PhD Qualifier- A study of cracks in natural rubber sheets: supersonic rupture and oscillatory instability

ACE 3.408
Chih-Hung Chen
PhD Qualifier- A study of cracks in natural rubber sheets: supersonic rupture and oscillatory instability

We have conducted both experiments and numerical simulations to investigate supersonic
cracks. The experiments are performed at 85 oC in order to remove strain-induced crystallites
that complicate experiments at lower temperature. Shear and longitudinal sound speeds are
measured to find the parameters needed to compare with a hyper-elastic theory including viscous
dissipation. We find that both experiments and numerical simulations support supersonic cracks,
and a transition from subsonic to supersonic is seen as we plot experimental crack speed curves
as a function of extension ratio based on different sizes samples. Both experiments and
simulations show two different scaling regimes for the crack speed: speed of subsonic cracks
scales with the elastic energy density while speed of supersonic cracks scales with the extension
ratio. Crack openings have qualitatively different shapes in two scaling regimes.
In addition to the study of supersonic cracks, we are interested in oscillatory instabilities in
rupture. An oscillatory instability of fast cracks in natural rubber sheets was observed by Deegan
et al. In these experiments, a systematic study of the amplitude and wavelength of oscillations as
a function of stretching ratios in x and y directions has been performed. After ruling out three
possible factors causing oscillations, we find that these oscillations come from a characteristic
length scale in the fracture system. Because the oscillatory instability cannot be explained by the
conventional scale-free theory-Linear Elastic Fracture Mechanics (LEFM), we introduce a
length scale involving Kelvin dissipation. By making this length sufficiently long, we are able to
reproduce the oscillatory instability in numerical studies. We are still working to determine how
accurately the current numerical models perform by attempting to obtain the closest possible fit
to experiments.