Crack propagation in brittle materials

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.