Fracture mechanics analysis on Smart-Cut technology. Part 1： Effects of stiffening wafer and defect interaction

In the present paper, continuum fracture mechanics is used to analyze the Smart-Cut process, a recently established ion cut technology which enables highly efficient fabrication of various silicon-on-insulator （SOI） wafers of high uniformity in thickness. Using integral transform and Cauchy singular integral equation methods, the mode-I and mode-II stress intensity factors, energy release rate, and crack opening displacements are derived in order to examine several important fracture mechanisms involved in the Smart-Cut process. The effects of defect interaction and stiffening wafer on defect growth are investigated. The numerical results indi- cate that a stiffener/handle wafer can effectively prevent the donor wafer from blistering and exfoliation, but it slows down the defect growth by decreasing the magnitudes of SIF＇s. Defect interaction also plays an important role in the splitting process of SOI wafers, but its contribution depends strongly on the size, interval and internal pressure of defects. Finally, an analytical formula is derived to estimate the implantation dose required for splitting a SOI wafer.     

Fracture mechanics analysis on Smart-Cut~ technology.Part 2:Effect of bonding flaws

In Part 2 of the paper on the Smart-Cut process,the effects of bonding flaws characterized by the size andinternal pressure before and after splitting are studied byusing fracture mechanics models.It is found that the bon-ding flaws with large size are prone to cause severe devia-tion of defect growth,leading to a non-transferred area ofthin layer when splitting.In a practical Smart-Cut processwhere the internal pressure of bonding flaws is very small,large interfacial defects always promote defect grow...     

Fracture mechanics analysis on Smart-Cut^R technology. Part 2： Effect of bonding flaws

In Part 2 of the paper on the Smart-Cut process, the effects of bonding flaws characterized by the size and internal pressure before and after splitting are studied by using fracture mechanics models. It is found that the bonding flaws with large size are prone to cause severe deviation of defect growth, leading to a non-transferred area of thin layer when splitting. In a practical Smart-Cut process where the internal pressure of bonding flaws is very small, large interfacial defects always promote defect growth in the splitting process. Meanwhile, increasing the internal pressure of the bonding flaws decreases the defect growth and its deviation before splitting. The mechanism of relaxation of stiffener constraint is proposed to clarify the effect of bonding flaws. Moreover, the progress of the splitting process is analyzed when bonding flaws are present. After splitting, those bonding flaws with large size and high internal pressure are vulnerable for the blistering of the thin film during high-temperature annealing.     

Study on steerability of articulated tracked vehicles — Part 1. Theoretical and experimental analysis

This paper presents theoretical and experimental analysis of steering performance of articulated tracked vehicles on level ground. A mathematical model for predicting the steerability of articulated units has been developed and computerized for numerical application. The accuracy of the analog has been verified by scale model tests.From the results of the simulation and scale model tests it was found that steerability was significantly improved and required sprocket torques for steering and track slippage were considerably decreased in articulated tracked vehicles when compared with a single and coupled tracked vehicles.     

On the methodologies of stress analysis of composite structures: Part 1: State of the art—phenomenological and physical methodologies

The rapidly increasing technological importance of composite materials and composite structures is leading to the development of new, more advanced models of their actual response to mechanical and thermal loads. This in turn results in the development of new experimental and analytical methods for determination of the mechanical and thermal responses of such structures and materials to various loads. In this respect the reliability and the predictive power of various methods and techniques of stress analysis become very important since all the analytical, experimental and numerical methods used for the determination, prediction and optimization of the actual mechanical responses of composite structures and materials are based on the concepts of strain and stress. Because of the inherently three-dimensional stress and strain states in composite materials and structures and the wide use of viscoelastic polymers as the matrix and some reinforcing fiber materials, a more rigorous type of modelling than had been common in the past is needed of all the involved physical phenomena which influence the strain and stress states at the local and global levels. Also, a more rigorous analysis of practical consequences of the physical and mathematical simplifications is required to assure reliability and accuracy of various methods of stress analysis. The influence of the above-mentioned factors on the reliability and applicability of analytical and experimental procedures is illustrated by examples of actual material responses.Part 2 of this paper presents theories and techniques of three new methods of strain/stress analysis which have been developed on the basis of comprehensive physical models of involved phenomena: the isodyne, strain gradient and thermoelastic effect methods. Presented examples illustrate the efficacy of these methods.     

Mathematical and numerical modeling of the non-associated plasticity of soils—Part 2: Finite element analysis

The method of the implicit standard material has allowed the formulation of a consistent mathematical model of the boundary value problem for the non-associated plasticity of soil. The mean accomplished steps are the achievement of the bipotential function, the recovering of the stress–strain relationship under a normality rule, introduction of the bifunctional and the proof of the solution existence. Here the mathematical model is discretized by the finite element method. First, the stress update scheme was formulated, the tangent matrix is explicitly derived and then the non-linear system is solved by the Newton–Raphson method where a new algorithm using a symmetrical tangent matrix is improved. This is in opposition to conventional non-associated plasticity, which uses a non-symmetric tangent matrix. Through the numerical examples we show the feasibility and the efficiency of the algorithm. It is also seen that we perform some studies of the numerical solutions, particularly the comparison between associated and non-associated limit load.     

Effects of a.c. Electric Field and Rotation on Bénard–Marangoni Convection

The coupled buoyancy and thermocapillary instability, the Bénard–Marangoniproblem, in an electrically conducting fluid layer whose upper surface is deformed and subject to a temperature gradient is studied. Both influences of an a.c. electric field and rotation are investigated. Special attention is directed at the occurrence of convection both in the form of stationary motion and oscillatory convection. The linear stability problem is solved for different values of the relevant dimensionless numbers, namely the a.c. electric Rayleigh number, the Taylor, Rayleigh, Biot, Crispation and Prandtl numbers. For steady convection, it is found that by increasing the angular velocity, one reinforces the stability of the fluid layer whatever the values of the surface deformation and the applied a.c. electric field. We have also determined the regions of oscillatory instability and discussed the competition between both stationary and oscillatory convections. This revised version was published online in July 2006 with corrections to the Cover Date.     

The effect of surfactants on air–water annular and churn flow in vertical pipes. Part 1: Morphology of the air–water interface

In this work, the influence of surfactants on air–water flow was studied by performing experiments in a 12 metre long, 50 mm inner diameter, vertical pipe at ambient conditions. High-speed visualisation of the flow shows that the morphology of the air–water interface determines the formation of foam. The foam subsequently alters the flow morphology significantly. In annular flow, the foam suppresses the roll waves, and a foamy crest is formed on the ripple waves. In the churn flow regime, the flooding waves and the downwards motion of the liquid film are suppressed by the foam. The foam is transported in foam waves moving upwards superposed on an almost stagnant foam substrate at the pipe wall. Foam thus effectively reduces the superficial gas velocity at which the transition from annular to churn flow occurs. These experiments make more clear how surfactants can postpone liquid loading in vertical pipes, such as in gas wells.     

On the effect of Lüders bands on the bending of steel tubes. Part II: Analysis

Part II of this study presents a modeling framework that is shown to successfully simulate all aspects of the inhomogeneous bending of tubes associated with Lüders banding reported in Part I. The structure is discretized with solid finite elements using a mesh that is fine enough for Lüders bands to develop and evolve. The material is modeled as a finitely deforming, J₂ type, elastic–plastic solid with an “up–down–up” response over the extent of the Lüders strain, followed by hardening. Regularization of the solution was accomplished by introducing a mild rate dependence of the material. Simulation of the rotation controlled bending experiments confirmed most of the experimental observations and revealed additional details of the localization. Thus, the initial uniform-curvature elastic regime terminates with the nucleation of localized banded deformation on the tensioned and compressed sides of the tube. The bands appear in pockets that propagate into the hitherto intact part of the structure while the moment remains essentially unchanged. The tube develops two curvature regimes; a relatively high curvature in the Lüders deformed section and a low curvature in the unaffected one. Simultaneously, the plasticized zone develops higher ovalization and wrinkles with a wavelength that corresponds to the periodicity of the banded pockets. For tubes with lower D/t and/or shorter Lüders strain the higher curvature eventually spreads to the whole structure at which point homogenous bending resumes. For tubes with higher D/t and/or longer Lüders strain the localized curvature, ovalization, and wrinkle amplitude are larger and cannot be sustained; the tube collapses prematurely leaving behind part of its length essentially undeformed. For every tube D/t there exists a threshold of Lüders strain separating the two types of behavior. This bounding value of Lüders strain was studied parametrically.     

On the effect of Lüders bands on the bending of steel tubes. Part I: Experiments

In several practical applications hot-finished steel pipe that exhibits Lüders bands is bent to strains of 2–3%. Lüders banding is a material instability that leads to inhomogeneous plastic deformation in the range of 1–4%. This work investigates the influence of Lüders banding on the inelastic response and stability of tubes under rotation controlled pure bending. Part I presents the results of an experimental study involving tubes of several diameter-to-thickness ratios in the range of 33.2–14.7 and Lüders strains of 1.8–2.7%. In all cases the initial elastic regime terminates at a local moment maximum and the local nucleation of narrow angled Lüders bands of higher strain on the tension and compression sides of the tube. As the rotation continues the bands multiply and spread axially causing the affected zone to bend to a higher curvature while the rest of the tube is still at the curvature corresponding to the initial moment maximum. With further rotation of the ends the higher curvature zone(s) gradually spreads while the moment remains essentially unchanged. For relatively low D/t tubes and/or short Lüders strains, the whole tube eventually is deformed to the higher curvature entering the usual hardening regime. Subsequently it continues to deform uniformly until the usual limit moment instability is reached. For high D/t tubes and/or materials with longer Lüders strains, the propagation of the larger curvature is interrupted by collapse when a critical length is Lüders deformed leaving behind part of the structure essentially undeformed. The higher the D/t and/or the longer the Lüders strain is, the shorter the critical length. Part II presents a numerical modeling framework for simulating this behavior.     

On a Crystalline Variational Problem, Part II:¶BV Regularity and Structure of Minimizers on Facets

For a nonsmooth positively one-homogeneous convex function φ:ℝ ⁿ → [0,+∞[, it is possible to introduce the class ?_φ (ℝ ⁿ ) of smooth boundaries with respect to φ, to define their φ-mean curvature κ_φ, and to prove that, for E∈?_φ (ℝ ⁿ ), κ_φ∈L ^∞(δE) [9]. Based on these results, we continue the analysis on the structure of δE and on the regularity properties of κ_φ. We prove that a facet F of δE is Lipschitz (up to negligible sets) and that κ_φ has bounded variation on F. Further properties of the jump set of κ_φ are inspected: in particular, in three space dimensions, we relate the sublevel sets of κ_φ on F to the geometry of the Wulff shape ?_φ≔{φ≤ 1 }. Accepted October 11, 2000?Published online 14 February, 2001     

Dynamics of trains and train-like articulated systems travelling in confined fluid—Part 1: Modelling and basic dynamics

The dynamics and stability of a train of flexibly interconnected rigid cylinders travelling in a confined cylindrical “tunnel” subjected to fluid dynamic forces is studied theoretically. Each cylinder, which is coupled to other cylinders and supported by springs and dampers, has degrees of freedom in the lateral translational and rotational directions. The kinetic, dissipation, and potential energies of the system and the generalized forces associated with the fluid dynamic forces acting on the system, such as inviscid fluid dynamic forces, viscous frictional forces, and form drag, are obtained first. Then the equations of motion are derived in a Lagrangian framework. The principal aim of this study is to investigate the effect of the aerodynamic forces on the dynamics of a high-speed train running in a tunnel, or more generally of a train-like system travelling in a coaxial cylindrical tube. The results of this study show that the system loses stability by flutter and that viscous frictional drag has a considerable effect on stability of the system. In addition, the mechanism of instability of the system is clarified with the aid of a study of the modal shapes and energy considerations.     

The effect of rider��s passive steering impedance on?motorcycle stability: identification and analysis

Many scientific papers deal with motorcycle stability (weave and wobble modes) but very seldom they take into account the passive response of rider??s body. This paper aims at studying the interaction of the rider??s arms and torso with the handlebar and the frame. First the rider??s steering impedance is identified from experimental tests on a motorcycle riding simulator, then this information is used on a motorcycle model and the effect on straight-motion stability is investigated by eigenvalues calculation.     

Investigation of bubble breakup and coalescence in a packed-bed reactor – Part 1: A comparative study of bubble breakup and coalescence models

In a packed-bed reactor a comparative study of bubble breakup and coalescence models has been investigated to study bubble size distributions as a function of the axial location. The bubble size distributions are obtained by solving population balance equations that describe gas–liquid interactions. Each combination of bubble breakup and coalescence models is examined under two inlet flow conditions: (1) predominant bubble breakup flow and (2) predominant bubble coalescence flow. The resulting bubble size distributions, breakup and coalescence rates estimated by individual models, are qualitatively compared to each other. The change of bubble size distributions along the axial direction is also described with medians. The medians resulting from CFD analyses are compared against the experimental data. Since the predictions estimated by CFD analyses with the existing bubble breakup and coalescence models do not agree with the experimental data, a new bubble breakup and coalescence model that takes account of the geometry effects is required to describe gas–liquid interactions in a packed-bed reactor.     

Analysis of vertical cracking phenomena in tensile-strained epitaxial film on a substrate: Part II. Application to InxGa1−xAs/InP system

Cracking phenomena in tensile-strained In_xGa_1?xAs epitaxial film on an InP substrate are analyzed via the formulation given in Part I [Lee, S., Choi, S.T., Earmme, Y.Y., 2006. Analysis of vertical cracking phenomena in tensile-strained epitaxial film on a substrate: Part I. Mathematical formulation. International Journal of Solids and Structures 43, 3401–3413], where the solution for a dislocation in an anisotropic trimaterial is used as a fundamental solution and the crack is modeled by the continuous distribution of dislocations. Misfit strains and stresses are evaluated as a function of indium content x in an In_xGa_1?xAs/InP system. A single crack and periodic cracks, respectively, induced by the misfit stresses are considered. The crack opening profile, the crack mouth displacement, and the energy release rate as a function of the crack length are obtained. The critical conditions for a single crack and periodic cracks, respectively, are thus obtained, and are found to depend on the film thickness, the crack length, and the period of the cracks. The results of these analyses are also compared with published data obtained from experiments.     

Upper Bounds on Deformations of Elastic-Workhardening Structures in the Presence of Dynamic and Second-Order Geometric Effects∗

Abstract

Discrete models of elastoplastic structures are considered, Piecewise linear yield conditions and hardening rules are assumed. On this basis, a deformation bounding method resting on the use of fictitious loads as proposed first by Ponter [6, 7], is developed for situations in which: (a) the geometry changes affect the equilibrium equations but their effects may be expressed by bilinear terms in the pre-existing stresses and additional displacements (“second-order geometric effects”); (b) inertia and viscous damping forces play a significant role. Comparisons are made with different bounding methods previously established by the author [3,4], for the same classes of structures and mechanical situations.     

Memristive oscillator based on Chua’s circuit: stability analysis and hidden dynamics

This paper presents a theoretical stability analysis of a memristive oscillator derived from Chua’s circuit in order to identify its different dynamics, which are mapped in parameter spaces. Since this oscillator can be represented as a nonlinear feedback system, its stability is analyzed using the method based on describing functions, which allows to predict fixed points, periodic orbits, hidden dynamics, routes to chaos, and unstable states. Bifurcation diagrams and attractors obtained from numerical simulations corroborate theoretical predictions, confirming the coexistence of multiple dynamics in the operation of this oscillator.