Out-of-plane displacement measurement near the crack tip during a crack propagation: Validation of a 3D formulation for a specimen in PMMA loaded in mode I.

The fundamental aim of this study is the determination zone of the 3D effects and the transient one at the vicinity of the crack tip during a crack propagation in brittle materials ( PMMA ) using an optical method (Michelson interferometer). With the obtained interferograms, we can extract the phase (thus the relief) by using a new numerical approach based on the principle of images correlation between real fringes and virtual fringes. Different dynamic tests are realized by a plate loaded in mode I under a constant loading. We compare the obtained data with the two-dimensional theory of Westergaard (plane stress hypothesis) [1]. With the divergence is established, we propose a new 3D formulation, based on a formulation employed for static crack, which takes into account 3D and transient effects. For the static cracks, the 3D effects relate to a presence of the state of three-dimensional stresses. However in dynamics, the transient effects appear and are related to the crack propagation velocity. The 3D effects and transient effects lead to results equivalent to experimental ones in terms of displacement but are completely different to results given by the two-dimensional theory near the crack tip. It is possible to quantify the zone when the plane stress hypothesis is not valid according to the crack propagation speed V. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)