The fact is it will never happen, people will prefer to use both of them, as we cannot expect illiterate and poor person will use bitcoin ever, he will be satisfied with fiat.
That is the reality that bitcoin will not replace fiat by any means, much better if people would treat to use them both as a currency for physical money as fiat and digital currency for bitcoin.
There is nothing wrong in using both of them, fiat is much in demand in the interior parts where internet and bitcoin has not reached yet, and it will surely take long time.