According to this datasheet (Table 12, page 10), modern Plexiglass has the following properties:
Tensile strength (0.25" specimen-0.2"/min)
--------------------------+---------+------------
Maximum psi | 10,500 | 10,200
Rupture psi | 10,500 | 10,200
Elongation, maximum % | 4.9 | 4.5
Elongation, rupture % | 4.9 | 4.5
Modulus of elasticity psi | 450,000 | 450,000
Poisson’s ratio | 0.35 | —
--------------------------+---------+------------
Flexural strength (span depth ratio 16, 0.1"/min)
--------------------------+---------+------------
Maximum psi | 16,000 | 15,000
Rupture psi | 16,000 | 15,000
Deflection, maximum in | 0.6 | 0.5
Deflection, rupture in | 0.6 | 0.5
Modulus of elasticity psi | 450,000 | 450,000
The datasheet also has the following statement (page 5):
Design stresses
Plexiglas sheet has good tensile and flexural strength properties. However, stress considerably below the values shown in Table 12 (page 10) will produce light surface cracks known as crazing.To avoid stress-crazing, design limits for continuously imposed loads should not exceed 1,500 psi for Plexiglas G sheet and 750 psi for Plexiglas MC sheet. Stresses of greater magnitude but short duration will not generally cause stress-crazing.
Whether the four or so hours it took to reach 9000 meters is enough to cause stress-crazing, I can't say, but maybe that was it. Given that the cracking was apparently violent enough to shake the craft, I doubt it, though.
So, a square Plexiglass sheet with a span/depth ratio of 16 will fail at 16000 psi. What isn't clear to me, however, is what precisely is meant by that. Is that the ultimate applied load or the maximum internal stress it can withstand? I'd guess it's the applied load, but it isn't clear (to me, at least) from the datasheet.
However, we (or at least I) have no idea what the span/depth ratio was in the Trieste, nor do we know if perhaps Plexiglass was weaker back then.
As to how it wasn't tested for such loads, it almost certainly was. One possible explanation would be a manufacturing or testing failure, where the conditions in the tests were different in some slight but significant way, or where the tests actually unknowingly weakened the bathyscaphe.
