ESTIMATION AND UTILIZATION OF STRUCTURE ANISOTROPY IN FORMING PIECES

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1 Cermics-Silikáty 61 (), (17) doi: /cs.17.9 ESTIMATION AND UTILIZATION OF STRUCTURE ANISOTROPY IN FORMING PIECES MAROS MARTINKOVIC Slovk University of Technology in Brtislv Fculty of Mterils Science nd Technology in Trnv, J. Bottu 5, Trnv, Slovk Republic # E-mil: mros.mrtinkovic@stub.sk Submitted September, 16; ccepted December 7, 16 Keywords: Stereology, Grin boundry, Fibres, Orienttion, Deformtion In most of cses, technologicl processing leds to microstructure nisotropy of mteril. Results obtined from the nlysis of nisotropy cn be used for evlution of mteril properties nd prmeters of technology processes. Stereologicl metllogrphy ws used for describing of structure nisotropy. In cse of plsticlly deformed mteril, degree of orienttion of grin boundries ws determined. Grin boundries re decomposed into isotropic, plnr nd liner oriented components specific surfce re of grin boundries nd these prmeters were mesured using oriented test lines stereology method. These results were used for estimtion of locl plstic deformtion using conversion model of orienttion grin boundries to deformtion of grins. Our proposed conversion method enbles estimtion of locl plstic deformtion in rbitrry plce of body with rbitrry stte of initil deformtion. In cse of short fibre reinforced thermoplstics oriented test plne stereology method ws used for estimtion of experimentl orienttion of fibres. Degree of orienttion ws estimted from the number of intersections of fibres with test plnes nd from these results components of n orienttion tensor re estimted. This method is very simple in comprison with current method which is bsed on mesurement of dimensions nd orienttion of lot of fibre intersections in nlyzed plne. INTRODUCTION Anisotropy of microstructure in cse of forming of metl or plstics depends on technology prmeters of processes. In cse of deformtion of metls grin boundries orienttion cn be observed, in cse of short fibre reinforced plstics orienttion of fibres. In the polycrystlline mteril (metl, lloy) the min microstructurl prmeter is grin boundry surfce interfce between individul grins. In cse of isotropic non deformed structure the grins hve isometric dimension men grin size or specific surfce re of grin boundries cn be mesured. In cse of nisotropic plsticlly deformed structure the grins hve nisometric dimension, it is necessry to describe their nisotropy [1]. The nisotropic microstructure is decomposed into isotropic, plnr nd/or liner oriented components - specific surfce re of grin boundries nd these prmeters re mesured using stereology []. Degree of grin boundry orienttion is estimted s rtio of oriented specific surfce re to totl specific surfce re. These results cn be used for estimtion of locl plstic deformtion in rbitrry plces in volume of forming pieces. Rel stte of grin shpe is quit impossible to describe, therefore model of conversion of degree of grin boundry orienttion to deformtion bsed on n idelized shpe (tetrkidechedron) of grins hs been proposed. Fibre orienttion in short fibre reinforced thermoplstics depends on injection moulding prmeters. The orienttion of simple fibre my be defined by the two ngles θ nd Φ. In short fibre reinforced thermoplstic component there re frequently millions of fibres, therefore ech individul fibre orienttion specifying is very imprcticl. The fibres orienttion in spce cn be described by the probbility distribution function, Ψ (θ, Φ). Nevertheless the mesurement is reltively complicted. Simpler stereology method cn be lso used for estimtion of experimentl orienttion of fibres. Degree of orienttion is estimted s oriented specific length of fibres (specific length of liner oriented components) to totl specific length of fibres (specific length of ll components). These results of mesurement cnnot be directly compred with components of orienttion tensor, so the method of estimtion of min three components of the orienttion tensor must be developed. ANISOTROPY OF DEFORMED MATERIAL In the polycrystlline mteril the min microstructurl prmeter with significnt dependence on deformtion is grin boundry i.e. surfce interfce between individul grins. In cse of nisotropic structure the grins hve nisometric dimensions re oriented. Cermics Silikáty 61 () (17) 141

2 o (δ) Mrtinkovic M. There re few wys how to mesure grin orienttion, for instnce estimtion of microstructurl nisotropy tensor [6]. Another wy is sclr mesurement of nisotropy i.e. determintion of degree of orienttion. The nisotropic microstructure is decomposed into isotropic, plnr nd liner oriented components using stereology methods [1] nd the both the oriented prt of specific surfce re (S V ) OR nd the totl specific surfce re (S V ) TOT of grin boundry re estimted. Degree of grin boundry orienttion O is estimted s (S V ) OR to (S V ) TOT rtio. Grin boundry orienttion cused by deformtion φ is the sme s direction of deformtion, s it is seen in Figure 1 ( undeformed nisotropic structure, b, c, d - nisotropic structure due to vrious types of deformtion). φ is true (logrithmic) strin defined from dimensions of elementry body before deformtion l nd fter deformtion l s l 1 l l ϕ = (1) On metllogrphic cut test lines were plced perpendiculr nd prllel to the grin boundries orienttion effected by strining (see Figure 1). Isotropic, dl ) b) plnr nd liner oriented specific surfce res of grins re estimted from the specific number (number to unit of length) of prllel test lines intersections with grin boundries nd perpendiculr lines ones (see Figure ) ccording to [1]. But orienttion is not the sme s deformtion; therefore it is necessry to develop model of conversion of grin boundry orienttion to deformtion. Locl strin estimtion It is completely impossible to describe ctul shpe of the grin in mteril structure exctly. Therefore deformtion of vrious idelized grin shpes cn be investigted. For instnce crystls cn be modeled by regulr polyhedron tetrkidechedron []. One method is bsed on dependence of the rtio of reltive surfce re of grin boundries in deformed stte S V nd undeformed stte S V to strin [3]. The method requires knowledge of the prmeter of structure in cse of zero vlue of initil deformtion, which is unknown in most of cses nd this prmeter is not the sme in the whole volume of pieces nd it depends on grin size. Our conversion method ws bsed on nlysis of orienttion deformtion reltion of grin. Dependence of true strin φ on orienttion O ws derived from three bsic equtions definition of deformtion (Eqution 1), definition of degree of orienttion nd invribility of volume (V = V initil volume is equl volume fter plstic deformtion). The solution of the system includes one free prmeter grin size. Solution of the system of equtions for used idelised grin shpes is independent on the initil dimension of grin strin depends only on shpe of grin nd it does not depend on its dimension. Due to it the method enbles estimtion of locl plstic deformtion from estimtion of microstructure nisotropy in rbitrry plce of body with rbitrry stte of initil deformtion. The solution nd the result re reltive complicted, so detiled c) d) Figure 1. Isometric no deformed structure () nd nisotropic structure due to vrious types of deformtion (b, c, d). ) b) Figure. Principle of oriented test lines stereology method Figure 3. Dependence of orienttion on deformtion. δ 14 Cermics Silikáty 61 () (17)

3 Estimtion nd utiliztion of structure nisotropy in forming pieces description is in [5]. Correltion between orienttion nd deformtion is illustrted in Figure 3, where reltionship between strin δ nd true strin φ is φ = ln (1 + δ) () Anlysis of technology process of cold drwing ws relized. The semi-product for wire ws hot rolled wire from ASTM 16 steel. This hot rolled wire ws cold drwn in two steps with incresing of dimeter reduction nd simultneous decresing of length nd the finl second step ws nlyzed. The dimeter of semiproduct ws 5.5 mm, dimeter of the wire fter first drwing ws 4.7 mm nd dimeter of the wire fter second drwing ws 3.99 mm. Scheme of longitudinl Ø Tble 1. Grin boundries orienttion O on ech nlysed plces nd corresponding deformtion φ. O Plce S M C φ Plce S M C S M C Ø 3.99 Drwing direction Figure 4. Scheme of longitudinl section of the smple with plces for the nlysis. section of the smple with fifteen plces for the nlysis is in Figure 4. Exmple of microstructures of wire in front of drwing die in plce M1 is in Figure 5, structure of wire behind the drwing die in plce S5 is in Figure 6. Mesured nd clculted degree of grin boundries orienttion in ech nlyzed plces nd corresponding deformtion φ converted ccording the method re in Tble 1. Orienttion nd deformtion is not equl in cross section of wire. The smllest is ner the surfce of wire, the gretest in the middle of wire rdius in ll plces long the wire. It mens tht due to deformtion strengthening during drwing wire deformtion mkes hevy influences on the mterils properties in the middle of wire rdius. Anisotropy of injection molded prts The orienttion of one fibre cn be defined by the two ngles: ngle θ nd ngle Φ shown in Figure 7. The components of p i re described with the ngles θ nd Φ, s follows: where p 1 = sin θ cos Φ, p = sin θ sin Φ, p 3 =cos θ (3) θ = cos 1 (4) The components of fibre orienttion tensor for group of n fibres re clculted s follows: n xx xy xz 1 k k ij = = pi p j yx yy yz i,j = x, y, z (5) n k = 1 zx zy zz Three min independent components for n individul fibre re s follows: xx b = 1 cos Φ b 1 b, yy = sin Φ, zz = (6) b 4 µm 4 µm Figure 5. Structure of wire in front of drwing die (plce M 1). Figure 6. Structure of wire behind the drwing die (plce S5). Cermics Silikáty 61 () (17) 143

4 Mrtinkovic M. Orienttion tensor is reltive simple estimted from the mesurement of dimensions nd ngles of lot of fibre intersections with nlysed plne, but the mesurement is more complicted. The fibre must not be ny size; they re perfectly circulr in cross-section nd hve the sme men dimeter. Stereologicl metllogrphy cn be lso used for estimtion of experimentl orienttion of fibres [1]. In the cse of short glss fibres reinforced thermoplstic its structure consists of thermoplstic mtrix nd reinforcing fibres, which hs some preferred orienttion in most of cses the structure is nisotropic. Determintion of orienttion degree is the wy of sclr mesurement of structure nisotropy. The nisotropic microstructure is decomposed into isotropic, plnr or liner oriented components using stereology methods nd the both the oriented prts of specific length of liner elements in spce (L V ) OR nd the totl specific length (L V ) TOT of fibres re estimted. Degree of fibre orienttion O is estimted s (L V ) OR to (L V ) TOT rtio. Oriented test plne method is used [1]. Test plnes re plced perpendiculr nd prllel to the orienttion direction (see Figure 9). Isotropic, plnr nd liner oriented specific length of fibres re estimted from the specific number P A (number per unit test re) of cross-sections between test perpendiculr plne nd fibres ccording to [1]. The fibres cn be ny size nd ny shpe. These results of mesurement cnnot be directly compred with components of orienttion tensor, so the method of estimtion of min three components of the orienttion tensor hs been proposed. The min three components of the second-order orienttion tensor using stereology cn be clculted s follows: ii = P Ax P + P (7) where i = x, y, z; P A is number of cross-sections between test plne nd fibres [-]; A i is investigted re [mm ]; P Ai is number of cross-sections between test plne (TP) nd fibres (see Figure 9) per unit of the test re [mm - ] Ai Ay + P Az z p Figure 9. Test plnes (TP) of nlysis. θ p 1 p 3 Φ p y Figure 7. Orienttion of single fibre (in spce nd in section plne) in polr coordintes by the two ngles (θ, Φ). y Φ b x Numericl modelling nd experimentl estimtion of fibre orienttion Experimentl specimen is injection moulded tensile br. Used thermoplstic is polypropylene with % volume frction of glss fibres. Dimeter of the fibre is. mm nd length is bout.5 mm. Injection moulded temperture is 8 C, pressure is 6 MP, pcking is 3.6 MP nd cooling time is 1 s. In this specimen six plces (see Figure 1) were nlyzed nd ech plce ws exmine in ech of three directions (X, Y nd Z). Fibres close to the mould wlls tend to be ligned prllel to the mould fill direction (MFD) (see Figure 9). Exmples of microstructure of the nlysed plce no. 6 in ll three cross sections re in Figure 11. Mesured nd clculted results in two nlysed plces (1 nd 6) re in Tble. Tble. Mesured nd clculted results in nlyzed plces 1 nd 6. TP X1 Y1 Z1 X6 Y6 Z6 Figure 8. Principle of oriented test plnes stereology method. P i P Ai ii Cermics Silikáty 61 () (17)

5 Estimtion nd utiliztion of structure nisotropy in forming pieces initil grin size in cse of idelized tetrkidechedron grins shpe strin lso depends only on shpe of grin nd it does not depend on grin dimensions. It llows estimtion of locl plstic deformtion from estimtion of microstructure nisotropy in rbitrry plce of body with rbitrry stte of initil deformtion s it ws seen in exmple of nlysis drwing process. Figure 1. Plce of nlysis. Numericl modelling of fibre orienttion ws relised using Moldex3D softwre t the sme technology conditions. This softwre llows to view results of fibre orienttion s n orienttion of the X direction, Y direction nd Z direction, which re components of orienttion tensor. Orienttion tensors obtined from stereology metllogrphy nd numericl simultion re very similr in ech from six nlysed plces. Results obtined from stereology nd numericl simultion in 6 nlysed plces (see Figure 1) re: ) Stereology metllogrphy estimted Numericlly modelled results b) RESULTS AND DISCUSSION The utiliztion of stereologicl metllogrphy llows describing structure nisotropy. In cse of plstic deformed mteril, degree of orienttion of grin boundries is determined. Grin boundries re decomposed into isotropic, plnr nd liner oriented components specific surfce re of grin boundries. Stereology method of oriented test lines ws used. Consequentil conversion of its vlues to strin leds to determintion of deformtions in three min xes. Proposed method of conversion of grin boundry degree orienttion to grin deformtion is independent on the Cermics Silikáty 61 () (17) c) Figure 11. Microstructure of the nlyzed plce no. 6 in three cross sections; ) X, b) Y, c) Z). 145

6 Mrtinkovic M. In cse of injection moulding prts, oriented test plne stereology method ws used for estimtion of experimentl orienttion of fibres. Degree of orienttion is estimted from the number of intersections of fibres with test plnes nd from these results components of n orienttion tensor. This method is very simple in comprison with current method which is bsed on mesurement of dimensions nd orienttion of lot of fibre intersections in nlysed plne nd there re no limits in dimensions or shpe of fibres. The fibre orienttion cn be controlled by injection prmeters nd these processes re often numericlly modelled. Estimtion of short glss fibre orienttion leds to experimentl verifiction of numericl simultion model, s it ws seen in exmple of nlysis injection moulding process. Also results of locl plstic deformtion estimted from grin boundries orienttion cn be used for verifiction of forming numericl model by compring these results with numeric simulted ones. CONCLUSIONS The utiliztion of stereology metllogrphy llows very simple nd effective experimentl estimtion of structure nisotropy of mterils. Estimtion of grin boundry orienttion llows determintion of dependence of the degree of orienttion to strin. It provides the possibility of setting three min strins in ech plce in volume of the deformed polycrystlline mteril. Estimtion of short glss fibre orienttion llows determintion of orienttion tensor. It leds to experimentl verifiction of numericl simultion model, which cn be optimized to obtin coincidence with experiments. These methods cn be pplied for ll types of mterils s metls, plstics or cermics. In cse of cermics, nlysis of deformtion of sintered prticles or nlysis of pores cn be done, moreover orienttion of cermic fibres in mtrix or fibre orienttion in cermic mtrix of composites cn be estimted. Acknowledgement This work ws supported by the VEGA Grnt No. 1/1/16 of the Grnt Agency of the Slovk Republic Ministry of Eduction nd by the Slovk Reserch nd Development Agency under the contrct No. APVV Mny thnks belong to Luks Likvcn MSc. for numericl modeling. REFERENCES 1. Sltykov S.A. (197). Stereometric metllogrphy. 3 rd ed. Metllurgi.. Rios P.R., Glicksmnb M.E. (6): Modeling polycrystls with regulr polyhedr. Mterils Reserch, 9, doi:1.159/s Zhu Q., Sellrs M.C., Bhdeshi H.K. D.H. (7): Quntittive metllogrphy of deformed grins. Mterils Science nd Technology, 3, doi:1.1179/ X Eberhrdt C., Clrke A. (1): Fibre orienttion mesurements in short glss fibre composites. Composites Science nd Technology, 61, doi:1.116/s (1)38-5. Mrtinkovic M., Minrik S. (16). Short notes on the grins modifiction by plstic deformtion, in: Hubbrd D. (Ed.): Plstic Deformtion. NOVA Publishers. pp Hrtley C.S. (6): Strin nd the quntittive chrcteriztion of nisotropic microstructures. Metllurgicl nd Mterils Trnsctions A: Physicl Metllurgy nd Mterils Science, 37, doi:1.17/s Jung S.W., Kim S.Y., Nm H.W., Hn K.S. (1): Mesurement of fiber orienttion nd elstic-modulus nlysis in short-fibre-reinforced composites. Composites Science nd Technology, 61, doi:1.116/s () Cermics Silikáty 61 () (17)