Statistics of martensitic nucleation

Nucleation statistics, incorporating the particle size effects and the temperature effects, of martensitic transformations in ZrO₂-containing ceramics and in Fe-Ni alloys was analyzed. A phenomenological potency distribution of nucleating defects, of the form of (excess driving force)², was found. Using a simple model of long range nucleating defects, of the type of a dislocation wall, a theoretical potency distribution was predicted. The model was in good agreement with the experimental data and with the phenomenological form, over a broad range of excess driving force. A universal potency distribution for intrinsic, pre-existing defects thus became apparent Experimental evidence was found, in literature and in new data reported here, that both the size effects and the universal potency distribution will be violated when nucleation is extrinsically induced, especially in very small particles or in strain-induced transformations. An essential distinction in the origin of nucleation, as reflected in nucleation statistics, can thus be drawn for classification of martensitic nucleation.     

Martensitic nucleation in ZrO2

A small particle experiment to investigate the tetragonal to monoclinic ZrO₂ (martensitic) transformation was performed using a CuZrO₂ model material prepared by internal oxidation. Incoherent spherical particles formed above 1173 K remained essentially untransformed at 4.2 K and after complete dissolution of the Cu matrix. Transformation was induced by deformation, and the transformed monoclinic particles were stable during reheat up to the highest original oxidation temperature. A twinning substructure was associated with all the monoclinic particles after transformation but no retained tetragonal phase was found. The results demonstrated that the transformation is nucleation controlled, that the strong constraint effect which suppresses the martensitic nucleation is due to the parent tetragonal matrix, and that the cause is the deviatoric transformation strain energy. Such high strain energy can be overcome only if the nucleation is assisted by the interaction energy with a defect. A closer examination of the application of the defect model containing [001]dislocations further suggests that the monoclinic nucleus has a coherent interface. The results of model calculations are in good agreement with the observation of the martensitic transformation at the M_s temperature around 1223 K in bulk ZrO₂ and the stability of small ZrO₂ particles at much lower temperatures; in the latter case, it was shown that the mere generation of one dislocation, e.g. by cold work, suffices to trigger the nucleation. Lastly, the particle size effect in CuZrO₂ is attributed to the size dependence of the interfacial stresses arising from the plastic deformation of the Cu matrix.     

Overview no. 45: On the nucleation of the martensitic transformation in zirconia (ZrO2)

The kinetics of the martensitic tetragonal (t)→monoclinic (m) transformation in ZrO₂ are nucleation-controlled, as they are in metals and alloys, and classical and non-clasical models for martensitic nucleation are considered in this paper. Transmission electron microscopy studies of the several types of transformation-toughened ZrO₂-containing ceramics now available do not reveal any obvious defects that could act as classical heterogeneous nuclei. This is true for t-ZrO₂ as a coherent precipitate phase, as an incoherent dispersed phase, as a fine-grain matrix phase, or as an incoherent precipitate phase in internally-oxidized alloys. On the other hand, nucleation via a Clapp-type localized soft mode mechanism at strain concentrations is consistent with all observations. Nucleation is always stress-assisted, even when the transformation occurs spontaneously. In these latter cases, the stresses arise from thermal expansion mismatch or thermal expansion anisotropy and are enhanced by the stress concentrations provided by particle or grain facets and corners.     

Martensitic growth in ZrO2—An in situ,small particle,TEM study of a single-interface transformation

An in situ TEM experiment on martensitic growth was performed using submicron ZrO₂ particles of a square-platelet shape. The transformation was between the orthorhombic and the monoclinic phases and involved a simple shear plus a dilatation in the shear plane. The o/m interface propagated at a speed of 2 nm/s, while maintaining a sharp habit plane which was stepped on the unit cell scale. The average inclination of this stepped interface obeyed the invariant plane strain condition. While no long-range stresses were present, dislocation-like line contrast was revealed at the steps. These results are analyzed in terms of the coherency dislocation concept. Fundamental properties, such as the interfacial energy, Peierls stress and nucleus size, have been deduced.     

Dislocation nucleation at metal-ceramic interfaces

The ductile vs brittle behaviour of metal-ceramic interfaces is discussed within an atomistic framework, in which the mechanical response of an interfacial crack is assumed to be ultimately controlled by the competition between atomic decohesion and dislocation nucleation ahead of the crack tip. As in later versions of the Rice-Thomson model, this competition may be evaluated in terms of the parameters G_cleave, the energy release rate for cleavage of the metal-ceramic interface, and G_disl, the energy release rate associated with the emission of a single dislocation within the metal. The various models of dislocation nucleation are discussed, with emphasis on an approach which makes use of Peierls-like stress vs displacement relations on a slip plane ahead of a crack tip. A recent analytical result by Rice shows that for a mode II or III shear crack, with a slip plane parallel to the ack plane, a dislocation is emitted when G = γ_us (G is the energy release rate corresponding to the “screened” crack tip stress field and γ_us is the “unstable stacking” energy associated with the sliding of atomic planes past one another). This treatment permits the existence of an extended dislocation core, which eliminates the need for the core cutoff radii required by the Rice-Thomson model of emission. Results are presented here for the nucleation of dislocations under more realistic assumptions for metal-ceramic cracks, namely, the emission on inclined slip planes within a mixed-mode crack-tip field. The specific case of a copper crystal bonded on a {221} face to sapphire is analyzed, and the results are used to interpret the recent experimental observations of Beltz and Wang [Acta metall. mater.40, 1675 (1992)] on directional toughness along this type of interface.     

Solidification behaviour of Al particles embedded in a Zr Aluminide matrix

A hyperperitectic Al-50 wt% Zr alloy has been manufactured by melt spinning, and the resulting microstructure has been examined by transmission electron microscopy. As-melt spun and annealed hyperperitectic Al-50 wt% Zr consist of a Zr aluminide matrix and an Al rich phase distributed in the form of small and large particles with sizes ∼ 15 and ∼ 100 nm, and as an irregular layer at the cell and grain boundaries. Diffraction analysis of the Zr aluminide matrix is consistent with the aluminide having a tetragonal unit cell with a = 4.014 Å and c = 17.32 Å, similar to equilibrium D0₂₃ tetragonal ZrAl₃ but with a different stoichiometry and different atomic ordering on alternate (004) planes. The Al rich particles show a (001)_Al (001)_Matrix; [100]_Al [100]_Matrix orientation relationship with the Zr aluminide matrix. The solidification nucleation kinetics of the Al rich particles have been examined by heating and cooling experiments in a differential scanning calorimeter over a range of heating and cooling rates. Solidification of Al rich particles is nucleated catalytically on the Zr aluminide matrix at an undercooling in the range 0–5 K. Analysis of the solidification nucleation kinetics of the Al rich particles supports the hypothesis that the classical spherical cap model of heterogeneous nucleation breaks down at low undercoolings and small contact angles.     

Dislocation emission and fatigue crack growth threshold

The stress intensity range ΔK below which no cyclic plastic deformation at the crack tip, and hence, no fatigue crack propagation occurs is investigated. The emission of dislocations from the crack tip is assumed as mechanism for the dislocation generation. For a mode III crack, a computer simulation is carried out to study the influence of the number of dislocations, the friction stress and the critical stress intensity, k_e, to emit a dislocation. If during loading only one dislocation is emitted, the return of this dislocation to the crack tip and the emission of a dislocation with an opposite sign and the recombination with the first dislocation are possible during unloading. The ΔK necessary for both mechanisms is about 2k_e. If during loading more than one dislocation is emitted, during unloading at first a certain number of disclocations return to the crack tip before a dislocation of opposite sign is emitted. The necessary ΔK to move one dislocation back to the crack tip during unloading decreases with increasing number of dislocations and reaches a constant values of about 1.1k_e. This value of ΔK then is roughly independent of the friction stress and k_e.     

TEM study on the nucleation and growth of hydride in LaNi5 alloy

The nucleation and growth of hydride in LaNi₅ alloy studied by analyzing dislocation structures after a cycle of hydrogen absorption and desorption. Prismatic dislocation loops and misfit superdislocations were observed depending on the stages of nucleation and growth. From analysis on the morphology, Burgers vector, and line vector of these dislocations, a model for the nucleation and growth of hydride is suggested.     

Oxide dispersion strengthened nickel-base heat resistant alloys by means of the spray-dispersion method

The spray-dispersion method, which produces a metal containing homogeneously dispersed fine oxide particles sprayed from outside into the molten metal stream, was applied to HASTELLOY^* X and Ni−Cr−W alloy. The condition of the dispersion of ZrO₂ particles and the mechanical properties were examined for ZrO₂ dispersed alloys. The addition of a dispersion controlling element, Nb or Ta, was found to be effective for decreasing the average particle diameter of sprayed particles and for increasing the volume fraction of the particles. Ultimate tensile strength and 0.2 pct proof strength were increased by ZrO₂ particle dispersion. And creep strength of ZrO₂ particle dispersed alloys was greater than that of non-dispersed ones. From these results, the production of oxide dispersed nickelbase heat resistant alloys has been established by the spray-dispersion method.     

Stress relaxation and solid solution hardening of cubic ZrO2 single crystals

Solid solution hardening in cubic ZrO₂ single crystals of varying Y₂O₃ contents (12.7, 15.2, 17.7, and 20.5 mol %) oriented for easy 100 〈011〉 slip has been studied at 1400°C. Strain rate cycling and stress relaxation experiments have been performed to characterize the thermally-activated deformation processes. The strain rate sensitivity is very low at small strains but increases with increasing strain; the values measured by stress relaxation are greater than those derived from the strain rate cycling experiments, and the relaxation curves show “inverse” curvature at small strains. The athermal component of the flow stress originating from long-range dislocation interactions was estimated from dislocation densities obtained from etch pit micrographs. The dislocation density increases with increasing Y₂O₃ concentration, but the densities are too small to cause the appreciable athermal component of the flow stress; we believe that significant recovery must have occurred during cooling. The stress relaxation data can be interpreted by assuming that the deformation itself is mainly athermal, but that thermally-activated recovery takes place during the deformation; the Y₂O₃ solute may cause hardening by decreasing the diffusion kinetics. Alternatively, it is possible that the flow stress is controlled by the intrinsic lattice resistance of secondary slip systems.     

Strain-induced nucleation of MnS in electrical steels

The nucleation of MnS was investigated during the creep of electrical steels. Precipitation start(P _s) times were measured in the temperature range from 800 °C to 1100 °C. Direct evidence regarding the locations of the nucleation sites was obtained by means of electron microscopy. The results show that both dislocations and grain boundaries act as nucleation sites for such strain-induced precipitation. The experimental data were analyzed using classical nucleation theory, on the basis of which it is demonstrated that nucleation at grain boundaries is dominant at the higher testing temperatures. TheP _s values in this temperature range are determined by the corresponding nucleation rate. As the temperature is decreased, however, nucleation on dislocations becomes more important. This is due to the additional driving force contributed by deformation-induced vacancies, as well as because the higher dislocation densities at the lower temperatures provide a higher density of potential nucleation sites. In addition, the influence of the growth of these particles following nucleation is considered in the analysis pertaining to theP _s curves.     

Deformation structure and nucleation of dynamic recrystallization in copper single crystals

The deformation structure of [189] oriented copper single crystals was investigated at incipient dynamic recrystallization for different deformation temperatures (T > 0.5 T_m and strain rates. For this purpose the dislocation arrangement was studied, and the cell size distribution was measured. The deformation structure contained kink bands as deformation inhomogeneities at all temperatures. With increasing temperature, the dislocation structure changed its nature from a typical cell structure with a tangled dislocation arrangement in the cell boundaries to a typical subgrain structure, where the subgrain boundaries had the character of small angle grain boundaries. In the investigated range of strain rates the structure transition occurred in a narrow temperature interval around T_t = 0.75 T_m. In the kink bands the dislocation structure was more recovered than in the matrix and the structure transition proceeded at a lower temperature. The average cell diameter was found to vary approximately reciprocally with the flow stress. The cell size distribution consisted of two components, which could be associated with matrix and kink band. The distribution of the matrix shifted continuously to larger cell sizes with increasing deformation temperatures. In the kink bands a stronger increase in subgrain size as well as the occurrence of very large subgrains was recognized for T >T₀ resulting in a pronounced broadening of the distribution. It is concluded that these subgrains grow discontinuously and thus, lead to dynamic recrystallization, when exceeding a critical size. At medium high temperatures the recrystallized structure was dominated by twin chains originating from the scatter of the deformation texture. The twinning of subboundaries is proposed as the nucleation mechanism of dynamic recrystallization in this temperature range.     

Stress-induced γ→ α martensitic transformation in two carbon stainless steels. Application to trip steels

The influence of the temperature θαof a prestraining of austenite above M_don the subsequent stress-induced γ→ α’ transformation in the(M _s, M_d) range is examined in two carbon stainless steels. It is shown that the yield stress, which is controlled by the transformation, increases with θαat given testing temperature and amount of prestraining. This behavior is related to the influence of θαon the nature and arrangement of the defects present in austenite after the prestraining: planar defects(i.e., stacking faults, twins, e platelets) predominate if θαis close to M_dwhereas undissociated dislocation cells are only to be observed if θif higher. This is consistent with the strong increase of the intrinsic stacking fault energy of the austenite, as inferred from measurements using the node method on a hot stage microscope. In addition, the ability of plane defects to propagate under stress is shown to be lower after a prestraining at higher θα, which is attributed to a segregation of impurity atoms on dislocations. It is concluded that the nucleation stress of the γ→ α’ transformation is the stress necessary to allow planar defects to propagate in the prestrained austenite. This work is part of a thesis prepared at the Centre des Matériaux de l’Ecole des Mines, Corbeil, France, and submitted at the University of Nancy, June 1972.     

Strengthening of steel by the method of spraying oxide particles into molten steel stream

A new technique, Spray-Dispersion Method, which produces a steel containing homogeneously dispersed fine oxide particles sprayed from outside into the molten steel stream has been developed. The conditions for the distribution of particles in solid steel, and the mechanical properties of A1₂O₃- or ZrO₂-dispersed steels were studied. The homogeneous distribution of fine oxide particles is obtained by the addition of a certain suitable controlling element which lowers the contact angle of molten steel on various oxides and the interfacial tension at the oxide—molten steel interface. Among others columbium (niobium) was found to be the most effective on decreasing the average particle size of sprayed oxides. Because of fine dispersion of particles of less than 120 nm, the strength of steels increased with their volume fractions; for example, 1.15 vol pct ZrO₂ causes an increment of 79 MN/m² in proof strength and 94 MN/m² in tensile strength. For practical applications, the Spray Dispersion Method makes it possible to produce 18 chromium-8 nickel austenitic stainless steels dispersion-strengthened by A1₂O₃ or ZrO₂ particles, and ThO₂-dispersed nickel with an average particle size of 61.4 nm and a volume fraction of 5.1 pct.     

Densification of Ni and TiAl by SPS: Kinetics and Microscopic Mechanisms

Densification by spark plasma sintering (SPS) of ductile (Ni) and brittle (TiAl) metallic materials has been studied to elucidate the mechanism of densification in the two cases. Isothermal densification experiments were carried out to determine the activation parameters in Ni. Transmission electron microscopy (TEM) observations of thin foils extracted by focused ion beam (FIB) in the contact regions between particles of TiAl and Ni powders are presented. Macroscopically, the most striking feature observed here is that the densification of Ni takes place in the wide temperature range of 0.2 to 1.0 T_m, whereas that of TiAl varies in the temperature range of 0.7 to 0.9 T_m, which is significantly narrower (T_m being the melting temperature of Ni and the peritectic temperature of TiAl). In Ni, the low activation energy (164 ± 30 kJ/mol), the high dislocation density in the interparticle contact region, and the formation of recovery cells involving dislocation climb indicate that the rate-controlling mechanism is probably self-diffusion in dislocations. In TiAl, high dislocation densities leading to reorganization into subboundaries point to dislocation climb mechanisms, which are kinetically controlled by volume diffusion. The difference in densification kinetics between Ni and TiAl is then accounted for in terms of the difference in their respective rate-controlling mechanisms operative during densification.

     

Influence of Grain Size and Age-Hardening on Dislocation Pile-Ups and Tensile Fracture for a Ti-AI Alloy

In an aged Ti-8.6 wt pct Al alloy macroscopic embrittlement occurs with increasing grain size and degree of age hardening. The influence of the grain sizeL on the true fracture strain can be described by εF ∼L-¹ Tensile crack nucleation is caused microscopically by strong dislocation pile-ups which crack the grain boundaries. Using transmission electron microscopy and equations from the dislocation theory, an experimental method was developed to determine quantitatively the shear stress concentrations at the grain boundaries which are produced by the dislocation pile-ups and cause crack nucleation. The experimental results show that for all investigated grain sizes and degrees of age hardening a critical local stress t* _C ≈ 38 GPa leads to crack nucleation. Based on this result equations were derived which describe the combined influence of grain size and age hardening on the true fracture strain and on the true fracture stress. These equations show a good agreement with the tensile test results.     

The precipitation of Ni3Nb phases in a Ni−Fe−Cr−Nb alloy

The age hardening of a Ni?Fe?Cr?Nb alloy containing 4.85 wt pct Nb has been studied using transmission electron microscopy. The major hardening phase in this alloy isγ*, DO₂₂-ordered Ni₃Nb, which precipitates as a fine dispersion of square plates. It is shown that nucleation ofγ* plates may be dependent upon matrix excess vacancy concentration, but nucleation ofγ* plates is also observed at dislocations and extrinsic stacking faults. Theγ* phase is metastable with respect to the orthorhombic Ni₃Nb phase, β, which precipitates by either a cellular or an intragranular reaction, depending upon the aging temperature. It is proposed that the intragranular nucleation of β laths proceeds by the growth of stacking faults from withinγ* plates; theγ* plates subsequently dissolve in favor of the β laths. Room temperature deformation of theγ* dispersion is shown to produce faults within theγ* plates; possible dislocation reactions occurring during this deformation are discussed.     

The effect of variables on martensitic transformation temperatures

A formulation is proposed for the factors which have an effect on the start of martensite. They should be subdivided depending on whether they affect the equilibrium temperature T_o (M_s < T_o: necessary condition) or the additional undercooling ΔT_m = T_o − M_s (sufficient for the onset of transformation). T_o depends on chemical composition, degree of order, hydrostatic stress, ΔT_m on nucleation and propagation of martensite inside the matrix. This, in turn, is affected by an external shear stress, and the resistance to shear, i.e. hardening mechanisms caused by point defects, dislocations, or particles. The course of M_s as the function of the period of isothermal aging provides an example for a different change of T_o and ΔT_m.     

High temperature creep of silicon carbide particulate reinforced aluminum

The effect of stress on the creep properties of 30 vol.% silicon carbide particulate reinforced 6061 aluminum (SiC_p-6061 Al), produced by powder metallurgy, has been studied in the temperature range of 618–678 K. The experimental data, which extend over seven orders of magnitude of strain rate, show that the creep curve exhibits a very short steady-state stage; that the stress exponent, n, is high (n > 7.4) and increases with decreasing the applied stress; and that the apparent activation energy for creep, Q_a, is much higher than the activation energy for self-diffusion in aluminum. The above creep characteristics of SiC_p-6061 Al are similar to those reported for dispersion strengthened (DS) alloys, where the high stress exponent for creep and its variation with stress are explained in terms of a threshold stress for creep that is introduced by the dispersoid particles. Analysis of the creep data of SiC_p-6061 Al using the various threshold stress models proposed for DS alloys indicates that the threshold stresses introduced by the SiC particulates are too small to account for the observed creep behavior of the composite. By considering an alternate approach for the source of the threshold stress in SiC_p-6061 Al, an explanation for the asymptotic behavior of the creep data of the composite is offered. The approach is based on the idea that the oxide particles present in the Al matrix, as a result of manufacturing the composite by powder metallurgy, serve as effective barriers to dislocation motion and give rise to the existence of a threshold stress for creep.     

Hydrogen-assisted ductile fracture in spheroidized 1518 steel

Hydrogen was introduced into smooth and notched tensile specimens of spheroidized 1518 steel by electrocharging under controlled galvanostatic conditions. The role of hydrogen during void nucleation and growth was investigated by identifying two different void nucleation modes. Hydrogen promoted void nucleation at average-sized carbide particles by reducing the critical interfacial strength, σ_C, from 1200 to 1000 MPa (using a dislocation model). The stress-induced hydrogen segregation to the particle interfaces during deformation was estimated to explain the hydrogen-reduced σ_C. Void growth in both longitudinal and lateral directions was enhanced by internal pressurization of hydrogen. In order to better quantify such hydrogen-enhanced void growth, the internal hydrogen pressure inside a void was calculated on the basis of thermodynamics. The final void coalescence stage was analyzed by assuming that the void nucleation rate follows a normal distribution.