Determination of Critical Stress for Dynamic Recrystallization of a High-Mn Austenitic TWIP Steel Micro-Alloyed with Van
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vation energy R = Thermodynamic constant T = Temperature K, n = Material hardening parameters ππ = Internal energy variation πππ = Thermal component πππ = Mechanical component ππ π‘ = Dislocation accumulated energy ππ‘ππ‘ = β‘ππΜ = Total energy ππ = Dissipated energy Μ = Dislocation accumulated energy ππ π‘ change in time πΜ 2 π = Total energy change in time ππΜ = Dissipated energy change in time π = Stress πΜ = Strain rate
π = πΎπ π ππ = πππ + πππ βππ π‘ = βππ‘ππ‘ + ππ Μ = βπΜ 2 π + ππΜ βππ π‘
π 2π ( 2) = 0 ππ πΜ πΆ π=β 3π·
Critical stress quotient C, D = Third grade equation coefficients
Number of equation 1 2 3
4
5
6 7
EXPERIMENTAL DETAILS Both non-microalloyed (TWIP-NM) and vanadium (TWIP-V) TWIP steels, were melted in an open induction furnace at the Foundry Lab of the IIM-UMSNH (Table II). After setting the chemical composition, the samples were thermo-mechanically treated by a hot rolling reduction of 50% and then solution heat treated, both at 1100 Β°C. Finally, the samples were water quenched in order to retain the microstructure. The high temperature uniaxial compression test samples were thermo-mechanically treated, cut, and painted with boron nitride to protect them from oxidation during tests. Table II. Chemical compositions, wt%. Steel C Mn Al Si N V Fe TWIP-NM 0.41 21.2 1.5 1.5 0.012 Balance TWIP-V 0.43 22.5 1.6 1.4 0.013 0.12 Balance
Three input variables were selected: chemical composition (TWIP-NM and TWIP-V), temperature (900, 1000 and 1100 Β°C) and strain rate (0.1, 0.01, 0.001 and 0.0001 s-1). Every test was performed in an E4 Quand Elliptical Heating Chamber protected with argon atmosphere to prevent superficial degradation by oxidation. The friction between superior faces of the samples and the anvils were reduced by using thin sheets of tantalum. Analytical details To determine the critical stress (ππ ) from experimental data, it is known that internal energy variation has thermal and stress components (equation 3, Table I), which can be expressed in terms of work (equation 4, Table I). Including the time, the work algebraic expression turns into a hardening strain rate equation (equation 5, Table I). The stress value considered to the DRX onset (ππ ) is at the inflection point of the true stress β true strain curve. Therefore, it is calculated from the nule second derivate of strain hardening rate in terms of stress when the strain rate (πΜ) is fixed (equation 6, Table I) [19-24]. Then, the strain hardening rate (π) graph is fitted to a third degree function to set the inflection point where critical stress (ππ ) is located (equation 7, Table I) [19-24]. π values were calculated from the activation energies required to the hot deformation (Q) obtained by Reyes-CalderΓ³n et al. [9]. RESULTS AND DISCUSSION Experimental data plots Figure 1 shows the influence of temperature on peak stress (ππ ), as it is a common hot deformation behavior, when temperature increases, the ππ values decrease; and if strain rate (πΜ) decreases, the ππ values decrease. Nevertheless, the ππ values reached do not help to find e
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