Ganesh Subbarayan

Constitutive Behavior of Sn3.8Ag0.7Cu and Sn1.0Ag0.5Cu Alloys at Creep and Low Strain Rate Regimes

Constitutive models for SnAgCu solder alloys are of great interest at the present. Commonly, constitutive models that have been successfully used in the past for Sn-Pb solders are used to describe the behavior of SnAgCu solder alloys. Two issues in the modeling of lead-free solders demand careful attention: 1) Lead-free solders show significantly different creep strain evolution with time, stress and temperature, and the assumption of evolution to steady state creep nearly instantaneously may not be valid in SnAgCu alloys and 2) Models derived from bulk sample test data may not be reliable when predicting deformation behavior at the solder interconnection level for lead-free solders due to the differences in the inherent microstructures at these different scales. In addition, the building of valid constitutive models from test data derived from tests on solder joints must de-convolute the effects of joint geometry and its influence on stress heterogeneity. Such issues have often received insufficient attention in prior constitutive modeling efforts. In this study all of the above issues are addressed in developing constitutive models of Sn3.8Ag0.7Cu and Sn1.0Ag0.5Cu solder alloys, which represent the extremes of Ag composition that have been mooted at the present time. The results of monotonic testing are reported for strain rates ranging from 4.02E-6 to 2.40E-3 s-1. The creep behavior at stress levels ranging from 7.8 to 52 MPa is also described. Both types of tests were performed at temperatures of 25degC, 75degC and 125degC. The popular Anand model and the classical time-hardening creep model are fit to the data, and the experimentally obtained model parameters are reported. The test data are compared against other reported data in the literature and conclusions are drawn on the plausible sources of error in the data reported in the prior literature.

Constitutive and Aging Behavior of Sn3.0Ag0.5Cu Solder Alloy

We describe double-lap shear experiments on Sn3.0Ag0.5Cu solder alloy, from which fits to Anands viscoplastic constitutive model, power-law creep model, and to time-hardening primary-secondary creep model are derived. Results of monotonic tests for strain rates ranging from 4.02E-6 to 2.40E-3 s-1, and creep response at stress levels ranging from 19.5 to 45.6 MPa are reported. Both types of tests were conducted at temperatures of 25degC, 75degC , and 125degC. Following an earlier study where Anand model and time hardening creep parameters for Sn3.8Ag0.7Cu and Sn1.0Ag0.5Cu solder alloys were reported, here we report power law model parameters so as to enable a comparison between all three alloys. Primary creep in Sn3.0Ag0.5Cu solder alloy is shown to be significant and are considered in addition to secondary creep and monotonic behavior. Aging influence on behavior is also shown to be significant. On the basis of experimental data, the following four aspects are discussed: 1) difference between testing on bulk versus joint specimen; 2) consistency between the creep and monotonic behaviors; 3) comparison against behaviors of Sn1.0Ag0.5Cu and Sn3.8Ag0.7Cu alloys as well as aganist Sn40Pb, 62Sn36Pb2Ag and 96.5Sn3.5Ag alloys; and 4) comparison of Sn3.0Ag0.5Cu and Sn3.8Ag0.7Cu relative to their aging response.

Constructive solid analysis: a hierarchical, geometry-based meshless analysis procedure for integrated design and analysis

Abstract In this paper, we propose an analysis methodology that is procedurally analogous to Constructive Solid Geometry (CSG) integrating design and analysis, and thereby enabling efficient optimal design. The procedure, due to its analogous nature to CSG, is termed Constructive Solid Analysis (CSA). The analysis methodology is partitioned, hierarchical and is based on constructing the boundary value problem for a compound geometry through operations on the field quantities defined on the primitives. Although the CSA procedure will allow any basis for approximating the fields, Non-Uniform Rational B-Splines (NURBS), currently popular in the geometric modeling literature, are used to represent the geometry of the primitives as well as the analysis fields. The use of the same basis to represent geometry and analysis fields enables ‘representational’ integration, and further, the developed methodology may be classified as a partition of unity meshless analysis scheme. A more general null-space solution scheme and a somewhat restrictive range-space solution scheme are outlined to solve the discretized equations resulting from the use of NURBS. Several representative problems from the field of linear elasticity are solved to demonstrate the validity of the procedure and to evaluate its computational cost relative to the finite element method. The optimal orientation of an elliptical hole to applied tractions is determined to demonstrate the power of the proposed methodology for shape optimal design.

An evaluation of back-propagation neural networks for the optimal design of structural systems: Part I. Training procedures

Design optimization using approximations based on feed-forward back-propagation neural network is the topic of much recent research. The neural network schemes that have been proposed in the literature for optimal design of structural systems differ in their architecture and training procedures. Furthermore, their utility vis-a-vis classical optimization techniques is not always clear. A systematic comparison of the efficiency and accuracy of the neural network-based solution schemes to classical structural optimization techniques is the aim of this and the companion paper. In this paper, the neural network training procedures used in the present evaluation are described in detail. When using first-order nonlinear programming algorithms with neural networks, the ability to approximate derivatives is important. Therefore, mainly for completeness of evaluation, two new training methods that use the derivative information are proposed in addition to the now common function-based training method. The first method uses the derivatives to create additional training points in the vicinity of the original points, based on Taylors series expansion. The second method attempts to minimize the error in derivatives while imposing the error in output functions as constraint. Expressions for analytical derivatives are derived for both function-based and derivative-based training. Significant savings in computational time are reported when calculating derivatives using built-in analytical derivatives instead of using finite difference derivatives. In the companion paper the proposed methods are applied to solve five optimization problems with varying degree of complexity. Approximately 1100 test cases are executed in the companion paper to compare the accuracy and efficiency of neural network-based optimization with the classical approaches.

High Resolution Characterization of Materials Used in Packages Through Digital Image Correlation

In this study, we demonstrate a simple, full field displacement characterization technique based on digital image correlation (DIC). We develop a robust correlation measure implemented in a code and use it to characterize materials at high spatial and displacement resolution. We describe the methods implemented in the DIC code and compare against those available in the literature. We show how sample preparation may be entirely eliminated by using the natural speckle inherent in specular (rough) surfaces. We demonstrate further that the use of natural speckle enables very high spatial resolution (100 microns or less) since creating artificial speckle patterns in miscroscale spatial regions is a significant challenge. The software is also designed to be robust to varying contrasts between the deformed and the undeformed images. Its accuracy is enhanced by using NURBS (Non-Uniform Rational B-Spline) as the interpolating function in the code. We demonstrate the developed software and the underlying procedure on several packaging problems of interest. We measure the CTE of Alumina (Al2O3) using its natural speckle, we calculate the strain and therefore the modulus during mechanical testing of composite materials and we characterize the time dependent behavior of a micro-fiber reinforced composite (RT/Duroid) at high temperature.Copyright

An evaluation of back-propagation neural networks for the optimal design of structural systems: Part II. Numerical evaluation

Abstract In the companion paper the neural network training procedures used in the present evaluation were described in detail. Also, in the companion paper, two new training methods that used the derivative information to build global approximations, and a mixed local-global approximation scheme were proposed in addition to the common function-based training method. In this paper, we carry out an exhaustive numerical evaluation of the proposed and existing methods using five test problems with varying complexity. Approximately 1100 test cases were run as part of the numerical evaluations. First, the efficiency of three different optimization algorithms used for training including a sequential quadratic programming algorithm, a Levenberg–Marquardt algorithm and a genetic algorithm is evaluated. The developed training schemes were next evaluated by comparing with the classical structural optimization methods. The two new derivative-based training methods were found to be more accurate but less efficient than function-based training. Further, compared with classical structural optimization by non-linear programming algorithms, including design sensitivity analysis, global approximation and mixed local-global approximation using neural networks were found to be far less efficient. With careful training, the neural networks were found capable of predicting the exact solution, but this ability depended considerably on the complexity of the original problem. In general, the accuracy of the network, which is a function of the training effort, suffered considerably in large problems. The most surprising observation of the present study was that the training process required over 90% of the total solution time, even when considerable effort was exercised at using the most efficient training procedure. As expected, the use of neural network approximations (once training was complete) speeded up the optimal design process significantly.

Predictive reliability models through validated correlation between power cycling and thermal cycling accelerated life tests

Aims to show that with careful modelling, the fatigue life of solder joints of identical geometry and microstructure can be predicted very accurately (through empirical correlations) under different environmental test or field use conditions. Here, on the TI 144 chip ‐scale package, the empirical correlation for fatigue life developed under thermal cycling conditions is used to predict the life under power cycling. This accurate model has served as the physical basis which in to demonstrate quantitatively the equivalence of thermal cycling and power cycling as valid accelerated life tests. Describes the great importance of spatial refinement, temporal refinement, and accurate boundary conditions, including the often ignored natural convection boundary conditions, and their effect on predicted life.

An Efficient Network Model for Determining the Effective Thermal Conductivity of Particulate Thermal Interface Materials

Particulate composites are commonly used in microelectronics applications. One example of such materials is thermal interface materials (TIMs) that are used to reduce the contact resistance between the chip and the heat sink. The existing analytical descriptions of thermal transport in particulate systems do not accurately account for the effect of interparticle interactions, especially in the intermediate volume fractions of 30%-80%. Another crucial drawback in the existing analytical as well as the network models is the inability to model size distributions (typically bimodal) of the filler material particles that are obtained as a result of the material manufacturing process. While full-field simulations (using, for instance, the finite element method) are possible for such systems, they are computationally expensive. In the present paper, we develop an efficient network model that captures the physics of interparticle interactions and allows for random size distributions. Twenty random microstructural arrangements each of Alumina as well as Silver particles in Silicone and Epoxy matrices were generated using an algorithm implemented using a Java language code. The microstructures were evaluated through both full-field simulations as well as the network model. The full-field simulations were carried out using a novel meshless analysis technique developed in the authors (GS) research [26]. In all cases, it is shown that the random network models are accurate to within 5% of the full field simulations. The random network model simulations were efficient since they required two orders of magnitude smaller computation time to complete in comparison to the full field simulation.

NURBS-based solutions to inverse boundary problems in droplet shape prediction

Abstract Inverse boundary problems are common in many areas of engineering. They arise in fluidstatics when liquid droplets are constrained between arbitrarily shaped solid surfaces, as when a molten solder droplet is used to assemble microelectronic devices. In this paper, we present a new method based on the Non-Uniform Rational B-Spline (NURBS) representation for solving the inverse problems arising in three-dimensional (3D) droplet shape prediction. The developed algorithm very naturally handles the contact (wetting) between the solid and liquid surfaces, without the need for additional contact detection schemes, by embedding a single parameter curve within the two parameter solid surface. An adaptive Legendre–Gauss integration method is used on the NURBS surfaces to calculate the potential energy of the system, thereby eliminating the need for mesh generation. Three problems motivated by microelectronics are solved to demonstrate the developed methodology: solder joints with circular and square pad shapes (with and without misalignment), and one where the droplet is constrained between a circular pad and a cylindrical surface. The meshless procedure developed here is expected to have wider applications to the iterative optimal design of engineering systems where mesh generation inhibits the automation of the design process.

Microstructurally Adaptive Model for Primary and Secondary Creep of Sn-Ag-Based Solders

Sn-Ag-based solders are susceptible to appreciable microstructural coarsening due to the combined effect of thermal and mechanical stimuli during service and storage. This results in evolution of the creep properties of the solder over time, necessitating the development of a thermo-mechanical history-dependent creep model for accurate prediction of the long-term reliability of microelectronic solder joints. In this paper, the coarsening behavior of Ag3Sn and Cu6Sn5 precipitates in ball grid array-sized joints of Sn-3.8Ag-0.7Cu solder attached to Ni bond-pads with four different thermo-mechanical histories is reported. Because of the substantial numerical superiority of Ag3Sn over Cu6Sn5, it was inferred that the evolution of mechanical properties during aging is controlled largely by the coarsening of Ag3Sn. An effective diffusion length (x̅) for Ag diffusion in Sn was defined, and it is shown to adequately describe the thermo-mechanical history dependence of Ag3Sn particle size. The shear creep behavior of these joints was experimentally characterized, and the entire creep data were fitted to a unified model combining exponential primary creep and power-law steady state creep. The parameter x̅ was then incorporated into the creep equation to produce a unified creep model, which can adapt to thermo-mechanical history-dependent microstructural coarsening in the solder. Predictions using this creep law show very good agreement with experimental creep data for several different test and microstructural conditions.