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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.

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...

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.

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.

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.