Summaries of the 1995 Outstanding Graduate and Undergraduate Papers

Prediction of Two-Phase Creep Behavior from Constituent Phase Behaviors in the Bi-Sn System

The eutectic Bi-42Sn alloy is attractive for soldering the growing number of temperature-sensitive electronic assemblies, for use in step soldering and, from an environmental standpoint, to replace lead-containing alloys. An accurate phenomenological description of the time-dependent deformation behavior of this key Bi-Sn solder alloy is the first step to understanding and predicting the thermal fatigue process assumed to be life-limiting in most electronics packages. This study focuses on determining the sources of the three regions of stress dependence by examining the creep behaviors of the individual tin and bismuth phases through the continuum mechanics creep model of Tanaka et al.

Essentially pure 99.99 wt.% tin and 99.999 wt.% bismuth were used to produce all alloys. Creep tests were performed at 120deg.C and at constant applied load at low straining rates. A single sample was used to collect data at various stresses at a single temperature; tests were run in order of increasing load. For constant displacement rate tests, a single sample was used for each test. To determine the effects of Bi-Sn eutectic morphology on the transient and steady-state creep behavior, the creep behavior of as-quenched samples was compared to that of samples quenched and aged at 120deg.C for 22 days. On some samples, a facet was polished into the gage section prior to testing to later observe the effects of creep on the surface structure of the sample.

The study explained the sigmoidal shape of the steady-state creep rate versus stress curve of the Bi-Sn eutectic alloy. At low stress (<3 MPa) in the Bi-42Sn eutectic alloy, the pure bismuth phase is load carrying, has a high stress exponent, and dominates the behavior exhibited by the alloy. At higher stresses, the exponential stress dependence of the tin-rich phases dominates the behavior, yielding an initially low stress exponent at intermediate stresses and increasing at higher stresses. The model also predicts normal transient strain behavior at all stresses.

Experimental results differed from model predictions in that age-coarsened Bi-42Sn creeps more rapidly than unaged alloy. This is explained in terms of the increasing amount of Sn-Sn and Bi-Sn boundary sliding absent in the unaged material (Figure A). Coarsening results in a tin-rich matrix phases and an increased amount of Bi-Sn and Sn-Sn boundary sliding, whereas, in the as-quenched state, the bismuth is the more continuous phase and no Bi-Bi sliding was observed.

--Dave Mitlin

Temporal Instabilities and Dissipative Structures in Fatigued Metals

Our obvious inability to treat instabilities in fatigue from the atomistic point of view resulted in an attempt to find a nontraditional approach to the problem. In this paper, the methods of self-organization theory and nonlinear dynamics are applied to the study of the Portevin-Le-Chatelier (PLC) effect in cyclically deformed (fatigued) metals. The main goal of this paper is to establish, via nonlinear dynamical modeling, the fundamental connection between microscopic dislocation mechanisms and the macroscopic mechanical response of cyclically deformed metallic alloys.

The experimental data on temporal patterning and the PLC effect were reviewed. Well-understood reactions between populations of dislocations and the assumption of homogeneous yielding were used to develop a mathematical model consisting of a system of nonlinear ordinary differential equations. A modified nonlinear model containing four equations proposed by Ananthakrishna et al. was used to describe the Yan-Hong-Laird bursts and the Neumann bursts. However, two modifications were introduced into the linear stability analysis because steady-state solutions do not exist for cyclic loading. Also, the 4th order Rosebrock algorithm with an automatically adjustable time step was used.

The study began by applying pure sinusoidal loading with various forcing frequencies and amplitudes to find a set of forcing parameters that qualitatively reproduced the phenomena observed in the experiment. The first three periods of a creep fatigue solution are shown in Figure B. A comparison of the stress curve to the mobile dislocation density curve shows a clear correspondence of peaks in dislocation density and peaks in stress; when stress goes down, the immobilized dislocations break free from the atmospheres of point defects and the mobile dislocation density undergoes a dramatic increase.

An attempt was also made to reproduce the Neumann bursts in a ramp-loaded metallic system. The bursts occur during the gradual increase of the stress amplitude from zero; the dislocation density bursts obtained in numerical simulations correlate to the characteristic stress-strain response observed in the experiment.

In conclusion, this modelling work reproduced and explained the experimentally observed stress serrations under pure harmonic loading, creep fatigue, and ramp loading, thus establishing the fundamental connection between the micro- and macromechanics of cyclic deformation.

--Michael Glazov