Complementary Experimental Techniques for Multi-Scale Modeling of Plasticity
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The above list, while far from exhaustive, is intended to underline the processes that must be taken into account in any multi-scale model of plasticity. Since the effects of small length-scale processes often propagate all the way to the macroscopic level, a fundamental understanding of plastic deformation can only be attained through some form of multi-scale modeling. What kinds of experimental information are required at these various length scales? Since the size and shape of the sample can be considered as model inputs, we will only consider the smaller length-scales. At the grain level, modelers can use information on the sizes, shapes, and orientations of the grains, as well as 3D maps of the internal stresses within the sample. Most of this information can be obtained using optical and scanning electron microscopy of etched sample surfaces, cross-sectional transmission electron microscopy (TEM), orientation imaging microscopy, and neutron diffraction residual stress measurements. Surface roughening can be measured by means of profilometry, optical and electron microscopy, and scanning probe microscopy. Residual stresses are more difficult to measure in single- and few-crystal specimens, but recent work using X-ray microbeams at the Advanced Photon Source promises to make such measurements possible."
In principle,
residual stresses in large single crystals could be measured using neutron diffraction, 20 and work on developing the necessary experimental techniques is currently in progress. Skipping down to the atomic level, most of the phenomena listed above cannot be measured directly using any existing or projected experimental techniques. In some cases, ab initio simulations can take the place of experimental measurements, but such simulations can only handle very small system sizes. In general, ab initio calculations cannot be used for many dislocation studies, since dislocations are extended 3D structures, incorporating large numbers of atoms. Multi-ion interatomic potentials have been developed2 1 3 for simulating such structures. Here, the many-body angular forces are accounted for through explicit three- and four-ion potentials. Parameters for the potentials are determined through comparison with ab initio calculations and with high-resolution TEM (HRTEM) measurements of selected grain boundary structures.24 HRTEM can also be used to measure directly the atomic spreading of dislocation cores,2 5 but such experiments are extremely difficult in materials with high stacking-fault energy, and surface effects must be taken into account in 26 their interpretation. At the next larger length scale where the curving shape of the individual dislocations becomes important (e.g., for dislocation-dislocation interactions), simpler potentials, such as embedded atom method and Lennard-Jones potentials, are used to handle the large numbers of atoms required.16, 27 Since these potentials are much less accurate than those discussed above, the simulation results often provide qualitative rather than quantitative infor
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