Y.Y. Earmme

On the unified approach to anisotropic and isotropic elasticity for singularity, interface and crack in dissimilar media

Abstract Proposed in this paper is the equivalence between anisotropic and isotropic elasticity for two-dimensional deformation under certain conditions. That is, the isotropic elasticity can be reconstructed in the same framework of the anisotropic elasticity, when the interface between dissimilar media lies along a straight line. Therefore, many known solutions for an anisotropic bimaterial are valid for a bimaterial, of which one or both of the constituent materials are isotropic. The usefulness of the equivalence is that the solutions for singularities and cracks in an anisotropic/isotropic bimaterial can easily be obtained without solving the boundary value problems directly. The interaction solutions of singularities, interfaces, and cracks in infinite anisotropic bimaterial are summarized, to be used for the cases of isotropic/isotropic and anisotropic/isotropic bimaterials. Conservation integrals also have the similar analogy between anisotropic and isotropic elasticity so that J integral and J-based mutual integral M are expressed in the same complex forms for anisotropic and isotropic materials, when both end points of the integration paths are on the straight interface. The use of J and M integrals together with the present equivalence are exemplified to obtain energy release rate, stress intensity factors, and T-stresses of interfacial cracks lying in the interface of anisotropic/anisotropic, isotropic/isotropic, or anisotropic/isotropic solids.

Measurement of time-dependent adhesion between a polymer film and a flat indenter tip

We revisited an elasticity problem of flat indentation on an elastic film bonded to a rigid substrate and obtained the force–depth relation in a simple form. With the obtained force–depth relation, Kendalls elastic equilibrium theory of adhesion was extended to the adhesion between a flat tip and a compressible elastic film. Thus, the thermodynamic work of adhesion at the moment of debonding of a flat tip from an elastic film was expressed in terms of pull-off force, elastic constants and geometric parameters. It is worth noting that the obtained relation for elastic films is still valid for viscoelastic films if viscoelastic losses are limited to the process zone of debonding. This makes it possible to study the time-dependent adhesion of viscoelastic polymer films. Indentation experiments with a flat diamond tip were performed on SU-8 films, and the results verified that the extended form of Kendalls theory correctly compensates the effect of the finite thickness of the films on the work of adhesion. The indentation results also showed that the work of adhesion is strongly dependent on the unloading velocity of the tip, while indentation depth and dwell time have only minor effects on the work of adhesion.

Strength Design and Minimization of Residual Stresses in Reversible GaAs Wafer Bonding Process

The GaAs wafer bonding process is investigated to reduce the mechanical failures of GaAs wafer based on strength design concept. Three-point bending experiment is performed to measure the fracture strength of GaAs wafer, of which cleavage takes place on (110) plane. We propose a simple method for minimizing the thermal residual stress in a three-layer structure, of which the basic idea is to use an appropriate steady-state temperature gradient to the wafer bonding process. The optimum bonding condition of GaAs/wax/sapphire structure is determined based on the proposed method. The effect of material anisotropy on the thermal residual stress is also analyzed by finite element method.

Measurement of Mechanical Properties and Residual Stresses of Bridged Gold Films and Circular Gold Membranes

In order to measure the mechanical properties of gold films on silicon substrate, two types of specimens, i.e., bridged films and circular membranes, are manufactured. Using a wedge tip, the bridged gold films are indented so that the films are pushed off, which is called as V-peel test. The load-deflection curves obtained by the V-peel test are analyzed with the concept of geometrically nonlinear beam by using the minimum potential energy theory together with Ritz method. Thus, Young’s modulus and residual stress of the bridged gold films are obtained. Blister test is also conducted to measure the Young’s modulus and residual stress of a circular gold membrane, of which deformation is measured by Twyman-Green interferometer. By gradually increasing the external pressure applied on the membrane, the interfacial fracture toughness between the gold membrane and silicon substrate is measured based on the concepts of interfacial fracture mechanics.

Elastic Singularity Interacting With Various Types of Interfaces

The elastic solution for a singularity in an anisotropic trimaterial with perfectly bonded interfaces was obtained in the previous work by Choi and Earmme. The term trimaterial denotes an infinite body composed of three dissimilar materials bonded along two parallel interfaces. It is shown in this paper that when the interfaces of an anisotropic trimaterial are one of the following types: (i) perfectly bonded, (ii) rigid, (iii) separated, (iv) separated without slip, and (v) slipping interfaces, the elastic solution for a singularity in the trimaterial has the same form as that for a singularity in a trimaterial with perfectly bonded interfaces, but with the bimaterial matrices properly altered.