Ductility of Nanocrystalline Materials
The ductility of nanocrystalline materials can be examined by tensile testing. In a tensile test ductility is related to the elongation at fracture or the reduction of area (at necking) at fracture. A classical approach to theoretical consideration of the ductility of nanomaterials is that of Morris [2], who uses the so-called Considère construction to describe the respective importance of stress level and work-hardening rate in controlling the geometric instability responsible for the onset of necking. Generally, a high work-hardening rate will result in large strain at the instability while a low work-hardening rate, typical of nanomaterials, will result in a small strain to failure or in extreme case no strain at all.
However, the stability of flow and consequently the degree of ductility of a (ductile) material in tensile test depends, in addition to its strain hardening, also on strain rate hardening characteristics (see, e.g., Hart [74]). As both of these characteristics may differ from those of the coarse
(or conventional) grain size materials, it is expected that the ductility of nanostructural materials differ from that of their coarse-grained counterparts.
A more complete treatment of the conditions for necking would include the strain rate sensitivity of the flow stress of nanostructural materials, which as already mentioned, typically also is different from that of coarse-grained materials. Hart [74] has shown that the instability in tensile test is determined by the equation y + m > 1 (3)
where y is the strain-hardening rate and m is the strain rate sensitivity of the flow stress. Since for metals m is generally less than unity (in fact, generally much less than unity), the strain-hardening exponent y must be clearly greater than zero for the flow to be stable. As nanocrystalline metals show only little strain hardening in tension, their tensile strain at the flow at necking often remains small.
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