Publications

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Soldered joints can be made with a wide range of base materials and filler metals that allow the assembly to meet its performance and reliability requirements. Structural solder joints have, as their foremost requirement, to provide mechanical attachment between base material structures. The joint is typically subjected to one, or a combination of, three loading configurations: (a) tensile or compressive force, (b) shear force, or (c) peel force. Solder filler metals and in particular, the so-called “soft solders” based on tin (Sn), lead (Pb), and indium (In), generally have a bulk strength that is less than that of the base materials. Finally, deformation occurs largely in the solder when the joint is subjected to an applied force.

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Ceramic to metal brazing is a common bonding process usedin many advanced systems such as automotive engines, aircraftengines, and electronics. In this study, we use optimizationtechniques and finite element analysis utilizing viscoplastic andthermo-elastic material models to find an optimum thermalprofile for a Kovar® washer bonded to an alumina button that istypical of a tension pull test. Several active braze filler materialsare included in this work. Cooling rates, annealing times, aging,and thermal profile shapes are related to specific materialbehaviors. Viscoplastic material models are used to represent thecreep and plasticity behavior in the Kovar® and braze materialswhile a thermo-elastic material model is used on the alumina.The Kovar® is particularly interesting because it has a Curiepoint at 435°C that creates a nonlinearity in its thermal strain andstiffness profiles. This complex behavior incentivizes theoptimizer to maximize the stress above the Curie point with afast cooling rate and then favors slow cooling rates below theCurie point to anneal the material. It is assumed that if failureoccurs in these joints, it will occur in the ceramic material.Consequently, the maximum principle stress of the ceramic isminimized in the objective function. Specific details of the stressstate are considered and discussed.

Ceramic to metal brazing is a common bonding process usedin many advanced systems such as automotive engines, aircraftengines, and electronics. In this study, we use optimizationtechniques and finite element analysis utilizing viscoplastic andthermo-elastic material models to find an optimum thermalprofile for a Kovar® washer bonded to an alumina button that istypical of a tension pull test. Several active braze filler materialsare included in this work. Cooling rates, annealing times, aging,and thermal profile shapes are related to specific materialbehaviors. Viscoplastic material models are used to represent thecreep and plasticity behavior in the Kovar® and braze materialswhile a thermo-elastic material model is used on the alumina.The Kovar® is particularly interesting because it has a Curiepoint at 435°C that creates a nonlinearity in its thermal strain andstiffness profiles. This complex behavior incentivizes theoptimizer to maximize the stress above the Curie point with afast cooling rate and then favors slow cooling rates below theCurie point to anneal the material. It is assumed that if failureoccurs in these joints, it will occur in the ceramic material.Consequently, the maximum principle stress of the ceramic isminimized in the objective function. Specific details of the stressstate are considered and discussed.

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Experiments were performed to characterize the mechanical response of a 15 pcf flexible polyurethane foam to large deformation at different strain rates and temperatures. Results from these experiments indicated that at room temperature, flexible polyurethane foams exhibit significant nonlinear elastic deformation and nearly return to their original undeformed shape when unloaded. However, when these foams are cooled to temperatures below their glass transition temperature of approximately -35 o C, they behave like rigid polyurethane foams and exhibit significant permanent deformation when compressed. Thus, a new model which captures this dramatic change in behavior with temperature was developed and implemented into SIERRA with the name Flex_Foam to describe the mechanical response of both flexible and rigid foams to large deformation at a variety of temperatures and strain rates. This report includes a description of recent experiments. Next, development of the Flex Foam model for flexible polyurethane and other flexible foams is described. Selection of material parameters are discussed and finite element simulations with the new Flex Foam model are compared with experimental results to show behavior that can be captured with this new model.

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Ductile failure of structural metals is relevant to a wide range of engineering scenarios. Computational methods are employed to anticipate the critical conditions of failure, yet they sometimes provide inaccurate and misleading predictions. Challenge scenarios, such as the one presented in the current work, provide an opportunity to assess the blind, quantitative predictive ability of simulation methods against a previously unseen failure problem. Rather than evaluate the predictions of a single simulation approach, the Sandia Fracture Challenge relies on numerous volunteer teams with expertise in computational mechanics to apply a broad range of computational methods, numerical algorithms, and constitutive models to the challenge. This exercise is intended to evaluate the state of health of technologies available for failure prediction. In the first Sandia Fracture Challenge, a wide range of issues were raised in ductile failure modeling, including a lack of consistency in failure models, the importance of shear calibration data, and difficulties in quantifying the uncertainty of prediction [see Boyce et al. (Int J Fract 186:5–68, 2014) for details of these observations]. This second Sandia Fracture Challenge investigated the ductile rupture of a Ti–6Al–4V sheet under both quasi-static and modest-rate dynamic loading (failure in (Formula presented.) 0.1 s). Like the previous challenge, the sheet had an unusual arrangement of notches and holes that added geometric complexity and fostered a competition between tensile- and shear-dominated failure modes. The teams were asked to predict the fracture path and quantitative far-field failure metrics such as the peak force and displacement to cause crack initiation. Fourteen teams contributed blind predictions, and the experimental outcomes were quantified in three independent test labs. Additional shortcomings were revealed in this second challenge such as inconsistency in the application of appropriate boundary conditions, need for a thermomechanical treatment of the heat generation in the dynamic loading condition, and further difficulties in model calibration based on limited real-world engineering data. As with the prior challenge, this work not only documents the ‘state-of-the-art’ in computational failure prediction of ductile tearing scenarios, but also provides a detailed dataset for non-blind assessment of alternative methods.

Predictions for ductile tearing of a geometrically complex Ti-6Al-4V plate were generated using a Unified Creep Plasticity Damage model in fully coupled thermal stress simulations. Uniaxial tension and butterfly shear tests performed at displacement rates of 0.0254 and 25.4 mm/s were also simulated. Results from these simulations revealed that the material temperature increase due to plastic work can have a dramatic effect on material ductility predictions in materials that exhibit little strain hardening. Furthermore, this occurs because the temperature increase causes the apparent hardening of the material to decrease which leads to the initiation of deformation localization and subsequent ductile tearing earlier in the loading process.

Experiments were performed to characterize the mechanical response of several different rigid polyurethane foams to large deformation. In these experiments, the effects of load path, loading rate, and temperature were investigated. Results from these experiments indicated that rigid polyurethane foams exhibit significant damage, volumetric and deviatoric plasticity when they are compressed. Rigid polyurethane foams were also found to be extremely strain-rate and temperature dependent. These foams are also rather brittle and crack when loaded to small strains in tension or to larger strains in compression. Thus, a phenomenological Unified Creep Plasticity Damage (UCPD) model was developed to describe the mechanical response of these foams to large deformation at a variety of temperatures and strain rates. This paper includes a description of recent experiments and experimental findings. Next, development of a UCPD model for rigid, polyurethane foams is described. Finite element simulations with the new UCPD model are compared with experimental results to show behavior that can be captured with this model.

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Tin (Sn) whiskers are not a recent development. Studies in the late 1930’s investigated thin filaments that grew spontaneously from Sn coatings used for the corrosion protection of electronic hardware. It was soon recognized that these Sn filaments, or whiskers, could create short circuits in the same electronic equipment. Figure 1a illustrates whisker growth in the hole of a printed circuit board having an immersion Sn surface finish. The engineering solution was to contaminate the Sn with > 3 wt.% of lead (Pb). The result was that whisker growth was replaced with hillock formation (Fig. 1b) that posed a minimal reliability concern to electrical circuits. Today, Pb-containing finishes are being replaced with pure Sn coatings to meet environmental restrictions on Pb use. The same short-circuit concerns have been raised, once again, with respect to Sn whiskers.

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Tin (Sn) whiskers are not a recent development. Studies in the late 1930’s investigated thin filaments that grew spontaneously from Sn coatings used for the corrosion protection of electronic hardware. It was soon recognized that these Sn filaments,or whiskers, could create short circuits in the same electronic equipment. Figure 1a illustrates whisker growth in the hole of a printed circuit board having an immersion Sn surface finish. The engineering solution was to contaminate the Sn with > 3wt.% of lead (Pb). The result was that whisker growth was replaced with hillock formation (Fig. 1b) that posed a minimal reliability concernto electrical circuits. Today, Pb-containing finishes are being replaced with pure Sn coatings to meet environmental restrictions on Pb use. The same short-circuit concerns have been raised, once again, with respect to Sn whiskers. The present authors have taken the approach that, in order to develop more widely applicable, first-principles strategies to mitigate Sn whisker formation, it is necessary to understand the fundamental mechanism(s) and rate kinetics underlying their development. Numerous mechanisms have been proposed by other authors to describe whisker growth, including static recrystallization by Boguslavsky and Bush.

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Numerous experiments were performed to characterize the mechanical response of several different rigid polyurethane foams (FR3712, PMDI10, PMDI20, and TufFoam35) to large deformation. In these experiments, the effects of load path, loading rate, and temperature were investigated. Results from these experiments indicated that rigid polyurethane foams exhibit significant volumetric and deviatoric plasticity when they are compressed. Rigid polyurethane foams were also found to be very strain-rate and temperature dependent. These foams are also rather brittle and crack when loaded to small strains in tension or to larger strains in compression. Thus, a new Unified Creep Plasticity Damage (UCPD) model was developed and implemented into SIERRA with the name Foam Damage to describe the mechanical response of these foams to large deformation at a variety of temperatures and strain rates. This report includes a description of recent experiments and experimental findings. Next, development of a UCPD model for rigid, polyurethane foams is described. Selection of material parameters for a variety of rigid polyurethane foams is then discussed and finite element simulations with the new UCPD model are compared with experimental results to show behavior that can be captured with this model.

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Our study was performed to validate a first-principles model for whisker and hillock formation based on the cyclic dynamic recrystallization (DRX) mechanism in conjunction with long-range diffusion. The test specimens were evaporated Sn films on Si having thicknesses of 0.25 μm, 0.50 μm, 1.0 μm, 2.0 μm, and 4.9 μm. Air annealing was performed at 35°C, 60°C, 100°C, 120°C, or 150°C over a time duration of 9 days. The stresses, anelastic strains, and strain rates in the Sn films were predicted by a computational model based upon the constitutive properties of 95.5Sn-3.9Ag-0.6Cu (wt.%) as a surrogate for pure Sn. The cyclic DRX mechanism and, in particular, whether long whiskers or hillocks were formed, was validated by comparing the empirical data against the three hierarchal requirements: (1) DRX to occur at all: εc = A D o m Z n , (2) DRX to be cyclic: D o < 2D r, and (3) Grain boundary pinning (thin films): h versus d. Continuous DRX took place in the 2.0-μm and 4.9-μm films that resulted in short stubby whiskers. Depleted zones, which resulted solely from a tensile stress-driven diffusion mechanism, confirmed the pervasiveness of long-range diffusion so that it did not control whisker or hillock formation other than a small loss of activity by reduced thermal activation at lower temperatures. Furthermore, a first-principles DRX model paves the way to develop like mitigation strategies against long whisker growth.

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A unified creep plasticity damage (UCPD) model for eutectic Sn-Pb and Pb-free solders was developed and implemented into finite element analysis codes. The new model will be described along with the relationship between the model's damage evolution equation and an empirical Coffin-Manson relationship for solder fatigue. Next, developments needed to model crack initiation and growth in solder joints will be described. Finally, experimentally observed cracks in typical solder joints subjected to thermal mechanical fatigue are compared with model predictions. Finite element based modeling is particularly suited for predicting solder joint fatigue of advanced electronics packaging, e.g. package-on-package (PoP), because it allows for evaluation of a variety of package materials and geometries.

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Predictions for the Sandia National Laboratories fracture challenge (Boyce et al. in Int J Fract 2013) were generated using a transient dynamic finite element code with a multi-linear elastic plastic failure model developed by Wellman (Simple approach to modeling ductile failure. Sandia National Laboratories, Albuquerque 2012). This model is a conventional, rate independent, von Mises plasticity model for metals with user-prescribed hardening as a function of equivalent plastic strain. In addition to conventional plasticity, this model has empirical criteria for crack initiation and growth. Ductile tearing predictions generated with this model were found to be in good agreement with experimental measurements and observations. © 2013 Springer Science+Business Media Dordrecht (outside the USA).

A unified creep plasticity damage (UCPD) model for Sn-Pb and Pb-free solders was developed and implemented into finite element analysis codes. The new model will be described along with the relationship between the model's damage evolution equation and an empirical Coffin-Manson relationship for solder fatigue. Next, developments needed to model crack initiation and growth in solder joints will be described. Finally, experimentally observed cracks in typical solder joints subjected to thermal mechanical fatigue are compared with model predictions. Finite element based modeling is particularly suited for predicting solder joint fatigue of advanced electronics packaging, e.g. package-on-package (PoP), because it allows for evaluation of a variety of package materials and geometries. Copyright © 2013 by ASME.

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Decisions on material selections for electronics packaging can be quite complicated by the need to balance the criteria to withstand severe impacts yet survive deep thermal cycles intact. Many times, material choices are based on historical precedence perhaps ignorant of whether those initial choices were carefully investigated or whether the requirements on the new component match those of previous units. The goal of this program focuses on developing both increased intuition for generic packaging guidelines and computational methodologies for optimizing packaging in specific components. Initial efforts centered on characterization of classes of materials common to packaging strategies and computational analyses of stresses generated during thermal cycling to identify strengths and weaknesses of various material choices. Future studies will analyze the same example problems incorporating the effects of curing stresses as needed and analyzing dynamic loadings to compare trends with the quasi-static conclusions.

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A unified creep plasticity damage (UCPD) model for Sn-Pb and Pb-free solders was developed and implemented into finite element analysis codes. The new model will be described along with the relationship between the model's damage evolution equation and an empirical Coffin-Manson relationship for solder fatigue. Next, two significant developments were needed to model crack initiation and growth in solder joints. First, an ability to accelerate the simulations such that the effects of hundreds or thousands of thermal cycles could be modeled in a reasonable amount of time was needed. This was accomplished by applying a user prescribed acceleration factor to the damage evolution; then, damage generated by an acceleration factor of cycles could be captured by the numerical simulation of a single thermal cycle. Second, an ability to capture the geometric effects of crack initiation and growth was needed. This was accomplished by replacing material in finite elements that had met the cracking failure criterion with very flexible elastic material. This diffuse crack modeling approach with local finite elements is known to generate mesh dependent solutions. However, introduction of an element size dependent term into the damage evolution equation was found to be effective in controlling mesh dependency. Finally, experimentally observed cracks in a typical solder joint subjected to thermal mechanical fatigue are compared with model predictions. Copyright © 2011 by ASME.

A unified creep plasticity damage (UCPD) model for Sn-Pb and Pb-free solders was developed and implemented into finite element analysis codes. The new model will be described along with the relationship between the model's damage evolution equation and an empirical Coffin-Manson relationship for solder fatigue. Next, two significant developments were needed to model crack initiation and growth in solder joints. First, an ability to accelerate the simulations such that the effects of hundreds or thousands of thermal cycles could be modeled in a reasonable amount of time was needed. This was accomplished by applying a user prescribed acceleration factor to the damage evolution; then, damage generated by an acceleration factor of cycles could be captured by the numerical simulation of a single thermal cycle. Second, an ability to capture the geometric effects of crack initiation and growth was needed. This was accomplished by replacing material in finite elements that had met the cracking failure criterion with very flexible elastic material. This diffuse crack modeling approach with local finite elements is known to generate mesh dependent solutions. However, introduction of an element size dependent term into the damage evolution equation was found to be effective in controlling mesh dependency. Finally, experimentally observed cracks in a typical solder joint subjected to thermal mechanical fatigue are compared with model predictions. Copyright © 2011 by ASME.

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