During the course of research on the propagation of microcracks in steel, another interesting project presented itself. Brendan McCormack [28] had carried out experimental tests on hip replacements. PMMA is an abbreviation of polymethylmethacrylate, which is a polymer that is used to secure a metal implant to the bone. Damage was caused by cracks appearing within the PMMA, and on the boundaries between the PMMA and the bone and metal. In particular it was noted that damage accumulation and failure could be caused by the initiation of a large number of small cracks throughout the structure, in such a fashion that the cement disintegrated. In such a situation the implant would loosen, causing failure, and would have to be replaced.
This method of failure is different from the case of a dominant crack growing beyond some threshold length, since damage is due to the family of cracks within the specimen rather than one single crack.
The analysis for this situation consisted of modelling the rate of formation of new cracks as a Poisson process, together with some modelling of the underlying growth [29].
While this analysis was for a different material, it still raised important questions
about populations of cracks, which in turn raises the question of the possibility of
interactions, i.e. coalescence. The next focus, then, in the case of the steel data
was to model the nature of coalescence within a specimen, with a view to improving the
reliability predictions. Spatial knowledge would allow direct consideration of
. Previous research revealed models for
coalescence, in a variety of different materials, such as for fiber reinforced
composites (Yushanov et al. 1995) [59]. Of particular interest was
research into coalescence in stainless steel, albeit for different loading at high
temperatures [17], which describes some of the ways in which cracks coalesce.
Previous work had been done in examining coalescence for the current data by Taylor et. al. (1995) [53]. This was a simple model which investigated some possible mechanisms underlying crack coalescence. Essentially two cracks were deemed to coalesce when they entered into a zone of influence between them. In the main, this paper recognised also that crack coalescence could be an important factor.