I think its safe to say that bitcoin will never replace fiat in our lifetime. The currencies are matter of faith, and for the moment bitcoin will remain a side player. Will it continue rising in popularity? I think yes. To the extent that it becomes successful, it will serve as a complement to fiat currencies, as well as other cryptocurrencies.
Yeah bitcoin will become more popular in future but people will prefer to use it as a secondary currency and will use it only for online purposes and to buy anything offline they will choose to use fiat as fiat is widely used and accepted in compare to bitcoins.
Bitcoin will not replace fiat but after knowing bitcoins people will reduce the usage of fiat for sure as even now people prefer to shop using credit cards so once they are aware about bitcoins they will surely switch to bitcoins for making payments.
Credit card is different from bitcoins. Credit card might also be digital but it's all about credit. People are addicted on using credit card because they are able to buy stuffs right away even when they cannot afford it yet. Bitcoin, on the other hand, is like the counterpart which is the debit card. Imagine a debit card that allows you to send money abroad without doing that much and without paying much. That's how bitcoin is.
But even when people aren't relying on cash nowadays, there's rarely people that's switching to using bitcoins because it's not that convenient enough to most people. There's very few places in the world where you can buy stuffs directly using bitcoins, meaning without converting your bitcoins to fiat first. The merchants are kind of the problem to some but the number of merchants accepting bitcoins will not increase unless the number of bitcoin users has increased tremendously.
In its current form Bitcoin is never going to be an improvement on digital fiat, which is what you have with debit and credit cards. The digital transfers by the cards are cheaper, faster, and offer legal protections that Bitcoin does not. Any one of those is a large advantage over Bitcoin, but taken together... Bitcoin doesn't compare.