Phenomenological Equations for Predicting γ + δ Two-Phase Region of Fe-Mn-Si-Cr-Ni Shape Memory Alloys

Three methods, i.e., optical metallographic method, differential scanning calorimeter (DSC), and thermal expansion, were evaluated to measure γ / γ + δ boundary temperature ( T γ/γ+δ ) and γ + δ / δ boundary temperature ( T γ+δ/δ ) of Fe-Mn-Si-based shape memory alloys. The optical metallographic method is most suitable and selected to determine the T γ/γ+δ and T γ+δ/δ temperatures of Fe-(14 to 25)Mn-(4.0 to 6.5)Si-(7 to 12)Cr-(2.0 to 8.5)Ni-(0.006 to 0.140)C alloys. Based on the above experimental data, the following phenomenological equations for predicting the T γ/γ+δ and T γ+δ/δ temperatures of Fe-Mn-Si-Cr-Ni-C shape memory alloys were established by nonlinear regression: T γ/γ+δ (°C) = 1762.83 + 18.46Mn − 0.38Mn 2 − 250.30Si + 19.71Si 2 + 28.66Cr − 3.20Cr 2 − 6.50Ni + 1.69Ni 2 + 289.44C; T γ+δ/δ (°C) = 2758.13 − 6.24Mn + 0.22Mn 2 − 387.82Si + 32.60Si 2 − 59.50Cr + 2.25Cr 2 + 16.75Ni − 1.61Ni 2 + 345.84C; chemical symbols represent weight percent of Mn, Si, Cr, Ni, and C elements. The two phenomenological equations provide a basis of composition design for the fabrication of training-free processed Fe-Mn-Si-based alloys utilizing δ → γ phase transformation.