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Multiscale modeling of mechanical shock behavior of environmentally-benign lead-free solders in electronic packaging

Description
With the increasing focus on developing environmentally benign electronic packages, lead-free solder alloys have received a great deal of attention. Mishandling of packages, during manufacture, assembly, or by the user may cause failure of solder joint. A fundamental understanding of the behavior of lead-free solders under mechanical shock conditions is…

With the increasing focus on developing environmentally benign electronic packages, lead-free solder alloys have received a great deal of attention. Mishandling of packages, during manufacture, assembly, or by the user may cause failure of solder joint. A fundamental understanding of the behavior of lead-free solders under mechanical shock conditions is lacking. Reliable experimental and numerical analysis of lead-free solder joints in the intermediate strain rate regime need to be investigated. This dissertation mainly focuses on exploring the mechanical shock behavior of lead-free tin-rich solder alloys via multiscale modeling and numerical simulations. First, the macroscopic stress/strain behaviors of three bulk lead-free tin-rich solders were tested over a range of strain rates from 0.001/s to 30/s. Finite element analysis was conducted to determine appropriate specimen geometry that could reach a homogeneous stress/strain field and a relatively high strain rate. A novel self-consistent true stress correction method is developed to compensate the inaccuracy caused by the triaxial stress state at the post-necking stage. Then the material property of micron-scale intermetallic was examined by micro-compression test. The accuracy of this measure is systematically validated by finite element analysis, and empirical adjustments are provided. Moreover, the interfacial property of the solder/intermetallic interface is investigated, and a continuum traction-separation law of this interface is developed from an atomistic-based cohesive element method. The macroscopic stress/strain relation and microstructural properties are combined together to form a multiscale material behavior via a stochastic approach for both solder and intermetallic. As a result, solder is modeled by porous plasticity with random voids, and intermetallic is characterized as brittle material with random vulnerable region. Thereafter, the porous plasticity fracture of the solders and the brittle fracture of the intermetallics are coupled together in one finite element model. Finally, this study yields a multiscale model to understand and predict the mechanical shock behavior of lead-free tin-rich solder joints. Different fracture patterns are observed for various strain rates and/or intermetallic thicknesses. The predictions have a good agreement with the theory and experiments.
ContributorsFei, Huiyang (Author) / Jiang, Hanqing (Thesis advisor) / Chawla, Nikhilesh (Thesis advisor) / Tasooji, Amaneh (Committee member) / Mobasher, Barzin (Committee member) / Rajan, Subramaniam D. (Committee member) / Arizona State University (Publisher)
Created2011
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Interval timing under a behavioral microscope: dissociating motivational and timing processes in fixed-interval performance

Description
Theories of interval timing have largely focused on accounting for the aggregate properties of behavior engendered by periodic reinforcement, such as sigmoidal psychophysical functions and their scalar property. Many theories of timing also stipulate that timing and motivation are inseparable processes. Such a claim is challenged by fluctuations in and…

Theories of interval timing have largely focused on accounting for the aggregate properties of behavior engendered by periodic reinforcement, such as sigmoidal psychophysical functions and their scalar property. Many theories of timing also stipulate that timing and motivation are inseparable processes. Such a claim is challenged by fluctuations in and out of states of schedule control, making it unclear whether motivation directly affects states related to timing. The present paper seeks to advance our understanding of timing performance by analyzing and comparing the distribution of latencies and inter-response times (IRTs) of rats in two fixed-interval (FI) schedules of food reinforcement (FI 30-s and FI 90-s), and in two levels of food deprivation. Computational modeling revealed that each component was well described by mixture probability distributions embodying two-state Markov chains. Analysis of these models revealed that only a subset of latencies are sensitive to the periodicity of reinforcement, and pre-feeding only reduces the size of this subset. The distribution of IRTs suggests that behavior in FI schedules is organized in bouts that lengthen and ramp up in frequency with proximity to reinforcement. Pre-feeding slowed down the lengthening of bouts and increased the time between bouts. When concatenated, these models adequately reproduced sigmoidal FI response functions. These findings suggest that behavior in FI fluctuates in and out of schedule control; an account of such fluctuation suggests that timing and motivation are dissociable components of FI performance. These mixture-distribution models also provide novel insights on the motivational, associative, and timing processes expressed in FI performance, which need to be accounted for by causal theories of interval timing.
ContributorsDaniels, Carter W (Author) / Sanabria, Federico (Thesis advisor) / Brewer, Gene (Committee member) / Wynne, Clive (Committee member) / Arizona State University (Publisher)
Created2015