This will most likely be the Google Glass, or Apple Glass concept device. Whenever that becomes mainstream. Idk about 1-2 years, but I'd say phone's will be replaced with that (for a lot of functionality, anyway) eventually.
Tech glasses of any type won't become mainstream. People don't want to wear glasses of any type when they don't need to. That's the same thing with VR glasses. VR won't become mainstream if people need to wear it on their face. Look how Google Glasses and 3D TVs flopped. People were amazed by it first, but they realised that it doesn't make sense in this form.
I think headsets in general WILL become mainstream but they won't be replacing the phone (or laptops, or tablets). Headsets are for doing specific tasks, not for general purpose. This isn't about if Tech can, it's about the threshold of public acceptance.
The odd thing about Google Glass is that it never became an actual consumer product - it stayed in "Explorer" mode until the end. The entire product was quite literally a "taste" of the future and not a full meal. The public "backlash" over Glass was way overblown, in terms of both technology and coverage. The people who were afraid of what it could do never used the actual device (if they did, their fears would be calmed because the device itself was quite limited and over marketed by Google). I also think the media picked up a small amount of people who were fearful and turned it into mass panic. All of this to say I wouldn't necessarily judge public acceptance based on Glass - it was over-inflated marketing by Google and over-inflated fear spreading by the media.
Augmented Reality glasses will come to the public sector and it will launch mass acceptance by somebody who "cracks the code" (figures out how to do it right), but part of that code cracking will be putting it in it's place - an accessory to the phone meant for specific applications, not a replacement for it.
Apple is smart to be doing AR on the the phone/iPad and seeing how people are going to use AR first before investing in glasses.