Revista Latinoamericana de Metalurgia y Materiales, Vol 11, N° 1y 2, 1992 65

Analysis of the initial stages of the superplastic fonning of the AA-7075 alloy using the Ashby-Verral model.

Alejandro Sanz and Joaquin Lira

National Surface and Interfaces Engineering Research Group. Materials Science Department.Simón Bolivar University. P. O. Box 89000. Caracas 1080 A. Venezuela.

Abstract

The superplastic phenomena is usually associated to large tensil elongations at high temperature and lowstresses. Superplastic forming has proved an efficient way for product shaping while obtaining homogeneousmicrostructure. The influence of initial grain size on the microstructural evolution and the strain kinetics havebeen studied using the Ashby- Verral model wich explains the superplastic flow in terms of a diffusiveaccomodation process. Some new aproaches have been used in order to apply the model which is matbematicallyexpresed in terms of some data not available in bibliography or hardly experimentally measurable. The grain sizewas not taken as a constant, grain growth kinetics was included in the ca1culations. The results show that thereis a tendency to stable (constant strain rate) deformation process, but the rate is lower than those imposed foreither research orindustrial applications, getting closer to the one requiered for dynamic recrystallization.

Key words: Ashby-Verral model, difusive accomodation, grain size, grain switching, superplasticity.

Resumen

El fenómeno de superplasticidad es usualmente asociado a grandes elongaciones a elevada temperatura ybajos esfuerzos. El conformado superplástico ha demostrado ser una manera eficiente para obtener la forma fmal yuna microestructura homogénea en las piezas fabricadas por este método. Usando el modelo de Ashby-Verral queexplica el flujo superplástico en términos de procesos difusivos, se estudia la influencia del tamaño inicial degrano en la evolución microestructural y la cinética de esfuerzos. Se utilizo un enfoque novedoso para aplicar elmodelo que. normalmente se expresa matemáticamente en términos de datos no disponibles en la bibliografía ydifícilmente medibles experimentalmente. El tamaño de grano no se tomo como constante y la cinética decrecimiento de grano se incluyo en los cálculos. Los resultados muestran que hay una tendencia a la estabilizacióndel proceso de deformación (tasa de deformación constante), pero la tasa es menor a la impuesta por lasaplicaciones industriales y de investigación, siendo cercana a la requerida para recristalización dinámica.

Palabras claves: modelo Ashby-Verral, acomodamiento difusivo, tamaño de grano, cambio de grano,superplasticidad.

Introduetion

Micrograins superplasticity is observed attemperatures above 0.4 of the melting temperatureand at stresses in which most of the metals andalloys would strain by diffusive creep. Thedominant mechanism is the on which individuallycontributes the most to the total strain,nevertheless, accomodation processes, wich areneed to keep continuity, are those that control theprocess kinetics [1, 2].

The Ashby- Verral model predictsquealitatively all the features of the superplasticflow with the exceptions of:a.- the fracture includes frecuently cavitation andb.- there is a small texture component in the finalmicrostructure.

The model postulates that superplasticity isa transition region between the difusionaccomodation process region (at low strain rates)and the difusion controled dislocation climb (wichoccur at high rates). At low strain rates, wherethe difusionally accomodated flow is responsiblefor

more than 99% of the whole strain rate, the sampleelongation is achieved by grain compatibilityduring the deformation process, these must chagetheir shape. One characteristic of this strain modeis that groups of four grains must strain together,cooperativelly, to keep the compatibility across thegrain boundary. At high strain rates thedislocations creep is responsible for more than99% of the strain rate, and the elongation of thesample is achieved by the shape change of eachindividual grain. At intermedite strains rates, bothmechanisms are active, and their contribution tothe total strain rate is higher than 1%. Since bothmechanisms is contributing to the total strain.

Figure 1 shows the models's mathematicalexpresion as well as the basic microstructuralstrain mechanism, known as the Ashby's grainswitching. [1, 2, 3, 4]

As can be seen, the Ashby- Verral model isexpresed in tenns of some data not easily availableeither in bibliography or experimentally

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66 Revista Latinoamericana de Metalurgia y Materiales, Vol 11, N° 1y 2, 1992

measurable. The present study uses some newapproaches to evaluate the superplasticdeformation of the alloys AA-7075 using theAshby- Verral model.

Methods

The Ashby- Verral model was evaluated forthe AA-7074 alloy taking as microstructuralvariables four different inicial sizes (do) ( mm, 5mm, 10 mm, and 15 mm) ata temperature of 700K (0.8 of the melting point). The study wasfocused on the evolution in the initial stages offorming of four microstructural parameters: strain,strain rate, threshold stress and grain size.

•[ total

•- E diCusl.on +

accomodAlioll(1)

•E DislDcalloll

clim.:b

Grain svitching

•[DislDealloll. : A D1G b { (J } (3)

clim.) kT G

The model requires some parameter estimation toevaluate the superplastic forming of the AA-7075alloy, these parameters are:a.- Atomic mode1: to calculate it, the atomic radiuswas taken as the one of the aluminum atoms (theones that are present in a bigger number in thealloy) and the volume was calculated as if theywere spheres.b.- Grain boundary difusivity: since this value isnot foun in the bibliography studied and based inthe study of Seith and Heurnann [5], it was takenas 1000 times the value of the buIk difusitity.

c.- Grain boundary width: it was calculated basedon the Nishiyama and Waserrmann interfacialdesajustments study [6]. Taken the AA-7075 alloyas a policrystalline solid in which the grainboundaries have big desajustment angles (> 15°)and that, basically the grain boundaries were theinterface between two FCC microstructures, the

o

numerical value calculated was 6,79 A. Thisvalue 18 in good agreement with the experimentally

o

measured value of 5 A obtained by Xingang et al.[7].

Difw:Jiveeccomodatíon

Fig. 1: The Ashby- Verral model fundamentalelements.

d.- Grain size: since in the existing bibliographythere is enough evidence that some dynamicallyinduced grain growth occured during thesuperplastic deformation, it was taken into accountusing the mode1 proposed by Senkov et al. [8] andlater confirmed by Sato et al.[9]. They pro posethe folowing ecuation:

D=DoeaG (4)a = 0.08 [4]

e.- Threshold stress: it has been assumed that untilreaching a critical stress value, the strain rate willremain zero, so using a non linear numericalmethod the value was calculated.

Resuming the above mentioned, tables 1and 2 show the parameters used as well as thehypotesis assumed in each case. .

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Revista Latinoamericana de Metalurgia y Materiales, Vol 11, N° 1y 2, 1992 67

Results and Discussion

It can be seen that the Ashby-Verral modelallows to calculate the threshold stress, given aninitial grain size. The numerical value of thethreshold stress depends only on the inicial grainsize and not on the temperature. AIthough theprevious statement is mathematecally valid for alltemperatures, it only makes sense at temperaturesabove 50% of the melting point where bothacomodation mechanisms are plausible. Thenumerical values obtained are shown in figure 2.It is worth to remark that the threshold stressincreases its numerical value as the grain size issmaller, behavior that is usually associated to coldworking conditions and that is ruled by ecuationslike the Hall and Petch. The athermal behavior(always above 50% of the melting temperature),the behavior of the threshold stress wíth the grainsize and the low stress values observed once thestrain is higher than some tens of strain suggest theexistance of an activation energy to start thesuperplastic flow and most of the data availablesugest that the value of this activation energy isequal to the activation energy for grain boundatydiffusion. Nevertheless, frecuentIy small changesin the chemistry of the boundaty (impurity orsolute atoms) are responsible for big changes inthe difusivity of the grain boundary.

The grain growth rate calculated are notecual for all inicial grain size since it depends notonly on the temperature but on the strain rateo Thesmaller the grain size, the larger the grain growthrateo

Since in all cases the strain rate tend to anasintothic value, even though this value differsfrom one original grain sizes to another. If duringthe accomodation secuence oí the grain boundarysliding process a stable satate is achieved, then thestructure of the interface should remain constantduring deformation. The previous staternent isonly achivable if together with the grain boundarysliding, a migration process occurs.

Conclusions

The approaches used allow to use theAshby- Verral model to study the superplasticforming of the AA-7075 alloy and to arrive to thefollowing conclusions:- The value of the threshold stress is athermal inthe range above 50% of the melting temperature.- The model sugest the existance of an activationenergy for starting the superplastic flow.- Most of the data available sugest that the value ofactivation energy is equal to those of the activationenergy for grain boundary diffusion.

- The Ashby- Verral model shows a tendency tostable state in the strain rate sugesting that the grainboundary sliding is acompanied by the migrationof the interface.

List of symbols

ao = latice parameterA = sub-structure parameterb = Burgers vectordO= initial grain sizeD = grain size (diameter)Db = bulk difusivityDI = grain boundary difusivityE = Young modulusk = Boltzmann constantm = strain sensibilituy coeffitientn= l/mQ = activation energyr = atomic radiusR = gases universal constantT = temperatureTf = absoiut melting temperatureO = grain boundary wideness€ = strain. The same symbol withan upper dot isthe strain rater = grain boundaty energy per unit arean= atomic volumeU = Poisson moduluso = stress

References

l. Oosh A. K. and Hamilton C. H. Metal trans A,13A. May 1982. pp. 743-773.

2. Edington C. H. Metal Trans, 13A, May 1982.pp. 703-742.

3. Vale S. H. and Hassledin P.· M. 111 WordConference in Materials Processing Sidney,Australia, May 2-5, 1982.

4. Hamilton J. W. III Word Conference inMaterials Processing. Sidney, Australia, May 2-5,1982.

5. Verhoeven J. D. Fundamentals of PhysicalMetallurgy. Willey & Sons. Boston,Massachusetts, 1986.

6. Aaronson H. r., Spanos O., Menos E.S.K.,Hall M. O., Lage III W. F. and Chattopadhyav K.Proceedings of the Symposium Phase boundaryeffects on defonnation, Toronto, Canada, Oct. 13-17 1990.

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68 Revista Latinoamericana de Metalurgia y Materiales, Vol 11, N° 1y 2, 1992

7. Xingang J., Qingling W., Jinazhong C. andLongxiang M. Proceedings of the SynponsiumHot deformation of aluminum alloys, Detroit,Miehigan, USA Oct. 8-10, 1990. ,

8. Nishiyama A and Waserrmann O. Proceedingsof the 7th Intemational Conference of Metals andAlloys. Montreal. Canada. Aug. 1985.

9. Sato o. Conference proceeding of the syposiumSuperplasticity and Superplastic Forming. Blaine,Washington, USA Oet. 1-4, 1988.

lO. ASM Metal Handbook, 10th edition. Vol 2.pp. 875.

11. Murkherjee A K. Metaltrans A. 13A, May1982. pp. 717-732.

12. Wert J. Conference proceedings"Microstructural control in Aluminum alloys'',Chicago, llliniois, USA. Sept. 2-5. 1988.

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Tahle l. General and especific constants values for the AA-7075 alloy

Constant numerical Units Observations andvalue references

k 1,381 x 10-23 J I KR 8,31 l/K molr 1,43 x 10-10 m Aluminum atomic

radius [10]~Io 4,05 x 10-10 m Aluminum latice

parameterA 100 The numerical value

isbetween 75 and 150.Murlkhejeerecornendsthe value of 100 [11]

8 6,79 x 10-10 m 1.- polycristalline ma-terial. Misfit angle <1>

bigger th,U115° (takenas 20°)2.- the grainboundaryis the interface of twoFCC zones.references: Nishiyamaand Wassermann [6]

o 5 x 10-10 m [7]

r 0,60 J 1m2 Value given by l.A,Wert [12]

E 9,65 x 1010 Pa [10]

'\) 0,33 [10]

Tf 911 K [ LO]Do 1 X 10-4 m2 I S [10]Q 84 x 103 J /11101 [10]

Table 2. Requiered parameters used to apply the Ashby- Verral model.

Parameter Formula numer icul Observations andvalue refe rences

n atomic n = (4/3)(1t r3) 1,22 x 10-29 1.- sphcrical atornic

volume geometry asumed

(rn ') 2.- atomic radiustaken as the one ofAluminun atoms.

b 'lo I 3 2,34 x lO-lO(m)Db Db ;::;Do e-Q/RT 9.0 x 10-17 T = 364,4 K, (0,4 Tf)

(m2 I s) 2,4 x 10-14 T = 455,5 K, (0,5 Tf)9.3 x 10-13 T;::; 546,6 K, (0,6 TO1.3 x 10-11 T ;::;637,7 K, (0,7 TO9.5 x 10-11 T = 728.8 K. (0.8 Tf)

4.4 x 10-10 T = 819.9 K, (0.9 TO

DI 103 Db temperature Base in the Seith and(m2 I s) dependent Heumann studies [5]

G E/2(1+'\) 3.63 x 1010(Pa)

LatinAmcricun Iournnl of Mct allurgy an d Muteriuls, Vol J 1, N" Jy 2, 1992

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e--lOlo...+-'(f) 1.•OOeo-l° ... El

-a- do = 111m

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time ( seconds )

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time ( seconds )

o' sr== e e I

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10

grain size

Figure 2 : General behevior during U"le inHial stages of the superpresttcforming of the AA-7075 61l0y using the Ashby-Verral model.

A11 SI unas

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