c reep strain rec overy of fe–ni–b amorphous m etallic ribbon

OFK: ÚEF SAV Košice 12.12.2007OFK: ÚEF SAV Košice 12.12.2007

A.A. Juríková, K. Csach, J. Miškuf,Juríková, K. Csach, J. Miškuf, VV.. O Ocelíkcelík * *

Department of Metal PhysicsDepartment of Metal PhysicsInstitute of Experimental PhysicsInstitute of Experimental PhysicsSlovak Academy of Sciences Slovak Academy of Sciences

* * University ofUniversity of Groningen,Groningen, DeptDept.. of Applied Physics of Applied Physics, , Materials Science Centre,Materials Science Centre, tthe Netherlandshe Netherlands

presented at:presented at:5-th Int5-th Internationalernational Conference on Measurement, Smolenice, Conference on Measurement, Smolenice, MayMay 2005 20051155-th Conference o-th Conference of slovak physicists, Starf slovak physicists, Staráá Lesn Lesnáá, 200, 20066

published in:published in:Central European Journal of Physics 5 (2) 2007Central European Journal of Physics 5 (2) 2007,, 177 177––187187

CCreep reep strain recstrain recovery of overy of Fe–Ni–B Fe–Ni–B amorphous amorphous mmetallic etallic ribbonribbon

CCreep reep strain recstrain recovery of overy of Fe–Ni–B Fe–Ni–B amorphous amorphous mmetallic etallic ribbonribbon


MMetallic glasses etallic glasses (MGs) –(MGs) – metastable metastable, , highly non-equilibrium structureshighly non-equilibrium structures

annealing annealing below below TTgg structural relaxationstructural relaxation (SR) (SR) – subtle rearrangements of the – subtle rearrangements of the

atomic structure to a more stable state atomic structure to a more stable state topological and chemical short-range topological and chemical short-range order order variations in many physical properties variations in many physical properties

AA hierarchy of internal stresseshierarchy of internal stresses of different ranges of different ranges : :

macroscopic quenchingmacroscopic quenching stresses (acting on scale of the wholestresses (acting on scale of the whole sample)sample) submacroscopic quenchingsubmacroscopic quenching stresses (several stresses (several hhundredths undredths mm)) local stresses oflocal stresses of intercluster boundariesintercluster boundaries or atomic levelor atomic level s stressestresses

At elevated temperatures theAt elevated temperatures thesese stresses disappear during stresses disappear during SRSR – this process – this process is is influencedinfluenced by applied by applied mechanical stressmechanical stress..

IntroductionIntroductionIntroductionIntroduction


stress-annealingstress-annealing ccreepreep strainstrain::

a a part of part of the the deformation energy is released upon subsequent annealing under deformation energy is released upon subsequent annealing under zero stress causing zero stress causing anelastic anelastic creep rcreep recoveryecovery macroscopically reversible macroscopically reversible deformation deformation but delayed in time:but delayed in time:

pre-deformed samples can partially restore their shape after stress removal pre-deformed samples can partially restore their shape after stress removal time- time-dependent anelastic strain recoverydependent anelastic strain recovery

anelasticity in MGs – process distributed over a anelasticity in MGs – process distributed over a range of activation energiesrange of activation energiesTaub and Spaepen (1984)Taub and Spaepen (1984):: the anelastic deformation response of MGs could not be the anelastic deformation response of MGs could not be described by a single relaxation process, a sum of exponential decays, spanning a described by a single relaxation process, a sum of exponential decays, spanning a spectrum of time constantsspectrum of time constants, is required to describe the anelastic component of the , is required to describe the anelastic component of the homogeneous strain response of amorphous alloys to applied stresshomogeneous strain response of amorphous alloys to applied stress

IntroductionIntroductionIntroductionIntroduction


A study of the A study of the activation energy spectra (AES)activation energy spectra (AES) possible help in understanding the possible help in understanding the atomic processes which take place during the relaxation in metastable systems. atomic processes which take place during the relaxation in metastable systems. Analysis of kinetics of anelastic deformation response Analysis of kinetics of anelastic deformation response useful informations about useful informations about the local short-range ordering and deformation defects in amorphous structure.the local short-range ordering and deformation defects in amorphous structure.

The The purposepurpose of the presented work: of the presented work:

to to report some results on creep strain recovery and report some results on creep strain recovery and SR SR processesprocesses in in Fe–Ni–B Fe–Ni–B metallic glassmetallic glass after after longtime loading longtime loading derived from derived from DSC and TMA DSC and TMA studiesstudies

to demonstrate how the activation energy spectra model isto demonstrate how the activation energy spectra model is approciated for the approciated for the description of creep strain recovery processdescription of creep strain recovery process in the materialin the material

AimAim AimAim


Material:Material:

amorphous metallic glassamorphous metallic glass : Fe: Fe4040NiNi

4411BB1919

the thickness of ribbon : the thickness of ribbon : 1717..33 m m

the width of samples : the width of samples : 4 4.0 mm.0 mm

Annealing:Annealing:

at temperatures at temperatures TTaa = = 1150 50 –– 300 300ooC C

time of the annealing: 20 hours time of the annealing: 20 hours under aunder an external n external tensile stress: 3tensile stress: 38383 MPa MPa

(or without stress (or without stress referenc reference e sspecimens)pecimens)

inside a tube furnaceinside a tube furnacein a flowing in a flowing nitnitrogen rogen atmosphereatmospherecooled down to room temperature (under the same stress) cooled down to room temperature (under the same stress) and unloadedand unloaded

ExperimentalExperimentalExperimentalExperimental


The The thermal analysisthermal analysis measurements measurements (changes of enthalpy (changes of enthalpy H H and length and length ll)) c carried out: arried out:

uusingsing: : differential scanning calorimeter differential scanning calorimeter (DSC) (DSC) and and thermomechanical analyserthermomechanical analyser (TMA) (TMA)

during linear heating with the rate of 20 Kminduring linear heating with the rate of 20 Kmin–1–1 and 10 Kmin and 10 Kmin–1–1

in a flowing in a flowing nitrogennitrogen atmosphere atmosphere

Perkin Elmer DSC 7Perkin Elmer DSC 7(diferen(diferential scanning calorimettial scanning calorimeteerr))

Setaram TMA 92Setaram TMA 92 (thermomechanic(thermomechanicalal anal analysyser)er)

ExperimentalExperimentalExperimentalExperimental


Results – DSCResults – DSC Results – DSCResults – DSC

DSC tracesDSC traces – – similar shape for samples similar shape for samples annealed under stress or without annealed under stress or without stress at a given annealing stress at a given annealing temperature temperature SR is qualitatively SR is qualitatively the samethe same– – start to have a different deviation start to have a different deviation at a temperature at a temperature TT ~ 200 ~ 200ooCC at a at a given heating rate for all given heating rate for all TTaa

DSC traces for the samples preannealed at indicated temperatures under and without stress, and the differences between them.

– – tthe more significant changes he more significant changes associated with SR associated with SR –– at the temperatures at the temperaturesTT ~ ~ TTaa + 100 + 100ooCC the energy the energy

accumulated during the creep starts to accumulated during the creep starts to releaserelease– – aat temperatures above t temperatures above TTxx == 441515ooC C

much much more more extensive release of energyextensive release of energy


The differences of DSC data between the reference sample and the sample

stress-annealed at the indicated TTaa .

there is no sequence with the there is no sequence with the temperature of annealingtemperature of annealing

aannealing under stress causes in nnealing under stress causes in general more intensive SR and so general more intensive SR and so a closer structure arrangementa closer structure arrangement




DSC traces for the samples stress-annealed at indicated temperatures.

each of the measured DSC each of the measured DSC curves shows an exothermic effectcurves shows an exothermic effect((connected withconnected with lowering a free lowering a free energy of the amorphous structure energy of the amorphous structure towards antowards an equilibrium glassy stateequilibrium glassy state))

for all annealing temperatures for all annealing temperatures TTaa: : the wide exothermic decreasesthe wide exothermic decreases their starts tend to shift towards their starts tend to shift towards high temperatures as the high temperatures as the stress-stress-annealed annealed TTaa increases: increases:

TT ~ ~ TTaa + 100 + 100ooCC


Results – Results – TMATMAResults – Results – TMATMA

The pure creep recovery curves The pure creep recovery curves were obtained by substracting were obtained by substracting the reference curves from curves the reference curves from curves measured on stress-annealed measured on stress-annealed samples.samples.

at temperatures below at temperatures below TTa a

linear elongation of samples due linear elongation of samples due to thermal expansionto thermal expansion

at temperatures at temperatures near near TTaa

creep creep strain recovery shrinking is strain recovery shrinking is superposedsuperposed

The change of length measured during linear heating for samples stress-annealed at different Ta and for a reference sample.


Results – Results – TMATMAResults – Results – TMATMA

The anelastic shear strain for the samples stress-annealed at indicated temperatures.

Activation energy spectraActivation energy spectra – – calculated from these calculated from these non-inon-isothermal sothermal experiments using a modern method experiments using a modern method based on Fourier techniquebased on Fourier techniques s

– – shear anelastic shear anelastic deformationdeformation

l l – – the length change of a samplethe length change of a samplell0 0 – – ththe e effective length of a sampleeffective length of a sample

ll0 0 == 15 mm15 mm

tthe he totaltotal anelastic strainanelastic strain:: up to up to 55 x 10 x 10–3–3

0/3 ll


Model and method of calculation AESModel and method of calculation AESModel and method of calculation AESModel and method of calculation AES

xxa expexp1)(

for non-isothermal experiment: for non-isothermal experiment: T = TT = Too++t , t , – constant heating rate – constant heating rate

described by equation:described by equation:

PP(T(T)) –– total total change change in time in time of of some measured physicalsome measured physical property propertyNN((EE)) – – spectrum of activation energiesspectrum of activation energiesaa(E(E,T,T)) –– an anisothermal characteristic annealing functionisothermal characteristic annealing function::

WW.. Primak 1955, Primak 1955, M.M. R.R. J.J. Gibbs et al.1983Gibbs et al.1983

convolution integralconvolution integral spectrum of activation energiesspectrum of activation energies can be calculated by can be calculated by the method using Fourier transformationsthe method using Fourier transformations

corr*

o fE

ETE

)(

0

d),()()( ETEENTP a

2lnln

kT

E

kT

ETx o

T

ab

k oln11

221)( TTTEo

Tb

k2

a, ba, b – constants – constants


Results – AESResults – AESResults – AESResults – AES

Creep recovery spectra calculated from the linear heating experiments.

Creep recovery spectraCreep recovery spectra:: – – a discrete character a discrete character consisting of a consisting of a finite number of peaksfinite number of peaks – – well defined well defined characteristic energies characteristic energies that probably correspond to the different that probably correspond to the different type of deformationtype of deformation defectsdefects in the in the amorphous structureamorphous structure It is evidentIt is evident: : the creep strain recovery the creep strain recovery is determined by the temperature of is determined by the temperature of stress-annealingstress-annealing The heightThe height of peaks in calculated of peaks in calculated AESAES tends to increase tends to increase with the with the increasing activation energy for a given increasing activation energy for a given stress-annealingstress-annealing temperature.temperature.

The positions of two most significant The positions of two most significant peaks in depending on thepeaks in depending on the stress-stress-annealing temperatureannealing temperature


Results – AESResults – AESResults – AESResults – AES

Peak positions depending on the annealing temperature.

TwoTwo tendencies of peak position tendencies of peak position dependence on the annealingdependence on the annealing temperature are evidenttemperature are evident::

ffor lower temperatures of or lower temperatures of annealing theannealing the c characteristic energy haracteristic energy of peaks decreases as the stress-of peaks decreases as the stress-annealingannealing temperature increases temperature increases for higher stress-annealedfor higher stress-annealed temperatures the opposite tendency temperatures the opposite tendency is observed. is observed.

connected with different structural connected with different structural states of the samples obtainedstates of the samples obtained during the stress-annealing at during the stress-annealing at different temperaturesdifferent temperatures


DiscussionDiscussionDiscussionDiscussion

DirectionalDirectional Structural Relaxation (DSR) modelStructural Relaxation (DSR) model by Khonik by Khonik et al.et al. ((19951995))::homogeneoushomogeneous plastic flow of plastic flow of MGsMGs as a result of as a result of SR SR oriented by the external stressoriented by the external stress

the non-isothermal strainthe non-isothermal strain recovery recovery a set of local a set of local atomic rearrangements, with atomic rearrangements, with distributed distributed AES,AES, in spatially separated regions of the structure in spatially separated regions of the structure – – 'relaxation centers''relaxation centers' – – oriented favooriented favouurably or unfavorably or unfavouurably to therably to the external stress.external stress.

IIn the samples stress-annealed atn the samples stress-annealed at lower temperatures both relaxation centers, the lower temperatures both relaxation centers, the parallel and theparallel and the antiparallel in sign to the external stress, rearrange during theantiparallel in sign to the external stress, rearrange during the strain recovery process. As the annealing temperature increasesstrain recovery process. As the annealing temperature increases the influence of the influence of antiparallely oriented relaxation centersantiparallely oriented relaxation centers decreases, thus for higher temperatures decreases, thus for higher temperatures only parallely orientedonly parallely oriented relaxation centers contribute to the creep strain recoveryrelaxation centers contribute to the creep strain recovery processprocess..


Short summaryShort summaryShort summaryShort summary

Different creep strain accumulation is realized during stress-annealing of Different creep strain accumulation is realized during stress-annealing of the the amorphous ribbon Fe–Ni–B amorphous ribbon Fe–Ni–B ddependependinging on the annealing temperature. This on the annealing temperature. This fact fact influenceinfluencess thethe structural relaxation structural relaxation and creep strain recovery processes in theand creep strain recovery processes in the metallic glassmetallic glass. .

Structural relaxation is qualitatively the same for samplesStructural relaxation is qualitatively the same for samples preannealed under preannealed under or/and without stress.or/and without stress.

Both relaxation centers,Both relaxation centers, the parallel and the antiparallel in sign to the external the parallel and the antiparallel in sign to the external stress,stress, rearrange during the creep strain recovery in the samplesrearrange during the creep strain recovery in the samples stress-annealed stress-annealed at lower temperatures. In the samplesat lower temperatures. In the samples stress-annealed at higher temperatures stress-annealed at higher temperatures only the relaxation centersonly the relaxation centers favofavouurably oriented to the external stress contribute to rably oriented to the external stress contribute to the creepthe creep strain recovery process in the Fe-based amorphous ribbon.strain recovery process in the Fe-based amorphous ribbon.


Thank for your attentionThank for your attention

c reep strain rec overy of fe–ni–b amorphous m etallic ribbon

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