Directionally solidified iron-base eutectic alloys

Pseudobinary eutectic alloys with nominal compositions of Fe-25Ta-22Ni-10Cr and Fe-15.5Nb-14.5Ni-6.0Cr were directionally solidified at 0.5 centimeter per hour. Their microstructure consisted of the fcc, iron solid-solution, matrix phase reinforced by about 41-volume-percent, hcp, faceted Fe2Ta fibers and 41-volume-percent, hcp, Fe2Nb lamellae for the tantalum- and niobium-containing alloys, respectively. The microstructural stability under thermal cycling and the temperature dependence of tensile properties were investigated. These alloys showed low elevated-temperature strength and were not considered suitable for application in aircraft-gas-turbine blades although they may have applicability as vane materials

Directionally solidified eutectic alloy gamma-beta

A pseudobinary eutectic alloy composition was determined by a previously developed bleed-out technique. The directionally solidified eutectic alloy with a composition of Ni-37.4Fe-10.0Cr-9.6Al (in wt%) had tensile strengths decreasing from 1,090 MPa at room temperature to 54 MPa at 1,100 C. The low density, excellent microstructural stability, and oxidation resistance of the alloy during thermal cycling suggest that it might have applicability as a gas turbine vane alloy while its relatively low high temperature strength precludes its use as a blade alloy. A zirconium addition increased the 750 C strength, and a tungsten addition was ineffective. The gamma=beta eutectic alloys appeared to obey a normal freezing relation

Primary arm spacing in chill block melt spun Ni-Mo alloys

Chill block melt spun ribbons of Ni-Mo binary alloys containing 8.0 to 41.8 wt % Mo have been prepared under carefully controlled processing conditions. The growth velocity has been determined as a function of distance from the quench surface from the observed ribbon thickness dependence on the melt puddle residence time. Primary arm spacings measured at the midribbon thickness locations show a dependence on growth velocity and alloy composition which is expected from dendritic growth models for binary alloys directionally solidified in a positive temperature gradient

Heat treating of a lamellar eutectic alloy (gamma/gamma prime + delta)

Eutectic superalloys are being developed at several laboratories for application as aircraft gas turbine airfoils. One such alloy was subjected to several heat treatments to determine if its mechanical properties could be improved. It was found that by partially dissolving the alloy at 1210 C and then aging at 900 C the tensile strength can be increased about 12 percent at temperatures up to 900 C. At 1040 C no change in tensile strength was observed. Times to rupture were measured between 760 and 1040 C and were essentially the same or greater than for as-grown material. Tensile and rupture ductility of the alloy are reduced by heat treatment. Photographs of the microstructure are shown

Microstructural changes caused by thermal treatment and their effects on mechanical properties of a gamma/gamma prime - delta eutectic alloy

Microstructural changes due to thermal treatments of a directionally solidified gamma/gamma'-delta eutectic alloy were investigated. Aging treatments of 8 to 48 hours and ranging from 750 to 1120 C were given to the alloy in both its as directionally solidified condition and after gamma' solutioning. Aging resulted in gamma' coarsening gamma precipitates in delta, and delta and gamma'' precipitates in delta. The tensile strength was increased about 12 percent at temperatures up to 900 C by a heat treatment. Times to rupture were essentially the same or greater than for as directionally solidified material. Tensile and rupture ductility in the growth direction of the alloy were reduced by the heat treatment

Carburization and heat treatment to cause carbide precipitation in gamma/gamma prime-delta eutectic alloys

In an attempt to improve their longitudinal shear strength, several directionally solidified eutectic alloy compositions with minor element modifications were pact, carburized, and heat treated to provide selective carbide precipitation at the cell and grain boundaries. The directionally solidified Ni-17.8 Nb-6Cr-2.5Al-3Ta (weight percent) alloy was selected for the shear strength evaluation because it showed the shallowest delta-denuded zone at the carburized surface. The carburization-carbide precipitation treatment, however, did not appear to improve the longitudinal shear strength of the alloy

Macrosegregation during plane front directional solidification of Csl-1 wt. percent Tll alloy

Macrosegregation produced during vertical Bridgeman directional solidification of Csl-1 wt. pct. Tll in crucibles of varying diameter, from 0.5 to 2.0 cm, was examined. Gravity driven convection is present in the melt even in the smallest crucible diameter of 0.5 cm. Observed solutal profiles are in agreement with the analytical boundary layer model of Favier which describes macrosegregation in the presence of convection. The scintillation efficiency of Csl decreases along the specimen length as the thallium iodide content of the alloy increases

Space Complexity of Perfect Matching in Bounded Genus Bipartite Graphs

We investigate the space complexity of certain perfect matching problems over bipartite graphs embedded on surfaces of constant genus (orientable or non-orientable). We show that the problems of deciding whether such graphs have (1) a perfect matching or not and (2) a unique perfect matching or not, are in the logspace complexity class \SPL. Since \SPL\ is contained in the logspace counting classes \oplus\L (in fact in \modk\ for all $k\geq 2$), \CeqL, and \PL, our upper bound places the above-mentioned matching problems in these counting classes as well. We also show that the search version, computing a perfect matching, for this class of graphs is in \FL^{\SPL}. Our results extend the same upper bounds for these problems over bipartite planar graphs known earlier. As our main technical result, we design a logspace computable and polynomially bounded weight function which isolates a minimum weight perfect matching in bipartite graphs embedded on surfaces of constant genus. We use results from algebraic topology for proving the correctness of the weight function.Comment: 23 pages, 13 figure

Generalization Bounds in the Predict-then-Optimize Framework

The predict-then-optimize framework is fundamental in many practical settings: predict the unknown parameters of an optimization problem, and then solve the problem using the predicted values of the parameters. A natural loss function in this environment is to consider the cost of the decisions induced by the predicted parameters, in contrast to the prediction error of the parameters. This loss function was recently introduced in Elmachtoub and Grigas (2017) and referred to as the Smart Predict-then-Optimize (SPO) loss. In this work, we seek to provide bounds on how well the performance of a prediction model fit on training data generalizes out-of-sample, in the context of the SPO loss. Since the SPO loss is non-convex and non-Lipschitz, standard results for deriving generalization bounds do not apply. We first derive bounds based on the Natarajan dimension that, in the case of a polyhedral feasible region, scale at most logarithmically in the number of extreme points, but, in the case of a general convex feasible region, have linear dependence on the decision dimension. By exploiting the structure of the SPO loss function and a key property of the feasible region, which we denote as the strength property, we can dramatically improve the dependence on the decision and feature dimensions. Our approach and analysis rely on placing a margin around problematic predictions that do not yield unique optimal solutions, and then providing generalization bounds in the context of a modified margin SPO loss function that is Lipschitz continuous. Finally, we characterize the strength property and show that the modified SPO loss can be computed efficiently for both strongly convex bodies and polytopes with an explicit extreme point representation.Comment: Preliminary version in NeurIPS 201