Formation of shear bands in plane sheet

The formation of shear bands in plane sheet is studied, both analytically and experimentally, to enhance the fundamental understanding of this phenomenon and to develop a capability for predicting material failure. The evolution of voids is measured and its interaction with the process of shear banding is examined. The evolving dilatancy in plasticity is shown to have a vital role in analysing the shear-band type of bifurcation, and tremendously reduces the theoretical value of critical stresses. The analyses, referring to both localized and diffuse modes of bifurcation, fairly explain the corresponding observations obtained through testing a dual-phase steer sheet and provide a justification of the constitutive model used.

Unloading characteristics of anti-plane shear crack in softening materials

The local characteristics of the anti-plane shear stress and strain field are determined for a material where the stress increases linearly with strain up to a limit and then softens nonlinearly. Two unloading models are considered such that the unloading path always returns to the origin while the other assumes the unloading modulus to be that of the initial shear modulus. As the applied shear increases, an unloading zone is found to prevail between a zone in which the material softens and another zone in which the material is linear-elastic even though the crack does not propagate. The divisions of these zones are displayed graphically.

Numerical analyses for the material bifurcation in plane sheet under tension

The various patterns (shear banding, surface wrinkling and necking) of material bifurcation in plane sheet under tension are investigated in this paper by means of a numerical method. It is found that numerical analysis can provide better ground for searching for the lowest critical loads. The inhomogeneity caused by void damage and the nonuniformity in the stress distribution across sheet thickness are proved to have detrimental effects on the material bifurcation. Nevertheless, material stability can be promoted by any means of depressing void damage or alleviating stress, even locally across the thickness. Besides, the peculiar behaviour of material bifurcation under slight biaxiality state is demonstrated. Copyright (C) 1996 Elsevier Science Ltd

Electronic structure of diluted magnetic semiconductor superlattices: In-plane magnetic field effect

The electronic structure of diluted magnetic semiconductor (DMS) superlattices under an in-plane magnetic field is studied within the framework of the effective-mass theory; the strain effect is also included in the calculation. The numerical results show that an increase of the in-plane magnetic field renders the DMS superlattice from the direct band-gap system to the indirect band-gap system, and spatially separates the electron and the hole by changing the type-I band alignment to a type-II band alignment. The optical transition probability changes from type I to type II and back to type I like at large magnetic field. This phenomenon arises from the interplay among the superlattice potential profile, the external magnetic field, and the sp-d exchange interaction between the carriers and the magnetic ions. The shear strain induces a strong coupling of the light- and heavy-hole states and a transition of the hole ground states from "light"-hole to "heavy"-hole-like states.

Non-modal instabilities of two-dimensional disturbances in plane Couette flow of a power-law fluid

Instabilities of fluid flows have traditionally been investigated by normal mode analysis, i.e. by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In this paper we study the instabilities of two-dimensional Couette flow of a polymeric fluid in the framework of non-modal stability theory rather than normal mode analysis. A power-law model is used to describe the polymeric liquid. We focus on the response to external excitations and initial conditions by examining the pseudospectra structures and the transient energy growths. For both Newtonian and non-Newtonian flows, the results show that there can be a rather large transient growth even though the linear operator of Couette flow has no unstable eigenvalue. The effects of non-Newtonian viscosity on the transient behaviors are examined in this study. The results show that the "shear-thinning/shear-thickening" effect increases/decreases the amplitude of responses to external excitations and initial conditions. (C) 2010 Elsevier B.V. All rights reserved.

Deformation, Phase Transformation and Recrystallization in the Shear Bands Induced by High-Strain Rate Loading in Titanium and its Alloys

alpha-titanium and its alloys with a dual-phase structure (alpha+beta) were deformed dynamically under strain rate of about 10(4) s(-1). The formation and microstructural evolution of the localized shear bands were characterized by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The results reveal that both the strain and strain rate should be considered simultaneously as the mechanical conditions for shear band formation, and twinning is an important mode of deformation. Both experimental and calculation show that the materials within the bands underwent a superhigh strain rate (9 x 10(5) s(-1)) deformation, which is two magnitudes of that of average strain rate required for shear band formation; the dislocations in the bands can be constricted and developed into cell structures; the phase transformation from alpha to alpha(2) within the bands was observed, and the transformation products (alpha(2)) had a certain crystallographic orientation relationship with their parent; the equiaxed grains with an average size of 10 mu m in diameter observed within the bands are proposed to be the results of recrystallization.

Elasticity, stability, and ideal strength of beta-SiC in plane-wave-based ab initio calculations

On the basis of the pseudopotential plane-wave method and the local-density-functional theory, this paper studies energetics, stress-strain relation, stability, and ideal strength of beta-SiC under various loading modes, where uniform uniaxial extension and tension and biaxial proportional extension are considered along directions [001] and [111]. The lattice constant, elastic constants, and moduli of equilibrium state are calculated and the results agree well with the experimental data. As the four SI-C bonds along directions [111], [(1) over bar 11], [11(1) over bar] and [111] are not the same under the loading along [111], internal relaxation and the corresponding internal displacements must be considered. We find that, at the beginning of loading, the effect of internal displacement through the shuffle and glide plane diminishes the difference among the four Si-C bonds lengths, but will increase the difference at the subsequent loading, which will result in a crack nucleated on the {111} shuffle plane and a subsequently cleavage fracture. Thus the corresponding theoretical strength is 50.8 GPa, which agrees well with the recent experiment value, 53.4 GPa. However, with the loading along [001], internal relaxation is not important for tetragonal symmetry. Elastic constants during the uniaxial tension along [001] are calculated. Based on the stability analysis with stiffness coefficients, we find that the spinodal and Born instabilities are triggered almost at the same strain, which agrees with the previous molecular-dynamics simulation. During biaxial proportional extension, stress and strength vary proportionally with the biaxial loading ratio at the same longitudinal strain.

可压剪切层线性稳定性特征直接数值模拟=Direct Simulation of the Linear Instabilities in Compressible Shear Layers

基于伪随机数生成技术促生白噪声扰动,以高精度迎风/对称紧致混合差分算法求解二维/三维非定常可压Navier-Stokes方程,揭示了可压自由剪切层初始剪切过程中扰动的线性演化特征,以及该过程对扰动波数和方向的内在选择性.验证了所用算法的有效性,表明线性理论同数值模拟相结合是可压剪切层研究的合理途径之一.

Closed form solutions of T-stress in plane elasticity crack problems

The T-stress is considered as an important parameter in linear elastic fracture mechanics. In this paper, several closed form solutions of T-stress in plane elasticity crack problems in an infinite plate are investigated using the complex potential theory. In the line crack case, if the applied loading is the remote stress or the concentrated forces, the T-stress can be derived from the basic field. Here, the basic field is defined as the field caused by the applied loading in the infinite plate without the crack. For the circular are crack, the T-stress can be abstracted from a known solution. For the cusp crack problems, the T-stress can be separated from the obtained stress solution for which the conformal mapping technique is used.

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.

A modified split hopkinson torsional bar in studying shear localization

A modified split Hopkinson torsional bar (SHTB) is introduced to eliminate the effect of the loading reverberation of the standard SHTB on the study of evolution of shear localization. The effect, the cause and the method by which to eliminate loading wave reverberation are carefully analysed and discussed. By means of the modified apparatus, the post-mortem observation of tested specimens can provide data on actual evolution of micro-structure and micro-damage during shear localization. Some test results of shear banding conducted with this apparatus support the use of the modified design. Moreover, the modification makes possible the correlation of evolving micro-structures to the transient shear stress-strain recording.

On post-instability processes in adiabatic shear in hot rolled steel

EXPERIMENTS carried out using a split Hopkinson torsional bar have shown that only one shear band develops in specimens of hot rolled steel which break during testing. We observed, however, that in specimens which were not deformed to failure, several fine shear bands appeared. We believe that these formed during the loading cycle before the appearance of the final shear band and were not due to the effect of unloading. So we developed a numerical model to study the evolution of shear banding from several finite amplitude disturbances (FADs) in both temperature and strain rate. This numerical model reveals the detailed processes by which the FADs evolve into a fully developed shear band and suggests that beyond instability, the so-called shear banding process consists of two stages: inhomogeneous shearing and true shear-banding. The latter is characterized by the collapse of the stress and an abrupt increase of the local shear strain rate.