36 A.T. Zehnder and N. Zella Similar behavior was found by Tschegg [8] in a study of mixed Mode I/Mode III fatigue crack growth in 4,340 steel. At the lowest cyclic stress intensity factors, where the fracture behavior is nominally brittle, it was observed that the crack grew along a series of planes oriented at 45ı to the initial crack front. These planes link up to form a macroscopically flat fracture surface containing numerous facets running radially and oriented at 45ı to the overall fracture plane producing the factory roof fracture profile. Similar fracture patterns are observed in ceramics [9] and [10]. At higher loads, where greater levels of crack tip plasticity occur Tschegg [8] observes that the fracture transitions to a surface that is macroscopically flat and no longer has the factory roof profile. These cracks grew in a self-similar manner with the local failure plane coinciding with the plane of maximum shear stress rather than the planes of maximum normal stress seen in brittle fracture. The transition from tensile to shear fracture has also been observed under monotonic loading. Working with circumferentially cracked rods of PMMA and 7,075 Al samples Liu et al. [11] observed that the PMMA rods always exhibited brittle failure with the factory roof type surface. The 7,075 rods transitioned from brittle to ductile fracture as the ratio of KI toKIII decreased. Post-fracture images of Liu et al.’s PMMA samples demonstrate another transition. Although fracture remains brittle the overall fracture surface is spiral (similar to that of a stick of chalk broken by twisting) for KI=KIII < 1:6 and is macroscopically flat (although with the factory roof profile) for KI=KIII >2:6. These observations were for a notch depth to diameter of .b a/=b D0:08. The exact transition point is not determined nor is the impact of different notch depths explored. In studies of failure criteria under tension and shear Berto et al. [12, 13] tested PMMA rods with U and V shaped notches and varying notch root radii. They observe that at a fixed notch depth the fracture surface transitions from spiral to flat as the notch root radius decreases. Note that Hull [14] provides a thorough review of crack surface evolution in the presence of Mode-III. For a thorough review of Mode I/Mode III fracture see [11]. Taking the results of refs [13] and [12] together it is observed that the overall fracture surface in cracked or notched rids that fail in a brittle manner can transition from a spiral to a flat but faceted surface as the level of tension to torsion increases and as the notch becomes sharper, concentrating load at the notch root. In the present work we further explore this transition by mapping out the spiral and flat fracture regimes for circumferentially notched PMMA rods with varying notch depth. The notches are approximately square with corner radii of less than 0.1 mm, sharp enough that, the fracture load is insensitive to notch radius [12]. Future work will explore the effects of varying tension/torsion ratio as well as notch depth ratio. 5.2 Experimental Method 5.2.1 Samples and Loading The test samples, see Fig. 5.1, are 203 mm long circumferentially notched, circular, PMMA rods, with diameter 2b D 25:4mm and notch depths, b a, ranging from 1.27 to 5.08 mm. Circumferential notches were cut in the samples using a steel cutting tool ground to a width of approximately 1 mm. The cutting speed was kept low to prevent melting of the PMMA during cutting. Tests were performed by monotonically loading the samples to failure in pure torsion in a servo-hydraulic axial-torsional testing system. The axial load was controlled at zero while the samples were twisted in rotation control. Hydraulic collet grips hold the samples in the axial-torsional servo-hydraulic testing machine. The distance between the grips is approximately 152mm. 2b 2a Fig. 5.1 Test specimens are circular rods with diameter, 2b D25:4mm, length of 203 mm and varying notch depth. The samples are loaded with torque, T
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