Deformation Anomalies of Higher Order during the Plastic Extention of Rheologically Complex Materials Deformacijske anomalije višje stopnje med plastičnim raztezanjem reološko kompleksnih materialov G. G. Shlomchack*, Dnepropetrovsk Metallurgical Institute, Ukraine I. Mamuzič, Metalurški fakultet, Sisak, Croatia F. Vodopivec, Institute of metals and technologies, Ljubljana, Slovenia New deformation anomalies of rheologically eomplex materials vvere discovered and demonstrated. It vvas found out that in the process of axial extention during the decrease of resistance to deformation secondary deformation heterogeneities take plače alternated vvith deformation homogeneities due to changes in resistance to deformation. Key vvords: rheology, tensile test, deformation, heterogeneities Odkrite so bile nove deformacijske anomalije reološko kompleksnih materialov in dokazane z raztržnimi preizkusi primernih kovin. Ugotovljeno je, da pri aksialnem raztezanju med zmanjševanjem odpora proti deformaciji prihaja do sekundarnih deformacijskih heterogenosti in homogenosti zaradi sprememb v odpornosti materiala proti deformaciji. Ključne besede: reologija, raztržni preizkus, deformacija, heterogenosti 1. Introduction The plaslicitv is essential for the irreversible ehange of form of materials and the obtention of a finished product. The measure ot plaslicitv is the extent of deformation energy aceumulated in the material up to the failure1 and it is generally established by testing in conditions of stress-strained state identity. The simplcst of such tests is the linear tension or compression of the specimens when the concepts of dcformability and plaslicitv are identic. Kaibishev defines good plasticity as "high stabilitv" against formation of the neck at uniaxial extention ol the specimcn and explains the possibilitv of using veritable stress-strain diagrams r)-e for the estimation of the plaslicitv'. Beside of the uniform elongation and neeking the test shows some parameters of the sensitivitv of the material to the strengthening rate as well as quantitative data on the plasticity. However the question remains of how to obtain better informations on the materials deformability by means of real stress-strain curves. Modern metallophv sics investigates the separate and combined influence of many factors on plaslicitv of metals and alloys. For example. on the basis of the analvsis of extensive experimental data M. Y. Dzugutov tried lo explain why the plaslicitv of high-alloved steel decreases and vvorked out a classification of this multiform plicnomenon '. However, the complex intcrrelation betvveen various factors and their influence upon the deformation processes makes the problem of the predietion of the def'ormability unsolvable ■ Dr. sc Georg GEORGIJEVIČ SHLOMCHACK. Dnepropetrovsk Metallurgical institute. t kraine vvithout spccial appropriate experiments. In ref. 3 the importance of plastometric tests is pointed out, but no suggcstion is proposed hovv lo use their results for deformability forecasts. In literature extensive informations on rhcological r)-e curves obtained by plastometric tests of various metals and allovs are found4 \ Their analvsis shovvs that plasticalIv deformed materials can be devided into rhcological simple vvith invariable or strictly inereasing funetion d-e and rhcologicallv complex vvith cxtreme on r)-e curves. Rhcological anomalies are vvell-knovvn and explained. Initial strain anomalies observed as neeking of specimens at tensile strain are knovvn too, but the regularities of their development are not fullv explored. The influence cd' test rate and temperature'', as vvcll as that of the material strueture7 vvere investigated, hovvever no attempts to study the dependence betvveen the regularities of strain and rhcological anomalies vvere published so far. This problem vvas solved by the experimentally discovered and theoretically explained phenomenon of highest order strain anomalies during the tests of rhcologicallv complex materials by plastic stretehing. 2. Theoretical anal vsis In the phenomenological analysis it is nccessarv to kcep in mind the condition of identity of rhcological curves rJ-e obtained bv stretehing and by compression and the fact that in the integral aspcct these curves hold ali the information on the changes in the material during the plastic deformation. During the tensile tests of unstrengthenable material any casual rcduction of specimen cross-section leads to rupture, if it is not compcnsated by strain hardening and the deformation in form ofthe necking preceding the rupture. Let's call this vvell known simple strain heterogeneity "simple strain anomalv". During tensile tests of strengthenable material the deformation vvith decreasing cross-section is localised in one section earlier than in others vvhich strengthen because of liquations. favourable orientation of crystallite. etc. and ceases to deform, vvhile other sections of the specimen less strengthened are involved in the flovv. Consequently in the beginning the deformation spreads vv ithin the vvhole volume ofthe material - vve observe the vvell-knovvn quasi-homogeneous strain of the specimen. According to phenomenological concepts it vvill be called "homogeneous strain of the first order". The follovving formation of the neck 011 the specimen vvill be called "heterogeneous strain of the first order" or "strain anomalv ofthe first order". On the base of the analvsis of true r)-e diagrams and their cxplanation ali materials are ciassificd bv the degree of their rheological complexity (Fig. I). The first rheological class are simple unstrengthenable materials. Bv stretching the specimens are deformed according to simple heterogeneous strain vvith formation of the neck and rupture (Fig. 1,1). In the second rheological order one finds simple strengthenable materials vvith a strictlv inereasing <)-e function (Fig. 1,11). A tvpical feature of sueh materials is the homogeneous strain of the first order. the formation ofthe neck - strain anomaly ofthe first order and rupture ofthe specimen. The third lo fifth classes are rheological complex materials. l ite third rheological class is charasterized bv a maximum on r)-e curves. The material (Fig. 1,111) of this type is stretehed through the stage of the first order homogeneous strain, then the neck is formed. The reason is not a laek of plasticitv as in second rheological class. but the influence of other mechanisms. The diminution ofthe resistance lo deformation is reached after a limited uniform elongation of the specimen. The process is follovved by a considcrable deerease of the relative elongation due to the accelerated formation of the neck, hovvever, the value of relative necking is not decreased at the same moment. This anomalv vvas called "heterogeneous strain anomalv ofthe second order"\ For the fourth rheological class of materials tvvo extreme on r)-e curve and an subsequent inerease of resistance to deformation after the first one (Fig. 1,IV) are tvpical. As in the čase of materials of the second class. the extention of the specimen begins vvith a homogeneous strain of the first order and then, in the materials of the third class. a heterogeneous strain of the second order is observed: the neck starts to form before the elongation et is attained. Herc the material reveals its remarkable propertv: the specimen does not fracture, but it is stretehed homogeneouslv in the region of the alreadv formed neck'1. The explanation is the secondarv inerease ofthe material resistance to deformation in the neck before et (Fig. 1,1 V). Outside the process is similar to the homogeneous strain of the first order, embracing only the neck region or. to be more exact, the transition /.one from the neck lo the main volume of the specimen. This strain anomalv is called according to the proposed terminolog) as "homogeneous strain of the second order". Manv metals (coppcr, aluminium, lead. etc.) have the remarkable propertv to restore the plasticitv in this vvuv. The further extension of the specimen brings the formation of a localised neck on the earlier elongated neck and causes "a heterogeneous strain anomalv ofthe third order". The fifth rheological class of materials is characterized bv relations r)-e vvith three or more extrema (Fig. I,V). During the extension the specimen passes through stages of strain tvpical for the IV rheological class. hovvever vvithout rupture in the localised neeks but vvith further strengthening and uniform elongation due to the homogeneous strain. This anomalv. is called "homogeneous strain of the third order". The follovving stage is the formation of a nevv localized neck on the elongated neck of "heterogeneous strain anomalv of the fourth order". and so on. Multistage strain anomalies of the highest orders on materials of the fifth rheological class are not evident as it is shovvn sehematicallv in Fig. 1,V. The reason are anomalv smooth changes betvveen the different stages and thus the changes are found only bv very careful observation. Rheolody of the material -classes l-V 6 1 6T0_6r Ot, Sample initial form Stage of stretching and tensile strain anomalies Hom strain I ordei Hom. stra!.. I order I Hom. strain I order r 0" r $ Figure 1: Tensile strain anomalies of materials vvith different rheologv. Slika 1: Anomalije pri nate/ni deformaciji materiala Fig. 2 shovvs a family of rheological curves for hot-rolled annealed pure titanium (99.9% )5 vvhich is at 900 C typical representative of an unstrengthenable material of the first rheological class, deformable according to the simple strain heterogeneitv type, vvhile at 700 C it is a tvpical representant of the second rheological class. Fig. 3a shovvs rheological curves for a carbon steel (0.43'; C. 0.26'i Si. 0.74% Mn. 0.022'r P. 0.016% S) representing a verv numerous third class of rheologicallv complex materials. Fig. 3c shovvs tj-e curves I »j a 160 120 80 40 1 1 — 700°C 1 10 r/^ "2.5 /0.5 J> 0.1 - 900°C 2.5 0.1 1 1 1 0 0.2 0.4 0.6 0.6 Vat ur a l stram Figure 2: Rheologicai curves of hot-rolled and annealed Ti (99.9%). Slika 2: Reološko krivulje toplo valjanega in žarjenega Ti (99.9% ). 1 1 1) - 10 — / -V5 i V 0.5 r\ 0.1 ■r 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 Tlotural str o in Figure 3: Rheologicai curves: a - steel C 45 al 900 C:b - copper (99.99% ) at 600 C; c - aluminium (99.5% ) al 4X0Cd: d - lead Cl (99.9X% ) at 20 C. Slika 3: Reološke krivulje: a - jeklo C 45 pri 900 C; h - baker (99.99% ) pri 600 C: c - aluminij (99.5% ) pri 4X0 Ch; d - svinec Cl (99.98% ) pri 20C. for a technicallv pure aluminium (99.57r) vvhich is a rheologically complex material of the fourth class with two cxtrema on the r)-e curves. Copper (99.99%) is at 600 C" a rhcologicallv complex materials of the fifth class vvith three of more extrema on d-e curves (Fig. 3b). 3. Experimental investigations The experimental investigations of strain anomalies were performed on lead, which has the remarkable property to recrystallize at room temperature (Fig. 4). Processes of its plastic deformation are similar to those during the hot deformation of steels and alloys. It is therefore exceptionally convenient for the modelling"■'-. The rheologicai properties of lead are unique. Fig. 3d shows rheologicai curves of lead (99.98',;) obtained on a cam plastometer at 18-20°C". At strain rate e = 0.005 s 1 lead softens completely bv rccrvstallization and it can be thus regarded as a rheologically simple unstrengthcnable material of the first class. At the speed of e = 0.01 to 0.1 s 1 it has complex relation 3-e with two extrema inherent to rheologically complex materials of the fourth class. By moderate strain rates (e = 0.1 to 0.5 s1) lead is a rhcologicallv simple strengthenable material of the second class. whilc at higher rates it is a rheologically complex material of the third class. S . The average strain rate of specimen No 2 was 0.02 s 1 (Fig. 1. IV) and a curve of the fourth rheological class was obtained. After a short deformation in the stage of strain homogeneitv of the first order the deformation continued by strain heterogeneity of the second order and a local ncck was formed. As the extension went on. deformation proceeded according to the sccondarv homogeneitv type. The ncck elongated on account of near-bv metal volumes and the specimen acquired the shape given in Fig. 6. No 2. Though quantitatively rheological anomalies (emax and emin deviations) of lead at tliis speed are onlv marked. strain anomalies and differenees between them are observed quite distinctlv. Specimen No 3 (200 mmpm) deformed as rheologieally simple strengthcnable material of the second class in conditions of homogeneous strain. Specimen No 4 (1500 mmpm) passed a short stage of homogeneous deformation according to heterogeneous strain type and IVacturcd attaining scarcelv an elongation of e = 3X'/r while retaining the value of .. = 100% vvaist. The fall of plasticity is due in tliis čase to the strain anomalv of the second order. Al tliis strain rate rheological curve of lead shovvs one maximum, which is a charaeteristic for materials of the third rheological class. The repetition of experiments confirmed the reliabilitv of the findings. The investigation of strain anomalies of highcr orders and the regularity of their occurrence suggest a solution ol some interesting problems and reveal the nature of the formation of the strain nidus during the rolling of rhcologicallv complex stcels14. Figure 6: Form of lead specimens stretehed at strain rate of mmpm: No I -0.5; No 2-1.(1; No 3 - 21)0; No 4 - 1500 Slika 6: Oblika svinčenih preizkušancev, deformiranih s hitrostjo deformacije: št. 1 -0.5; št.2- 1.0: št.3 - 200: št.4 - 1500. 4. Conclusion A phenomenon of strain anomalies of highcr orders of rhcologicallv complex materials was determined experimentally and explained. It reveals itself in the process of plastic uniaxial evtension. according to the rheological curve ri-6. Sccondarv and further strain heterogeneities appear alternated with secondary and following homogeneities vvhich inerease the resistance to deformation. Considering the proposed rheological classification ol' materials the understanding of regularities ol' strain anomalies can be used for the solution of theoretieal and technological problems connected vvith the predietion ol' the development ol' plastic deformations and of the rupture of rheologicallv complex materials. References H. L. Colmogorov. A. A. Bogotov, B. A. Migachov, E. Ci. Zudov. M. H. Freidzon: Metalurgia. 1977. 336. - O. A. Cav bishev: M. Metalliirgia. 1975. 2X0. 3 M. Y. Dzugutov: M. Metalliirgia. 1977. 4.S0. 4 P. 1. Poluhin. G. Y. Gun, A. I. Galkin: Metalliirgia. 1983, 352. M. Suzuki: Report oflnst. of Industrial Science. Universitv of Tokvo. IX. 1968. 3. 139-240. 6 A. V. Bobiliov: Mechanical and technological properties ol' metals Manual: Metalliirgia. 1980, 290. D. Rittel. R. Aharonov, G. Feigin. 1. Roman: Acta MetaUurgica ci Matcrialia. 39. 1991, 4. 719-724. s (i. G. Shlomchack: Strain Features of rheologicallv comple.v metals: Kiev, 1991, Dep. in UkrNIINTI IX.8.91, No 1167-Uk 91. ' G. G. Shlomchack: Regularilv of strain heterogeneitv and plaslicilv anomalies of rheologicallv comple.v and cvtra -comple.v materials: Kiev. 1991, Dep. in UkrNIINTI 12.1.291. No 1589-Uk 91. '"A. Burkhard: Mechanical and technological properties of pure metals; M. Metallurgizdat. 1941, 443. " G. G. Schlomchack, G. A. Fen, V. G. Kutsav: Izvestia nizov. Chcrnava metalliirgia. 19X0, 3. 61-65. 12 G. G. Shlomchack: Izvestia AN USSR, Metals. 1976, 6. "G. G. Shlomchack. V. G. Vrublevskv. R. N. Filchakov: The change of rheological properties of lead bv modification: Kiev, Dep. in UkrNIINTI. 16.0589, No 1267 - Uk 89. "G. G. Shlomchack: The model/ing of the rolling process: Coloured film, 35 mm., parts 1 and 2. Produced bv laboratorv of technical education of the Ministrv of ferrous metallurgv. USSR, Dnepropetrovsk, 1991.