5 Fracture Surface Transition for Notched Bars in Torsion 37 5.2.2 Nominal Stress Intensity Factors Although the sample contains a square notch, not a sharp crack, results will be presented in terms of the nominal stress intensity factors, KIII computed assuming a sharp crack of the same depth as the notch [15], KIII D 2T a3 p .b a/r a b F3 a b ; F3 D 3 8"1C0:5 a b C0:375 a b 2 C0:313 a b 3 C0:273 a b 4 C0:208 a b 5#; (5.1) where T is the torque, b the radius, anda is the radius of the uncracked region. 5.3 Results Torsional fracture experiments were performed on samples with notch depths systematically varied from 0 to 0.4 of the radius and the fracture. As the notch depth was increased it is observed that the fracture transitions from an overall spiral surface to a mixed spiral and flat surface to a nominally flat surface. Examples of each of the three types of surfaces are given in Fig. 5.2. The spiral surface is the surface you would obtain by twisting a piece of chalk to failure. The spiral-flat surfaces are a mix of the spiral surface with a region of nominally flat fracture. The flat fracture surface is anything but flat at the small scale. As in other studies of Mode-III fracture the surface consists of a sawtooth surface consisting of linked facets at approximately 45ı to the axis of the rod. Multiple microfractures emanate from the main fracture surface into the interior of the rod as can be seen in Fig. 5.2. Figure 5.3 plots the fracture surface type versus the normalized notch depth. For the shallowest notches, .b a/=a 0:1 the fracture surfaces are always spiral or spiral/flat. For deep notches, .b a/=b 0:3 the surface is always nominally flat. In the transition zone0:1< .b a/=a<0:3the surfaces are a mix of spiral/flat and flat with predominantly flat surfaces for notches with .b a/=a>0:2. Computing the nominal stress intensity factor for all experiments, see Fig. 5.4, it is seen that the nominal fracture toughness KIII is 3.5–4.5 MPapmand does not vary with notch depth. To develop a better understanding of the fracture surfaces as well as of the structure of the interior cracks micro-CT scans were performed on several samples. And example, showing mating fracture surfaces for a nominally flat surface sample is shown in Fig. 5.5. The figure shows that multiple facets develop from the initial crack front. These facets are spaced 2–4 mm apart. As the crack grows towards the center of the sample, the facets merge and coarsen. 5.4 Summary and Future Work Notched rods of PMMA were tested in torsion to fracture. As the notch depth increases, the overall fracture surface transitions from a spiral fracture to a nominally flat, but locally faceted surface. The transition occurs between 0.1 to 0.3 notch depth to radius fraction. Future work will map out the fracture surfaces for varying notch ratios of tension to torsion as well as varying notch depth, resulting in an experimentally obtained phase map in the space of notch depth and KI W KIII. Results of the work will be presented as a challenge for testing the ability of computational models to predict these complex and evolving fracture surfaces. Acknowledgements This work was supported by a grant from Cornell’s Engineering Learning Initiatives. This work was enabled by use of the Cornell University Biotechnology Resource Center (BRC).
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