Crack-tip behaviour in metals is among the most basic problems in mechanics of materials. Yet, long-standing experimental evidence suggests that crack-tip twinning in face-centred-cubic (f.c.c.) metals is highly dependent on the material, temperature and loading rate, and previous simulations and models predict twinning in aluminium, where it has never been observed. Here, this discrepancy between theory and experiment is resolved through a new model guided and validated by extensive multiscale simulations. Both the analytic model and simulations reveal a transition fromcrack-tip twinning at short times to full dislocation formation at long times. Applied to a host of f.c.c. metals, the model agrees with experimental trends as it predicts large differences in the thermal activation needed for full dislocation emission to dominate. More broadly, this work demonstrates the necessity of multiscale modelling and attention to rate dependence for accurate description of material behaviour and computationally guided material design.