4 A.S. Jain and H.V. Tippur Fig. 1.4 Comparison of mixed-mode stress intensity factors from r-DGS and finite element simulation 1 0.8 0.6 0.4 0.2 –0.2 –0.4 –0.6 0 0 KI and KII (MPa√m) 200 400 600 800 1000 1200 1400 Load (N) KI from fx KII from fx KI from fy KII from fy KI from FEA KII from FEA factors. The results thus obtained are plotted in Fig. 1.4 for different load levels. A finite element analysis for the problem was carried out using ABAQUS™ software package to complement mixed-mode stress intensity factors obtained experimentally and details of the same are suppressed here for brevity. Figure 1.4 shows the variation of these computations overlaid on the experimental results. A good match between the two is evident from the plot, suggesting the feasibility of r-DGS for studying mixed-mode fracture problems. 1.4 Dynamic Mixed-Mode Experiments The crack-tip deformation measurements under mixed-mode (I/II) conditions for an edge notched PMMA specimen (130 60 8.9mm3) during stress wave propagation were performed using a long-bar impactor used in conjunction with high-speed photography and r-DGS method. The schematic of the experimental setup is as shown in Fig. 1.5. The loading device consisted of an aluminum 7075-T6 long-bar (25.4 mm diameter and 2 m long) with a cylindrical impacting head, a gas-gun and a high-speed digital camera. The long-bar was aligned co-axially with the barrel of the gas-gun housing a 305 mm long, 25.4 mm diameter aluminum striker. The crack-tip deformations were photographed using a Cordin 550 high-speed digital camera equipped with 32 CCD sensors and two high-energy flash lamps to illuminate the target plate. A beam splitter positioned between the lens and the specimen at 45ı angle was used to view the speckle pattern on the target via the reflective face of the specimen. The cylindrical tip of the long-bar was registered against the notch-free edge of the specimen. To achieve mixed-mode loading an eccentricity of 20 mm with respect to the crack line and the axis of the long-bar (see, Fig. 1.6) was used. As in the quasi-static experiments, one of the faces of the specimen (130 mm 60mm) was made specularly reflective by sputter coating it with aluminum. In these experiments, the distance between the target plate and specimen was ( D) 102 mm (and the distance between the camera lens and the specimen was 715mm). A set of 32 reference images (one image from each CCD sensor of the high-speed camera) prior to loading was captured by operating the camera at 150,000 frames per second. Next the camera was triggered as the striker contacted the long-bar. A second set of 32 speckle images was captured at the same framing rate while the specimen was experiencing transient loading. The deformed and reference image pairs recorded by the same sensor of the high-speed camera were paired and correlated to obtain orthogonal displacements ıx andıy on the target plane (see, Fig. 1.1). These were subsequently converted into surface slopes .@w=@x/ and.@w=@y/ on the specimen plane. Figures 1.7 show r-DGS contours near a dynamically loaded mixed-mode crack-tip for a time instant just before crack initiation. The contour plots of surfaces slopes in Fig. 1.8 represent the ones for the post-initiation regime following crack kinking from its initial orientation. The stress intensity factors in the pre-crack initiation phase was performed in the global coordinate system (x and y) defined at the crack-tip aligned with the loading direction and the specimen edges (Fig. 1.2). The stress intensity factors for a
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