Title: Effect of compressibility and aspect ratio on performance of long elastic seals,
Abstract: Recent experiments show no statistical impact of seal length on the
performance of long elastomeric seals in relatively smooth test fixtures.
Motivated by these results, we analytically and computationally investigate the
combined effects of seal length and compressibility on the maximum differential
pressure a seal can support. We present a Saint-Venant type analytic shear lag
solution for slightly compressible seals with large aspect ratios, which
compares well with nonlinear finite element simulations in regions far from the
ends of the seal. However, at the high- and low-pressure ends, where fracture
is observed experimentally, the analytic solution is in poor agreement with
detailed finite element calculations. Nevertheless, we show that the analytic
solution provides far-field stress measures that correlate, over a range of
aspect ratios and bulk moduli, the calculated energy release rates for the
growth of small cracks at the two ends of the seal. Thus a single finite
element simulation coupled with the analytic solution can be used to determine
tendencies for fracture at the two ends of the seal over a wide range of
geometry and compressibility. Finally, using a hypothetical critical energy
release rate, predictions for whether a crack on the high-pressure end will
begin to grow before or after a crack on the low-pressure end begins to grow
are made using the analytic solution and compared with finite element
simulations for finite deformation, hyperelastic seals.