Which stresses a material more: constant high pressure or alternating between low to high Let's say we have a glass container with fluid at 7 MPa and another one with fluid alternating between 3 MPa and 7 MPa (or any arbitrary numbers). The highest pressure in the alternating one is equal to the pressure in the stable one.
Which container breaks first? Is there a general rule for this? Does it depend on the material or shape etc. of the container?
 A: This is really more of a materials science question than a physics question. From a physics standpoint, the maximum stress experienced by the container will be the same in both cases since the maximum internal pressure of the container is the same in both cases. 
From a materials standpoint there may well be a big difference in the time to failure for the two cases. The word that describes the materials science issue that you are interested in is called "fatigue". Some metals such as aluminum undergo considerable fatigue weakening if they are subjected to cyclic stresses rather than just a steady stress. What happens is that small micro-cracks appear at stress points and then, with repeated stress cycling, the small cracks grow larger and larger over time, often resulting in catastrophic failure of the part.
Gradual fatigue induced damage leading to catastrophic structural failure was responsible for the in-flight breakup and loss of several de Havilland Comet airliners in the early part of the commercial jet age. Fatigue was also a contributing factor in the development of significant deck and hull cracks in WWII Liberty ships. Material fatigue is probably also the reason that no company (to my knowledge) makes car mufflers out of aluminum despite aluminum's excellent resistance to rusting. The vibrations that any car muffler experiences would probably lead to fatigue-induced failure of an aluminum muffler before long. 
I'm not sure offhand what the the sensitivity of glass is to fatigue but there is evidence that fatigue of glass can be an issue. For the question that you posed about glass containers, the survival time of the glass container subjected to a constant pressure should be at least as long as the glass container subjected to a cyclic pressure. 
