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.
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.
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.
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. 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.
A 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 Do mZn, (2) DRX to be cyclic: Do < 2Dr, 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. A first-principles DRX model paves the way to develop like mitigation strategies against long whisker growth.
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.
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.
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.
A unified creep plasticity damage (UCPD) model for Sn-Pb solder is developed in this paper. Stephens and Frear (1999) studied the creep behavior of near-eutectic 60Sn-40Pb solder subjected to low strain rates and found that the inelastic (creep and plastic) strain rate could be accurately described using a hyperbolic Sine function of the applied effective stress. A recently developed high-rate servo-hydraulic method was employed to characterize the temperature and strain-rate dependent stress-strain behavior of eutectic Sn-Pb solder over a wide range of strain rates (10{sup -4} to 10{sup 2} per second). The steady state inelastic strain rate data from these latest experiments were also accurately captured by the hyperbolic Sine equation developed by Stephens and Frear. Thus, this equation was used as the basis for the UCPD model for Sn-Pb solder developed in this paper. Stephens, J.J., and Frear, D.R., Metallurgical and Materials Transactions A, Volume 30A, pp. 1301-1313, May 1999.
Legislated requirements and industry standards are replacing eutectic lead-tin (Pb-Sn) solders with lead-free (Pb-free) solders in future component designs and in replacements and retrofits. Since Pb-free solders have not yet seen service for long periods, their long-term behavior is poorly characterized. Because understanding the reliability of Pb-free solders is critical to supporting the next generation of circuit board designs, it is imperative that we develop, validate and exercise a solder lifetime model that can capture the thermomechanical response of Pb-free solder joints in stockpile components. To this end, an ASC Level 2 milestone was identified for fiscal year 2010: Milestone 3605: Utilize experimentally validated constitutive model for lead-free solder to simulate aging and reliability of solder joints in stockpile components. This report documents the completion of this milestone, including evidence that the milestone completion criteria were met and a summary of the milestone Program Review.
Glass-to-metal (GTM) seals maintain hermeticity while allowing the passage of electrical signals. Typically, these seals are comprised of one or more metal pins encapsulated in a glass which is contained in a metal shell. In compression seals, the coefficient of thermal expansion of the metal shell is greater than the glass, and the glass is expected to be in compression. Recent development builds of a multi-pin GTM seal revealed severe cracking of the glass, with cracks originating at or near the pin-glass interface, and propagating circumferentially. A series of finite element analyses (FEA) was performed for this seal with the material set: 304 stainless steel (SS304) shell, Schott S-8061 (or equivalent) glass, and Alloy 52 pins. Stress-strain data for both metals was fit by linear-hardening and power-law hardening plasticity models. The glass layer thickness and its location with respect to geometrical features in the shell were varied. Several additional design changes in the shell were explored. Results reveal that: (1) plastic deformation in the small-strain regime in the metals lead to radial tensile stresses in glass, (2) small changes in the mechanical behavior of the metals dramatically change the calculated stresses in the glass, and (3) seemingly minor design changes in the shell geometry influence the stresses in the glass significantly. Based on these results, guidelines for materials selection and design of seals are provided.
Accurate material models are fundamental to predictive structural finite element models. Because potting foams are routinely used to mitigate shock and vibration of encapsulated components in electro/mechanical systems, accurate material models for foams are needed. A viscoplastic foam constitutive model has been developed to represent the large nonlinear and rate dependent crush of a polyurethane foam throughout an application space defined by temperature, strain rate and strain levels. Validation of this viscoplastic model, which is implemented in the transient dynamic Presto finite element code, is being achieved by modeling and testing a series of structural geometries of increasing complexity that have been designed to ensure sensitivity to material parameters. Both experimental and analytical uncertainties are being quantified to ensure fair assessment of model validity. Quantitative model validation metrics are being developed to provide a means of comparing analytical model predictions with experimental observations. This paper focuses on model validation of foam/component behavior over a wide temperature, strain rate, and strain level range using a Presto viscoplastic finite element model. Experiments include simple foam/component test articles crushed in a series of drop table tests. Material variations of density have been included. A double blind validation process is described that brings together test data with model predictions.
The foam material of interest in this investigation is a rigid closed-cell polyurethane foam PMDI with a nominal density of 20 pcf (320 kg/m3). Three separate types of compression experiments were conducted on foam specimens. The heterogeneous deformation of foam specimens and strain concentration at the foam-steel interface were obtained using the 3-dimensional digital image correlation (3D-DIC) technique. These experiments demonstrated that the 3D-DIC technique is able to obtain accurate and full-field large deformation of foam specimens, including strain concentrations. The experiments also showed the effects of loading configurations on deformation and strain concentration in foam specimens. These DIC results provided experimental data to validate the previously developed viscoplastic foam model (VFM). In the first experiment, cubic foam specimens were compressed uniaxially up to 60%. The full-field surface displacement and strain distributions obtained using the 3D-DIC technique provided detailed information about the inhomogeneous deformation over the area of interest during compression. In the second experiment, compression tests were conducted for cubic foam specimens with a steel cylinder inclusion, which imitate the deformation of foam components in a package under crush conditions. The strain concentration at the interface between the steel cylinder and the foam specimen was studied in detail. In the third experiment, the foam specimens were loaded by a steel cylinder passing through the center of the specimens rather than from its end surface, which created a loading condition of the foam components similar to a package that has been dropped. To study the effects of confinement, the strain concentration and displacement distribution over the defined sections were compared for cases with and without a confinement fixture.
An interdisciplinary team of scientists and engineers having broad expertise in materials processing and properties, materials characterization, and computational mechanics was assembled to develop science-based modeling/simulation technology to design and reproducibly manufacture high performance and reliable, complex microelectronics and microsystems. The team's efforts focused on defining and developing a science-based infrastructure to enable predictive compaction, sintering, stress, and thermomechanical modeling in ''real systems'', including: (1) developing techniques to and determining materials properties and constitutive behavior required for modeling; (2) developing new, improved/updated models and modeling capabilities, (3) ensuring that models are representative of the physical phenomena being simulated; and (4) assessing existing modeling capabilities to identify advances necessary to facilitate the practical application of Sandia's predictive modeling technology.
Honeycomb is a structure that consists of two-dimensional regular arrays of open cells. High-density aluminum honeycomb has been used in weapon assemblies to mitigate shock and protect payload because of its excellent crush properties. In order to use honeycomb efficiently and to certify the payload is protected by the honeycomb under various loading conditions, a validated honeycomb crush model is required and the mechanical properties of the honeycombs need to be fully characterized. Volume I of this report documents an experimental study of the crush behavior of high-density honeycombs. Two sets of honeycombs were included in this investigation: commercial grade for initial exploratory experiments, and weapon grade, which satisfied B61 specifications. This investigation also includes developing proper experimental methods for crush characterization, conducting discovery experiments to explore crush behaviors for model improvement, and identifying experimental and material uncertainties.
The main objective of this project was to develop reliable, low-cost techniques for joining silicon nitride (Si{sub 3}N{sub 4}) to itself and to metals. For Si{sub 3}N{sub 4} to be widely used in advanced turbomachinery applications, joining techniques must be developed that are reliable, cost-effective, and manufacturable. This project addressed those needs by developing and testing two Si{sub 3}N{sub 4} joining systems; oxynitride glass joining materials and high temperature braze alloys. Extensive measurements were also made of the mechanical properties and oxidation resistance of the braze materials. Finite element models were used to predict the magnitudes and positions of the stresses in the ceramic regions of ceramic-to-metal joints sleeve and butt joints, similar to the geometries used for stator assemblies.
Computational materials simulations have traditionally focused on individual phenomena: grain growth, crack propagation, plastic flow, etc. However, real materials behavior results from a complex interplay between phenomena. In this project, the authors explored methods for coupling mesoscale simulations of microstructural evolution and micromechanical response. In one case, massively parallel (MP) simulations for grain evolution and microcracking in alumina stronglink materials were dynamically coupled. In the other, codes for domain coarsening and plastic deformation in CuSi braze alloys were iteratively linked. this program provided the first comparison of two promising ways to integrate mesoscale computer codes. Coupled microstructural/micromechanical codes were applied to experimentally observed microstructures for the first time. In addition to the coupled codes, this project developed a suite of new computational capabilities (PARGRAIN, GLAD, OOF, MPM, polycrystal plasticity, front tracking). The problem of plasticity length scale in continuum calculations was recognized and a solution strategy was developed. The simulations were experimentally validated on stockpile materials.