On the kinematics of continuous distribution of dislocations in plasticity

1976 ◽  
Vol 14 (1) ◽  
pp. 65-73 ◽  
Author(s):  
George J. Weng ◽  
Aris Phillips
Keyword(s):  
Continuous Distribution ◽  
Distribution Of Dislocations

scholarly journals The ’t Hooft–Polyakov monopole in the geometric theory of defects

2020 ◽  
Vol 34 (12) ◽  
pp. 2050126
Author(s):  
M. O. Katanaev
Keyword(s):  
Physical Interpretation ◽  
Continuous Distribution ◽  
Geometric Theory ◽  
Yang Mills ◽  
Monopole Solution ◽  
Distribution Of Dislocations

The ’t Hooft–Polyakov monopole solution in Yang–Mills theory is given new physical interpretation in the geometric theory of defects. It describes solids with continuous distribution of dislocations and disclinations. The corresponding densities of Burgers and Frank vectors are computed. It means that the ’t Hooft–Polyakov monopole can be seen, probably, in solids.

A Tension Crack Impinging Upon Frictional Interfaces

1989 ◽  
Vol 56 (2) ◽  
pp. 291-298 ◽  
Author(s):  
Anna Dollar ◽  
Paul S. Steif
Keyword(s):  
Continuous Distribution ◽  
Fiber Composites ◽  
Solution Technique ◽  
Tension Crack ◽  
Tension Axis ◽  
Finite Crack ◽  
Crack Tips ◽  
Frictional Interface ◽  
Well Posed ◽  
Distribution Of Dislocations

A crack impinging normally upon a frictional interface is studied theoretically. We employ a solution technique which superposes the solution of a crack in a perfectly-bonded elastic medium with a continuous distribution of dislocations which represent slippage at the frictional interface. This procedure reduces the problem to a singular integral equation which is solved numerically. Specifically, we consider the problem of an infinite sheet subjected to uniaxial tension containing a finite crack which lies normal to the tension axis and has both crack tips impinging normally on frictional interfaces. The limiting problem of a semi-infinite crack impinging on a frictional interface is considered as well. Posed as model problems for cracking in weakly bonded fiber composites, these studies reveal the effective blunting that can result when a weak interface serves to deflect a propagating crack.

Fracture Related to a Dislocation Distribution

1979 ◽  
Vol 46 (4) ◽  
pp. 817-820 ◽  
Author(s):  
C. Vilmann ◽  
T. Mura
Keyword(s):  
Plastic Zone ◽  
Critical Stress ◽  
Continuous Distribution ◽  
Crack Tip ◽  
Plastic Zone Size ◽  
Plastic Work ◽  
Zone Size ◽  
Line Theory ◽  
Distribution Of Dislocations

The plastic flow at the crack tip is characterized by a model compatible with slip line theory. From this model it is shown that a continuous distribution of dislocations may be derived. Then assuming that these dislocations are emitted from the crack tip and move along slip lines to their final position, the Peach-Koehler force is used to calculate the plastic work involved. Since the plastic zone size is dependent on crack length, two plastic effects are present upon propagation. Primarily the distribution of dislocations present moves along with the crack tip, secondarily new dislocations are emitted to fill the larger plastic zone. These effects yield plastic work which is dependent on both σ2 and σ4, with σ being the applied stress. This dependancy yields a critical stress relationship different from that proposed by either Irwin or Orowan. It also leads to the determination of a subcritical flaw size, i.e., one which will never become unstable.

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