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In the present work crack growth (crack tip movement) is interpreted as
indentation of the influence zone into undisturbed material under the action
of an end load. At the investigation, we should differentiate between two stages of fracture.
The first one is the stage of the elementary cell fracture with characteristic time tchar,
and the second one is the fracture propagation between elementary cells with characteristic time
t*≠tchar. The delamination follows the loss
of stability of the influence zone. Stability of the influence zone by indentation
is investigated. From mathematical reason we approximate the shape of the influence
zone not as a wedge, but as a thin equivalent plate. We can investigate the loss
of stability of a rod which clutched between elastic thick foundations under
the effect of end load P(X,t) and additional "noise of fracture'".
According to definition, the additional perturbation (fracture of an elementary cell)
is a shock one. The principal difference of the considered processes is
in the fact that the shock acts not along the beam axis,
and the system loses its stability not as a result of a shock load but as a result
of a quasi-static load under conditions of parametrical perturbation.
The non-homogeneity is represented by additional terms (change of fracture noise parameters).
The full analytical solution of the problem is received in the form of composition of exponents and generalized hypergeometric functions. The possibility of resonance modes is shown. |
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