Discrete dislocation simulations of precipitation hardening in superalloys

The low-temperature yield stress of a nickel-based superalloy, containing up to 40% Ni₃A1 precipitates (γ′), is calculated by discrete dislocation simulations. A pair of screw or 60°(a/2) ?110? dislocation glides under external stress across a {111} plane of γ phase, intersected by a random distribution of either spherical or cubic γ′ precipitates. The stress is raised until the dislocations can cut or bow round all the obstacles. In this paper the emphasis is on the cutting regime which is prevalent when the precipitates are small and/or have low antiphase-boundary (APB) energies. From a large number of simulations in the cutting regime, the effects of size, shape, volume fraction and APB energy are found to be as follows: The yield stress is proportional to the square root of the volume fraction of γ′. The yield stress depends weakly on the precipitate size in the size range 20–400?nm, for APB energies of 150, 250 and 320?mJ?m^?2. The yield stress depends linearly on the APB energy for APB energies up to 320?mJ?m^?2 in the size range 50–200?nm. At a precipitate size of 100?nm, cubes are weaker obstacles than equivalent spheres by about 25% for an APB energy of 320?mJ?m^?2; however, the shape effect on strengthening decreases with decreasing APB energy and decreasing precipitate size. When a coherency stress (from a lattice parameter mismatch of 0.3%) is added, the yield stress increases by about 10%. When solid-solution strenthening is added, it is potent when the solute is in the γ matrix, but much less potent when the solute is in γ′. When the γ′ precipitates are larger than 400?nm across and the APB energy greater than 250?mJ?m^?2, significant Orowan looping occurs. The yield stress drops inversely as the precipitate size and becomes insensitive to the APB energy but sensitive to the shear modulus. Many of these results from the full simulations differ from the analytical models of strengthening in superalloys but they can be rationalized from the results of simulations on simple homogenized precipitate structures.     

Tailorable thermal expansion hybrid structures

A design concept is presented for a macro or microstructure that combines materials with differing thermal expansion to achieve an overall effective expansion that differs substantially from either of the constituents. Near-zero-CTE and isotropic negative expansion designs are achieved by creating compliant structures where overall expansion is compensated by internal bending deformation. Such structures have application where dimensional stability is required when subject to large thermal gradients, e.g. space mirrors. In this paper, we present closed form analytic expressions for prediction of the effective expansion, and consequent internal stressing, of the structure, as well as several finite element simulations that demonstrate the design performance under non-uniform thermal load.     

On a super-diffusive, nonlinear birth and death process

The explicit and fully analytic transient solution for the transition probability density associated with a nonlinear birth and death process on Z is constructed. The time-dependent variance is proportional to t+Bt² (with B being a constant), thus exhibiting a super-diffusive behavior. The space continuous limit of this process is a well-known diffusion process with nonlinear drift for which the transition probability density is also known explicitly in a very simple way.     

On Gribov ambiguity in finite temperature Abelian gauge theory

It is shown that there is Gribov ambiguity in finite temperature Abelian gauge theory if the gauge theory is defined on the full gauge orbit space. This is demonstrated geometrically and by an explicit construction of solutions to the Gribov equation. Its effects on the evaluation of the temperature-dependent partition function are noted using the Faddeev-Popov procedure.     

On stochastic games

In this paper, we consider the stochastic games of Shapley, when the state and action spaces are all infinite. We prove that, under certain conditions, the stochastic game has a value and that both players have optimal strategies.Part of this research was supported by NSF grant. The authors are indebted to L. S. Shapley for the useful discussions on this and related topics. The authors thank the referee for pointing out an ambiguity in the formulation of Lemma 2.4 in an earlier draft of this article.     

Percolating through networks of random thresholds: finite temperature electron tunneling in metal nanocrystal arrays

We investigate how temperature affects transport through large networks of nonlinear conductances with distributed thresholds. In monolayers of weakly coupled gold nanocrystals, quenched charge disorder produces a range of local thresholds for the onset of electron tunneling. Our measurements delineate two regimes separated by a crossover temperature T*. Up to T* the nonlinear zero-temperature shape of the current-voltage curves survives, but with a threshold voltage for conduction that decreases linearly with temperature. Above T* the threshold vanishes and the low-bias conductance increases rapidly with temperature. We develop a model that accounts for these findings and predicts T*.