Humphrey Bogart did not receive an Oscar nomination for portraying Duke Mantee in The Petrified Forest.
Humphrey Bogart plays the bank robber and made his first break out with this film. This break out did not make him a leading man, but rather propelled him to a prominent supporting player. Apparently it was Leslie Howard who insisted Bogart reprise his stage role as Duke Mantee, a role that is well built up by the film until his appearance in the last act of the film. His first appearance though is not excessively dramatic as he and his gang make hijack a car, but at least it builds up to his far more dramatic entrance into the diner. Well Bogart is indeed a natural fit for the criminal type and does match exactly what it is described about Duke especially well. Bogart's good at bringing that sort of needed rough command to the character as well brings the violent nature of the man in his eyes as he enters the diner. The Duke comes in and technically speaking takes over the film even though he does not really have that many lines of dialogue with much of his time being spent watching the other people in the diner complain about their lives.
Bogart though carries a strong menace with his mere presence while being able to bring a great deal of intention to himself merely in the way he watches over the people, while Duke waits for the rest of gang to appear including his girlfriend. The film already gives the description of the killer as basically a sunken man and Bogart matches this rather well in his physical expression of Duke's face. Bogart is able to keep a certain tension through his performance, even though the film kinda wastes it a bit with it's decision to perhaps make the civilians and the gang a little too chummy. After all even when one of the guys in the diner tries to take down the gangster they seem to try their best not to hurt him for it. Bogart though meets the demands as the hard man who is both feared and oddly looked up to because of notoriety. Bogart is able to project himself with that slightly larger life anti-ego in a way. Bogart is very good in the way he has Duke's manner to be modest in that he is not technically speaking really a flamboyant sort. Bogart though makes it impossible not to notice him as there is something striking about his explosive personality even though he's keeping it under control for the moment.
The most remarkable element of Bogart's performance though is that he does not portray Duke as a particularly happy man even in his escape. There is a certain sorrow and anguish that Bogart effectively brings in the man as though he is well aware that he probably won't make it out of the night alive. Bogart though is particularly good in his moments where he interacts with the failed author and current drifter Alan (Howard) who wishes for Duke to kill him that way he can give his life insurance money to someone he cares about. They technically are both men starring into a void, but Bogart expresses well the difference in Duke over Alan, as the Duke seems wholly confused over Alan's willingness to die. Now I do have to admit I do have a few reservations towards Bogart's performance here as there is a bit of unneeded theatricality such as the way he holds his arms when walking around which does not quite work, and leaves his performance here not nearly as assured as some of his later work. Also his whole character is wrapped up in a way that feels a bit unsatisfying although that is hardly Bogart's fault. Nevertheless this is still a strong portrayal and it is easy to see why it became his first major break through as an actor.