THE EFFECT OF MAGNETIC FIELDS ON PHASE TRANSFORMATIONS IN .
ETALSbyC.T.PETERSThesis Submitted to the University of Surreyfor the Degree of Doctor of Philosophy
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TOMYPARENTS
C O N T E N T SAbstract1Introduction2Symbols Used in the Text,4Part I6Chapter 1The Formation-of Martensite in SteelsChapter 2Effect of Magnetic Fields on MartensiteFormation37Experimental Work - The Effect of MagneticFields on Isothermal Martensite Formation49Discussion of Experimental Work74Chapter 3Chapter 4Part IIChapter 3General Properties and TransformationProcesses of Fe-Co Alloys92Chapter 6Experimental Work on Fe-Co Alloys105Chapter 7Discussion of Experimental Results119Chapter 8Conclusions150LReferences153\Appendix I I ;'Appendix II j158i"\
ABSTRACTThis thesis investigates and explains the effect of strongmagnetic fields on two types of phase transformation.The first of theseis a diffusionless, martensitic transformation, occurring isothermallyin a Pe -26pNi -2 Mn alloy.The experimental results have been usedto deduce information about the nature of martensite embryos, and tendto support the K a u f m a n C o h e n model, rather than the more recent RagharanCohen proposals.The second transformation studied was the bcc -* fee transformationin Pe - Co alloys containing 30 - 50 wt.foCo.This is the first timethat systematic information has been established for magnetic field effectson diffusion - controlled, high temperature transformations.The experi mental results have been used to check the accuracy of empirical phase stability data, and to assess the general validity of current models describing nucleation kinetics.Generally, similar explanations of the magnetic effect apply toboth transformations, but certain of the nucleation parameters can bedifferentiated.The size of critical embryos, deduced from the experi mental data, is much larger (r 200 &)for martensite nucleationthan for diffusion - controlled nucleation at high temperatures (r 70 &)Also, the calculated nucleus / matrix interfacial energy for martensiteembryos is about 110 erg / cm(i.e. appreciable incoherency) whereasfor diffusion - controlled nucleation this parameter has the much lowervalue of 25 - 30 erg / cm9indicating that nuclei are fully coherent.
IntroductionPrevious work has clearly demonstrated that phase transformationsin metals can he affected by the presence of magnetic fields, both interms of the temperature at which a transformation occurs, and also withrespect to the transformation kinetics.In general, magnetic fieldshave a significant effect only on transformations in which the parentand product phases differ considerably in their magnetic properties; theeffect is largest when one phase is ferromagnetic whilst the other isparamagnetic.In a.magnetic field, the free - energy of ferromagneticphases is lowered significantly relative to non - ferromagnetic phases;hence the stability of the ferromagnetic phase is increased.The magnetic effect has previously been extensively investigatedduring the athermal martensitic transformation in various steels.Thepurpose of the research reported in this Thesis was to extend theinvestigation of the magnetic effect to other phase transformations,starting with isothermal martensitic transformations.In these, exhibitedby, for example, certain Fe - Ni, Fe - Ni - I-ln and Fe - Hi - Cr alloys,the amount of martensite formed at a given temperatureTbelow Mg isdependent on time, and not merely on the temperature difference (T - Hg).Various models have been proposed for the nucleation of isothermalmartensite; it was hoped'that experimental data for the magnetic effecton such transformations could be used to assess the relative merits ofcompeting hypotheses.All the work described so far has been confined to investigationof the magnetic effect on low - temperature, diffusionless transformations.Theoretically, the magnetic effect should be generally exhibited by anyphase change, given that the competing phases differ markedly in theirmagnetisation.fee and feeIn order to verify this, the diffusion controlled bcc ** bcc transformations in three Fe - Co alloys were investigated.
It was hoped to demonstrate that magnetic fields affect transformationtemperatures and transformation kinetics, and also to verify whether theobserved changes were compatible with the same model used for the magneticeffect on martensitic transformations.In addition, the magnetic effecton transformation kinetics provides an opportunity of testing competingmodels for solid state nucleation many of which remain largely uncheckedexperimentally. The experimental work in the Thesis is divided into two parts;the first deals with magnetic effects on isothermal martensitic trans formations, whilst the second part is concerned with the diffusionaltransformation in Fe - Co alloys.This is an arbitrary division sincethe magnetic effect has, in both cases, the same origin and explanation;however the experimental techniques used to investigate the two modesare widely different, as are the quantitative treatments of their kinetics,and it was therefore considered desirable to consider each transformationseparately in detail.Information derived from both sources Inas beencombined to form the general conclusions made in the final Chapter ofthe Thesis.
Denotes bcc phase in Fe - Co systemDenotes ferrous martensite phaseMartensite strain-energy factor(2 x 10103erg/cm ).Frequency factor for diffusional nucleationTemperature at which martensite transforms to austeniteon heatingMagnetisation at temperatureTBurgers vector of dislocation loopMartensite embryo semi-thicknessGrain diameterEuler's constant(0.577.)Hall voltageChemical free-energy per unit volumeExcess free-energy of mixingVolume fraction of transformed phaseGibbs free-energy per unit volumesDiffusional growth rate of product phaseDenotes fee phase in Fe - Co systemMagnetic field strengthSaturation magnetisation per unit volumeBoltzmann's constant(l. 38 x 10“16 erg/ K)Martensite burst temperatureTemperature at which austenite transforms to martensiteon coolingDenotes thickness:length ratio of martensite platesShear Modulus
NNucleation rate of product phasen Initial concentration of martensite embryosvLattice vibration frequencyQActivation energy for diffusionRUniversal gas constant (1.987 cal/mole/ K)rEmbryo or nucleus radiusSEntropy per unit volumeaInterfacial energy per unit areaTcCurie temperature KTqTemperature at which competing phases (specified) have(10equal free energy0Contact angle of nucleivAverage martensite plate volumeAwActivation energy for nucleation13sec—1)
EIB STEELSIntroductionThe martensitic transformation in steels has long been oneof the least-understood solid-state phase transformations.Thisarises mainly from the complex variety of possible crystallographicrelationships between parent and product phases, the wide spectrumof observed transformation kinetics and the failure of classicaltransformation theory to predict or explain these kinetics.In presenting a review of the progress which has been madein the understanding of the mechanisms of martensitic reactions, itis proposed to treat the subject in two stages, namely:a)Observed kinetics of martensite formation.b)Theories of martensite nucleation and growth.In this way, whilst recognising that these two aspects of theproblem are fundamentally inseparable, the major areas of controversymay be more easily identified.1.2Kinetics of the Austenite-» Martensite TransformationBecause of the wide variety of transformation kinetics exhibitedby different ferrous alloys, it is intended to describe separatelythe four major transformation modes which have been distinguished,namely:h)( inUii)(iv)The ’athermal' modeThe ’burst' transformationThe 1thermoelastic1 modeThe ’isothermal' mode
Although it will be shorn later that from the viewpoint ofoperational nucleation, these four subdivisions are purely arbitrary,their use will serve to clarify the rather confusing variations inreaction kinetics.1.2.1The 'Athermal1 TransformationThis kinetic behaviour is commonly observed in plain carbonsteels and low-alloy steels.Transformation from austenite tomartensite begins at a well defined temperature (denoted M ) oncooling.The Mg temperature has been found to be virtually independentof the cooling rate (Bibby and Parr, 1964).However, a criticalminimum cooling rate is required in order to suppress equilibriumphase changes such as the formation of bcc ferrite or other austenitedecomposition products.with composition.The critical cooling rate varies markedlyBelow MQ the extent of transformation dependsonly on the amount of undercooling(a T) below M .Transformationtakes place extremely rapidly during quenching to the reaction temper ature, and no transformation to martensite occurs during furtherisothermal holding.(Howard and Cohen, 1948).The relationship between the extent of transformation and theamount of undercooling (AT) below MQ has been extensively investigated(e.g. Harris and Cohen, 1949; Koistenen and Marburger, 1959; Brook et alI960).Harris and Cohen (1949) derived the following empiricalexpression for the relationship between the volume fraction of martensiteformed (f), and the undercooling below K :of 1 - 6.956 xlo"15[455 - at] 5,32Equation (1)whilst Koistinen and Marburger (1959) proposed the simpler relationship:
f 1 - exp (-1.1 x 10 AT)Equation (2)Both these relationships give reasonable agreement with experi mental data for the early stages of transformation, although equation (2)has a wider range of accuracy.Entwisle (l97l) pointed out that during the first 50 pet oftransformation, it was not possible from experimental data to distinguishthe foregoing empirical relationships from a linear dependence ofAT,fon(Figure l) in agreement with the findings of Brook et al (i960).With the exception of Cobalt, all elements which dissolve inaustenite lower the M .bInterstitial alloying elements are approximatelyone order of magnitude more effective in lowering M than substitutionals.Various attempts have been made to derive empirical relations allowingcalculation of Mg knowing the alloy composition.The formula of Stevensand Haynes (1956) is fairly accurate for describing the Mof low alloysteels:Mg ( C) 33 Mn - 17 N i ’fo - 17 Cr561 - 474fo- 21 Mo(wt. pet.)Many attempts have been made to correlate the driving force forthe martensitic reactionaAGY" 0t y- (y , where AGv( G 1 -G)is the difference in volume free energy between austenite and martensite,with the extent of transformation.Magee (1970) has derived the followingrelationship between these two parameters, assuming that the number ofnew martensite plates formed due to an increase in driving force isdirectly proportional to the change in the driving force.1 - f Y aexp [K (— —) AT]Equation (3)
Pig.li—Ico0 xsu0q.«iB]Ai uoxq.o'euA umioAVolume fraction of martensite formed at diffetemperatures below Ms* in Fe-10 Ni-0.6 C.r l
(This assumption is supported by the work of Magee and Paxton (1968) whodemonstrated that the amount of martensite formed under an applied stressis linearly proportional to the stress level, equivalent to a drivingforce).Equation (3 )is similar to the empirical equation previouslysuggested by Koistinen and Marburger (Equation 2 ).For small undercoolings, Equation (3 ) reduces to:( A GT * a )f - K d— —ATEquation (3b)As already noted, experimental results indicate a linear relation ship betweenfandAT over a range ofequation (3b) hence appears correct.correct, the slope of the linefvalues; the general form ofMoreover, if this relationship isd f*( i.e.)should be directlyd Tproportional tody-*a— )i .e . (-ASY a) .d f*Brook et al (i960) have demonstrated thatcan in somed T1cases be correlated directly with a sY" II , but were hampered by lackof available thermodynamic data.However Satyanarayana et al (1968)were able to obtain the value ofASY"*"adirectly by superimposinga strong magnetic field during transformation.The magnetic field changesthe driving force‘for the martensitic reaction, hence causing a shift intheo.Knowing the change in driving force, and the corresponding-shift, the value ofA S Y"*amay be obtained.rate of martensite formation below d fd ToIt was shown that the is directly proportional
toIA SI,as shown in Figure (2 ) giving additional support toequation (3b).Cooling rate variations have little or no effect on the Mgtemperature, but influence the progress of transformation below Mg,owing to the phenomenon of stabilisation.Stabilisation occurs as aresult of slowing down, or interruption of cooling before completetransformation has occurred, resulting in a retardation of transformation.If a partially transformed specimen is held isothermally, before thetemperature is again lowered, renewed transformation only occurs aftera considerable temperature hysteresis.(Harris and Cohen, 1949; Kinsmanand Shyne, 1967).The latter have proposed a stabilisation mechanism involving carbonsegregation to dislocations in the martensite/austenite interface: thispins the interface and hinders further transformation.This model issupported by the work of Philibert (l956) who showed that the stabili sation phenomenon disappeared from nickel steels when all carbon wasremoved from the specimens,1.2.2The 1Burst1 TransformationThis transformation mode is strongly evident in some Fe - Hi andFe - Hi - C alloys, and its kinetics differ markedly from those ofathermal transformations.Transformation commences abruptly during cooling at temperatureM , and a volume of martensite is formed in a single event, called au'burst*,The burst is accompanied by the evolution of a considerableamount of energy (often an audible ’click1 may be heard) which may causea large rise in local temperature.In some cases, up to 70 pet martensite can form in a single burst,
r H H —1 HCO ] Hi—1i—1 H HCOini—ivo0Q/%ZV/&9
accompanied by a temperature rise in excess of 30 deg. C.Entwisle andFeeney (l969) showed that burst transformations were influenced by priorheat treatment; raising the austenitising temperature from 800 C to 1200 Craised HL by 40 C.X)This effect was assigned to a change in the potencyof the martensite embryos.It was also shown that the magnitude of theburst was a function both of the burst temperature (l*L) and of the prioraaustenitic grain size.1.2.3( See Figure3)Thermoelastic and Stress - Induced TransformationThe initial formation of thermoelastic martensite may obey athermalor burst kinetics or a mixture of these.The difference between thermo-elastic martensite and normal martensite lies in the reversibility ofthe austenitemartensite transformation.Thermoelastic martensitesoften have a temperature hysteresis of only 20 degrees between MA(austenite start temperature).oandMoreover, the martensite transformsback to austenite in exactly the reverse order of its formation.Reversible thermoelastic martensite may also be formed by theapplication of stress above M„.Ogives rise to large strains.The formation of stress-induced martensiteOn removal o f .the stress, the martensitereverts completely to austenite (though showing a stress-strain hysteresisbetween loading and unloading) together with complete strain recovery.These phenomena are intimately linked with pseudoelasticity and theshape-memory effect.'Although this type of transformation is most common in non-ferroussystems (e.g. Au - Cd, Ni - Ti, Cu - Zn etc.) it also occurs in somestainless steels and other iron base alloys.Further discussion of thermoelastic martensites will not beattempted in this thesis.Comprehensive reviews e.g. Tas, Delaey and
ObservedComputed 50 C1000.040.060.080.100.12Mean Grain Size (mm)Pig.5Variation of burst size with temperatureand grain size.(Entwisle & Feeney 1969) 0.14
Deruyttere (1974) are available in the literature.1.2.4The Isothermal TransformationIn most martensitic transformations, an isothermal component iseither not operative, or is obscured by a predominant athermal reaction.Kurdjumov and Maksimova (1948, 1951), poineered the investigation ofisothermal transformations, having discovered this reaction mode in anFe - Ni - Mn alloy.This system has formed the basis of the majorityof subsequent investigations.In the absence of prior athermal martensite, isothermal transformationkinetics are as shown in Figure (4 ).In a typical reaction, transformationcommences slowly, accelerates rapidly to a maximum rate (which may remainconstant for a time) then dies away slowly.As the reaction temperatureis lowered, the overall transformation rate increases, together with thetotal amount of martensite formed.Below a certain temperature levelhowever, the rate of reaction begins to decrease, leading to C - shapedtime - temperature - transformation curves, (Figure 5 ) similar to thosefound for diffusional isothermal transformations.The C - curve behaviourhas been amply demonstrated by the work of Cech and Hollomon,Shih et al, (l955), and Pati and Cohen, (1969).(l953)»The existence of C -curve kinetics has been explained in the following manner by Pati andCohen (1969).At temperatures near M , thermal fluctuations are large, but thedriving force for the transformation is low, which means that a very largemartensite nucleus is necessary.rate is slow.Thus the transformation (or nucleation)As the temperature is lowered below M , the requiredbnucleus size' decreases giving easier and more rapid nucleation.Belowa certain temperature, however, thermal energy drops to a level where it
p a u itio js u e t lj;U0TC).0'l3iIt!lFig.4Kineticsof isothermalmartensiteformation(schematic).
oinOI—1oOAofor isothermal martensitic transformationin Fe-23 .2 Ni-3 *62 Mn alloy.odiagramo
is difficult for embryo growth, although’the driving force is large.Therefore the nucleation rate again decreases.The isothermal kinetics in Fe - Ni - Mn alloys have been foundto be very sensitive to changes in grain size (Raghavan and Entwisle,1965).It was found that the ’incubation time1 (defined as the time toform 0.2 o martensite) varied inversely as the cube of the grain diameter(Figure 6), indicating that the nucleation sites are uniformly distributedin the austenite, and do not depend on the amount of grain boundary areain the sample; that is to say that grain boundaries do not supply effectivenucleation sites for martensite formation.The shape of experimental isothermal transformation curves hasbeen quantitatively explained using two concepts, namely:(1)Autocatalysis(2)Austenite partitioningAutocatalysis may be defined for present purposes as the creationof new nucleation sites in the vicinity of a newly-formed volume ofmartensite.Autocatalysis greatly increases the concentration of avail able nucleation sites, leading to an increasing nucleation rate, as thetransformation proceeds.As more and more martensite forms, the remaining austenite becomesseverely 'networked' (partitioned) by martensite plates.The existingplates hamper the growth of newly-formed ones, reducing the volume ofmartensite
Previous work has clearly demonstrated that phase transformations in metals can he affected by the presence of magnetic fields, both in terms of the temperature at which a transformation occurs, and also with respect to the transformation kinetics. In general, magnetic fields have a significant effect only on transformations in which the parent and product phases differ considerably in their .
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