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NTRODUCTION

FERRITIC stainless steels (FSSs) find potential applications in various industries because of their good mechanical properties and corrosion resistance. Addition of alloying elements to iron-chrome systems, as well as the mechanical and thermal treatments (i.e., hot and cold rolling and annealing) can modify their microstructure and, consequently, generate steels with different properties.[1] The microstructural changes that occur during the deformation and annealing procedures depend on the recovery, recrystallization, and grain growth kinetics.[2] Recrystallization kinetics can be described as the variation in recrystallized volume fraction (Xv) as a function of annealing time, usually at isothermal conditions. Material softening has been reported to be related to recrystallization, which occurs during annealing.[2] XV corresponding to the softened volume fraction (XS) can be determined from the PAULA OLIVEIRA MALTA, DAVI SILVA ALVES, ALINE OLIVEIRA VASCONCELOS FERREIRA, IANE DUTRA MOUTINHO, CAROLINA ARRIEL PEDROSO DIAS, and DAGOBERTO BRANDA˜O SANTOS are with the Metallurgical and Materials Engineering Department, Universidade Federal de Minas Gerais - UFMG, Belo Horizonte, MG 3106200, Brazil. Contact e-mail: [email protected] Manuscript submitted June 1, 2016. Article published online January 6, 2017 1288—VOLUME 48A, MARCH 2017

deformed material hardness (Hdef), recrystallized material hardness (Hrex), and the hardness of the annealed material at time t (Ht): XS ¼

Hdef  Ht : Hdef  Hrex

½1

XV can also be determined with the electron backscatter diffraction (EBSD) technique by the evaluation of the grain orientation spread (GOS) and kernel average misorientation (KAM).[3,4] The Johnson–Mehl–Avrami–Kolmogorov (JMAK) model establishes a pioneer mathematical modeling of the recrystallization kinetics of rolled metals through Eq. [2] where k is a pre-exponential constant and n is the Avrami exponent[5]: XV ¼ 1  eðktn Þ:

½2

This model presumes that the new grains are spherical, grow equally along the three dimensions, are _ and grow formed at a constant nucleation rate N, linearly into the work-hardened matrix with a growth _ In mid 1980s, the JMAK model was enhanced by rate G. DeHoff[6] to include reactions that exhibited site saturation by the microstructural path method (MPM). Later, other researchers[3,5] defined MPM parameters METALLURGICAL AND MATERIALS TRANSACTIONS A

_ rates as _ and grain growth (G) such as nucleation (N) functions of annealing time:   4C Cðm þ 1Þ N_ ¼  t3m2n1 ; KS  P2 Cð2n  2m þ 1Þ  Cð3m  2nÞ

investigated to compare the conventional methodology of microhardness measurement with the orientation imaging microcopy (OIM) technique employing the GOS and KAM parameters.

½3 II. k G_ ¼  n  tnm1 ; C

½4

2k  n   ; C nm

½5

Pffi

where Ks is the shape factor (4p); C is the Gamma factor; and C, P, and m are the parameters of recrystallization kinetics. The use of this mathematical approach, however, does not provide information on the relative amount of text