Hall-Petch analysis of dislocation pileups in thin material layers and in nanopolycrystals
- PDF / 336,714 Bytes
- 7 Pages / 584.957 x 782.986 pts Page_size
- 61 Downloads / 160 Views
A potential order-of-magnitude increase in Hall-Petch (H-P)-based strength level for nanoscale grain-size structures is an important enabler of electronic thin film material design applications. Dislocation pileups of smaller lengths in such thin film materials are blocked in a screw orientation at the through-thickness grain boundaries of relatively larger grains. For fully nanopolycrystalline materials, both strength and strain rate sensitivity measurements exhibit complementary H-P reciprocal square root of grain size dependencies. An additional increase in strength level is predicted for transition from a pileup to a single dislocation loop expanding against the grain boundary obstacle. In opposition, disordered grain boundaries are responsible for a reduced H-P stress intensity, ke. And at the limiting high stresses reached at lower-limiting nanoscale grain sizes, reversed H-P dependences are obtained both for the strength and strain rate sensitivity.
I. INTRODUCTION
Pioneering work on dislocation pileups against thin (oxide) films began in 1959 as an extension of the Ph.D. thesis researches of Head at Bristol.1 His work was further extended to a Hall-Petch (H-P) type of analysis for dislocation pileups within elastically anisotropic materials2 and to catastrophic pile-up releases at obstacle breakthroughs.3,4 An important concern in current researches is with pileups within the thin films themselves and, especially, within both larger and smaller nanoscale grain structures as well as within counterpart bulk materials. Already there is clear demonstration that the mechanical strength levels of isolated nanopolycrystalline thin layer or bulk materials developed for electronic or other design applications are approximately an order of magnitude higher than that for the same materials with conventional microstructures.5
small numbers, for example, providing the relation for relative shear strength decrease caused by addition of each dislocation to a single ended pileup of n dislocations of Ds=s ¼ 1=n :
ð1Þ
The cross-hatched area for each pile-up geometry in Fig. 1 covers the limiting H-P slope values, or stress intensities, that could be fitted to the theoretical dependencies; and, the linear dependencies defined inside the figure area are the fracture mechanics relations for edge crack, internal two-dimensional crack, and circular crack geometries. The top-end scale of the figure gives, with dislocation Burgers vector, b, or dislocation core radius, r0 5 ;0.2 nm and, say, ℓ/b 5 25, an indicated grain diameter of ;5 nm. A. One or few grains through the thickness
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2013.10
Figure 2 provides a pioneering determination of H-P results for an Al-1% Si alloy film of 1 lm thickness tested in plane stress by means of a Beams-type bulge test.7 Brotzen has provided a helpful review of the bulge test method and other test methods for thin film materials.8 Attention is directed in the figure to the experimental scatter and otherwise indication of low
Data Loading...
