Phenomenological Theory Of Martensitic Transformations Research Articles

Structural study on the tetragonal to monoclinic transformation in arc-melted ZrO 2-2mol.%Y 2O 3—II. Quantitative analysis

Previously obtained experimental data on the herringbone tetragonal to monoclinic transformation were subjected to a quantitative analysis based on the phenomenological theory of martensitic transformation. The basic equation of the theory was modified so that the twinned structure of the parent phase was properly taken into account. A scheme of the transformation mechanism was proposed which agreed with the experimental observations. The scheme includes slip on a {101}〈101̄〉 m system as the lattice invariant shear along with four non-equivalent lattice correspondences, resulting in a habit plane of the (7̄02) m or the {702} c type in the underlying average cubic basis. A few consequences of the twinned structure of the parent lattice are also discussed.

Structural study on the tetragonal to monoclinic transformation in arc-melted ZrO 2-2mol.%Y 2O 3—I. Experimental observations

Martensitic transformation from the tetragonal to monoclinic phase in an arc-melted ZrO 2-2mol.%Y 2O 3 alloy was studied by using XRD and EM. The parent phase had a so-called herringbone structure, in which the monoclinic phase was introduced either by a thinning procedure for EM specimens or by aging of bulk specimens at 573 K. The resulting monoclinic phase was in a thin-plate form with a habit approximately on the (3̄01) m plane. The plate contained planer faults on the {101} m plane which corresponds to the twin plane of the matrix. The faults were interpreted as evidence of a lattice invariant shear. The lattice orientation was such that the b- and c-axes of the monoclinic lattice remained parallel to two of the principal axes of a tetragonal cell. The lattice parameters of both phases were also determined so that the present results can be examined in the succeeding paper on the basis of the phenomenological theory of martensitic transformation.

Isothermal martensite transformation in a 1.80 Wt Pct C steel

The linear products formed isothermally at 373 K in a 1.80 wt pct C steel (Ms = 346 K) were examined by means of transmission electron microscopy. They were first reported as “black line products” by Greninger and Troiano. The isothermal product was of a thin plate with about 0.5 μm width, and it contained {112}b transformation twins and revealed a habit plane of {3 15 10}f. The orientation relationship between austenite and product was close to the Nishiyama relationship. These crystallographic data were in good agreement with those calculated by the phenomenological theory of martensitic transformation. Consequently, the product was determined not to be lower bainite, but isothermal martensite. The black color of isothermal martensites resulted from the fact that they were easily etched by the precipitates of epsilon carbide formed during the isothermal holding.

Electron microscopic study ofθ-phase martensite in Ni-Mn alloys

Electron microscopic observations have been made onθ-phase Ni-Mn martensites which form in nearly stoichiometric Ni-Mn alloys. Three fundamental variant-variant pairs, the “A/B”, “A/C”, and “A/D” types, have been identified as well as other combinations of variants with the aid of crystallographic information given by the phenomenological theory of martensitic transformations. The complex mixing of variants, the abundant presence of dislocations, and the large twinning shear have been pointed out as main crystallographic factors hindering the shape-memory-type deformation in this alloy system, in addition to weak grain boundaries. A new grouping of martensite variants is suggested which as a group cancels the shape strain as well as that found in the normal fundamental plate groups. The new grouping also gives the proper combination of variants for which the intersection becomes a single crystal.

The crystallography of the martensitic transformation in equiatomic nickel-titanium

The phenomenological theory of martensitic transformations is applied to the various observed transformation modes in the shape memory alloy nickel-titanium. Since the martensitic phase has a crystal structure which can be considered to be a monoclinic distortion of the orthorhombic B19 structure of gold-cadmium and is twinned internally, a treatment based on the formulation of Lieberman. Wechsler and Read has been used. New experimental evidence is presented to show that one of the observed twinning modes in the martensite can be identified as a type II mode, with the shear direction η 1 being derived from a cell edge of the parent B2 phase. The theoretical predictions for this mode and the mode where the twinning is type I with K 1 = (11 1 ̄ ) M are found to be in satisfactory agreement with the available experimental results. A third twinning mode, of Type I with K 1 = (001) M is shown to be unable to produce the lattice invariant shear necessary in the martensitic transformation.

The growth mechanism of AuCu II plates

The relationship between the growth mechanisms of AuCu II and martensite plates is considered and it is concluded that lengthening and thickening of AuCu II plates involves the gliding of transformation dislocations at a rate determined by the rate of ordering at the dislocations. This mechanism, which is compatible with the phenomenological theory of martensitic transformations, is shown to account for the reported lengthening kinetics and the observed dependence of thickening rate on interface orientation. It is also shown to be capable of generating the essential features of the morphology of the pyramidal groups of four plates characteristically produced by this transformation. This morphology is not compatible with a proposed ledge mechanism in which disordered ledges are considered to migrate a thousand times faster than the plates lengthen.

Experimental studies of the crystallography of the precipitation of β vanadium hydride

The structure of the interface between β vanadium hydride plates and the parent b.c.c. solid solution of hydrogen in vanadium has been studied by transmission electron microscopy, and measurements have been made of the shape strain and orientation relationship. The results are generally in good agreement with the predictions of the phenomenological theory of martensitic transformations. The prediction that the interface dislocations generating the lattice invariant shear should be resolvable has been confirmed, and direct confirmation obtained of the hypothesis that the complementary shear system is {112} 〈 11 1〉. For the identity correspondence and specific shear system (112) B [ 11 1] R the predictions of the theory that the habit plane is near (2̄27) B and the displacement direction near [22̄7] B have been confirmed by the electron microscopy and the shape strain measurements. The measured magnitudes of both shape and complementary strains agree well with predicted values. Orientation determinations from Laue and Kossel patterns indicate that the [001] direction of the hydride is inclined to the (001) plane and are compatible with monoclinic hydride structures in which either χ or β is greater than 90°. However, measurements of the orientation relationship are generally in better agreement with predictions of the theory for structures with β 〉 90°.

The crystallography of the precipitation of β vanadium hydride

The phenomenological theory of martensitic transformations is applied to the precipitation of β vanadium hydride from b.c.c. solutions of hydrogen in vanadium. The predictions of the theory are examined for a body centred tetragonal hydride structure and for a range of monoclinic structures compatible with the reported mode of hydrogen ordering. This reaction, which involves substantial diffusion of hydrogen, exhibits martensitic relief effects and the habit plane near {221} is distinctly different from the {h0k} habit planes exhibited by a number of transformations involving similar changes in structure. It is shown that the habit plane and the reported orientation relationship are predicted, within experimental error, when the complementary shear is assumed to occur on the (112) B[1̄1̄1] B system. These predictions are obtained using the initial and final lattice parameters; correct predictions are not obtained if it is assumed that transformation occurs in regions of high hydrogen concentration. Since the complementary shear plane is not a plane of symmetry, (112) twins cannot form with equivalent correspondences and the hydride plates are not expected to be twinned. The interface should therefore contain dislocations and the small magnitude calculated for the complementary shear implies that these should be resolvable in the electron microscope.

Twinning in γ′ Cu–Al–Ni Martensite with Cu<SUB>3</SUB>Ti Type Ordered Structure

The {121}γ′ and {101}γ′ twinnings in γ′ Cu–Al–Ni martensite with Cu3Ti type ordered structure, whose sublattice is HCP, have been analyzed by the theory of deformation twinning and the phenomenological theory of martensitic transformations. As a result the following conclusions have been reached:(1) The twinning elements of {121}γ′ twinning consistent with the phenomenological theory are as follows. K1=(\bar1\bar21)γ′, η1=[1,‾0.7954,‾0.5907]γ′, K2=(1,‾1.5036,‾0.5036)γ′, η2=[\bar1\bar11]γ′, s=0.261.(2) In spite of the ordered structure, the original structure can be restored by the above twinning mode and simple and small shuffles, thus providing a theoretical background for experimental evidences such as the mobile nature of twin boundaries and the absence of extra spots in electron diffraction patterns.(3) {101}γ′ twins are considered to be variants of martensite rather than a lattice invariant strain in a variant of martensite.(4) In spite of (3), {101}γ′ twinning can be treated by the theory of deformation twinning, and no structural change is introduced by the twinning with the required twinning shear and simple and small shuffles. This is consistent with the experimental findings.(5) No distinction can be made between the mechanism of deformation twinning and that of transformation twinning in the present martensite, although the structure is ordered.(6) It is suggested that the absence of {10\bar12} twinning as a lattice invariant shear in most hexagonal martensites is due to the fact that no solutions of the phenomenological theory exist for δ nearly equal to unity.

The orientation relationship of the (225) F martensitic transformation in an Fe-Mn-C Alloy

Measurements of habit planes and orientation relationships are reported for (225) F martensite plates in an Fe-6%Mn-0.9%C alloy previously used for shape strain determinations. The measurements confirm that the closepacked lines [11̄0] F and [111̄] B are not exactly parallel. No differences in habit plane or orientation relationship were detected between plates formed at a free surface and interior plates. By considering the complementary strain of the phenomenological theory of martensitic transformations to be composed of a shear on the martensite twinning elements and an unknown “supplementary” strain, the orientation measurements are used to determine the displacement of lines in the (225) F habit plane by this supplementary strain. It is shown that although reliable information can be obtained about the displacement of [11̄0] F, more accurate measurements would be needed to determine the displacement of the line in the habit plane at right angles to [11̄0] F.

Formation of Hcp and Bcc phases in auslenitic iron alloys

The formation of the hcp (∈) and bcc (α) structures in pure iron under high pressure conditions, as well as the morphological and crystallographic aspects of martensitic transformation to these structures at atmospheric pressure in iron alloys, are reviewed., It is concluded that the unique features of α- or lath martensite formation are not dependent upon the presence of the ∈ phase. Application of the phenomenological theory of martensitic transformation has not successfully rationalized the crystallography of lath-martensite. The criterion for ∈- and α-phase formation is established using the regular solution approximation and appropriate lattice stability parameters. In particular, the ∈ phase can be formed in Fe−Ni−Cr compositions through stress-induced transformation attending α-martensite formation. Further consideration suggests that the ∈→α transformation is not expected at atmospheric pressure at temperatures below approximately 500°K in the alloys considered. Thus, two martensitic transformations, γ→∈ and γ→α, can occur jointly in certain alloys.

The formation of Hcp and Bcc phases in austenitic iron alloys

The formation of the hcp (∈) and bcc (α) structures in pure iron under high pressure conditions, as well as the morphological and crystallographic aspects of martensitic transformation to these structures at atmospheric pressure in iron alloys, are reviewed., It is concluded that the unique features of α- or lath martensite formation are not dependent upon the presence of the ∈ phase. Application of the phenomenological theory of martensitic transformation has not successfully rationalized the crystallography of lath-martensite. The criterion for ∈- and α-phase formation is established using the regular solution approximation and appropriate lattice stability parameters. In particular, the ∈ phase can be formed in Fe−Ni−Cr compositions through stress-induced transformation attending α-martensite formation. Further consideration suggests that the ∈→α transformation is not expected at atmospheric pressure at temperatures below approximately 500°K in the alloys considered. Thus, two martensitic transformations, γ→∈ and γ→α, can occur jointly in certain alloys.

Stacking Disorder in Martensite of Cu-Zn Alloy

The faulting in stacking sequence of close-packed layers of the martensite in Cu–38.6 at. %Zn alloy has been studied by electron diffraction, utilizing the selected area diffraction technique of electron microscopy. Observed diffraction spots were shifted and diffused owing to the stacking faults. The shifts of sports were analyzed by the Kakinoki-Komura theory with Reichweite s =3, and the stacking fault probabilities α were found to be between 0.13 and 0.43, α being a fault parameter representing the cubic type stacking faults. The result is compared with the case of the Cu-Al martensite: the predominant type of stacking faults is cubic type for the Cu-Zn martensite while hexagonal type for the Cu-Al martensite. This difference is explained by the phenomenological theory of martensitic transformation.

The crystallography of the B.C.C. to orthorhombic γ′ 1 martensite transformation in copper-tin alloys

The habit plane, shape strain and orientation relationships associated with the formation of orthorhombic γ 1′ martensite plates in Cu-14.95 at.% Sn alloys have been measured. The results are compared with the predictions of the phenomenological theory of martensitic transformations first by assuming the complementary strain to be a shear on the martensite twinning system, and secondly by using the measured habit plane to derive a complementary strain, orientation relationship and displacement direction. The results indicate that the complementary strain does not appear to be a simple shear.

Measurement of the shape strain for the (225) and (259) martensitic transformations

Measurements of the shape strain are reported for an Fe-Ni-C alloy having a (259) F habit plane and for Fe-Mn-C and Fe-C alloys, both of which have (225) F habit planes. The results for the Fe-Ni-C alloy are in excellent agreement with the predictions of the phenomenological theory of martensitic transformations. The results for the (225) F transformation differ from previous results in that the dilatation parameter δ is not significantly different from unity and the shape strains cannot be distinguished from invariant plane strains. The displacement direction, d, of the invariant plane strain is found to vary significantly in different plates. When the measurements are interpreted assuming δ = 1, the d results are found to lie approximately in a plane containing [11̄0] F. The new results for d lie on the opposite side of the (111) F plane to previous results and are compatible with the observed sense of rotation of the (111) F plane on transformation to martensite. The significance of this result in relation to the phenomenological theory of martensitic transformations is discussed. It is demonstrated that although the new d results differ from earlier ones they confirm the conclusion reached by Morton and Wayman that the phenomenological theory cannot account simultaneously for the measured shape strain and orientation relationship in the (225) F transformation.

The crystallography of the cubic to orthorhombic transformation in the alloy AuCu

The habit plane, orientation relationships and shape change associated with the transformation to the ordered orthorhombic phase in the alloy CuAu have been measured and are shown to conform with the phenomenological theory of martensitic transformations. (2–4) The agreement with the theory is systematically better when some dilation of the habit plane is permitted. It has been found that groups of four plates having an irrational habit close to {110} c develop into compound plates parallel to {110} c.