What is the strength of human cornea?
Normal pressure in the eye1,2 is between 10 and 21 mmHg (somewhere around 1.3-2.8 kPa or 0.01-0.03 atm) with pathology occurring at around 30 mmHg.3  Clearly the cornea can handle that, but how much more?  There's a lot more evidence as far as I could see for how well surgeries hold up, with 150-300+ mmHg (20-40 kPa, 0.2-0.4 atm).4  One source5 from 1998 cites work supposedly showing that the stroma:


  gives the cornea 100 times more strength than is necessary to withstand the maximum intraocular pressure under physiological conditions.


So maybe around 200 kPa, for just the stroma?  Interestingly, a new eye layer was discovered earlier this year; this Dua's Layer is incredibly thin - 15 microns - but can withstand pressures of around 100-200 kPa (750-1500 mmHg, 1-2 atm).6,7  The large range there is due to some conflicting numbers in those links; the 200 kPa is the more widely reported one, but again, that's just for one layer.

Then, of course, there is this: a beautiful 2009 thesis by Jill Aliza Bisplinghoff from Virginia Tech which thoroughly examines the issue.  As an answer to your question, it includes the following such gems:


  The high rate pressurization of 20 human eyes resulted in a mean rupture pressure of 0.97 ± 0.29 MPa (7275.60 ± 2175.18 mm Hg)... A student T-test revealed that the difference in the rupture pressure between the equatorial mean of 0.93 ± 0.30 MPa (6975.57 ± 2250.19 mm Hg) and the meridional mean of 1.13 ± 0.21 MPa (8475.70 ± 1575.13 mm Hg) was not significant (p=0.16)


and


  A pneumatic cannon was used to impact eyes with a variety of projectiles at multiple velocities... The projectiles selected for the test series included a 6.35 mm diameter metal ball, a 9.25 mm diameter aluminum rod, and an 11.16 mm diameter aluminum rod... A range of internal eye pressures were produced that varied from 1256 mmHg (24.3 psi) to 22843 mmHg (442 psi)... [and] resulted in zero globe rupture.