<title>Contributions of interferometry to the field of fracture mechanics</title>

Abstract

The difference between theoretical and experimental strength of solids, leads to the assumption that the presence of defects under the form of cracks is responsible for this difference. The classical work of Griffith on glass provided the foundations for the generalization ofthis model to explain the process of fracture of materials. The fracture of materials is then associated with the presence of very large stress and strain gradients in a small region, the crack tip. To experimentally verify the theoretical results of fracture mechanics, it is necessary to make observations at different levels of spatial resolutions depending of the actual physical size of the corresponding cracks. The actual level of resolution selected depends on the actual physical size of the crystal defect that one wants to observe. If one wants to observe individual dislocations, the level of the resolution is of the order of 10'°m to 105m. if one wants to observegrain domains, the level of resolution is io8 to 104m, and if one wants to analyze composites, the level of resolution is 10 to 102m. Eight orders of magnitude are required to observe the different levels. To make observations at these different levels, different type of radiations are required depending on the resolution. Using conventional optics, one can make observations from 10m up. To proceed to make observations one must use a mathematical model, the most commonly used model is the continuum mechanics model. In this model, it is assumed that the deformations of a body can be represented by analytical functions with continuous derivatives up to the third order. This model implies to ignore the discrete nature of matter and replace it by an ideal medium, the continuum. In this model the deformations of the body are characterized by combinations of the derivatives of the displacement function. This model is used at all the levels of resolutions that we have referred to, from few atomic distances in the case of dislocations, to sizes of the order of 102m in concrete structures with large aggregates. If one looks at a given problem, for example concrete with large aggregates, one can look to the displacement field in a given region at the level of 102m, and go on observing the same field at the different levels of resolution that we have mentioned. One will observe different details of the same field with increasing resolutions. The situation is similar to that of fractal geometry, the deeper one looks the more detail appears. But unlike the simple rule of self-similitude existing in fractal geometry, the different levels are related by more complicated rules. If one considers the displacements, both in direction and magnitude, the displacements between two points are the average of the displacements of the points that appear between these two points at higher levels of resolution. In the case of fracture mechanics, the level of observation depends of how deep one wants to look in the chain leading to fracture. If one wants to look at the level used by the continuum mechanics approach that analyzes the elasto-plastic singular field, one should select a spatial resolution such that the statistical fluctuation caused by the presence of individual grains are smoothed out.