the Critical Thickness of Dislocation-free Stranski-Krastanov Growth Atop a Deformabile Substrate

1993 ◽  
Vol 317 ◽  
Author(s):  
Michael Grinfeld
Keyword(s):  
Small Mass ◽  
Theory Of Elasticity ◽  
Shear Stresses ◽  
Mass Force ◽  
Solid Films ◽  
Asymptotic Formulae ◽  
Solid Substrates ◽  
Mismatch Stress ◽  
Critical Film Thickness ◽  
Static Energy

AbstractWe investigate the influence of mass forces (in particular, of gravitation and van der Waals forces) on the critical film thickness of thin films attached to solid substrates and establish corresponding corrections of the earlier published formula Hcril = ΣΜ/τ2 (where Σ is the surface energy, Μ - the shear Modulus, and τ - the mismatch stress). It is assumed that the films’ particles are able to rearrange their relative positions in the lattices, and the equilibrium rearrangement is determined by minimizing the total static energy. Recently, it was demonstrated that morphological stability of interfaces in crystalline solids with the rearrangement is extremely sensitive to the presence of shear stresses. Equilibrium theory of elasticity of pre-stressed solids with the rearrangement of their material particles has already allowed the prediction of the appearance of corrugations in He4 films and to explain the dislocation-free Stranski-Krastanov pattern of epitaxial growth of thin solid films. The explicit asymptotic formulae announced here are especially useful in the case of small mass force, the effects of which can be detectable and even significant for some of the above mentioned phenomena.

The Stress Driven Islands Formation in Epitaxial Films and Solid HE4 Films.

1992 ◽  
Vol 280 ◽  
Author(s):  
Michael A. Grinfeld
Keyword(s):  
Surface Energy ◽  
Shear Modulus ◽  
Film Thickness ◽  
Epitaxial Films ◽  
Morphological Instability ◽  
Thin Solid Films ◽  
Solid Films ◽  
Mismatch Stress ◽  
Critical Film Thickness ◽  
Morphological Patterns

ABSTRACTWe discuss the static and quasi-static problems appearing in the theory of morphological instability of interfaces. The approach has allowed to predict the corrugations in He4 films and to explain the dislocation-free Stranski-Krastanow pattern of epitaxial growth of thin solid films with the critical film thickness H = σμ/τ2 (σ is a surface energy, μ- the shear modulus, and τ - the mismatch stress). In this paper we discuss possible morphological patterns of corrugations and their changes which appear in result of the stress driven “rearrangement” destabilization of originally flat interfaces.

Axisymmetric Stress Analysis and Strength Evaluation of Bonded Shrink Fitted Joints of Circular Pipes Subjected to Internal Pressure and Tensile Loads

2000 ◽  
Author(s):  
Masahide Katsuo ◽  
Toshiyuki Sawa ◽  
Masahiro Yoneno
Keyword(s):  
Internal Pressure ◽  
Stress Analysis ◽  
Joint Strength ◽  
Tensile Load ◽  
Theory Of Elasticity ◽  
Shear Stresses ◽  
Stress Distributions ◽  
Strength Evaluation ◽  
Circular Pipes ◽  
Hollow Cylinders

Abstract This study deals with the stress analysis and the strength evaluation of a bonded shrink fitted joint of circular pipes subjected to an internal pressure and a tensile load. In the analysis, two pipes and the adhesive are replaced with finite hollow cylinders, and the stress distributions in the joint are analyzed by using the axisymmetric theory of elasticity. From the numerical calculations, the following results are obtained: (1) Both the compressive and shear stresses at the interface between the adherend and the adhesive increase as Young’s modulus of the adherend increases. (2) The stress becomes singular at the edges of the interfaces. (3) The joint strength can be evaluated using the compressive and shear stresses near the edge of the interface. In the experiments, bonded shrink fitted joints consisting of dissimilar circular pipes were manufactured, and rupture tests of the joints were carried out by applying an internal pressure, and a tensile load to the joints. From the results, the joint strength of the bonded shrink fitted joint was found to be greater than that of the shrink fitted joint. Furthermore, the numerical results are in fairly good agreement with the experimental ones.

Bending analysis of sandwich plates with composite face sheets and compliance functionally graded syntactic foam core

2016 ◽  
Vol 230 (20) ◽  
pp. 3606-3630 ◽  
Author(s):  
Mohammad Javad Lashkari ◽  
Omid Rahmani
Keyword(s):  
Plate Theory ◽  
Theory Of Elasticity ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Rectangular Plates ◽  
Governing Equations ◽  
Positive Role ◽  
Virtual Displacement ◽  
The Core ◽  
Composite Face

In this paper, the problem of a rectangular plate with functionally graded soft core and composite face sheets is considered using high order sandwich plate theory. This theory applies no assumptions on the displacement and stress fields in the core. Face sheets were treated using classical theory and core was exposed to the theory of elasticity. Governing equations and boundary conditions are derived using principle of virtual displacement and the governing equations are based on eight primary variables including six displacements and two shear stresses. This solution is able to present localized displacements and stresses in places where concentrated loads are exerted to the structure since the displacements in the core can take a nonlinear form which could not be seen in the previous theories such as classical and higher order shear theories. This theory is suitable for rectangular plates under all types of loadings distributed or concentrated which can be different on upper and lower face sheets at the same point. The results were compared with the published literature using theory of elasticity and showed good agreement confirming the accuracy of the present theory. Subsequently, the solution for the core with functionally graded material is presented and effectively indicates positive role of functionally graded core.

Realistic Modeling of Edge Effect Stresses in Bimaterial Elements

1990 ◽  
Vol 112 (1) ◽  
pp. 16-23 ◽  
Author(s):  
J. W. Eischen ◽  
C. Chung ◽  
J. H. Kim
Keyword(s):  
Thermal Loading ◽  
Thermal Stresses ◽  
Theory Of Elasticity ◽  
Shear Stresses ◽  
Strength Of Materials ◽  
Approximate Methods ◽  
Interfacial Stresses ◽  
Distribution Of Stress ◽  
Laminated Structures ◽  
Peak Value

A classic paper by Timoshenko in 1925 dealt with thermal stresses in bimetal thermostats and has been widely used for designing laminated structures, and in contemporary studies of stresses in electronic devices. Timoshenko’s analysis, which is based on strength of materials theory, is unable to predict the distribution of the interfacial shear and normal stresses known to exist based on more sophisticated analyses involving the theory of elasticity (Bogy (1970) and Hess (1969)). Suhir (1986) has recently provided a very insightful approximate method whereby these interfacial stresses are estimated by simple closed-form formulas. The purpose of the present paper is to compare three independent methods of predicting the interfacial normal and shear stresses in bimaterial strips subjected to thermal loading. These are: 1.) Theory of elasticity via an eigenfunction expansion approach proposed by Hess, 2.) Extended strength of materials theory proposed by Suhir, 3.) Finite element stress analysis. Two material configurations which figure prominently in the electronics area have been studied. These are the molydeneum/aluminum and aluminum/silicon material systems. It has been discovered that when the two layers are nearly the same thickness, the approximate methods adequately predict the peak values of the interfacial stresses but err in a fundamental manner in the prediction of the distribution of stress. This may not be of concern to designers who are interested mainly in maximum stress alone. However, it has been shown that if one layer is relatively thin compared to the other, the approximate methods have difficulty in predicting both the peak value of stress and its associated distribution.

Failure of micron scale Single Crystal Silicon bars due to torsion developed by MEMS micro instruments

1998 ◽  
Vol 518 ◽  
Author(s):  
Taher Saif ◽  
N. C. MacDonald
Keyword(s):  
Single Crystal ◽  
Single Crystal Silicon ◽  
Theory Of Elasticity ◽  
Shear Stresses ◽  
Electrostatic Actuator ◽  
Crystal Silicon ◽  
Cross Sectional ◽  
Lever Arm ◽  
Spring Constants

AbstractWe present an experimental study on a single crystal silicon (SCS) bar subjected to pure torsion using MEMS micro instruments. The bar is in the form of a pillar, anchored at one end to the silicon substrate. It is attached to a lever arm at the other end. The pillar has a minimum cross sectional area at its mid height. The cross section coincides with the (100) plane of SCS. Torsion is generated by applying two equal forces on the lever arm on either side of the pillar. Two micro instruments apply the forces. Each consists of an electrostatic actuator and a component that calibrates it. The actuator generates high force (≈ 200 µN at 50 V) and is capable of developing large displacements (≈ 10 μm). Calibration involves determination of the force generated by the actuator at an applied voltage, as well as the linear and higher order spring constants of its springs. Each microinstrument is thus calibrated independently.With the application of forces by the two micro instruments, a torque is generated which twists the pillar. The angle of twist at different applied voltages are recorded using an angular scale. The corresponding torques are determined from the calibration parameters of the actuators. Torque is applied until the pillar fractures. Two such sample pillars, samples 1 and 2, are tested. There cross sectional areas are 1 and 2.25 µm2. We find that both the pillars behave linearly until failure. The stresses prior to fracture are evaluated based on anisotropic theory of elasticity. Samples 1 and 2 fail at shear stresses of 5.6 and 2.6 GPa respectively. The fracture surfaces seem to coincide with the (111) plane of SCS.

Reinforcement of Timber Beams with Prestressed Wires

2013 ◽  
Vol 778 ◽  
pp. 596-603
Author(s):  
João Henrique Jorge de Oliveira Negrão
Keyword(s):  
Mass Production ◽  
Bending Strength ◽  
Small Mass ◽  
Shear Stresses ◽  
Large Span ◽  
Glued Laminated Timber ◽  
Post Tension ◽  
Wood Part ◽  
Limited Scope ◽  
Timber Beams

This paper presents and discusses the possibility of improving the bending strength of timber beams through the use of prestress. The emphasis is put on various methods of imposing the prestress force and transferring it into the wood part: i) through post-tension, with the force being mechanically anchored on the ends of the wood elements; ii) through pre-tension, with the anchorages being either mechanical, as in the previous system, or glued, with the force being gradually transferred through shear stresses along a certain length of the wire/wood interface. Although the risk of failure due to tension perpendicular to the grain in the anchorage regions exists, it is not specifically studied in here, due to the limited scope of the study. The main conclusion is that any of the procedures may be advantageously used with either small (mass-production) or large-span glued-laminated timber beams and, though they are mostly suited to the production of new elements, they may also be adapted to the strengthening of existing beams.

Theory of Filler Reenforcement in Natural and Synthetic Rubber. The Stresses in and about the Particles

1944 ◽  
Vol 17 (4) ◽  
pp. 865-874 ◽  
Author(s):  
John Rehner
Keyword(s):  
Elastic Constants ◽  
Surrounding Medium ◽  
Radial Distance ◽  
Theory Of Elasticity ◽  
Shear Stresses ◽  
Synthetic Rubber ◽  
Stress Components ◽  
Applied Tension ◽  
Infinitesimal Deformations ◽  
Range Of Values

Abstract An attempt is made to develop a general theory of filler reënforcement by determining the stresses occurring in and about a spherical particle imbedded in a rubberlike medium subjected to an applied tension. For a system containing a single particle rigidly attached to the adjacent medium, an application of the theory of elasticity shows that, for infinitesimal deformations, the stress components within the particle are independent of the radial distance from the origin, taken at the center of the particle. The stress components at a given point in the surrounding medium depend on the elastic constants both of the particle and of the medium, on the radius of the sphere, on the distance from the origin, and on the angle between the direction vector and the applied tension. Expressions are given for the average stresses in media containing many (independent) particles. Theoretical values of the bulk moduli of the synthetic rubbers considered in the treatment are derived from sound velocity data. Curves showing the spatial distribution of radial and shear stresses are presented for a range of values of elastic constants to be expected for different kinds of filler particles and rubberlike materials.

Studies on Water in the Hydration Chamber of a Modified Electron Microscope

1970 ◽  
Vol 28 ◽  
pp. 544-545
Author(s):  
R. C. Moretz ◽  
G. G. Hausner ◽  
D. F. Parsons
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Electron Microscope ◽  
Steady State ◽  
Room Temperature ◽  
Small Mass ◽  
Equilibrium Pressure ◽  
Biological Objects ◽  
Mechanical Pump ◽  
Differential Pumping

Use of the electron microscope to examine wet objects is possible due to the small mass thickness of the equilibrium pressure of water vapor at room temperature. Previous attempts to examine hydrated biological objects and water itself used a chamber consisting of two small apertures sealed by two thin films. Extensive work in our laboratory showed that such films have an 80% failure rate when wet. Using the principle of differential pumping of the microscope column, we can use open apertures in place of thin film windows.Fig. 1 shows the modified Siemens la specimen chamber with the connections to the water supply and the auxiliary pumping station. A mechanical pump is connected to the vapor supply via a 100μ aperture to maintain steady-state conditions.

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