Recently, the breakup of spiral and concentric ringed spherulites has been observed experimentally in isothermal crystallization of poly(vinylidene fluoride) in its blends with ethylene vinyl acetate copolymer. To elucidate the phenomenon of spiral breakup in polymer spherulites, a theoretical simulation has been undertaken in the framework of the phase field model of solidification based on time-dependent Ginzburg-Landau equations (TDGL model C) pertaining to the conserved concentration and nonconserved phase field order parameters. The concentration order parameter was described in terms of the Landau-type potential, while the crystal order parameter was expressed in terms of an asymmetric double-well potential to account for the nonequilibrium nature (i.e., metastability) of polymer crystallization. After inserting these potentials into the TDGL model C, the resulting coupled time-evolution equations show the emergence of the target and spiral patterns that undergo fragmentation at a very shallow supercooling. It is concluded that the depth of supercooling is the major contributor to the formation of the spirals and subsequent breakup of the spiral arms.