the anisotropy of the deformation twinning behaviour of iron-nickel martensite crystals possessing a...

The Anisotropy of the Deformation Twinning Behaviour of Iron-Nickel Martensite CrystalsPossessing a Transformation Twin MicrostructureAuthor(s): M. Bevis and E. O. FearonSource: Proceedings of the Royal Society of London. Series A, Mathematical and PhysicalSciences, Vol. 354, No. 1676 (Apr. 21, 1977), pp. 9-25Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/79197 .

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Proc. R. Soc. Lond. A. 354, 9-25 (1977)

Printed in Great Britain

The anisotropy of the deformation twinning behaviour of iron-nickel martensite crystals possessing

a transformation twin microstructure

BY M. BEVISt AN'D E. 0. FEARON

Department of Metallurgy and Materials Science, University of Liverpool (t See p. 25)

(Communicated by F. C. Frank, F.R.S. - Received 15 May 1975 - Revised 10 June 1976)

[Plates 1-6]

Martensite crystals in metal alloys often possess a transformation microstructure which consists of an array of microtwins. The presence of this type of microstructure would be expected to influence the ease of propagation of deformation modes and therefore to be a controlling factor in the deformation behaviour of martensite crystals. The deformation twinning behaviour of internally twinned martensites ill bulk specimens has been studied comprehensively for the first time, and was made possible by the use of the Kossel microdiffraction technique for the determination of the orientation of the narrow martensite crystals.

The investigation of the operative deformation twinning modes in both as-transformed and deformed Fe-29-33 0 Ni martensites showed that twinning occurs almost exclusively on {1 12} planes and that the number of variants formed and the relative predominance of the operative variants is modified by the microtwirnning which accompanies the transformation. This is explained in terms of the intersection mechanisms of the deformation twins and transformation twins.

1. INTRODUCTION

(a) General introduction

The macroscopic shape change associated with martensite transformations in metal alloys approximates closely to an invariant plane strain (Wayman i964,

I968; Christian I965; Acton, Bevis, Crocker & Ross I970). In general a lattice invariant deformation must however be associated with the transformation process if this type of macroscopic shape change is to occur. Polymer crystals (Allan & Bevis I 974) are important exceptions where the macroscopic shape change can be an invariant plane strain without the introduction of a lattice invariant deformation. In a wide range of body-centred cubic and tetragonal ferrous martensites the lattice invariant deformation has been shown to consist of a single set of {I 12}b twins. The subscript b indicates that the indices of the twin plane are referred to the unit cell of

[ 9 1



10 M. Bevis and E. 0. Fearon

the body-centred lattice of the martensite crystal. The {I 12}b transformation twins are usually several hundred angstroms thick and are most densely packed at the centre of the martensite plate as shown in the transmission electron micrographs in figure 1 a, plate 1. The transformation twins are delineated by fine striations on the surfaces of etched martensite crystals as shown in the optical micrographs in figures

trace 1

' \X '~ -A---3- trace 2

~~JK> ~~(b)

FIGURE 1 (b)

FIGURE 1 (a). Transmission electron micrograph illustrating the transformation twin microstructure which occurs within Fe-Ni martensite plates. (b) Schematic representation of the most general type of martensite substructure observed in four iron-nickel alloys with compositions in the range Fe-29-33 % Ni. (c) Transmission electron micrograph showing a deformation twin which has propagated through transformation twins and slip bands of the type referred to in figure l b.

9 and 11, plates 3 and 4, for example. In the range of the body-centred cubic Fe- 29-33 % Ni martensites which are the subject of the investigation reported in this paper two set of {1 I} slip bands as well as the set of {I 12}b twins are observed within the martensite plates. A schematic representation of the microstructure of Fe-Ni martensites given by a recent study of the crystallography of the transformation of these alloys (Fearon & Bevis I974) is shown in figure 1 b. The angular relationship between the transformation twin plane and the plane defined by the martensite midrib was approximately the same in all martensite plates and in all cases the transformation twin plane was indexed as (1 21)b. The observed slip planies were



Proc. R. Soc. Lond. A, volume 354 Bevis & Fearon, plate 1

0.2

FIGURE 1 (a) AND (c). For description see opposite.

(Facing p. 10)




2~~~~~~~~~2

FIGURES 2~-5. Fjor descriptionl see opposite.



Deformation twinning behaviour of iron-nickel martensite crystal's 11

always of the type (01 l)b and (l IO)b and the former which was the most predominant of the two was approximately parallel to a {1 1 1} plane in the parent austenite crystals. In the present paper the same system of indexing is used throughout so that for all of the results quoted the operative transformation twin system will be (121)b.

Ferrous martensites and martensites in most metals, their alloys and minerals exhibit a microstructure consisting of microtwins or stacking faults and in some cases bands of slip dislocations. The presence of microstructures of the type referred to must influence the relative predominance of crystallographically equivalent deformation modes.

The transmission electron micrograph in figure 1 c, plate 1, illustrates the transformation twin and slip band microstructure referred to above which is found in martensite plates in an Fe-Ni alloy. Deformation twins for example have to propagate through the transformation twins and slip bands so that an anisotropy in deformation twinning behaviour would be expected to occur. Very little quantitative information has been obtained about the influence of the microstructure of martensites on their deformation behaviour because of the difficulty of determining the orientation of the small martensite crystals in bulk specimens (Richman I963;

Rowlands, Fearon & Bevis I968). Electron microscopy has been used to study deformation twin-transformation twin interactions in Fe-Ni and Fe-Ni-C martensites (Krauss & Pitsch i964a, b; Tamura, Yoshimura, Iwasaki & Ibaraki I965;

Kounicky I970 a, b) but the relative predominance of the deformation modes cannot be readily established by using this technique.

The development of the back-reflexion Kossel technique for the determination of the orientation of microcrystals (Bevis & Swindells I967) and in particular for the study of the microstructural detail in martensite crystals (Rowlands, Fearon & Bevis I 970) enables the influence of the microstructure of martensites on some of the operative deformation modes to be studied quantitatively. The authors have used the Kossel technique, etching techniques, and two surface trace analyses to identify the effect of transformation twins on the operation of deformation twins and their propagation mechanisms in a large number of plates in a range of Fe-29-33 % Ni martensites. Only deformation by twinning was considered because of the diffi- culties associated with the identification of the operative slip systems in martensite plates in bulk material.

DESCRIPTION OF PLATE 2

FIGURE 2. Deformation twins formed by the impingement of martensite plates and due to accommodation effects along a boundary parallel to the midrib of martensite plate 3.4.

FIGuRE 3. Deformation twins formed by the impingement of martensite plates and due to accommodation effects along a boundary parallel to the midrib of martensite plate 4. 1.

FIGURE 4. Deformation twins formed along a boundary parallel to the midrib plane as a result of transformation accommodation effects in martensite plate 3.3.

FIGURE .5. Twinning on {5, 8, 11} in plate 3.3.




The full orientations of martensite and austenite crystals could be obtained readily in the body-centred cubic Fe-29-33 % Ni alloys and it was possible to establish the relative orientations and indices of both the transformation and deformation twin systems. This permitted a quantitative consideration of the mechanisms by which deformation twins could propagate through an internally twinned martensite. The majority of the results presented in this paper were obtained from an Fe-32 % Ni alloy as for this composition the martensite plates exhibited well defined and exten- sive transformation twinning. The methods used in the preparation, deformation and crystallographic analysis of these specimens are given in ? 2.

The investigation was divided into two parts. First, an examination was made of the types of deformation twin-transformation twin interactions which occur as a result of accommodation stresses during the transformation process. Secondly, an examination was made of the additional twinning modes and interactions which occur as a result of an externally applied stress. The results of the two parts of the investigation are described in ??3 and 4(a) respectively, and the influence of an externally applied stress on the deformation behaviour over and above that due to the transformation process itself is discussed in ? 4 (a).

2. EXPERIMENTAL PROCEDURES

(a) Preparation of specimens for deformation studies of as-transformed material

Four specimens were prepared for deformationi studies of the as-transformed martensite phase from single crystals transformed 50 % during the initial transformation burst by cooling to temperatures in the range 208-163 K. Parallel sided specimens cut from the single crystals were numbered consecutively from 1 to 4 and were all approximately 7 mm x 4 mm x 4 mm in size and were prepared from alloys having the following compositions: Fe-29.7 % Ni (specimen 1), Fe-31.21 % Ni (specimen 2), Fe-32.81 % Ni (specimens 3 and 4). The preparation of the binary alloys and the method used to grow the second crystals has been described previously, Fearon & Bevis (I974).

(b) Preparation of spectmens for deformation studies of as-transformed and deformed material

From a preliminary series of experiments carried out on a number of specimens prepared from an Fe-32.81 % Ni single crystal transformed by complete immersion in liquid nitrogen for 10 min, it was established that profuse deformation twinning of the martensite phase could be produced by rapid compression at liquid nitrogen temperature. A single specimen 7.5 mm x 4.2 mm x 4.2 mm in size, designated as specimen number 5, was prepared from this alloy and was used to investigate the effects of an externally applied stress on the operative deformation twin modes within the martensite phase. The specimen was deformed in compression at a temperature of 77 K along an axis parallel to its longest dimension, producing a reduction in length of 3.7 % at an initial strain rate of 1.1 x 1 0- s-1.



Deformation twinning behaviour of iron-nickel martensite crystal8 13

Because of the many different martensite orientations present with respect to the compression axis a single specimen was considered sufficiently representative of the general effects arising from an externally applied stress and it was found that a reduction in le:ngth of about 4 %, while giving rise to profuse deformation markings would not result in a loss of definition of the observed transformation structure.

(c) Analytical techniques

A conventional two surface stereographic analysis was carried out to establish the habit planes of deformation twins formed in the martensite with respect to the mar- tenisite lattice basis. The trace analysis followed the preparation of the surfaces of the single crystals by mechanical polishing and electrolytic etching, as described by Fearon & Bevis (I974), and the determination of the full orientations of the indi- vidual martensite plates using the Kossel divergent beam X-ray technique, Bevis & Swindells (i967). The Miller indices of these planes were established by rotating the experimentally determined crystal orientation to an (001) standard orientation. The deformation twin habit plane poles then fell within 3? of the poles on the standard projection representing possible twin modes.

Fine structure within the deformation twins which had been selectively etched was identified from transmission electron microscopy of selected area surface replicas. It was possible to relate the features observed in the replicas to the correspond- ing areas of the specimen surface by a detailed examination of the area of the specimen from which each part of the replica was taken.

3. DEFOIRMATION TWINNING IN AS-TRANSFORMED MARTENSITE

(a) Experimental results

Examination of a large number of as-transformed martensite plates showed that as many as five twins of different crystallographic variants can be formed as a result of the transformation process. A detailed study of twin morphology showed that there are two ways in which the twins are formed. The most obvious of these is

by impingement of one martensite plate on another, the twins being formed in the

vicinity of the point of impingement as illustrated in figures 2 and 3, plate 2. A less obvious way in which the twins appear to form which is nevertheless the

most common is to relieve the accommodation stresses generated by the growth of

the martensite plate. This occurs at a stage in the growth of the martensite plate when the interface is planar and still parallel to the martensite midrib. The subse-

quent growth of the martensite plate appears in many instances to be arrested at the tips of the twins, giving rise to an irregular notched appearance at the parent- product interface. This feature is also illustrated in figures 2, 3 and 4, plate 2, from which it is apparent that the broken lines drawn along the twin tips are parallel to the midrib traces within the martensite plates.

The results of an analysis of the deformation twins which have formed during transformation in a total of fifteen martensite plates selected from the four




specimens examined are shown in table 1. In all cases the transformation twins have been indexed as (121)b. The relative orientations of the (121)b transformation twins and the deformation twins have been established, and for any one martensite plate the operative deformation twin variants are given in the appropriate row of table 1. In all of the micrographs shown in this section the deformation twin variants have

TABLE 1. THE DEFORMATION TWINS OBSERVED IN FIFTEEN MARTENSITE

PLATES IN AS-TRANSFORMED SPECIMENS

(The transformation twin plane in all cases was indexed as (12 2)b. The indices of the deformation twin variants are given ini the second row of the table heading and the notation given in the first row is used and described in ? 3 (b). Results obtained by single and two surface trace analysis are represented by a 1 or a 2 respectively. The results marked * are from traces which were not well defined.)

operative deformation twins martensite -

plate A10 A20 A20 B1+ B2 B2- C1- C1- C2- C2- C2+ C2+ number 121 112 211 121 112 211 121 121 112 211 112 211

1.1 2*. . 22 . 2 2 2 2.1 . . . 2 1 . 1 2 . 1* 2.2. . 2 2 2 3.1 . . . 2 . . 2 2

3.2 . . . 2 . 2 2 3.3. . 2 2 2 3.4 . . . 2 2 . . 2 3.5 . . . 2 2 . 2 2 . . 1* 3.6 . . . 2 . . 2 2

3.7. . 2 2 2 3.8 . . . 2 . 2 2 2 1*

4.1 . . . 2 2 . 2 2 4.2 . . . 2 1 . 1 2 4.3 . . . 2 . . 2 2

4.4 . .1 2 2

inclination angle/deg 90 30 30 90 30 30 54.6 54.6 73.2 73.2 73.2 73.2

been identified and are correct relative to the (121)b transformation twins. With the exception of a single set of {5, 8, 1 1} twins one of which is illustrated in figure 5, plate 2, all of the deformation twins observed were of the {1 12}b type. The results are summarized in table 2 where all single surface analysis results and results based on less well defined traces have been omitted. It is clear from table 2 that certain deformation twin variants predominate.

In addition to the results presented in table 1 a number of features were examined of relevance to the identification of the mechanisms by which deformation twins propagate through an internally twinned matrix. All deformation twins except for one isolated case propagated undeviated by the transformation twins. This conclu- sion is obvious from an examination of a deformation twin which has propagated through twinned and untwinned regions of a martensite plate. In the cases of plates 3.2, 3.3 and 4.1 well defined etch traces within deformation twins could be analysed.



Deformation twinning behaviour of iron-nickel martensite crystals 15

In the case of specimen 4. 1, the replica technique was used to reveal the presence of etch traces within deformation twins. The three cases differ in the type of information which can be obtained from them and are presented separately.

In addition to the twin traces observed within plate 3.2, there also existed three sets of slip traces which were determined to be (01l)b, (1lO)b and (1lO)b. Single surface analysis of the etch traces within the twin (l21)b illustrated in figure 6, plate 3, showed that these were consistent with the incorporation of bands of (1l1)b

slip by the deformation twin.

TABLE 2. SUMMARY OF THE OBSERVED DEFORMATION TWI:N VARIANTS

(Only those results based on a full two surface analysis of well defined etch traces have been included.)

deformation AlO A20 A20 B1+ B2- B2- C1- C1- C2- C2- C2+ C2+ twin variant ...

total number 0 0 0 10 5 4 12 15 0 0 0 0 of observed twins

Two surface trace analysis of the etch traces withini twin (121) b which is shown in figure 5, plate 2, showed that the trace resulted from the incorporation of the transformation twins in the deformation twin. This is clearly supported by the continuity of etch traces across the deformation twin boundary.

An electron micrograph obtained by a selected area replica technique is shown in figure 8, plate 3, which illustrates the displacement of the transformation twin traces within deformation twin (121 )b. This was confirmed by single surface trace analysis to be consistent with the incorporation of the transformation twins within the deformation twin. This is again supported by the continuity of etch traces across

the deformation twin boundary. Figure 9, plate 3, is an optical micrograph which illustrates the relative positions of the transformation twins and deformation twins (121)b and (121)b.

An electron micrograph of a replica taken from twin (I21)b is shown in figure 10, plate 4. The internal etch traces are consistent with the incorporation of (10 )b slip bands by the deformation twin.

(b) Deformation twin-transformation twin interactions

In order to understand why certain deformation twins are predominant, it is

essential initially to classify the mechanisms which allow deformation twins to

propagate u:ndeviated by their interaction with the transformation twins. This

latter requirement which results directly from experimental observations restricts

the possibilities to those described by Sleeswyk (i962) and by Liu (I963). In the

following sections the deformation twin and the transformation twins are to be

considered as the crossing and crossed twins respectively. Sleeswyk (i962) has considered mechanisms involving the decomposition of



16 M. Bevis aind E. 0. Fearon

twinning partials into emissary dislocations which can penetrate the boundaries of the twins. The dislocation reactions necessary for this to occur depend on the relative orientations of the emissary dislocation and the crossed twin boundary. As a result of the reactions at the boundary the crossed twin width would be either increased, decreased or unchanged. In the latter two cases the propagating deformation twin would not be deviated as a result of its interaction with the crossed twin. These three conditions resulting from Sleeswyk's dislocation concept of twin growth are represented in the first row of table 1 by the symbols +, - and 0 respectively, and strictly apply only when the crossing and crossed twins are both formed under the action of a uniaxially applied stress.

TABLE 3. SUMMARY OF TXlE SECONDARY TWIN TYPES FORMED AS A

RESULT OF LIU TYPE TWIN INTERSECTIONS

secondary twin mode necessary conditions 'm i' value A {112} {552} (111> <115> q7 deformation twin//yI1 transformation twin 3 B {552} {112} <115> <111> Y2 deformation twin//X1y transformation twin 3 C {172} {712} <511> <115> Y'q Y2 deformation twin//Vl transformation twin 9

The alternative approach suggested by Liu (i963) involves the secondary twinning of the crossed twin. There are again three possibilities which give rise to different secondary twinning systems when they are referred to the deformation twin lattice basis. The twinning elements of these secondary twin modes, which have been labelled A, B and C are given in table 3. Modes A and B are reciprocal modes and the fraction of lattice shuffles required to restore the lattice in a twin orientation for each of the secondary twinning modes is given by ( 1- n-1), where 1/rn is the fraction of lattice points restored to their correct twin positions (Bevis & Crocker I968). The relative orientations of the twinning directions in the crossing and crossed twins determine the type of secondary twin mode which would be formed as the result of the intersection as indicated in table 3. From a consideration of the criteria which govern the operation of twin modes (Bilby & Crocker I965; Christian I965) it is extremely unlikely that a type C secondary twin would be formed as this involves shuffling of 1. of the atoms.

The notation used to identify the three types of secondary twin has been combined with that used to identify the Sleeswyk type of interaction to give a description of the possible interaction mechanisms between crossing and crossed twins. This combined notation is used in the first row of table 1. In addition it has been necessary to introduce a further distinction according to the relative orientations of the plane of shear of the crossing twin and the twin plane of the crossed twin for any one type of secondary twin mechanism. The angle of inclination between the plane of shear of the deformation twin (crossing twin) and the transformation twin (crossed twin) plane is given in the last row of table 1. When the angles for two given types of secondary twin system are the same this implies the crystallographic equivalence of the twin-twin interactions. To distinguish between secondary twins of the same type




which result from non-equivalent intersection mechanisms the letter identifying the secondary twin type is followed by either 1 or 2. Examination of the notation used to describe the twin-twin interactions will indicate which of the proposed mechanisms if any will allow the deformation twin to propagate undeviated.

Under the c-ondition where both twins form under the action of a uniaxial stress the deformation twins associated with interaction mechanisms C2+ would not be expected to operate because of the complex shuffles associated with the secondary twin mode. The increase in width of the crossed twin which would result from the dislocation interaction concept also rules this out as a feasible intersection mechanism. In the case of both C1 and C2 the secondary twinning mode would not be expected to operate for the reasons applicable to C2+. However in these cases it is possible that the deformation twin could propagate undeviated by the transformation twins as a result of a detwinning process.

Both the detwinning and secondary twinning processes are feasible in the case of B2 twins, whereas only the latter process could apply in the case of B1+ twins. In the case of AlO and A20 no twinning dislocations are produced in the crossed twin boundary and therefore there would be no change in the crossed twin width. The crossing twin however, would propagate undeviated by its interaction with the crossed twins. The result of this type of dislocation interaction must be to re-orien- tate the volume of the crossed twin which is penetrated by the crossing twin. This is an equivalent situation to that envisaged by secondary twinning, involving the shuffling of two thirds of the atoms as determined by the crystallography of secondary twinning mode A.

(c) The observed deformation modes in as-transformed martensite

Reference to table 2 shows that no A type twinning modes are observed in as- transformed material. In the A type modes the twinning directions are all parallel to

[lIllb which is the twinning direction associated with the transformation twins. These modes would not therefore be expected to operate because the stresses which would norma]ly give rise to twins having a [l1l]b shear direction can be accommoda- ted by local variations in transformation twin size and distribution.

All of the B type twins are observed to operate in as-transformed martensite and of the three modes of this type one is observed much more frequently than the other two. Examination of the notation used at the heading of table 2 shows that the most

predominant B type twin cannot occur by a detwinning process although the crossing and crossed twins cannot be considered to be formed under conditions of a uniaxially applied stress in this system. Indeed if both transformation and deformation twins were formed under conditions of a uni-axially applied stress then the B1+ mode would not arise at all since a resolved shear stress criterion then governs the simultaneous operation of the two twinning modes as shown in table 4. Deformation twinning mole B1+ must therefore propagate by a secondary twinning process as supported by the results of the replica study of the displaced transformation twin traces within the deformation twin in martensite plate 4.1 described in ? 3 (a). This



18 M. Bevis and E. 0. Fearon result is entirely consistent with the displacement of traces expected by a secondary twinning process. The two deformation twins B2- can propagate either by detwinning or by secondary twinning though no evidence was obtained to establish whether either or both of these modes of propagation operate. Of the six possible C type modes the two C2+ twins cannot occur by a detwinning process and are very unlikely to arise as a result of secondary twinning. Only the two Cl - twins of the remaining four twin modes are observed to operate and these are the most predominant modes observed in all of the martensite plates examined. The mode of propagation must be by detwinning or some equivalent process because the secondary twinning process is unlikely to operate for any of the C type twins (see, for example, figure 11, plate 4). The non-appearance of the C2- twin mode is thought to be associated with the nature of the transformation process and will be discussed in more detail in ? 4 (b).

TABLE 4. DEFORMATION TWIN MODES WHICH CAN BE FORMED SIMULTANEOUSLY

WITH (121) TRANSFORMATION TWINS UNDER CONDITIONS OF UNIAXIAL STRESS

deformation Al0 A20 A20 B1+ B2 B2 C1 Cl C2 C2_ C2+ C2+ twin variant ... 121 112 211 121 112 211 121 121 112 211 112 211

simultaneous formation with yes yes yes yes yes yes yes yes transformation twin no no no no

An analysis of traces appearing within the C type twins in martensite plates 3.2 and 4.1 showed that these were consistent with the incorporation of slip bands within twins rather than secondary twin traces. The analysis of plate 4.3 showed that the traces within the deformation twin C 1 resulted from the shear of the transformation twin although the number of traces displaced in this way was very small compared to the number of transformation twins intersected. The tendency was to cause pronounced notching of the deformation twin interface in these instances as shown in figure 7. These observations support generally the view that the propagation of the C type twins is not by a secondary twinning process.

(d) Secondary twinning

The experimental results obtained from the as-transformed martensite supported conclusively the operation of a secondary twinning process in the propagation of accommodation twins through the internally twinned regions of martensite plates. A detailed analysis of the crystallography of the secondary twinning process has been made for the A and B type twins which can feasibly propagate in this manner.

The procedure adopted in this study was to make plots of the atomic configuration in the plane of shear of the deformation twin and parallel planes in the matrix and the crossed twin. To simplify the procedure only the orientation of the crossed twin was varied so that in all of the plane of shear plots the matrix and deformation (crossing) twin plane of shear are identical. The plane of shear plots relating to Al0, A20, B1+ and B2- secondary twin types are shown in figures 12-19, plates 4 and 5.




midril)b

1 2 1),~~~~~~~~! W-

(112)b ( im

* 121) )1

FIGURE 6. Incorporation of slip bands in C1 deformation twins as observed in pla.te 3.2.

FIGURE 7. The shear of some transformation twin traces by a C 1 deformation twin in martensite plate 3.3. Not all twin traces intersected are continuous across the deformation twin.

FIGuRE 8. Electron micrograph of a surface replica showing the incorporation of transformation twin traces by a B 1+ deformation twin in martensite plate 4.1.

FIGURE 9. Optical photomicrograph showing the relative orientations of the twins slhown in figure 8 and 11, plates 3 and 4, in martensite plate 4.1.

(Facing p. 18)



PDroc. R. Soc. I,ond. A, volum e 354 Bevis & F7earon, plate 4

11W~~~~~~~~~~~~~~~~~~~~~~~25II1 rxm 1 7 T --f, I-F I: I It

12~ ~ ~~1(Li{W 13)1; 14I lslpi)l ttOp)iO



Deformation twinning behaviour of iron-ntckel martensite crystals 19

Figure 12 shows the incorporation of an Al0 transformation twin by a deformation twin propagating in the matrix region M. The diagram shows the relative orientations of the different crystalline regions which arise as a result of the deformation twinning shear. It is not intended to be a representation of the structure of twinning dislocations at the tip of the deformation twin which would be much less blunt than indicated. All boundaries shown in the diagram are perpendicular to the plane of the paper and the actual atomic positions which result from the shear of the transformation twin (region T) by the deformation twin (region D) are shown in region S of the diagram. Region S is clearly not restored in a twin configuration as a result of the shear.

Figure 13 is the same plane of shear plot as figure 12 but shows the magnitude and direction of the atomic shuffles required to restore the region S in a twin orientation with respect to the region D. It is clear that two thirds of the atoms have to undergo shuffles to restore the structure in a twin orientation relationship. The secondary twin volume is clearly of the same orientation as the matrix M and the deformation twin D is effectively split into two narrower twins.

The process described above would not be expected to occur because the applied stress which would promote the growth of the deformation twin would equally well promote the growth of the transformation twins. The latter process of transformation thickening would clearly be the most favourable one. However, for the situation where the deformation and transformation twins have the same twinning direction but different twinning planes then the transformation twin thickening mechanism could not be a substitute for the proposed secondary twinning mechanism.

DESCRIPTION OF PLATE 4 FIGU:RE 10. Electron micrograph of a surface replica showing the incorporation of slip bands

within a C1K deformation twin.

FIGU:RE 11. Large Cl deformation twins in martensite plate 3.3. These were the most predominant twins observed in all martensite plates examined.

FIGURE 12. The plane of shear plots given in figures 12-16, plate 4 show the incorporation of transformation twin T by a deformation twin D propagating in a matrix M giving rise to the secondary twin region S. Figures 12-14 represent A type secondary twinning and figure 12 shows the atomic positions within region S resulting from the shear of atoms in region T by the propagating deformation twin for an Al0 interaction. All boundaries are perpendicular to the paper.

FIGURE 13. As for figure 12 showing the atomic shuffles necessary to restore region S in a twin orientation.

FIGuRE 14. The effect of reversing the direction of the atomic shuffles shown in figure 13. The secondary twin volume now has the same orientation as the deformation twin.

FIGuRE 15. B type secondary twinning is represented in figures 15 and 16 and this diagram shows the atomic positions within region S resulting from the shear of atoms in region T by the deformation twin for a B1? interaction. All boundaries are perpendicular to the plane of the paper. The atomic shuffles necessary to restore the region S in a twin orientation are indicated by arrows.

FIGURE 16. The effect of reversing the atomic shuffles shown in figure 15. The secondary twin volume now has the same orientation as the deformation twin.



20 M. Bevis anid E. 0. Fearon

Figure 13, plate 4, also describes the plane of shear plot for the A20 secondary twins. Other than that in the A20 twins the crossed twin boundary is no longer perpendicular to the plane of the diagram.

Figure 14, plate 4 shows the effect of reversing the direction of shuffles required to produce the A type secondary twinning illustrated in figure 13. The result is to produce a secondary twin orientation which is identical to that of the deformation twin. This is effectively a detwinning process.

The B1+ configuration resulting from the shear of the transformation twin T by the deformation twin D is represented in figure 15, plate 4 by the open circles. It is evident that there is no complete twin orientation relationship between region S and regions D, M or T. All of the boundaries in this figure are perpendicular to the plane of the paper. If two thirds of the atoms undergo shuffles then the region S is restored in a twin orientation as expected from the form of the B type {225}b twinning mode. As a result of the shuffles indicated there exists not only the expected twin relationship in the boundary section Y-Z but also a twin relationship about the boundary section X-Y. The boundary X-Y will have the largest area and is therefore likely to be of greater significance in determining whether or not a twin mode is feasible from a consideration of boundary energies. It is clearly at least as important to consider the orientation relationship about boundaries of the type X-Y as about boundaries of the type Y-Z in an examination of the feasibility of possible secondary twinning mechanism.

The plane of shear plots for the B2- secondary twins will differ from figure 15, plate 4, only in that the transformation twin boundaries will not be perpendicular to the plane of the diagram.

Figure 16, plate 4, shows the effect of reversing the direction of the shuffles required to produce the B type secondary twin illustrated in figure 15. The result is to restore the deformation twin orientation within the secondary twin volume.

The presentation given above has shown that crystallographically the secondary twinning modes of the A and B types other than AG are feasible twinning modes with respect to all of the interfaces produced. The shuffle mechanisms involved are small and occur within the plane of shear. It has further been shown that identical but opposite shuffles can restore the secondary twin volume in the same orientation as the crossing twin with the consequent reduction in the X-Y boundary energy. How- ever, it should be noted that in this case the Y-Z boundary is not a twin boundary with respect to regions T and S and as such is a high energy boundary. In addition, when the deformation twin D first penetrates the transformation twin T, YZ is greater than XY, so that configuration of figure 15 which makes YZ a twin boundary should be the favoured one. The same applies to each successive thickness increment of D.

The experimental results described in ? 3 (a) support the operation of the secondary twinning process illustrated in figure 15 where the shear of the transformation twin boundaries could be observed within the deformation twin.



Deformation twtnntng behaviour of iron-nickel martensite crystals 21

4. TWINNING OF MARTENSITE DEFORMED BY COMPRESSION

(a) Experimental results

The profuse twinning produced in the martensite plates of specimen 5 by compression at liquid nitrogen temperature is illustrated in figure 17 which is a compo- site optical photomicrograph of the surface of the specimen from which the Kossel patterns were obtained. The result of an analysis of the deformation twins which have formed both during transformation and as a result of compression in a total of

TABLE 5. THE DEFORMATION TWINS OBSERVED IN FIFTEEN DIFFERENT MARTENSITE

PLATES IN A SPECIMEN DEFORMED BY COMPRESSION AT 77 K

(The transformation twin plane in all cases was indexed as (121)b and the indices of the deformation twin variants are given in the second row of the table heading. The notation used in the first row of the t,able heading is the same as that used for previous tables and again the symbols 1 and 2 have been used in the table to denote results obtained by single or two surface analysis l espectively.)

operative deformation twins martensite - - _ _

plate AIO A20 A20 B1+ B2 B2 C1 C1 C2 C2 C2+ C2+ number 121 112 211 121 112 211 121 121 112 211 112 211

5.1 2 . . 2 2 2 2 2 2 2 . 2 2 2 . 2 3 2 . . 1 . 1 2 . 1 1 4 2 . . . 2 2 2 2 5 . 2 2 . . . 2 2 . . 1 2 6 . . 2 . . . 2 2 1 2 2 7 2 2 . 2 2 . 2 2 1 2 8 2 2 . 2 . 2 2 . 2 9 . . 2 2 . 2 2 2 . . 1 1 10 2 . 2 2 2 2 1 2 . 1 11 . 2 1 . 2 . 2 . . 1 . 2 12 2 . . 2 . 2 2 2 13 2 . . 2 . 2 2 2 14 2 . 2 . 2 . 2 15 2 2 . 2 . 2 2

15 martensite plates of different crystallographic variants are shown in table 5. Once again the transformation twins have been indexed as (121)b and the notation described in ?3 (b) is shown in the top row of the table. In this case all the twins identified by two surface analysis were of the {1 12}b type. There were two twin modes which were not {1 12}b twins both of which could have been {310}b twins and one of these could also have been a {, 8, 1 1}b twin. The results obtained by a complete two surface trace analysis are summarized in table 6 from which it is clear that additional twin modes over and above those occurring in as-transformed material are operative.

In a number of cases one or two-surface trace analysis was carried out on traces appearing within deformation twins from which it was possible to obtain further information relating to the propagation mechanisms of the various deformation




twin modes. In six deformation twins which occurred in martensite plates of different variants it was found that profuse twinning had occurred on one or two different {1 1 2}b systems within the deformation twins themselves as identified by one or two surface trace analysis. This retwinning of deformation twins is illustrated in figures 18 and 19, plate 5. In martensite plate 5.2 the traces within the B1+ twin were

TABLE 6. SUMMARY OF THE OBSERVED DEFORMATION TWIN VARIANTS AFTER COMPRESSION

(Only those results based on a full two-surface analysis have been included.)

deformation AIO A20 A20 B1+ B2 B2 C1- C1 C2 C2 C2+ C2+ twin variant ... 121 112 211 121 112 211 121 121 112 211 112 211

total number 11 5 6 9 7 7 14 9 1 3 1 3 of observed twins

found to be consistent with the incorporation of the transformation twins within the deformation twin by a secondary twinning process as illustrated in figure 20. The deflected transformation twin within the (121) deformation twin was approximately parallel to the (212) plane and in agreement with the orientation expected from the secondary twinning process. The indices of the sheared transformation plane with respect to the deformation twin basis may be determined from the correspondence which defines the crystallography of the deformation twin (Bevis & Crocker I968).

(b) Comparison of twin modes in as-transformed and deformed materials

The same number of plates were examined for the occurrence of deformation twins in the as-transformed and deformed martensite. Reference to tables 2 and 6 which summarize the number and types of twin modes which operate in the two cases shows that marked differences arise. The most important of these is that the A type twins are formed readily by deformation as illustrated in figures 19 and 21, plates 5 and 6 but are not observed in the as-transformed material.

It is apparent that the A type twins are able to propagate easily in the internally twinned matrix but do not arise in the as-transformed martensite for the reasons discussed in ? 3 (c). Both of the twin propagation mechanisms considered in ? 3 (b) are feasible for twins of the type A20 and woufd result in no deviation of either the crossed or crossing twin planes. The predominance of the AIO twinning over A20 twinning could be due to the low energy process of transformation twin thickening when compared with the secondary twinning mechanism proposed for the propagation of A20 deformation twins.

There is no significant change in the number of B type or C1 type twins observed. The C1 twins are the most predominant in both the as-transformed and deformed martensites. The C2 and C2+ twins were observed to be operative in the deformed martensite though they were not present in the as-transformed material. The fact that C2 twins do occur in the deformed material suggests that there is a well de-



Proc. B. Soc. Lond. A, volume 354 Bevis & Fearon, plate 5

Cc

C4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~) l

co

I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Po -4 Q

~~~ a': *..~~~~~~~~~~~~~~.A ' /~~~~~~~C

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Proc. R. Soc. Lond. A, volume 354 Bevi8 & Fearon, plate 6

A~

212 ~ ~ ~ 21Z

112

FIGURE 20. Secondary twinning as a result of the incorporation of transformation twins in B 1+ deformation twins in martensite plate 5.2.

FIGURE 21. AIO and A20 deformation twinning in martensite plate 5.14.




fined back stress associated with the transformation which does not produce C2- twins as accommodation twins. The occurrence of C2+ twins which have propagated undeviated by the transformati6n twins shows that a detwinning intersection mechanism is possible when crossing and crossed twins are formed independently of each other. The retwinning observed within C1 twins suggests that these twins have propagated by a detwinning process since it is unlikely that they would be able to deform readily by twinning if they consisted of alternate regions of twin and secondary twin volumes.

5. CONCLUDING REMARKS

The main points arising from the investigation of the operative deofrmation twinning modes in iron-nickel martensites may be summarized as follows:

(a) Deformation twins arise in as-transformed martensite as a form of accommodation twinning.

(b) Accommodation twins are nucleated by the impingement of martensite plates and also as a result of the reverse stress set up by the transformation process itself. The latter nucleation occurs at some stage during the growth of a martensite plate when the interface is still planar and parallel to the midrib trace, giving rise to notching of the boundary at the deformation twin tips.

(c) In general deformation twins propagate undeviated through the transformation twinned regions of martensite plates, either by secondary twinning or by a detwinning process.

(d) Deformation twinning in as-transformed martensite is restricted to five out of the twelve possible {1 124b twin systems.

(e) Iron-nickel martensite is deformed by twinning on all {1 124b planes as a result of rapid compression at low temperatures but the frequency of occurrence of the different deformation twin variants is modified by the presence of transformation twins.

(f) Both the observed results and the differences in deformation behaviour between as-transformed and deformed martensite are entirely consistent with the requirements of the proposed propagation mechanisms.

The investigation has shown that a martensite plate can deform on all twelve {1 124b twinning systems despite the presence of {1 124b transformation twins and {1 1041b bands of slip dislocations. This is a somewhat surprising result as it has not been demonstrated previously that deformation twins can propagate through deformation twins. However, the occurrence of particular {1 124b deformation twinning modes is biased by the presence of the transformation twins as shown in tables 2 and 6. Twins A10, B1+ and Cl- are predominant, while twins C2- and C2+ are the least numerous. The investigation has also demonstrated that secondary twinning is a viable propagation mechanism, at least in cases where the crossed twin is small in dimensions compared to the crossing twin. Detailed dark field electron microscopy studies of these interactions would provide valuable information in establishing more fully the precise propagation mechanisms of the various types of




twin modes described. It is felt however, that such mechanisms would not apply to crystal systems other than cubic where the reduced symmetry rules out the special relationships necessary for the secondary twinning and detwinning processes considered.

It should also be noted that the most predominant deformation twin modes in tables 2 and 6 are those for which the index 2 of the {1 1 2}b twin plane is in the same relative position as the index 2 in the {I 12}b transformation twin plane. Observa- tions of this nature in iron-carbon martensites have been attributed (Tamura & Ohyama I967) to the tetragonality of the martensite structure although clearly this could not be the case in the present investigation. While it is not clear at the present time what causes this preferential twinning it clearly cannot arise as a result of the effect of tetragonality, associated with the presence of carbon atoms, on the crystallography of the twinning process.

Finally, it is emphasized that work of the nature reported in this paper is only possible when the orientations of small volumes of crystal can be accurately determined and readily related to subsequent trace analysis. In this respect electron microscopy is not entirely satisfactory as it is necessary to work with thin films which may not give results truly representative of bulk materials and because the accuracy which can be achieved in this way is not always good. When the Kossel technique is combined with the methods of interpretation described it is possible to satisfy all the requirements necessary for a detailed investigation of the martensite transformation and an examination of the deformation behaviour of the transformation product in bulk material.

The authors wish to acknowledge the financial support given by the Science Research Council, the Air Force Materials Laboratory, O.A.R. United States Air Force and the University of Liverpool.

The authors would also like to thank Dr N. Swindells and Dr P. C. Rowlands for many useful discussions, Professor F. C. Frank, F.R.S., for valuable comments on the manuscript, and Professor D. Hull for his support and the provisioin of facilities.

REFER NCES

Acton, A. F., Bevis, M., Crocker, A. G. & REoss, N. D. H. 1970 Proc. R. Soc. Lond. A 320, 101. Allan, P. & Bevis, M. 1974 Proc. R. Soc. Lond. A 341, 75. Bevis, M. & Crocker, A. G. I968 Proc. R. Soc. Lond. A 304, 123. Bevis, M. & Swindells, N. I967 Phys. stat. sol. 20, 197. Bevis, M. & Swindells, N. I973 J. mater. Sci. 8, 898. Bilby, B. A. & Crocker, A. G. I965 Proc. R. Soc. Lond. A 228, 240. Christian, J. W. 1965 The theory of transformations in metals and alloys. Oxford: Pergamon

Press. Fearon, E. 0. & Bevis, M. 1974 Acta. Met. 22, 991. Kounicky, J. I97oa, b Phys. Stat. Sol. (a) 2, 447 (b) 2, 455. Kraiss, G. & Pitsch, W. i964a Acta Met. 12, 278. Krauss, G. & Pitseh, W. i9646 Arch ?isenhi-ttenwesen, 35, 667. Lill, Y. C. I963 Tians. Metall. Soc. A.I.M.E. 227, 775.



Deformation twinning behaviour of iron-nickel martensite crystaIs 25

Richman, R. H. I963 Trans. Metall. Soc. A.I.M.E. 227, 159. Rowlands, P. C., Fearon, E. 0. & Bevis, M. I968 Trans. Metall. Soc. A.I.M.E. 242, 1559. Rowlands, P. C., Fearon, E. 0. & Bevis, M. 1970 J. mater. Sci. 5, 769. Sleeswyk, A. W. I962 Acta Met. 10, 705. Tamura, I. & Ohyama, T. I967 Memoirs Eng. Faculty, Kyoto University XXIX, 306. Tamura, I., Yoshimura, H., Iwasaki, N. & Labaraki, M. I965 Memoirs of the Institute of

Scientific and Industrial Research. Wayman, C. M. I964 Introduction to the crystallography of martensitic transformations.

New York: Macmillan. Wayman, C. M. I968 Adv. Mlaterials Res. 3, 147.

M. Bevis is now at the Department of Non-metallic materials, Brunel University.



the anisotropy of the deformation twinning behaviour of iron-nickel martensite crystals possessing a...

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