a mechanism for the strain-induced nucleation of martensitic

Journal of the Less-Common Metals Elsevier Sequoia S.A.. Lausanne - Printed in The Netherlands

107

A MECHANISM FOR THE STRAIN-INDUCED NUCLEATION OF MARTENSITIC TRANSFORMATIONS*

G. B. OLSON and MORRIS COHEN

Department of Metallurgy and Materials Science, Massachusetts Institute qf Technology, Cumbridge, Massachusetts (U.S.A)

(Received January 18th, 1972)

SUMMARY

The previous work of Professor W. G. Burgers and Dr. A. J. Bogers is used to develop a mechanism of strain-induced martensitic nucleation, involving two intersecting shear systems. We distinguish between strain-induced nucleation and stress- assisted nucleation, the latter involving the same sites and embryos as does the regular spontaneous transformation. The strain-induced nucleation, on the other hand, depends on the creation of new sites and embryos by plastic deformation; this phenomenon may also contribute in a major way to autocatalytic nucleation during the course of martensitic transformation.

For the case of strain-induced nucleation, it is possible to focus on specific intersecting-shear systems when the austenitic stacking-fault energy is low and E (h.c.p.) martensite can form as a part of the shear displacements. It then becomes feasible to extend the intersecting-shear mechanism from this special case to alloys of higher stacking-fault energy, where E is no longer stable relative to the austenite.

It should be noted, however, that these events are very early stages in the formation of martensitic plates and relate primarily to the genesis of embryos; the actual growth start-ups which determine the operational (measured) nucleation rates may be controlled by subsequent processes.

INTRODUCTION

We are privileged to take part in this international tribute to the distinguished Professor W. G. Burgers, and take this opportunity to present some ideas about a subject which has fascinated him for many years, namely the nucleation of martensitic transformations. Professor Burgers’ interest in this phenomenon is typified by his classic paper withA. J. Bogers on “Partial dislocations on the { 1 lo} planes in the b.c.c. lattice and the transition of the f.c.c. into the b.c.c. lattice”‘. This remarkable piece of

Dedicated to Professor Dr. W. G. Burgers in celebration of his 75th birthday. This paper is based on research at the Massachusetts Institute of Technology sponsored by the

Office of Naval Research under Contract No. N00014-67-A-0204-0027 and by the National Science Foundation under Grant No. GK-26631.

J. Less-Common Metals, 28 (1972)

108 G. B. OLSON, M. COHEN

work has stimulated us to build on it, and we now wish to extend the Bogers-Burgers model to strain-induced nucleation.

Although most investigations on the kinetics of martensitic reactions have dealt with the spontaneous transformation unassisted by externally applied stresses, the fact remains that virtually the total portion of such transformations (at least in iron-base alloys) involves autocatalytic nucleationzP4. Because of the macroscopic displacements which accompany martensitic transformations, the surrounding parent phase is plastically strained, and it seems reasonable to assume that strain- induced nucleation contributes to the autocatalysis.

Still another important aspect of strain-induced nucleation arises from the circumstance that, when this type of nucleation is systematically studied through intentionally-imposed plastic deformation, the nucleation sites and corresponding embryos can be identified’ - ‘, at least in special cases, and channeled into specific models. It should be emphasized, however, that we are concerned here with nucleation events which do not necessarily determine the observed nucleation rates3. The latter quantities are operational in the sense that the measurements reflect only the frequency of growth start-ups which produce martensitic units of a visible size’. The rate-con- trolling steps for triggering-off such growth are treated elsewhereg*“. In the present paper, on the other hand, we consider only the genesis of nucleation sites and embryos by plastic deformation, this being a precursor to whatever may control the later growth start-up process.

STRESS-ASSISTED VS. STRAIN-INDUCED NUCLEATION

The complex interrelationships among applied stress, plastic strain, and martensitic transformations have been studied extensively by Bolling and Richman” - l4 in Fe-Nix and some Fe-Ni-Cr-C alloys. They were able to define a temperature, M,” (lying above M,), below which “yielding” under applied stress is initiated by the onset of martensite formation, and above which yielding under stress is initiated by regular slip processes in the parent phase. Accordingly, the temperature dependence of the yield stress is negative (normal) above M,“, but is positive below M,“. In the latter regime, the stress to start the martensitic transformation (and hence yielding) ap- proaches zero as the MS temperature is approached.

These relationships are illustrated schematically in Fig. 1. At temperatures under Mp, the yielding which accompanies the martensitic transformation occurs below the regular yield stress (oY) of the austenite (as extrapolated from higher to lower temperatures). Here, the observed yield stress follows a temperature dependence consistent with the dependence of MS on applied elastic stress16. We regard the nucleation under these conditions as being stress-assisted.

Above M,“, however, the applied stress must reach or exceed @Y in order to initiate the martensitic transformation. As indicated by Fig. 1, there is evidence (serrated stress-strain curves)14,15 that the stress at which the transformation is initiated at temperatures just above Mf follows the regular yield strength o,,. At still higher temperatures the initiating stress rises above (TV until a temperature limit is reached at Md*. It is important to note that, in the temperature range above M,“, the

* The symbol M, has its usual meaning here, being the temperature above which martensite is not produced by plastic deformation.


NUCLEATION OF MARTENSITIC TRANSFORMATIONS 109

_- Md

Temperature --+ Fig. 1. Schematic representation of interrelationships between stress-assisted (below Mp) and strain- induced(aboveM,“)nucleationofa’martensiteinFe-Ni-Calloys.After resultsofBolIingandRichman”- 14,

stress at which transformation is initiated lies significantly below the relatively-steep stress-assisted transformation line extrapolated up from below M,“. Therefore, we postulate that the nucleation occurring above Mf is different in kind from the stress- assisted nucleation manifested below M,“. This distinction is easily rationalized on the supposition that plastic deformation at 0,. and above introduces new, highly-potent sites which allow nucleation at appreciably lower stresses than in the case of stress- assisted nucleation. Hence, we consider the nucleation above M,” to be (plastic) strain- induced.

We can now summarize this overall situation. At the usual MS, the chemical driving force is sufficiently large for the pre-existing nucleation sites or embryos in the parent austenite to become operative without the application of stress. At temperatures between MS and M,“, such nucleation can still occur, but only with the aid of applied stress. This is the stress-assisted transformation regime. Here, the required initiating stress is in the elastic range (below gY), but increases with increasing temperature because of the concommitant decrease in chemical driving force. At M,“, the initiating stress for nucleation, based on the original sites and embryos, reaches o,, and plastic straining enters the picture. Evidently, the resulting strain-induced nucleation can be activated at lower stresses than the stress-assisted nucleation, and so the initiating stress tends to follow gY just above M,“. At still higher temperatures, however, the further reduction in chemical driving force necessitates additional plastic straining in order to produce detectable amounts of transformation; this requires the initiating stress to rise above aY.

The foregoing description applies particularly to paramagnetic austenites. Bolling and Richman13 have shown that, below M,“, the stress-assisted transformation characteristics are rather similar for both paramagnetic and ferromagnetic austenites.



On the other hand, above M,” the strain-induced transformation tends to be suppressed if the austenite is ferromagnetic. Although this curious behavior requires further elucidation, it appears that the ferromagnetic state has a strong inhibiting effect on strain-induced nucleation in contrast to its negligible effect on stress-assisted nucleation; this can be taken as additional evidence for the separate nature of the two types of nucleation.

Neutron irradiation experiments” on austenitic stainless steel demonstrate convincingly that the strain-induced transformation is primarily dependent on plastic strain rather than on the acting stress. The amount of martensitic transformation as a function of plastic strain was found to be the same in both the annealed and irradiated materials, even though the latter was much stronger (due to radiation damage) than the former.

SPECIAL SITES FOR STRAIN-INDUCED NUCLEATION

The formation of E (h.c.p.) martensite in y’(f.c.c.) austenite of low stacking-fault energy is well-established5. There are also some instances in which E has been observed to provide favorable nucleation sites for the formation of a’ (b.c.c. or b.c.t.) martensite. Figure 2, taken from a study by Venables’, shows ~1’ formed at the intersection of two E plates in an austenitic stainless steel (Type 304) deformed at 78 K. This is clearly a case where a nucleating site has been created by plastic straining. The u.’ thus generated may be construed as a strain-induced embryo; it has not triggered-off into a countable martensitic plate in the sense of operational nucleation, as discussed earlier.

Lagneborg6 has reported that the intersections of active slip systems with .E

plates may also produce favorable sites for a’ nucleation. Manganon and Thomas’ found that a’ can be nucleated by the intersection of two E plates or by the intersection of an E plate with a twin or grain boundary in the austenite.

Notwithstanding these instances in which E intersections obviously play a definite role in the strain-induced nucleation of a’ martensite, it can be argued that the

Fig. 2. Nucleation of a’ (b.c.c.) martensite at the intersection of two E (h.c.p.) plates in austenitic (f.c.c.) stainless steel. Venables’.



E phase is not necessary for this purpose, even in those alloys where E can form. Lagneborg6 has noted, later confirmed by Goodchild et al.‘*, that a’ can be generated in austenitic grains which are so oriented relative to the tensile-straining axis that E formation is suppressed. Similarly, Breedis and Kaufman” have also concluded that CI’ can nucleate independently of the E, particularly in those cases where the E is not even thermodynamically stable with respect to either the y or a’.

There seems to be a real correlation in Fe-Ni-Cr alloys between decreasing stacking-fault energy of the f.c.c. austenite and increasing ease of CI’ formation with plastic strain ‘OJ~ In such experiments, E is found in the alloys of lowest stacking- . fault energy, but there is no accompanying discontinuity in the observed trend of ci formation with stacking-fault energy. Thus, although strain-induced nucleation is favored by low stacking-fault energy, the formation of E does not appear to be a necessary condition.

Despite these limitations, the E intersection mode of strain-induced IX’ nucleation is worthy of detailed attention because the site and associated crystallography have been well determined. It is also conceivable that, even in instances where E is not detected, E or faulted E may actually participate in some transient way, and so the E case may offer tangible clues concerning other possible intersection mechanisms. Moreover, there is a dynamic aspect to such intersections which should not be over- looked. When austenitic stainless steel is plastically strained (about 15%) at 60°C some E is formed, and then considerably more appears on cooling under load to - 30°C but the resulting conversion to CI’ is much smaller than when the austenite is plastically strained to 15 % directly at - 30°C6. Clearly, strain-induced nucleation to c(’ takes place more readily during plastic deformation than under applied stress after the deformation

INTERSECTING-SHEAR MECHANISMS FOR AN F.C.C.-B.C.C. TRANSFORMATION

The observations of CI’ nucleation at the intersections of E plates with other E plates, with active slip systems, or with twin boundaries, all have a common feature. The region of intersection defines a lath- or rod-shaped volume which has been doubly sheared, and further, the elements of both shears are of the type (111\(112),,,. We shall now examine this double-shear feature as a mechanism for transforming austenite to martensite. Bogers and Burgers’ have already built an excellent foundation for this problem with their ingenious hard-sphere model, reproduced here in Figs. 3 and 4.

Figure 3(a) and (d)* illustrates an f.c.c. packing of spheres lying in { 11 l}rcc planes. Before dealing with the transition to a b.c.c. structure, it is instructive to visualize the configuration of spheres after a regular f.c.c. twinning shear, shown in Fig. 3(c) and (f), h w erein successive layers parallel to the close-packed plane PVQ have shifted by a,,,/6( 112) in the direction QT perpendicular to PV. The result of this twinning shear is that the shear plane PVQ and its conjugate plane PVS remain as close-packed [ 111 ]rcc planes, whereas the other two close-packed planes QSV and QSP become { 1001_rcc p lanes. Thus, the 60” angle denoted in Fig. 3(a) is enlarged to 90” in Fig. 3(c).

* Figure 3(dHf) are sections through the hard-sphere model in Fig. 3(aHc), corresponding to ( 1 lOif,, planes. Such planes are normal to the shear plane PVQ and contain both the shear direction QT and the dilatational direction.



Fig. 3. Hard-sphere model illustrating twinning shear a,,/6( 112> in austenite and the intermediate position corresponding to af,,/18(l12) where the initially close-packed plane QSV takes on the geometry of a { 1 lo;,,,, plane in Q’S’V’. Bogers and Burgers*.

Fig. 4. Stacking of fllO),,,-type planes in hard-sphere model (a) after the a,,/18(211) shear in Fig. 3(b) and(e), and(b) after the successive shearing of these { 110) ,,,-type planes to achieve the proper stacking in a regular b.c.c. structure. Bogers and Burgers’.

J. Less-Common Met&, 28 (1972)


If we now trace the paths taken by the hard spheres during the transition from Fig. 3 (a) and (d) to 3 (c) and (f), each sphere must ride up to a saddle-point position between the initial and final states. Hence a dilatational component normal to the shear plane is involved; this expansion amounts to 5.4% at one-third of the twinning sheur, a,,,/18(112), as shown in Fig. 3(b) and (e). Figure 3(b) further indicates that the shear plane PVQ and its conjugate plane PVS are still dimensionally unchanged, but the planes QSV and QSP are distorted in such a way that the 60” angle in Fig. 3 (a) is enlarged to 70” 32’ in Fig. 3 (b), thus attaining the geometry of a ( 1 10)t,CC plane. Although the stacking sequence of these planes is not correct for a true b.c.c. structure, the latter can be obtained if successive planes (parallel to QSV or QSP) are sheared according to Fig. 4’. Referred to the b.c.c. structure, this shear corresponds to a displacement of a,,,/8( 110) on each plane, whereas referred to the f.c.c. structure, this corresponds to a displacement of arJl2( 112) or just one-half of a twinning shear. Again, because of the hard-sphere packing there is a dilatation normal to the shear plane. Since each of the above shears entails a dilatational component, they are more accurately described as invariant-plane strains.

According to the Bogers-Burgers model, then, a b.c.c. structure can be generated from an f.c.c. structure by two invariant-plane strains (either successively or simultaneously), which can be thought of as one-third and one-half f.c.c. twinning shears. For convenience, we shall call these the T/3 and T/2 shears.

Bogers and Burgers’ point out that their first shear (T/3) must involve displacements on each (ill],,, p lane of ar,,/18( 112), the latter being one-third the Burgers vector of a Shockley partial dislocation, ur,,/6( 112). They also suggest the possibility that such partial displacements might occur by the “spreading” of a Shockley partial dislocation over a number of successive {ill),,, planes. This idea, although seemingly strange at first thought, is not difficult to imagine. In the con- ventional glide motion of an u,,,/6( 112) partial dislocation, the atoms pass through appropriate positions for the T/3 shear proposed in the Bogers-Burgers model. Under conditions of sufficient chemical driving force, the atoms may tend to “stick in the b.c.c. positions” corresponding to the ar,,/lS( 112) displacement (Fig. 3(b) and (e)) rather than continue through to the full Burgers-vector displacement of a,,,/6( 112) (Fig. 3(c) and(f)). H owever, the full Burgers vector can be conserved if the atoms in an adjacent plane are concurrently “dragged along” to the proper “b.c.c. positions“. In this way, the T/3 shear of the Bogers-Burgers model can be achieved by an array of u,,,/6( 112) partial dislocations, averaging one on every third (111 ).rcc plane.

A problem arises in connection with the second (T/2) shear. Bogers and Burgers suggest that this shear may involve b.c.c. partial dislocations with ut,,,/8( 110) vectors since these have been previously proposed to explain b.c.c. twinning”. However, the existence of such partial dislocations is not generally accepted. We can circumvent this difficulty by considering the second shear (T/2) relative to the f.c.c. instead of the b.c.c. structure. This comes about naturally in the shear-intersection mechanism to be described below.

A schematic intersection of partial-dislocation arrays for the strain-induced formation of a b.c.c. embryo in f.c.c. austenite is illustrated in Fig. 5. The plane of this diagram is parallel to (1 10)rcc, and perpendicular to VQ in Fig. 3. Then, planes (ill) rcc and (lil),,, correspond to PVQ and QSV, respectively. The T/2 shear (the second of the Bogers-Burgers shears) can be accomplished (with spreading) by an array of



Fig. 5. Schematic illustration of intersecting shears due to two arrays of n&6( 112) partial dislocations in austenite. One array (T/3) has partial dislocations on every third { 11 l}rcc plane and averages one-third of a twinning shear, while the other array (T/2) has partial dislocations on every second { lll}r,, plane and averages one-half of a twinning shear. The resulting doubly-faulted intersection has an exact b.c.c. structure.

a rCC/6 [21i] partial dislocations on every second (lil),,, plane, just as the T/3 shear (the first of the Bogers-Burgers shears) can be accomplished (with spreading) by an array of afcc/6 [211] partial dislocations on every third (ill) plane. Each of these Burgers vectors has a component out of the plane of the diagram. The partial dislocations are shown in their positions (I) after the intersection process, and the stacking faults left behind outside the intersected region are denoted by heavy lines. (Of course, these faults will be bounded at their other ends by other partial dislocations.)

The Bogers-Burgers dislocation-spreading hypothesis is most likely to be valid within the intersected volume and during the intersection event. Under these conditions, the atoms can attain their true b.c.c. positions which, as we have seen, happen to lie intermediate between the full displacements involved in the regular gliding of a,,,/6( 112) partial dislocations. When referred to the f.c.c. structure, the



intersected volume is “doubly faulted” (lighter solid lines in Fig. 5) but this region now has a true b.c.c. structure.

It is more realistic to picture the intersection event, not as a collision of two fronts of moving partial dislocations, but as the intersection of one moving array with a stationary packet of stacking faults left behind by the prior passage of another array of partial dislocations. This situation is readily visualized from the fact that the set of stacking faults left behind by the T/2 dislocation array produces exactly an E (h.c.p.) plate; in other words, the h.c.p. structure can be modeled as a shear of ar,,/6( 112) on every second ( 111 I.rcc plane.

We now examine the intersection of a T/3 array with the coherent interface of an E plate. One can well imagine that a barrier of this type will cause the T/3 set of partial dislocations to pile up at the interface. A likely plane in the E for the passage of these dislocations would be (1Oil). Every second basal plane in the h.c.p. structure is in the proper position for a T/2 shear (except for the dilatation), and all that is necessary to generate the exact configuration of a T/2 shear is a “shuffle” on every second plane by a displacement of a ,,,/12 [21i]. Moreover, if the atoms behave as hard spheres, these shuflIes will produce the afore-mentioned dilatation. It can be shown that the conversion of the E structure to an exact T/2 shear configuration transforms the (loil),,, plane into a uniformly distorted (ill),,, plane. Returning now to the intersecting T/3 array, we find that the ar,,/6 [211] partial dislocations in the Tj3 packet can glide on the uniformly distorted (il l)rcc planes. If these T/3 partials can spread on entering the intersected region, as discussed earlier, their resulting passage through the intersection will generate b.c.c. martensite. Put in another way, the formation of the b.c.c. structure allows the blocked dislocations to pass through the intersected volume.

In accordance with theoretical estimates for the critical size of a nucleus, it is improbable that a small number of intersecting dislocations could enter the E plate, since the volume of martensite would then be subcritical. Consequently, we should expect the blocked dislocations to continue to pile up at the E interface during the plastic straining until the T/3 shear packet is thick enough to create a supercritical volume in the intersected region under the conditions at hand. A more general postulate regarding strain-induced nucleation might then be: if the motion of a large enough array of appropriate partial dislocations in the parent phase is impeded by intersecting a set of stacking faults (not necessarily E) in which enough of the atomic positions coincide with the “other shear” of the Bogers-Burgers model, the required shuffling of the atomic planes within the set of stacking faults will take place concurrently with the spreading of the entering partial dislocations, and then the passage of these dislocations through the intersected region can occur by the formation of b.c.c. martensite.

From an experimental standpoint, the most commonly reported strain-induced nucleation site is the intersection of two E plates. It is already evident that an E plate can accomplish the T/2 shear with the aid of shuffles. However, in order for the other e plate to provide the equivalent of a T/3 shear, it would have to be highly faulted. Strain-induced E is, indeed, often observed to be highly faulted, and it is conceivable that local regions exist in such E where the average shear matches that of a T/3 array.An alternative for the cast of relatively perfect E plates is that one-third of the dislocations attempting to pass into the intersection from the second plate may be left at the interface. producing a semicoherent interface. Hence, operation of the proposed inter-

.f. Less-Common Metals, 28 (1972)

116 G. 8. OLSON, M. COHEN

setting-shear mechanism is feasible even when only I: plates are involved. The proposed intersecting-shear mechanism for E plates offers a good explana-

tion for Lagneborg’s finding6 that E formed by plastic straining at low temperatures leads to much more effective b.c.c. nucleation sites than does the same plastic straining at higher temperatures (also generating E) and then cooling under load to the low temperature. In the intersection processes described, the b.c.c. structure can only nucleate ~~~i~g the intersection event and only if there is a substantial chemical driving force for the f.c.c.-b.c.c. transformation at play. At the higher temperature, where this driving force is small or nonexistent, the intersection mechanism may actually regenerate the f.c.c. phase, as proposed by Sleeswijk23.

A further deviation from the “ideal” T/3-T/2 shear-intersection case is that of an E plate penetrating an f.c.c. twin boundary. Consider the leading a rcJ6 [2li] partial dislocations of an advancing E plate (the T/2 array in Fig. 5) colliding with a (il l)foc twin boundary (parallel to the plane of the T/3 array in Fig. 5). The twinned lattice across the (71 l)fcc boundary can be equivalently described by a twinning shear of a,,,/6(112) on every (ill),,, plane in either of the [211],,,, [El],,, or [TlZJ,,, directions. To cross into the twinned region, the partial dislocations should glide on the planes in the twin that correspond to the glide planes in the untwinned region. Because of the three equivalent twinning shears, there are three correspondences, but they do not permit the dislocations to cut straight across the twin. Nevertheless, this could become feasible for one of the correspondences if the appropriate shuttles of (illhcc planes in the twin could occur to produce the T/3 shear configuration during the deformation. However, inasmuch as there are relatively few positions in the twin which are already T/3 shear positions, it may be anticipated that the intersection of E plates with f.c.c. twin boundaries will be a less potent mechanism for b.c.c. nucleation than the case of two intersecting E plates and, moreover, a higher chemical driving force will be required. This is in line with the fact that b.c.c. nucleation at E- plate/twin-interfa~ intersections is less common than at E/E intersections6,

In alloys of slightly higher stacking-fault energy where the E phase is not stable relative to the austenite, packets of stacking faults in the f.c.c. structure (with no evidence of an h.c.p. phase) are sometimes associated with nucleation of b.c.c. marten- sitez4. Here, it may be presumed that the nucleation takes place when the intersection of two such packets locally approximates the conditions represented by Fig. 5; for example, one packet with a stacking-fault probability of l/3 intersecting a second packet with a stacking-fault probability of l/2. Inasmuch as the length of these packets (distance between pairs of partial dislocations) will decrease with increasing stacking- fault energy, and so might the thickness and number of these packets, the probability of packet intersections will also decrease with increasing stacking-fault energy. This relationship could account for the adverse effect of stalking-fault energy on the propensity to strain-induced nucleation.

Plausibility arguments have now been presented here for mechanisms by which the two shears of the Bogers-Burgers model can bring about the observed nucleation sites. l-lowever, an important aspect not yet considered is the problem of coherency strains. In the idealized shear intersections which can be analyzed in detail, the b.c.c. phase thus nucleated is fully coherent with its surroundings. The coherency strains have to be accommodated by a dilatation normal to the stacking- fault arrays outside the intersected region. In the case of E intersections, the accom-

J. Less-Common Met& 28 (1972)


modation would distort the h.c.p. structure to a non-ideal c/a ratio. The coherency strains are further increased because the real b.c.c. structure in iron has a smaller atomic diameter than provided by the hard-sphere model of f.c.c. iron. It may be expected, therefore, that at some point in its formation, the b.c.c. region will undergo plastic deformation to relieve the coherency strains and so create a semicoherent interface. This deformation process is also likely to cause a rigid-body rotation of the intersected region, all of which will influence the orientation relationships and interface planes of the embryo thus formed.

CONCLUSIONS

Evidence for the separate nature of stress-assisted and strain-induced nucleation of martensitic transformations has been presented. The indications are that stress-assisted nucleation depends on the same nucleation sites or embryos which are responsible for the usual spontaneous transformation, whereas the strain-induced nucleation involves the creation of new sites or embryos by plastic deformation. It is likely that strain-induced nucleation plays an important role in the autocatalytic nucleation observed in regular martensitic transformations.

Strain-induced nucleation occurs in austenites with a wide range of stacking- fault energies at lower stresses than does stress-assisted nucleation at comparable temperatures. When the stacking-fault energy is very low and E martensite can form, the nucleation sites and ci embryos are generated by two intersecting shear systems in the austenite with the elements { 11 l} (112). The proposed mechanism is consistent with the Bogers-Burgers two-shear model, but is an extension thereof to embrace plausible dislocation motions.

The strain-induced a’ embryos generated in this way are initially coherent. The formation of semicoherent interfaces and the subsequent growth start-ups which enter into the operational (measured) nucleation rates constitute still later stages in the formation of the usual martensitic plates.

ACKNOWLEDGMENTS

The authors deeply appreciate the stimulating interest and critical guidance offered by Professor J. W. Christian during the development of ideas presented here.

They are also indebted to the Office of Naval Research and the National Science Foundation for the support of resea’rch which provided the general back- ground for this paper.

REFERENCES

1 A. J. Bogers and W. G. Burgers, Acta Met., 12 (1964) 255. 2 V. Raghavan and A. R. Entwiste, Iron Steel Inst. Spec. Rept. No. 93, 1965, p. 20. 3 S. R. Pati and M. Cohen, Acta Met., 17 (1969) 189. 4 S. R. Pati and M. Cohen, Acta Met., 19 (1971) 1327. 5 J. A. Venables, Phil. Msg., 7 (1962) 35. 6 R. Lagneborg, Acta Met., 12 (1964) 823. 7 D. L. Manganon and G. Thomas, Met. Trans., 1 (1970) 1577. 8 M. Cohen. to be published in Met. Trans. as a part of the E. C. Bain Symposium (October 1971), Detroit,

Michigan.



9 V. Raghavan and M. Cohen, to be published in Acta Met. (March 1972). 10 V. Ragahavan and M. Cohen, submitted to Acta kfet.

11 G. F. Boiling and R. H. Richman, Scripta Met., 4 (1970) 539. 12 G. F. Bolling and R. H. Richman, Phil. Mag., 19 (1969) 247. 13 G. F. Bolling and R. H. Richman, Acta Met., 18 (1970) 673. 14 R. H. Richman and G. F. Bolling, Met. Trans., 2 (1971) 2451. 15 R. H. Richman, private communication. 16 J. R. Pate1 and M. Cohen, Acta Met., 1 (1953) 531. 17 A. L. Bement, Effects of Residual Elements on Properties of Austenitic Stainless Steels, Am. Sot. Testing

Mater. STP418, 1967, p. 46. 18 D. Goodchild, W. T. Roberts and D. V. Wilson, Acta Met., 18 (1970) 1137. 19 J. F. Breedis and L. Kaufman, Met. Trans., 2 (1971) 2359. 20 J. S. Dunning, Univ. Calif. (Berkeley) Rept. UCRL-19052, 1969. 21 F. Lecroisey and A. Pineau, to be published; private communication from W. G. Burgers. 22 J. B. Cohen, R. Hinton, K. Lay and S. Sass, Acta Met., 10 (1962) 894. 23 A. W. Sleeswijk, Phil. Mug., 7 (1962) 1597. 24 P. M. Kelly, Acta Met., 13 (1965) 635.


a mechanism for the strain-induced nucleation of martensitic

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