27 The Separation of Eigen Stresses
297
electromagnetic case virtually reversed. The process of elementary dislocation loop
creation occurs whenever low-energetic elastic fields come into play, because of the
relatively low creation energy required. However, the acceleration of a dislocation
requires a high-energetic environment. This conclusion is completely proven correct
by the experiment. Plastic deformations are practically accompanied by intensive
dislocation creation processes from the very beginning. We can only expect microplastic processes in low-energetic regions; in other words, we can expect dislocation
motions as described by the sine-Gordon equation, for example the propagation of
a kink along a line of dislocation and also the creation and destruction of elementary dislocation loops that lead on the line of dislocation to the so-called kink pair
creation, cf. Günther [35].
The formulation of phenomena in solids in the system of the Special Theory
of Relativity as we found for the so-called structural eigen strain using Eqs. (411)
and (412) is not only of pure academic interest. We expect, from the application
of theoretical quantum field methods on these equations, an approach to the theory
of plasticity. This theory thus depends, from the point of view developed here, on
the secondary relativistic effects, i.e. with the relativistic consequences arising from
quantisation. The use of the relativistic spacetime structure in a solid, as developed
from the sine-Gordon equation is therefore no longer left to us. The relativistic time
of the moving, internal observer in the crystal leads to far-reaching consequences,
namely to a theoretical concept of elasto-plastic interactions based on the concept of
the quantum field theory.
The internal observers of our crystal, that we approximate as our continuum, can
include the structural elastic strain ε
I , v that are described by Eqs. (411) and (412)
in their considerations without any deviation from their Special Theory of Relativity.
Which role do Eq. (413) play? These equations break every Lorentz symmetry. The
displacement vector s therefore has to be excluded from such considerations. There
is however a way out of this dilemma, but this cannot be discussed here. Such a
displacement vector always defines a coordinate transformation—it can be ’transformed away’. The result of this would be special relativistic equations at arbitrary
coordinates, even in accelerated reference systems. This leads us mathematically into
the world of the General Theory of Relativity, a problematic situation for the solid
that we do not wish to follow here.
297
electromagnetic case virtually reversed. The process of elementary dislocation loop
creation occurs whenever low-energetic elastic fields come into play, because of the
relatively low creation energy required. However, the acceleration of a dislocation
requires a high-energetic environment. This conclusion is completely proven correct
by the experiment. Plastic deformations are practically accompanied by intensive
dislocation creation processes from the very beginning. We can only expect microplastic processes in low-energetic regions; in other words, we can expect dislocation
motions as described by the sine-Gordon equation, for example the propagation of
a kink along a line of dislocation and also the creation and destruction of elementary dislocation loops that lead on the line of dislocation to the so-called kink pair
creation, cf. Günther [35].
The formulation of phenomena in solids in the system of the Special Theory
of Relativity as we found for the so-called structural eigen strain using Eqs. (411)
and (412) is not only of pure academic interest. We expect, from the application
of theoretical quantum field methods on these equations, an approach to the theory
of plasticity. This theory thus depends, from the point of view developed here, on
the secondary relativistic effects, i.e. with the relativistic consequences arising from
quantisation. The use of the relativistic spacetime structure in a solid, as developed
from the sine-Gordon equation is therefore no longer left to us. The relativistic time
of the moving, internal observer in the crystal leads to far-reaching consequences,
namely to a theoretical concept of elasto-plastic interactions based on the concept of
the quantum field theory.
The internal observers of our crystal, that we approximate as our continuum, can
include the structural elastic strain ε
I , v that are described by Eqs. (411) and (412)
in their considerations without any deviation from their Special Theory of Relativity.
Which role do Eq. (413) play? These equations break every Lorentz symmetry. The
displacement vector s therefore has to be excluded from such considerations. There
is however a way out of this dilemma, but this cannot be discussed here. Such a
displacement vector always defines a coordinate transformation—it can be ’transformed away’. The result of this would be special relativistic equations at arbitrary
coordinates, even in accelerated reference systems. This leads us mathematically into
the world of the General Theory of Relativity, a problematic situation for the solid
that we do not wish to follow here.