Three kinds of ethylene-octene copolymers (POE) were melt-blended with high-density polyethylene (PE-HD) in different proportions. Detailed characterizations were conducted to analyze their structural differences of POE and its effects in toughening PE-HD. The higher molecular weight POE can improve the toughness of PE-HD. 60:40 PE-HD/POE is elongated to break up to 700% while impact strength is 84.7 kJ/m(2)at -30 degrees C, which is 21-fold of PE-HD. In the brittle to ductile transition (BDT) during impact, the fracture mechanism changes from the crazing mode to the shear yield-plastic deformation mode. The BDT temperature decreases as the POE molecular weight and its content increase. The interface strength in tension is estimated to access their effects. The Boltzmann-type models were successfully extended to describe the typical S-shaped curves in BDT of notched impact strength vs POE content or temperature. The supplementary decay model is suggested for the attenuation in toughening. Transition map in impact is proposed to select the use range of composition (c) and temperature (T) for high toughness. The curves are converted into 3D graph ofT-c-impact strength for illustrating their coupling-separate effects, and further into the contour map of impact strength inT-cspace for finding their partial equivalence.