Near tip strain evolution under cyclic loading

J. Tong et alii, Frattura ed Integrità Strutturale, 25 (2013) 44-49; DOI: 10.3221/IGF-ESIS.25.07 Special Issue: Characterization of Crack Tip Stress Field Near tip strain evolution under cyclic loading J. Tong, Y.-W. Lu, B. Lin University of Portsmouth, UK Y. H. Tai Rolls-Royce plc, UK J.R. Yates University of Manchester, UK ABSTRACT. The concept of ratchetting strain as a crack driving force in controlling crack growth has previously been explored at Portsmouth using numerical approaches for nickel-based superalloys. In this paper, we report the first experimental observations of the near-tip strain evolution as captured by the Digital Image Correlation (DIC) technique on a compact tension specimen of stainless steel 316L. The evolution of the near-tip strains with loading cycles was studied whilst the crack tip was maintained stationary. The strains were monitored over the selected distances from the crack tip for a given number of cycles under an incremental loading regime. The results show that strain ratchetting does occur with load cycling, and is particularly evident close to the crack tip and under higher loads. A finite element model has been developed to simulate the experiments and the simulation results are compared with the DIC measurements. KEYWORDS. DIC; FE; Ratchetting; Crack tip mechanics; Fatigue crack growth. INTRODUCTION T he concept of ratchetting strain as a crack driving force in controlling crack growth has been investigated utilising a variety of constitutive models, including elastic-plastic, visco-plastic and crystal-plastic formulations, for nickelbased superalloys [1-3]. Crack tip deformation fields were examined for both stationary and growing cracks at room and 650C using the finite element method. Distinctive strain ratchetting behaviour near the crack tip was identified in all cases, leading to progressive accumulation of tensile strains normal to the crack growth plane. It was hypothesised that this tensile strain may be responsible for material separation leading to crack growth. Most recently the concept has been applied successfully [4] to fatigue crack growth of a nickel alloy in vacuum at a range of temperatures, where the influence of oxidation is removed. Although this latest work appears to be very encouraging, no direct experimental evidence is yet available to support this line of reasoning. In this paper, we present the first series of experimental results on the measurement of the near-tip strains as a function of the number of loading cycles in a compact tension specimen of stainless steel 316L using the DIC method. Finite element analysis has also been carried out on the specimen and the near-tip strain results from the simulation are compared with those obtained experimentally. 44 J. Tong et alii, Frattura ed Integrità Strutturale, 25 (2013) 44-49; DOI: 10.3221/IGF-ESIS.25.07 EXPERIMENTAL METHODS T he material used for the investigation was stainless steel 316L. A compact tension (CT) specimen was employed with a width of 56 mm, a thickness of 7 mm and a machined notch size of 24 mm. An average grain size of the material along the rolling direction was found to be approximately 28.5 µm. The specimen was pre-cracked first in a servo-hydraulic test machine under cyclic tension, allowing a crack growth of ~2.05 mm to obtain a final crack length of ~26.05 mm. The cyclic testing was then conducted at constant load amplitude with the range of load increased after a given number (20) of cycles, as shown in Fig. 1. The evolution of the strain fields near the crack tip was monitored during the cyclic loading using the digital image correlation (DIC) technique. The DIC system employed is a stereomicroscope system, Vic-3D Micro™ by Correlated Solutions [5]. Speckle patterns were painted on the specimen surface to facilitate the image analysis, and a resolution of 1224 x 1024 pixels was achieved through the use of the cameras coupled with the microscope. Four series of tests were conducted where the near-tip strains were monitored and recorded using the DIC method. A loading frequency of 0.1 Hz was used for the testing to allow sufficient time to collect the data. The images were captured at a framing rate of 5 per second for each cycle and about 50 images were recorded for each cycle. The field of view of the images was approximately 2.15 x 1.80 mm, giving a pixel size of 1.76 µm. 6 Load [KN] 5 4 3 Test 3-4 Test 3-5 Test 3-6 Test 3-7 2 1 0 60 80 100 120 140 160 Number of Cylces Figure 1: The cyclic loading scheme used for the experiment. Digital image correlation has been used extensively to determine fracture parameters using the displacement data extracted from digital images [6, 7]. The basic principles of DIC are to take a set of sequential images for a deformed object, with the first image taken before deformation serves as a reference and the subsequent images acquired at different deformation stages from the same region correlated with the reference image. The algorithm is based on the mathematical correlation of the intensity changes of the sequentially recorded digital images, and implemented through a procedure of finding the best correlation between the two images. Digital images are usually divided into smaller interrogation windows, or sub-sets, a matching process is performed on each of these sub-sets. A full field map of displacements/strains of each subset may be obtained when the correlation process is completed successfully. In the current work, LaVision DaVis 8.1.1 was employed to carry out the image correlation [8]. The size of the subsets was chosen as 28 x 28 pixels with a step size of 3 pixels, sufficient to provide a high spatial resolution and good image correlation quality as well as acceptable computational cost. To study the near-tip strain evolution with load cycles, regions of interest near the crack tip were selected and strain distributions studied. Specifically, two points ahead of the crack and on the crack plane, R2 and R4, were monitored, where the distance to the crack tip, R2 = 28.5 µm and R4 = 57 µm, as illustrated in Fig. 2. These values were selected to be either the same as the average grain size of the material (R2) or about double the average grain size (R4). The strain data at each location were obtained from an average value of multiple points within a 25 µm x 25 µm square. During the loading cycles, the crack length was also monitored and corrected post testing when micro crack growth was detected, such that the values of R2 and R4 stay the same throughout the tests. Micro-crack growth was indeed detected during some of the loading sequences (Test series 3-1 to 3-3, omitted in Fig. 1). These were excluded in the subsequent ratchetting analyses. 45 J. Tong et alii, Frattura ed Integrità Strutturale, 25 (2013) 44-49; DOI: 10.3221/IGF-ESIS.25.07 Figure 2: The random speckle pattern on the specimen and a typical displacement map extracted from the DIC measure (...truncated)