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Self Forces on Moving Dislocations
Xanthippi Markenscoff
Professor of Applied Mechanics
University of California,San Diego
La Jolla,CA 92093-0411
xmarkens@UCSD.Edu
Summary
Eshelby's definition of the force on an elastic singularity is generalized to dynamics through the Eshelby "cut and reinsert" thought experiment, and the resulting expression is defined as the dynamic J integral , and coincides with an expression that is invariant under the Noether theorem transformation.
Through this thought experiment the dynamic L and M integrals are also defined as the moment on an an elastic singularity (change of energy with respect to rotation of the defect) and change of energy with respect to a self-scaling parameter respectively and coincide with the other expressions obtained by Noether's theorem.
The dynamic force on an elastic singularity is surface-independent and it coincides with the energy -release rate if the singularities are such that the integrals exist.
For a moving dislocation in a generally accelerating motion the self-force as defined from the above expression of the dynamic J integral is explicitly calculated, as well as the effective mass which is defined as the coefficient of the acceleration in the self-force expression.
The divergent integrals are smoothed out by a ramp-core model, which allows for the core-width to vary with acceleration. A variable core width model is also presented for a static dislocation in order to estimate the Peierls lattice friction stress.
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