Effects of temper level on the dependence of fatigue crack growth threshold and crack closure on the prior austenitic grain size

An attempt has been made to systematically investigate the effects of microstructural parameters, such as the prior austenite grain size (PAGS), in influencing the resistance to fatigue crack growth (FCG) in the near-threshold region under three different temper levels in a quenched and tempered high-strength steel. By austenitizing at various temperatures, the PAGS was varied from about 0.7 to 96 μm. The microstructures with these grain sizes were tempered at 200 °C, 400 °C, and 530 °C and tested for fatigue thresholds and crack closure. It has been found that, in general, three different trends in the dependence of both the total threshold stress intensity range, ΔK th , and the intrinsic threshold stress intensity range, ΔK eff, th , on the PAGS are observable. By considering in detail the factors such as cyclic stress-strain behavior, environmental effects on FCG, and embrittlement during tempering, the present observations could be rationalized. The strong dependence of ΔK th and ΔK eff, th on PAGS in microstructures tempered at 530 °C has been primarily attributed to cyclic softening and thereby the strong interaction of the crack tip deformation field with the grain boundary. On the other hand, a less strong dependence of ΔK th and ΔK eff, th on PAGS is suggested to be caused by the cyclic hardening behavior of lightly tempered microstructures occurring in 200 °C temper. In both microstructures, crack closure influenced near-threshold FCG (NTFCG) to a significant extent, and its magnitude was large at large grain sizes. Microstructures tempered at the intermediate temperatures failed to show a systematic variation of ΔKth and ΔKeff, th with PAGS. The mechanisms of intergranular fracture vary between grain sizes in this temper. A transition from “microstructure-sensitive” to “microstructure-insensitive” crack growth has been found to occur when the zone of cyclic deformation at the crack tip becomes more or less equal to PAGS. Detailed observations on fracture morphology and crack paths corroborate the grain size effects on fatigue thresholds and crack closure.

Nonlinear effects on rotating disk flow in a cylindrical casing

The flow due to a finite disk rotating in an incompressible viscous fluid has been studied. A modified Newton-gradient finite difference scheme is used to obtain the solution of full Navier-Stokes equations numerically for different disk and cylinder sizes for a wide range of Reynolds numbers. The introduction of the aspect ratio and the disk-shroud gap, significantly alters the flow characteristics in the region under consideration, The frictional torque calculated from the flow data reveals that the contribution due to nonlinear terms is not negligible even at a low Reynolds number. For large Reynolds numbers, the flow structure reveals a strong boundary layer character.

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.

Asymptotic and finite element analyses of mode III dynamic crack growth at a ductile-brittle interface

In this work, dynamic crack growth along a ductile-brittle interface under anti-plane strain conditions is studied. The ductile solid is taken to obey the J(2) flow theory of plasticity with linear isotropic strain hardening, while the substrate is assumed to exhibit linear elastic behavior. Firstly, the asymptotic near-tip stress and velocity fields are derived. These fields are assumed to be variable-separable with a power singularity in the radial coordinate centered at the crack tip. The effects of crack speed, strain hardening of the ductile phase and mismatch in elastic moduli of the two phases on the singularity exponent and the angular functions are studied. Secondly, full-field finite element analyses of the problem under small-scale yielding conditions are performed. The validity of the asymptotic fields and their range of dominance are determined by comparing them with the results of the full-field finite element analyses. Finally, theoretical predictions are made of the variations of the dynamic fracture toughness with crack velocity. The influence of the bi-material parameters on the above variation is investigated.

Code design casing deterministic annealing

We address the problem of designing codes for specific applications using deterministic annealing. Designing a block code over any finite dimensional space may be thought of as forming the corresponding number of clusters over the particular dimensional space. We have shown that the total distortion incurred in encoding a training set is related to the probability of correct reception over a symmetric channel. While conventional deterministic annealing make use of the Euclidean squared error distance measure, we have developed an algorithm that can be used for clustering with Hamming distance as the distance measure, which is required in the error correcting, scenario.

Mixed convection heat transfer from the bottom tip of a cylinder spinning about a vertical axis in a saturated porous medium

The present work is a numerical study of heat transfer characteristics from the bottom tip of a cylinder spinning about a vertical axis in an infinitely saturated porous medium. The problem is axisymmetric. The non-dimensionalized governing equations are solved using the SIMPLER algorithm on a staggered grid. The influence of rotational Reynolds numbers and Darcy numbers on the heat transfer for a Grashof number of 104 and Prandtl number of 7.0 is studied. It is found that for very high Darcy numbers, over a wide range of rotational Reynolds numbers, the heat transfer takes place mainly due to conduction. The convective heat transfer takes place for lower Darcy numbers and for higher rotational Reynolds numbers. Moreover, there is a rapid increase in the overall Nusselt number below a certain Darcy number with increase in the rotational Reynolds numbers. The effect of the Darcy number and the rotational Reynolds number on the heat transfer and fluid flow in the porous medium is depicted in the form of streamline and isotherm plots. The variation of the overall Nusselt number with respect to the Darcy number for various rotational Reynolds numbers is plotted. The variation of the local Nusselt number with respect to the radial coordinate at the heated tip of the vertical cylinder is plotted for various Darcy and rotational Reynolds numbers.

Plantlet production from shoot tip cultures of red sandalwood ( Pterocarpus santalinus L.)

Red sandalwood (Pterocarpus santalinus L.), belonging to the family Fabaceae, is one of the most valuable trees, and has limited distribution in India. In view of its high price, restricted distribution and usefulness as a timber tree, there is urgent need to obtain improved lines, in both quality and quantity. We have established a method for production of complete plantlets by tissue culture. We report here the successful development of red sandalwood plantlets by induction of multiple shoots from shoot tips, and successful transfer of micropropagated plants to soil.

Performance of a mixed flow pump with varying tip clearance .2.

Measurements in a mixed flow pump of non-dimensional specific speed k = 1.89[N-S = 100 r/min (metric)] are analysed to give loss distribution and local hydraulic efficiencies at different flowrates and values of tip clearance. Fairly close agreement is obtained between the relative flow angles leaving the blading as predicted by simple deviation and slip models and derived from the measurements. The head developed is broken up into two parts: that contributed by Coriolis action and that associated with blade circulation. It is suggested that lift coefficients based on blade circulation are of limited value in selecting blade profiles. The variation of pump efficiency with tip clearance is greater than that reported for centrifugal pumps.

Flow induced by an asymmetrically placed disk rotating coaxially inside a cylindrical casing

In this paper, the flow due to a rotating disk non-symmetrically placed with respect to the height of the enclosing stationary cylinder is analyzed numerically. The full Navier-Stokes equations expressed in terms of stream function and vorticity are solved by successive over-relaxation for different disk radii, its distance from the bottom casing and rotational Reynolds numbers. It is observed that the flow pattern is strongly influenced by the size and the position of the disk. When the disk is very close to the top casing and small in radius, there are two regions of different scales and the vortices in the region of small scale are trapped between the disk and the top casing. Further, the variation of the moment coefficient is determined for different positions and sizes of the rotating disk. The calculations shows that the frictional torque increases rapidly, when the disk approaches the top casing. This finding is of importance for the design of vertical rotating disk reactors applied in chemical vapor deposition.

Degradation and Failure of Field Emitting Carbon Nanotube Arrays

It has been observed experimentally that the collective field emission from an array of Carbon Nanotubes (CNTs) exhibits fluctuation and degradation, and produces thermal spikes, resulting in electro-mechanical fatigue and failure of CNTs. Based on a new coupled multiphysics model incorporating the electron-phonon transport and thermo-electrically activated breakdown, a novel method for estimating accurately the lifetime of CNT arrays has been developed in this paper. The main results are discussed for CNT arrays during the field emission process. It is shown that the time-to-failure of CNT arrays increases with the decrease in the angle of tip orientation. This observation has important ramifications for such areas as biomedical X-ray devices using patterned films of CNTs.

A differential geometric method for kinematic analysis of two- and three-degree-of-freedom rigid body motions

In this paper, we present a novel differential geometric characterization of two- and three-degree-of-freedom rigid body kinematics, using a metric defined on dual vectors. The instantaneous angular and linear velocities of a rigid body are expressed as a dual velocity vector, and dual inner product is defined on this dual vector, resulting in a positive semi-definite and symmetric dual matrix. We show that the maximum and minimum magnitude of the dual velocity vector, for a unit speed motion, can be obtained as eigenvalues of this dual matrix. Furthermore, we show that the tip of the dual velocity vector lies on a dual ellipse for a two-degree-of-freedom motion and on a dual ellipsoid for a three-degree-of-freedom motion. In this manner, the velocity distribution of a rigid body can be studied algebraically in terms of the eigenvalues of a dual matrix or geometrically with the dual ellipse and ellipsoid. The second-order properties of the two- and three-degree-of-freedom motions of a rigid body are also obtained from the derivatives of the elements of the dual matrix. This results in a definition of the geodesic motion of a rigid body. The theoretical results are illustrated with the help of a spatial 2R and a parallel three-degree-of-freedom manipulator.

Effect of lattice orientation on crack tip constraint in ductile single crystals

In this work, the effect of lattice orientation on the fields prevailing near a notch tip is investigated pertaining to various constraint levels in FCC single crystals. A modified boundary layer formulation is employed and numerical solutions under mode I, plane strain conditions are generated by assuming an elastic-perfectly plastic FCC single crystal. The analysis is carried out corresponding to different lattice orientations with respect to the notch line. It is found that the near-tip deformation field, especially the development of kink or slip shear bands is sensitive to the constraint level. The stress distribution and the size and shape of the plastic zone near the notch tip are also strongly influenced by the level of T-stress. The present results clearly establish that ductile single crystal fracture geometries would progressively lose crack tip constraint as the T-stress becomes more negative irrespective of lattice orientation. Also, the near-tip field for a range of constraint levels can be characterized by two-parameters such as K-T or J-Q as in isotropic plastic solids.

Fracture and R-curves in high volume fraction Al2O3/Al composites

Fracture toughness and fracture mechanisms in Al2O3/Al composites are described. The unique flexibility offered by pressureless infiltration of molten Al alloys into porous alumina preforms was utilized to investigate the effect of microstructural scale and matrix properties on the fracture toughness and the shape of the crack resistance curves (R-curves). The results indicate that the observed increment in toughness is due to crack bridging by intact matrix ligaments behind the crack tip. The deformation behavior of the matrix, which is shown to be dependent on the microstructural constraints, is the key parameter that influences both the steady-state toughness and the shape of the R-curves. Previously proposed models based on crack bridging by intact ductile particles in a ceramic matrix have been modified by the inclusion of an experimentally determined plastic constraint factor (P) that determines the deformation of the ductile phase and are shown to be adequate in predicting the toughness increment in the composites. Micromechanical models to predict the crack tip profile and the bridge lengths (L) correlate well with the observed behavior and indicate that the composites can be classified as (i) short-range toughened and (ii) long-range toughened on the basis of their microstructural characteristics.