Critical Beha vior of a Depinning Dislocation

2000 ◽  
Vol 652 ◽  
Author(s):  
Stefano Zapperi ◽  
Michael Zaiser
Keyword(s):  
Stress Field ◽  
Long Range ◽  
Critical Exponents ◽  
Critical Stress ◽  
Threshold Stress ◽  
Random Media ◽  
Analytical Estimate ◽  
Depinning Transition ◽  
Elastic String ◽  
Theoretical Predictions

ABSTRACTThe dynamics of dislocations at yield can be understood within the framew ork of the depinning transition of elastic manifolds in random media. Close to the threshold stress for their long-range motion, the geometry and dynamics of dislocations are characterized by a set of critical exponents. We consider a single flexible dislocation gliding through a random stress field, taking in to account long-range self stresses, and estimate the critical stress where depinning takes place. Simulations of a discretized lattice model confirm the analytical estimate and yield numerical values of the critical exponents which are in agreement with theoretical predictions for an elastic string mo ving on a plane.

CRITICAL STRESS-INDUCED RELAXATION IN RELATION TO LONG-RANGE ORDERING, IN Au3Cu, AND SELF-INDUCED ORDERING, IN AuNi SOLID SOLUTIONS

1987 ◽  
Vol 48 (C8) ◽  
pp. C8-519-C8-524
Author(s):  
G. RENAUD ◽  
M. BELAKHOVSKY ◽  
J. HILLAIRET ◽  
M. WUTTIG ◽  
G. BESSENAY ◽  
...  
Keyword(s):  
Long Range ◽  
Solid Solutions ◽  
Critical Stress ◽  
Long Range Ordering

scholarly journals Depinning exponents of the driven long-range elastic string

2007 ◽  
Vol 2007 (01) ◽  
pp. P01019-P01019 ◽  
Author(s):  
Olaf Duemmer ◽  
Werner Krauth
Keyword(s):  
Long Range ◽  
Elastic String

Phase transition to long-range ferromagnetism inAu82Fe18and the associated critical exponents

1986 ◽  
Vol 33 (7) ◽  
pp. 5010-5015 ◽  
Author(s):  
A. K. Gangopadhyay ◽  
S. B. Roy ◽  
A. K. Majumdar
Keyword(s):  
Phase Transition ◽  
Long Range ◽  
Critical Exponents

The Physical Meaning of Astatic Equilibrium in Saint-Venant’s Principle for Linear Elasticity

1969 ◽  
Vol 36 (3) ◽  
pp. 392-396 ◽  
Author(s):  
C. A. Berg
Keyword(s):  
Stress Field ◽  
Elastic Body ◽  
Long Range ◽  
Small Volume ◽  
Boundary Surface ◽  
Small Region ◽  
Main Body ◽  
Linear Elastic ◽  
Loading System ◽  
Linear Elastic Body

When a boundary loading which is not only self-equilibrated but has the additional property that the loading system remains self-equilibrated when all the forces are rotated through an arbitrary angle about their points of application (astatic equilibrium), is applied to a small region of the surface of a linear elastic body, the long range stress field produced by the loading is in general of smaller order (with respect to the radius of the loaded segment of the boundary) than would be the long range stress field produced by a loading system which was merely self-equilibrating but which would not continue to be self-equilibrating if each force were rotated (von Mises [3], Sternberg [6]). The physical distinctions between astatic equilibrium loadings and merely self-equilibrated loadings, and the physical reasons why astatic equilibrium loadings produce smaller long range stresses, are examined. It is pointed out that astatic equilibrium loadings always produce zero mean deformation in a linear elastic body and that, therefore, if a small volume element, in the neighborhood of a small patch of the boundary surface subject to astatic equilibrium loading were considered as an isolated body, this small volume would undergo no mean deformation and would be easier to fit back into the main body than if it had been subject to merely self-equilibrated loading which would have caused mean deformation.

scholarly journals Determination of tensile strength of concrete and rocks by using the Brazilian test in the confrontation with the failure criteria

2014 ◽  
Vol 13 (2) ◽  
pp. 191-200
Author(s):  
Jakub Gontarz ◽  
Jerzy Podgórski
Keyword(s):  
Tensile Strength ◽  
Stress Field ◽  
Brittle Material ◽  
Critical Stress ◽  
Failure Criteria ◽  
Brazilian Test ◽  
Compression Tests

The paper presents the analysis of the Brazilian compression tests considering the possibilities of determining the proper tensile strength. These analyses include the precise designation of the stress field without singularity at the point of application of force, the evaluation of critical stress in the light of classical and contemporary failure criteria for a brittle material, and determination of the position of the point where the destructive crack is expected to be initiated in the sample.

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