Multi-length scale modeling of martensitic transformations in stainless steels

Phase-field Simulation of Habit Plane Formation during Martensitic Transformation in Low-carbon Steels

“…[18][19][20][21][22] The MT in steels have been simulated by simultaneously modeling the cubic → tetragonal lattice deformation and the plastic deformation in the γ and/or α ′ phases. [23][24][25][26][27][28][29][30][31][32][33] In most of these studies, the elastic energy calculation is based on the microelasticity theory; 14,34) hence, the long-range elastic interaction between the transformation strain (Bain strain), plastic strain, and external applied stress is automatically taken into account and its effect on the microstructure evolution has been successfully simulated. However, the formation of the {111} γ habit plane has not yet been simulated; although Yeddu et al 26) predicted the habit plane of an infinitesimal α ′ phase as ( 111) γ , the final habit plane was determined to be ( 2 11) γ after the growth of the α ′ phase.…”

Strain-induced martensitic transformation in stainless steels: A three-dimensional phase-field study

“…Molar volume (V m ) = 7 Â 10 À6 m 3 mol À1 Interface thickness (d) = 1 nm Interfacial energy (c) = 0.01 J m À2 [47] Bain strains: 1 = 0.1316, 3 = À0.1998 Lattice constants: a FCC = 3.5918 Å , a BCC = 2.874 Å [48] Elastic constants of austenite: C 11 = 209 GPa, C 12 = 133 GPa, C 44 = 121 GPa [49] Elastic constants of martensite: C 11 = 248 GPa, C 12 = 110 GPa, C 44 = 120 GPa [40] Initial yield stresses: r aust y ¼ 500 MPa [50], r mart y ¼ 800 MPa [51] Hardening modulus H = 738 MPa [52] Density q = 7900 kg m À3 [53] Plastic relaxation rate (k) = 5 GPa À1 s À1 Interfacial kinetic coefficient (L) = 1 m 3 J À1 s À1 3.1.5. Shear strain loading Fig.…”

“…The microstructure evolution under different stress states, such as uniaxial tensile and compressive, biaxial tensile and compressive, shear and triaxial loadings, is studied. The input data for the simulations are acquired by using the CALPHAD method [41], which calculates the thermodynamic data, and the ab initio method to calculate the elastic constants of martensite [40]. The other necessary input data, such as the lattice constants, the elastic constants of austenite, the yield stresses for different phases and the density of steel are acquired from experimental measurements in order to ensure a physically based model.…”

“…The phase-field method [24][25][26] has been successfully used to study the microstructure evolution during martensitic transformations [8,[27][28][29][30][31][32][33][34][35][36][37][38][39][40]. The simulations clearly show some of the typical characteristics of the transformation, such as twinned microstructure evolution and autocatalysis [36], the effect of plasticity on the morphology [37], habit planes and rotations of variants during the transformation [37], the effect of embryo potency on the transformation [38], the stress-assisted martensitic microstructure evolution under different stress states and the TRIP effect [39].…”

Teoría cristalográfica de la transformación martensítica

“…Según Bhadeshia [6] y Yeddu et al [18], una transformación homogénea es aquella donde los puntos colineales permanecen colineales, y las líneas coplanares permanecen coplanares. Para el caso particular de la correspondencia de (2).…”