Field reliability extrapolations from accelerated tests necessitate simulation of a variety of material behaviors under general loading conditions. The Hierarchical Incremental Single Surface (HiSS) yield function ( Desai, C. S., 2001, Mechanics of Materials and Interfaces: The Disturbed State Concept, CRC Press, Boca Raton, FL. ) has been applied extensively to a wide range of materials, from solders and silicon to ceramics and geotechnical materials, for simulating continuous-yield elastoplastic and elastoviscoplastic behavior. This work presents a continuous-yield function that avoids problems with HiSS for thermal and tensile loading. Validations are presented for eutectic Pb ∕ Sn data of Wang et al. (Wang, Z., Desai, C.S., and Kundu, T., 2001, “Disturbed State Constitutive Modeling and Testing of Joining Materials in Electronic Packaging,” report to NSF for Materials Processing and Manufacturing Division Grant 9812686, University of Arizona, Tucson, AZ ). Limitations on the range of validity of the elastoplastic and the Perzyna elastoviscoplastic formulations are discussed.

Ultrasonic nondestructive inspection of large-diameter pipes is important for health monitoring of ailing infrastructure. Longitudinal stress-corrosion cracks are detected more efficiently by inducing circumferential waves; hence, the study of elastic wave propagation in the circumferential direction in a pipe wall is essential. The current state of knowledge lacks a complete solution of this problem. Only when the pipe material is isotropic a solution of the wave propagation problem in the circumferential direction exists. Ultrasonic inspections of reinforced concrete pipes and pipes retrofitted by fiber composites necessitate the development of a new theoretical solution for elastic wave propagation in anisotropic curved plates in the circumferential direction. Mathematical modeling of the problem to obtain dispersion curves for curved anisotropic plates leads to coupled differential equations. Unlike isotropic materials for which the Stokes-Helmholtz decomposition technique simplifies the problem, in anisotropic case no such general decomposition technique works. These coupled differential equations are solved in this paper. Dispersion curves for anisotropic curved plates of different curvatures have been computed and presented. Some numerical results computed by the new technique have been compared with those available in the literature.

The finite element procedure with the unified disturbed state modeling concept presented in Part I, Basaran et al. (1998), is verified here with respect to laboratory test results for Pb40/Sn60 eutectic solder alloy. This solder alloy is a commonly used interconnection material for surface mount technology packages. It is demonstrated that the proposed procedure provides highly satisfactory correlation with the observed laboratory behavior of materials and with test results for a chip-substrate system simulated in the laboratory.

Accurate prediction of the thermomechanical cyclic behavior of joints and interfaces in semiconductor devices is essential for their reliable design. In order to understand and predict the behavior of such interfaces there is a need for improved and unified constitutive models that can include elastic, inelastic, viscous, and temperature dependent microstructural behavior. Furthermore, such unified material models should be implemented in finite element procedures so as to yield accurate and reliable predictions of stresses, strains, deformations, microcracking, damage, and number of cycles to failure due to thermomechanical loading. The main objective of this paper is to present implementation of such an unified constitutive model in a finite element procedure and its application to typical problems in electronic packaging; details of the constitutive model are given by Desai et al. (1995). Details of the theoretical formulation is presented in this Part 1, while its applications and validations are presented in Part 2, Basaran et al. (1998).

The disturbed state concept (DSC) presented here provides a unified and versatile methodology for constitutive modeling of thermomechanical response of materials and interfaces/joints in electronic chip-substrate systems. It allows for inclusion of such important features as elastic, plastic and creep strains, microcracking and degradation, strengthening, and fatigue failure. It provides the flexibility to adopt different hierarchical versions in the range of simple (e.g., elastic) to sophisticated (thermoviscoplastic with microcracking and damage), depending on the user’s specific need. This paper presents the basic theory and procedures for finding parameters in the model based on laboratory test data and their values for typical solder materials. Validation of the models with respect to laboratory test behavior and different criteria for the identification of cyclic fatigue and failure, including a new criterion based on the DSC and design applications, are presented in the compendium paper (Part II, Desai et al., 1997). Based on these results, the DSC shows excellent potential for unified characterization of the stress-strain-strength and failure behavior of engineering materials in electronic packaging problems.

The constitutive modeling approach based on the disturbed state concept (DSC) described in Part I, provides a unified basis for the characterization of thermomechanical response of materials and joints in electronic chip-substrate systems. Using the material constants given in Part I, the DSC model predictions, obtained by integrating the incremental constitutive equations, are shown here to provide satisfactory backpredietions of stress-strain, fatigue, and failure responses of typical solder materials. The DSC also provides a simple criterion based on the critical disturbance to identify cyclic fatigue failure. Model predictions show good correlation with those from previous models. It is also shown how the DSC model can be used for design applications. Overall, based on Papers I and II, it can be stated that the DSC can provide a new and powerful means to characterize the thermomechanical behavior of materials and joints in a number of problems in electronic packaging.

Traditionally V(z) curves are generated by acoustic microscopes. However, because of the high costs of the commercially available acoustic microscopes, their use is rather limited. In this paper it is shown how V(z) curves, which contain quantitative information about the material under inspection, can be generated using two ultrasonic transducers instead of an acoustic microscope. A theoretical analysis is given to synthesize V(z) curves of orthotropic plates by this technique. A basic mechanics problem of the reflection of plane waves by an orthotropic plate immersed in a fluid is solved for this purpose. Theoretically synthesized V(z) values are compared with experimental results.

A theoretical analysis is carried out to synthesize the V(z) curves of multilayered solids immersed in water. Solid layers attenuate ultrasound and change its phase. A liquid layer may be located in between two solid layers. The goal of this analysis is to avoid the three major simplifying assumptions of the presently available techniques, as paraxial approximation, assumption of perfect reflection and ambiguous pupil function or incident field strength variation in the illuminated region. Presently available techniques developed for conventional acoustic microscopes can avoid some but not all of these assumptions for computing the V(z) curve. In this paper, the analysis is carried out for a spherical cavity lens with a large aperture angle. The V(z) curve for a uniform glass half-space is synthesized analytically and compared with experimental results. Analytical results are also presented for chromium plated glass specimens and biological cells on uniform glass half-space. Such an exact analysis of multilayered specimens is necessary for material science research as well as cell research in biology, because advanced engineering composite materials and biological cells in culture have multiple layers.

Scattering of elastic waves by a subsurface crack in an orthotropic half-space subjected to a surface line load of arbitrary angle of inclination is studied. Green’s functions are developed and used along with the representation theorem to reduce the problem to a set of simultaneous singular integral equations in the Fourier transformed domain. Solution to these equations is then obtained by expanding the unknown crack opening displacement (COD) in terms of Chebyshev polynomials. Numerical results are given for specific examples involving orthotropic materials.

The scattering of elastic waves by a circular crack situated in a transversely isotropic solid is studied here. The axis of material symmetry and the axis of the crack coincides. The incident wave is taken as a plane longitudinal wave propagating perpendicular to the crack surface. A Hankel transform representation of the scattered field is used, and after some manipulations using the boundary conditions this leads to an integral equation over the crack for the displacement jump across the crack. This jump is expanded in a series of Legendre polynomials which fulfill the correct edge condition and the integral equation is projected on the same set of Legendre polynomials. The far field is computed by the stationary phase method. A few numerical computations are carried out for both isotropic and anisotropic solids. Results for the isotropic solid compare favorably with those available in the literature.

In this paper, the dynamic response of delamination cracks in a layered fiber-reinforced composite plate is analytically studied. The plate is subjected to an antiplane loading and its surface response is computed in absence as well as in presence of delaminatioin cracks. To what extent the surface response is influenced by the presence of internal delamination cracks is investigated here. This study is important for nondestructive evaluation of internal damage in composites due to delamination. The problem is formulated in terms of integral equations in frequency domain. These equations are then solved by expanding the unknown crack opening displacement in a complete set of Chebychev’s polynomials, whose coefficients are solved by satisfying the traction-free condition at the crack surface. The time histories are obtained numerically by inverting the spectra via Fast Fourier Transform (FFT) routine. The results show significant influence of delamination crack geometries on the surface response of the plate.

In this paper, the transient response of an interface crack, in a two layered plate subjected to an antiplane stress field, is analytically computed. The problem is formulated in terms of semi-infinite integrals following the technique developed by Neerhoff (1979). It has been shown that the major steps of Neerhoff’s technique, which was originally developed for layered half-spaces, can also be applied to layered plate problems. An improved method for manipulation of semi-infinite singular integrals is also presented here. Finally, the new method is coded in FORTRAN program and numerical results for a sample problem are presented.

The interaction of time harmonic elastic waves with an edge crack in a plate is studied. The crack is assumed to be normal to the plate surface and its depth small compared to plate thickness. Only plane strain deformations are considered. The incident waves are assumed to be either plane body waves (compressional (P) or inplane shear (SV) ) of arbitrary angle of propagation or surface Rayleigh waves propagating at right angles to the crack. For each incident wave type the complete high frequency diffracted field on the plate surface is calculated. Solution is obtained by the application of an asymptotic theory of diffraction. Application to ultrasonic inspection techniques is indicated.