With a view to investigating the influence of a crystal grain size on fracture behaviours under high concentration of stress and triaxial constraint a notched tensile test was made over a temperature range from −196° to 20°C for an industrial mild steel of grain diameters 15, 45 and 150 microns. The change in a grain size was brought about by changing the normalizing condition. From the mechanical test including an examination of COD, measured using a clip gauge, and metallographical and fractographical observations under a scanning electron microscope, the following results were obtained: (1) With decrease in testing temperature, a fracture below the yield stress occurred in all the three specimens and the fracture stress transition temperature T_L was lower in the finer-grained specimen. (2) The decrease in grain diameter resulted in an increase in fracture stress σ_F for fracture below yield stress. σ_F tends towards several tens of kilogrammes per square millimetre, with an appreciable fall with decrease in temperature, in the extrapolated single crystal specimen. (3) The transition in fracture stress took place in an abrupt manner, and the abrupt change in fracture stress at T_L was more pronounced in the finer-grained specimen.