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The double yield (DY) phenomenon observed in a wide variety of semi-crystalline polymers (SCP) adds difficulties in the material characterization. In this paper, a constitutive model, termed as explicit semi-crystalline polymer (ESCP) model, is proposed to study DY phenomenon as well as the rate- and temperature-dependent thermomechanical response below the glass transition temperature. The underlying yield kinetics due to the morphological changes of the spherulite micro-structure is represented by a rheological analogue described by a physically-based amorphous intermolecular resistance and a rate-independent crystalline interlamellar resistance. Independently-identified viscoelastic response and network resistance are also implemented to complete the model description. The activation and disclosure of the crystalline component depend on the saturated state of amorphous phase. The proposed model is validated against ex- perimental data obtained from different authors for three commonly used SCPs: nylon 101, LDPE and PA6. A straightforward parameter identification procedure, requiring a minimum number of calibration tests, is presented to illustrate the model usage. The thermomechanical-coupled analyses provide satisfactory predictions using simulated models of a cylinder compression and dogbone tensile tests at different rates, where the self-heating and thermal softening effects are naturally captured by the model.