Stress Intensity Factor Gauging by Digital Image Correlation: Application in Cyclic Fatigue

Abstract

A fatigue crack in steel (CCT geometry) is studied via digital image correlation. The measurement of the stress intensity factor (SIF) change during one cycle is performed using a decomposition of the displacement field onto a tailored set of elastic fields. The same analysis is performed using two different routes, namely, the first one consists in computing the displacement field using a general correlation technique providing the displacement field projected onto finite element shape functions, and then analysing this displacement field in terms of the selected mechanically relevant fields. The second strategy, called integrated approach, directly estimates the amplitude of these elastic fields from the correlation of successive images. Both procedures give consistent results, and offer very good performances in the evaluation of the crack tip position (uncertainty of about 20 lm for a 14.5-mm crack), SIFs (uncertainty <1 MPa ffiffiffiffi m p ) and opening properties.

Identification of a crack propagation law by digital image correlation

“…This intermediate step introduces an additional uncertainty to the computation of SIFs. This is why integrated approaches are proposed to perform in a single step the measurement and identification procedures [30,5].…”

“…A measurement result is shown in Figure 3. The displacement field is subsequently post-processed (via least squares fit) by using reference fields, namely, Williams' series relevant for small scale yielding when the latter region is excluded from the analysis, by resorting to a least squares technique [1,21,22,5]. These fields u = u x + iu y take the following expression in the crack frame (crack tip at the origin, and crack path along the negative x axis) resorting to the complex plane, z = r exp(iθ)…”

“…Another route was proposed by Hamam et al [5]. It consists in considering so-called supersingular displacement fields, and more precisely, the first one that is usually discarded in a purely elastic analysis.…”

“…The latter ones could be determined by analyzing crack opening displacements measured by DIC [3,4]. These conditions could also be studied thanks to the analysis of SIF histories [5]. Crack propagation laws were also determined when the crack tip position was optically determined when using a long-distance microscope [7], or by using the crack opening displacements [8].…”

“…This type of approach was applied both on numerical simulations [27], and experimental results [5,28,2,26]. It will be used herein to follow the crack tip in a cyclic test during which propagation occurs.…”