for references: russian physics journal. 2018. v.61. doi … · 2019-03-08 · on the x-ray...

Екатеринбург · · · · +7(343) 375 94 03 [email protected] · · · · cae.urfu.ru

© Техноцентр компьютерного инжиниринга УрФУ · · 2018

1

Для ссылок : название журнала и выходные данные статьи / For references:

Russian Physics Journal. 2018. V.61. N 1. P. 7-13. DOI 10.1007/s11182-018-1358-x

Thermal coefficient of linear expansion modified by dendritic segregation in nickel-iron alloys O. M. Ogorodnikova, E. V. Maksimova UDC 669.1:536.424

The paper presents investigations of thermal properties of Fe–Ni and Fe–Ni–Co casting alloys affected by the heterogeneous distribution of their chemical elements. It is shown that nickel dendritic segregation has a negative effect on properties of studied invars. The mathematical model is pro-posed to explore the influence of nickel dendritic segregation on the thermal coefficient of linear expansion (TCLE) of the alloy. A computer simulation of TCLE of Fe–Ni–Co superinvars is performed with regard to a heterogeneous dis-tribution of their chemical elements over the whole volume. The ProLigSol com-puter software application is developed for processing the data array and re-sults of computer simulation.

Keywords: iron-nickel alloy, casting superinvar, thermal coefficient of linear expan-sion, dendritic segregation.

Introduction Constantly growing research interest in FeNi alloys [1] is explained by

their application in heat-resisting assemblies of aerospace structures [2], optoe-lectronic devices [3] and high-frequency engineering equipment [4]. Such useful invar parameter as a low thermal coefficient of linear expansion (TCLE) allows manufacturers to provide soft assembly parts [5] with bearing parts produced therefrom. Constructional invars having almost similar TCLE [6], create a stress-strain state in functional glass, ceramics and composites exposed to varia-ble temperature field. A number of previously published works concerns a na-noscale state of invars after the pressure exposure [7]. At the same time, casting alloys [8, 9] are rather relevant for the production of large-scale heat-resisting parts possessing macro-isotropical mechanical properties.



2

Among low-expansion FeNi-based alloys, Fe–Ni–Co superinvars possess the lowest TCLE [10]. Unique casting superinvars and mold castings production techniques were developed in Ural Federal University, Ekaterinburg, Russia [11, 12]. Experiments showed that after crystallization, casting superinvars are cha-racterized by nickel dendritic segregation which has a negative effect on the ef-fective volume-averaged TCLE values [13]. Thermal treatment of large-scale casting superinvars cannot provide levelling the heterogeneous distribution of chemical elements due to the low diffusion of nickel atoms in the FCC lattice [14]. Therefore, the alloy behavioral models should be adjusted at a design stage of precision part production in the integrated computer-aided design/computer-aided engineering (CAD/CAE) software programs [15]. The industrial applica-tions of CAE programs allow rather accurately to compute the temperature fields within the crystallization range [16].

The improvement of behavioral models of Fe–Ni–Co alloys in order to in-crease the accuracy of predictions in computer simulation of production processes [17] and finished products [18] is a relevant problem of the efficient use of expensive CAE programs. At design stages of casting technology, it is important to consider the dependence between the technology-driven structural and functional properties of the alloy. Updating files consisting the data on supe-rinvar properties during the computer-aided analysis of casting products and technologies [19], is performed through the amendments to the effective TCLE value modified by dendritic segregation.

The aim of this work is to study the TCLE of Fe–Ni–Co casting superin-vars produced in-situ and establish a fast TCLE prediction using the approxima-tion method for experimental data array with regard to technology-driven hete-rogeneous distribution of the alloy chemical elements and crystallization beha-vior.

Materials and methods Casting superinvars containing Fe-28-35 wt.% Ni-0-6 wt.% Co and those

alloyed with niobium and chromium were studied with the use of cylindrical specimens having 5 mm diameter and 50 mm length. Witness specimens were manufactured in-situ using a suction casting machine equipped with quartz tubes, preliminarily molten and cured in alumdum crucibles at 1530–1550°С. The TCLE of α20–100 °С was measured on a certified quartz dilatometer. The analysis of the concentration of chemical elements in the alloy was performed on the X-ray microanalyser JXA-860M using polished sections. After etching the polished sections in a Marble solution (50 ml hydrochloric acid, 2 g copper sulphate, 50 ml ethyl alcohol, 50 ml water), the microstructure was observed with optical metallography methods. Superinvars were studied both after crystal-lization and annealing processes. The ProLigSol computer software application



3

[20] was developed especially for processing the data array and results of com-puter simulation.

Results and discussions Optical images of the dendritic-cellular microstructure shown in Fig. 1а, b

as well as a high heterogeneity of the chemical composition, characterize both casting invars and superinvars. Niobium alloying provides the formation of equiaxed grains as presented in Fig. 1c. Independently of the morphology of the crystalline structure and the way of its formation, the nickel dendritic segrega-tion remains which is observed due to etching the metallographic specimen. The areas low in nickel are more susceptible to etching and form the surface texture. The nickel content is reduced relative to its average content at the centre of grains and dendritic cells.

Fig. 1. Optical micrographs of microstructure of Fe-36wt.%Ni-2.5wt.%Cr invar (а, b) and modified Fe-32.5 wt.% Ni-3.7wt.% Co-0.5wt.% Nb superinvar (c, d).

After crystallization a partial secondary recrystallization occurs during cooling, which leads to the displacement of grain boundaries and the enlarge-ment of the structural components, but has no a substantial effect on the initial heterogeneous distribution of chemical elements. Therefore, we observe two boundary networks in Fig. 1b, d, namely the high-temperature network formed due to the heterogeneous nickel distribution at a point of the solidus temperature and the finite network of the large-angle grain boundaries.

The assumption about the nickel segregation made according to optical observations of etched specimens is supported by direct measurements of the nickel concentration on a polished specimen surface using the electron probe microanalysis. The nickel distribution over a 100 μm square of Fe-32 wt %Ni-4 wt %Co invar is illustrated in Fig. 2. Dark places inside dendritic cells are areas low in nickel. In order to generate this image, the discrete digital data obtained after the electron probe microanalysis are processed in MatLab software applica-tion and then presented graphically. During the data processing and visualiza-

a b c d

200 μm 100 μm 80 μm 100 μm



4

100 μm

tion, this image is split into surface elements the size of which corresponds to the experimental resolution.

Fig. 2. Graphics image of nickel concentration in Fe-32 wt %Ni - 4 wt % Co invar.

Fig. 3. Experimental function f(w) for cylindrical specimens of Fe-32wt%Ni-4wt%Co superinvar with different diameters: a – 5 mm (curves 2, 3); b – 30 mm (curves 5, 6).

As can be seen from Fig. 3а, the quantification of results obtained in the

electron probe microanalysis represents a normalized function f of the relative surface elements and the observed nickel concentration w. The experimentally obtained function f(w) describes nickel segregation.

Nickel microsegregation in the volume of a large-scale casting with a complex geometry can vary due to different rates of the melt cooling and solidi-fication in thin walls and heating units. The influence of the solidification rate of



5

Fe-32 wt.% Ni-4 wt.% Co superinvar on nickel segregation and its concentration spectrum is studied on casting cylindrical specimens having the diameter of 5 and 30 mm. The experimental function f(w) of these specimens which describe nickel segregation in Fig. 3, represents the superposition of two Gaussians in the form

2max

0 max 2( )( ) exp

2w wf w f f

⎛ ⎞−= + −⎜ ⎟⎜ ⎟σ⎝ ⎠

, (1)

where w is the nickel content; fmax is the maximum height; wmax is the maximum position; σ2 is the dispersion.

The analysis results of decomposition parameters of nickel concentration spectra are summarized in Table 1. These parameters describe the nickel distri-bution between the central and boundary area of the structural elements.

TABLE 1. Decomposition parameters of nickel concentration spectra

in Fe-32wt.% Ni-4wt.%Co superinvar specimens with 5 and 30 mm diameter.

Curves in Fig. 3

Maximum positionwmax, wt.% Ni

Half width max-imum, wt.% Ni

Maximum height fmax, arb.

units 2 31.4 2.479 0.1369 3 33.0 3.834 0.0529 5 31.4 2.440 0.1185 6 32.9 2.115 0.0821

A comparison of superinvar specimens with 5 and 30 mm diameters

shows that the size of dendritic cells is respectively 30 and 100 μm, however the nickel distribution in their central part is similar. During the computer simula-tion, dendritic cells are approximated by a unit ball radius. The dependence be-tween the nickel concentration w(r) along the radius r of the unit ball which represents the structural components of the casting alloy, is obtained via the in-tegration of the nickel segregation function f(w) throughout the specimen with regard to normalization:

1 ( ) ( ) 1

Vw r dv r

wV=∫ or

12

0

3 ( ) 1r

w r r drw =

=∫ , (2)

where w is the average nickel concentration in the alloy; w(r) is the nickel con-tent in dv(r) = 4πr2dr area limited by spheres with r and r + dr radii.

In this experiment, the effective volume-averaged TCLE values are meas-ured on the standard specimens. The experimental results include segregation effects and allow verifying the computer models. The effective volume-averaged



6

TCLE values ⎯α of cylindrical specimens follow the law of additivity. They can be calculated via the volume integration of a certain theoretical dependence be-tween the local TCLE values α and nickel concentration w which supposes a uniform distribution of chemical elements:

( )1 ( )V

w r dvV

α = α∫ . (3)

The evaluation of the effective TCLE values requires the theoretical de-pendence of superivar TCLE on σ(w) composition. In the absence of dendritic segregation, this dependence is obtained by the inverse modeling. The informa-tion base for the input data on the computer aided analysis of TCLE values of Fe-Ni-Co alloys includes measurements on 500 witness specimens. The TCLE dependence on the chemical composition of ternary alloys is obtained after the statistical data processing. In Fig. 4а the TCLE dependence is presented as iso-parametric curves. It should be taken into consideration that nickel segregation experimentally proved by the electron probe microanalysis is 3% for the given surface of Ni,Co( )wα .

Fig. 4. Experimental TCLE – chemical composition dependence of Fe-Ni-Co cylindrical spe-cimens with 5 mm diameter and 3% nickel segregation (а); theoretical TCLE–chemical com-position dependence of Fe-Ni-Co cylindrical specimens at uniform nickel distribution (b).

The experimental dependence Ni,Co( )wα obtained using TCLE measure-ments on cylindrical specimens with 3% nickel segregation is connected with the required theoretical dependence σ(w) by the following integral equation:

0

0

2Ni,Co 1 2 0( ) const const ( ) ( )

w w

ww w w w dw

+δα = + − α∫ , (4)

a b



7

where w0 is the minimum nickel concentration at the centre of dendritic cell; δw is the degree of nickel dendritic segregation.

The numerical calculation of the integral equation is carried out with the square approximation of segments of the experimental surface α(wNi, Co). The resulting value is α(w) theoretical surface which reflects the TCLE values of Fe-Ni-Co superinvars in the assumption of the uniform nickel distribution in them. The theoretical surface α(w) is shown in Fig. 4b. According to theoretical calcu-lations, the reduction in the degree of nickel segregation in superinvars is ac-companied by the TCLE drop throughout the invar compositions investigated. In practice, it is impossible to fully level the nickel dendritic segregation in casting superinvars. Thus, in order to reduce the nickel dendritic segregation from 3 down to 1.25%, a 1250°С homogenizing annealing is required either in vacuum or shielding atmosphere during 48 hours.

In the state diagram of iron-nickel low-expansion alloys, their composi-tion locates next to the concentration boundary of the allotropic polymorphic transformation γ→α. There is a risk that within the low-temperature range, when using casting alloys with well-defined superinvar characteristics, the formation of martensite phase will occur due to the dendritic segregation in the inner areas of austenitic dendritic cells low in nickel. The TCLE of martensite is 11.5⋅10–6 K–1, which is an order of magnitude more than that of austenitic superinvar. The X-ray phase analysis proves the martensite phase formation in Fe-28-32 wt.% Ni alloy specimens exposed to cryogenic temperatures. The amount of residue mar-tensite in these specimens increases from 7.5 to 11.5% with the increase in the nickel content from 28 tо 32%.

A metallographic analysis shows that the formation of martensite phase depends on nickel microsegregation. After cooling down to the liquid nitrogen temperature and 10 min curing, the formation of martensite phase in Fe-32% Ni invar is observed at the centre of the dendritic cell low in nickel (Fig. 5а). The formation of martensite phase in invars causes a significant TCLE increase which is proved by quartz dilatometer measurements. When FeNi-based auste-nitic alloys containing 33–35% nickel are immersed into liquid nitrogen, their TCLE is not changed. The loss of invar properties is observed in alloys having not less than 33% nickel in which the formation of martensite phase is induced by cryogenic temperatures. Figure 5b depicts the TCLE calculation results ob-tained for superinvar compositions in the light of the possible martensite phase formation caused by segregation.



8

Fig. 5. Optical micrographs of Fe-32% Ni invar after cooling down to 77 K (а) and theoretical dependence of TCLE and chemical composition of ternary Fe–Ni–Co alloys with possible martensite formation (b).

Calculations show that in the case of superinvars, each of ten weight per-

cent of martensite phase causes the TCLE increase not less than by 1⋅10–6 K–1.

Conclusions The obtained results indicate that nickel microsegregation in Fe–Ni–Co

invars led to the increase in the effective values of the thermal coefficient of li-near expansion. A dangerous suppression of invar properties occurred in Fe-28-32wt.% Ni alloys at temperature decrease down to 77 K due to the formation of martensite phase at the centre of dendritic cells produced by nickel dendritic se-gregation. A mathematical model was developed to evaluate the effective TCLE values of ternary Fe–Ni–Co alloys depending on dendritic segregation. The ProLigSol computer software application was developed for processing the data array and results of computer simulation of the thermal coefficient of linear ex-pansion. The proposed mathematical model can be used for correcting a com-puter analysis of stress-strain states of designed parts made of invars with a glance to a heterogeneous distribution of chemical elements over the whole vo-lume.

Acknowledgements The authors like to express their gratitude towards the management and

workers of the Research and Development Centre ‘Linvar’ for their production support and encouragement during this work. Personal thanks go to Vladislav Ivanovich Chermenskii, PhD, the Deputy Director Research, ‘Linvar’.

a

200 μm

b



9

References

1. V. V. Sagaradze, N. V. Kataeva, I. G. Kabanova, et al., Phys. Met. Metallogr., 115, No. 7, 661-671 (2014).

2. O. M. Ogorodnikova, E. V. Maksimova, and M. V. Pokazanev, Dual Technology, No. 1(66), 19–24 (2014).

3. A.M. Savitskiǐ and I.M. Sokolov, J. Opt. Technol., 76, No. 10, 666-669 (2009). 4. V. I. Chermenskii, S. V. Rabinovich, M. D. Kharchuk, et al., Aviation Industry, No. 3,

37–39 (2008). 5. J. H. Zhu, S. J. Geng, and D. A. Ballard, Int. J. Hydrogen Energy, 32, 3682–3688

(2007). 6. O. M. Ogorodnikova, E. V. Chermenskaya, S. V., Rabinovich and S. V. Grachev,

Phys. Met. Metallogr., 88, No. 4, 355-359 (1999). 7. V. A. Shabashov, A. V. Litvinov, Kataeva N.V., et al., Phys. Met. Metallogr, 115, No.

9, 871-883 (2014). 8. O. M. Ogorodnikova, Foundry. Technologies and Equipment, No. 2, 32–34 (2015). 9. O. M. Ogorodnikova and S. V. Martynenko, Metally, No. 5, 19–24 (2012).

10. M. V. Chukin, N. V. Koptseva, E. M. Golubchik, et al., Metallurgist, 58, No. 3-4, 321-326 (2014).

11. S. V. Rabinovich, M. D. Kharchuk, V. I. Chermenskii, M. Yu. Rusin, A. Ya. Anikin, L. V. Golementsev, and S. M. Kubakhov, RF Patent No. 2183228 (June 10, 2002).

12. S. V. Rabinovich, M. D. Kharchuk, V. I., Chermenskii M. Yu. Rusin, and A. S. Kha-mitsaev, RF Patent No. 2243281 (December 27, 2004).

13. O. M. Ogorodnikova, S. V. Rabinovich, M. D. Kharchuk, and V. I. Chermenskii, Phys. Met. Metallogr., 76, No. 4, 118–122 (1993).

14. O. M. Ogorodnikova and E. V. Maksimova, Met. Sci. Heat Treat., 57, No. 3-4, (717), 143-145 (2015).

15. O. M. Ogorodnikova, Information technology of CAD/CAM/CAE, No. 2, 30–34 (2014).

16. O. M. Ogorodnikova, Izv. Vyssh. Uchebn. Zaved., Fiz., 54, No. 1/3, 144–149 (2011). 17. O. M. Ogorodnikova, Russ. J. Nondestruct., No. 8, 568–575 (2011). 18. Y. Liu, X. Lu, C. Bai, et al., J. Indust. Eng. Chem., 30, 106–111 (2014). 19. J. Shang, J. Yan, and N. Li, J. Alloy. Compd., 611, 91–95 (2014). 20. O. M. Ogorodnikova, RF Certificate of State Registration of Software No.

2012616120 (July 4, 2012).

for references: russian physics journal. 2018. v.61. doi … · 2019-03-08 · on the x-ray...

Documents