Newman did not make that many films with Joanne as his co-star. In one of the best, "From the Terrace", they had an adversarial relationship.
Newman in "Cat on a Hot Tin roof", "The Left-Handed Gun," "Exodus", "The Hustler", "Hud", "Cool Hand Luke", et al, defined masculinity in the movies in the late 1950s and all through the 1960s. Joanne Woodward wasn't in a single one of them.
My favorite Newman film from that era is "The Young Philadelphians"!