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  • Materials Science and Engineering A311 (2001) 162173

    Estimation of the amount of retained austenite in austemperedductile irons using neural networks

    M.A. Yescas a, H.K.D.H. Bhadeshia a,*, D.J. MacKay b

    a Department of Materials Science and Metallurgy, Uniersity of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UKb Caendish Laboratory, Uniersity of Cambridge, Madingley Road, Cambridge CB3 0HE, UK

    Received 21 August 2000; received in revised form 9 November 2000

    Abstract

    Many of the properties of austempered ductile iron depend on the austenite which is retained following the bainite reaction. Aneural network model within a Bayesian framework has been created using published data to model the retained austenite content.The model allows the quantity of retained austenite to be estimated as a function of the chemical composition and heat treatmentparameters. The computer programs associated with the work have been made freely available (http //www.msm.cam.ac.uk/map/mapmain.html) 2001 Elsevier Science B.V. All rights reserved.

    Keywords: Retained austenite; Austempered; Bainite; Ductile iron; Neural networks

    www.elsevier.com/locate/msea

    1. Introduction

    Austempered ductile iron (ADI) has a microstructurecontaining spheroidal graphite embedded in a matrixwhich is in general a mixture of bainitic ferrite, austen-ite and some martensite [13]. The bainitic ferrite isgenerated by the isothermal transformation of austenitein the bainite transformation temperature range; thisheat treatment is known as austempering.

    The large concentration of silicon typically present ingraphitic cast irons has a key role in the development ofthe microstructure of austempered irons. The siliconhinders the precipitation of carbides during the bainitetransformation [4,5]. The austempering time must en-sure that the formation of bainitic ferrite adequatelyenriches the residual austenite with carbon, allowingmuch of it to be retained to room temperature. Unfor-tunately, prolonged austempering causes the decompo-sition of the residual austenite into a mixture ofcarbides and ferrite [6]. This is detrimental to themechanical properties.

    The austempering process is therefore conventionallydefined in two stages [7]. The end of the first stagecorresponds to the maximisation of the fraction ofbainitic ferrite and the enrichment of the austenite, thesecond with the onset of carbide precipitation. The timeinterval between these two stages is the heat treatmentwindow (Fig. 1). The effect of austempering can beoptimised within the confines of this window: too shortan austempering time leads to an inadequate enrich-ment of the austenite and hence a lower retainedaustenite content. Austempering beyond the commence-ment of stage II causes carbide precipitation and onceagain, a reduction in the retained austenite content. Theextent of the heat treatment window is reducedby the presence of inevitable solidification-inducedchemical segregation, since the transformations occur atdifferent times in different regions of the sample. It thusbecomes difficult, if not impossible, to define an idealaustempering time for the whole of the cast iron com-ponent.

    The problem of designing these cast irons clearlyinvolves many variables and considerable complexity.The purpose of the work presented here was to developa quantitative model which makes possible the estima-tion of retained austenite content as a function of allthese variables, using a neural network techniquewithin a Bayesian framework [8].

    * Corresponding author. Tel.: +44-1223-334301; fax: +44-1223-334567.

    E-mail address: hkdb@cus.cam.ac.uk (H.K.D.H. Bhadeshia).

    0921-5093/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved.PII: S0921 -5093 (01 )00913 -3

  • M.A. Yescas et al. / Materials Science and Engineering A311 (2001) 162173 163

    2. The technique

    A neural network is a general method of regressionanalysis in which a flexible non-linear function is fittedto experimental data, the details of which have beenreviewed extensively [810]. It is nevertheless worthemphasising some of the features of the particularmethod used here, which is due to MacKay [11,12]. Themethod, in addition to providing an indication of theperceived level of noise in the output, gives error barsrepresenting the uncertainty in the fitting parameters.The method recognises that there are many functionswhich can be fitted or extrapolated into uncertain re-gions of the input space, without excessively compro-mising the fit in adjacent regions which are rich inaccurate data. Instead of calculating a unique set ofweights, a probability distribution of sets of weights isused to define the fitting uncertainty. The error barstherefore become large when data are sparse or locallynoisy.

    The Bayesian framework for neural networks has afurther advantage. The significance of the input vari-ables is automatically quantified [11,12]. Consequently

    the significance, perceived by the model of each inputvariable can be compared against metallurgicalexperience.

    The general form of the model is as follows, with yrepresenting the output variable and xj the set of inputs.

    y=i

    w ij(2)hi+ (2),where hi= tan h

    j

    w ij(1)xj+ i(1)

    .

    (1)

    The subscript i represents the hidden units (Fig. 2), the terms are biases and the weights. Thus, the statementof Eq. (1) together with the weights and coefficientsdefines the function giving the output as a function ofthe inputs.

    A potential difficulty with the use of powerful regres-sion methods is the possibility of overfitting data. Toavoid this, the experimental data can be divided intotwo sets, a training data set and a test data set. Themodel is produced using only the training data. The testdata are then used to check that the model behavesitself when presented with previously unseen data. Thetraining process involves a search for the optimumnon-linear relationship between the input and the out-put data and is computer intensive. Once the network istrained, estimation of the outputs for any given set ofinputs is very fast.

    3. The variables

    The analysis is based on published data and is there-fore limited to quantities that are readily measured andfrequently reported. For example, in order to predictthe quantity of retained austenite it would be ideal toinclude the fraction of bainite as an input, but this israrely measured in practice. Therefore, a pragmatic setof variables must be chosen which implicitly contain allthe information needed to estimate the amount ofretained austenite.

    The set of inputs (Table 1) therefore included thedetailed chemical composition in wt.%, the austenitisa-tion temperature in C and time in min (T and t,respectively), and the austempering temperature andtime (TA and tA, respectively). This is almost all that isnecessary to define the retained austenite volume frac-tion (Vr). However, due to a lack of appropriate data,no explicit account can be taken of the incompletedissolution of car bides during austenitisation. Failureto do this should reflect in a greater uncertainty in thepredictions that are made using the trained neuralnetworks. A total of 1910 experimental data were col-lected from published literature [1352] and digitised.Table 2 shows a selection of ductile iron alloys includedin the database.

    In discussing the microstructure, we shall distinguishbetween the volume fraction of residual austenite (V),

    Fig. 1. Schematic representation of the development of microstruc-ture during austempering, together with an illustration of the pro-cessing window. Martensite is present only when the sample is cooledto room temperature before the austempering has been completed.

    Fig. 2. The structure of the network.

  • M.A. Yescas et al. / Materials Science and Engineering A311 (2001) 162173164

    Table 1The variables used to develop the neural network model

    Maximum MeanInput element Standard deviationMinimum

    3.97Carbon (wt.%) 3.582.3 0.165Silicon (wt.%) 1.57 3.78 2.57 0.21

    1.52Manganese (wt.%) 0.340.01 0.230.74 0.160.0 0.17Molybdenuma (wt.%)

    0.0Nickela (wt.%) 3.82 0.29 0.531.60 0.23Coppera (wt.%) 0.290.0

    1050 900800 34Austenitising temperature (C)15Austenitising time (min) 240 97 34

    455 350 39Austempering temperature (C) 23060000 10390.5 5625Austempering time (min)

    6.556 3.659Austempering time ln {tA/s} 0.9481.4772.03 0.4140.875 0.418ln {ln {V}}

    a Molybdenum, nickel and copper were frequently not reported in publications since they were not deliberate additions, in which case theirconcentrations were set to zero.

    Table 2A selection of alloys intended to illustrate the range covered in the database used to create the neural network model

    Mn MoC NiSi Cu V Cr Ti Ref

    0.36 0.01 0.07 0.042.54 03.63 0.04 0 [14]0.20 0.30 0 0.783.67 02.45 0 0 [17]0.21 0 1.6 1.62.5 03.3 0 0 [16]0.963.16 02.82 0 0.07 0.02 0 0 [18]0.57 0.06 0.1 02.33 0.043.56 0 0 [26]0.53 0.26 1.34 03.66 02.51 0 0 [30]0.44 0.01 0.06 0.062.52 03.7 0.05 0 [29]

    2.443.53 0.5 0.25 0 1.37 0 0 0 [55]0.25 0.13 0 0.392.81 03.51 0 0 [33]

    2.02.5 0.74 0 3.8 0 0 0.02 0 [42]0.373.3 02.2 0 0 0 0 0 [22]0.67 0.25 0 0.25 0 0 02.64 [34]3.52

    which is the untransformed austenite at the austemper-ing temperature, and the volume fraction of retainedaustenite (Vr) which remains untransformed at ambi-ent temperature. One approach is to use the neuralnetwork with the austempering time as the input. How-ever, this is not justified metallurgically since the frac-tion is not expected to vary linearly with time, but asthe logarithm of time. The evolution of volume fractionwith time in nucleation and growth reactions follows asigmoidal behaviour. This is because the bainite reac-tion associated with the first stage of austempering, andindee