Existing and emerging methods in computational mechanics are rarely validated against problems with an unknown outcome. For this reason, Sandia National Laboratories, in partnership with US National Science Foundation and Naval Surface Warfare Center Carderock Division, launched a computational challenge in mid-summer, 2012. Researchers and engineers were invited to predict crack initiation and propagation in a simple but novel geometry fabricated from a common off-the-shelf commercial engineering alloy. The goal of this international Sandia Fracture Challenge was to benchmark the capabilities for the prediction of deformation and damage evolution associated with ductile tearing in structural metals, including physics models, computational methods, and numerical implementations currently available in the computational fracture community. Thirteen teams participated, reporting blind predictions for the outcome of the Challenge. The simulations and experiments were performed independently and kept confidential. The methElectronic supplementary material The online version of this article (doi:10.1007/s10704-013-9904-6) contains supplementary material, which is available to authorized users.Sandia National Laboratories, Albuquerque, NM, USA e-mail: blboyce@sandia.gov ods for fracture prediction taken by the thirteen teams ranged from very simple engineering calculations to complicated multiscale simulations. The wide variation in modeling results showed a striking lack of consistency across research groups in addressing problems of ductile fracture. While some methods were more successful than others, it is clear that the problem of ductile fracture prediction continues to be challenging. Specific areas of deficiency have been identified through this effort. Also, the effort has underscored the need for additional blind prediction-based assessments.

The most commonly used solder for electrical interconnects in electronic packages is the near eutectic 60Sn-40Pb alloy. This alloy has a number of processing advantages (suitable melting point of 183°C and good wetting behavior). However, under conditions of cyclic strain and temperature (thermomechanical fatigue) the microstructure of this alloy undergoes a heterogeneous coarsening and failure process that makes the prediction of solder joint lifetime complex. A finite element simulation methodology to predict solder joint mechanical behavior, that includes microstructural evolution, has been developed. The mechanical constitutive behavior was incorporated into the time dependent internal state variable viscoplastic model through experimental creep tests. The microstructural evolution is incorporated through a series of mathematical relations that describe mass flow in a temperature/strain environment. The model has been found to simulate observed thermomechanical fatigue behavior in solder joints.

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/m 3 ). 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. Published by Elsevier Ltd.

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Rigid, closed-cell, polyurethane foam consists of interconnected polyurethane plates that form cells. When this foam is compressed, it exhibits an initial elastic regime, which is followed by a plateau regime in which the load required to compress the foam remains nearly constant. In the plateau regime, cell walls are damaged and large permanent volume changes are generated. As additional load is applied, cell walls are compressed against neighboring cell walls, and the stiffness of the foam increases and approaches a value equal to that of solid polyurethane. When the foam is loaded in tension, the cell walls are damaged and the foam fractures. A constitutive theory for rigid polyurethane foam has been developed. This theory is based on a decomposition of the foam in two parts: a skeleton and a nonlinear elastic continuum in parallel. The skeleton accounts for the foam behavior in the elastic and plateau regimes and is described using a coupled plasticity with continuum damage theory. The nonlinear elastic continuum accounts for the lock-up of the foam due to internal gas pressure and cell wall interactions. This new constitutive theory has been implemented in both static and dynamic finite element codes. Numerical simulations performed using the new constitutive theory are presented. EXPERIMENTAL OBSERVATIONSigid, closed-cell, polyurethane foam consists of R interconnected polyurethane plates. This material is manufactured by having a gas expand inside liquid polyurethane, which solidifies in a foamed state. Shaw and Sata (11, Patel and Finnie (2), Zaslawsky POLYMER ENGINEERING AND SCIENCE, MID-MARCH 1995, VOI. 35, NO. 5