Displacement and Plastic Distortion Fields Produced by Dislocations in Anisotropic Media

1971 ◽  
Vol 38 (4) ◽  
pp. 865-868 ◽  
Author(s):  
T. Mura
Keyword(s):  
Dislocation Density ◽  
Unique Solution ◽  
Integral Method ◽  
Anisotropic Media ◽  
Fourier Integral ◽  
Elastic Fields ◽  
Uniform Velocity ◽  
Plastic Distortion ◽  
History Of ◽  
Distribution Of Dislocations

The fundamental relations among dislocation density tensors, plastic distortion tensors, and dislocation flux tensors are introduced by the Fourier integral method. The proposed method is analytical rather than geometrical and powerful for further analysis of elastic fields. This method is applied to find displacement and plastic distortion fields for a given distribution of dislocations in anisotropic media. Since these quantities are not state quantities, the unique solution is obtained by designating a history of creation of the dislocations. In this paper the history is given in terms of the direction of motion in which the dislocations are introduced in the material from infinity with infinitely small uniform velocity.

Transient Response of a Rigid Spherical Inclusion in an Elastic Medium

1965 ◽  
Vol 32 (3) ◽  
pp. 637-642 ◽  
Author(s):  
C. C. Mow
Keyword(s):  
Exact Solution ◽  
Elastic Medium ◽  
Transient Response ◽  
Integral Method ◽  
Spherical Inclusion ◽  
Time History ◽  
Fourier Integral ◽  
Incident Pulse ◽  
History Of

The transient response of a rigid spherical inclusion of arbitrary density embedded in an elastic medium owing to an incident pulse is examined in this paper. The Fourier-integral method is used, and an exact solution of the response is obtained. It is found that the acceleration and velocity of the inclusion are substantially different from those of the medium. A slight difference in the time history of the displacement between the inclusion and the medium is also noted.

Elastic fields of inclusions in anisotropic media

1971 ◽  
Vol 5 (3) ◽  
pp. 759-768 ◽  
Author(s):  
N. Kinoshita ◽  
T. Mura
Keyword(s):  
Anisotropic Media ◽  
Elastic Fields

Statistics of Internal Elastic Fields and Dislocation Density Tensor in Deformed FCC Crystals

2008 ◽  
Vol 1130 ◽  
Author(s):  
Jie Deng ◽  
Anter El-Azab ◽  
B.C. Larson
Keyword(s):  
Probability Density Function ◽  
Dislocation Density ◽  
Probability Density ◽  
Density Function ◽  
Dislocation Dynamics ◽  
Dynamics Simulation ◽  
Pair Correlations ◽  
Density Tensor ◽  
Elastic Fields ◽  
Dislocation Density Tensor

ABSTRACTThe statistics of internal elastic fields and dislocation density tensor associated with arbitrary 3D dislocation distributions have been modeled using probability density function and pair correlations. Numerical results for these quantities have been obtained for dislocation structures generated by the method of dislocation dynamics simulation.

The Stresses in a Flat Curved Bar Resulting From Concentrated Tangential Boundary Loads

1954 ◽  
Vol 21 (2) ◽  
pp. 151-159
Author(s):  
Ning-Gau Wu ◽  
C. W. Nelson
Keyword(s):  
Plane Stress ◽  
Integral Method ◽  
Radial Direction ◽  
Fourier Integral ◽  
Concentric Circles

Abstract The Fourier integral method is applied to plane-stress problems of a curved bar bounded by two concentric circles and loaded by concentrated tangential boundary loads. The solutions presented may be combined with results given in previous papers (1, 2) dealing with radial boundary loads so as to obtain the stresses in a curved bar loaded by any combination of concentrated boundary loads inclined at any angle to the radial direction.

scholarly journals XI. The electrification of two parallel circular discs

1924 ◽  
Vol 224 (616-625) ◽  
pp. 303-369 ◽  
Keyword(s):  
Exact Solution ◽  
Integral Method ◽  
Electrical Potential ◽  
Fourier Integral ◽  
Infinite Plane ◽  
Laplace’S Equation ◽  
Laplace's Equation ◽  
The Earth

The only problem relating to two electrified circular discs, placed parallel to each other, for which an exact solution has been obtained hitherto, is the classical one of Nobili’s rings. This was solved by Riemann,* by an application of the Bessel-Fourier integral method. In this problem the discs are circular electrodes fixed to two infinite conducting planes, which are themselves connected together by the earth or by a wire at infinity. If the axis of z is that of the two co-axial discs, and perpendicular to the infinite plane conducting sheets, the electrical potential V satisfies Laplace’s equation at all points between the plates, and the further conditions (1) ∂V/∂ z = 0, z = ± a , p > p 1 (2) ∂v/∂ z = A/√(r 1 2 —r 2 ), z = ± a , p < p 1 where A is a constant, 2 a is the distance between the plates, bisected by the origin, p 1 is the radius of either disc, and p is the distance of any point from the axis of z . In fact ( z , p ) are the two cylindrical polar co-ordinates on which V can alone depend.

Examination of Dislocation Structures Near Crack TIP Region of B2 NiAl Alloys

1996 ◽  
Vol 460 ◽  
Author(s):  
B-C. Ng ◽  
B. Simkin ◽  
M. A. Crimp
Keyword(s):  
Thermal Treatment ◽  
Dislocation Density ◽  
Brittle Material ◽  
Contrast Imaging ◽  
Near Surface ◽  
Crystalline Defects ◽  
Crack Tips ◽  
Point Bend ◽  
Distribution Of Dislocations

ABSTRACTThe structure and distribution of dislocations in the region of crack tips and crack edges have been examined in single crystal stoichiometric B2 NiAl using electron channeling contrast imaging (ECCI). ECCI, which allows examination of near surface substructural crystalline defects in bulk specimens, has been carried out for undeformed as well as in-situ deformed 4-point bend specimens. Images of dislocations at crack tips and along the crack fracture surfaces have been studied. Observations have been correlated with variations in thermal treatment corresponding with brittle and toughened conditions. A higher dislocation density was observed over a larger region in front of crack tips for the toughened materials as compared to brittle material.

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