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A Statistical Theory of Solid Solution Hardening
Author(s) -
Labusch R.
Publication year - 1970
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.19700410221
Subject(s) - obstacle , statistical theory , dislocation , critical resolved shear stress , fleischer , expression (computer science) , plane (geometry) , mathematics , statistical physics , classical mechanics , materials science , crystallography , physics , thermodynamics , computer science , geometry , chemistry , statistics , german , shear rate , history , programming language , archaeology , political science , viscosity , law
The critical shear stress τ c to move a dislocation through a random array of obstacles in the glide plane is calculated using a statistical theory. The result is an expression for τ c in terms of the obstacle concentration, the line tension of the dislocation, and of the interaction force between the dislocation and a single obstacle. Fleischer's solution of the same problem is not reproduced by the statistical theory. Quantitatively the two results are not very different, but our new result is supported by some recent experimental evidence. Furthermore the theory provides a definite prescription how to combine the concentrations and interaction forces of obstacles of different kinds in the expression for τ c .