Fluorine-Containing Molecules Serve as Structure-Directing Agents in Synthesis of Molecular Sieves
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ing, one of the most fundamental questions associated with crack dynamics is the maximum speed that cracks can propagate. Depending on the type of loading (e.g., tensile, shear, or antiplane shear), there is a unique maximum speed cracks can achieve. For tensile-loaded cracks, theory predicts that this limiting speed is the Rayleigh wave speed, the speed of elastic waves on a surface. Recent theoretical work, including atomistic simulations, has challenged this classical view. Now, P.J. Petersan and co-workers from the University of Texas at Austin have shown experimentally that tensileloaded cracks in rubber can actually propagate faster than the Rayleigh wave speed and even break the sound barrier. As reported in the July issue of Physical Review Letters (105504), Petersan and colleagues identified the intersonic crack speed by the observation of shock fronts near the crack tip by high-speed photography (see Figure 1). The experiments were conducted using highly stretched sheets of rubber. In this nonlinear material, cracks in tension (mode I) exceeded the shear wave speed and traveled in the intersonic range between shear and longitudinal wave speeds. These results have important implications for understanding fundamental crack dynamics, demonstrating that the classical understanding of crack dynamics needs to be revised. What is the physical explanation for this phenomenon? Through observations made earlier in large-scale molecular dynamics simulations, M.J. Buehler and H. Gao of Max Planck Institute, Stuttgart, and F.F. Abraham of Almaden Research Center in San Jose discovered that hyperelasticity (i.e., the elasticity of materials at large strains), although mostly neglected in existing theories of fracture, is crucial in understanding crack dynamics. In their article published in the November 13, 2003, issue of Nature (p. 141), Buehler and colleagues hypothesized that energy flow toward a crack tip occurs in a region whose size is described by a so-called characteristic energy length scale χ. This length scale competes with the size of the hyperelastic region. If the size of the region of energy flow χ is comparable to the size of the hyperelastic region (rH), energy flow is completely dominated by the local largestrain or hyperelastic properties. “For instance,” Buehler said, “if material stiffens with strain as in the case of rubber used in Petersan’s experiments and in the molecular dynamics simulations, energy flow is enhanced because of the stiffer material properties, and cracks can thus break through the sound barrier. The observation of intersonic mode I 686
Figure 1. Multiple-exposure photograph of a crack propagating in a rubber sample ( λ x = 1.2, λ y = 2.4); speed of the crack, ~56 m/s.
cracks in rubber seems to be an example for the importance of hyperelastic effects in real materials. ” Petersan said, “We agree that the rupture of rubber opens up a new regime in the study of fracture and look forward to understanding the mechanism which explains it.”
Fluorine-Containing Molecules Serve as St
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