In this contribution we propose a dynamic gradient damage model as a phase-field approach for studying brutal fracture phenomena in quasi-brittle materials under impact-type loading conditions. Several existing approaches to account for the tension-compression asymmetry of fracture behavior of materials are reviewed. A better understanding of these models is provided through a uniaxial traction experiment. We then give an efficient numerical implementation of the model in an explicit dynamics context. Simulations results obtained with parallel computing are discussed both from a computational and physical point of view. Different damage constitutive laws and tension-compression asymmetry formulations are compared with respect to their aptitude to approximate brittle fracture.