Suggestion of a new dimensionless number for dynamic plastic response of beams and plates

A dimensionless number, termed response number in the present paper, is suggested for the dynamic plastic response of beams and plates made of rigid-perfectly plastic materials subjected to dynamic loading. It is obtained at dimensional reduction of the basic governing equations of beams and plates. The number is defined as the product of the Johnson's damage number and the square of the half of the slenderness ratio for a beam; the product of the damage number and the square of the half of the aspect ratio for a plate or membrane loaded dynamically. Response number can also be considered as the ratio of the inertia force at the impulsive loading to the plastic limit load of the structure. Three aspects are reflected in this dimensionless number: the inertia of the applied dynamic loading, the resistance ability of the material to the deformation caused by the loading and the geometrical influence of the structure on the dynamic response. For an impulsively loaded beam or plate, the final dimensionless deflection is solely dependent upon the response number. When the secondary effects of finite deflections, strain-rate sensitivity or transverse shear are taken into account, the response number is as useful as in the case of simple bending theory. Finally, the number is not only suitable to idealized dynamic loads but also applicable to dynamic loads of general shape.

Torsional impact of transversely isotropic solid with functionally graded shear moduli and a penny-shaped crack

The torsional impact response of a penny-shaped crack in an unbounded transversely isotropic solid is considered. The shear moduli are assumed to be functionally graded such that the mathematics is tractable. Laplace transform and Hankel transform are used to reduce the problem to solving a Fredholm integral equation. The crack tip stress fields are obtained. Investigated are the influence of material nonhomogeneity and orthotropy on the dynamic stress intensity factor. The peak value of the dynamic stress intensity factor can be suppressed by increasing the shear moduli's gradient and/or increasing the shear modulus in a direction perpendicular to the crack surface.

The Influence of Strain Gradient on the shear Band in a Saturated Soil

The dynamic localization of saturated soil is investigated by considering the influence of higher strain gradient. It is shown that the strain gradient has a significant influence on the evolution of shear band in saturated soil and that the width of shear band is proportional to the square root of the strain gradient softening coefficient. The numerical simulation is processed to investigate the influences of shear strain gradient and other factors on the evolution of shear band.

Dynamic recrystallization induced by plastic deformation at high strain rate in a Monel alloy

An investigation has been made into the plastic deformation behavior of a Monel alloy deformed at high strain rate of 10(5) s(-1) by split Hopkinson bar. The results reveal that there are some equiaxed grains with an average size of 150 nm in diameter in the center of the shear bands, suggesting that this microstructure characteristics be developed by dynamic recrystallization, arising from the deformation and the rapid temperature rise in the band. Analysis shows that the plastic strain rate and the mobile dislocation density play a key role in the new crystallized grain formation and growth. Based on grain boundary energy change and diffusion mechanism, the grain growth kinetics is developed for plastic deformation at a high strain rate.

Dynamic Fracture Instability Of Tough Bulk Metallic Glass

We report the observations of a clear fractographic evolution from vein pattern, dimple structure, and then to periodic corrugation structure, followed by microbranching pattern, along the crack propagation direction in the dynamic fracture of a tough Zr41.2Ti13.8Cu12.5Ni10Be22.5 (Vit.1) bulk metallic glass (BMGs) under high-velocity plate impact. A model based on fracture surface energy dissipation and void growth is proposed to characterize this fracture pattern transition. We find that once the dynamic crack propagation velocity reaches a critical fraction of Rayleigh wave speed, the crack instability occurs; hence, crack microbranching goes ahead. Furthermore, the correlation between the critical velocity of amorphous materials and their intrinsic strength such as Young's modulus is uncovered. The results may shed new insight into dynamic fracture instability for BMGs. (C) 2008 American Institute of Physics.

Two-Dimensional Kinetics Of Beta(2)-Integrin And Icam-1 Bindings Between Neutrophils And Melanoma Cells In A Shear Flow

Cell adhesion, mediated by specific receptor-ligand interactions, plays an important role in biological processes such as tumor metastasis and inflammatory cascade. For example, interactions between beta(2)-integrin ( lymphocyte function-associated antigen-1 and/or Mac-1) on polymorphonuclear neutrophils (PMNs) and ICAM-1 on melanoma cells initiate the bindings of melanoma cells to PMNs within the tumor microenvironment in blood flow, which in turn activate PMN-melanoma cell aggregation in a near-wall region of the vascular endothelium, therefore enhancing subsequent extravasation of melanoma cells in the microcirculations. Kinetics of integrin-ligand bindings in a shear flow is the determinant of such a process, which has not been well understood. In the present study, interactions of PMNs with WM9 melanoma cells were investigated to quantify the kinetics of beta(2)-integrin and ICAM-1 bindings using a cone-plate viscometer that generates a linear shear flow combined with a two-color flow cytometry technique. Aggregation fractions exhibited a transition phase where it first increased before 60 s and then decreased with shear durations. Melanoma-PMN aggregation was also found to be inversely correlated with the shear rate. A previously developed probabilistic model was modified to predict the time dependence of aggregation fractions at different shear rates and medium viscosities. Kinetic parameters of beta(2)-integrin and ICAM-1 bindings were obtained by individual or global fittings, which were comparable to respectively published values. These findings provide new quantitative understanding of the biophysical basis of leukocyte-tumor cell interactions mediated by specific receptor-ligand interactions under shear flow conditions.

Dynamic mode I perturbation solution for a moving crack unsteadily

Rice et al. (Jounal of Mechanics and Physics of Solids 42, 813-843) analyze the propagation of a planar crack with a nominally straight front in a model elastic solid with a single displacement component. Using the form of Willis er al. (Journal of the Mechanics and Physics of Solids 43, 319-341), of dynamic mode I weight functions for a moving crack, we address that problem solved by Rice ei al. in the 3D context of elastodynamic theory. Oscillatory crack tip motion results from constructive-destructive interference of stress intensity waves. Those waves, including system of the dilatational, shear and Rayleigh waves, interact on each other and with moving edge of crack, can lead to continuing fluctuations of the crack front and propagation velocity. (C) 1997 Elsevier Science Ltd.

Formation of adiabatic shear band in metal matrix composites

A modified single-pulse loading split Hopkinson torsion bar (SSHTB) is introduced to investigate adiabatic shear banding behavior in SiCp particle reinforced 2024 Al composites in this work. The experimental results showed that formation of adiabatic shear band in the composite with smaller particles is more readily observed than that in the composite with larger particles. To characterize this size-dependent deformation localization behavior of particle reinforced metal matrix composites (MMCp), a strain gradient dependent shear instability analysis was performed. The result demonstrated that high strain gradient provides a deriving force for the formation of adiabatic shear banding in MMCp. (C) 2004 Elsevier Ltd. All rights reserved.

Adiabatic shear localization: occurrence, theories, and applications

Prevalence Of Shear Banding In Compression Of Zr41Ti14Cu12.5Ni10Be22.5 Pillars As Small As 150 Nm In Diameter

Recently, the size dependence of mechanical behaviors, particularly the yield strength and plastic deformation mode, of bulk metallic glasses (BMG) has created a great deal of interest. Contradicting conclusions have been drawn by different research groups, based on various experiments on different BMG systems. Based on in situ compression transmission electron microscopy (TEM) experiments on Zr41Ti14Cu12.5Ni10Be22.5 (Vit 1) nanopillars, this paper provides strong evidence that shear banding still prevails at specimen length scales as small as 150 nm in diameter. This is supported by in situ and ex situ images of shear bands, and by the carefully recorded displacement bursts under load control its well as load drops under displacement control. Finite element modeling of the stress state within the pillar shows that the unavoidable geometry constraints accompanying such experiments impart a strong effect on the experimental results, including non-uniform stress distributions and high level hydrostatic pressures. The seemingly improved compressive ductility is believed to be due to such geometry constraints. Observations underscore the notion that the mechanical behavior of metallic glasses, including strength and plastic deformation mode, is size independent at least in Vit 1. (C) 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Dynamic behaviors of mode III interfacial crack under a constant loading rate

In an earlier study on intersonic crack propagation, Gao et al. (J. Mech. Phys. Solids 49: 2113-2132, 2001) described molecular dynamics simulations and continuum analysis of the dynamic behaviors of a mode II dominated crack moving along a weak plane under a constant loading rate. The crack was observed to initiate its motion at a critical time after the onset of loading, at which it is rapidly accelerated to the Rayleigh wave speed and propagates at this speed for a finite time interval until an intersonic daughter crack is nucleated at a peak stress at a finite distance ahead of the original crack tip. The present article aims to analyze this behavior for a mode III crack moving along a bi-material interface subject to a constant loading rate. We begin with a crack in an initially stress-free bi-material subject to a steadily increasing stress. The crack initiates its motion at a critical time governed by the Griffith criterion. After crack initiation, two scenarios of crack propagation are investigated: the first one is that the crack moves at a constant subsonic velocity; the second one is that the crack moves at the lower shear wave speed of the two materials. In the first scenario, the shear stress ahead of the crack tip is singular with exponent -1/2, as expected; in the second scenario, the stress singularity vanishes but a peak stress is found to emerge at a distance ahead of the moving crack tip. In the latter case, a daughter crack supersonic with respect to the softer medium can be expected to emerge ahead of the initial crack once the peak stress reaches the cohesive strength of the interface.

Strain rate-dependent shear band behavior in bulk metallic glasses

In this article, we review our recent advances in understanding the deformation behavior of a typical tough Zr41.2Ti13.8Cu12.5Ni10Be22.5 (Vit 1) bulk metallic glass (BMG), as a model material, under various loading modes and strain rates, focusing particularly on the rate-dependence and formation mechanism of shear-banding. Dynamic and quasi-static mechanical experiments, including plate shear, shear punch and spherical indentation, and continuum as well as atomistic modeling on shear-banding are discussed. The results demonstrate that higher strain rate slows down the annihilation process of free volume, but promotes the free-volume coalescence, which is responsible for the rate-dependent shear banding. The physical origin of shear bands, that is the free volume softening underpinned by irreversible rearrangements of atoms, is unveiled. Finally, some concluding remarks are given.

Fracture behavior of a Zr-metallic glass under dynamic compression

Dynamic planar compressive experiments on a typical tough Zr-BMG (Bulk Metallic Glass) were carried out under impact velocity of 500-600 m/sec and strain rate of 10(6)/s. The fracture surface of samples exhibits different fracture patterns at different parts of the sample. At a corner close to the front loading boundary, fracture patterns from the free edge toward the centre changed from equiaxial veins in microscale to periodic corrugations in nanoscale; in the middle of the sample, the fracture surface contains glazed zones laid out orderly along the same boundary. FEM simulation was performed to investigate the stress distributions in the impacted sample under a short duration impact loading. It has revealed that the fracture patterns changing from the free edge toward the centre were resulted from the fracture modes' changing from the tensile dominant fracture to the shear dominant fracture. Whereas at the middle part of the sample, fracture initiated from several parallel shear bands propagating close to the same boundary is due to a large strain or much higher shear stress in this area.

Multi-mode Vortex-induced Vibration of Slender Cable Experiencing Shear Flow

The dynamic characteristics of slender cable often present serried modes with low frequencies due to large structure flexibility resulted from high aspect ratio (ratio of length to diameter of cable), while the flow velocity distributes non-uniformly along the cable span actually in practical engineering. Therefore, the prediction of the vertex-induce vibration of slender cable suffered from multi-mode and high-mode motions becomes a challenging problem. In this paper a prediction approach based on modal energy is developed to deal with multi-mode lock-in. Then it is applied to the modified wake-oscillator model to predict the VIV displacement and stress responses of cable in non-uniform flow field. At last, illustrative examples are given of which the VIV response of flexible cable in nonlinear shear flow field is analyzed. The effects of flow velocity on VIV are explored. Our results show that both displacement and stress responses become larger as the flow velocity increasing; especially higher stress response companied with higher frequency vibration should be paid enough attention in practical design of SFT because of its remarkable influence on structure fatigue life.

Polymer concentration, shear and stretch field effects on the surface morphology evolution during the spin-coating

Polymer concentration and shear and stretch field effects on the surface morphology evolution of three different kinds of polymers (polystyrene (PS), polybutadiene (PB) and polystyrene-b-polybutadiene-b-polystyrene (SBS)) during the spin-coating were investigated by means of atomic force microscopy (AFM). For PS and SBS, continuous film, net-like structure and particle structure were observed at different concentrations. For PB, net-like structures were not observed and continuous films and radial array of droplets emerged. Moreover, we compared surface morphology transitions on different substrate locations from the center to the edge. For PS, net-like structure, broken net-like structure and irregular array of particles were observed. For SBS, net-like structure, periodically orientated string-like structure and broken-line structure appeared. But for PB, flower-like holes in the continuous film, distorted stream-like structure and irregular distributions of droplets emerged. These different transitions of surface morphologies were discussed in terms of individual material property.