13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- occupied space. During initial loading at both temperatures, cracks formed in the matrix normal to the loading direction at positions where the matrix lay over a transverse fiber tow. With increasing load, the cracks grew through the transverse tows until they met an underlying axial tow (at loads in the range ~40 N to 70 N), where they were deflected. At 25°C this deflection involved formation of multiple splitting cracks (Fig. 5a), which progressed incrementally along the centers of the axial tows as the load was increased to the peak value of 150 N. Above 1600°C, the deflection of the crack at each tow involved a single crack that grew along the edge of the axial fiber tows as the load increased to 120 N (Fig. 5b), whereupon there was a large load drop. By influencing the access of ambient gas to the internal reinforcing fibers, differences in crack paths such as these could potentially have a large effect on subsequent high-temperature oxidation damage. Figure 4. Sectional view of the heating chamber in a test rig designed to permit x-ray μCT imaging during testing at high temperature [27]. The x-ray beam passes through a load-supporting Al window, whose absorption is constant during rotations of the chamber and specimen and therefore does not impair image quality. The sample is held by water-cooled grips in the center of a sealed cell, which can be evacuated or filled with a selected gas. A hexapole arrangement of six 150 watt halogen lamps and reflectors gives a spherical hot zone of diameter ~5 mm. 5. Rapid computation of multiple discrete damage events A critical element of high-fidelity simulations of failure is the ability to introduce new cracks during the execution of a simulation at locations and with orientation that are determined by the current local stress or strain fields. A major contribution to virtual test development has been the new formulation of finite elements (extended finite element method or X-FEM and others) that achieve this objective [28-32]. The augmented finite element method (A-FEM) [33, 34], similar in form to a conceptual element introduced earlier [29], has achieved detailed representations of generic multi-crack configurations and particularly high computational efficiency. Key attributes include: breakable elements that allow cracks to be introduced across which cohesive tractions exist, following a prescribed nonlinear fracture law; and breakable cohesive elements that allow the correct description of the local stress state around crack bifurcations or coalescence events (Fig. 6).
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