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Microstructurally small fatigue crack (MSFC) formation includes stages of incubation, nucleation and microstructurally small propagation. In AA 7075-T651, the fracture of Al 7 Cu 2 Fe constituent particles is the major incubation source. In experiments, it has been observed that only a small percentage of these Fe-bearing particles crack in a highly stressed volume. The work presented here addresses the identification of the particles prone to cracking and the prediction of particle cracking frequency, given a distribution of particles and crystallographic texture in such a volume. Three-dimensional elasto-viscoplastic finite element analyses are performed to develop a response surface for the tensile stress in the particle as a function of the strain level surrounding the particle, parent grain orientation and particle aspect ratio. A technique for estimating particle strength from fracture toughness, particle size and intrinsic flaw size is developed. Particle cracking is then determined by comparing particle stress and strength. The frequency of particle cracking is then predicted from sampling measured distributions of grain orientation, particle aspect ratio and size. Good agreement is found between the predicted frequency of particle cracking and two preliminary validation experiments. An estimate of particle cracking frequency is important for simulating the next

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.

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Automated simulation of arbitrary, non-planar, 3-D crack growth in real-life engineered structures requires two key components: crack representation and crack growth mechanics. A model environment for representing the evolving 3-D crack geometry and for testing various crack growth mechanics is presented. Reference is made to a speci"c implementation of the model, called FRANC3D. Computational geometry and topology are used to represent the evolution of crack growth in a structure. Current 3-D crack growth mechanics are insu$cient; however, the model allows for the implementation of new mechanics. A speci"c numerical analysis program is not an intrinsic part of the model, i.e. "nite and boundary elements are both supported. For demonstration purposes, a 3-D hypersingular boundary element code is used for two example simulations. The simulations support the conclusion that automatic propagation of a 3-D crack in a real-life structure is feasible. Automated simulation lessens the tedious and time-consuming operations that are usually associated with crack growth analyses. Speci"cally, modi"cations to the geometry of the structure due to crack growth, remeshing of the modi"ed portion of the structure after crack growth and reapplication of boundary conditions proceeds without user intervention.

Robust gear designs consider not _nly crack initiation, but crack propagation trajectoriesfor a fail-safe design. In actual gear operation, the magnitude as well as tt e posit;on of the force charges as the gear rotates through the mesh. A study [o determine the effect of moving gear tooth load on crack propagation predictions was performed. Twodimensional almlysis of an involute spur gear and three-dimensional analysis of a spira!: _._ b_vel pinion gear using the finite element method and boundary element method were studied and compared to experiments. A modified theory for predicting gear crack propagation paths based on the" criteria of Erdogan and Sih [I8] was investigated.Crack simulation based on calculated stress intensity factors and mixed mode crack angle prediction techniques using a simple static analysis in which tlle tooth load was located at the highest point of single tooth contact was validated. For three-dimensional analysis, however, the cmalysis was valid only as long _s the crack did rot approach the contact region on the tooth.