Crack spacing in strained films

2004 ◽  
Vol 120 ◽  
pp. 201-208
Author(s):  
B. B. Guzina ◽  
D. H. Timm ◽  
V. R. Voller
Keyword(s):  
Thermal Loading ◽  
Characteristic Length ◽  
Axial Strain ◽  
Analytical Models ◽  
Length Scale ◽  
Characteristic Length Scale ◽  
Transverse Cracks ◽  
Space Length ◽  
Saturation Limit ◽  
Wide Range

Consider a thin film resting on a relatively thick substrate. When the substrate is subjected to an axial strain transverse cracks, normal to the direction, of the applied strain may appear in the film. It is observed that, for a given strain, the spacing between such cracks is uniform, with a clearly identifiable characteristic length scale that can be used to provide bounds on the spacing. Further, as the strain is increased, there is a densification of the cracks up to a saturation limit. Beyond the saturation limit additional strain produces no further cracks and the characteristic crack length scale for the given system remains fixed. This paper presents analytical models that can be used to predict the characteristic length scale both at the saturation limit and during the densification process. The models are shown to be applicable across a wide range of length scales; with abilities to determine the crack space length scale in both asphalt pavements (~100m) subjected to a thermal loading and strained ceramic films (~100μm).

Development-Length Requirements for Fully Developed Laminar Flow in Concentric Annuli

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
R. J. Poole
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Channel Flow ◽  
Characteristic Length ◽  
Radius Ratio ◽  
Length Scale ◽  
Development Length ◽  
Characteristic Length Scale ◽  
Annular Gap ◽  
Wide Range

In this technical brief we report the results of a systematic numerical investigation of developing laminar flow in axisymmetric concentric annuli over a wide range of radius ratio (0.01<Ri/Ro<0.8) and Reynolds number (0.001<Re<1000). When the annular gap is used as the characteristic length scale we find that for radius ratios greater than 0.5 the development length collapses to the channel-flow correlation. For lower values of radius ratio the wall curvature plays an increasingly important role and the development length remains a function of both radius ratio and Reynolds number. Finally we show that the use of an empirical modified length scale to normalize both the development length and the characteristic length scale in the Reynolds number collapses all of the data onto the channel-flow correlation regardless of the radius ratio.

Identification of the characteristic length scale for fatigue cracking in fretting contacts

1998 ◽  
Vol 08 (PR8) ◽  
pp. Pr8-159-Pr8-166 ◽  
Author(s):  
S. Fouvry ◽  
Ph. Kapsa ◽  
F. Sidoroff ◽  
L. Vincent
Keyword(s):  
Characteristic Length ◽  
Fatigue Cracking ◽  
Length Scale ◽  
Characteristic Length Scale

scholarly journals Lettau’s Contribution to the Obukhov Length Scale: A Scientific Historical Study

2021 ◽  
Author(s):  
Thomas Foken ◽  
Michael Börngen
Keyword(s):  
Characteristic Length ◽  
Stability Parameter ◽  
Historical Study ◽  
Length Scale ◽  
Characteristic Length Scale ◽  
Obukhov Length ◽  
The Future

AbstractIt has been repeatedly assumed that Heinz Lettau found the Obukhov length in 1949 independently of Obukhov in 1946. However, it was not the characteristic length scale, the Obukhov length L, but the ratio of height and the Obukhov length (z/L), the Obukhov stability parameter, that he analyzed. Whether Lettau described the parameter z/L independently of Obukhov is investigated herein. Regardless of speculation about this, the significant contributions made by Lettau in the application of z/L merit this term being called the Obukhov–Lettau stability parameter in the future.

Mesoscopic Disorder

MRS Bulletin ◽  
1994 ◽  
Vol 19 (5) ◽  
pp. 11-13 ◽  
Author(s):  
D.A. Weitz
Keyword(s):  
Molecular Level ◽  
Characteristic Length ◽  
Disordered Materials ◽  
Length Scale ◽  
Interconnected Network ◽  
Characteristic Length Scale ◽  
Fiber Network ◽  
Disordered Structure ◽  
Reading Glasses ◽  
Strong Scattering

Disorder characterizes most of the materials that surround us in nature. Despite their great technological importance, materials with ordered crystalline structures are relatively rare. Examples of disordered materials, however, abound, and their forms can be as varied as their number. The paper on which these words are printed has a disordered structure composed of a highly interconnected network of fibers. It has also been coated with particulate materials to improve its properties and the visibility of the ink. The reading glasses you may require to focus on these words are composed of a glass or polymer material that is disordered on a molecular level. Even the structure of your hand holding this magazine is disordered. These and virtually all other disordered materials are typically parameterized by a characteristic length scale. Above this length scale, the material is homogeneous and the effects of the disorder are not directly manifest; below this characteristic length the disorder of the structure dominates, directly affecting the properties.The range of characteristic length scales for the disordered materials around us is immense. For the glass or polymer of your reading glasses, it is microscopic; the disorder is apparent only at the molecular level, while above this level the material is homogeneous. For the paper on which this magazine is printed, the scale is larger; the paper is white partly because the disordered fiber network has within it structures that are comparable in size to the wavelength of light, resulting in strong scattering of the light.

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