On the feasibility of crack propagation tracking and full field strain imaging via a strain compatibility functional and the Direct Strain Imaging method

The simultaneous tracking of the trajectory of a moving crack along with the measurement of the corresponding full field strain fields associated with this motion due to quasi-static or dynamic impact loading, is a problem of high interest from both the perspectives of the engineering practice and engineering science alike. However, full field optical methodologies have not yet been able to address the issues arising in experiments with moving boundaries such as dynamically evolving cracks. Such a problem requires solving simultaneously the problem of identifying the dynamically evolving geometry of the cracks as well as the problem of introducing these cracks into the full-field representation of a relevant full field method. In the present work we are introducing a methodology that can solve this problem. Specifically, we describe an optical method that can be used to detect dynamically evolving discontinuities on the surface of a body even if they are invisible to the eye, by using a strain compatibility functional that makes no continuity assumptions about the underlying medium. The relevant data from this process are then introduced in a full field representation that leads to an acceptable estimation of the discontinuous strain field. The proposed method is based on the recently introduced Direct Strain Imaging method that can be used to visualize and quantify the full fields of the strain tensor components. Synthetic numerical experiments were performed to generate synthetic crack propagation data along with the associated strain fields in order to assess the feasibility of the proposed method. The approach employed for this purpose was that of applying the extended finite element method to solve the problem of a propagating crack in an elastic medium with inclusions and holes under quasi-static tension. Finally, we present the results of detecting the synthetically produced crack trajectory as well as the relevant strain fields.