The Rheological Model of Deformation Nidus in the Process of Rolling
Reološki model deformacijskega prostora v procesu valjanja
G. G. Shlomchack, Dnepropetrovsk Metallurgical Institute, Ukraine
I. Mamuzič, Metalurški fakultet, Sisak, Hrvatska
F. Vodopivec, Inštitut za kovinske materiale in tehnologije, Ljubljana
On the basis of contemporary ideas on the metal pressure shaping theory and investlgation results of the metal stress-strained state during rolling and uslng variation prinolples of mechanics, the plastometric classification of metals and alloys, a nevv rheological model of the high deformation nidus is proposed in this work. The model explains the regularities in the distribution of plastic deformation intensity in the non-contact zones as vvell as the formation of the feed front end deformation in dependence of the plastometric properties of metals. Experimental data confirming the validity of the model are given also.
Key vvords: rolling, plastometry, rheology, deformation, straining, deformation nidus.
Na osnovi sodobnih pogledov o teoriji oblikovanja kovin, raziskav napetostnega stanja v kovini med valjanjem, z uporabo variacijskih načel mehanike in plastometrične razvrstitve kovin in zlitin, se predlaga nov reološki model visoko deformiranega prostora. Ta model razlaga regularnosti v porazdelitvi intenzitete plastične deformacije v coni brez kontakta in nastanek čela deformacijskega prehitevanja v odvisnosti od plastometričnih lastnosti kovin. V članku so priloženi eksperimentalni podatki, ki potrjujejo veljavnost modela.
Ključne besede: valjanje, plastometrija, reologija, deformacijska utrditev, deformacijski prostor.
1. Introduction
In spite of the intensive development of mathematical mod-elling and experimental methods of mechanics. the theorv of rolling at present doesn't dispose of reliable informations on the mechanism of building-up of the deformation nidus. F.speciallv little is knovvn on the regularities of metal flow at unstable stages of the process. This may result in the slov, development of blooming rolling tcchnologv. a lovv rolling yield and sometimes also in an unsuitable quality of semifabricate.
The plastometrical (rheological) properties of metals play a very important role in the formation of the deformation nidus. The influence of rheologv on the development of regularities of deformation at rolling of rheologically complex materials is es-peciallv important by extremes on i r - e curves. In references 1 and 2 the higher order deformation anomalies during the testing of rheologicallv complex materials by means of plastic tension-al are described. The neeking of the sample vvith the decrease of resistance to deformation (da/de<0) on the (r - e curve represents the secondarv deformation heterogeneity. With increased resistance to deformation. according to the o - e curve, a second sccondarv deformation homogeneitv appears in form of uniform elongation of the neck. Thus, changes on the do/de curve are al-ternated by anomalies in deformation gradient and intensity. This is the base for the proposed rheological classification of materials shovvn in fig. 1 and established on the basis of experi-mental data: I class- simple unstrengthenable materials; II class-simple strengthenable materials; III-V classes - complex strengthenable materials.
The experimental investigation of the deformation nidus stress strained statc vvas realised considering the requirements of
the similarilv theorv (3) and using a laboratory device (4). It vvas necessary to reveal the mechanism of the formation of the knurl on the ends of rollings-a vvide-spread defect on blooming rolling (fig. 2).
Figure 2: Widely spread defect: knurl on the front end of the rolling: a-general vievv; b-during rolling on the blooming "1300" at 1150"-1200"C; e-laboratorv model of knurling.
Slika 2: Zelo razširjena napaka: odprta ustnica in čelo valjanca: a-splošen pogled; b-po valjanju na blumingu "1300" pri 1150"C-1200"C; c-laboratorijski model ustničenja
Rheolody ot the material -
classes l-V
I

6 J t,
Sample initial form
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6
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6,
IV
6,*
6r
! lUT2
S, S2
C, s, S, &4
rti
4-1
Stage of stretching and tensile strain anomalies
Het. simple strain
[ti

rfi
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X6r
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Hom. Het strain strain I order 1 order
6ti
Hom. strain I order

Hom. strain 1 order
rh-6T,
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Hom. strain I order
Het. strain 2 order
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i'
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Figure 1: Rheological classes of materials Slika I: Reološki razredi kovin in zlitin
2. Experimental vvork and analvsis of the results
Laboratorx device for modelling
The investigated unstable process is a complex phvsical phe-nomenon in vvhich ali parameters: geometrical, rheological, evo-lution of deformation, stressed-deformed state and others change in time. A special automated lahoratory equipment vvith modem measuring instruments vvas build for the modelling of this process considering the similarity criteria. The base of this device is a nevv rolling mili vvithout spindles (fig. 3) - a model of blooming (5). vvith roll diameter of 80...200 mm and length of 120 mm, and a rolling force of 0,3 MN. The main drive is a di-rect-current motor of 1,5 kW. The circumferential speed of rolls varies vvithin the ranges of 0-100 mmph and of 2-50 mmps. On the device it is possible to obtain an unfinished rolling (an in-stantaneous deformation nidus) by means of "shooting off' the upper roll at a determined moment and use modern investigation 296
Figure 3: General vievv of the new laboratorv rolling mili Slika 3: Splošen pogled na novo laboratorijsko valjamo
methods such as moire, photoelasticity, filming and strain mea-surement to measure the integral characteristics of the proeess (efforts, moments, displacements and others).
The laboratorv equipment includes also auxiliary devices for the preparation and realization of the trial: presses, stamps. ten-sometric and optical instruments, etc. Ali parts of the device are unified in an integrated svstem vvith an automatic programmed control vvhich ensures the precision and quality of the tests.
The rheological mode!
Lead-a natural model of hot steels and allovs. has the remar-cable propertv of recrystallization at room temperature. It de-forms at lovv efforts, it is brazed reliably after grating using the moire method and has a perfect plasticitv.
A careful studv of its rheology shovvs one more lead propertv (fig. 4). At various strain rates shovvs plastometric curves of different rheological classes, from simple unstrengthenable I class (at e<0.01 s"1) and strengthenable II class (ate= 1... 13,5 s"1) to complex strengthenable III class (at e = 13,5...60 s"1) and IV class (6 = 0.01 s'1).
This behavior makes it possible to use lead and its alloys as rheological models for different steels and alloys. Earlier investigations (61 shovved that its use makes it possible to respect strictlv the similaritv eriteria in the modeling of rolling processes on rolls of optical and organic glass by means of photoelastic observations. Technically pure lead (99,98% Pb) vvas used in this vvork.
MPa 120
80
40
	Al		
	2,5 S/	Iš<	
			
			
		60	
			
			
			
		l$-<	
			
0,2
0,4
0,6
Figure 4: Plastometric curves Pb (99.98% ) and Al (99.7%) at 2()"C Slika 4: Plastometrične krivulje /a 99,98% Pb in za 99.7% Al pri 20"C
Nuelea ofmaximum strain rates during the rolling
Experimental investigations of the mechanism of the formation of the deformation nidus vvere performed after a theoretical and experimental analysis of the metal stress-strained statc. Fig. 5a shovvs the intensitv field of strain rates H(x,y) obtained by solution of the v ariation problem using the methods proposed in ref. 7. Fig. 5b shovvs the experimental data for a stable proeess of rolling obtained by the moire method. Fig. 5c shovvs the field of strain rates e(x,y) at the initial stage of cogging of the slab edges by edging rolls obtained by mathematical simulation using the method of finite elements (8).
/ a
Figure 5: The field of strain rates in s1 obtained by the methods of: a-finite differences (7): b-moire patterns and c-finite elements (8) Slika 5: Polje deformacijskih hitrosti v s"1 izračunano po metodah: a-končne razlike (7); b-moire figure in e-končni elementi (8)
Though the methods vvere different, their results agree vvell and shovv scveral common features of the deformed statc in the deformation nidus: I-high heterogeneity of the deformation; 2-extension of plastic regions far beyond the geometrical limits of the deformation nidus, and the presence of the nuelea vvith maximum intensity of strain rates Hmax (hatched regions). The Hmax nuelea on fig.5a (Hmax = 3 s"1) and'fig. 5b (Hmax = 2.5 s"') are located in the initial contact regions at the very beginning of the deformation nidus.
An important conclusion can be derived from these results. the location of Hmax nuelea does not depend on the degree of metal fullness of the deformation nidus (see fig. 5c).
Mechanism of the formation of the knurl
The unstrengthenable metal through the regions of strain rates maximum intensitv (Hmax nuelea) strives the flovv tovvards the nearest free surface-tovvards the front end of the rolled piece. From the Hmax nucleus, as the source, it strives forvvard in direc-tion of the rolling, overtaking the roll surface and the central part of the metal. This is hovv the knurl is formed (fig. 6a).
In čase of rolling of strengthenable metal the size of the knurl depends on the strain hardening degree. This hardening grovvs adjacent, to contact lavcrs and reaches in the nucleus a HmaN suf-ficient to deplace the stretehing to deeper layers of the metal dovvn to the center. Central lavcrs rush forvvard and flatten the front edge of the rolled piece up to the complete elimination of the knurl (6b,c). Thus. the extension of strain in the front end of the rolled piece is determined by the rheological properties of the metal. During the hot rolling alternated by softeming and re-crystallization phenomena the rolling speed plays and important role. At lovv speed the to Hmax strengthened nucleus has the time to soften. This explains the formation of the knurl vvhile at high rolling speed and the virtual absence of softening the knurl is not formed.-
Pictures of the samples in fig. 6a vvere obtained at different stages of the formation of the strain nidus and before the stabili-sation of the rolling proeess. The rolling vvas performed in the high-speed regime of the third rheological class, vvhen the addi-tional softening, vvhich causes a strain heterogeneity of the sec-
ond order, occurs in the Hlllas nucleus. The layers adjacent to the contact surface do not soften not only because of shortage of time. but also because of the do/de<0 rheological anomaly. Sliding on the roll the metal in these lavers is literally extruded from the strain nidus tvvisting towards the centre of the sample, and the formation of the knurl is intensified to the maximum.
During the rolling of lead in the regime of the second rheological class (e = 1... 1,5 s"1) the adjacent to contact layer of the metal has 110 time to soften and that prevents the formation of the knurl (fig. 6b).
Several experiments under the same conditions, but vvith different rolling speeds vvere performed additionallv on alluminium vvith the aim to check the reliability of the explained mechanism. The plastometric characteristic of alluminium shovvs that it is a material of the second rheological class vvith strictlv inereasing funetion <7 - e (see fig. 4). In the deformation nidus it practically does not soften at room temperature. Thus the metal adjacent to the contact surface, strengthened by the passage of Hmax nuelea (see fig. 5), is not elongated in the direetion of the exit from the rolls and deeper layers of the metal are deformed. If at the first moment the adjacent to the contact layer of alluminium, vvhich had no time to slrengthen, outpaces the central area then, because of the strengthening, their deformation is delayed, vvhile the central area is rushed forvvard outpacing the adjacent to the contact layers and prevents the formation of the knurl (see fig. 6c).
Thus, the mechanism of the formation of the strain nidus during the rolling is determined by the degree of metal rheological complexity.
The plants producing rolled carbon steels lose a considerable quantity of metal because of the cuttings. During the blooming rolling the shrinkage cavity is elongated simultaneously vvith the formation of the knurl and the quantity ofrejects is inereased. For
1	1_ _1--1--J
0 0,1 0,4 D,S 0,s 0 D,2 0,4 D,s Z
Figure 7: Plastometric eurves of carbon steel (0.43% C; 0.26% Si: 0.74% Mn; 0.022% P: 0.016% S) at 900"C: a-from ref. (9), (10) (dotted line); and b-from ref. tli) Slika 7: Plastometrične krivulje za ogljikovo jeklo (0,43% C: 0,26% Si: 0.74% Mn; 0,022% P; 0.016% S) pri 900"C: a-iz ref. (9), (10) (pikčasta črta); in b-iz ref. lil)
Figure 6: The modification of the front end of the rolled piece during the rolling at 20"C: a-lead in the high-speed regime of the third rheological class at do/decO; b-lead in the regime of the second rheological class at dcr/de>0 (moire stripes: u and- vertical and horizontal displacements);
e-aluminum (99.7%) at ali speeds
Slika 6: Sprememba čela valjanea med valjanjem pri 20"C: a-svinec pri velikohitrostnem režimu tretjega reološkega področja z d<r/d€<0: b-svinec v režimu drugega reološkega področja do/de>0 (moire pasovi, u in v - navpični in vodoravni premiki); c-99,7% Al pri vseh hitrostih
that reason the elimination of the knurl with increased speed of gripping during blooming rolling of carbon steel incots (0.43% C; 0.26% Si: 6.74% Mn; 0.22%" P; 0.016% S) was checked. It failed because of the rheological properties of the steel (fig. 7). The plastometric curves from ref. |9| and |10| were used under assumption that the steel vvas rheologically simple and of the second class (see fig. 7a). In reality, according to the investigations of Suzuki. it is complex (fig. 7b) and of the third rheological class 11|. The reason for the knurling vvere the deformation anomalies of the second order at d|/d|<0. A diminution of the knurling could be obtained only by means of decrease of the deformation degree (in Hmax nucleus).
The analvsis of the rheology of carbon steels (0.2 - 1.0% C) according to Suzuki shovved that these steels vvere rheologically complex of the third class vvith the maxima on cr - e curves at ali strain rates and temperatures. That means that the propensity to deformation anomalies is inherent to these steels. The formation of the knurl is inevitable and the only way to diminish it remains the change of the rolling regimes or of the form of the ingots.
Formation of the prenidus plastie zone
Fig. 8 shovvs the results of several experiments performed vvith the aim to explore the development of deformation in the prenidus zone by modelling on the laboratory rolling mili. Samples-ingots 40x40x200 mm prepared vvith high accuracy from preliminarlv pressed and vvith stabilized properties (annealing one hour at 100"C and ageing at 25°C during 60 days) lead (99.98% Pb) vvere rolled vvith 80 mm rolls vvith a deformation e = 25%.
Figure 8: The shape of the deformation nidus during the rolling of metals vvith different rheology
Slika 8: Oblika deformacijskega prostora med valjenjem jekel z različno reologijo
The extension of the prenidus plastie region vvas determined bv means of moire stripes and indicator devices operating vvith the error of+0.01 mm. Differences in rheology of the deformed material vvere achieved by change of strain rates in the range of e = 0.0005.. 0.01 and 1.5 s1.
During the rolling in regime of simple unstrengthenable first class the prenidus deformation vvas maximal (see fig. 8, I, AB). During rolling in the regime of the second rheological class (vvith maximum strengthening) the extension of the prenidus plastie zone vvas maximal. Strain homogeneity of ihe first order pro-motes the inclusion of layers of metal more distant from the rolls into ihe deformation. These materials are optimal from ihe rolling technology stand point.
The processes of the development of the second order strain heterogeneity vvere observed during the rolling of the material of the third rheological class vvith a maximum on the o - e curve (see fig. 8, III, ACI. The extension of the zone of non-contact deformation in front of the rolls vvas smaller than in the previous čase and the displacement of "C" point-the beginning of contact of the metal vvith the rolls. tovvards the line of roll centres vvas observed constantly. This could produce a strain heterogeneity of the second order vvith elongation of the surface Iayers joining points "D" and "C" in an avalanehe and could lead to the de-struetion of metal. especially vvhen concentrators of stresses in form of defects are present.
3. Conclusions
A nevv model for the formation of the plastie deformation nidus during the rolling vvas devcloped using a rheological clas-sification of metals based on experimental data:
1.	It is shovvn. that the strained state of metal in the nidus of deformation is characterized by the presence of regions vvith maximum strain rates - H1Ilas nuclea and depends substantiallv on the rheologv of the metal.
2.	The mechanism of formation of the widely spread defect-knurl on the ends of the rolled pieces is explained. It vvas ascertained that the formation of the knurl depends on the rheology of the metal and the rolling speed.
3.	Regularities of the formation of the non-contact prenidus zone of plastie deformation vvere ascertained.
4.	Rheological (r - e data available in scientific literature should be used carefully because in many cases methods of mathe-matical "smoothing" vvere used for processing the results of plastometric investigations and rheological anomalies fell-out of the researcher's field of vision.
5.	References
1	G.G. Shlomchack: Deformation features of the rheologicallv complex materials. Deposited in UkrNlINTl 13.08.91 T. No."
1 167-Uk91, Kiev. 1991. 11 pp.
2	G.G. Shlomchack: Detection of regularities of deformation heterogeneities and anomalies of plasticity of rheologicallv complex and supercomplex materials. Deposited in UkrNlINTl 12.12.91.. No. 1589-Uk91. Kiev. 1991.21 pp.
3	G.G. Shlomchack. G.A. Fen, V.G. Kutsav: Izv. Vuzov. ChM.No. 3. M. 1980, pp 79-82.
4	G.G. Shlomchack, G.A. Fen, V.G. Kutsav: "Pressure shaping of metals", M. "Metallurgia", Dmetl, Research No. 60, pp. 121-122.
5	G.G. Shlomchack: Laboratory rolling mili, Russian patent 29.08.91. on the claim No. 4930929/27/035063.
6	G.G. Shlomchack: Izv. Ac. Sc. USSR. Metals No. 6, 1978. pp. 102-106.
7	G.A. Fen, G.G. Shlomchack and coll.: Metallurgia and coke chemistry, issue 46, Technicka, 1975. pp. 109-113.
8	H. Nicaido. T. Naoy, K. Sibata: Transi, from Jap. KI-73789, COONTI, Sosei to kako. v. 24. No. 268, 1983. pp. 486-492.
9	I.Y. Tarnovsky and coll.: Mechanical properties of steel at hot pressure shaping. Metallurgizdat, Sverdlovsk, 1960. p. 264.
1,1 V.I. Zyzin, M.Y. Brovman, A.F. Melnikov: M., Metallurgia.
1964. p. 270; 1964. p. 270. " H. Suzuki: Report of the Inst. of Industrial Science, the University of Tokyo, 1968, v. 18. No. 3. pp. 139-240.