On kuhnels 9-vertex complex projective plane

We present an elementary combinatorial proof of the existence and uniqueness of the 9-vertex triangulation of C P2. The original proof of existence, due to Kuhnel, as well as the original proof of uniqueness, due to Kuhnel and Lassmann, were based on extensive computer search. Recently Arnoux and Marin have used cohomology theory to present a computer-free proof. Our proof has the advantage of displaying a canonical copy of the affine plane over the three-element field inside this complex in terms of which the entire complex has a very neat and short description. This explicates the full automorphism group of the Kuhnel complex as a subgroup of the automorphism group of this affine plane. Our method also brings out the rich combinatorial structure inside this complex.

Processing map for hot working of Ni–16Cr–8Fe alloy (IN 600)

The hot deformation characteristics of IN 600 nickel alloy are studied using hot compression testing in the temperature range 850-1200-degrees-C and strain rate range 0.001-100 s-1. A processing map for hot working is developed on the basis of the data obtained, using the principles of dynamic materials modelling. The map exhibits a single domain with a peak efficiency of power dissipation of 48% occurring at 1200-degrees-C and 0.2 s-1, at which the material undergoes dynamic recrystallisation (DRX). These are the optimum conditions for hot working of IN 600. At strain rates higher than 1 s-1, the material exhibits flow localisation and its microstructure consists of localised bands of fine recrystallised grains. The presence of iron in the Ni-Cr alloy narrows the DRX domain owing to a higher temperature required for carbide dissolution, which is essential for the occurrence of DRX. The efficiency of DRX in Ni-Cr is, however, enhanced by iron addition.

Structural Behavior of Story-High Cement-Stabilized Rammed-Earth Walls under Compression

A rammed-earth wall is a monolithic construction made by compacting processed soil in progressive layers in a rigid formwork. There is a growing interest in using this low-embodied-carbon building material in buildings. The paper investigates the strength and structural behavior of story-high cement-stabilized rammed-earth (CSRE) walls, reviews literature on the strength of CSRE, and discusses results of the compressive strength of CSRE prisms, wallettes, and story-high walls. The strength of the story-high wall was compared with the strength of wallettes and prisms. There is a nearly 30% reduction in strength as the height-to-thickness ratio increases from about 5 to 20. The ultimate compressive strength of CSRE walls predicted using the tangent modulus theory is in close agreement with the experimental values. The shear failures noticed in the story-high walls resemble the shear failures of short-height prism and wallette specimens. The paper ends with a discussion of structural design and characteristic compressive strength of CSRE walls. DOI: 10.1061/(ASCE)MT.1943-5533.0000155. (C) 2011 American Society of Civil Engineers.

On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM)

By using the strain smoothing technique proposed by Chen et al. (Comput. Mech. 2000; 25: 137-156) for meshless methods in the context of the finite element method (FEM), Liu et al. (Comput. Mech. 2007; 39(6): 859-877) developed the Smoothed FEM (SFEM). Although the SFEM is not yet well understood mathematically, numerical experiments point to potentially useful features of this particularly simple modification of the FEM. To date, the SFEM has only been investigated for bilinear and Wachspress approximations and is limited to linear reproducing conditions. The goal of this paper is to extend the strain smoothing to higher order elements and to investigate numerically in which condition strain smoothing is beneficial to accuracy and convergence of enriched finite element approximations. We focus on three widely used enrichment schemes, namely: (a) weak discontinuities; (b) strong discontinuities; (c) near-tip linear elastic fracture mechanics functions. The main conclusion is that strain smoothing in enriched approximation is only beneficial when the enrichment functions are polynomial (cases (a) and (b)), but that non-polynomial enrichment of type (c) lead to inferior methods compared to the standard enriched FEM (e.g. XFEM). Copyright (C) 2011 John Wiley & Sons, Ltd.

Analysis of geometric and strain effects in homo-Diels-Alder reactions

Molecular mechanics calculations have been carried out to quantify the key geometric and strain effects which are likely to control the homo-Diels-Alder reactivity of 1,4-dienes. The criteria considered include C1..C5 and C2..C4 distances in the diene, twist angle of the two pi units, and the magnitude of strain increase as a result of cycloaddition. By first considering these factors in a number of non-conjugated dienes with known reactivity, the ranges of values within which the reaction is favoured are proposed. Calculations are also reported on several substrates which have not been investigated so far. Promising systems for experimental study are suggested which, in addition to being intrinsically interesting, would place the present proposals on a firm basis.

Consolidation behavior of clayey soils under radial drainage

For Barren's degree of consolidation, U-r, versus the time factor, T-r, relationship for soils undergoing consolidation with radial drainage for the equal vertical strain condition, a simple method has been developed to determine the value of the coefficient of consolidation with radial drainage c(r). Theoretical log(10)(d(e)(2)/t) versus U-r curves where d(e) is the diameter of influence and r is the real time for the different known value of c(r) have been generated. A method has been developed wherein both the theoretical and experimental behaviors of soils undergoing consolidation with radial drainage can be simultaneously compared and studied on the same plot. The experimental log(10)(d(e)(2)/t) versus U-r curves have been compared with the theoretical curves. Effects of initial compression, secondary compression, and duration of load increment are studied. Simple procedures are presented for calculating the values of c(r) using the experimental log(10)(d(e)(2)/t) versus U-r curves. A comparative study of the coefficient of consolidation and the coefficient of permeability between the cases of vertical and radial drainage has been done.

Dynamic recrystallisation during hot working of Zr-2 center dot 5Nb: Characterisation using processing maps

The characteristics of the hot deformation of Zr-2.5Nb (wt-%) in the temperature range 650-950 degrees C and in the strain rate range 0.001-100 s(-1) have been studied using hot compression testing. Two different preform microstructures: equiaxed (alpha + beta) and beta transformed have been investigated. For this study, the approach of processing maps has been adopted and their interpretation carried out using the dynamic materials model. The efficiency of power dissipation given by [2m/(m + 1)], where m is the strain rate sensitivity, is plotted as a function of temperature and strain rate to obtain a processing map. A domain of dynamic recrystallisation has been identified in the maps of equiaxed (alpha + beta) and beta transformed preforms. In the case of equiaxed (alpha + beta), the stress-strain curves are steady state and the dynamic recrystallisation domain in the map occurs with a peak efficiency of 45% at 850 degrees C and 0.001 s(-1). On the other hand the beta transformed preform exhibits stress-strain curves with continuous flow softening. The corresponding processing map shows a domain of dynamic recrystallisation occurring by the shearing of alpha platelets followed by globularisation with a peak efficiency of 54% at 750 degrees C and 0.001 s(-1). The characteristics of dynamic recrystallisation are analysed on the basis of a simple model which considers the rates of nucleation and growth of recrystallised gains. Calculations show that these two rates are nearly equal and that the nucleation of dynamic recrystallisation is essentially controlled by mechanical recovery involving the cross-slip of screw dislocations. Analysis of flow instabilities using a continuum criterion revealed that Zi-2.5Nb exhibits flow localisation at temperatures lower than 700 degrees C and strain rates higher than 1 s(-1).

Characterization of hot deformation behaviour of Zr---2.5Nb---0.5Cu using processing maps

The characteristics of hot deformation of beta-quenched Zr-2.5Nb-0.5Cu in the temperature range 650-1050 degrees C and in the strain rate range 0.001-100 s(-1) have been studied using hot compression testing. For this study, the approach of processing maps has been adopted and their interpretation done using the Dynamic Materials Model. The efficiency of power dissipation given by [2m/(m + 1)], where m is strain rate sensitivity, is plotted as a function of temperature and strain rate to obtain a processing map. The processing map for Zr-2.5Nb-0.5Cu within (alpha + beta) phase field showed a domain of dynamic recrystallization, occurring by shearing of alpha-platelets followed by spheroidization, with a peak efficiency of 48% at 750 degrees C and 0.001 s(-1). The stress-strain curves in this domain had features of continuous flow softening and all these are similar to that in Zr-2.5Nb alloy. In the beta-phase field, a second domain with a peak efficiency of 47% occurred at 1050 degrees C and 0.001 s(-1) and this domain is correlated with the superplasticity of beta-phase. The beta-deformation characteristics of this alloy are similar to that observed in pure beta-zirconium with large grain size. Analysis of flow instabilities using a continuum criterion revealed that the Zr-2.5Nb-0.5Cu exhibits flow localization at temperatures higher than 800 degrees C and strain rates higher than about 30 s(-1) and that the addition of copper to Zr-2.5Nb reduces its susceptibility to flow instability, particularly in the (alpha + beta) phase field.

Plane wave analysis of conical and exponential pipes with incompressible mean flow

The general equation for one-dimensional wave propagation at low flow Mach numbers (M less-than-or-equals, slant0·2) is derived and is solved analytically for conical and exponential shapes. The transfer matrices are derived and shown to be self-consistent. Comparison is also made with the relevant data available in the literature. The transmission loss behaviour of conical and exponential pipes, and mufflers involving these shapes, are studied. Analytical expressions of the same are given for the case of a stationary medium. The mufflers involving conical and exponential pipes are shown to be inferior to simple expansion chambers (of similar dimensions) at higher frequencies from the point of view of noise abatement, as was observed earlier experimentally.

Processing map for hot working of powder

The constitutive flow behavior of a metal matrix composite (MMC) with 2124 aluminum containing 20 vol pct silicon carbide particulates under hot-working conditions in the temperature range of 300 °C to 550 °C and strain-rate range of 0.001 to 1 s-1 has been studied using hot compression testing. Processing maps depicting the variation of the efficiency of power dissipation given by [2m/(m + 1)] (wherem is the strain-rate sensitivity of flow stress) with temperature and strain rate have been established for the MMC as well as for the matrix material. The maps have been interpreted on the basis of the Dynamic Materials Model (DMM). [3] The MMC exhibited a domain of superplasticity in the temperature range of 450 °C to 550 °C and at strain rates less than 0.1 s-1. At 500 °C and 1 s-1 strain rate, the MMC undergoes dynamic recrystallization (DRX), resulting in a reconstitution of microstructure. In comparison with the map for the matrix material, the DRX domain occurred at a strain rate higher by three orders of magnitude. At temperatures lower than 400 °C, the MMC exhibited dynamic recovery, while at 550 °C and 1 s-1, cracking occurred at the prior particle boundaries (representing surfaces of the initial powder particles). The optimum temperature and strain-rate combination for billet conditioning of the MMC is 500 °C and 1 s-1, while secondary metalworking may be done in the super- plasticity domain. The MMC undergoes microstructural instability at temperatures lower than 400 °C and strain rates higher than 0.1 s-1.

Optimization of cold and warm workability in 304 stainless steel using instability maps

The deformation characteristics of stainless steel type AISI 3O4 under compression in the temperature range 20 degrees C to 600 degrees C and strain-rate range 0.001 to 100 s(-1) have been studied with a view to characterizing the flow instabilities occurring in the microstructure. At strain rates less than 5 s(-1), 304 stainless steel exhibits flow localization, whereas dynamic strain aging occurs at intermediate temperatures and below 0.5 s(-1). At room temperatures and strain rates less than 10 s(-1), martensite formation is observed. To avoid the preceding microstructural instabilities, cold and warm working should be carried out at strain rates greater than 5 s(-1). The continuum criterion, developed on the basis of the principles of maximum rate of entropy production and separability of the dissipation function, predicts accurately all the preceding instability features.

Sputtered thin-film strain gauges for differential pressure measurement

A differential pressure transducer with sputtered gold films as strain gauges has been designed and fabricated. The construction details of the sensing element assembly are given. The details of the strain gauge film configuration employed and the thin-film deposition process are also presented. Information on the output characteristics of the differential pressure transducer such as effect of pressure cycles on output, thermal stability, bidirectional calibration results obtained and individual gauge stability is reported.

Effect of Strain Rate on Ductile-to-Brittle Transition Temperature of a Free-Standing Pt-Aluminide Bond Coat

The ductile-to-brittle transition temperature (DBTT) of a free-standing Pt-aluminide (PtAl) bondcoat was determined using the microtensile testing method and the effect of strain rate variation, in the range 10(-5) to 10(-1) s(-1), on the DBTT studied. The DBTT increased appreciably with the increase in strain rate. The activation energy determined for brittle-to-ductile transition, suggested that such transition is most likely associated with vacancy diffusion. Climb of aOE (c) 100 > dislocations observed in analysis of dislocation structure using a transmission electron microscope (TEM) supported the preceding mechanism.