Cracks in rubber under tension exceed the shear wave speed

The shear wave speed is an upper limit for the speed of cracks loaded in tension in linear elastic solids. We have discovered that in a non-linear material, cracks in tension (Mode I) exceed this sound speed, and travel in an intersonic range between shear and longitudinal wave speeds. The experiments are conducted in highly stretched sheets of rubber; intersonic cracks can be produced simply by popping a balloon.Comment: 4 pages, 5 eps figure

Measurement of Resonant Frequency and Quality Factor of Microwave Resonators: Comparison of Methods

Precise microwave measurements of sample conductivity, dielectric, and magnetic properties are routinely performed with cavity perturbation measurements. These methods require the accurate determination of quality factor and resonant frequency of microwave resonators. Seven different methods to determine the resonant frequency and quality factor from complex transmission coefficient data are discussed and compared to find which is most accurate and precise when tested using identical data. We find that the nonlinear least-squares fit to the phase vs. frequency is the most accurate and precise when the signal-to-noise ratio is greater than 65. For noisier data, the nonlinear least squares fit to a Lorentzian curve is more accurate and precise. The results are general and can be applied to the analysis of many kinds of resonant phenomena.Comment: 29 pages, 11 figure

Oscillating Fracture in Rubber

We have found an oscillating instability of fast-running cracks in thin rubber sheets. A well-defined transition from straight to oscillating cracks occurs as the amount of biaxial strain increases. Measurements of the amplitude and wavelength of the oscillation near the onset of this instability indicate that the instability is a Hopf bifurcation