Chapter 4 Properties of nanomaterials
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Hardness and Strength<br />
Hardness and strength <strong>of</strong> conven;onal grain size materials (grain diameter, d > 1 μm) is a func;on <strong>of</strong> grain<br />
size. For duc;le polycrystalline materials the empirical Hall-Petch equa;on In terms <strong>of</strong> yield stress, is<br />
σο = σi + kd -1/2 , where σο = yield stress, σi = fric;on stress opposing disloca;on mo;on, k = constant, and<br />
d = grain diameter . And for hardness, is Hο = Hi + kd -1/2 .<br />
To explain these empirical observa;ons, several models have been proposed, which involve either<br />
disloca;on pileups at grain boundaries or grain boundary disloca;on networks as disloca;on sources. In<br />
all cases the Hall-Petch effect is due to disloca;on mo;on/genera;on in materials that exhibit plas;c<br />
deforma;on.<br />
It is clear that as grain size is reduced through the nanoscale regime ( 1 μm) metals. The experimental results <strong>of</strong> hardness measurements,<br />
show different behavior for dependence on grain size at the smallest nc grains (
Change language