Abstract: This paper studies the mathematical simulation of the properties-temperature curve of ductile-brittle transition process for materials and finds the best mathematical model of ductile-brittle transition. That is T=Tc-1/b ln(Ymax-Ymin/Y-Ymin-1) where Y----the test value; T----test temperature ; To----the transition temperature; Ymax----the upper shelf value of the curve; Ymin----the under shelf value of the curve, 1/b---a constant relating to temperature range of transition. If 1/b is unknown, it should be found by two points. Their temperature interval should not less than 30K(Three points will be better) 1/b=T2-T1/ln(Y′2-Y′1Y′2/Y′1-Y′1Y′2) Y′=Y1/Ymax Y′2=Y2/Ymax where T1 and T2 are test temperatures, Y1 and Y2---the test values at T1 and T2 respectively. According to the mathematical model mentioned above, the following conversion is found. Tc=TNDT+3.48 1/b where Tc and TNDT are the energy ductile---brittle transition temperature and ail-ductile transition temperature respectively. These relationships obtained above, not only find the common principle for determining the material’s ductile-brittle transition temperature and the mathematical method of a quantitative analysis for ductile-brittle transition’s process, but also find the method to translate the properties transition curves into the mechanism transition ones, and the basis to build the mechanism diagram of cold-brittle fracture.

Key words: 材料, 定量分析, 韧脆转移, 数学模拟, Array type, Oscillation Buoy , Raft type , Structure design, Wave energy