Hall-Petch Analysis of Yield, Flow and Fracturing

1994 ◽  
Vol 362 ◽  
Author(s):  
Ronald W. Armstrong
Keyword(s):  
Fracture Toughness ◽  
Grain Size ◽  
Size Dependence ◽  
Theoretical Work ◽  
Ultrafine Grain ◽  
Size Refinement ◽  
Strain Behavior ◽  
Grain Sizes ◽  
Early Results ◽  
Pile Up

AbstractThe explanation for the grain size dependence of the polycrystal yield stress or cleavage stress of steel, investigated in complementary studies by Hall and Petch, is rooted in dislocation pile-up theory first described by Eshelby, Frank and Nabarro just a step away from previous theoretical work on the stress concentrating properties of cracks. Beginning from Cottrelllocking of dislocations at grain boundaries by carbon that is responsible for the pronounced yield point behavior and the grain size dependence of the yield strength of steel, the same concepts have been shown to apply for the complete stress/strain behavior of steel and other materials. Other mechanical properties such as fatigue strength show a similar dependence on grain size. A notable application of such grain size based considerations has been to the ductile-brittle transition and fracture toughness properties of steel and related materials — because refinement of grain size both strengthens a material and improves its fracture toughness. Early results for the polycrystal hardness dependence on grain size gave evidence that the strength benefits of grain size refinement ought to extend to ultrafine grain sizes.

Simulation of the interaction of plastic zone dislocations with the grain boundary at brittle-plastic transition temperatures in molybdenum

2021 ◽  
Vol 2021 (3) ◽  
pp. 77-85
Author(s):  
K. M. Borysovska ◽  
◽  
N. M. Marchenko ◽  
Yu. M. Podrezov ◽  
S. O. Firstov ◽  
...  
Keyword(s):  
Fracture Toughness ◽  
Grain Size ◽  
Grain Boundary ◽  
Plastic Zone ◽  
Grain Boundaries ◽  
Crack Tip ◽  
Dynamics Simulation ◽  
Density Of Dislocations ◽  
Grain Sizes ◽  
Pile Up

The (DD) method was used to model the formation of the plastic zone of the top of the cracks in polycrystalline molybdenum. Special attention was paid to take into account the interaction of dislocations in the plastic zone with grain boundaries. Structural sensitivity of fracture toughness was analyzed under brittle-ductile condition. Simulations were performed for a range of grain sizes from 400 to 100 μm, at which a sudden increase in fracture toughness with a decrease of grain size was experimentally shown. We calculated the value of K1c taking into account the shielding action of dislocations. The position of all dislocations in the plastic zone at fracture moment was calculated. Based on these data, we obtained the dependences of dislocation density on the distance from the crack tip thereby confirming significant influence of the grain boundaries on plastic zone formation. At large grain sizes, when the plastic zone does not touch the boundary, the distribution of dislocations remained unchanged. As grains reduce their size to size of the plastic zone, they start formating a dislocation pile – up near the boundaries. Dislocations on plastic zone move slightly toward the crack tip, but the density of dislocations in the middle of the grain remains unchanged, and fracture toughness remains almost unchanged. Further reduction of the grain size leads to the Frank-Reed source activation on the grain boundary Forming dislocation pile-up of the neighbor grains. Its stress concentration acts on dislocations of the first grain and causes redistribution of plastic zone dislocations. If the reduction in grain size is not enough to form a strong pile-up, density of dislocations on plastic zone increases slightly and crack resistance increases a few percent. Further reduction of grains promotes strong pile-up, dislocations move to crack tip, and its density on plastic zone increases. Crack is shielded and fracture toughness increases sharply. The calculation showed that the fracture toughness jump is observed at grain sizes of 100—150 μm, in good agreement with the experiment. Keywords: dislocation dynamics simulation, molybdenum, fracture toughness, grain size, plastic zone, brittle-ductile transition.

scholarly journals Is Superplasticity in the Future of Nanophase Materials?

1990 ◽  
Vol 196 ◽  
Author(s):  
R. W. Siegel
Keyword(s):  
Mechanical Properties ◽  
Grain Size ◽  
Room Temperature ◽  
Grain Boundary Sliding ◽  
Atomic Clusters ◽  
Diffusional Creep ◽  
Ultrafine Grain ◽  
Grain Sizes ◽  
Nanophase Materials ◽  
Boundary Sliding

ABSTRACTThe ultrafine grain sizes and high diffusivities in nanophase materials assembled from atomic clusters suggest that these materials may have a strong tendency toward superplastic mechanical behavior. Both small grain size and enhanced diffusivity can be expected to lead to increased diffusional creep rates as well as to a significantly greater propensity for grain boundary sliding. Recent mechanical properties measurements at room temperature on nanophase Cu, Pd, and TiO2, however, give no indications of superplasticity. Nonetheless, significant ductility has been clearly demonstrated in these studies of both nanophase ceramics and metals. The synthesis of cluster-assembled nanophase materials is described and the salient features of what is known of their structure and mechanical properties is reviewed. Finally, the answer to the question posed in the title is addressed.

scholarly journals Grain Size Dependence of Fracture Toughness in an Ultrahigh Strength Maraging Steel

1983 ◽  
Vol 69 (1) ◽  
pp. 145-152 ◽  
Author(s):  
Yoshikuni KAWABE ◽  
Seiichi MUNEKI ◽  
Junji TAKAHASHI
Keyword(s):  
Fracture Toughness ◽  
Grain Size ◽  
Maraging Steel ◽  
Size Dependence ◽  
Ultrahigh Strength

Optimization of Particle Size and Distribution by Hydrostatic Extrusion

2007 ◽  
Vol 561-565 ◽  
pp. 869-872 ◽  
Author(s):  
Małgorzata Lewandowska ◽  
Kinga Wawer
Keyword(s):  
Mechanical Properties ◽  
Fracture Toughness ◽  
Grain Size ◽  
Aluminium Alloys ◽  
Hydrostatic Extrusion ◽  
Nanometer Scale ◽  
Second Phase ◽  
Size Refinement ◽  
Second Phase Particles ◽  
Fatigue And Fracture

Hydrostatic extrusion (HE) as a method of metals forming is known for about 100 years. Recently, it has been utilized as an efficient way of grain size refinement down to nanometer scale. In the case of engineering metals, HE processing alters not only grain size but also second phase particles such as intermetallic inclusions and precipitates. During HE processing, these particles significantly change their size, shape and spatial distribution. These changes are accompanied by improvement in properties of processed metals such as fatigue and fracture toughness. In the present work, changes of second phase particles induced by HE are described in a quantitative way for aluminium alloys. Their impact on mechanical properties is also discussed.

The Fracture Toughness of Ice Over a Range of Grain Sizes

1988 ◽  
Vol 110 (2) ◽  
pp. 192-196 ◽  
Author(s):  
W. A. Nixon ◽  
E. M. Schulson
Keyword(s):  
Fracture Toughness ◽  
Grain Size ◽  
Research Laboratory ◽  
Circular Cylinders ◽  
Notched Specimen ◽  
Grain Sizes ◽  
Freshwater Ice ◽  
Thayer School ◽  
Percent Decrease

Tests have been performed at −10°C on circumferentially notched right circular cylinders of randomly oriented granular polycrystalline freshwater ice, to determine whether grain size affects fracture toughness (KIc). Grain sizes, as measured by the linear intercept method, varied from 1.6 mm to 9.3 mm in diameter. The circumferentially notched specimen was used because of the ease with which it can be manufactured from right circular cylinders, made regularly and with considerable accuracy of alignment for some years now by workers of the Thayer School Ice Research Laboratory. A slight (25 percent) decrease in values of KIc is observed as grain size increases over the range investigated. Consideration is given to the cause of this effect and to its possible contribution to the scatter in KIc values observed by earlier workers. Other possible causes of this scatter are indicated.

Enhanced Densification and Grain-Size Refinement in Cation-Doped Tetragonal Zirconia

2010 ◽  
Vol 62 ◽  
pp. 227-231
Author(s):  
Keijiro Hiraga ◽  
Hidehiro Yoshida ◽  
Koji Morita ◽  
Byung Nam Kim
Keyword(s):  
Grain Size ◽  
Relative Density ◽  
Grain Growth ◽  
Sintering Temperature ◽  
Initial Density ◽  
Tetragonal Zirconia ◽  
The Other ◽  
Size Refinement ◽  
Grain Sizes ◽  
Materials Used

In tetragonal zirconia, possibility is investigated of densification with finer grain sizes under the combination of doping and sintering in air. The materials used are CIP'ed compacts of 3-mol%-yttria-stabilized tetragonal zirconia (3Y-TZP) doped with a small amount of cations. For a given sintering temperature and initial density of the compacts, while the doped cations enhances densification in the latest stage of sintering, the effect is different in grain growth during densification: a doped cation tended to enhance grain growth, whereas the other cations tended to suppress grain growth. As a result, the doping of the latter cations brings about a grain size finer than that of the undoped 3Y-TZP for a given relative density.

Observation of slip propagation across grain boundaries in Ni3Al

1986 ◽  
Vol 44 ◽  
pp. 864-865 ◽  
Author(s):  
I. Baker ◽  
E.M. Schulson ◽  
J.A. Horton
Keyword(s):  
Grain Size ◽  
Yield Strength ◽  
Room Temperature ◽  
Size Dependence ◽  
Direct Evidence ◽  
Specimen Preparation ◽  
Fine Grained ◽  
Room Temperature Yield Strength ◽  
Pile Up ◽  
Preparation Techniques

Recent modelling of the grain size dependence of the room-temperature yield strength of Ni3Al has invoked the concept of dislocation pile-ups. The idea is that the yield strength measured in the Liiders regime (i.e. the Liiders band propagation stress) represents not the stress to independently nucleate slip in each grain but the stress required to propagate slip through the material. This paper presents direct evidence of slip propagation from one grain to the next and thus validation of the use of a pile-up model for Ni3Al.Miniature tensile specimens (3 mm x 7 mm x0.2 mm), made from an extruded rod of fine-grained (∽10 μm) Ni3Al containing 0.35 at.% boron, were strained under tension whilst being observed in a Philips EM 430T operated at 300 KV. Details of the design and operation of the straining stage and of the specimen preparation techniques are given elsewhere.

The grain size dependence of fracture toughness in an Al-6.0% Zn-2.5% Mg alloy

1978 ◽  
Vol 13 (5) ◽  
pp. 945-950 ◽  
Author(s):  
Takeshi Kawabata ◽  
Osamu Izumi
Keyword(s):  
Fracture Toughness ◽  
Grain Size ◽  
Size Dependence ◽  
Mg Alloy

Grain-size dependence of cleavage fracture toughness in mild steel

Nature ◽  
1978 ◽  
Vol 276 (5683) ◽  
pp. 50-51 ◽  
Author(s):  
D. A. CURRY
Keyword(s):  
Fracture Toughness ◽  
Grain Size ◽  
Mild Steel ◽  
Cleavage Fracture ◽  
Size Dependence

scholarly journals Grain Size Dependence of the Fracture Toughness of Silicon Nitride Ceramics

1991 ◽  
Vol 99 (1148) ◽  
pp. 320-323 ◽  
Author(s):  
Takeshi KAWASHIMA ◽  
Hiromi OKAMOTO ◽  
Hideharu YAMAMOTO ◽  
Akira KITAMURA
Keyword(s):  
Fracture Toughness ◽  
Grain Size ◽  
Silicon Nitride ◽  
Size Dependence ◽  
Nitride Ceramics
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