Mathematical and numerical correction of the DIC displacements for determination of stress field along crack front

Abstract

The digital image correlation method (DIC) has wide application to determine the singular (stress intensity factor) and non-singular (T-stress) components of the stress field in the vicinity of the crack-tip. DIC has a simple implementation and provides large arrays of experimental data. However, it requires an a priori or post processed determination of the rigid body shifting and the crack-tip position.A method for mathematical processing of the experimental displacement fields obtained by means of DIC is presenting and validating in this work. The method provides an accurate and direct solution for the problem of simultaneous determination of the body displacement and the position of the crack-tip and crack plane orientation as well as appropriate terms of Williams’s series expansion. It is basin on geometric and kinematic relations and involves a solution of multiparametric minimization. As a result, this procedure allows better accuracy in the estimation of fracture mechanics parameters.An interactive Matlab program with graphical user interface was developed for implementation of the method. The program has a wide functionality for filtration and selection of the experimental data presented in the form of displacement fields as well as for control of the solution and it verification. Possibility of automatic accounting of the real position and orientation of the crack by means of definition of appropriate geometrical parameters, allows simplifying the procedure for measurement of the displacement fields and post processing. The method has a great potential for application to full-scale engineering components and allows automatic tracking of a fatigue crack with simultaneous determination of the fracture mechanics parameters.The efficiency of the approach has been demonstrated on real fatigue crack on compact tension specimens with different crack lengths and loading conditions.It should be noted, that the proposed method can be using as a basis of the determination of the fracture mechanics parameters along the crack front. For this purpose three steps must be performing:– Calculation of dominated terms of William’s series expansion in the vicinity of the crack tip on the specimen surface, using the described method.– Implementation of previously developed experimental and numerical method of the inverse problem solution for calculation of the loading parameters act on the crack region. The corresponding boundary problem of the solid mechanics is employing with obtained information related to the crack tip location and local (near the tip) displacement fields which are restored via the expansion terms.– Solution of the direct problem for numerical calculation the stress intensity factor and the T-stress along the crack front at determined load parameters and crack geometry.