Search

The orientation relationship, habit plane, parent-product interface at the atomic level, twin relationship, and plastic deformation resulting from the δ→α′ isothermal martensitic transformation in Pu-Ga alloys are examined using optical microscopy, transmission electron microscopy (TEM), and finite element calculations. The δ → α′ transformation exhibits a ∼20 vol pct collapse when the fcc δ phase transforms to the monoclinic α′ phase, which results in unique and intriguing crystallography and morphology. Here, we show that the orientation relationship is very close to that previously reported by Zocco et al. (1990), but has small rotational misalignments between the two phases both parallel and perpendicular to the $$ \left[ {110} \right]_\delta ||\left[ {100} \right]_{\alpha '} $$ direction. The amount of plastic deformation is exceedingly large due to the ∼20 vol pct collapse, and TEM is used to quantify the difference in dislocation density between untransformed δ matrix and regions of δ adjacent to the transformed α′. The twins contained in α′ plates are shown to have a (205) α orientation as the lattice invariant deformation and are found to be composed of two alternating variants that share a common α′ direction, but differ by a 60 deg rotation about α′ . A combination of electron diffraction and optical microscopy has been employed to examine the macroscopic habit plane, and the analysis suggests that a large fraction of the observed habit planes are on or near {111} δ . Finally, high resolution TEM reveals that the interface is faceted on {111} δ exhibiting a series of terrace and ledges.

In a Pu–2.0 at.% Ga alloy, it is observed experimentally that the amount of the martensitic α′ product formed upon cooling the metastable δ phase below the martensite burst temperature ( M b ) is a function of the holding temperature and holding time of a prior conditioning (“annealing”) treatment. Before subjecting a sample to a cooling and heating cycle to form and revert the α′ phase, it was first homogenized for 8 h at 375 °C to remove any microstructural memory of prior transformations. Subsequently, conditioning was carried out in a differential scanning calorimeter apparatus at temperatures in the range between −50 and 370 °C for periods of up to 70 h to determine the holding time and temperature that produced the largest volume fraction of α′ upon subsequent cooling. Using transformation peak areas (i.e., the heats of transformation) as a measure of the amount of α′ formed, the largest amount of α′ was obtained following holding at 25 °C for at least 6 h. Additional time at 25 °C, up to 70 h, did not increase the amount of subsequent α′ formation. At 25 °C, the Pu–2.0 at.% Ga alloy is below the eutectoid transformation temperature in the phase diagram and the expected equilibrium phases are α and Pu 3 Ga, although a complete eutectoid decomposition of δ to these phases is expected to be extremely slow. It is proposed here that the influence of the conditioning treatment can be attributed to the activation of α-phase embryos in the matrix as a beginning step toward the eutectoid decomposition, and we discuss the effects of spontaneous self-irradiation accompanying the Pu radioactive decay on the activation process. Subsequently, upon cooling, certain embryos appear to be active as sites for the burst growth of martensitic α′ particles, and their amount, distribution, and potency appear to contribute to the total amount of martensitic product formed. A modeling approach based on classic nucleation theory is presented to describe the formation of α-phase embryos during conditioning. The reasons why the holding times during conditioning become eventually ineffective in promoting more α′ formation on cooling are discussed in terms of the differences in the potency of the embryos created in the δ matrix during conditioning and in terms of growth-impeding volume strains in the matrix resulting from an increasing number of martensite particles, thus opposing further growth. It is suggested that the disparate amounts of the α′ formation reported in the literature following various studies may be in part a consequence of the fact that conditioning times at ambient temperatures are inevitably involved in any handling of radioactive samples prior to testing.

The thermodynamics and kinetics of the fcc (delta) to monoclinic (alpha-prime) phase transformation and its reversion in a plutonium-gallium alloy have been studied using differential scanning calorimetry, resistometry, and dilatometry. Under ambient conditions, the delta phase is metastable in a Pu-2.0 at. pct Ga alloy. Thermal cycling to below the ambient temperature results in a partial transformation to the alpha-prime phase; this transformation is composition-invariant and exhibits martensitic behavior. Because this transformation results in an unusually large 25 vol pct contraction that cannot be fully accommodated by purely elastic adjustments, the transformation mode is expected to involve burst formation of individual alpha-prime particles. However, upon cooling, these individual bursts were not resolved by the above techniques, although signals corresponding to the overall accumulation of many alpha-prime particles were observed. On the other hand, upon heating, signals from differential scanning calorimetry, resistometry, and dilatometry showed a series of discrete changes occurring in periodic increments beginning at approximately 32 °C. These features correspond to the cooperative reversion of many alpha-prime particles to the delta phase; they appear to be the result of an interplay between the autocatalytically driven reversion of a cascade of individual martensite units and self-quenching caused by small changes of temperature or stress accompanying each individual transformation burst. The heat of the delta/alpha-prime transformation is estimated to be about +4 kJ/mol.

A new stress-accommodating crystallographic mechanism of the δ→α martensitic transformation in plutonium alloys is proposed. According to this mechanism, an orientation variant of the α phase is produced by a combination of a homogeneous strain and shuffling of the alternating close-packed (111)δ planes. It is shown that the formation of stable transformation-induced twins whose twin-plane orientations and twin-shear directions do not depend on the small variations of the crystal-lattice parameters is the preferred stress-accommodating mode. Only these stable twins have dislocation-free twin boundaries, while the twin boundaries of all others are decorated by an ultradense distribution of partial dislocations. The theory predicts a crystal-lattice rearrangement mechanism involving the (205)α\(((01\bar 1)_\delta )\) stable twins. The corresponding invariant plane-strain (IPS) solutions, with special emphasis on the two simplest shuffling modes (the single and double elementary modes), are presented and compared with the existing experimental observations. It is shown that the habit-plane orientation is highly sensitive to the input values of the crystal-lattice parameters and, especially, to the accuracy of the measured volume change in the δ→α transformation. An analysis of these effects on the habit-plane orientation and orientation relations is also presented.

Charging many metal films or powders with hydrogen results in the growth of second-phase metal hydride particles. A large volume difference between hydride and metal can induce plastic deformation and result in a significant hysteresis upon removal of the hydrogen. For a palladium hydride system (with an 11% volume change), we estimate this hysteresis with calculations of the elastic and plastic works of multiple forward and reverse transformations using a two-dimensional finite-element model and find reasonable agreement between finite-element estimates and experimental observations. We also use a three-dimensional phase-field model to determine the effects of particle interactions, but for the isotropic dilation in the Pd/PdH system, these interactions do not apparently have a significant effect.

We present ab initio ideal strength calculations in body-centered cubic (bcc) tungsten for ‘pencil-glide’ slip on {110}, {112}, and {123} planes and for the {100} cleavage strength. We use these results to analyze the tensile and shear strengths of other bcc metals. In all bcc metals, the minimum shear strength on any plane containing 〈111〉 is ≈0.11/S〈111〉, where S〈111〉 is the elastic compliance for any shear in a 〈111〉 direction. The ideal cleavage strength on {100} for many bcc metals is ≈0.083/s11 where s11 is the single crystal elastic compliance. Comparison of the ideal shear and tensile strengths offers a measure of the inherent ductility or brittleness of a material.

We present recent ab initio calculations of the ideal shear strengths of aluminum and copper using pseudopotential density functional theory within the local density approximation. Structural relaxations orthogonal to the applied shear significantly reduce the values of ideal shear strength, resulting in strengths of 8–9% of the shear modulus for both Al and Cu. However, the geometry of the relaxations in Al and Cu is very different. To some degree, this can be explained using experimentally measured third-order elastic constants.

Using pseudopotential density functional theory within the local-density approximation, we calculate the ideal shear strengths of W for slip on {110}, {112} and {123} planes allowing for complete structural relaxation orthogonal to the applied shear. The strengths in the weak directions on all planes are found to be very nearly equal (about 18GPa, or 11% of the shear modulus G). Moreover, the shear instability occurs at approximately the same applied shear strain (17–18%). This unusual isotropy is explained in terms of the atomic configurations of high-energy saddle points reached during shear. Analysis of these saddle points may also offer a simple explanation for the prevalence of the pencil glide of dislocations on planes containing a (111) direction in bcc metals. Finally, we calculate the ideal cleavage strengths of W on {100} and compare our calculated ideal shear and cleavage strengths with experimental nanoindentation and whisker measurements. All these results can be rather simply unders...

The ideal structural steel combines high strength with excellent fracture toughness. In this paper we consider the limits of strength and toughness from two perspectives. The first perspective is theoretical. It has recently become possible to compute the ideal shear and tensile strengths of defect-free crystals. While the ferromagnetism of bcc Fe makes it a particularly difficult problem, we can estimate its limiting properties from those of similar materials. The expected behavior at the limit of strength contains many familiar features, including cleavage on {100}, slip on multiple planes, "conditionally" brittle behavior at low temperature and a trend away from brittle behavior on alloying with Ni. The behavior of fcc materials at the limit of strength suggests that true cleavage will not happen in austenitic steels. The results predict an ideal cleavage stress near 10.5 GPa, and a shear strength near 6.5 GPa. The second perspective is practical: how to maximize the toughness of high-strength steel. Our discussion here is limited to the subtopic that has been the focus of research in our own group: the use of thermal treatments to inhibit transgranular brittle fracture in lath martensitic steels. The central purpose of the heat treatments described here is grain refinement, and the objective of grain refinement is to limit the crystallographic coherence length for transgranular crack propagation. There are two important sources of transgranular embrittlement: thermal (or, more properly, mechanical) embrittlement at the ductile–brittle transition, and hydrogen embrittlement from improper heat treatment or environmental attack. As we shall discuss, these embrittling mechanisms use different crack paths in lath martensitic steels and, therefore, call for somewhat different remedies.

This paper investigates the conditions of elastic stability that set the upper limits of mechanical strength. Following Gibbs, we determine the conditions that ensure stability against reconfigurations that leave the boundary of the system unchanged. The results hold independent of the nature of properties of the loading mechanisms but are identical with those derived previously for a solid in contact with a reservoir that maintains the Cauchy stress. Mechanisms that control the stress in some other way may add further conditions of stability; nonetheless, the conditions of internal stability must always be obeyed and can be consistently used to define the ultimate strength. The conditions of stability are contained in the requirement that λ ijkl δe ij δe kl ≥ 0 for all infinitesimal strains, where λ ijkl = 1/2(B ijkl + B klij ), and B is the tensor that governs the change in the Cauchy stress t during incremental strain from a stressed state τ: t ij = T ij + B ijkl δe kl . Since λ has full Voigt symmetry, it can be written as the 6 x 6 matrix λ ij with eigenvalues λ α . Stability is lost when the least of these vanishes. The conditions of stability are exhibited for cubic (hydrostatic), tetragonal (tensile) and monoclinic (shear) distortions of a cubic crystal and some of their implications are discussed. Elastic stability and the limits of strength are now being explored through first-principles calculations that increment uniaxial stretch or shear to find the maximum stress. We discuss the nature of this limiting stress and the steps that may be taken to identify orthogonal instabilities that might intrude before it is reached.

There has been continued debate over the relative importance of crack closure and other sources of Kmax dependence in metallic fatigue crack growth. Crack closure is believed to be a very important physical mechanism that is a source for the observed dependence of fatigue on load ratio or Kmax. It is unclear whether the difficulty in observing some hypothesized crack closure is the result of the very small distances over which contact may occur, or whether new mechanisms which operate in front of the crack tip are affecting crack growth. From the existing experimental fatigue data, two driving force models have been developed, one based on crack closure and a ΔKeffective term, and a second based on two terms: ΔK and Kmax. We show how these two driving force models are mathematically compatible with each other, examine what these models say about microstructural mechanisms of fatigue crack growth, and discuss the implications of each model on mechanical design of structures, materials design, and materials science. If there is to be continued debate over the relative importance of closure behind the crack tip and of the effects of stresses in front of the crack tip, we believe the debate should focus on the physical micro-mechanisms involved, rather than on analysis of the mechanical driving forces of crack growth or far field estimates of crack closure.

The ideal shear strength is the minimum stress needed to plastically deform an infinite dislocation-free crystal and is an upper bound to the strength of a real crystal. We calculate the ideal shear strengths of Al and Cu at zero temperature using pseudopotential density functional theory within the local density approximation. These calculations allow for structural relaxation of all five strain components other than the imposed shear strain and result in strengths on ${111}$ planes of 1.85 and 2.65 GPa for Al and Cu, respectively ( $8%$-- $9%$ of the shear moduli). In both Al and Cu, the structural relaxations reduce the ideal shear strengths by $35%$ to $45%$, but the directions of relaxation strain in each are qualitatively different.

This article reports research on the initiation and growth of small fatigue cracks in a nickel-base superalloy (produced commercially by INCO as INCOLOY* 908) at 298 and 77 K. The experimental samples were square-bar specimens with polished surfaces, loaded in fourpoint bending. The crack initiation sites, crack growth rates, and microstructural crack paths were determined, as was the large-crack growth behavior, both at constant load ratio (R) and at constant maximum stress intensity (Kmax). Small surface cracks initiated predominantly at (Nb,Ti)xCy, inclusion particles, and, less frequently, at grain boundaries. Small cracks grew predominantly along {111} planes in individual grains and were perturbed or arrested at grain boundaries. For values of ΔK above the large-crack threshold, ΔKth, the average rate of smallcrack growth was reasonably close to that of large cracks tested under closure-free conditions. However, short-crack growth rates varied widely, reflecting the local heterogeneity of the microstructure. The threshold cyclic stress (Δσth) and the threshold cyclic stress intensity (ΔKσth) for small surface cracks were measured as functions of the crack size, 2c. The results suggest that a combination of the fatigue endurance limit and the threshold stress intensity for closure-free growth of large cracks can be used to define a fatigue-safe load regime.

It was experimentally observed that a single Pu-2.0 at% Ga sample can be thermally cycled many times, with nearly the same amount of transformation and reversion during each cycle, provided that the sample is annealed at 375°C for 8 hours and then conditioned at 25°C for at least 6 hours. The ambient temperature conditioning period is crucial for obtaining the same amount of transformation to alpha-prime in each thermal cycle. Here, we present results from a series of experiments that investigate the effects of conditioning time and temperature on alpha-prime_formation. When the sample is conditioned at 25°C for times between 0 and 6 hours, the amount of alpha-prime formed is a function of conditioning time. For conditioning treatments between 6 and 70 hours, however, the amount of alpha-prime_formed is nearly constant. Conditioning treatments at –50°C, 150°C, and 370°C all resulted in less alpha-prime_formation than the 25°C treatments. We hypothesize that embryos of the thermodynamically stable alpha phase form during the conditioning treatments, and these embryos form alpha-prime upon subsequent cooling. This result is an indirect confirmation of the Russian Pu-Ga equilibrium phase diagram.

Martensitic transformations can occur via two modes: thermoelastic and burst. In thermoelastic martensites, deformation can be accommodated elastically and transformations occur smoothly with changes in temperature or stress. Burst martensitic transformations require both elastic and plastic deformation to accommodate strain; individual martensite particles form at the speed of sound, and the overall accumulation of martensite may increase in discrete, incremental steps. Here, we examine a unique martensitic transformation and reversion in a Pu-2.0 at% Ga alloy and show evidence that they proceed via the burst mode. Upon cooling from ambient conditions, the metastable delta phase partially transforms martensitically to the alpha-prime phase with a volume contraction of 20%. This large volume change suggests a burst transformation. Furthermore, using differential scanning calorimetry (DSC), we observed that the alpha-prime to delta reversion proceeds in discrete increments, which appear as sharp peaks in DSC data. The DSC data is compared to similar results obtained using dilatometry and resistometry. This incremental progression is believed to be the result of autocatalytic cascades of many alpha-prime particles reverting nearly-simultaneously to the delta phase. Finite-element modeling suggests that residual stresses in the regions of reverted alpha-prime particles may catalyze (or retard) additional transformation. These stresses could initiate cascades of alpha-prime particles that revert nearly-simultaneously. The cascades are likely quenched by stress and/or temperature changes resulting from the transformation itself. During the forward delta to alpha-prime transformation, burst events are not observed with the above techniques. The transformation, however, is still expected to proceed via the burst martensite mode because of the large volume changes required. Because alpha-prime must be nucleated in the delta matrix before it can grow as an individual burst, the transformation may not occur cooperatively. These individual bursts may be too small to be resolved by the above techniques, and the signal observed corresponds to a cumulative total of all the events.

We have calculated the phonon spectra of aluminum as a function of strain using density functional perturbation theory for $⟨110⟩$, $⟨100⟩$, and $⟨111⟩$ uniaxial tension, as well as relaxed $⟨112⟩{111}$ shear. In all four cases, phonon instabilities occur at points away from the center of the Brillouin zone and intrude before the material becomes unstable according to elastic stability criteria. This is the first time the ideal strength of a metal has been shown to be dictated by instabilities in the acoustic phonon spectra. We go on to describe the crystallography of the unstable modes, all of which are shear in character. This work further suggests that shear failure is an inherent property of aluminum even in an initially dislocation-free perfect crystal.

The delta‐to‐alpha transformation in Ga‐stabilized plutonium alloys has many unusual features. It is a thermally activated martensitic transformation with double‐c transformation kinetics. The alpha product has an approximately 20% smaller volume than delta, but its volume can change an additional 2% depending on the transformation path. The thermally induced transformation also rarely proceeds to more than 40% completion. We use ab‐initio techniques to look at local ordering of gallium in the alpha phase and use continuum elastoplastic energy calculations to understand the possible effects of plastic deformations during the transformations. We discuss how local ordering and plastic deformation may explain some of the unusual features of the transformation.

The δ to α′ phase transformation in Pu-Ga alloys is intriguing for both scientific and technological reasons. On cooling, the ductile fcc δ-phase transforms martensitically to the brittle monoclinic α′-phase at approximately −120°C (depending on composition). This exothermic transformation involves a 20% volume contraction and a significant increase in resistivity. The reversion of α′ to δ involves a large temperature hysteresis and begins just above room temperature. In an attempt to better understand the underlying thermodynamics and kinetics responsible for these unusual features, we are examining the δ/α' transformations in a Pu-0.6 wt% Ga alloy using differential scanning calorimetry (DSC) and resistometry. Both techniques indicate that the martensite start temperature is −120°C and the austenite start temperature is 35°C. The heat of transformation is approximately 3 kJ/mole. During the α ′ → δ reversion, “spikes” and “steps” are observed in DSC and resistometry scans, respectively. These spikes and steps are periodic, and their periodicity with respect to temperature does not vary with heating rate. With an appropriate annealing cycle, including a “rest” at room temperature, these spikes and steps can be reproduced through many thermal cycles of a single sample.

In delta phase Pu-Ga alloys, the transformation from the ductile face-centered cubic (fcc) δ phase that is retained at room temperature to the brittle low-temperature monoclinic alpha-prime phase is a thermally activated diffusionless transformation with double-c kinetics. Accurate modeling of the phase transformation requires detailed understanding of the role of plastic flow during the transformation and of the crystallographic transformation path. Using transmission electron microscopy (TEM), we find a significant increase in dislocation density in δ near the α′ plates, which suggests that plastic deformation contributes to the accommodation of the 20% reduction in volume during the transformation. Analysis of a series of optical micrographs of partially transformed alloys suggests that the α′ habit plane is usually nearly perpendicular to δ. However, a small number of TEM observations support a habit plane near or , in agreement with earlier work.