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Crystallography of low alloy iron martensites 1967

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CRYSTALLOGRAPHY OF LOW ALLOY IRON MARTENSITES by PAUL WILLIAM JEFFREY A THESIS SUBMITTED IN PARTIAL FUIJILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN THE DEPARTMENT OF METALLURGY We accept this thesis as conforming to the standard required from candidates for the degree of MASTER OF SCIENCE Members of the Department of Metallurgy THE UNIVERSITY OF BRITISH COLUMBIA April, 1967. In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I ag r ee t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r ag ree t h a t p e r m i s s i o n f o r e x - t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r an by the Head o f my Depar tment o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n - c i a l g a i n s h a l l no t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Depar tment o f Metallurgy The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, Canada Date May 5, 1967 ABSTRACT The morphology and crystallography of the martensite transformation in pure iron and low alloy Fe-C, Fe-Mn, Fe-Hn-Si, Fe-Ni steels which contain no retained austenite was studied. Single surface trace analyses by transmission electron microscopy on directions parallel and normal to the martensite substructure were found to be consistent with the martensite crystals having the form of plates rather than needles. The directions normal to the martensite substructure plates were consistent with a £l45J M habit plane. Optical studies of the martensite surface shears within prior austenite grains revealed that 4 shear variants generally occur. However grains containing 5 or- more shear variants could be found which appears to suggest an austenite habit plan© close to bint different from { i l l ] * » A single surface trace analysis of the martensite surface shears using the austenite annealing twin vestiges to orient the grain was consistent with an austenite habit plant ~ 7° from [ i l l ] A , Two inhomogeneous shear systems were found to predict the experimental results when applied to the Wechsler, Lieberman, Read theory of martensite transformations. They are ( l 0 0 ^ [ 0 l o ] A and ( l l l ) A [ l l 2 ] A The (ill}, system is to be generally preferred as its predicted habit planes ( 7.12° from [ l l l } A and 5.03° from (l45^ M are more consistent with the trace analyses. Preliminary work included an investigation of the maraging properties of the Fe-Mn-Si system. ACKNOWLEDGEMENT The a u t h o r would l i k e t o ex t e n d h i s s i n c e r e t h a n k s t o h i s r e s e a r c h d i r e c t o r , Dr. D. Tromans f o r h i s g u i d a n c e and h e l p d u r i n g t h i s work. The f r e e l y g i v e n a d v i c e and a s s i s t a n c e by members o f t h e f a c u l t y , s t a f f and s t u d e n t body was i n v a l u a b l e t o the c o m p l e t i o n o f t h i s work and i s g r e a t l y a p p r e c i a t e d . The f i n a n c i a l s u p p o r t . p r o v i d e d by t h e N a t i o n a l R e s e a r c h C o u n c i l and Defence R e s e a r c h Board i s g r a t e f u l l y acknowledged. TABLE OF CONTENTS Page I. INTRODUCTION AND AIM OF INVESTIGATION 1 II. GENERAL FEATURES OF MARTENSITE TRANSFORMATIONS 2 III. PREVIOUS WORK 4 IV. EXPERIMENTAL. 8 1. Materials 8 2. Alloy Preparation 8 3. Alloy Analysis 8 4. Surface Shears 9 5. Electron Microscopy 10 V. RESULTS 11 1. Surface Shears H 2. Electron Microscopy 11 3. Calculations 12 VI. DISCUSSION OF RESULTS 38 1. Surface Shears 38 2. Electron Microscopy 40 3. Calculations 41 VII. CONCLUSIONS ........ 45 V I I I . SUGGESTIONS FOR FUTURE WORK 47 IX. APPENDICES (I) Wechsler, Lieberman, Read Phenomenological theory of martensite transformations 48 (II) Investigation of Maraging Properties of Fe-Mn-Si System 60 TABLE OF CONTENTS (continued) Page 1. General ... . 60 2. Alloy P reparat ion and Analysis 62 3. Results • 63 4. Discussion of Results 67 5. Future Work 71 X, REFERENCES 79 LIST OF FIGURES Plfl'i. No. I a n 1 Variation ©f Calculated Martensite Habit Plan© vdth Vj sN/S t i > i • > l • • l l • ( l l • • a « i • • i • • > l i M • l i i i l i l • t i 24 2 Varlatien ©£ Galeulatgd Auitmite Habit Plant vdth \/j S\/S I I I y 1 I I I I M I I t l 1 1 1 > N I I H I • • i I 1 I t >1 M l l l l 24 3 Pure Iron. Martensit© Surface Shears. 1060 X 25 4 Pure Iron. Martensite Substructure. 29000 X,....... 25 5 Fe-0.06$ G. Martensite Surface Shears. 530 X 26 6 Fe~0.06$ C, Martensite Substructure.' 29000 X. 26 7 F©-0.17$ G, Martensite Surface Shears. 1430 X..... 27 8 Fe-0,17# C. Mar tens i te Substructure . 29000X 27 9 Fe-6.C# M n . Martensi te Surface Shears. 1100 X . . . . 28 10 Fe-6.0/S Mn. Martens i te Subst ructure . 29000 X 28 11 Fe-1.7% Si-7.83# Mn. Martens i te Surface Shears. 1060 X 29 12 Fe~l„7$ Si-7.83$ Mn. Martensi te Substructure. 29000 X 29 13 Fe-10.79# N i . Martens i te Surface Shears. 1060 X . . . . , 30 14 Fe-10.79^ N i . Martensi te Substructure , 29000X..... 30 LIST OF FIGURES (continued) Fjg. No„ Page 15 Fe-„r$ C. Austenite Annealing Twin vestiges within Prior Austenite Grains » ........... 31 16 Pure Iron: Single Surface Trace Analysis (Directions) 32 17 Pure Iron: Single Surface Trace Analysis (Normals) 32 18 Fe-.06# C. Single Surface Trace Analysis (DirectiorB ) 33 19 Fe-,06# G, Single Surface Trace Analysis (Normals) 33 20 Fe~.17$ G. Single Surface TraeeAnalysis (Directions) 34 21 Fg-.17# G. Single Surface Trace Analysis (Normals) 34 22 F§-6.0$ Mn. Single Surface Trace Analysis (Direetiens) 35 23 Fe-6,G$ Mn. Single Surface Trace Analysis (Nornals) 35 24 Fe«l.?$ Si-7«83$ Mn, Single Surface Trace Analysis ( D i r e c t i o n s ) • i « a i > « > • • > i > • M > > M »«>••> < 1 • • M u 36 25 Fe~l.?g Si-7.S3$ Mn. Single Surface Trace Analysis (Normals)•••^••••••••••o«»ao»»««*«»*****«»«*»****««* 3o 26 Fe-10.79^ Ni. Single Surface Trace Analysis (Directions) 37 27 Fe-10979#Ni. Single Surface Trace Analysis (Normals) 37 28 Relation Between b.c.t. and f.c.c. Unit C e l l s , . . . . . . . . 48 29 Orthogonal Basis Formed by unit vectors 4*/v,^ ....... 51 30 S l i p Shear "g" in Basis Defined by ^,v:}w 51 31 T y p i c a l Massive Martensite Structure ................. 64 32 Fe-Mn and Fe-Ni Binary Phase Diagrams................. 72 33 Fe—Si Binary Phase Diagram............................. 73 34 Fe-1.0% Si~4°5$ Mn. Aging Curves...................... 74 35 Fe-6.0$ Mn. Aging Gurves ............................ 74 36 Fe-1 .7$ Si - 7 „ 8 3 $ Mn. Aging Gurves 75 LIST OF FIGURES (continued) F JK» NoA Page 37 Fe - 4 . 0 $ S i - 8 .0$ Mn. Aging Curves . . . . . . . . 75 38 Fe-4„79# Si - 8.08$ Mn. Aging Curves 76 39 Fe - 5 , 1 5 $ S i - 9 .43$ Mn. Aging. Curves« 76 40 Fe - 5 . 9 3 $ s i - 13.58$ Mn. Aging Curves 77 41 Fe-6,3C# S i -19 ,40# Mn. Aging Curves. 77 42 Fe~2.5$ Si - 6 . 0 $ Mn~0.5$ T i . Aging Curves 78 1 LIST OF TABLES Table No. Page 1 F&-»17# C, Annealing Twin Vestige Analysis. ..... 13 2 Fe-,17^ 0. Annealing Twin Vestige Analysis 13 3 Fe-6.0$ Mn. Annealing Twin Vestige Analysis..... 14 4 Pe-6.C# Mn. Annealing Twin Vestige Analysis.......... 14 5 Pure I ron , S ing le Surface Normal A n a l y s i s . . . . . . . . . . . . 15 6 Fe-,06# 0, S ing le Surfas© Normal A n a l y s i s . . . . . . . . . . . » 16 7 Fe*-, 17$ C , S ing le Surface Normal Ana l ys i s . » » . , » « • . . . . 17 8 Fe-6»0$ Mn. S ing le Surface Normal A n a l y s i s . . . , . « . . . * * 18 9 Fe-1.7# Mn. S ing le Surface Normal A n a l y s i s . . . 19 10 Fe-I0.79$ N i , S ing le Surface Normal A n a l y s i s , . . , 20 11 Comparison of S ing le Surface D i r e c t i o n Ana l ys i s with 12 Ca l cu la ted va lues of d i s l o c a t i o n shear (g) and shape 22 deformation (S) f o r two choices of the inhomogeneous shear 13 Ca l cu l a ted p a r a l l e l i s m between i nd i c a t ed shear elements f o r two choices of the inhomogeneous s h e a r , , . . . . . . . . . . . . 22' LIST OF TABLES (continued); Table No. Page 14 Ca l cu la ted d i r e c t i o n cosines f o r aus ten i te (H/0 and martensite (%) habi t planes f o r two choices of the inhomogeneous shear 0 < > o < > o > B o o o o e o«o» o e « o i > * o o»<>>»»»o« o 23 15 Ca l cu la ted angles between given planes f o r two choices of the inhomogeneous shear <> a . o » « • » < > . o«» 23 16 Ana l y s i s of A l l o y s i n Weight Percent 65 17 S t ructures present a f t e r coo l ing from the Austen i te £^G£P_Ono o o o o o e o o • o oo « o o o o « « o o c o o e e e o o o o * « o o o o o o o e o s e * « « 66 INTRODUCTION AND AIM OF INVESTIGATION This work began as an examination of the transformation substructure and aging characteristics of the martensitic Fe-Mn-Si alloys. The similarity between the Fe-Mn and Fe-Ni binary phase diagrams suggested that a Fe-Mn base maraging steel could be developed in analogy to the commercial Fe-Ni maraging steels. While suggestions of a martensite aging reaction were found the work was largely fruitless; and so i t was decided to terminate the aging studies and concentrate on the crystallography and morphology of low alloy ferrous martensites in general. The decision to concentrate on the crystal- lography and morphology was strengthened by the fact that preliminary studies on the substructure showed deviations from what was generally accepted in the literature* The habit planes in a number of these low alloy martensites were determined. The phenomenological theory of iron martensites as given by Wechsler, Lieberman, and Read was used in an attempt to theoretically explain the experimental results. The body of the thesis considers the work on the crystallography and morphology while Appendix II contains the preliminary studies carried out bn the aging characteristics. GENERAL FEATURES OF MARTENSITE TRANSFORMATIONS - 2 - Some alloys exhibit dual behaviour in that they can transform into different structures depending on the cooling rate. For example, in low nickel steel with an air cool there appears a structure formed by a nucleation and growth process known as equiaxed alpha. But at much higher cooling rates the above nucleation and growth may be too slow and the large driving force (free energy) may become sufficient to cause a shear type of transformation. This is called a martensitic transformation and involves the cooperative movement of many atoms. Evidence that martensitic transformations do not involve atomic interchange l i e in the facts that the product phase is of the same composition as the parent, and that alloys already ordered remain ordered after the transformation. A special kind of martensitic transformation is mechanical twinning where the driving force i s deformation rather than in- ternal free energy. The experimental observation most commonly associated with marten- sitic transformations is the til t i n g on the surface of a sample which was polished before quenching to martensite. This observed- tilting preserves lines (vectors) as lines and planes as planesj for example, a scratch made on a surface before transformation will show no observable discontinuity where i t crosses the boundary from parent to product phases, Hence i t appears that the product in a martensite transformation i s coherent with the parent* The interface, or plane of contact, between the parent and product phases is called the "Habit Plane"; i t is the plane of the lattice along which the martensite plates form. Another experimental feature used to identify a specific transformation i s the "Orientation Relationship" which states the parallel planes and parallel directions in the parent and product phases. Rational habit planes or rational pairs of parallel lines and planes are not predicted by current martensite theories. - 3 - There are two common types of martensite formed, massive and acicular. Acicular martensite is found in F e-Ni (30 - 33$ Ni) and Fe-C ( % C > 0„6) binaries1 both acicular martensites are characterized by retained austenite and a twinning shear mode. When the amount of solute (substitutional or interstitial) is sufficient so as to suppress the equiaxed (X structure but not so much as to form the acicular structure there appears massive marten- site,, A polished .surface after a massive martensite transformation appears as many shear plates with only a few unique orientations enclosed within the thermally etched prior austenite grain boundaries. Under the electron micro- scope is observed many parallel martensite plates whose thickness is of the same order as the shear platesj but the relation between the two is not fully understood,, Within the martensite plates large tangles of dislocations are seen, hence the reason for considering the dislocation shear mode to be operative. The boundary between the martensite plates is irregular and wavy and could be due to small distortions in the habit plane. It should be noted that the shear plates which form on the polished surface necessarily have different boundary conditions than plates formed within the specimen and hence one must be careful ln interpreting their significance. -PREVIOUS WORK - 4 - The alloys on which most crystallographic studies have been done are those whose Mg temperature is below room temperature. The reason for this is that in these alloys i t is possible to obtain the parent (austenite) and product (martensite) phases coexisting, with the product phase of a size large enough to be observable without optical aid. The habit plane of the martensite crystal can then be accurately obtained by two surface trace analysis. The orientation relationship between the two phases can be found by straddling a martensite plate with an X-ray beam so that the photograph will contain reflections from the austenite as well as from the martensite. In alloys with low amounts of solute (both Interstitial and substitutional) Mf is above room temperature, hence there is no retained austenite. The habit plane can only be determined by the method of single surface trace analysis which is very hard pressed in most cases to give an unique result. The orientation relationship cannot be determined without both phases being present. The martensitic transformation has been observed in pure iron by Jflibby and Parr (l) and Wayman and Altstetter (2), Wayman and Altstetter found the surface shears to be consistent with an apparent [ l l l ] ^ habit plane and the martensite crystals to be plate-like rather than needle-like. I t should be noted that needles which l i e along O-IQ)^ can appear to have a pseudo {lll}A habit plane (3). One of the definitive papers in the crystallography of Fe-C is that due to Greninger and Troiano ( 4 ) . They found,through a two surface trace analysis of the twin band vestiges,that in steels with %G) 1.4 the martensite plates were parallel to (25<)}A, with 0.4$^S<JU4# the plates were parallel to f225J < 4 9 while in steels with C <JD,4$ the martensite crystals vrere needle shaped and formed in a plate-like array along the f U l L planes. „ 5 - Bowles (5) found that the {lll}^ habit plane is comprised of laths parallel to a <^10lXdirection and is not therefore a true habit plane. Kelly and Cutting (6) by the method of single surface trace analysis found that the long axis of the martensite crystals were parallel to ^ l l l ^ , , while the traces normal to the crystals were not consistent with any particular plane0 Hence they concluded that the martensite crystals are likely needles rather than plates 0 If the Kurdjumov-Sachs orientation relationship is assumed then < ( l l l ^ is parallel to (110% , This (110% direction has been reported by other workers (4,5,7). It is not known for sure whether the crystallography of stain- less steels is the same as low carbon alloys, but work such as that done by Kelly and Nutting support the view. They found two different types of martensite, one type as in high carbon steels and a 20$ Ni - 0.8$ C steel had a plate-like substructure which was internally twinned while the second type as in low carbon and 18-8 stainless steels had a substructure com- posed of so called needles which were not internally twinned. Owen, Wilson and Bell (8) state that they observed only 4 different massive martensite shear traces within any volume formed from a single austen- ite grain. This was taken as evidence that the martensite crystals form on the [ l l l \ A planes. The appearance of the surface shears in Fe-Mn binaries has been found to be very similar to those in Fe-Ni„ Scatter has been observed (9,10) in crystallographic determina- tions of the {2591A habit plane,, that is great&r than that attributable to experimental technique. The scatter is perhaps partially explainable by slight internal stresses which distort the habit plane, but this cannot be the complete answer as the calculated poles due to such a stress l i e on a curve in the stereographic triangle, where as observed scatter (lO) is as great normal to this curve as along i t . Though quite a number of phenomenological c r y s t a l l o g r a p h i c theories have been published three of them have gained the widest acceptance; they are those due to Wechsler, Lieberman, Read (WLR) ( l l , 12), Bowles, Mackenzie (BM) (13) and Bullough, B i l b y (BB) (14). The WLR theory assumes that the habit plane i s undistorted and unrotated while the BM theory assumes the habit plane to be unrotated but does allow small d i s t o r t i o n s i n the region of one percent 0 The BB theory assumes an undistorted habit plane but enables other parameters t o be r e a d i l y varied,, A l l three of these theories are e s s e n t i a l l y equivalent i n that they are based on the idea that the t o t a l shape deformation accompanying the martensite transformation i s , at l e a s t approximately, an i n v a r i a n t plane s t r a i n . Comparisons of the 3 theories are contained i n ( l5 , 16, 17)9 In the i r o n base martensites these theories have been able to pre** di e t the {259^ and (3, 10, 15}^ habit planes but are not so successful with the {225j^, unless a 105% d i l a t i o n of the habit plane i s allowed,, Recently a theory by Lieberman and Bullough (13) which incorporates the observation that martensite plates with a [22$^A habit are composite (consist of twinned and untwinned regions) appears t o account f o r the {225?A habits. With a l l three of the theories i t i s possible to predict the aus- t e n i t e and martensite habit planes from a knowledge of the l a t t i c e parameters of the austenite and martensite and of the s l i p system operative, A given s l i p system i s used pr disgarded on the following basiss ( l ) the calculated habit plane corresponds to that determined experimentally (2) the values of g, the l a t t i c e i n v a r i a n t shear, and S, the macroscopic shear, must be r e l a t i v e l y small* (3) the s l i p system should be one commonly operative i n that type of phase0 Wechsler, Read and Lieberman (19) investigated the s l i p systems along [lll}^ planes with regard to t h e i r a p p l i c a l i t y to the ^225JA habit, Of more i n t e r e s t t o the present work though was the fa c t that the s l i p system (lll ) ^ | l 2 l ] ^ predicts a habit plane close to j " l l l ^ p and also has r e l a t i v e l y small values of g and S„ Otte ( 2 0 ) investigated a number of different slip systems and compared the calculated habit planes to those commonly observed experi- mentally! also considered was the effect which variations in the volume ratio of martensite to austenite has on the calculated habit planes. Computer programs were used by Grocker and Bilby ( 2 l ) with the Bullough and Bilby theory to examine the crystallographic features of martensite reactions in steels. One interesting comment they make is that virtually any habit plane cou],d be predicted by making a suitable choice of dislocation shear; hence they had to limit their analysis to those shear systems commonly observed in either the austenite or martensite, A surface martensite which formed at 20 - 30° C above the M8 temperature f o r the bulk material has been reported by Honma (22) i n Iron alloys of between 20 and 30% N i , Similar results were obtained by Kloetermann and Burgers (23) i n a Fe - 30.2$ Ni - 0,4$ G alloy. The surface martensite was found to form as needles down to a depth of from 5 -»30/<. This surface martensite has been explained (24) as being caused by a reduction of the strain energy term which i s Introduced i n calculating the critical embroyo size for martensite formation. The question of the presence of a surface martensite was examined within the department on Fe - Ao8$ Cu martensite, Down to a depth of approximately „010 inch the martensite was-observed to be uniform with no distinct surface martensite layer. - 8 - EXPERIMENTAL MATERIALS t The iron stock used has the trade name "Ferrovac E" and was obtained from the Crucible Steel Company of America. The impurities in weight percents were as follows. C .005, Mn .0005, P .003, S .005, Si .006, Ni .02, Cr .006, V .004, W .01, Mo .001, Co .006, N .00085, \ .0030, \ .000025, Cu .01. Ferrosilicon was obtained from Esco Refinery of Port Coquitlam. The silicon content was analyzed to be 86.7 wt.$. Electrolytic manganese was used in preparing alloys, ALLOY PREPARATIONi Four of the six alloys studied were prepared by induction melting under an argon atmosphere, A fused magnesia crucible was used but because these invariably crack i t was found necessary to place them inside larger silicon carbide crucibles. The gap between the two crucibles was fi l l e d with alumina and sealed with refractory cement. The iron was melted f i r s t , then ftuuoViNG ADDITIONS the manganooe and silicon- added portion by portion, waiting 4 to 5 minutes between each portion to allow thorough melting and stirring of the fresh charge. This procedure is most important as several melts were found to be in inhomogen- eous. The heats were c h i l l casts into iron moulds. The quantity of each alloy cast was approximately 300 gms. The Fe - .17$ C alloy used was a commercial mild steel. The pure iron "alloy" was Ferrovac E, ALLOY ANALYSIS The compositions of the six alloys studied were analysed to be* (1) Pure iron (2) F e - .06$ C • . . (3) Fe - .17$ C (4) Fe - 6.0$ Mn (5) Fe - 1.7$ Si - 7.83$ Mn (6) Fe - 10.79$ Ni The Fe- 6,0$ Mn alloy was analysed (along with those listed in the Appendix II) by X-ray fluorescence, while the Fe - 1.7$ Si - 7.83$ Mn and F e - 10.79$ Ni alloys were analysed chemically. The carbon alloys were analysed by burning a sample of known weight in pure oxygen, collecting and weighing the CO2 formed, and then calculating the Wt, $ C in the sample. The method used for th© analysis by X-ray fluorescence i s as follows. Six alloys as.listed i n Appendix II were chemically analysed, these were used as standards in the determination of the calibration chart which compares the ratio of the heights of the manganese K«., Krtipeak and i r o n K/3; peak against percent manganese. The fact that there was a 3rd element present, silicon up to 6 percent, will slightly affect the accuracy of the calibration curve. Specimans used on the X-ray fluorescence unit were approximately x £ M x with one face polished on 3/0 grit paper,, SURFACE SHEARS: The surface shears caused by the martensitic transformation were studied as follows. Samples approximately x % w were polished either elec- trolytically or with diamond paste. Samples of pure i r o n , Fe - 0 6$ C, and Fe - ,17$ C were .030 in. thick while those of Fe - 6.0$ Mn, F© - 1,7$ Si - 7.83$ Mn, and Fe - 10.79$ Ni were about 0,100 in. thick. The specimans were sus- pended in a dissociated ammonia atmosphere (3%+^) for 1^ hours at a temperature of approximately 1250°C„ The presence of nitrogen in the atmos- phere appeared to have no effect on the surface shears formed as specimans which were treated in a pure % atmosphere gave similar shear configurations. A soaking time of 1^ hours was used to ensure stabilization of the austenite grain growth. It was found necessary to quench from a temperature as high as 1250°C because otherwise the austenite grains were so small as to inhibit - 10 - formation of the martensite surface shears. After soaking at 1250 C the specimans were quenched directly into brine, at which time the surface shears formed on the pre-polished surface, ELECTRON MICROSCOPY; Material to be used for electron microscopy was first hot rolled from the cast thickness of 0.5 inch down to approximately ,040 inch. The surfaces were cleaned of oxide in a warmed 15$ solution of sulfuric acid in water and subsequently cold rolled, to obtain a smooth surface, down to a thickness of ,025 inch. Samples of approximately ̂  x | inch were cut from the sheet, annealed at 1050 C for 1 hour in a atmosphere and then quenched into brine. The sample was then chemically polished down to a thickness of about ,003 inch in a warmed solution of the following composition* HCl 20 c.c. H3P04 20 c.c. HN03 50 c.c. CH3COOH 100 c.c. It was necessary to stir the solution vigorously so as to ensure an even attack. Because the chemical polishing solution rapidly decomposes i t must be discarded after polishing each speclman, Ohoosing the thinnest areas left by the chemical polishing proeess the speclman was electropollshed by the Bollman technique (25) in a solution of the following compositions Water 7 c.c. Chromic Acid 25 gms. Acetic Acid 135 c.c. The foils were studied using a Hitachi Hu - 11A electron, microscope at an accelerating voltage of 100 KV, Single Surface Trace Analyses Single surface trace analyses were used to investigate the austenite and-martensite habit planes. The austenite habit plane was investigated using the austenite annealing twin vestiges to orient the grain with respect to the austenite axes. This can be done by finding 3 twin vestiges within any one prior austenite grain and by using the fact that the twinning plane i n the austenite i s ^ l l l ] . In t h i s analysis i t was possible to obtain any number up to h traces from one oriented grain. The analysis was carried out "by o p t i c a l microscope at 200X. Transmission electron microscopy was used to investigate the martensite habit plane. The zone axis of the plane of the image was obtained from a selected area d i f f r a c t i o n pattern of the sub- structure plate under consideration.. Each substructure plate was oriented by comparing with s p e c i f i c crystallographic directions on the selected area d i f f r a c t i o n pattern. RESULTS SURFACE SHEARS A l l six of the alloys studied were found to undergo a martensitic transformation as evidenced by the presence of surface shears on a speciman polished before quenching. The surface shears were found to be limited by the boundaries of the austenite grains which were thermally etched during the austenizing treatment• Only a small number of orientations to the surface shears were found within any one prior austenite grain, with 4 being the greatest number commonly observed. But in a l l six alloys areas were observed where 5, 6 or 7 traces were present (figs. 3» 5j 7S 9» Hj> ̂ 3̂ » appearance of the surface Bhears for a l l six alloys was very similar 0 Tables 1 to 4 give the stated angular measurements made during the single surface trace analysis of the surface shears in the F© - ,17$ C and F@ - 6,0$ Mn alloys. Fig, 15 shows the typical appearance of the annealing twin vestiges, ELECTRON. MICROSCOPY A single surface trace analysis was carried out on a l l six alloys, Th© grsat circles connecting the directions parallel and normal to th© martensite crystals with the aone of the surface, ar© plotted in Figs, 16, 18, 20, 22, 24, 26 and 17, 19* 21, 23, 25, 27 respectively. The angles which the above great circles for directions normal to the crystals make with each of [l00J M, foil},,, ( l l l } M , {112k, fl45? M » a n d the calculated plane*are given in tables 5 to 10. The great circles for directions parallel to the martensite crystals are compared with the directions <̂ 111̂ >M in table 11. Electron micrographs of the martensite substructure are given in Figs. 4j> 6, 8, 10, 12, L4. * Calculated plane refers to that predicted using the system (111) A [112]A with V-j- = 1.04 i n the Wechsler, Lieberman, Read, Theory. . - 12 CALCULATIONS For the inhomogeneous shears ( l U ^ [ll2]^ and (lOo)A [oio]^ the values of "g" (dislocation shear) and MS M (Shape deformation) were calculated as per appendix I for values of Vj of 1.00, 1.03, 1.04 and 1.08866. The results are contained in table 12. The parallelism between close packed planes and directions in the austenite and martensite for the above slip systems and values of Vj are,'given in table 13. The calculated habit planes In the austenite and martensite are given In table 14} with the same results plotted in Stereographies triangles GRAINS DEGREES GRAINS DEGREES GRAINS DEGREES 1 0.5 0.0 0.0 2.0 4 0.0 7 0.0 0.5 0.0 4.0 3.0 2.0 0.0 2 0.5 5 0.5 2.0 • . 0.0 2.0 8 2.0 0.0 0̂ 0 0.0 3 1.0 6 0.0 1.0 0.0 1.0 . - Table \r Fe - ,17$C, Annealing twin vestige analysis. Angles are those between surface shear nor- mals and calculated austenite habit plane. GRAINS DEGREES . GRAINS DEGREES GRAINS DEGREES 1 2.0 4.0 2,0 0.0 . 4 7 2.0 6.0 22.fr 6,0 2.0 2.0 2.0 2 2.0 5 0.0 4.0 0.0 8,0 S 3.5 5.0 7.5 2.0 3 4aO 6 1.0 • 2.0 2";o 6,0 Table.. 2. Fe -,17$G, Annealing twin vestige analysis. Angles are those between surface shear directions and \110)A, - 14 GRAINS ' DEGREES GRAINS DEGREES GRAINS DEGREES 1 3,0 3 1.0 5 2.0 0.0 1,0 1.0 0.0 2.0 2.0 2 0.0 . 4 1.0 0.0 5.0 0.5 0.5 Table 3. Fe- 6.0$ Mn. Annealing twin vestige analysis. Angles are those between surfa<feEnormals and calculated austenite habit plane. GRAINS DEGREES GRAIN DEGREES GRAIN DEGREES 1 0.0 3 2.0 5 0.0 2.0 ' 5.0 3.0 3.0 7.0 3.5 2 9.5 4 1.5 2.0 . 1.5 4.5 8.5 Table_4o. Fe - 6.0$ Mn, Annealing twin vestige analysis. Angles are those between surface shear directions and (l!0)A . Table 5* Pure Iron. Single Surface Trace Analysis. Angles given are those between normals to martensite substructure plates and indicated planes. ZONE DEGREES FROM 4 fiooj {110} f i l l ] [112] {145} Calculated '00l\> • 41.5 3.5 3.5 1,0 3.0 1.0 pll\ 2.0 2.0 33.0 22.0 8.0 11.0 16.0 0.0 16,0 9.0 4.0 0.0 39.5 2.0 10.0 2.0 2.0 2.0 tint 9.5 7.0 22.0 6.5 1.0 0.0 15.0 n.o 20.0 0.5 2.0 3.0 15.0 11.0 16.0 0.5 2.0 3.0 17.5 8.0 16.0 2.5 3.5 0.0 oiz] 19.0 6.5 11.0 4.0 4.0 2.0 20.5 8.0 7.0 • 1.0 2.0 1.0 112J 37.0 1.0 18.0 7.5 0,0 3.0 37.0 4.0 11.0 2.0. 0.0 2.0 17.0 0.0 10.0 0.0 5.0 10.0 16.5 3.5 9.0 2.0 2.0 6.5 15.0 6,0 8.0 3.0 1.0 3.5 16.0 • 10.0 0.0 0.5 1.0 . 1.0 i to? 17.0 9.0 20.0 6.0 0.0 0.0 8.0 13.0 10.0 2.5 2.0 1.5 25.0 9.0 8,0 2.0 2,0 0.0 8.0 2.0 •  20.0 10,0 6.0 n.o 6.5 3.5 20.0 10,0 5.0 9.0 7.0 5.0 20,0 10,0 4.0 8.5 6.0 5.5 20,0 10.0 3.0 8.0 m 2,0 14.5 13.0 4.0 8.0 6.0 - 16 Table 6* F e - .06$ C 0 Single Surface Trace Analysis. Angles given are those between normals to martensite substructure plates and indicated planes. ZONE DEGREES FROM (lOOJ {lio} [111] (112? {145} Calculate. {001} 42.5 2.5 2.0 2.0 4.0 1.5 {011} 39.0 4.0 16.0 4.0 3.0 - 1.0 { n i l 23.0 1.0 27.0 8.5 2.0 2.0 7.5 6.0 8.5 4.0 0.5 0.5 10.5 7.5 12.0 5.0 0.5 2.0 13.0 8.0 14.0 3.5 0.5 2.0 {012] 15.5 10,0 18.0 0.5 0.0 4.0 21.0 5.5 7.5 2.0 2.0 2.0 21.0 6,0 7.5 1.5 2.5 1.5 18.0 6.0 6.5 3.5 0.5 0.0 18.0 6,5 5.5 3.5 0.5 0.0 12.0 10.0 6.0 3.0 0.0 1.0 [113] 14.0 1.0 16,0 6.0 6.0 5.0 16.0 3.5 18.0 7.0 3.0 3.0 16.0 6.0 19.0 7.0 1.0 2.0 17.5 8.5 20.0 7.0 2.0 1.0 (123] 25.0 8.0 11.0 2.0 0.0 1.0 32.0 3.0 17.0 1.0 3.5 1.0 (133? 5.0 6.0 22.0 0.0 3.0 0.0 {014I 34.0 4.0 12.0 10.0 2,0 0.0 10.5 2.0 6,0 8.0 3.0 0.0 1.1151 15.0 9.5 3.5 4.0 2.0 1.0 {135? 3.5 16.0 9.5 3.5 6.0 6,0 12,0 11,0 6.0 3.0 0.0 1.0 13.0 5.5 3.0 6.5 1.0 1.0 12.0 7.0 0.0 4.5 0.5 1.0 - 17 - Table ft Fe - .17$ C. Single Surface Trace Analysis. Angles given are those between normals to martensite substructure plates and indicated planes. ZONE . , DEGREES FROM fiooj {110? {111] (112] {145$ Calculated {001} 38.5 6.5 6.0 4.0 0.5 3.0 35.5 9.5 7.5 5,5 3.5 5.5 fmj 24.0 16.0 16.5 2.5 6.0 2.5 22.0 2,0 26.0 8.0 2.5 8.5 19.5 5.5 23.0 5.0 2.0 3.5 18.5 6.0 22.0 4.0 3.0 2.0 13.0 9.0 15.5 2.0 3.0 0.0 14.0 9.5 19.0 1.0 2.0 3.5 (012} 14.0 . 10.5 17.5 0.0 0.0 2.0 24.0 1.0 0.0 10.0 4.0 7.0 26.0 2.0 2.0 8.0 2.0 4.5 • .30.0 4.0 4.0 4.5 1.0 2.0 {112} 6.0 3.0 24.0 12.0 .' 3.0 1.0 12.0 9.0 7.5 5.0 1.0 0.0 {122} 16.0 6.0 4.5 3.0 2.5 0.0 10.0 7.0 16.0 4.0 0.0 5.0 {113} 8.0 10.0 16.0 4.0 1.0 3.0 12.0 5.5 14.0 1.5 0.5 4.0 11.0 6.0 14.0 1.5 0.5 4.0 (123} 18.0 6.0 4.5 : 3 . 0 1.0 1.0 {l33j 30.5 0.5 9.0 3.5 1.0 3.0 [115] 15.0 12.0 0.0 0.0 1.0 1.5 {135} 3.0 9.0 6.0 3.5 2.0 4.5 13.0 4.5 4.0 8.0 2.0 3.0 {353} 18.0 6,0 3.5 4.5 0.5 2.0 13.0 7.5 14.0 0.5 2.0 2.5 (317} 4.0 3.0 25.0 14.0 0.0 3.5 - 18 - Table 8! Fe - 6.0$ Mn. Single Surface Trace Analysis. Angles given are those between normals to martensite substructure plates and indicated planes. ZONE DEGREES FROM £100} {no? [ m l Calculated . {coil 16.5 13.0 24.0 9.0 1.0 0.5 44.0 2.0 0.5 0.0 5.0 3.0 39.5 6.0 4.0 2.5 1.0 2.0 (on] 35.0 .. 0.5 18.0 0.5 0.0 4.0 35.0 0.5 18.0 0.5 0.0 4.0 35.0 0.5 18.0 0.5 0.0 4.0 40.0 3.0 15.0 2.5 4.0 0.0 19.0 14.0 10.0 8.0 3.0 2.5 t - -* 19.0 14.0 10.0 » 8.0 3.0 2.5 { 111] 23.5 0.5 29.0 10.0 3.0 8.5 23.5 0.5 29.0 10.0 3.0 8.5 21.5 3.0 26.0 8.0 1.0 6.5 20.0 4.5 24.0 6.0 0.5 4.5 19.0 7.5 21.5 4.0 3.0 2.0 17.0 10.0 19.0 2.0 2.0 1.0 012 12.5 10.0 8.0 2.0 1.0 0.0 26,0 4.0 3.5 4.5 1.0 0.0 26.0 2.0 10.5 6.0 2,0 0.5 {1121 32.5 1.0 20.0 3.0 1.0 0.0 18.0 10.0 20.0 . 10.0 1.0 1.5 | 1227 6.0 10.0 16.0 2.5 0.0 2.0 14.0 0.0 16.0 6.0 7.0 7.0 18.0 4.0 14.5 3.5 2.0 6.5 24.0 2.0 12.0 4.0 0.5 0.5 1331 24.0 4.0 10.0 3.0 0.5 0.5 33.0 2.0 12.0 2.0 0.5 2.0 [l35l 28.0 . 6.5 11.0 2.5 0.5 2.0 - 19 - Table 9* Fe - 1.7$ Si _ 7,83$ Mn. Single Surface Trace Analysis. Angles given are those between normals to martensite substructure plates and indicated planes. ZONE DEGREES FROM [100J {no3 f i l l ] "{112} {145] Calculated {001} 44.5 0.0 . 0.0 0.0 5.5 3.0 42.5 2.5 2.0 1.0 3.5 1.0 41.0 4.0 3.0 2.0 2.5 0.5 37.5 7.0 6.0 4.0 1.0 4.0 4.0 8.0 28.0 18.0 2.0 7.0 3.0 6.0 30.0 20.0 4.0 9.0 2.0 4.0 32.0 22.0 6.0 11.0 18.0 25.0 14.5 0.0 5.0 11.0 33.0 4.0 15.0 4.0 3.0 0.0 f i l l ] 36.0 0.5 20.0 0.5 0.0 3.5 23.5 1.0 27.0 9.0 3.0 1.0 22.5 3.0 26.5 8.5 2.0 6.5 20.5 7.0 23.5 5.5 1.5 3.0 15.5 11.0 28.5 0.0 0.0 2.0 13.0 8.0 14.0 3.5 4.0 1.5 {012} 10.5 7.5 12.0 5.0 3.0 7.5 20.0 3.0 9.5 6.0 3.0 0.5 21.0 5.0 8.0 2.5 1.0 2.5 {1I2] 22,0 6.5 15.0 1.5 0.5 0.0 12.5 10.0 7.0 4.5 0.5 0.0 J013]. 18.0 1.0 8.5 10,0 3.0 4.5 11,0 5.0 13.5 5.0 1.0 6.0 [113] 13.0 . 1.0 15.0 2.0 4.0 6.5 18.0 12.0 22.0 8.0 2.0 0.0 25.0 11.0 5.5 4.0 0.5 4.0 26,0 1.0 13.5 5.5 1.0 6.0 {115] 26.0 0.0 14.0 4.5 2.0 0.0 15.0 7.0 4.0 4.5 2.0 1.0 15.0 7.5 3.5 4.0 2,5 1.0 [ l 3 3 l 30.0 4.0 13.0 0.0 2.0 1.0 {135? 4.0 .15.0 10.0 2.0 6.0 3.0 (353} 11.5 9.0 9.5 3.0 2.5 2.0 - 20 - Table 10: Fe - 10.79$ Ni. Single Surface Trace Analysis. Angles given are those between normals to martensite substructure plates and indicated planes. ZONE DEGREES FROM fioo] {110} [111} {112} {145} Calculated fOOl* 35.0 7.5 8.0 5.5 3.0 5.5 42.0 2.5 . 2.0 1.5 4.0 2.0 40.5 4.0 3.5 2.5 2.0 0.0 39.0 5.5 4.5 3.0 1.0 2.0 35.0 7.5 8.0 5.5 3.0 5.5 foui 31.0 14.0 11.0 4.0 7.0 8.0 29.5 9.5 10.5 4.0 0.0 1.0 (111} 23.5 3.0 27.0 8.5 2.0 7.0 22.5 3.0 26.0 8.0 1.0 6.0 20.0 6.0 22.0 4.0 3.0 3.0 {012} 17.5 10.0 19.0 1.0 3.0 1.0 20.0 2.0 10.0 5.5 1.0 0.0 20.0 3.5 9.5 4.0 0.0 1.5 20.0 4.0 9.0 3.5 0.5 2.0 22.0 8.0 7.0 0.5 3.0 0.0 {112} 23.0 4.0 4.0 4.5 0.5 2.0 13.5 8.0 8.0 4.0 3.0 2.0 \122] 12.0 16.0 0.0 5.0 0.0 1.5 (0131 12.0 14.0 0.5 3.5 0.5 2.0 |H3} 3.5 5.5 3.0 1.0 0.5 2.0 3.5 7.5 4.0 1.0 1.0 3.0 /133* 10.0 6.5 12.0 0.0 2.0 2.0 . 13.0 14.0 4.0 1.5 5.5 2.0 {115} 8.5 3.0 20.0 8.5 4.0 2.5 - 21 - Table 11. S ing le Surface Trace Ana l ys i s Angles given are those between d i r e c t i ons of martensite substructure p la tes and (lll}M . ZONE PURE IRON Fe - ,06 C F e - . 17 C Fe -6 .0 Mn Fe-1.7 S i 7.83 Mn Fe-10.79 Ni {on] 2.5 2.5 6.0 4.0 0.5 2.0 . 8.5 1.0 2.0 3.5 18 .0 22.5 3.5 5.0 6.0 8.0 r i 11.5 [on] 1.0 4.0 4.0 0.5 10.0 v. 4.0 1.0 4.0 19 .5 15.5; 15 .0 16.5 2.0 3.0 r ~ i 4.5 M 6.0 6.0 2.0 1.5 0.5 2.0 8.0 8.0 5.5 3.5 1.5 3.5 10.0 10.0 6.5 3.5 5.0 6.5 10.0 10.0 10.5 5.0 10.0 9.5 18 .0 18 .0 13.0 8.0 13.5 C •) 9.0 10.0 16.0 {012J 1.0 0.0 6.0 24.0 4 . 0 3.5 1.5 10.0 7.0 0.5 2.0 9.5 12.5 4.0 4.5 1.5 10.5 7.0 2.0 r •) 7.0 {1125 3.0 1.0 1.0 7.0 0.5 2.0 4.0 3.0 3.0 6.0 C -\ 9.0 {122] 16.5 1.0 8.0 2.0 7.0 {013I 6.0 2.5. 1.5 4.0 3.0 15.5 8.0 2.0 9.0 7.0 2.0 18 .0 9.0 3.0 13.0 8.0 20.0 20.0 11.5 20.0 9.5 22.0 6.0 2.0 0.0 f l23l 1.0 2.0 5.0 {133} 5.0 2.0 2.5 0.0 1.0 2.5 ; 6.0 1.0 [014] 6.5 4.0 {115J 10.5 2.0 1.5 8.5 [135? 6.5 ' 2.5 1.0 7.0 6.5 19.0 7.0 4.0 6.0 6.5 10.0 {353} 7.0 10.0 10.0 - 22 - (lll) A[H2] A (ioo)A[oio]A V I g S g S 1.00 .251131 .231575 .231566 .466238 1.03 .275677 .224947 .251413 .484876 1.04 ,284290 .222686 .257906 .488759 1.08866 ,353555 .142965 .288672 .516840 Table 12,, Calculated values of dislocation shear (g) and shape deformation (S) for two choices of the inhomogeneous shear. (100), [oio]A Vi K : (011)„ [01l]A : [ l l l ] M (lll) A : (01l)H [011]a : [ l l l ] M - 1.00 4.30° 0.78° 6.08° 0.95° 1.03 3.50° 0.50° 6.60° 0.72° 1.04 3.20° 0.48° 6.70° 0.62° 1.08866 0.0° 0.0° 7.40° 0.0° Table 13. Calculated parallelism between indicated shear elements for two choices of the inhomogeneous shear. - 23 - 112] A (lOO^OlO], V I % H A H M 1.00 -.585345 -.665241 ,584838 -.035818 .470595 -.179279 .521031 .620593 .660242 .724813 .621682 .783283 1.03 -.634885 -.715669 .602539 -.040314 .479003 -.214413 .531538 .643951 .606198 .664714 .595327 .764005 1.04 -.653270 -.732110 .608047 -.041695 .479698 -.228936 .534671 .649478 .585768 . .641558 .586860 .759230 1.08866 -.816495 -.816492 .632453 -.048919 .408239 -.408250 .547721 .681372 .408256 .408246 .547725 .730303 Table 14. Calculated direction cosines for austenite (%) and martensite (HM) habit planes for two choices of the inhomogeneous shear. (lll) A[ll2] A H,[oio] A V I % • [Hi] H M » ,145] % • {m} H M J [145] 1.00 1.03 1.04 1.08866 7.77° 6.75° 7.12° 19.47° 4.08° 5.43° 5.03° 19.10° 4.17° 3.27° 3.22° 3.97° 6.83° 6.73° 6.75° 7.45° Table 15: Calculated angles between given planes f o r two choices of the inhomogeneous shear, % = Austenite habit plane H$4 = Martensite habit plane \ ~ 24 - F i g . l : Va r i a t i on o f Ca lcu la ted Martens i te Habit Plane with V j . Inhomogeneous Shear System V I (n4rii2]A ifioo)4[oio]A 1.00 i 5 1.03 2 6 1.04 3 7 1.08866 4 8 F i g . 2: Va r i a t i on o f Ca lcu la ted Aus ten i te Habit Plane with V j . Inhomogeneous Shear System (ni)4[ii2] A H j o i o ] , 1.00 l 5 1.03 2 6 1.04 3 7 1.08866 4 8 Fig. 3. Pure Iron. Martensite Surface Shears. 1060 X. Fig. 5. F e - 0.06$ C. Martensite Surface Shears. 530 X. Fig. 7. F e - 0.17$ C Martensite Surface Shears. 1430 X, Fig. 9. F e - 6.0$ Mn. Martensite Surface Shears. 1100 X. F i g . 12. F e - 1.7$ S i - 7.83$ Mn. Martensite Substructure. 29000 X Fig. 13, F e - 10.79$ Ni. Martensite Surface Shears, 1060 X, F i g . 1 5 . Fe - .11% C. 200X. A u s t e n i t e A n n e a l i n g Twin V e s t i g e s w i t h i n p r i o r a u s t e n i t e g r a i n s . Fig. 16. Pure Iron* Single Surface Trace Analysis Standard (oOl) Cubic Projection. © Zone axis of plane of image X Direction of substructure plates in image plane Fig. 17. Pure Iron : Single Surface Trace Analysis, Standard (OOl) Cubic Projection. O Zone axis of plane of Image X Direction of Normal to substructure plates in Image Plane. Fig. 18. Fe - . 0 6 $ C. Single Surface Trace Analysis. Standard (OOl) Cubic Projection ° Zone axis of plane of Image. X Direction of Substructure plates in Image Plane. Fig. 1 9 . Fe - .06$ C. Single S u r f a c e Trace Analysis. Standard (OOl) Cubic Projection. © Zone axis of Plane of Image. X Pirection of Normal to Substructure plates in Image Plane. - 34 - Fig, 20. F e - .17$ C. Single Surface Trace Analysis, Standard (OOl) C ubic Projection. © Zone axis of Plane of Image. X Direction of Substructure plates in Image Plane. Fig. 21. F e - .17$ C, Single Surface Trace Analysis. Standard (OOl) Cubic Projection. © Zone axis of Plane of Image. X Direction of Normal to Substructure plates in Image Plane. Fig, 22, F e - 6,0$ Mn. Single Surface Trace Analysis, Standard (OOl) Cubic Projection. O Zone axis of Plane of Image. X direction of Substructure plates in Image Plane. Fig. 23. Fe - 6.0$ Mn. Single Surface Trace Analysis. Standard (OOl) Cubic Projection. © zone axis of Plane of Image. X Direction of Normal to Substructure plates in Image Plane. Fig. 24. F e - 1.7$ Si _ 7.83$ Mn. Single Surface Trace Analysis. Standard (OOl) Cubic Projection. ® Zone axis of Plane of Image. X Direction of Substructure plates in Image Plane. Fig. 25. Fe - 1.7$ Si - 7.83$ Mn. Single Surface Trace Analysis. Standard (OOl) Cubic Projection. o Zone axis of Plane of Image. X Direction of Normal to Substructure plates in Image Plane. Fig. 26. F e - 10.79$ Ni 0 Single Surface Trace Analysis. Standard (OOl) Cubic Projection. © Zone axis of Plane of Image X Direction of Substructure plates in Image Plane. Fig. 27. F e - 10.79$ Ni. Single Surface Trace Analysis. Standard (OOl) Cubic Projection. O Zone axis of Plane of Image. X Direction of Normal to Substructure Plates in Image Plane. - 38 - DISCUSSION OF RESULTS SURFACE SHEARS The formation of surface shears is used u n i v e r s a l l y throughout the the martensite l i t e r a t u r e as an important c r i t e r i o n as to whether or not a martensite transformation has taken place. A l l s i x of the a l l o y s studied were found t o form surface shears and furthermore the shears i n a l l a l l o y s appear a l i k e which suggests that the mechanism of the martensite transformation i s similar,, The shears were found contained within thermally etched boundaries which are assumed to be those of the high temperature austenite phase (8) 0 Owen, Wilsonj, and B e l l (8) i n t h e i r study of the massive martensite structures i n Fe-Ni state that they found no more than 4 d i f f e r e n t o r i e n t a t i o n s to the surface shears within any volume formed from an austenite grain. This l e d them to believe that the habit plane i s In t h i s study 4 i s the la r g e s t number of unique shears which r e g u l a r l y appear, but with d i l i g e n t observation i t i s possible to f i n d martensite volumes which have formed from austenite grains with 5 or more unique orien t a t i o n s , .From a study of the photograph which Owen,, Wilson and B e l l present as an example of the surface shears i n Fe-Ni i t would appear that they came to t h e i r conclusion possibly because t h e i r austenite' g r a i n size was too small, hence not allowing a l l pos s i b l e shear orie n t a t i o n s to form. From the study of the r e l a t i v e numbers of time i n which 4 or 5 orientations appear i t would seem that the austenite habit plane i s close to' £ L H J , The percentage of a g r a i n which has transformed martensiticall'y depends on the temperature of the a l l o y r e l a t i v e to the M s and temperatures. As a speciman i s quenched a small portion i s transformed instantaneously to ma.rtr=rio.ito a n fjoon as the M R temperature i s reached,, I t now may well be that the o r i e n t a t i o n o i a l l subsequent martensite formed as the temperature i s dropped from M s to Mf i s determined by the f i r s t c r y s t a l s formed at Mgo - 39 - From strain energy considerations i t may also be that only a small number of the possible different orientations will manifest themselves once the first ^crystals are formed at Ms, Hence possibly the reason for seldom observing more than 4 different orientations to the shear traces. If this were the case then the fact that only 4 orientations are usually observed would not necessarily imply a habit plane close to { l l l } A , The appearance of austenite annealing twin vestiges in these alloys complicates the counting of the number of shear orientations within a volume formed from an austenite grain, but does open up the possibility of being able to predict the austenite habit plane. Greninger and Troiano (4) investigated the low carbon martensites by a study of the austenite twin vestiges and observed a f l l l j austenite habit plane* With this in mind i t was decided to study the twin vestige s in the F e - . 1 7 $ C and Fe - G-,0% Mn alloys^ which are representative of those examined in this thesis. The twin vestiges gave the orientation of the grain.relative to the austenite axis and hence i t was possible to compare the surface shear normals and directions to specific crystallographic directions. In tables 1 and 3 can be seen the extremely close agreement between the calculated austenite habit plane ( 7 , 1 2 degrees from fl l l } ^ ) and the great circles drawn between the directions normal to the surface shears and the pole of the grain. Identical results have also been observed by work within the department (30) on the Fe— 4.8$ Cu martensite. From tables 2 and 4 i t can be seen that the shear traces are.in the majority of cases consistent with the directions <̂ 11C>>A « However the: fact that there arc a s i g n i f i c a n t number of shear traces whose directions are not consistent with <J110)/i would appear to rule out the possibility that the martensite c r y s t a l s are needles whose axis is along <^lld)A , Plates which are elongated i n a direction close to <flld)^ in the habit plane could though be consistent with the data i n Tables 2 and 4» - 40 - ELECTRON MICROSCOPY t From the results of the s i n g l e surface trace a n a l y s i s i t i s not possible to state the martensite habit plane with assurance. It is possible though to say that the martensite habit plane i s not a plane of low indices, because iYom the t a b l e s 5 to 10 i t can be seen that for the martensite habits fioo] , , { i l l } and{ll2} a large number of the traces are greater than 5 degrees (the generally accepted criterion) away. A single surface trace analysis is to a large extent a statistical method in that i t can only hope to predict a given habit plane when a large number of traces (i.e. 25 - 30) are used, and when a l l these traces are consistent with a plane whose poles are grouped into a few discrete regions. I t does appear though that the trace analyses on a l l 6 alloys are consistent with the {l45lM and calculated (using (lll) A[ll2] A with Vj = 1,04) habit planes, The (l45]M habit plane gives a slightly better f i t . But what must be realized is that the poles of the {l45^ plane are so situated on the stereogram that i t is possible to draw a number of random traces (i.e. 30) and s t i l l have no trace deviate by more than 8 - 9 degrees from a fl45j pole. The poles calculated using (lll)^pli] with Vj ~ 1.04 are distributed similarly to the {145}M poles but do not cover the stereogram as thoroughly. Hence p o s s i b l y the reason why the f i t is not quite as good as for {l45^ . In summary, i t can be seen from F i g s . 16, 18, 20, 22, 24, 26 that the poles of the martensite habit plane must be w e l l d i s t r i b u t e d around the stereogram. Such a d i s t r i b u t i o n i s given by £l45] and by the plane c a l c u l a t e d using ( i l l ] . [112]̂  with Vj s 1,04 i n the WLR theory. The d i r e c t i o n s p a r a l l e l to the martensite needles were not found to be consistent with <̂ 111% d i r e c t i o n s as found by'Kelly and Nutting (6) i n low G s t e e l s . As can be seen from Table 11 i t would be possible to conclude that the t r a c e s are p a r a l l e l to ( l l i ) ^ i f a s u f f i c i e n t number of traces were - 41 - not examined, and i t i s suspected that t h i s i s the case with the work of K e l l y and Nutting, Bowles (5) believed that the observed f l l l ^ A habit plane was composed of l a t h s p a r a l l e l to < 1̂01̂ A d i r e c t i o n s and hence must be considered only a pseudo habit plane. I f an o r i e n t a t i o n r e l a t i o n s h i p close to Kurdjumov- $achs i s v a l i d then <(l01)A i s approximately p a r a l l e l to <(lll)> M , But t h i s work has shown that martensite c r y s t a l s do not have a common d i r e c t i o n of <̂ 111̂  . Hence a true habit plane close to f l l l ^ i s a p o s s i b i l i t y . The experimental evidence i s inconsistent with the p o s s i b i l i t y of the martensite c r y s t a l s being needles as no common d i r e c t i o n was found. The fa c t that a common plane was i d e n t i f i e d though does not rule out the p o s s i b i l i t y that the plates may be elongated i n a given d i r e c t i o n within the habit plane. CALCULATIONS; To explain t h e o r e t i c a l l y the experimental r e s u l t s the following must be predicted by the theory. (1) An austenite habit plane close to f i l l ] A (2) A martensite habit plane close to [ l45?N\ (3) An o r i e n t a t i o n r e l a t i o n s h i p close to Kurdjumov - Sachs. Items ( l ) and (2) are the r e s u l t s of the experimental work while item (3) i s assumed as the Kurdjumov - Sachs r e l a t i o n s h i p i s found i n Fe-Ni massive martensite ( 8 ) and i n low carbon martensites ( 2 6 ) , Also the theory-must predict r e l a t i v e l y small values of g, the s l i p shear, and S, the macroscopic shear, from the use of s l i p systems which are equivalent to those normally found i n eit h e r of the two phases. I t has been pos s i b l e to f i n d two s l i p systems which when applied to the WLR theory are able to s a t i s f y the above requirements; they are (ll4 [Il2J Aand (l00)A[010]A . Crocker and B i l b y (21) by use of computer programs, studied thoroughly the problem of p r e d i c t i n g the f i l l ] 4 habit plane using the general theory of Bullough and B i l b y , They came to the conclusion that only the shear mode (lie) [ l l o ] M o r the equivalent mode ( l l O j ^ l l C ^ w e r e p o s s i b i l i t i e s . Hence i t was decided to in v e s t i g a t e using the WLR theory the system (llo) M[lloJ M which i s eqviivalent t o (lOO^foio]^ by the correspondence matrices. The c a l c u l a t e d values of 11 g" and "S" are given i n tab l e 12, I f i t i s r e a l i z e d ; that the magnitude of "g" can range from 0,2-*1.7 and of "S" from 0.14-*1.9 depending on the shear mode, then those values predicted using flOo)A [oio]A are r e l a t i v e l y low. The s i g n i f i c a n c e of the magnitudes of "g" and "S" are not w e l l understood; but i t seems reasonable that "g", a measure of the amount of d i s l o c a t i o n s l i p , and "S", a measure of the deformation necessary to accomodate the change i n macroscopic shape w i l l be important f a c t o r s i n determining the energy associated with the formation of a martensite p l a t e . The parameter w i l l be defined f a r t h e r on. In table 13 are given the ca l c u l a t e d angles between c e r t a i n planes and d i r e c t i o n s f o r the (lOo)^ [old] A system. The o r i e n t a t i o n r e l a t i o n s h i p can be seen t o be close to Kurdjumov - Sachs. From t a b l e 15 i t can be seen that HA i s 3-* 4° from f i l l ] A while % i s ~ 7 degrees from {lh5J M . Hence we see that the system (100)a[010JA s a t i s f i e s the c r i t e r i o n s . Otte (20) has also i n v e s t i g a t e d the commonly observed s l i p systems i n the austenite and martensite bub again, as with the work of Grocker and Bi l b y , he only goes as f a r as c a l c u l a t i n g the austenite habit plane. I f we allow a greater deviation from [ l l l j ^ than have Crocker and B i l b y the system fin) [ii2J 4 i s also found to f i t the previously stated c r i t e r i o n s . I t predicts values of "g" (table 12) Vhich are approi&imately as those f o r (lObj, [oio] 4 but the L]S« values are only h a l f those f o r ( lOo) 4 [oio] . Furthermore the o r i e n t a t i o n r e l a t i o n s h i p (table l l ) i s c l o s e r to Kurdjumov - Sachs than f o r (lOo)A[oiojA . ^ l l l]^[li2J A p r e d i c t s an austenite habit plane - 43 - about 7 degrees (table 15) from {lll^and a martensite habit plane within 5 degrees of {l45] M. By the correspondence matrices (see Appendix I) the systems (lOO^OloJ^ and ( l l l^ l l i i ] ^ can be shown to be equivalent respectively to (llO^p.10^ and (oil) M[oilL. Observing that: a[ll0] = a / 2 [ l l l ] + a / 2 [ i l l J a [Oil] = a/2 [111] + a / 2 [ l l l ] i t i s seen that systems (llo) Mjllo] M and ( o i l ) M | b l l | usual b,c»e, slip mode { o i l ^ ( l l l % M are equivalent to the There are no other slip systems which when applied to the WLR theory predict the experimental results and satisfy a l l the orlterions, The variable Vj has been defined asi The WLE theory does not recognise the «S but its effect can nevertheless be incorporated in the theory, In the present work the value of V has been assumed to be 1,04 (20) as this is the most common value observed, Xt was not possible to measure V in the alloys investigated as there i s no retained austenite at 're'om temperature, ' , . By varying 8 we are effectively introducing a uniform dilation of the habit plane, There is some doubt regarding the validity of the dilation parameter, 'However i t does appear reasonable that the interface between two phases of different volumes will be distorted in some way. Whether i t is compressed or expanded one can not sayj but the limits of 8 are certainly between ,986 and 1,015 which correspond to values of Vj of 1,00 and 1,08866 respectively. The physical meaning of the values of 8 are as follows! with 8 z ,9Q6 the "volume" of material at the interface is under where! V = volume r a t i o of martensite to austenite S z interface d i l a t i o n parameter - 44 - compression so that the volumes of both phases are the same| with £> = 1.015 we have the atomic packing along close packed directions the same in both phaseso The purpose of varying & in this work was twofold, one to see i f the required criterions could be more closely met, and two, to determine i f the uncertainty in the true value of V would greatly affect the results,, Though calculations were not done for a 1,05 i t can s t i l l be seen from tables 12,, 13, and 15 that the calculated data would not vary to any great degree within the range of Vj from 1.03 to l005e It should perhaps be summarized here the evidence which supports the assumption that the crystallography of a l l six alloys examined can be explained by one treatments (1) Previous workers have found the crystallography of low carbon and stainless steels to be the same, (2) The physical appearance of the surface shears in a l l six alloys were observed to be the same. The shears in a l l alloys exhibited at least 5 different orientations. (3) The appearance of the martensite substructure In a l l alloys was identical. (4) At room temperature after quenching no austenite phase i s retained,, (5) A l l the alloys form a b 0 c o C e martensite,, (6) The martensite traces plotted on a stereogram appear to be consistent with the same crystallographic planes and directions. CONCLUSIONS (1) The following alloys were observed to form martensite surface shears': Cl) Pure iron (2) F e - .06$ C (3) F e - .17$ C (4) Fe - 6 .0$ Mn (5) F e - 1 .7$ Si - 7.83$ Mn (6) F e - 10,79$ Ni The surface shears suggest an austenite habit plane close to but deviating from f i l l ] . (2) A single surface trace analysis of the surface shears in the Fe - 0,17$ C and Fe - 6 .0$ Mn alloys is consistent with the habit plane predicted using the WLR phenomenological martensite theory. This habit plane is 7.12 degrees from f l l l l A . The observed direction of the martensite crystals in the Fe - 0,17$ 0 and Fe - 6 .0$ Mn alloys was not found to be consistent with the (I1Q)A directions. However this does not rule out the possibility that the martensite crystals are plates elongated in a direction close to ^110% in the habit plane, (3) The martensite habit plane for a l l 6 alloys is not a low index plane such as {OOl} , {oi l] j { m } > { l l 2 } « The traces were found to be consistent with a { l45^ martensite habit but due to the limitations inherent in a single surface analysis this is not conclusive. TheWLR theory predicts a martensite habit plane 5,03° from {145} . The directions parallel to the martensite crystals in a l l alloys were not found to be consistent with the ^-11^ martensite directions. Hence i t can be concluded that the martensite crystals are not needles whose axis is along < 1̂11̂ M but are rather plates or plates elongated in a given direction within the habit plane. A l l evidence suggests that the crystallography in a l l 6 alloys is the same. • - 46 - (4) The two inhomogeneous shear systems (lll)^[ll2]^ and (lOC^[oio]A were found to satisfy a l l theoretical and experimental criterions when introduced into the WLR theory of martensite transformations. The system (lll)„ | l l i J A is to be preferred as i t generally gives results closer to those desired, (5) If i t is assumed that V = 1,04 then i t is not necessary to introduce a habit plane dilation parameter S into the WLR theory to satisfy the experimental results. SUGGESTIONS FOR FUTURE WORK - 47 - There is a vast amount of work s t i l l to be done to obtain a complete understanding of the crystallography of iron martensites. Some suggestions relative to the type of martensites examined in this work are. (1) A thorough study of the following features which characterize the surface shears due to the martensite transformation* (a) occurence (b) magnitude of shears (c) number of orientations formed (2) Work on dotorming- the austenite habit planes in alloys with no retained austenite but with visible austenite annealing twin vestiges. (3) More alloys of different compositions from the 6 investigated should be made up and studied to determine the composition range over which the same crystallographic features are observed. (4) Computer programs should be written so that the effect of variations in certain parameters within the theory can easily be checked as to whether or not they improve the f i t between theoretical and experimental results. - 48 - APPENDIX I BAIN DISTORTION AND CORRESPONDENCE MARTICES A b.c.c. structure can be formed from a f.c.c. structure by a con- t r a c t i o n along one f . c . c . axis with a corresponding expansion along the other two a x i s . This d i s t o r t i o n i s known as the "Bain D i s t o r t i o n " . O [ooi] f , [001], o O [fool - S [too], F i g , 28 [OJOl Shown i n F i g . 28 i s a b.c.t. c e l l w i t h i n the f.c.c, structure; by a p p l i c a t i o n of the Bain d i s t o r t i o n we transform the b.c.t. c e l l i n t o a b.c.c, c e l l . I t can be seen from'Fig. .28 that d i r e c t i o n s i n the b.c.c, are rel a t e d t o those i n the f . c . c . phase by the equation; I I T o V A At, 0 ! /u7 o o \ /\ a. j The planes i n the two structures are s i m i l a r l y r e l a t e d by! a* (Mz ^ NeRKftu CoMftoAJCNTS 1 \ I i T o \/ ur \ v3 \ 0 O 2 /\ ^ , p 49 These two matrices are known as the Correspondence Matrices, They are applicable only i n the context of Fig, 28j they would not f o r instance give the b'.cc. martensite habit plane once the f 0c„c. austenite habit plane has been found, THEORETICAL TREATMENT OF MARTENSITE TRANSFORMATION IN STEEL This appendix will attempt to give a simplified non-rigorous treatment of the theory of martensite transformations following closely the notation and treatment as used by Wayman (3). In this appendix the austenite (f,c,c,) basis and martensite (b,c,c) basis will be denoted by the subscripts nf" and "b" respectively. First to define a few of the symbols and terms used* (1) A matrix will be represented by a capital letter, i.e. A,R , (2) A vector will be represented by symbols such as % , (3) The transpose of a vector or matrix will be identified by priming, i.e. Transpose As A', . The operation of transposing a matrix simply interchanges rows and columns. Suppose" A = A B C D then A' = A C B D (4) Vectors w i l l be represented by columns. For example, suppose the vector r has components u, v, w thens \M \ The transpose of a vector i s defined i n the same we . . way as matrix, i . e . 1 — \ 1 ^> w y (5) When the components of a vector are used, these components must be given as the d i r e c t i o n cosines. with + ^ + w * "= 1 1 (6) By a "Change of Basis" we simply mean that we are expressing the components of a vector f o r instance, r e l a t i v e to a new coordinate system. This treatment w i l l be based on Wechsler, Liebermann, Read (WLR) theory of martensite transformations. This theory makes possible the c a l c u l a t i o n of the habit plane ( i n the austenite & martensite) and the shape deformation from a knowledge of the l a t t i c e parameters of the f . c . c . and b.c.c. structures and the s l i p system operative. The fundamental concept underlying the WLR treatment i s the existence of a common undistorted plane between the parent (austenite) and product (martensite) structures. The Bain d i s t o r t i o n does not leave a common undistorted plane (the habit plane) between the f . c . c . and b.c.c. structures, and i t i s therefore necessary to combine with the Bain d i s t o r t i o n a c r i t i c a l amount of s l i p shear. The Bain d i s t o r t i o n and s l i p shear do leave an undistorted plane but they do not leave the plane unrotated, hence a r o t a t i o n i s introduced to return the plane to i t s o r i g i n a l o r i e n t a t i o n . The shape deformation (P^, an invar i a n t plane strain) f o r the complete transformation can be written as the product of 3 matrices. = RBP where s R - the r o t a t i o n B s the Bain D i s t o r t i o n P s the C r i t i c a l S l i p Shear F i r s t the matrix B which represents the Bain d i s t o r t i o n will be determined. I f the contraction i s along [00l]^with equal expansions along [lOO]^ and [010]f the b . c . c . structure i s obtained$ and i n t h i s case matrix B has the forms (1) B l"l> o o \ o i - o 0 0 "li j "73 / l eu 2 v \ C L V J 3 r> O 3b - 51 - Cb >&b a r e * n e lattice parameters of the martensite. When the transformation i s f,c.c.-*b.c.c. Cb= <2j> . V is"£he volume ratio of martensite to austenite, about 1.04 for most f.c.c. b.c.c. transformations. The WLR theory considers S , an interface dilation parameter, to be unity; the factor is used, in the Bowles-MacKenzie theory. Secondly the matrix P which expresses the slip shear must be determined. Let us assume a shear along the unit vectors in a plane whose normal is parallel to the unit vector 2L ; let a 3rd direction be defined by the unit vector & given by the cross product, ^ = * 3f With these 3 new mutually perpendicular unit vectors (orthonormal vectors) a new basis in which the shear has a very single form can be constructed. In other words a basis defined by the directions <g,1fiW. (fig. 29) rather than by the directions [l00]^ , [Oio]^ , [oOl]^ » h* 8 be e n formed. tt Fig, 29 i - / / 0 / 4 , • / / / / f t Fig. 30 From-Fig.-30: • if v'' W o + ' v +. 0 In Matrix Form w' = 0 t o + V...,. 5 01 A T ' 0 / r 0 The subscript "o" or^h^matrix P<» designates the basis, i.e. the new basis is the "o" basis. » Before the product between the two matrices "B" and "P0 " can be - 52 formed the two matrices must be r e l a t i v e to the same basis. Hence the "B" matrix must be r e f e r r e d from the " f " basis ( f . c . c , basis) to the "o" b a s i s . ^.This can be done using matrix R5 (3) whose columns are given by the coordinate of the "o" basis r e l a t i v e to the " f " basis ( 3 ) . In other words (2) / Z(t -u-, w , \ Mi. V 7 W i \ ^ 3 V 3 W3 / A " S i m i l a r i t y Transformation" (27, 28) i s ' used t o carry out the C o n v e r s i o n R R , • B 0 - R 5 B , R s Performing the matrix m u l t i p l i c a t i o n using! Or • v — 1 • w • w = 1 A • v IT * W 0 0 0 4 = h a (3) Bo = A 3 V , A oj, + - u £ A Now B 0 PQ can be calculateds M3W3^\ R P ^ 3 w 3 A v 3 w3 A. ^ 3 V 3 A w 3 A ( A 3 g + ^ ) % + W 3 A As the matrix i s going to be diagonalized, a symmetric Matrix Jo i s defined as^ <X — FL F0 ~ 7* + ^ f e - 7-\) where s 'tf = (^3$ + ^ 3 } - 53 - The symmetric matrix Jo describes the effect of the Bain distortion and the slip shear g, but the fact that there is a critical value to the shear g has not yet been taken into consideration. It has been shown (ll) that a necessary and sufficient condition for the presence of an undistorted habit plane is for one of the eigenvalues of the distortion matrix J 0 to be unity. This condition can perhaps be made plausible by the following consideration. The general form of the eigenvalue equation iss A )L — X X where ^ = Matrix — = Vector (eigenvector) ^ = Scalar quantity (eigenvalue) The equation says that i f a matrix A operates upon a vector _xthe length ' u ' the vector is changed but not its orientation. Hence i f the eigenvalue ~#\ is unity the vector & is unrotated and unchanged in magnitude5 the conditions desired. Now forming the equations Jo * =• ( J o - = 0 % For nontrivial solutions of this system of equations the following condition must be met DETERMINANT Jo V £<• y ] -- 0 From the determinant the characteristic equation (3) is ( ^ j 3 - T(y)z + Q(tf) ~ D = 0 D = D E T [ j . ] = 7 t * % * Q - tf[i-i3*3v3+fvf\ + y^[i^^v3 + ?( ' - ^3)] - 5 k - T h r e e e i g e n v a l u e s A* ^ a r e o b t a i n e d f r o m t h e c h a r a c t e r i s t i c e q u a t i o n . The c r i t i c a l v a l u e o f s h e a r g i s o b t a i n e d b y d e m a n d i n g t h a t one o f t h e e i g e n v a l u e s ( "h? ) b e u n i t y . S u b s t i t u t i n g )w = 1 , D , T, Q , i n t o t h e c h a r a c t e r i s t i c e q u a t i o n t h e r e r e s u l t s t h e g u a d r a t i c f o r t h e c r i t i c a l s h e a r g . U) A 3Z + ^ 3 * c ~ 0 c=c-vXr«/)V , I n g e n e r a l t w o d i f f e r e n t v a l u e s o f g r e s u l t . A s ' ) h a s b e e n f o r c e d t o b e a f a c t o r i n t h e c h a r a c t e r i s t i c e q u a t i o n , t h e o t h e r t w o e i g e n v a l u e s a r e o b t a i n e d b y d i v i d i n g t h e c h a r a c t e r i s t i c e q u a t i o n b y ( ^ - I ) To o b t a i n ' (5) (tf) x + ( i - T ) O v ) + D = O U s i n g one o f t h e v a l u e s o f g i n t h e e x p r e s s i o n f o r T , t h e o t h e r t w o e i g e n v a l u e s >\ a n d ^ c a n b e s o l v e d f r om e q u a t i o n 5 * Once t h e e i g e n v a l u e s \ f , . ^ 3 a r e s o l v e d f o r t h e c o r r e s p o n d i n g e i g e n v e c t o r s ( x " J / i ( r t ) ( x w / , i w ) (x® r® f) c a n b e f o u n d a s f o l l o w s . \ / / x w \ Ja H~ X 1* or i n explicit, form ^ 3 y(<) * \ J31 J3Z J 3 3 / T h e s e e i g e n v e c t o r s h a v e b e e n s o l v e d f o r ( 3 , 2 9 ) * w i t h t h e s o l u t i o n s d i v i d e d * R e f e r e n c e (29) u s e s d i f f e r e n t l y l a b e l e d c o o r d i n a t e s y s t e m , t o u s e t h e s e s o l u t i o n s s i m p l y r e p l a c e t h e " 2 " s u b s c r i p t s i n r e f . (29) w i t h " 3 " , - 55 - into 3 cases depending on whether (l) W>, = 0 ( 2 ) W3 = 1 (3) ^ 3 0 , 1 The eigenvalues can also be determined by finding a new basis "d" in which the matrix «J0 is diagonal in form. These diagonal elements are the eigenvalues )\~, , • "A\ , . J 0 — F0 Fo — R4- Fj R«r The matrix Rj^ defines the similarity transformation between the "o" basis and the new "d" basis. The columns of R^ are given by the eigenvectors solved for above* i,e* 1 x<" y ( 2 ) i(t) The basic premise is that in the habit plane any vector 2 must not have its magnitude changed by the action of the matrices B and P , Expressing this algebraically in the "f" basis'> i ' P ' B ' B . P * = I I The analagous equation in the "d" basis would be I ' F / H = n which when written in explicit forms o o \ / x \ K. 0 o % ) y \ 2 / y W Multiplying out > x 2 + ( K - 1 ) / + - 1)2' = 0 Since >,, equals unity- y 1 - £ a r b i t r a r i l y setting / „ i n t o 3 cases depending on whether (l) W-i = O (2) W3 = 1 (3) ^3 3= 0,1 The eigenvalues can also be determined by finding a new basis "dn in which the matrix Jo is diagonal in form,, These diagonal elements are the eigenvalues )\~, , • )\\ , . Jo — F0 R> — R4- Fd Rv The matrix defines the similarity transformation between the "0" basis and the new "d11 basis„ The columns of R̂  are given by the eigenvectors solved f o r above, i.e. "x&> \ y l , ) Z(3) J The basic premise is that in the habit plane any vector 2. must not have its magnitude changed by the action of the matrices B and P, Expressing this algebraically in the "f" basis? I' P ' B ' B P l = 1 1 v.. The analagous equation in the "d" basis would be i . Fd 1 = 1 1 w which when written in explicit form? t o o \/x\ P O >N3 / y \ 2 I w Multiplying out X -+ 0 Since "X, equals unity. a r b i t r a r i l y setting ?•= / ( 6 ) / = 1 Where $ 6 j another as can Hence one undistorted vector i n the habit plane i s ^0,Sy K , I be seen by i n s p e c t i o n i s [l;0,<?"|. The normal to the habit plane b, i s then given by the cross product ° [ l , 0 , 0 ] x [ 0 , £ K , f ] = [ 0 , l , S R K ] Normalizing There are i n general 4 solutions to ft(d) , corresponding to the 2 values of g and , The degeneracy of solutions i s discussed by Wechsler (29). i s a unit vector along the habit plane normal r e l a t i v e to the "d" b a s i s . The eigenvectors which comprise R^ can be r e f e r r e d to the "f" basis from the "o" basis by the matrix R^s (e) jy!'l)\ 1 #1 y(0 — Ax \ SCA3 ^ 3 \ I"/ ,1,3 The [x(eJ} y ^ 2 W] f orm the columns of the matrix which expresses the transformation between the "d" b a s i s and the " f " b a s i s , Hence the habit plane r e l a t i v e to the ' " f " basis i s found from: / x w ( 9 ) yd) y a) , 0 ) \ ,<}) \ ^ 1 M ?fV / i s a.unit vector p a r a l l e l to the habit plane normal r e l a t i v e to the austenite a x i s . Next must be found the habit plane r e l a t i v e to the martensite axis. The d i r e c t i o n s [ I T o ] . [l I o ] f j [0 o /]^ are not rotated by the Bain d i s t o r t i o n . Sr. as can be seen by the application of the matrix B to these three directions. Furthermore the lattice invariant shear P has no effect on crystallographic directions. Hence in the expression for the complete martensite transfor- mation Pi - RBP> only the rotation R can affect the crystallographic directions. The martensite habit plane is given as the direction cosines of the habit plane measured from the martensite axis. The martensite axes (fig. 28) are given by the effect of the rotation R on the three austenite directions. The matrix R can be determined by realizing that i t must counteract the rotation introduced by BP, If pf i s applied to any two vectors in the austenite habit plane, by the use of Euler's theorem (3) the angle of rotation and rotation axes necessary to return these two vectors into their i n i t i a l positions can be determined. As so far only F Q has been determined, Ff can by obtained by carrying out a transformation from the " 0 " to the "f" basis. This is done from the equation. (10) •& = RsF.Ri Suppose that V and <r are any two vectors in the austenite habit plane, then applying Ff: (11) , = Ff \? .(T, = RP cr then bylEuler's theorem a vector along the desired axis of rotation is (12) [Vi-V j X [err - cr] _ y> [o-„- cr ]•[« , + V] ~ The magnitude of t h i s vector determines the angle of rotation 6 0 (13) |r I = TAN The desired unit vector with components R PZ} P3 is obtained by normalizing £ , The general form of the matrix which expresses a rotation by an angle 8 about the unit direction [ R • R, P3 ] can be shown to be (3) (14) R = R a ( l - cose )+cose p,pa(i -cos*)-p3siwe R - c o s e ) + P2SINe Pip,(i-co5e)+ f3SIN9 p*(i-lose) + cos e P lP J(i-cose)- fiswe P3 P,(l-Cose)-p25lN0 ftPt(|-COSfl)+P,SWfl p3(|-Cose)+ Cos 6 Now as previously mentioned the p o s i t i o n of the martensite axes r e l a t i v e to the austenite axes a f t e r the a p p l i c a t i o n of P, are given by« ( 1 5 ) R [ l T o ] = [ a , b , c ] R[MO] = [ d , e , f ] R [ o o i ] = [<3,b,c] These components form the matrix which expresses the transformation between the austenite and martensite b a s i s . Hence the unit vector p a r a l l e l to;the martensite habit plane fc(b) i s obtained from the equations ( 1 6 ) b c d .e P \ 3 h i / The shape deformation r e l a t i v e to the austenite axes i s given by (17) f? = R B P = R Fr applying R f> t o the habit plane normal i n the parent material (austenite): The d i r e c t i o n of the shape deformation i s then given by vector subtraction R F f P, it) — (f) The magnitude of the vector R fp ^ gives the magnitude of the shape deformation. Now to consider the p a r a l l e l i s m between d i r e c t i o n s and planes i n the austenite and martensite* For example, suppose i t i s desired to c a l c u l a t e the angle Q between [ l l l ] f and [ 0 1 l ] b s ( 1 ) Form A ' [ i l l ] and normalize, ( 2 ) Take dot product with [ o i l ] b . ( 3 ) Divide b y / 2 " to obtain cos 9 <• NUMERICAL CALCULATIONS The following is a suggested procedure for calculating numerically the austenite and martensite habit planes and the shape deformation. (1) Assume a specific slip system of the form (M, , , ^ 3 ) ^ "frl 5 , Vj J (2) Calculate and T J 3 equation 1. (3) Solve for the two values of g, equation 4. (4) Pick one value for g (usually the smaller) and solve for 7>\ and \\ , equation 5» (5) Calculate the habit plane normal relative to the "d" basis, equation 7. (6) Depending on the value of U/3 calculate the three eigenvectors relative to the "d" basis. References (3* 29). See text of appendix, (7) Refer these eigenvectors to the "f" basis, equation 8. (8) Calculate the habit plane normal in the "f" (austenite) basis, equation 9. (9) Calculate F 0 s equation 3. (10) Calculate F f, equation 10. (11) Choose any two vectors V , CT in the austenite habit plane, work out equation 11. (12) Calculate equation 12. Normalize r. (13) Calculate & equation 13, (14) Calculate R, equation 14. (15) Work out equation 15. (16) Obtain the martensite habit plane from equation 16, (17) The shape deformation i s determined as given from equation 17 onwards. - 60 - APPENDIX I I INVESTIGATION OF MARAGING PROPERTIES OF F e-M n-Sj SYSTEM GENERAL The term "maraging" i s used to describe an age hardening treatment given t o a carbon free i r o n martensite structure. There are three basic types of i r o n - n i c k e l base maraging steels5 those containing 12$ Ni (32), 18$ Ni (31, 33, 34, 35, 36), 20 - 25$ Ni (36). The high n i c k e l content i s to ensure a d u c t i l e martensite structure while supplementary additions such as molybdenum, cobalt, titanium are added to cause the age hardening response. The most us e f u l maraging s t e e l to date has proven to be that with the approximate composition Fe-18$ Ni-8$ G©-4$ Mo-0.4$ T i . The t y p i c a l aging treatment f o r t h i s s t e e l simply consists of a one hour anneal at 800 degrees G, an a i r cool to room temperature followed by a three hour aging treatment at 450° G . The strengthening appears to r e s u l t from ordering and p r e c i p i t a t i o n reactions, but the exact mechanism's are not c l e a r l y understood and are the subject of much i n v e s t i g a t i o n . The great s i m i l a r i t y between the i r o n - n i c k e l and iron-manganese binary phase diagrams ( F i g , 32.) suggests that i t might be possible to develop a manganese maraging s t e e l i n analogy to the n i c k e l maraging s t e e l s (31~*"3°). A p a r t i a l s u b s t i t u t i o n of manganese f o r n i c k e l has already been aff e c t e d by Patterson and Richardson (3?) i n that they developed a s t e e l of composition 12.5$ N i s 2$ Mn, 8$ Co, 4$ Mo, 0.2$ T i s 0.1$ A l which i s comparable with the usual Fe-Ni maraging s t e e l s . They found that manganese substitutes equivalently f o r n i c k e l i n a r a t i o of one part Mn f o r 3 parts Ni, They a l s o suggest that to improve the Fe-Ni-^Mn maraging s t e e l s an increase i n Mn along with a corresponding drop i n cobalt should be investigated. Goldman and Manec (38) have c a r r i e d out experiments on the k i n e t i c s and mechanism of hardening i n a - 61 - Fe-12$ Mn-5$ Ni~4$ Ti maraging steel, while Keiichi Qhta (39) reports that in a Fe-4.85$ Ni-2.66$ Mn-2.52$ Si-0.52$ Ti steel there is an increase in hardp.ess from 28 to 53 Rockwell C on tempering 4 hours at 500° G. Earlier work by Decker, Eash and Goldman (3l) had suggested that manganese had undesirable effects but this now appears to be erroneous, at least up to the additions reported above. Also Kattus (40) has developed a 3-11$ Mn, 1.5 - 2.0$ Si, 0.6 - 1.25* Ti, 0.4 - 3.4$ Mo steel which shows an ultimate strength increase from 85,000 to 160,000 psi after aging for several hours at 480° C. Richardson (4l) discovered that Fe-Mn-Ni alloys without auxiliary hardeners shows the typical increase in strength after a maraging treatment. The aim of the present investigation was to develop a nickel free maraging steel with the use of manganese and silicon additions. Maraging properties were to be looked for among those alloys which had a soft martensite structure on cooling from the austenite. The manganese was added to ensure a martensitic transformation while the silicon addition was to provide the hardening mechanism. As can be seen from the Fe-Si binary phase diagram (Fig. 33), Fe-Si alloys in the region of 6$ can take part in an ordering reaction. The idea was to quench the alloys from the disordered phase ( « ) so that they would s t i l l be disordered, and hopefully, soft at room temperature. Then with the subsequent aging treatment within the ordered et phase i t was hoped that the alloys would harden. The maraging properties of the Fe-Mn binary were also examined. In order to determine the optimum alloy composition the manganese content was varied from 0 to 20$ with variations ©f silicon between 0 and 6$. The effect o f varying the aging temperature was also investigated. ALLOY PREPARATION AND ANALYSIS - 62 - The materials and the procedure used in the preparation of the alloys are as given in "Experimental" of this thesis, A total of 17 alloys were cast but five had to be discarded because the composition was not homogeneous. The methods of alloy analysis are the same as those used in the "Experimental"• It was not found possible to analyse for silicon by X-ray fluorescence! hence the Si content was assumed to be correct whenever the Mn content was analysed to be so. The analysis of the alloys used is given in Table.16. Details of preparation of specific alloys are shown on the age hard$n£jng curves Figs. 34 to 42. Homogenization was carried out in a horizontal tube furnace under an atmosphere of dissociated ammonia ( 3 ^ + % ) , Specimans were quenched directly from a vertical tube furnace into brine or water. Specimans were polished before hardness tests, hence any effects due to the dissociated ammonia atmosphere should be minimized. The aging curves were obtained by holding the speciman at temperature for a given length of time, quenching in water, measuring the hardness and then returning the same speciman to the furnace for another predetermined length of time before repeating the process. No special atmosphere was used for the aging tests. If there i s a martensite transformation present in a speciman the cooling curve should show a decrease in slope at the transformation temperature. A Chromel - Alumel thermocouple was spot welded to the sample which was then heated into the austenite region with a torch. The thermocouple was attached to an oscilloscope which displayed the cooling curve as a function of millivolts and time. The formation of bubbles on the surface of the speciman when quenching in water prevents a smooth cooling curve and hence covers any change - 63 « in slope. It was therefore necessary to coat the surface of the speciman on the side of the thermocouple with refractory cement. While this procedure reduces slightly the cooling rate i t does allow a smooth cooling curve to be obtained, Specimans for optical examination were lapped progressively down to 3/0 grit paper, then polished with diamond paste. Polishing with alumina was found to cause pitting. Etching was performed with a 1$ solution of HN03 in alcohol (Nital), Specimans used on the diffractometer were approximately x $?x x £" with one face polished with 3/0 grit paper. RESULTS The two alloys F e - 6,0$ Mn and Fe - 1,7$ Si - 7.83$ Mn were found to exhibit surface shears (Figs. 9 and 11 ) which are the commonly accepted criterion as to whether or not a martensitic transformation has taken place. No other alloys were examined for surface shears. These two alloys and the four given below did have the same etched structure (Fig. 3 l ) s F e - 7.3$ Mn Fe - 9.5$ Mn Fe - 1.0$ Si - 4,5$ Mn F e - 4.0$ Si - 8.0$ Mn The structure in Fig. 31 is very similar to that found in Fe-Ni martensites by Owen et. al. (13). None of the alloys given in Table 16 other than the above six were found to show this martensitic etched structure. - 64 - F i g . 3 1 : T y p i c a l Massive Martensite Structure. 1 7 5 X. Surface Polished and Etched i n N i t a l . The i d e n t i f i a b l e phases as determined from the studies on the diffractometer are given i n Table 1 7 . Cooling curves of the following a l l o y s were studied: F e - 7 . 3 $ Hn, F e - 4 . 7 9 $ S i - 8 .08$ Mn, Fe - 5 . 1 5 $ s i - 9 . 4 3 $ Mn, F e - 5 . 9 3 $ S i - 1 3 . 5 8 $ Mn, Fe - 6 .30$ S i - 1 9 . 4 0 $ Mn. The expected cooling curve a r r e s t during a i r cooling and water quenching was only observed with the Fe - 7 . 3 $ Mn a l l o y . Age hardening experiments were c a r r i e d out on a l l a l l o y s (Table 1 6 ) except Fe - 7 . 3 $ Mn, F e - 9 . 5 $ Mn and F e - 1 6 . 5 $ Mn. See Fi g s . 3 4 to 4 2 f o r the age hardening curves obtained. - 65 - METHOD OF ANALYSIS ALLOY CHEMICAL X-RAY FLUORESCENCE 1 Fe-6.0% Mn X . 2 f-Fe-7.3$ Mn X 3 Fe-9.5$ Mn X 4 Fe-l6.5$ Mn X 5 Fe-1.0* Si-4.5$ Mn X 6 Fe-1.7* Si-7,83^ Mn X 7 Fe-4.0$ Si-8.0C# Mn X 8 Fe-4.79# Si_8.08$ Mn X 9 Fe-4.79$.Si-9.43^ Mn X 10 Fe-5.93$ Si-13.58$ Mn X 11 Fe-6.30$ Si-19.40$ Mn X 12 Fe-2.50$ Si-6.0$ Mn-.5 Ti X Table 16. Analysis of Alloys i n Weight Percent, - 66 - ALLOY COOLING MEDIA OBSERVED STRUCTURE A l R BRINE Liq. N2 (b.cc.) (fee.) e 1. Fe-6aOMn X X 2. Fe-7.3Mn X X 3. Fe-9.5Mn X X 4. Fe-l6.5Mn X X 1 X X X X 5. Pe-1 Si-4.5 Mn X X 6. Fe-.17 Si-7.83 Mn X X X X 7. Fe-4.0 Si-8.0 Mn X X X X 8. Fe-4,79 Si-8.08 Mn X X X X 9- Fe-5.15 Si-9.43 Mn X X X X 10, Fe-5.93 Si-13.58 Mn X X X X 11. Fe~6.30 Sl-19.40 Mn X X ? X X X j 12, Fe~2,5 Si-6,0 Mn~0.5 .Ti 1 X X Table 17, Structures Present After Cooling from the Austenite Region. - 67 - DISCUSSION OF RESULTS OPTICAL AND DIFFRACTOMETER STUDIES Of the four Fe-Mn binary a l l o y s studied the Fe~6.C# Mn, Fe-7.3# Mn and Fe-9o5$ Mn had the t y p i c a l massive martensite appearance ( F i g , 30) whi le the Fe-l6 „5$ Mn d id not . Fur ther as can be seen from Table 17 the f i r s t 3 a l l o y s form a b 0 c , c 0 i r o n phase, whereas the Fe-.l605# Mn has a p a r t i a l f . c . c , p a r t i a l h.cp. s t ruc ture with the presence of the b . c . c . phase quest ionable . These r e s u l t s are in agreement with Tro iano and McGuire (42). The appearance of the €-phase in the Fe-Mn b inary complicates the s i t u a t i o n and i t i s not poss ib l e to form a completely analagous range o f a l l o y s to those found i n i r o n - n i c k e l up t© 33 wt, % (8 ). An a l l o y which forms the h.cp, 6 - phase i n a s im i l a r manner i s Fe=18# Cr - 9$ N i „ Otte (43) has assoc ia ted the presence of s tack ing f a u l t s i n the 18-9 s t a i n l e s s s t e e l wi th the formation of the € « phases The fac t that s u s c e p t i b i l i t y t o f a u l t i n g increases with Mn but i s l i t t l e a f f e c t ed by Ni content leads one to suspect that the formation of the <?- phase i n the Fe~Mn b inary but i t s absence i n the Fe-Ni b ina ry i s a t t r i b u t a b l e t o f a u l t i n g . I t i s commonly recognized In the l i t e r a t u r e (42, 43̂  45 ,46 ) tha t the € ^phase i s intermediate i n the t r a n s i t i o n from f . c . c , to b . c . c . s t ruc tu res . As can be seen from Table 17 the a l l o y Fe-6„30# Si-19.40$Mn forms / and € s t ruc tures on an a i r coo l but on the more r ap id water quench i t forms an & s t ruc tu r e . A l so an a i r cooled sample of Fe-16.5$ Mn was co ld worked with the r e s u l t that the 6 and <x phases formedo Hence i n e f f ec t the fo l low ing transformat ions were observed... % ~* % + € Fe-6.30$ Si-19.40$M n A i r Cool % ~* o< Fe-6.30# 81-19.40$ M n Water Quenched 3 _ * t f + € - » 6 + w F e~l6,5$ Mn Cold Work These three equations s t rong ly suggest that £ i s an intermediate phase between the # and 6 s t ruc tu res 0 The ternary a l l o y s s tudied which d isp layed the massive martensite s t ructure ( F i g . 31) were Fe - 1,0$ S i - 4.5$ Mn, Fe - 1.7$ S i - 7.83$ Mn and Fe - 4.0$ S i - 8.0$ Mn. The Fe - 1.7$ S i - 7.83$ Mn a l l o y exh ib i ted martens i t i c surface shears; i t i s probable that the other two te rnary a l l o y s would have a l so i f they had been s tud ied . From Table 17 i t can be seen that these 3 a l l o y s a l l possess an OC s t ruc tu re on a i r coo l ing to room temperature. However t h i s f a c t i s not necessa r i l y cons is tent with these 3 a l l o y s be ing mar tens i t i c because most o f the other a l l o y s a l so have an CX s t ruc ture on a i r c o o l i n g . The explanat ion probably l i e s i n the s i l i c o n content. As can be seen from the Fe~Sl phase diagram ( F i g , 33) there i a a If loop up to about 2,5wt$ S i , and as the Fe-Jfe b ina ry Is at s u f f i c i e n t l y high temperatures a JC-»« t r a n s f o r - mation i s obtained on quenching Fe-Mn-Si (Si<^2,5Wt,$) systems. At s i l i c o n contents s l i g h t l y over 2.5$ the in f luence of the ^ Fe-Mn s t ructure w i l l p r e - dominate and t h e t r a n s f o r m a t i o n s t i l l forms; which accounts f o r the F e -4.0$ S i - 8,0$ Mn system being mar t ens i t i c . A l so t h i s a l l o y was not analysed f o r s i l i c o n loses on cas t ing and hence i t s t rue s i l i c o n content i s l i k e l y somewhere between 3.5 and 4 ,0$, As the Fe - 4.79$ S i - 8,08$ Mn a l l o y i s reached the mar tens i t i c s t ruc ture no longer forms on coo l ing and i t appears that now the in f luence of the s i l i c o n predominates and the equ i l i b r ium structure i s preserved from h igh to room temperature. Th i s reasoning a lso holds fo r the Fe - 5.15$ S i - 9,43$ Mn a l l o y . In the two a l l o y s of higher manganese content predominance may be re turn ing t o the Mn as we observe ( F i g , 5) the # s t ruc ture i n both the Fe - 5.93$ S i - 13.58$ Mn and Fe - 6.30$ S i - 19.40$Mn. In the a l l o y o f lower Mn content ( F e - 5,93$ S i - 13.58$ Mn) there i s some quest ion as to whether ;br^not the observed (X i s the product of a mar tens i t i c *.,'V>-£'-.i; t rans format ion ; but i n the a l l o y of h igher Mn content the fac t that the OC only forms on r ap id quenching suggests that i t i s m a r t e n s i t i c To conf i rm this i t would be necessary to determine whether or not shears form on the surface of a speciman which had been polished before quenching from high temperatures. No optical or cooling curve studies were made on the Fe-2.5$ Si-6.0$Mn 0.5$ Ti alloy but in analogy to alloys of similar Mn and Si contents i t is probably safe to assume that the 0( structure formed at room temperature is martensitic. COOLING CURVES; Of those alloys tested only the Fe - 7.3$ Mn showed a change in slope in i t s cooling curve. Because of the experimental limitations i t is not possible to determine the transition temperature with any more accuracy then to say that i t lies somewhere between 360 and 390° C. This temperature range was observed with both air cooled and water quenched specimans, Gomersall and Parr (44) carried out cooling curve experiments in the same way and obtained comparable results. As no cooling curve arrest was noticed when water quenching the Fe - 6,30$ Si - 19.40$ Mn alloy i t would appear not to be martensitic! the optical studies also bear this out. However the"fact that its water quenched structure suggests a martensitic transformation shows that more work must be done on this alloy, AGING TESTS 8 The data obtained is presented graphically in Figs. 34 to 42. A l l of the alloys except Fe - 4.79$ Si ~ 8,08$ Mn showed a tendency to harden. The greatest hardness increase was only 8 Rockwell G -points (Fe - 5*-93$'Si-— 13.58$ Mn) while the average was 2 —>-3 ^c Points. Kattus (40) has developed alloys similar in composition to those examined here which show a hardness increment of some 25 points (Rc 10 to Rc 35). Two of the alloys, Fe - 4.0$ Si-8.0$ Mn and F e - 4.79$ Si - 8.08$ Mn do have this hardness but i t was not found - 70 - possible to obtain them in the soft condition before the maraging treatment. The 4 alloys most extensively studied, Fe - 6.0$ Mn, Fe - 1.0$ Si - 4.5$ Mn, F e - 1.70$ Si - 7.83$ Mn, and F e - 4.0$ Si - 8.0$ Mn do show a typical type of maraging curve. The optimum aging temperature and aging time for the highest strength was 450° C. and approximately 1/2 hour for a l l 4 alloys. With aging at 400, 500, and 600° C the same strength was not reached. Aging at 400° G does not cause the curves to f a l l off appreciably after 4 1 hours as they do with aging at 500 and 600° C, The f a l l off in hardness with high temperature'aging is probably du© to a breakdown of the martensite ^! structure with a reversion to the austenite. A l l 4 of these alloys are martensitic after quenching from the austenite. The other alloy which was marteaaitie at room temperature was F§ « 2,5$ Si » 6,0$ Mn » 0.5$ Ti, and while i t was net as extensively studied a@ the above four i t did §hew similar maraging curves8 Th« other 4 alleys whose aging eharaeteristies were .investigated are Fe - 4.79$ i i - 8.01$ Mn, F e - 5.15 $ Si - 9.43$ Mn, Fe - 5.93$ Si - 13.58Jfifa, and Fe » 6.30$ Si - 19«40$Mn, Thegta alloys are probably not marteneitie at 200m temperature with the possible exception of F© ~ 6,30$ Si - 19.40$ Mn in the water quenched condition. The above non**marten@itic alloys lose their hardness much more slowly while aging at 600° 6 than do the 5 martensitic alloy®. This may be expected as the softening mechanism operable in the martensitic alloys will not apply here, where the softening i s likely due to a realignment and annealing out of dislocation©. The slight hardening increment observed for a l l alloys except Fe - 4.79$ Si - 8.08$ Mn, is probably due to an ordering process involving the silicon. According to the Fe-Si phase diagram (Fig. 33) the ordering should not take place until 6$ Si at 450° C. The fact that the two alloys which show the largest hardening increment also contain the largest silicon content support - 71 - the fact that silicon is taking part in ordering. Other work conducted - within the department on the Fe-Si binary is consistent with the idea thai ordering causes slight hardening. FUTURE WORK Much work remains to be done on these Fe-Mn base maraging steels in an attempt to obtain a useful product. Possible suggestions are as follows s 1. Continue the systematic investigation of the maraging properties by varying (a) proportions of manganese and silicon (b) aging -: temperatures and time, . 2. Examine the ordering reaction in the Fe-Si binary in an attempt to determine i f the silicon addition is beneficial. 3. Attempt to explain why the Fe-Mn binary with no silicon additions also'shows a hardening increment. 4. Study effects of additional elements such as titanium. 5o Study the occurence and crystallography of the h.cp. 6 phase in the Fe-Mn binary.  op Weight Perc ent'' S i l i con Fig, 3 3 ! Fe - Si Binary Phase Diagram, V i ! L. 1 2 3 4 Aging Time, Hours Fi g , 3 4 . F e - 1,0$ S i - 4,5$ Mn. Aging curves. - Hotrolled 950° C - Annealed 950°- C; l/2 hour, a i r cooled - Curve ( l ) Aged 450° C Curve ( 2 ) Aged 400° C Curve '(3) Aged 500° C Curve ( 4 ) Aged 600° C Aging Time, Hours F i g - 35. Fe - 6.0$ Mn. Aging curves. - Hotrolled 950° C - Annealed 950° C,•1/2 hour, a i r cooled - Curve ( l ) Aged 450° C Curve (2) Aged 40C" C Curve (3) Aged 500° C Curve (4) Aged 600° C i i -= 1 f 1 1 I 1 2 3 4 Aging Time, Hours Fi g , 3 6 , F e - 1 . 7 0 $ S i - 7 . 8 3 $ M n. Aging Curves - Hotrolled 9 5 0 ° C„ - Annealed 9 5 0 ° C ? 1 / 2 Hour, A i r Cooled - Curve ( l ) Aged. 4 0 0 ° C. Curve (2) Aged 4 5 0 ° 0. Curve ( 3 ) Aged 5 0 0 ° C. Curve ( 4 ) Aged 6 0 0 ° C. 1 2 3 4 Aging T i m e s Hours Fi g . 3 7 . F e - 4.0$ S i - 8.0$ Mn, Aging Curves* -Hotrolled 950° C. -Annealed 950° C, l / 2 Hour, A i r Cooled. -Curve ( l ) Aged 400° C. Curve ( 2 ) Aged 450° C. Curve ( 3 ) Aged 600° C. ^urve (4) Aged 500° C. 26 - 22 - " i ±~. Y t Aging Time, Hours Fig. 38. Fe - 4.79$ Si - 8.08$ Mn. Aging Curves. - Homogenized 1100° C, 24 Hours. - Hotrolled 900° C. - Annealed 900° C5 1 Hour. Curve (l) Air Cooled, Aged 600° C. Curve (2) Water Quenched, Aged 600° C. Aging •Time, Hours Fig. 39. Fe - 5.15 $ Si - 9.43$ Mn. Aging Curves - Homogenized 1100° C, 24 Hours. - Hotrolled 900° C. - Annealed 900° C, 1 Hour. Curve (l), Air Cooled, Aged 600° C. Curve (2), Water Quenched, Aged 600° 1 2 3 4 Aging Time, Hours F i g . 40. F e - 5.93$ S i - 13.58$ Mn. Aging Curves - Homogenized 1100° C, 24 Hours. - Hotrolled 900° C. - Annealed 900° C, 1 Hour Curve ( l ) A i r Cooled, Aged 600° C. Curve (2) Water Quenched, Aged 600° C. 1 2 3 4 Aging Time, Hours i g . 41. F e - 6.30$ S i - 19.40$ Mn. Aging Curve - Homogenized 1100° C, 24 Hours. - Hotrolled 900° C. - Annealed 900° C, 1 Hour. Curve ( l ) A i r Cooled. Aged 600° C. Curve (2) Water Quenched, Aged 600 20 I i i i i 1 1 2 3 4 - Aging Time, Hours FigV 42. F e - 2.5$ Si - 6.0$ Mn - 0.5$ Ti. Aging Curves - Hotrolled 950° C 0 - Annealed 1950° C, 1/2 hour, Air Cooled. - Curve (l) Aged 400° C. Curve (2) Aged 500° C, - 79 - REFERENCES (I) M. J . Bibby and J . Gordon Parr2 JISI, 202, 1964, 100 - 104. %2) *G, M. Wayman and C 0 J . A l t s t e t t e r s Acta Met., 2Q, 1962, 992. (3) C. M. Wayman: "Introduction to the Crystallography of Mart e n s i t i c Transformations" MacMillan seri e s i n material science, 1964. (4) A. B 0 Greninger and A. R. Troianos Trans. AIME9 140, 1940, 307. (5) J 0 S. 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Margenau and G0 M. Murphy1 "The Mathematics of Physics and Chemistry" D. Van Nostrand Co., Inc. (28) H. Goldsteins "Classical Mechanics", Addison - Wesley Publishing Company Inc. (29) M.:':S. Wechsler s Acta Met., 2, 1959 , 793. (30) D, Tromanss Dept. of Metallurgy, University of British Columbia; Private Communication. (31) B. P. Decker, J. T, Eash, A. J. Goldman? ASM Trans. Quart. I £ , 1962, 58. (32) E. P. Sadowskis ASM Metals Eng. Quarterly, Feb. 1965, 56. (33) J. R. Mihalisins ASM Trans. Quart., £2, 1966, 60. (34) 0o P„ Miller, W. I. Mitchells JISI, 201, 1965, 895. (35) Sc Floreen, G0R0 Speichs ASM Trans. Quart., jJZ, 1965, 645. ( 3 6 ) Seminar on Maraging Steels, International Nickel Co., A p r i l j 1 9 6 2 . (37) W. R. Patterson, L. S. Richardsons ASM Trans. Quart, 52, 1966, 71. (38) A„ J. Goldman, J. Manenc t ASM Trans. Quart., j>8, 1965, 645. (39) Keiichi Ohtas Technol. Repts., Kansai Univ. 1, ..No. 1, 65 - 71 (1959). 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