Numerical simulations of void growth near a notch tip in ductile single crystals

The objective of this work is to study the growth of a cylindrical void ahead of a notch tip in ductile FCC single crystals under mode I, plane strain, small scale yielding (SSY) conditions. To this end, finite element simulations are performed within crystal plasticity framework neglecting elastic anisotropy. Attention is focussed on the effects of crystal hardening, ratio of void diameter to spacing from the notch and crystal orientation on plastic flow localization in the ligament connecting the notch and the void as well as their growth. The results show strong interaction between shear bands emanating from the notch and angular sectors of single slip forming around the void leading to intense plastic strain development in the ligament. Further, the ductile fracture processes are retarded by increase in hardening of the single crystal and decrease in ratio of void diameter to spacing from the notch. Also, a strong influence of crystal orientation on near-tip void growth and plastic slip band development is observed. Finally, the synergistic, cooperative growth of multiple voids ahead of the notch tip is examined.

Determination of mode 1 notch stress intensity factor by the photoelastic technique

The structural integrity of any member subjected to a load gets impaired due to the presence of cracks or crack-like defects. The notch severity is one of the several parameters that promotes the brittle fracture. The most severe one is an ideal crack with infinitesimal width and infinitesimal or zero root radius. Though analytical investigations can handle an ideal crack, experimental work, either to validate the analytical conclusions or to impose the bounds, needs to be carried out on models or specimens containing the cracks which are far from the ideal ones. Thus instead of an ideal crack with infinitesimal width the actual model will have a slot or a slit of finite width and instead of a crack ending in zero root radius, the model contains a slot having a finite root radius. Another factor of great significance at the root is the notch angle along which the transition from the slot to the root takes place. This paper is concerned with the photoelastic determination of the notch stress intensity factor in the case of a “crack” subjected to Mode 1 deformation.

Modified Proportional V-Notch Weirs

Seven different shaped modified proportional V-notches were designed and pertinent data for their use are given in tables 1 - 4. It is shown that the indication accuracies of these weirs are more than that of the conventional V-notch. For five of the designed weirs the indication accuracies are more than that of the conventional rectangular weir at lower heads of flow. All these proportional weirs, except the parabolic based weir, have added advantages over the V-notch in regard to fixing and finding the crest level. Experiments with five weirs (four symmetrical and one unsymmetrical) having rectangular bases and one (symmetrical) with a parabolic base show very good agreement with the theory and give consistent values for the coefficient of discharge, Cd, varying between 0.588 and 0.605, within the ranges of the experiments.

Cooperation of Notch and Ras/MAPK signaling pathways in human breast carcinogenesis

Background: Recent studies have implicated aberrant Notch signaling in breast cancers. Yet, relatively little is known about the pattern of expression of various components of the Notch pathway, or its mechanism of action. To better understand the role of the Notch pathway in breast cancer, we have undertaken a detailed expression analysis of various Notch receptors, their ligands, and downstream targets at different stages of breast cancer progression. Results: We report here that there is a general increase in the expression levels of Notch 1, 2, 4, Jagged1, Jagged2, and Delta-like 4 proteins in breast cancers, with simultaneous upregulation of multiple Notch receptors and ligands in a given cancer tissue. While Notch3 and Delta-like1 were undetectable in normal tissues, moderate to high expression was detected in several cancers. We detected the presence of active, cleaved Notch1, along with downstream targets of the Notch pathway, Hes1/Hes5, in similar to 75% of breast cancers, clearly indicating that in a large proportion of breast cancers Notch signaling is aberrantly activated. Furthermore, we detected cleaved Notch1 and Hes1/5 in early precursors of breast cancers - hyperplasia and ductal carcinoma in situ suggesting that aberrant Notch activation may be an early event in breast cancer progression. Mechanistically, while constitutively active Notch1 alone failed to transform immortalized breast cells, it synergized with the Ras/MAPK pathway to mediate transformation. This cooperation is reflected in vivo, as a subset of cleaved Notch positive tumors additionally expressed phopsho-Erk1/2 in the nuclei. Such cases exhibited high node positivity, suggesting that Notch-Ras cooperation may lead to poor prognosis. Conclusions: High level expression of Notch receptors and ligands, and its increased activation in several breast cancers and early precursors, places Notch signaling as a key player in breast cancer pathogenesis. Its cooperation with the Ras/MAPK pathway in transformation offers combined inhibition of the two pathways as a new modality for breast cancer treatment.

Inverted V-Notch: Practical Proportional Weir

This paper presents a practical linear proportional weir of simple geometric shape in the form of an inverted V-notch or inward trapezium. The flow through this weir, of half-width w and altitude d, for depths above 0.22d is proportional to the depth of flow measured above a reference plane situated at 0.08d for all heads in the range 0.22d<=h<=0.94d, with a maximum percentage deviation of ±1.5 from the theoretical discharge. The linear relationship between head and discharge is based on numerical optimization procedures. Nearly 75% of the depth of inverted V-notch can be used effectively as the measuring range. Experiments with four weirs, with different vertex angles, show excellent agreement with the theory by giving an average coefficient of discharge for each weir varying from 0.61–0.62.

Improved Inverted V-Notch or Chimney Weir

This paper is devoted to the improvement of the measuring range of inverted V-notch (IVN) weir, a practical linear sharp-crested weir, designed earlier by the writers. The range of linearity of IVN can be considerably enhanced (by more than 200%) by the addition of a retangular weir of width 0.265W (W = half crest width) at a depth of 0.735d (d = altitude of IVN), above the crest of the weir, which is equivalent to providing at this depth two vertical straight lines to the IVN, resulting in a chimney-shaped profile; hence, the modified weir is named chimney weir. The design parameters of the weir, that is, the linearity range, base flow depth, and datum constant, which fixes the reference plane of the weir, are estimated by solving the nonlinear programming problem using a numerical optimization procedure. For flows through this weir above a depth of 0.22d, the discharges are proportional to the depth of flow measured above a reference plane situated at 0.08d above the weir crest for all heads in the range 0.22d <= h <= 2.43d, within a maximum percentage deviation of ±1.5 from the theoretical discharge. A significant result of the analysis is that the same linear head-discharge relationship governing the flow through the IVN is also valid for the extended chimney weir. Experiments with three different chimney weirs show excellent agreement with the theory by giving a constant average coefficient of discharge for each weir.

The phenomenon of notch in an NEMP simulator and its reduction

The effect of variation in the switching instant of the output switch of the pulser circuit used in energizing an NEMP simulator on the voltage fed to the simulator and hence the electric field within the working volume of the simulator has been studied. Depending upon the instant at which the output switch closes, the amplitude and the wave shape of the voltage that is fed to the illuminator varies. This wave shape of the output voltage from the pulser circuit determines the shape and characteristics of the electric field within the working volume of the simulator. To study the effect of variation in the switching instant on the vertical electric field within the working volume, the vertical electric field has been computed in time and frequency domains. For certain switching instants, the electric field shows a sharp reduction in its amplitude after the peak which is called the notch. The presence of notch results in the test object not getting illuminated with all the frequencies of interest. The notch has been successfully reduced by suitably modifying the pulser circuit.

Ductile fracture by multiple void growth and interaction ahead of a notch tip in polycrystalline plastic solids

The objectives of this paper are to study the effects of plastic anisotropy and evolution in crystallographic texture with deformation on the ductile fracture behaviour of polycrystalline solids. To this end, numerical simulations of multiple void growth and interaction ahead of a notch tip are performed under mode I, plane strain, small scale yielding conditions using two approaches. The first approach is based on the Hill yield theory, while the second employs crystal plasticity constitutive equations and a Taylor-type homogenization in order to represent the ductile polycrystalline solid. The initial textures pertaining to continuous cast Al-Mg AA5754 sheets in recrystallized and cold rolled conditions are considered. The former is nearly-isotropic, while the latter displays pronounced anisotropy. The results indicate distinct changes in texture in the ligaments bridging the voids ahead of the notch tip with increase in load level which gives rise to retardation in porosity evolution and increase in tearing resistance for both materials.

Interaction between a notch and cylindrical voids in aluminum single crystals: Experimental observations and numerical simulations

A combined 3D finite element simulation and experimental study of interaction between a notch and cylindrical voids ahead of it in single edge notch (tension) aluminum single crystal specimens is undertaken in this work. Two lattice orientations are considered in which the notch front is parallel to the crystallographic 10 (1) over bar] direction. The flat surface of the notch coincides with the (010) plane in one orientation and with the (1 (1) over bar1) plane in the other. Three equally spaced cylindrical voids are placed directly ahead of the notch tip. The predicted load-displacement curves, slip traces, lattice rotation and void growth from the finite element analysis are found to be in good agreement with the experimental observations for both the orientations. Finite element results show considerable through-thickness variation in both hydrostatic stress and equivalent plastic slip which, however, depends additionally on the lattice orientation. The through-thickness variation in the above quantities affects the void growth rate and causes it to differ from the center-plane to the free surface of the specimen. (c) 2012 Elsevier Ltd. All rights reserved.

Finite element simulations of notch tip fields in magnesium single crystals

Recent experiments using three point bend specimens of Mg single crystals have revealed that tensile twins of {10 (1) over bar2}-type form profusely near a notch tip and enhance the fracture toughness through large plastic dissipation. In this work, 3D finite element simulations of these experiments are carried out using a crystal plasticity framework which includes slip and twinning to gain insights on the mechanics of fracture. The predicted load-displacement curves, slip and tensile twinning activities from finite element analysis corroborate well with the experimental observations. The numerical results are used to explore the 3D nature of the crack tip stress, plastic slip and twin volume fraction distributions near the notch root. The occurrence of tensile twinning is rationalized from the variation of normal stress ahead of the notch tip. Further, deflection of the crack path at twin-twin intersections observed in the experiments is examined from an energy standpoint by modeling discrete twins close to the notch root.

Notch sensitivity in nanoscale metallic glass specimens: Insights from continuum simulations

Recent experiments have shown that nano-sized metallic glass (MG) specimens subjected to tensile loading exhibit increased ductility and work hardening. Failure occurs by necking as opposed to shear banding which is seen in bulk samples. Also, the necking is generally observed at shallow notches present on the specimen surface. In this work, continuum finite element analysis of tensile loading of nano-sized notched MG specimens is conducted using a thermodynamically consistent non-local plasticity model to clearly understand the deformation behavior from a mechanics perspective. It is found that plastic zone size in front of the notch attains a saturation level at the stage when a dominant shear band forms extending across the specimen. This size scales with an intrinsic material length associated with the interaction stress between flow defects. A transition in deformation behavior from quasi-brittle to ductile becomes possible when this critical plastic zone size is larger than the uncracked ligament length. These observations corroborate with atomistic simulations and experimental results. (C) 2015 Elsevier Ltd. All rights reserved.