• porous crack plasticity
• ESPI
• crack
• cohesive crack
• brittle materials
• process zone

The aim of this research has been the study of the mechanisms that control the crack
propagation in brittle materials, in a region close to the crack tip. Two different kind
of materials have been considered: glass float and glass ceramic. The basic idea to
develop this investigation has been the accurate measurement of the Crack Opening
Displacement (COD) during the crack propagation. In fact, the shape of the tip profile
is a consequence of the phenomena which rule the stress distribution at the crack tip
and, the consequent macroscopic behaviour of the material.
To allow a precise measurement of the COD, an interferometric technique called
Electronic Speckle Pattern Interferometry (ESPI) has been adopted. With respect
to other optical techniques, ESPI system works on the phase changes between two
distinct laser beams deriving by the same laser source and reflected by the specimen
surface, providing a precision higher than the wavelength of the laser source. To
avoid an instantaneous failure due to the brittle nature of the investigated materials,
every specimen has been naturally pre-cracked and then tested under strain-driven
three point bending, pausing opportunely the loading to stabilize the crack evolution.
The ESPI results have been compared with the classical solutions of the Linear Elastic
Fracture Mechanics (LEFM). Since in this solution the COD directly depends by
the square root of the distance from the crack tip, it’s particularly instructive to report
the same graphs in bi-logarithmic scales, obtaining a linear trend for LEFM, with
slope 1/2 . This procedure permitted to note a considerable difference in the crack
behaviour of the materials investigated. In glass, all the crack profiles presented a
slope lower than 1/2 at the crack tip, and consequently a “wider” COD with respect to
the LEFM profile. In glass ceramic instead, the profiles showed a higher slope than 1/2 at the tip, and so a “tighter” COD at the tip, similar to a cusp.
By these observations, an accurate FEM model has been studied to reproduce the
experimental results. In particular, two different models have been considered. The
first one was the cohesive model `a la Barenblatt, where the presence of cohesive
forces at the neighbourhood of the crack tip provides the typical cusp profile. The
second one was a local damage model, where different phenomena are able to develop
a degradation of the material in a process zone, providing a wider COD profile
at the tip with respect to LEFM trend.
Comparing the experimental results with the numerical profiles obtained by a specific
calibration of the fem models, we found the following conclusions. In glass,
nucleation and coalescence of microvoids seem to be the main cause which determines
the COD profile observed. This is well described through a model of porous
plasticity `a la Gurson-Tvergaard. In glass ceramic instead, the ESPI COD was reproduced
only assuming a distribution of cohesive forces far behind the crack tip.
These actions would derive by crack bridging phenomena due to the intergranular
microstructure of glass ceramic.