The relationship between Joe and Chris certainly evolves over the course of the play. At the beginning, Chris still holds the fairly immature position of seeing his father on a pedestal. He believes his father to be virtuous, hard-working, and loving of all (family, neighbors, co-workers). I say immaturely because as children move into young adulthood, they are usually more able to see their parents as three-dimensional people, but Chris has avoided this step. You could argue that he consciously makes this choice to avoid the truth, but it would seem to be more of subconscious decision. As more and more information is revealed about the truth of the shipment of parts and Larry's death, Chris is forced to see the reality of his father. He is hugely disappointed in his father's failings, and he is not moved by his father's justifications that he did for the family. Joe cannot face his son's disapproval; the relationship is not sturdy enough to survive the ugly realities of Joe's actions.
In terms of the title of the play, Chris cannot make clear to his father that it's not about just Joe, Larry and Chris. Joe should have considered all of the soldiers killed his sons; then he would never have made the choice to ship the parts for his family's sake.
The father-son relationship is critical to the theme of the play. At first, Joe Keller rationalizes his wartime crimes because they enabled him to make money to pass on to his sons and for one of his sons to inherit his company. However, as Miller reveals during the action of the play, there is far more to the father-son relationship than money. Taking responsibility for your actions and being a role model were things Joe Keller ignored when he allowed defective parts to sent from his factory. The consequences of the lack of responsibility are tragic. Upon hearing that his father is guilty of war crimes, Joe's older son commits suicide. His wife refuses to believe the death was suicide. Eventually, Chris, Joe's younger son finds the truth and is devastated. Joe sees his only recourse for not being a role model, is to commit suicide to punish himself for his crime. Unfortunately,he is also punishing Chris, his mother and Kate, who are left to pick up the pieces.