Slightly more massive stars do expand into red giants, but their helium cores are not massive enough to reach the temperatures required for helium fusion so they never reach the tip of the red-giant branch. When hydrogen shell burning finishes, these stars move directly off the red-giant branch like a post-asymptotic-giant-branch (AGB) star, but at lower luminosity, to become a white dwarf. A star with an initial mass about will be able to reach temperatures high enough to fuse helium, and these "mid-sized" stars go on to further stages of evolution beyond the red-giant branch.
Slightly more massive stars do expand into red giants but their helium cores are not massive enough to reach the temperatures required for helium fusion so they never reach the tip of the red-giant branch When hydrogen shell burning finishes these stars move directly off the red-giant branch like a post-asymptotic-giant-branch (AGB) star but at lower luminosity to become a white dwarf A star with an initial mass about will be able to reach temperatures high enough to fuse helium and these "mid-sized" stars go on to further stages of evolution beyond the red-giant branch