Returning to the University of Iowa College of Medicine in 1972 to join its faculty, Phelps succeeded his mentor Armaly as director of the department of ophthalmology's glaucoma service.
In 1984, after rising to the rank of full professor, Phelps was appointed chair of the university's ophthalmology department, widely recognized as one of the foremost eye clinics in the country.
He died eighteen months later at the age of 47, survived by his wife Margaret Dorsey Phelps, whom he married in 1964, his four children, his parents, and his brothers.
At its first meeting, convened in his honor in Iowa City in 1987, a Hawthorn tree was planted, which still stands outside the ophthalmology department, to commemorate his life and contributions.
In a keynote address, Armaly described him as "a prolific contributor of new knowledge" who left a "scientific legacy admirable in its size, variety, and quality," concluding, "There is hardly an area in glaucoma that did not interest him and benefit from his research effort."