 2.0.1903 15.7 2.79 2.5.1861 19.2 5.02 3.0.1838 22.8 6.27 4.0.1807 29.9 8.00 5.0.1777 36.8 9.85 5.9.1717 42.1 13.1 Th-RZ2 (.495"x.254") 0.0.2131 0.0 0.00 1.0.2125 7.9 0.28 1.5.2117 11,9 0.66 2.0.2085 15.6 2.17 2.5.2032 19.0 4.76 3.0.2009 22.5 5.90 4.0.1978 29.6 7.45 5.0.1947 36.5 9.03 5.7.1915 40.9 10.7 Th-RZ3 (.495"x.254") 0.0.2071 0.0 0.00 1.0.2066 7.9 0.24 1.5.2061 11.9 0.48 2.0.2039 15.7 1.56 2.5.1982 19.0 4.40 3.0.1956 22.6 5.70 4.0.1924 29.6 7.36 5.0.1896 36.5 8.85 5.7.1871 41.4 10.2 Th-RT1 (.490"x.309") 0.0.2114 0.0 0.00 1.0.2111 6.6 0.14 2.0.2107 13.2 0.33 5.0.2100 19.7 0.66 4.0.2075 25.9 1.86 5.0.2029 31.7 4.10 6.0.1970 37.0 7.05 7.0.1898 40.9 12.9 7.8.1811 44.6 15.5 Th-RT2 (.500x.231") 0.0.2170 0.0 0.00 1.0.2164 8.6 0.27 2.0.2156 17.2 0.64 3.0.2135 25.6 1.62 4.0.2073 33.1 4.56 5.0.1986 39.8 8.87 5.9.1871 44.5 14.8 Th-RT3 (.495"x.269") 0.0.2161 0.0 0.00 1.0.2156 7.5 0.23 2.0.2151 15.0 0.46 3.0.2141 22.3 0.93 4.0.2104 29.3 2.66 5.0.2045 35.6 5.52 5.8.2015 39.0 7.00 Th-RT6 (.500"x.2375) $ 0.0.2528 0.0 0.00 1.0.2528 8.4 0.00 Th-RZ6 (.500"x.253") 2.0.2525 168 0.11 3.0.2513 25.1 0.59 0.0.2410 0.0 0.00 3.5.2500 28 8 1.12 1.5.2409 11.8 0.04 3.8.2460 31.5 2.73 2.0.2399 15.7 0.45 2.3.2350 17.4 2.52 3.0.2285 22.5 5.35 4.5.2221 32.9 8.30 TEXTURED Mg-4%Li PLYCI2YSTAIS (in plane-strain compression): Li-ZT1 (.495"x.232") 0.0.2575 0.0 6.0o 0.5;2569 4.3 0.15 1.0.2562 8.7 0.43 1.5 2549 12.9 0.94 2;0.2525 17.1 1.90 2.5.2499 21.2 2.92 3.0;2465 25.0 4.29 4;0.2355 52.0 8.84 4.6.2242 35.1 13.8 Li-ZT2 (.495'x.252") 0.0.2554 0.0 0.00 1.0;2545 8.0 0.55 1;5.2537 12.0 0.67 2.0.2521 15.8 1.30 2.5.2501 19.6 2.08 3.0;2475 23.3 3.15 4.0.2403 30.2 6.10 5.0.2258 35.7 12.3 L1-ZT5 (.495"x.270") 0.0.2569 0.0 0.00 1.0;2561 7.5 0.31 1.5.2554 11.2 0.58 2.0.2543 14.8 1.02 2.5.2525 18.4 1.73 3.0.2504 21.7 2.55 4.0.2445 28.3 4.95 4.9.2340 33.3 9.33 Li-ZT6 (.500"x.307") $ 0.0.2597 0.0 0.00 1.0.2595 6.5 0.07 2.0.2590 13.0 0.27 3.0.2566 19.3 1.20 4.2.2500 26.6 3.82 Li-ZR1 (.495"x.241") Li-TR1 (.500"x.200") 0.0;2541 0.0 0.00 0.0.2780 0.0 0.00 0;5.2537 4.2 0.15 0.5.2770 5.0 0.36 1.0.2529 8.3 0.47 1.0.2752 9.9 1.01 1.5.2517 12.5 0;95 1.5.2721 14.7 2.14 2.0.2498 16.5 1.72 2.0.2665 19.2 4.22 3.0.2451 24.3 3.61 2.5.2591 23.4 7.04 4.0.2355 31.2 7.60 3.0.2496 27.1 10.7 5.0.2160 36.0 16.2 3.3.2435 28.9 13.3 5.3.2097 37.3 19.2 Lj-TR2 (.500"x.219") Li-ZR2 (.500"x.218") 0.0.2160 0.0 0.00 0.0.2590 0.0 0.00 0.5.2152 4.6 0.37 0*5.2586 4.6 0.15 1.0.2140 9.1 0.93 1.0.2579 9.1 0.42 1.5.2122 13.5 1.78 1.5.2566 13.6 0.93 2.0.2088 17.7 3.39 2.0;2543 18.0 1.83 2.5.2044 21.6 5.52 2.5.2516 22.3 2.90 3.0.1993 25.4 8.05 3.0;2483 26.4 4.22 3.8.1872 30.0 14.3 4.0.2346 33.4 9.90 4.4.2245-35.3 14.4 Li-TR3 (,495"x.217") Li-ZR3 (.485"x.216") 0.0.2070 0.0 0.00 1.0.2054 9.3 0.77 0.0.2562 0.0 0.00 2.0.2004 18.0 3.24 1.0.2551 9.5 0.43 3.0.1901 25.7 8.53 2;0.2513 18.7 1.93 3.9.1770 31.4 15.7 3.0.2450 27.4 4.47 4.0.2299 34.5 10.8 4.3.2220 35.9 14.3 Li-ZR6 (.495"x.2583) $ 0.0.2595 0.0 0.00 1.0.2594 7.8 0.03 2.0.2580 15.5 0.58 3.0.2554 23.1 1.60 4.0.2498 30.1 3.82 Li-TZl (.495"x.259") 0.0.2551 0.0 0.00 0.5.2548 3.9 0.11 0.8.2545 6.2 0.23 1.0.2539 7.8 0.47 1.5.2487 11.4 2.55 2.0.2431 14.9 4.82 3.0.2357 21.7 7.90 4.0.2298 28.4 10.5 5.0.2203 34.0 14.7 6.1.2020 38.6 23.3 Li-TZ2 (.495"x.258") 0.0.2390 0.0 0.00 0.5.2386 3.6 0.16 0.8.2381 6.2 0.37 1.0.2375 7.8 0.63 1.5.2328 11.4 2.64 C.0.2274 14.9 4.98 3.0.2206 21.8 8.00 4.0.2148 28.3 10,7 5.0.2056 34.0 15.1 5.6.1970 356.8 19.3 Li-TZ3 (.495"z.259") 0.0.2332.0.0 0.00 0.5.2327 3.9 0.21 1.0.2317 7.8 0.64 1.5.2277 11.4 2.36 2.0.2222 14.9 4.83 2.5.2188 18.3 6.36 3.0.2158 21.7 7.75 4.0.2108 28.3 10.1 4.6.2070 32.3 11.9 Li-TZ6 (.485"x.2587) $ 0.0.2992 0.0 0.00 1.0.2990 8.0 0.06 1.4.2978 10.9 0.47 1.6.2947 12.2 1.52 1.9.2898 14.3 3.18 2.5.2830 18.9 5.57 Li-RZ1 (.495"x.257") 0.0.2011 0.0 0.00 0.5.2005 3.9 0.29 1.0.1997 7.8 0.70 1.5.1969 11.5 2.12 2.0.1915 15.0 4.89 2.5.1881 18.4 6.68 3.0.1854 21.8 8.13 4.0.1809 28.4 10.6 5.3.1709 35.8 16.2 Li-RZ2 (.495"x.258") 0.0.1990 0.0 0.00 0.5.1985 3.9 0.25 1.0.1979 7.8 0.55 1.5.1945 11.5 2.27 2.0.1896 14.9 4.74 2.5.1864 18.4 6.55 3.0.1840 21.8 7.85 4.0.1797 28.4 10.2 5.4.1677 36.1 17.1 I,-RZ3 (.490"x.259") 0.0.2041 0.0 0.00 1.0.2024 7.9 0.83 2.0.1951 15.1 4.51 3.0.1881 21.9 8.17 4.0 1838 28.6 10.5 4.8.1790 33.5 13.1 Li-RZ6 (.500"x.2590) $ 0.0.2668 0.0 0.00 0.5.2667 3.8 0.03 1.0.2660 7.7 0.30 1.6.2627 12.5 1.56 1.9.2575 14.4 3.55 2.9.2498 20.6 6.59 Li-RT1 (.500"x.288") 0.0.2108 0.0 0.00 0.5.2105 3.6 0.14 1.0.2100 6.9 0.38 1.5.2091 10.3 0.81 2.0.2068 13.6 2.10 2.5.2040 16.8 3.28 3.0.2006 19.8 4.95 4.0.1916 25.3 9.55 5.0.1815 30.2 14.9 5.6.1750 32.5 18.6 Li-RT2 (.500"x.269") 0.0.2002 0.0 0.00 0.5.1999 3.7 0.15 1.0.1995 7.4 0.35 1.5.1982 11.0 1.00 2.0.1959 14.5 2.16 2.5.1928 17.9 3.76 3.0 1880 21.0 6.28 4.0.1795 26.8 10.9 5.1.1664 32.0 18.5 Li-RT3 (.500'x.275") 0.0.2175 0.0 0.00 1.0.2167 7.2 0.36 1.5.2157 10.8 0.83 2.0.2137 14.3 1.76 2.5.2107 17.6 3.18 3.0.2067 20.8 5.10 4.0.1968 26.4 10.0 4.9.1865 30.9 15.4

92 UNIAXIAL TENSILE oND COCMPESSIVE TESTS OF POLYGdY6TtLS R is specimen dimension in the rolling direction; T is specimen dimension in the transverse direction; Z is specimen dimension in the thickness direction of the textured polycrystalline sheet material. e, eT, and ez are calculated true strains in the three respective directions. Load Stress R e T eT e (lb) (ksi) (in) () (in) ( (in) ( Rolling Direction Tensile Test (Pure Mg): 0 0.0 2.600 0.00.2606 0.00.2500 0.00 580 8.8 2.621 0.80.2604 0.07.2493 0.68 800 12,1 2.634 1.30.2600 0.23.2476 0.96 970 14.6 2.650 1.90.2596 0.38.2467 1.33 1100 16.5 2.667 2.54.2590 0.61.2458 1.70 1165 17.3 2.680 3.03.2586 0.77.2452 1.93 1280 18.9 2.705 3.94.2577 1.12.2439 2.48 1325 19.4 2.719 4.47.2573 1.28.2430 2.86 Transverse Direction Tensile Test (Pure Mg): 0 0.0.2634 0.00 2.600 0.00.2500 0.00 730 11.1.2633 0.03 2.602 0.07.2499 0.03 910 13.8.2632 0.07 2.606 0.23.2498 0.07 1020 15.4.2629 0.19 2.610 0.38.2496 0.16 1260 18.9.2625 0.34 2.625 0.96.2493 0.28 1385 20.7.2616 0.68 2.638 1.46.2485 0.60 1445 21.5.2613 0.81 2.648 1.83.2483 0.68 1520 22.5.2607 1.03 2.664 2.41.2478 0.88 1530 22.4.2594 1.53 2.685 3.22.2471 1.17 Rolling Direction Tensile Test (Mg-.5%Th): 0 0.0 2.600 0.00.2620 0.00.2543 0.00 900 13.5 2.605 0.19.2618 0.07.2541 0.07 1300 19.5 2.608 0.30.2617 0.11.2540 0.11 1700 25.5 2.615 0.57.2615 0.19.2537 0.23 1820 27.3 2.630 1.15.2611 0.34.2530 0.51 1850 27.7 2.638 1.45.2605 0.57.2524 0.75 1870 28.0 2.645 1.72.2600 0.76.2520 0.91 1890 28.3 2.652 1.98.2596 0.92.2515 1.11 1900 28.4 2.660 2.27.2591 1.11.2510 1.30 Transverse Direction Tensile Test (Mg-.5%Th): 0 0.0.2604 0.00 2.600 0.00.2537 0.00 800 12.1.2602 0.07 2.606 0.23.2533 0.15 1460 22.1.2600 0.15 2.612 0.46.2529 0.32 1590 24.0.2598 0.23 2.620 0.76.2523 0.55 1640 24.8.2593 0.42 2.630 1.15.2518 0.75 1670 25.3.2589 0.57 2.638 1.45.2514 0.91 1695 25.6.2584 0.77 2.647 1.79.2510 1.07 1705 25.7.2581 0.89 2.654 2.06.2506 1.23 1725 25.8.2575 1.12 2.664 2.44.2502 1.38 Rolling Direction Tensile Test (Mg-4%Li): 0 0.0 2.610 0.00.2586 0.00.2579 0.00 800 12.0 2.618 0.30.2584 0.07.2577 0.07 900 13.4 2.631 0.80.2578 0.31.2572 0.27 960 14.2 2.641 1.18.2572 0.54.2569 0.38 1000 14.8 2.649 1.49.2567 0.74.2566 0.50 1055 15.5 2.662 1.98.2559 1.05.2562 0.66 1085 15.9 2.670 2.26.2555 1.21.2559 0.78 Transverse Direction Tensile Test (}g-44Li): 0 0.0.2612 0.00 2.600 0.00.2608 0.00 500 7.3.2611 0.03 2.603 0.11.2607 0.03 685 10.0.2607 0.19 2.613 0.50.2601 0.26 740 10.9.2605 0.26 2.620 0.76.2599 0.34 820 11.9.2599 0.50 2.631 1.19.2594 0.53 880 12.7.2594 0.69 2.643 1.64.2590 0.69 935 13.4 2584 1.08 2.655 2.08.2586 0.85 Load Stress R eR T eT Z eZ (lb) (ksi) (in) (%) (in) () (in) ( Rolling Direction Compression (Pure Mg): 0 0.0.2685 0.00.2991 0.00.2450 0.00 280 3.8.2668 0.63.2995 0.13.2473 0.93 350 4.7.2637 1.80.2998 0.23.2513 2.53 450 5.9.2599 3.25.3006 0.50.2550 3.98 600 7.8.2569 4.41.3018 0.90.2590 5.55 900 11.6.2527 6.06.3030 1.30.260 7.10 Transverse Direction Compression (Pure Mg): 0 0.0.2565 0.00.3070 0.00.2499 0.00 200 3.1.2566 0.11.3065 0.16.2506 0.28 300 4.6.2571 0.31.3037 1.08.2539 1.60 450 6.8.2583 0.78.2990 2.63.2589 3.56 700 10.5.2608 1.74.2933 4.57.2632 5.18 1000 14.8.2620 2.18.2900 5.70.2660 6.23 Thickness Direction Compression (Pure Mg): 0 0.0.2671 0.00.3031 0.00.2470 0.00 400 4.9.2674 0.11.3032 0.03.2467 0.12 800 9.9.2698 1.01.3042 0.36.2450 0.81 1000 12.2.2721 1.86.3060 0.95.2433 1.52 1200 14.5.2744 2.69.3063 1.05.2417 2.17 1500 17.9.2782 4.05.3079 1.57.2388 3.37 1700 20.1.2820 5.43.3095 2.08.2363 4.42 Rolling Direction Compression (Mg-.5%Th): 0 0.0.2780 0.00.2979 0.00.2500 0.00 800 10.7.2779 0.03.2979 0.00.2500 0.00 1160 15.6.2770 0.36.2980 0.03.2521 0.84 1225 16.2.2735 1.64.2983 0.13.2562 2.46 1400 18.1.2680 3.69.2994 0.50.2604 4.07 1700 21.4.2580 7.43.3009 1.00.2642 5.52 Transverse Direction Compression (Mg-.5%Th): 0 0.0.2780 0.00.3077 0.00.2500 0.00 1000 14.4.2781 0.03.3061 0.52.2520 0.80 1100 15.8.2781 0.03.3052 0.81.2536 1.44 1200 16.9.2786 0.21.3020 1.87.2572 2.86 1400 19.3.2797 0.61.2948 4.28.2622 4.77 1800 24.4.2820 1.43.2889 6.30.2670 6.60 Thickness Direction Compression (Mg-.5%Th): 0 0.0.2800 0.00.2990 0.00.2512 0.00 500 6.7.2799 -.03.2990 0.00.2510 0.08 1000 13.3.2799 -.03.2990 0.00.2509 0.11 1600 21.3.2802 0.07.2995 0.16.2503 0.35 2000 26.4.2814 0.50.3012 0.73.2485 1.08 2500 32.3.2849 1.75.3054 2.12.2436 3.08 Rolling Direction Compression (Mg-4%Li): 0 0.0.2908 0.00.3000 0.00.2511 0.00 810 10.7.2895 0.44.3004 0.13.2521 0.39 900 11.7.2856 1.82.3015 0.50.2552 1.63 1000 12.9.2829 2.75.3025 0.83.2579 2.66 1200 15.2.2770 4.86.3037 1.23.2620 4.25 1600 19.8.2700 7.43.3055 1.83.2680 6.51 Transverse Direction Compression (Mg-4%Li): 0 0.0.2870 0.00.3069 0.00.2502 0.00 700 9.7.2873 0.10.3053 0.52.2520 0.71 850 11.6.2887 0.59.3002 2.20.2559 2.22 1000 13.5.2892 0.76.2977 3.04.2579 3.00 1250 16.4.2910 1.38.2890 6.00.2648 5.67 1600 20.6.2920 1.73.2832 8.03.2689 7.20 Thickness Direction Compression (Mg-4*Li): 0 0.0.2860 0.00 o.3011 0.00.2540 0.00 1000 11.6.2867 0.24.3018 0.23.2532 0.31 1300 15.0.2872 0.41.3030 0.63.2517 0.91 1700 19.3.2891 1.08.3052 1.36.2483 2.25 2000 22.5.2911 1.78.3077 2.14.2461 3.15 2400 26.3.2951 3.12.3130 3.87.2394 5.90

UNIVERSITY OF MICHIGAN 3 901 5 03023 85321111111111 3 9015 03023 8532