Carbon Diffusion and Kinetics During the Lath Martensite Formation

Calculations verify that carbon diffusion may occur during the lath martensite fomtion. Accordingly,the diffusion of int2rstitial ator ions must be taka into account nhfn martmitic transformtion is defined as a diffusionless transformation. In derivation of the kinetics equation of the ath& martensitic transfomtion,rzgardng the c a r h diffusion, i .e.the enrichment of the austenite during the lath martensite formtion, and form being function of the temperature and the carbon content in austenite, the kinetics equation is modified to a genera. form as: f=l-eXp@(C, -Co)+(Ms-Tq) I where CO and Cr are carbon contents in the austenite before and aftsr yenchirig respectively. Consequently,the alloying element not only influences Hs, but also the diffusibility of carbon and bth factors govern the munt of retained austenite in quenched stee? which dcminates in determing the toughness of the steel. 1. CARBON DIFFUSION DURING THE FORMATION OF LATH MARTENSITE Rao and Thomas[l] found from high resolution TEM that in quenched steel with low or medium carbon the retained austenite is trapped between the lath martensite. Lattice images indicated substantial carbon enrichment of the retained austenite(from 0.27% to 0.4-1.04%)at lath martensitelaustenite interphase boundaries. Sarikaya et alE21 confirmed such an enrichment from transmission electron microscope(TEM), convergent beam electron diffraction(CBED) and field ion-atom probe(F1AP). Primary calculation[3J showed that in a quenched steel with 0.27%C, the time required for carbon diffusion from martensite to enrich the EIN boundary to 1.04%C, being 2x10'* to 10" see, can keep pace with the formation of lath martensite, considering that carbon diffusion may be driven by the chemical potential resulting from the different solubility of carbon in martensite and ferrite. TEM experiments revealed a small amount of twinned martensite in a quenched O.12C-low Ni and Cr steel[3]. The present author has pointed out that the diffusion of carbon may occur concomitantly with lath martensite formation, however, the formation mechanism of lath martensite is typically displacive and is not identical with that of bainitel3-51. By solution of Fick's law for the case of diffusion in a plane sheet with uniform initial distribution and surface concentration for the carbon concentration profile as shown in Fig I, 211 =15~10~cm, 2~=lxl0-'cm, and T=700K. Following the data in [I] and [2],the time required for the carbon diffusion to enrich the-retained ajstenite during the formation of lath martensite is calculated to be 7.25~16~ to 3x10sec and that for the equalization of the enriched austenite to be 2x10~' sec [4 ,5 ] . Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1995851 JOURNAL DE PHYSIQUE IV Figve 1: Sketch of carbon concentration profile in martensite(#) and ntained austaite in a quenched steel with 0.27%C The time required for the carbon diffusion to enrich the interphase boundary dislocation to 1.04%C during the growth of the lath martensite is calculated to be 3 . 2 ~ 1 6 ~ 2.5x10-' sec, taking T=700K and the dislocation density=l~~~/cm'. In comparison with the time for formation of a martens'te lath from the experimental data of the growth -+ rate of lath martensite,i.e. lo-' -10 sec, the calculation implies that carbon diffusion may keep pace with, or slightly lag behind, the formation of lath martensite. The time required for the equalization of the enriched austenite is at least one order of magnitude lower than the formation of lath martensite, implying that the carbon diffusion may occur, but is not a major, or necessary process in lath martensite transformation. 2. DEFINITION OF A MARTENSITIC TRANSFORMATION Raferring the definitions of a martensitic transformation given by various authors from 1951 to 1990 as reviewed in the previous paperr61 and considering the carbon diffusion during the lath martensite formation as described in the previous sectjon and also the fact that the formation of the isothermal martensite in the retained austenite in a queched ball bearing steel with 1%C and 1.5%Cr is also driven by the carbon diffusionf7J,the present author[6] has defined a martensite transfornation as a first order, nuclsation-growth transformation with shape change and surface relief characterized by an invariant plane strain as a result of the diffusionless shear displacement of substitutional atoms(ions). The displacement includes homogeneous and inhomogeneous shear. %,it seems better to add "homogeneous and inhomogeneous" before "shear displacement" in the above definition for modification. The characteristics of lath martensite formation are consistent with the definition given above and it is ideally martensitic. 3. KINETICS OF ATHERMAL MARTENSITIC TRANSFORMATION Yagee[8] has derived a kinetics equation for an athermal martensitic transformation as f =1-exp [-b(Ns-Tq) 1 (1) where f stands the volume fraction of martensite formed, Tq the temperature of quenching medium and d refers a constant which depends on the conposition of material. The experimental data for plain carbon steels with carbon content 0.37% to 1.10% given by Koistinen and Marburgerr91 may serve as evidence in support of the above relationship taking d=1.10~10-'. Although the average volume of martensite formed at different temperatures is not a constant as it is assumed in the derivation of equation (11, Magee's equation can express approximately the extent of an athermal martensitic transformation in steels with high or medium carbon content. As Tq 1s taken as room teinperature, from equationfl), one may conclude that the higher the !Is, the lower will be the amount of the retained austenite,i.e. the amount of (1-f), which was taken to be a general rule for a long term. In derivation of Magee's squation,the change in free energy per unit volume accompanying the martensitic transformation,hG,is considered to be a function of temperature only. However,during lath martensits formation, there nay be carbon diffusion. Consequently, 4G is a function of not only temperature but also the carbon content in austenite and Magee's equation should be modified. The present author and his co-workers[lO] have derived a kinetics equation in general form, which applies even to low-carbon steels: f=l-exp[$ (Ct -Cs) -d(Ms-Tq) 1 (2) or the amount of the retained austenite, f(Y) can be expressed as: f (Y)=l-f=exp[$(C, -C.) -d(Ms-Tq) ] (3) where $='ii?(d&/~~), band C, represent the carbon contents in austenite before and after quenching, respectively. Equation(3) is significant not only in expressing the extent of an athermal martensite formation but also in predicting the fracture toughness of quenched steels with a microstructure of lath martensite,since the amount of retained austenite governs the toughness parameter of the steel[il]. In high or medium carbon steels, carbon diffusion nil1 not occur during the martensitic transformation because Ms is too low. In this case,Ct=Co,and equation(2) reduces to equation(1). Addition of alloying elements in steel affects not only Ms, but also the diffusion coefficent of carbon in martensite,and both factors determine the amount of retained austenite. Manganese lowers Ms and slightly affects the diffusibility of carbon in stael. Thus, in steel containing Mn, the amount of retained austenite increases moderately with the decrease of Ms. Nickel lowers Ms but raises the diffusibility of carbon in martensite, and accordingly in Wi-stee1,the amount of the retained austenite increases rather drastically nith the decrease of Ms. Strong carbide forming elements, such as niobium and rare earth element lower Ms too, but decrease the diffusion coefficient of carbon, in turn decreasing the value of C,in equation(2). Addition of rare earth elements in a 0.27C-1Cr steel lower considerably the amount of the retained austenite in spite of lowering Ms[IO]. According to the principle stated above,the effect of various alloylnq elenents on the amount of the retained austenite in a quenched steel nay be predicted[12]. Experinental results from the literaturs[lO,ll] confirm the prediction qualitatively and also verify equation(1).