by Tias Maiti and Philip Eisenlohr
A plastically dilatational material model is proposed that enables to simulate the mechanical response of non-compact geometries (containing free surfaces) by means of established spectral methods without any particular adaptations, i.e. in combination with arbitrary constitutive laws describing the remainder of the simulated geometry and under mixed boundary conditions. The versatility of this material model and more accurate representation of empty space in comparison to an isotropic elastic model employing low stiffness is demonstrated for the cases of void growth under biaxial extension and grain-scale deformation behavior of an oligocrystalline dogbone-shaped aluminum sample under uniaxial tension.
Tias (Maiti) successfully defended his thesis on July 27, 2017. He modeled stage II hardening that is frequently observed in single crystal tension experiments using a Crystal Plasticity Fast Fourier Transform framework with physics-based material models. We wish Tias all the best for his upcoming endeavor in Portland, OR!
From left to right: Aritra Chakraborty (PhD student), Markus Sudmanns (PhD student visiting from Karlsruhe Institute of Technology, Germany), Zhuowen Zhao (PhD student), Dr. Tias Maiti, Dr. Philip Eisenlohr (advisor), Eureka Pai Kulyadi (PhD student) and Mingwan Zhu (Master student).
by Aritra Chakraborty and Philip Eisenlohr
The feasibility to determine the adjustable parameters of single crystal plasticity constitutive laws by an inverse approach that minimizes the deviation between the measured and simulated indentation response of individual grains (of a polycrystalline sample) is investigated for the case of face-centered cubic (fcc) lattice structure. Optimization uses the Nelder–Mead (NM) simplex algorithm, which was modified to navigate parameter space regions where objective function evaluations fail. A phenomenological power-law is assumed as the constitutive description for crystal plasticity. Simulated cases of indentation with prescribed constitutive parameter values serve as the virtual reference. A sensitivity analysis revealed that the initial and saturation slip resistance tau_0 and tau_sat are the most dominant pa- rameters while the hardening slope h_0 has less influence. Reproducibility and robustness are analyzed for different objective functions involving the load–displacement response and residual surface topography for several indentation crystal orientations. Concurrent optimization of load–displacement and topography consistently provided the least scatter in the optimized parameter values from the target solution compared to either one individually and essentially independent of indentation crystal orientation. Deviations in slip activity were typically of the same order of magnitude as the combined deviations of load–displacement and surface topography response. Optimization of more than one crystallographic indentation response at once did not improve the parameter estimation quality but proportionally increases the evaluation effort. It is concluded that for fcc materials one single crystal indentation experiment suffices to closely quantify the two most influential parameters of a phenomenological constitutive plasticity law when the objective function of the modified NM simplex algorithm proposed herein combines the load–displacement response and residual surface topography.
by Piyush Jagtap, Aritra Chakraborty, Philip Eisenlohr, and Praveen Kumar
Here, we attempt to understand the age-old question of “where do whiskers in Sn coatings grow?” by performing grain orientation mapping in conjunction with a simple analysis of the stress field in the vicinity of a whisker grain. Electron back-scatter diffraction (EBSD) was used for orientation mapping of Sn grains in a 4 μm thick Sn coating deposited on brass. It was observed that whiskers consistently grew from low-index grains with (100) or near-(100) orientations that were surrounded by grains with similar orientations, which were then partially surrounded by grains with high-index planes, such as (211), (321) and (420). Strong elastic anisotropy and overall a high fraction of high-angle grain boundaries were also consistently observed in the vicinity of whiskers. In addition, full-field three-dimensional crystal elasticity simulations were performed using the EBSD orientation maps to analyze local stress variations in the vicinity of the whisker grain. These simulations indicate the presence of a high compressive hydrostatic stress around the whisker grain, which could then possibly create conducive conditions for whisker growth observed experimentally.
by Philip Eisenlohr, Pratheek Shanthraj, Brendan Vande Kieft, Thomas R. Bieler, Wenjun Liu, and Ruqing Xu
A multistep, non-destructive grain morphology reconstruction methodology that is applicable to near-surface volumes is developed and tested on synthetic grain structures. This approach probes the subsurface crystal orientation using differential aperture x-ray microscopy on a sparse grid across the microstructure volume of interest. Resulting orientation data are clustered according to proximity in physical and orientation space and used as seed points for an initial Voronoi tessellation to (crudely) approximate the grain morphology. Curvature-driven grain boundary relaxation, simulated by means of the Voronoi implicit interface method, progressively improves the reconstruction accuracy. The similarity between bulk and readily accessible surface reconstruction error provides an objective termination criterion for boundary relaxation.