Laboratory Study of Rock Deformation and Fracture - Ultra and Extremely Low Frequency Electromagnetic Fields - page 351

screening of surface charges by ions absorbed from air. So one can expect that the
charge density on the surfaces of growing main crack is much greater than that
measured several minutes after the destruction of sample. The indirect hints towards
the existence of high charge density and strong electric field during the crack growth
are the electric discharges between crack sides, radio and optical emissions and other
phenomena observed during the fracture of solid.
The electrons that were captured by surface traps can release from these traps
due to thermal fluctuations thereby producing a population of free electrons near the
crack surface. These electrons can be accelerated by the strong electric field resulted
from the fluctuation-mosaic charges distributed on the crack sides. In the model by
Molotskiy and Malyugin ( 1983 ) the crack surface is considered as a plane x;y.The
surface charges density is supposed to be a twice periodic function of coordinates x

and y given by: † c D † m cos .k x x/ cos k y y , where k x and k y are the parameters
of periodic structure of the charge distribution, and † m stands for maximal charge
density. Then the electric potential in the whole space can be derived from Laplace's
equation with corresponding boundary conditions at the crack surface and infinity.
In what follows we use the simplest way to estimate the electron energy in the
framework of this approach.
Let l be the typical size of the charged cells so that k x D k y D =l.Atsmall
distances from the cell and far away from its boundaries the electric field is similar to
that of infinite charged plane. The field amplitude in the vicinity of the center of the
charged cell can thus be estimated as E † m =."" 0 /. This upward-directed electric
field decreases at the short distances from the surface with attenuation distance on
the order of l, because the charge density distribution is an alternating-sign function
with spatial period of l. Consequently the electron emitted from the crack surface
and accelerated by this field could accumulate the maximal energy w eEl
el† m =."" 0 /. This estimation agrees with the results by Molotskiy and Malyugin
( 1983 ) on the order of magnitude.
The transverse electric field directed perpendicular to the crack sides is a short-
range one. To explain how the electrons can accumulate the observed energy of
10-100 keV one needs to introduce a great local density † of the surface charges.
During the dynamical stage of fracture the value of † m should be 2-3 order of
magnitude greater than the residual charge density on the surfaces of the fractured
sample.
Other mechanism of the high-energy electron production during the fracture of
dielectrics has been proposed by Surkov ( 1986 ) and Gershenzon et al. ( 1986 ). It is
very likely that the electron releasing from the surface traps can be accelerated by
the longitudinal electric field which is parallel to the crack sides. This long-range
electric field is caused by opposite electric charges situated at the tip and sides of
the growing crack.
Now we examine this mechanism for charge separation between crack tip and its
sides during quasi-brittle fracture of a crystal dielectric that results in the generation
of the longitudinal electric field inside the crack (Surkov 1986 ). The large surface
curvature at the crack tip results in an enhancement of mechanical stress near the tip
up to the level which is several orders of magnitude greater than the average stress