Can you do failure analysis as a university professor? I will equivocate a little, and say maybe. Certainly there are a lot of university professors that teach courses on failure analysis, and some are actively involved in research that involves failure analysis of mechanical components (fatigue, fracture, high temperature behavior, etc.). I think most Mechanical or Materials engineering departments have at least one class devoted to failure analysis in some manner, often seeking out contributions from industry for teaching and/or research purposes.
There is a wide range of programs and their focus, so it will depend a lot on how "academic" you would want the research to be. At one end of the spectrum (very academic), take a look at The Fracture Control Program headed by Prof. Sehitoglu at the University of Illinois:
Mechanical Science & Engineering - University of Illinois
Prof. Socie's work at UofI on fatigue, especially multiaxial fatigue, is another example of the type of work that is performed at a large academic research institution. On the other end of the spectrum, there are smaller universities that may offer a better fit. One example would be North Dakota State University, where Wayne Reitz is a faculty member, and also runs his own business conducting failure analysis:
Mechanical Engineering - North Dakota State University
Other universities with significant activities in this area include UT-Knoxville (lots of work with ORNL), Purdue University, Michigan Technological University, and really any of the other Big Ten Universities. Also, take a look at the ASM International and TMS websites, and look at the conference presentations in the areas of fatigue, fracture, etc. to get a feel for some of the current work being done.