There is no common word neither for copper nor for iron. That means it was not spread during copper or iron age. It was spread during neolithic from Anatolia, in Balkans and Danube valley. Danubian neolithic culture based on bull power and 4 wheeled chariot, was civilization which spoke PIE. We must know that barbarian s take the language and culture from civilization and not vice versa. Neolithic was civilization while steppe people were nomads, without civilization, they were barbaric people. They were incorporated into Old Europe just like Visigoths and others were incorporated into Roman Empire, and just like them they were assimilated into the language of the civilization.
Also there was no only one spread. It is against all linguistic evidence, which tells us that every IE language in itself is mixing of 2 or more IE dialects, for example english bull and cow, albanian buall and kau, slavic bivo and goved etc. These are variants PB and KG.
The word for copper varies from one language to another: copper and other derivatives are later dvelopment from name Cyprus which produced it. Bakar in balkans is borrowed from turkish. So we must exclude the two names.
In latin copper was called AES, AERIS
In baltic it is called varš, varis, (latin and baltic, seems a bit simmilar)
In slavic it is called MED, медь, медзь, мідь, miedź
In greek it was called chalkós
In italian it is called rame, just like in albanian rem, although I don't where this word comes from.
Iron on the other hand:
Latin ferrum
baltic dzelzs, geležies (simmilar to slavic, but not others)
Slavic Zhelez, железо, but also GVOZDE, гвожђе
Albanian hekur, from gr. anchyra
greek Sidero
Germanic Eisen,
Celtic iarann (iron), iarainn
So there was no Whole IE spread in the copper or iron age, but it was earlier. Barbaric people from the east were incorporated and assimilated into Old Europe becaming IE, and they spred in diffrent times in all directions.
There are 4 genetic groups linked to IE:
1. R1a were blonde, blue-eyed, blood group B, mtDna U5, satem language, they formed balto-slavic, and indo-iranian families of peoples.
2. R1b were red-haired, freckling, Rh-, some of them Alpine race, in the begining basque language, and the assimilated into IE by civilized neolithic farmers, and today speaking kentum language.
3. Haplogroup I in the north, blonde, blue-eyed, creating germanic family.
4. True IE, neolithic farmers: G, Ev13, J2b, and mtDna H, blood group A, speaking old Centum, from them were created PaleoBalkanic peoples: Greeks, illyrians, thracians, and Anatolians.