4 research outputs found
Perkutanni transhepaticke biliarni drenaze: jejich vyuziti a perspektivy v moderni intervencni radiologii
Available from STL Prague, CZ / NTK - National Technical LibrarySIGLECZCzech Republi
The behaviour of small fatigue cracks, and some basic modelling approaches for the phenomenon.
The behaviour of small cracks has been explained by various different mechanisms
(e.g. microstructural barriers, closure, stress state etc). The majority of models already
developed are based on a single mechanism (e.g. crack closure, effect of microstructure),
while the rest of the processes occurring simultaneously in the material are either considered
to play a minor role or are included in fitting parameters obtained from experiments.
Consequently the models are suitable only for materials and conditions similar to those used
in the ‘fitting’ tests and thus hard to generalise and adapt for common engineering use. This
work therefore aims to provide the foundation to develop a combination of the generalised
crack closure model and the microstructural models including the effects of the varying
microstructure and environment, respectively, to create a comprehensive and realistic model
reflecting the major processes influencing small crack behaviour. A thorough review of the
current literature and approaches applied for the modeling of small and short cracks is
presented. The Distributed Dislocation Technique has been identified as a particularly
suitable candidate for the modeling of the problem. Initial trials with the model proposed by
Navarro and de los Rios however showed certain shortcomings in their model caused mainly
by unjustified simplifications. The Distributed Dislocation Technique has been evaluated
against an FE approach for the case of a kinked crack and shown to be potentially a very
powerful tool for the solution of crack problems.
Two numerical methods for solution of singular integral equations have been tested to
allow for maximum accurate evaluation of plastic zone size (important in later stages of the
model’s development). While the Lobatto-Chebyshev method offers a comfortable solution of
the singular integral equations, its fixed calculation and collocation points invalidate it for the
evaluation of plastic zone size. The Gerasoulis’ method is, on the other hand, more
cumbersome to apply, thanks to the weight functions, which can be rather lengthy, but it’s
flexible calculation and collocation points should enable more accurate evaluation of plastic
zone size. Nonetheless, both methods demonstrated very good results for all problems, on
which they were tested, even for a relatively limited number of calculation points.
Incorporating microstructure more accurately into the model was approached by
assuming (1) that a crack will grow into the adjacent grain on the slip plane with the highest
resolved shear stress, if the resolved normal stress on the plane is tensile (2) that the slip
would initiate from a source of dislocations in the grain. Five typical grain orientations (e.g.
Cube, Goss, Brass, Cu, and S) were investigated and a number of possible scenarios were
followed in the modelling. A dependence of the slip direction on the position of the source of
dislocations and grain orientation was demonstrated. Although only a 2D consideration of the
problem is needed for the model, the calculation of the resolved stresses was conducted in
3D and only the final slip direction was transformed to a 2D intersection of the slip plane with
the surface of the specimen.
Two ways to capture the presence of sources of dislocations in the structure were
proposed and their suitability for the model should be further investigated in future work. The
stochastic nature of the position of the dislocation sources regarding the crack tip can be
represented either by a single dislocation source randomly placed, or by a number of
dislocation sources randomly distributed in the grain. In the first case the calculation will be
quicker and easier, as only one point will be considered, in the second case the reality of the
problem will be represented better, but the calculation will be more complicated. The
consideration of the microstructure in the model introduced an additional parameter into the
model. Such microstructural qualities as width of grain boundaries, density of sources of
dislocations, inclination of the material toward planar or wavy slip, etc. can be appreciated in
the model by means of the position, distribution and also number of dislocation sources
considered in the model. This offers a platform for very realistic representation of the small
crack propagation. Nevertheless, the possibility of incorporation of these parameters into the
model and their mutual interaction must be fully understood and thus, some simplifying
assumptions will have to be introduced into any future developments of the model