- Tim Rupert
- Aparna Singh
- Hyunjung Yi
- ShinYoung Kang
Li, Ju. “The Mechanics and Physics of Defect Nucleation.” MRS Bulletin 32 (2007): 151-159.
Minor, Andrew M., et al. “A New View of the Onset of Plasticity During the Nanoindentation of Aluminum.” Nature Materials 5 (2006): 697-702.
Van Vliet, Krystyn J., et al. “Quantifying the Early Stage of Plasticity Through Nanoscale Experiments and Simulations.” Physical Review B 67 (2003): 104105.
(a) What is the average Young’s elastic modulus of the Au nanopillar in Fig. 1A of Li? From comparison of these data with E of Au reported in the literature, do you infer that elastic properties of Au are size-dependent down to these sample diameters?
(b) Derive the expression used several times by Li relating the maximum shear stress generated within an indented material as a function of applied load, Young’s elastic modulus, and indenter radius. You may wish to consult K. Johnson’s Contact Mechanics.
(b) The papers you have selected study the onset of plasticity via the applied contact load of indentation. Explain and illustrate why the location of homogeneous dislocation nucleation under an indenter is expected to occur below the indented material free surface, rather than at the indenter/material interface.
(c) Derive the location of maximum shear stress (i.e., depth) for indentation with a Hertzian elastic sphere for the case of 2-D indentation (i.e., the sphere is really a cylinder). Johnson’s Contact Mechanics and the PRB (2003) and its cited papers are good references.
(d) Minor, et al. show interesting experiments that enable visualization of dislocations in a thin foil of Al during indentation, similar in goal to the MD simulations of Al discussed in your other two papers. Discuss how well the authors justified the assumption that the load-drops in the load-displacement data correspond to homogeneous dislocation nucleation, as opposed to heterogeneous dislocation nucleation from grain boundaries or motion of pre-existing dislocations. This analysis should include consideration of images, reported data, and expected values of required stresses, dislocation spacing, and sufficient “perfect crystal” size comparable to the elastic strain field of an indenter.
(b) The papers you have chosen focus on the initial stages of plastic deformation, or incipient plasticity, in ductile metals. Consider Fig. 9 in paper 3, illustrating a dislocation loop passing through a single crystal of Al under indentation pressure. Consider a bulk metal vs. a thin film of the same material on a rigid substrate, explain how you would expect the load required to keep plastically deforming the material t a depth of 1 micron would differ.
(c) Compute the fracture stress of this Al according to the Griffith criterion, assuming an initial crack size at the resolution of the TEM used in Minor’s indentation experiments. Compare this to the published fracture strength of single crystal Al, and discuss.
(d) Delamination of films can also be treated as fracture, but this time at an interface between two dissimilar materials. Using Griffith again, compute the tensile stress required to delaminate an Al film from a Si substrate, if there is an initial blister at the film/substrate interface of width 1 micron. Then state whether you’d expect the film to first fracture due to opening of initial cracks within the film (of initial size stated in c), or to delaminate from the substrate when loaded in tension normal to the film/substrate interface.
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