Petrarch's term didn't become a widespread label; the centuries immediately following him didn't study history dogmatically the way a modern liberal studies education demands. It was a German classical scholar named Christoph Cellarius (1638-1707) who standardized the three general periods of the past two millenia with his mammoth work Universal History Divided into an Ancient, Medieval, and New Period. "Medieval" was from the Latin medium aevum (literally, "middle age"). This triple division struck the right note and entered the realm of conventional wisdom.
Still, the "Dark Ages" didn't go out of fashion, although its definition and popularity shifted. The American Cyclopaedia in 1883 said:
The Dark Ages is a term applied in its widest sense to that period of intellectual depression in the history of Europe from the establishment of the barbarian supremacy in the fifth century to the revival of learning about the beginning of the fifteenth, thus nearly corresponding in extent with the Middle Ages.The Encyclopaedia Britannica, 11th edition (1911) defined the Dark Ages as the period from the fifth to the tenth centuries, affirming that "the Dark Age was a reality."
In 1929, however, the 14th edition of Britannica removed the term "Dark Ages" and stated:
the contrast, once so fashionable, between the ages of darkness and the ages of light has no more truth in it than have the idealistic fancies which underlie attempts at mediaeval revivalism.A scholarly view of the "Dark Ages" has largely been eliminated in favor of the generic term "medieval" to distinguish between the Classical and Modern eras (Cellarius would be proud). In fact, because artistic, cultural, political and technological (et alia) development is a continuum, the division of "eras" has been muddled with a recent trend to refer to the Renaissance as the "Early Modern Era" (I remember a lecture from my grad school days in which we joked that maybe the Middle Ages would soon be labeled the "Really Early Modern Era."
Part of this desire to eliminate the concept of "dark" Ages is also 20th century understanding that not only was the period not a complete intellectual wasteland, but also that there were at least three "re-births" of education and art prior to what we think of as the European Renaissance.
But that's a topic for another day.