My chest does not often burn when I workout.?

So I am lifting in the gym and it was chest day. I use heavy weights. When I do a bench press or any type of chest workout like cable crossovers, I only feel the pain in my arms. I mean the next day my chest feels sore and all that so I know my chest has been worked out. But most of my soreness is in my arms. Is it normal to have sore arms while working out your chest? By the way, no, I am not doing any of the workouts wrong.