First-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems

An n degree-of-freedom Hamiltonian system with r (1¡r¡n) independent 0rst integrals which are in involution is calledpartially integrable Hamiltonian system. A partially integrable Hamiltonian system subject to light dampings andweak stochastic excitations is called quasi-partially integrable Hamiltonian system. In the present paper, the procedures for studying the 0rst-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems are proposed. First, the stochastic averaging methodfor quasi-partially integrable Hamiltonian systems is brie4y reviewed. Then, basedon the averagedIt ˆo equations, a backwardKolmogorov equation governing the conditional reliability function, a set of generalized Pontryagin equations governing the conditional moments of 0rst-passage time and their boundary and initial conditions are established. After that, the dynamical programming equations and their associated boundary and 0nal time conditions for the control problems of maximization of reliability andof maximization of mean 0rst-passage time are formulated. The relationship between the backwardKolmogorov equation andthe dynamical programming equation for reliability maximization, andthat between the Pontryagin equation andthe dynamical programming equation for maximization of mean 0rst-passage time are discussed. Finally, an example is worked out to illustrate the proposed procedures and the e9ectiveness of feedback control in reducing 0rst-passage failure.

Characterization of the Fracture Work for Ductile Film Undergoing the Micro-Scratch

The interface adhesion strength (or interface toughness) of a thin film/substrate system is often assessed by the micro-scratch test. For a brittle film material, the interface adhesion strength is easily obtained through measuring the scratch driving forces. However, to measure the interface adhesion strength (or interface toughness) for a metal thin film material (the ductile material) by the microscratch test is very difficult, because intense plastic deformation is involved and the problem is a three-dimensional elastic-plastic one. In the present research, using a double-cohesive zone model, the failure characteristics of the thin film/substrate system can be described and further simulated. For a steady-state scratching process, a three-dimensional elastic-plastic finite element method based on the double cohesive zone model is developed and adopted, and the steady-state fracture work of the total system is calculated. The parameter relations between the horizontal driving forces (or energy release rate of the scratching process) and the separation strength of thin film/substrate interface, and the material shear strength, as well as the material parameters are developed. Furthermore, a scratch experiment for the Al/Si film/substrate system is carried out and the failure mechanisms are explored. Finally, the prediction results are applied to a scratch experiment for the Pt/NiO material system given in the literature.

用高速阴影技术研究K9玻璃中的失效波=Investigations of Failure Waves in K9 Glass Using Shadowgraph

用高速阴影摄影技术研究了爆轰加载下K9 玻璃样品中波的传播和压缩区内损伤破坏的物理图象 和规律。实验中观测到冲击波阵面后有一个移动速度为2. 1～2. 2 mm/μs 的黑色阴影区边界,即失效波(Failure wave) ;实验发现只有当冲击载荷接近材料的HEL 时,在冲击波和失效波之间的区域才有少量的微裂纹成 核和长大,而在冲击载荷较低时却没有观察到;同时实验中观测到失效波萌生于被撞击面,并在两块玻璃的交 界面上观测到失效波的再生。这些结果表明失效波的产生基本与冲击相变无关,主要与玻璃样品表面的初始 损伤有关,换言之,失效波是玻璃样品表面微裂纹在冲击波作用下失稳扩展造成的。

Statistical and stochastic description of microvoid evolution observed in dynamic failure of ductile materials

A brief review is presented of statistical approaches on microdamage evolution. An experimental study of statistical microdamage evolution in two ductile materials under dynamic loading is carried out. The observation indicates that there are large differences in size and distribution of microvoids between these two materials. With this phenomenon in mind, kinetic equations governing the nucleation and growth of microvoids in nonlinear rate-dependent materials are combined with the balance law of void number to establish statistical differential equations that describe the evolution of microvoids' number density. The theoretical solution provides a reasonable explanation of the experimentally observed phenomenon. The effects of stochastic fluctuation which is influenced by the inhomogeneous microscopic structure of materials are subsequently examined (i.e. stochastic growth model). Based on the stochastic differential equation, a Fokker-Planck equation which governs the evolution of the transition probability is derived. The analytical solution for the transition probability is then obtained and the effects of stochastic fluctuation is discussed. The statistical and stochastic analyses may provide effective approaches to reveal the physics of damage evolution and dynamic failure process in ductile materials.

Shear Localization In Dynamic Deformation: Microstructural Evolution

Investigations made by the authors and collaborators into the microstructural aspects of adiabatic shear localization are critically reviewed. The materials analyzed are low-carbon steels, 304 stainless steel, monocrystalline Fe-Ni-Cr, Ti and its alloys, Al-Li alloys, Zircaloy, copper, and Al/SiCp composites. The principal findings are the following: (a) there is a strain-rate-dependent critical strain for the development of shear bands; (b) deformed bands and white-etching bands correspond to different stages of deformation; (c) different slip activities occur in different stages of band development; (d) grain refinement and amorphization occur in shear bands; (e) loss of stress-carrying capability is more closely associated with microdefects rather than with localization of strain; (f) both crystalline rotation and slip play important roles; and (g) band development and band structures are material dependent. Additionally, avenues for new research directions are suggested.

Measurement Of Fracture Toughness And Interfacial Shear Strength Of Hard And Brittle Cr Coating On Ductile Steel Substrate

The fracture toughness and interfacial adhesion properties of a coating on its substrate are considered to be crucial intrinsic parameters determining performance and reliability of coating-substrate system. In this work, the fracture toughness and interfacial shear strength of a hard and brittle Cr coating on a normal medium carbon steel substrate were investigated by means of a tensile test. The normal medium carbon steel substrate electroplated with a hard and brittle Cr coating was quasi-statically stretched to induce an array of parallel cracks in the coating. An optical microscope was used to observe the cracking of the coating and the interfacial decohesion between the coating and the substrate during the loading. It was found that the cracking of the coating initiated at critical strain, and then the number of the cracks of the coating per unit axial distance increased with the increase in the tensile strain. At another critical strain, the number of the cracks of the coating became saturated, i.e. the number of cracks per unit axial distance became a constant after this critical strain. Based on the experiment result, the fracture toughness of the brittle coating can be determined using a mechanical model. Interestingly, even when the whole specimen fractured completely under an extreme strain of the substrate, the interfacial decohesion or buckling of the coating on its substrate was completely absent. The test result is different from that appeared in the literature though the identical test method and the brittle coating/ductile metal substrate system are taken. It was found that this difference can be attributed to an important mechanism that the Cr coating on the steel substrate has a good adhesion, and the ultimate interfacial shear strength between the Cr coating and the steel substrate has exceeded the maximum shear flow strength level of the steel substrate. This result also indicates that the maximum shear flow strength level of the ductile steel substrate can be only taken as a lower bound estimate on the ultimate shear strength of the interface. This estimation of the ultimate interfacial shear strength is consistent with the theoretical analysis and prediction presented in the literature.

Basic Mechanical Behaviors And Mechanics Of Shear Banding In Bmgs

In this paper, some basic mechanical behaviors of bulk metallic glasses (BMGs) were discussed. It can be found from the discussions that the mechanical behaviors of BMGs are mainly due to the formation and operation of shear bands in BMGs. Furthermore, the relevant mechanics of shear banding were investigated in the paper. The theoretical analysis of deformation coupling thermal softening and free volume creation softening demonstrates that the free volume creation and thermal softening can jointly promote the formation of shear bands in BMGs, and the observed post mortem. shear band width looks more like that governed by free volume creation. (C) 2007 Elsevier Ltd. All rights reserved.

Investigation Of Mode Ii Crack Growth Following A Very High Speed Impact

A recoverable plate impact testing technology has been developed for studying fracture mechanisms of mode II crack. With this technology, a single duration stress pulse with submicrosecond duration and high loading rates, up to 10(8) MPam(1/2)s(-1), can be produced. Dynamic failure tests of Hard-C 60# steel were carried out under asymmetrical impacting conditions with short stress-pulse loading. Experimental results show that the nucleation and growth of several microcracks ahead of the crack tip, and the interactions between them, induce unsteady crack growth. Failure mode transitions during crack growth, both from mode I crack to mode II and from brittle to ductile fracture, were observed. Based on experimental observations, a discontinuous crack growth model was established. Analysis of the crack growth mechanisms using our model shows that the shear crack extension is unsteady when the extending speed is between the Rayleigh wave speed c(R) and the shear wave speed c(S). However, when the crack advancing speed is beyond c(S), the crack grows at a steady intersonic speed approaching root 2c(S). It also shows that the transient mechanisms, such as nucleation, growth, interaction and coalescence among microcracks, make the main crack speed jump from subsonic to intersonic and the steady growth of all the subcracks causes the main crack to grow at a stable intersonic speed.

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.

Threshold diversity and trans-scales sensitivity in a finite nonlinear evolution model of materials failure

We present a slice-sampling method and study the ensemble evolution of a large finite nonlinear system in order to model materials failure. There is a transitional region of failure probability. Its size effect is expressed by a slowly decaying scaling law. In a meso-macroscopic range (similar to 10(5)) in realistic failure, the diversity cannot be ignored. Sensitivity to mesoscopic details governs the phenomena. (C) 1997 Published by Elsevier Science B.V.

On separated shear layer of blunt circular cylinder

Separated shear layer of blunt circular cylinder has been experimentally investigated for the Reynolds numbers (based on the diameter) ranging from 2.8 x 10(3) to 1.0 x 10(5), with emphasis on evolution of separated shear layer, its structure and distribution of Reynolds shear stress and turbulence kinetic energy. The results demonstrate that laminar separated shear layer experiences 2 similar to 3 times vortex merging before it reattaches, and turbulence separated shear layer takes 5 similar to 6 times vortex merging. In addition, relationship between dimensionless initial frequencies of K-H instability and Reynolds numbers is identified, and reasons for the decay of turbulence kinetic energy and Reynolds shear stress in reattachment region are discussed.

Vibration analysis of laminated shells using a refined shear deformation theory

A previously published refined shear deformation theory is used to analyse free vibration of laminated shells. The theory includes the assumption that the transverse shear strains across any two layers are linearly dependent on each other. The theory has the same dependent variables as first-order shear deformation theory, hut the set of governing differential equations is of twelfth order. No shear correction factors are required. Free vibration of symmetric cross-ply laminated cylindrical shells, symmetric and antisymmetric cross-ply cylindrical panels is calculated. The numerical results are in good agreement with those from three-dimensional elasticity theory.

Evolution of thermoplastic shear localization and related microstructures in Awl/SiCp composites under dynamic compression

The localized shear deformation in the 2024 and 2124 Al matrix composites reinforced with SiC particles was investigated with a split Hopkinson pressure bar (SHPB) at a strain rate of about 2.0x10(3) s(-1). The results showed that the occurrence of localized shear deformation is sensitive to the size of SiC particles. It was found that the critical strain, at which the shear localization occurs, strongly depends on the size and volume fraction of SiC particles. The smaller the particle size, the lower the critical strain required for the shear localization. TEM examinations revealed that Al/SiCp interfaces are the main sources of dislocations. The dislocation density near the interface was found to be high and it decreases with the distance from the particles. The Al matrix in shear bands was highly deformed and severely elongated at low angle boundaries. The Al/SiCp interfaces, particularly the sharp corners of SiC particles, provide the sites for microcrack initiation. Eventual fracture is caused by the growth and coalescence of microcracks along the shear bands. It is proposed that the distortion free equiaxed grains with low dislocation density observed in the center of shear band result from recrystallization during dynamic deformation.

First-passage failure of quasi-integrable Hamiltonian systems

The first-passage failure of quasi-integrable Hamiltonian si-stems (multidegree-of-freedom integrable Hamiltonian systems subject to light dampings and weakly random excitations) is investigated. The motion equations of such a system are first reduced to a set of averaged Ito stochastic differential equations by using the stochastic averaging method for quasi-integrable Hamiltonian systems. Then, a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. Finally, the conditional reliability function, and the conditional probability density and moments of first-passage time are obtained by solving these equations with suitable initial and boundary conditions. Two examples are given to illustrate the proposed procedure and the results from digital simulation are obtained to verify the effectiveness of the procedure.

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.