Optimal and noise-robust extraction of Fracture Mechanics parameters from kinematic measurements

The paper is devoted to an optimal (i.e. noise-robust) determination of stress intensity factors and crack tip locations based on a displacement field measured over an arbitrarily shaped domain. As the minimization of the noise sensitivity is included within the proposed extraction technique, this is especially dedicated to corrupted displacement fields, e.g. as measured by an optical technique. The main idea is to construct for mode I and II fields an extracting function so that its L2 scalar product with the actual displacement field yields the sought parameter. The extracting function is also constrained to be orthogonal to a set of admissible elastic fields. Two applications are considered to illustrate the technique. The first example deals with a fatigue crack in steel for which small scale yielding occurs. A second example with a low signal/noise ratio illustrates the capability of the approach to analyze a crack in silicon carbide with sub-pixel openings.