We propose to extend the well-known Doi-Edwards theory to model the viscosity divergence caused by shear-induced crystallization occurring upon startup flow experiments in segmented block copolymers ((M) over bar (w) = 50 kg mol(-1)). Unlike models such as Convective Constraint Release in which the chain relaxation is accelerated by the shear, we propose to increase the final relaxation time of the polymer within the memory function to take into consideration the progressive association of the hard-segments. To this aim, we make use of the Avrami equation in which we parametrize the crystallization rate to depend on the shear rate in a linear way. In this context and contrary to what is generally proposed for supramolecular polymers, we consider the hard-segments aggregation as an irreversible process (infinite lifetime) due to the crystalline nature and the high-functionality of the resulting topological nodes. The exponential trend of the Avrami process is then validated by stress relaxation experiments performed at different levels of strain. Moreover, the growth mode parameter, usually assigned to the geometry of the crystallites, is found to be independent of the shear rate and in excellent agreement with a previous work in which we investigated the quiescent crystallization of the same system. We finally apply our model to fit data measured at different temperatures, well-confirming the development of hard-segments' crystallites from the very first stages of the isothermal shearing process. (C) 2019 The Society of Rheology.