Ductility of Nanostructured Materials
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ve to mechanical testing carried out in tension, or with a signif icant tensile stress component such as in bending. It is not sufficient to evaluate mechanical behav ior in compression since ductile failure instabilities may be inhibited and brittle crack propagation is much more difficult. Two classes of failure criteria can be considered and applied to our analysis of ductility in nanostructured materials: 4 (1) Force instability in tension;5 necking generally begins at maximum load during tensile testing; the amount of uniform elongation depends on strain hardening such that true uniform strain eu = n in a cylindrical specimen (or eu = 2n for a sheet) where n is the strain hardening coefficient. For an ideally plastic material (such as amorphous alloys) where n = 0 the necking instability would begin just as soon as yielding occurred. (2) Crack nucleation or propagation insta bility, where the imposed stress concen tration at an existing flaw exceeds the critical toughness value of the material. 6 The first criterion implies simply that the sample is mechanically stable until the rate of work hardening falls to a level determined by the flow stress (and prior strain) at that time. Materials with a high capacity for strain hardening are therefore stable, while those with little capac ity for strain hardening are potentially unstable. The second approach considers the stress intensity K at a pre-existing flaw (or /, the energy or work input required to reach that State) as the sample is increasingly loaded. 6 Work must be supplied from the external source to produce the elastic stress concentration at the notch tip, to produce the local plastic strain as the notch Starts to deform, and to achieve global plasticity in the case where the material shows some Overall ductility. These three terms all vary with
the initial flaw size considered to be the same as the grain (powder) size, 6 and assuming the flow stress and fracture tough ness to be Constants, it should be possible at sufficiently fine grain sizes to achieve global plasticity before brittle, local crack propagation sets in. Given the strong in crease in flow stress with decreasing grain size at the nanoscale, the competition between plastic flow and fracture is difficult to predict.
Ductility of Single-Phase Metallic Nanocrystalline Materials at Temperatures Below 0.5 Melting Point In order to measure meaningful duc tility values (i.e., with tensile stress c o m p o n e n t s ) , sufficiently large and porosity-free samples are required. With improvements in processing methods, such samples are becoming available but data are still limited. The majority of studies have been carried out on samples which have been Consolidated from particulates by, for example, the inert-gas condensation method 7 or mechanical attrition of powders. 8 This section will review work that has been carried out on the ductility of metals which exhibit significant ductility with conventional ("coarse") grain sizes (typi cally > 1 /iim). Most mechanical property studies of n
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