Near tip strain evolution of a growing fatigue crack

M.-L. Zhu et alii, Frattura ed Integrità Strutturale, 33 (2015) 67-72; DOI: 10.3221/IGF-ESIS.33.09 Focussed on characterization of crack tip fields Near tip strain evolution of a growing fatigue crack M.-L. Zhu University of Portsmouth, UK East China University of Science and Technology, China Y.-W. Lu, C. Lupton, J. Tong University of Portsmouth, UK ABSTRACT. Near tip full-field strains in a growing fatigue crack have been studied in situ using the Digital Image Correlation (DIC) technique in a compact tension specimen of stainless steel 316L under tension-tension cyclic loading. An error analysis of displacements and strains has been carried out, and the results show that the precision of displacements and strains in the wake of the crack is worse than that in front of the crack. A method for the determination of crack tip location is proposed for the DIC analysis. Strain ratchetting is observed ahead of the growing fatigue crack tip and found to be dependent on the distance to the crack tip; whilst normal strains appear to stabilise behind the crack tip. KEYWORDS. DIC; Crack tip; Error analysis; Fatigue crack growth; Strain ratchetting. INTRODUCTION A lthough strain-based approaches have been proposed [1, 2] to deal with fatigue crack growth since the 60s, our interest in this line of enquiry began some 10 years ago, mainly using numerical simulations [3-7], where near-tip strain ratchetting was found to be common in several materials, regardless the constitutive laws used [3-5] or the numerical simulation strategies [4-6]. We hypothesise that if the normal strain near and ahead of the crack tip continues to accumulate with fatigue cycles, the material ahead of the crack tip will eventually fail thus prompting crack growth. Although this concept has been successfully applied to rationalise fatigue crack growth in nickel-based superalloys [3], direct experimental validation was not possible until very recently, when the first experimental evidence of near-tip strain ratchetting was reported for stationary [8] and growing cracks [9] using in situ DIC systems. The strain distribution near a fatigue crack tip obtained from the DIC analysis may be influenced by data processing parameters used in the DIC analysis. An accurate assessment of the near-tip strains based on the DIC technique requires the knowledge of the errors in the measured displacements and strains; hence methods may be developed in the testing and analysis to minimize the errors. Strain ratchetting behaviour has been observed for relatively straight cracks [8, 9], whilst evaluation of the strain evolution in a growing crack along a tortuous path is more challenging. Determination of the exact location of the crack tip in such a situation is another challenge, which is important to a quantitative interpretation of crack tip micro-mechanical behaviour. In the present work, we report an error assessment of the displacements and strains measured using the DIC system; and a method to determine the locations of the instantaneous crack tip with a tortuous path. The evolution of normal strain range with fatigue cycles was tracked and the critical strain values at incipient crack growth were obtained. 67 M.-L. Zhu et alii, Frattura ed Integrità Strutturale, 33 (2015) 67-72; DOI: 10.3221/IGF-ESIS.33.09 EXPERIMENTAL METHODS T he material studied is stainless steel 316L, which has yield strength of 280 MPa. An average grain size was measured as approximately 17 μm. A standard compact-tension specimen was used, with a width of 60 mm, a thickness of 7 mm and a machined notch size of 12 mm. Pre-cracking was carried out under load-control using a load shedding scheme. The maximum load was decreased manually step-by-step from 10 kN to 6 kN, and the load was maintained constant at each step. The load ratio and loading frequency were 0.1 and 10 Hz, respectively, during the entire pre-cracking process. Crack growth was monitored by both the direct current potential-drop (DCPD) technique and surface replicas. The latter readings were taken as the true surface crack lengths whilst crack lengths from DCPD readings are indicative of the average crack lengths which were used to calculate the stress intensity factor K. The pre-cracking was terminated when the crack length reached 15 mm, after which a crack growth test was conducted for work reported in [9]. Further crack growth was allowed to remove the influence of pre-history and the original crack length in this work was 24.15 mm (a/W ≈ 0.4). A random speckle pattern was applied on to one of the specimen surfaces with graphite powder deposited on a white paint background. The random speckle pattern generated from the current study may be described by its grey level intensity profile, which was a bell-shaped distribution and was deemed appropriate for image correlation purposes. The imaging system (LAVISION, GMBH) consists of a CCD camera (2456 × 2058 pixels) and a Schneider Kreuznach F2.8 50mm lens with 100mm extension tubes. A region of interest, a rectangle of 1.67  1.4 mm with the crack tip in the centre, was selected for imaging in order to capture the near-tip strain data ahead and behind the crack tip. A resolution of 0.68 µm/pixel was achieved. An increasing loading scheme was applied to grow the crack into a steady-state condition at a load ratio of 0.1, from Pmax = 6 kN to 8.8 kN at a step about 10%. The loading waveform is trapezoidal with a 10 second loading/unloading and a 2 second hold at minimum and maximum loads. During the loading cycle, 23 images were collected during loading/unloading at a frequency of one image per second. Optical Microscopy (OM) was used to monitor the crack in situ and verify the crack tip position and the crack growth morphology. DETERMINATION OF THE CRACK TIP A n accurate determination of the crack tip position during crack growth is important in the DIC analysis in order to capture accurately the strains near the crack tip. This is especially true when the resolution of the image is limited by the pixel size. In this work, we propose a method for locating the crack tip by a combination of information from OM and the displacement distribution from DIC analysis. Fig. 1 presents a flow chart of the method. Firstly, determine the horizontal position of the crack tip x0 (in pixel) from the reference image collected by the DIC system and the image from the optical microscopy OM. The value x0 may be determined from the reference image facilitated by the neighbouring speckles. Secondly, calculate the average displacement value ܸഥ௬ from the full data set of the displacement component in the Y direction. The values of Vy were obtained from image correlation between Pmax and Pmin. The value of y0 for the crack tip may be obtained when Vy (x0, y0) is equal to ܸഥ௬ . The crack tip location (x0, y0) is thus determined. The rigid body displacement was removed prior to this operation. In the case of stationary cracks, the crack tip loc (...truncated)