Closure to “Discussion of ‘The Effect of Two Rigid Spherical Inclusions on the Stresses in an Infinite Elastic Solid’” (1966, ASME J. Appl. Mech., 33, pp. 715–718)

1966 ◽  
Vol 33 (3) ◽  
pp. 718-718
Author(s):  
Joseph F. Shelley ◽  
Yi-Yuan Yu
Keyword(s):  
Elastic Solid ◽  
Spherical Inclusions

The Effect of Two Rigid Spherical Inclusions on the Stresses in an Infinite Elastic Solid

1966 ◽  
Vol 33 (1) ◽  
pp. 68-74 ◽  
Author(s):  
Joseph F. Shelley ◽  
Yi-Yuan Yu
Keyword(s):  
Stress Field ◽  
Uniaxial Tension ◽  
Elastic Solid ◽  
Displacement Function ◽  
Hydrostatic Tension ◽  
Series Form ◽  
Spherical Inclusions ◽  
Spherical Cavities ◽  
In Series ◽  
The Common

Presented in this paper is a solution in series form for the stresses in an infinite elastic solid which contains two rigid spherical inclusions of the same size. The stress field at infinity is assumed to be either hydrostatic tension or uniaxial tension in the direction of the common axis of the inclusions. The solution is based upon the Papkovich-Boussinesq displacement-function approach and makes use of the spherical dipolar harmonics developed by Sternberg and Sadowsky. The problem is closely related to, but turns out to be much more involved than, the corresponding problem of two spherical cavities solved by these authors.

Observation of dislocations in dynamically loaded Cu-SiO2

1986 ◽  
Vol 44 ◽  
pp. 424-425
Author(s):  
D. S. Pritchard
Keyword(s):  
Electron Microscope ◽  
Strain Rate ◽  
Single Crystal ◽  
Transmission Electron Microscope ◽  
Volume Fraction ◽  
Screw Dislocations ◽  
Spherical Inclusions ◽  
Transmission Electron ◽  
Crystal Dispersion ◽  
Strain Rate Loading

The effect of varying the strain rate loading conditions in compression on a copper single crystal dispersion-hardened with SiO2 particles has been examined. These particles appear as small spherical inclusions in the copper lattice and have a volume fraction of 0.6%. The structure of representative crystals was examined prior to any testing on a transmission electron microscope (TEM) to determine the nature of the dislocations initially present in the tested crystals. Only a few scattered edge and screw dislocations were viewed in those specimens.

The microstructure change of low-carbon electrical steels by residual aluminum

1989 ◽  
Vol 47 ◽  
pp. 286-287
Author(s):  
C.K. Hou ◽  
C.T. Hu ◽  
Sanboh Lee
Keyword(s):  
Annealing Treatment ◽  
Low Carbon ◽  
Electrical Steels ◽  
Vacuum Degassing ◽  
Spherical Inclusions ◽  
Residual Aluminum ◽  
Average Grain Size ◽  
The Matrix ◽  
Fine Size ◽  
To Come

The fully processed low-carbon electrical steels are generally fabricated through vacuum degassing to reduce the carbon level and to avoid the need for any further decarburization annealing treatment. This investigation was conducted on eighteen heats of such steels with aluminum content ranging from 0.001% to 0.011% which was believed to come from the addition of ferroalloys.The sizes of all the observed grains are less than 24 μm, and gradually decrease as the content of aluminum is increased from 0.001% to 0.007%. For steels with residual aluminum greater than 0. 007%, the average grain size becomes constant and is about 8.8 μm as shown in Fig. 1. When the aluminum is increased, the observed grains are changed from the uniformly coarse and equiaxial shape to the fine size in the region near surfaces and the elongated shape in the central region. SEM and EDAX analysis of large spherical inclusions in the matrix indicate that silicate is the majority compound when the aluminum propotion is less than 0.003%, then the content of aluminum in compound inclusion increases with that in steel.

The internal stability of an elastic solid

2000 ◽  
Vol 80 (12) ◽  
pp. 2827-2840 ◽  
Author(s):  
J. W. Morris Jr, C. R. K Renn
Keyword(s):  
Elastic Solid ◽  
Internal Stability
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