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This study explores the possibility of using a unified theory of creep-fatigue, similar to the Halford-Manson strain-range partitioning method, for examining the effect of cyclic temperature range on fatigue life, over a wide range of temperatures. Other investigators have attempted similar techniques before for solder fatigue analysis. The present study is different since it proposes an energy-partitioning technique rather than strain-partitioning to examine the dependence of solder fatigue behavior on temperature dependent changes in the relative amounts of plastic and creep strains. The solder microstructure also dictates creep behavior but is assumed to be a given invariant parameter in this study. In other words, this study is targeted at as-cast microstructures and does not address post-recrystallization behavior. A sample solder joint of axisymmetric configuration, commonly found in leaded through-hole mounting technology, is analyzed with the help of nonlinear finite element methods. The strain history is determined for constant-amplitude temperature cycling with linear loading and unloading, and with constant dwells at upper and lower ends of the cycle. Large-deformation continuum formulations are utilized in conjunction with a viscoplastic constitutive model for the solder creep-plasticity behavior. Relevant material properties are obtained from experimental data in the literature. The results show significant amounts of rachetting and shakedown in the solder joint. Detailed stress-strain histories are presented, illustrating the strain amplitude, mean strain and residual stresses and strains. For illustrative purposes, the hysteresis cycles are partitioned into elastic, plastic and creep components. Such partitioned histories are essential in order to implement either the Halford-Manson strain-range partitioning technique or the energy-based approach suggested here, for analyzing the creep-fatigue damage accumulation in solder material. This study also illustrates the role and utility of the finite element method in generating the detailed stress-strain histories necessary for implementing the energy partitioning approach for creep-fatigue damage evaluation. Solder life prediction is presented as a function of cyclic temperature range at a given mean temperature.

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This article presents a new application of two-scale asymptotic homogeni zation schemes to predict the orthotropic thermal conductivity of plain-weave fabric rein forced composite laminates. A unit-cell, enclosing the characteristic periodic repeat pat tern in the fabric weave, is isolated and modeled. A new three-dimensional series-parallel thermal resistance network is developed to solve a steady-state heat transfer boundary value problem (BVP) for this unit-cell. Laminate effective orthotropic thermal conduc tivities are obtained analytically and numerically as functions of (1) thermal conductivity of the constituent materials, (2) fiber volume fraction, and (3) weave style. The analyti cally predicted thermal conductivity values are compared with numerical finite element predictions, with existing models in the literature and with experimentally obtained values.

Carbon nanotube (CNT) based binder-free, syringe-printable inks, with graphene oxide being used as dispersants, have been designed and developed based on the unique ellipsoidal-particle-shape-mediated arrest of the coffee-stain effect.

The combined effects of elastic and inelastic strains on solder joint reliability are investigated. Experimental data from high-cycle fatigue tests of solder are combined with data from low-cycle fatigue tests to obtain a plot of total strain amplitude against cycles to failure. The generalized Coffin-Manson fatigue equation is used to describe this relationship. The transition fatigue life of approximately 7000 cycles indicates that elastic strains play a significant role in the fatigue damage of solders at a life of 103 cycles or higher. The results suggest that the commonly adopted approach of relating only inelastic strain, or the total strain, to fatigue life with a single power law relationship may be inadequate when predicting solder joint reliability. Instead, both elastic strains and plastic strains should be considered, especially when the electronic assembly is subjected to a combination of large amplitude thermal loads and relatively lower amplitude vibrational loads. A methodology is presented to evaluate the combined effects of simultaneous vibration and thermal cycling of solder joints. This combined loading situation is simulated by superposing the effects of the vibrational and thermal loads. The damage due to each load-type acting individually is determined and then superposed to assess the overall effective fatigue life of the joint. As a first order approximation, a linear superposition rule is utilized, Miner’s rule. Reliability predictions from this simple superposition model are then compared to standard low cycle thermal fatigue models.