Interface Layer Effect On The Stress Distribution Of A Wafer-Bonded Bilayer Structure

The interface layer plays an important role in stress transfer in composite structures. However, many interface layer properties such as the modulus, thickness, and uniformity are difficult to determine. The model developed in this article links the influence of the interface layer on the normal stress distribution along the layer thickness with the layer surface morphology before bonding. By doing so, a new method of determining the interfacial parameter(s) is suggested. The effects of the layer thickness and the surface roughness before bonding on the normal stress distribution and its depth profile are also discussed. For ideal interface case with no interfacial shear stress, the normal stress distribution pattern can only be monotonically decreased from the interface. Due to the presence of interfacial shear stress, the normal stress distribution is much more complex, and varies dramatically with changes in the properties of the interface layer, or the dimensions of the bonding layers. The consequence of this dramatic stress field change, such as the shift of the maximum stress from the interface is also addressed. The size-dependent stress distribution in the thickness direction due to the interface layer effect is presented. When the interfacial shear stress is reduced to zero, the model presented in this article is also demonstrated to have the same normal stress distribution as obtained by the previous model, which does not consider the interface layer effect.

Plane strain asymptotic fields for cracks terminating at the interface between elastic and pressure-sensitive dilatant materials

The plane strain asymptotic fields for cracks terminating at the interface between elastic and pressure-sensitive dilatant material are investigated in this paper. Applying the stress-strain relation for the pressure-sensitive dilatant material, we have obtained an exact asymptotic solution for the plane strain tip fields for two types of cracks, one of which lies in the pressure-sensitive dilatant material and the other in the elastic material and their tips touch both the bimaterial interface. In cases, numerical results show that the singularity and the angular variations of the fields obtained depend on the material hardening exponent n, the pressure sensitivity parameter mu and geometrical parameter lambda.

Statistical analysis of synthetic earthquake catalogs generated by models with various levels of fault zone disorder

The stress release model, a stochastic version of the elastic rebound theory, is applied to the large events from four synthetic earthquake catalogs generated by models with various levels of disorder in distribution of fault zone strength (Ben-Zion, 1996) They include models with uniform properties (U), a Parkfield-type asperity (A), fractal brittle properties (F), and multi-size-scale heterogeneities (M). The results show that the degree of regularity or predictability in the assumed fault properties, based on both the Akaike information criterion and simulations, follows the order U, F, A, and M, which is in good agreement with that obtained by pattern recognition techniques applied to the full set of synthetic data. Data simulated from the best fitting stress release models reproduce, both visually and in distributional terms, the main features of the original catalogs. The differences in character and the quality of prediction between the four cases are shown to be dependent on two main aspects: the parameter controlling the sensitivity to departures from the mean stress level and the frequency-magnitude distribution, which differs substantially between the four cases. In particular, it is shown that the predictability of the data is strongly affected by the form of frequency-magnitude distribution, being greatly reduced if a pure Gutenburg-Richter form is assumed to hold out to high magnitudes.

Torsional impact response of a penny-shaped interface crack in bonded materials with a graded material interlayer

In this paper, the dynamic response of a penny-shaped interface crack in bonded dissimilar homogeneous half-spaces is studied. It is assumed that the two materials are bonded together with such a inhomogeneous interlayer that makes the elastic modulus in the direction perpendicular to the crack surface is continuous throughout the space. The crack surfaces art assumed to be subjected to torsional impact loading. Laplace and Hankel integral transforms are applied combining with a dislocation density,function to reduce the mixed boundary value problem into a singular integral equation with a generalized Cauchy kernel in Laplace domain. By solving the singular integral equation numerically, and using a numerical Laplace inversion technique, the dynamic stress intensity factors art obtained. The influences of material properties and interlayer thickness on the dynamic stress intensity factor are investigated.

Singularity of dynamic stress fields around an interface crack between viscoelastic bodies

The singular nature of the dynamic stress fields around an interface crack located between two dissimilar isotropic linearly viscoelastic bodies is studied. A harmonic load is imposed on the surfaces of the interface crack. The dynamic stress fields around the crack are obtained by solving a set of simultaneous singular integral equations in terms of the normal and tangent crack dislocation densities. The singularity of the dynamic stress fields near the crack tips is embodied in the fundamental solutions of the singular integral equations. The investigation of the fundamental solutions indicates that the singularity and oscillation indices of the stress fields are both dependent upon the material constants and the frequency of the harmonic load. This observation is different from the well-known -1/2 oscillating singularity for elastic bi-materials. The explanation for the differences between viscoelastic and elastic bi-materials can be given by the additional viscosity mismatch in the case of viscoelastic bi-materials. As an example, the standard linear solid model of a viscoelastic material is used. The effects of the frequency and the material constants (short-term modulus, long-term modulus and relaxation time) on the singularity and the oscillation indices are studied numerically.

Characteristics of the interface of a laser-quenched steel substrate and chromium electroplate

The interface of a laser-discrete-quenched steel substrate and as-deposited chromium electroplate was investigated by ion beam etching, dissolving-substrate-away and using a Vickers microhardness tester, in an attempt to reveal the mechanism that the service life of the chromium-coated parts is increased by the duplex technique of laser pre-quenching plus chromium post-depositing. The laser quenching of the steel substrate can reduce the steep hardness gradient at the substrate/chromium interface and improve the load-bearing capacity of chromium electroplate. Moreover, the laser quenching prior to plating has an extremely great effect on the morphologies and microstructure of the substrate/chromium interface: there is a transient interlayer at the original substrate/chromium interface while there is not at the laser-quenchedzone/chromium interface; the near-substrate surface microstructure and morphologies of the free-standing chromium electrodeposits, whose substrate was dissolved away with nital 30% in volume, inherit the periodically gradient characteristics of the laser-discrete-quenched substrate surface. (c) 2006 Elsevier B.V. All rights reserved.

Determination of interface properties between micron-thick metal film and ceramic substrate using peel test

Peel test measurements have been performed to estimate both the interface toughness and the separation strength between copper thin film and Al2O3 substrate with film thicknesses ranging between 1 and 15 mu m. An inverse analysis based on the artificial neural network method is adopted to determine the interface parameters. The interface parameters are characterized by the cohesive zone (CZ) model. The results of finite element simulations based on the strain gradient plasticity theory are used to train the artificial neural network. Using both the trained neural network and the experimental measurements for one test result, both the interface toughness and the separation strength are determined. Finally, the finite element predictions adopting the determined interface parameters are performed for the other film thickness cases, and are in agreement with the experimental results.

Studies on terrestrial interface processes in arid areas, China

In the present paper, we have elucidated the importance of energy and water cycling in arid areas to investigate global climate and local economics. Then, we were concerned with the physical arguments as how to stratify the soil, and the stability of the numerical scheme in the mathematical model for predicting temperature variation and water motion. Furthermore, we discuss the methods to estimate evaporation in arid areas. Numerical simulation of energy and water cycling at the Acsu Observatory, CAS, Xinjiang province and Shapuotou Observatory, CAS, Ningxia Province are conducted as case studies. The results show that the laws of terrestrial processes are rather typical in these arid areas. Planting drought-endurable trees can alleviate unfavourable conditions to a certain extent. (C) 1997 Academic Press Limited.

Micromechanics analyses of interface crack

A new mechanics model based on Peierls concept is presented in this paper, which can clearly characterize the intrinsic features near a tip of an interfacial crack. The stress and displacement fields are calculated under general combined tensile and shear loadings. The near tip stress fields show some oscillatory behaviors but without any singularity and the crack faces open completely without any overlapping when remote tensile loading is comparable with remote shear loading. A fracture criterion for predicting interface toughness has been also proposed, which takes into account for the shielding effects of emitted dislocations. The theoretical toughness curve gives excellent prediction, as compared with the existing experiment data.

The annular crack in a nonhomogeneous matrix surrounding a fiber under torsional loading .2. The crack going through the bimaterial interface into the fiber

The axisymmetric problem of an elastic fiber perfectly bonded to a nonhomogeneous elastic matrix which contains an annular crack going through the interface into the fiber under axially symmetric shear stress is considered. The nature of the stress singularity is studied. It is shown that at the irregular point on the interface, whether the shear modulus is continuous or discontinuous the stresses are bounded. The problem is formulated in terms of a singular integral equation and can be solved by a regular method. The stress intensity factors and crack surface displacement are given.

A new method for evaluation of stress intensities for interface cracks

A new method is presented for calculating the values of K-I and K-II in the elasticity solution at the tip of an interface crack. The method is based on an evaluation of the J-integral by the virtual crack extension method. Expressions for calculating K-I and K-II by using the displacements and the stiffness derivative of the finite element solution and asymptotic crack tip displacements are derived. The method is shown to produce very accurate solutions even with coarse element mesh.

Variable power singular interface elements for a crack normal to the bimaterial interface

Zero thickness crack tip interface elements for a crack normal to the interface between two materials are presented. The elements are shown to have the desired r(lambda-1) (0 < lambda < 1) singularity in the stress field at the crack tip and are compatible with other singular elements. The stiffness matrices of the quadratic and cubic interface element are derived. Numerical examples are given to demonstrate the applicability of the proposed interface elements for a crack perpendicular to the bimaterial interface.

Kinking of an interface crack between 2 dissimilar anisotropic elastic solids

A detailed analysis of kinking of an interface crack between two dissimilar anisotropic elastic solids is presented in this paper. The branched crack is considered as a distributed dislocation. A set of the singular integral equations for the distribution function of the dislocation density is developed. Explicit formulas of the stress intensity factors and the energy release rates for the branched crack are given for orthotropic bimaterials and misoriented orthotropic bicrystals. The role of the stress parallel to the interface, sigma0 is taken into account in these formulas. The interface crack can advance either by continued extension along the interface or by kinking out of the interface into one of the adjoining materials. This competition depends on the ratio of the energy release rates for interface cracking and for kinking out of the interface and the ratio of interface toughness to substrate toughness. Throughout the paper, the influences of the inplane stress sigma0 on the stress intensity factors and the energy release rates for the branched crack, which can significantly alter the conditions for interface cracking, are emphasized.

Collapsed isoparametric element as a singular element for a crack normal to the bi-material interface

It is shown that the variable power singularity of the strain field at the crack tip can be obtained by the simple technique of collapsing quadrilateral isoparametric elements into triangular elements around the crack tip and adequately shifting the side-nodes adjacent to this crack tip. The collapsed isoparametric elements have the desired singularity at crack tip along any ray. The strain expressions for a single element have been derived and in addition to the desired power singularity, additional singularities are revealed. Numerical examples have shown that triangular elements formed by collapsing one side lead to excellent results.