The mathematical model of morphology evolution of spherulites and shish-kebabs in the shear flow is deduced based on the Eder model. The model considers that the nucleation and growth of spherulites are determined by the static temperature

while the nucleation and growth of shish-kebabs are determined by the flow

which is depended on the first normal stress difference of the system and the shear rate respectively. In order to calculate the nucleation density of the shish-kebabs

the two-phase suspension model of Zheng is introduced. The model treats the stress as the combination of the amorphous phase and semi-crystalline phase. The amorphous phase is described by FENE-P model while the semi-crystalline phase is depicted by a rigid dumbbell model. Based on the mathematical model

the Monte Carlo method and the finite difference method are constructed

respectively. The former is to capture the crystal growth while the latter is to calculate the equation of the system. By using these methods

the 2D crystallization in the shear flow is simulated. The evolution of spherulites and shish-kebabs is given. Also

the effects of shear time and shear rate on the nucleation density of shish-kebabs

crystallization rate

the viscosity of the fluid and the system stress are discussed. Numerical results show that the Monte Carlo method is valid which not only captures the morphology evolution of crystals successfully

but also predicts the crystallization rate well. In addition

the increase of the shear time or the shear rate will increase the nucleation density of shish-kebabs and the crystallization rate.