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We extend the model-free data-driven paradigm for rate-independent fracture mechanics proposed in Carrara et al. (2020), Data-driven Fracture Mechanics, Comp. Meth. App. Mech. Eng., 372 to rate-dependent fracture and sub-critical fatigue. The problem is formulated by combining the balance governing equations stemming from variational principles with a set of data points that encodes the fracture constitutive behavior of the material. The solution is found as the data point that best satisfies the meta-stability condition as given by the variational procedure and following a distance minimization approach based on closest-point-projection. The approach is tested on different setups adopting different types of rate-dependent fracture and fatigue models affected or not by white noise.