Using the default convergence settings will usually result in reasonable results, however, sometimes important results of interest such as stress or displacement around specific areas may not show good convergence with the defaults.
Changing the defaults can help. It is better to pick ‘measures’ of interest to converge on rather than the defaults which are generally of no interest. If you are calculating stress then you should pick that as a convergence measure. If you only need the displacement at a particular point then pick that. Sometimes you may need to create measures to calculate data at a specific location. Whatever measures you choose, you should also pick ‘strain energy’. Strain energy must converge to have a valid solution. If you have large elements in high stress gradients areas you may also want to increase the plotting grid for better resolution.