Materials Science and Engineering A 462 (2007) 164–168 Modeling the heterogeneous microstructur ati ersity blic o pril 2 Abstract Densifica ing p dation proce crys under high t he fib consolidatio estig ing densific heter for an adeq e me is then pres e ele out, enablin be c achieved. © 2006 Elsevier B.V. All rights reserved. Keywords: Metal-matrix composites; Microstructural evolution; Densification behavior; Recrystallization; Grain growth 1. Introdu During mechanism [1,2]. In ad proceed ine ing from th under vacu � and � ph ture, and it the flow st sensitivity tallization found to b number of have been and it is w ucts depen ∗ Tel.: +82 E-mail ad 0921-5093/$ doi:10.1016/j ction the consolidation, densification occurs by several s such as plastic flow, diffusion, and power-law creep dition to these mechanisms, microstructural changes vitably by either grain refinement or growth result- e thermal effect and non-uniform stress concentration um hot pressing. In two-phase Ti–6Al–4V alloy, both ases undergo grain growth at an elevated tempera- has been found that increasing grain size increases ress, and tends to reduce the maximum strain rate [3]. Under certain conditions of hot working, recrys- of microstructure also may occur, and it is usually e an important grain size control mechanism [4]. A fabricating techniques for metal-matrix composites developed including liquid and solid state processes, ell known that the performance of finished prod- ds on the processing techniques which are directly 2 2220 0421; fax: +82 2 2298 4634. dress:
[email protected]. related to the reinforcement arrangement that is closely con- nected with the deformation behavior of composite materials [5,6]. Deformation behavior, together with heterogeneous micro- structural evolutions is important in densification processes, and therefore, this paper addresses the role of inhomogeneous distribution of grain size in Ti-base metal-matrix composites (Ti-MMCs) and its effect on consolidation behavior. The work essentially continues a newly developed methodology in which microstructural influences on consolidation behavior have been presented combined with the constitutive equations of Ti-MMCs enabling the deformation behavior to be predicted during the process. As detailed in [7], heterogeneous microstructures have been investigated by means of two types of possible mechanisms such as grain growth and recrystallization. According to the fiber distribution, different types of morphology including equiaxed �, transformed �, and Widmansta¨tten � of the matrix materi- als were quantified. Attempt has been extended here to develop the mechanisms-based constitutive equations for heterogeneous microstructural evolution in consolidation processes. The elasto- viscoplastic constitutive model for porous materials coupled with the non-uniform microstructural evolution is implemented – see front matter © 2006 Elsevier B.V. All rights reserved. .msea.2006.04.148 composites in the consolid T.-W. Kim ∗ School of Mechanical Engineering, Hanyang Univ Sungdong-Ku, Seoul 133-791, Repu Received 30 August 2005; received in revised form 18 A tion in metal-matrix composites occurs by several mechanisms includ ss. In addition, microstructural changes proceed inevitably by either re emperature environment and stress concentration particularly around t n have been analyzed, and the relations to densification behavior inv ation rate but the non-uniform fiber distribution that is related to the uate modeling of microstructures. A material model coupled with th ented for consolidation. The model has been implemented into finit g the deformation behavior together with the level of densification to es of Ti-base metal-matrix on processes , 17 Haengdang-Dong, f Korea 006; accepted 25 April 2006 lastic flow, diffusion, and power-law creep in the consoli- tallization or grain growth due to the phase transformation ers. Heterogeneous microstructures prior to and following ated. Increasing temperature or pressure leads to increas- ogeneous microstructural evolution should be considered chanisms-based heterogeneous microstructural evolution ment software so that process simulation can be carried ompared with experimental data. Good comparisons are T.-W. Kim / Materials Science and Engineering A 462 (2007) 164–168 165 into finite element software so as to the spatial variations of het- erogeneous microstructures together with deformation behavior can be pred 2. Heterog mechanism Experim preforms u uum hot pr following c to densifica based anal developme [7,8]. As it is microstruc neous grain ment. This vacuum ho The evolut are shown s compressio under high of matrix f been chang the deform tion of plat of lamella geneous m stage of vac lizations oc followed b in [7], the the level of erogeneous effect, and materials p areas aroun ing dynam Furthermor in addition acicular W uniaxially g area of mat 3. Modelin Ti-MMCs Heterog bution of g properties, two-phase of � grain t higher diffu is considere been chang Schematic diagrams showing the evolution mechanisms of heteroge- ircrostructures of Ti-MMCs in consolidation processes: (a) hot com- , (b) recrystallization, and (c) grain growth. resulting in microstructural refinement, that is associated crystallization. ing the consolidation, internal porosity can be elimi- and thus the overall densification rate for the material e given by a dilatation rate. The detail descriptions of sto-viscoplastic constitutive models for porous materials e found elsewhere [12–14]. As discussed in previous [7,8], a number of mechanisms operate in the high ature deformation of Ti–6Al–4V including diffusional grain boundary sliding, and dislocation creep. Among the utive equations employed in the model, however, only growth kinetics was considered for the microstructural icted during the processes. eneous microstructures and evolution s ents have been conducted on the SiC/Ti–6Al–4V sing the foil–fiber–foil technique and subsequent vac- essing. Heterogeneous microstructures prior to and onsolidation have been quantified, and the relations tion behavior investigated by means of mechanism- ysis. The experimental process employed for the nt of Ti-MMCs has been described in detail elsewhere obvious from the results, a dramatic evolution of tures is incorporated in the changes with heteroge- size and distribution according to the fiber arrange- formation of heterogeneous microstructure during t pressing depends on various factors in each stage. ion mechanisms of heterogeneous mircrostructures chematically in Fig. 1. Firstly, at the fist stage of hot n, plastic deformation of Ti–6Al–4V alloy occurs temperature environment. The initial microstructure oil consisted of equiaxed � and transformed � has ed into Widmansta¨tten � and transformed � during ation. Both shorter segments � derived from separa- e-like � during hot deformation, and the globularity microstructure also affect the evolution of hetero- icrostructures [9,10]. Secondly, at the intermediate uum hot pressing, both dynamic and static recrystal- cur particularly at the areas with stress concentration y hot deformation of matrix materials. As discussed dynamic recrystallization much more depends on stress rather than the temperature. Finally, the het- microstructures are controlled by furnace cooling the coarse microstructure at the middle area of matrix resents one of the evidences of this process. At the d fiber, particularly, the dislocations generated dur- ic recrystallization may be annihilated in this stage. e, the grain growth of equiaxed � continues, and to this the lamellar structures as transformed � or idmansta¨tten � are mutually bounded together. The rown thick plate of � are also observed at the middle rix materials. g the heterogeneous microstructures of eneous microstructure such as grain size or distri- rain size is important since it affects mechanical which result eventually in material failure [11]. In materials such as the Ti–6Al–4V alloy, the presence ends to constrain the growth of � phase, which has a sivity. The initial microstructure of Ti–6Al–4V foil d to form an equiaxed� and transformed�, but it has ed into short segments � or globular � by hot defor- Fig. 1. neous m pression mation with re Dur nated, may b the ela may b works temper creep, constit grain 166 T.-W. Kim / Materials Science and Engineering A 462 (2007) 164–168 evolution during the deformation as follows: ˙d = α1 + β1 ¯ε˙p dμ where d is rate, and α accounts fo describes t modeling a lution in co Experimen with defor adequate model. Heterog been show mansta¨tten the fiber lo a stress con recrystalliz centration tures rather spatial vari rial has be and C, resp The highes A, and ther microstruc uniform str icant defor not expect both static at location an equiaxe results in th [15], the m heterogene follows: dDRX = D dSRX = D3 1 ¯d2 = VDR d2DR where the recrystalliz respectivel given as Z meaning. T to each op D1–D5 are been devel and a least tally measu determine for the mat Table 1 Material parameters for modeling the heterogeneous microstructure in finite element simulation 0.42 × 10−9 0.73 × 10−6 1.801 0.012 −0.14 0.503 0.66 −0.01 together with critical strain for the determination of the tallisation have been obtained from the finite element anal- d thus the overall grain size, ¯d can be determined by using . (4) according to the detailed microstructural evolutions. ults . 2 sh with tes th g at t onso the ctly broa w st f gra truc of co f he n ca dict e gr as Fi truc ly ac eeme cas e on expe ic re xperimentally measured mean grain size for Ti-MMCs at 900 ◦C under of 30 MPa. The positions A, B and C are indicated in Fig. 1(a). (1) the mean grain size, ¯ε˙p is effective plastic strain 1, β1, and μ are material parameters. The first term r the normal grain growth while the second term he deformation enhanced grain growth. A modified pproach for the heterogeneous microstructural evo- nsolidation process has been focused in this work. tally determined microstructural features coupled mation behavior are therefore used to represent an mechanisms-based heterogeneous microstructural eneous microstructures of Ti–6Al–4V in MMCs have n to be an equiaxed �, transformed � and Wid- � with various sizes and distributions according to cation and distance. Due to the effect of hot pressing, centration promotes the microstructure of dynamic ation. In other areas where relatively low stress con- exists, the microstructure is controlled by tempera- than the levels of stress. In order to investigate these ations of microstructure, as shown in Fig. 1, the mate- en divided into three different areas denoted A, B, ectively, according to the relative distances to fiber. t level of stress–strain can be estimated at location efore, much more significant deformation-enhanced tural change is expected. At location C, generally ess state exists, but the levels of strain are low. Signif- mation enhanced microstructural change is therefore ed. Because of relatively close distance to fibers, and dynamic microstructural changes are expected B. The recrystallised grain size usually looks like d shape, and it is considered that the mechanism e softening process. By employing the Sellars model echanisms-based evolution equations considering the ous grain size distribution then may be presented as 1Z D2 (2) dD4ini ε D5 (3) X X + VSRX d2SRX + VGG d2GG (4) subscripts DRX, SRX, and GG represent dynamic ation, static recrystallization, and grain growth, y. The Zener–Holloman parameter, Z in Eq. (2) is = ε˙ exp(−Q/RT ), where Q, R, T have their usual he Vs mean the volume fractions corresponding erating mechanisms, dini is initial grain size, and material parameters. Computational methods have oped for the determination of material parameters, square error technique was used [16]. Experimen- red data of grain size against time were employed to the parameters. The material parameters determined rix materials at 900 ◦C are given in Table 1. A peak α1 β1 μ D1 D2 D3 D4 D5 strain recrys ysis, an the Eq 4. Res Fig ations indica loadin fully c during is dire to the the flo tions o micros levels tions o has bee the pre only th where micros spatial all agr for the than th can be dynam Fig. 2. E pressure and discussion ows experimentally measured mean grain size vari- time in each area. As discussed in [8], 3 or 5 min e intermediate time to reach the full dense state after arget temperatures, and 10 min means approximately lidated time. As can be seen, grain growth occurs consolidation. Grain size or grain size distribution related to the microstructural inhomogeneity so as der the distribution of grain size shows the higher ress [11]. From the results it follows that the varia- in size in materials, reflecting the inhomogeneity of ture, may lead to considerably different achievable nsolidation. In order to predict the spatial distribu- terogeneous microstructures, finite element analysis rried out using a unit-cell model [7,8]. Fig. 3(a) shows ed spatial variation of grain size obtained by using ain growth kinetics for the microstructural evolution, g. 3(b) shows the mechanisms-based non-uniform ture model. As can be seen, the grain size varies cording to the location of fibers, and a good over- nt with experimental observation has been achieved e of mechanisms-based non-uniform model rather ly grain growth model. The highest level of stress cted around the fiber, and therefore more significant crystallization has been found than at other positions. T.-W. Kim / Materials Science and Engineering A 462 (2007) 164–168 167 Fig. 3. Predicted distributions of grain size for Ti-MMCs at 900 ◦C under pressure of 30 MPa: (a) only grain growth for microstructural evolution from 7.438 to 8.388�m (dark to bright) [7,8], and (b) mechanisms-based non-uniform microstructural evolution from 1.572 to 12.1�m (dark to bright). The recrystallization of the matrix materials plays an important role enabling fine microstructures together with effective bond- ing to be achieved [17]. Despite the fine microstructure around the fibers, severe hete centration o related to th dation has b Fig. 4. Fig. stress, and conditions, the results show that the effect of the change of microstructure on mechanical properties is reasonably well predicted by the model. By employing the material parameters determined from an opti- on p or ha a com crost re lea mod truc catio Fig. 4. Predic bright) for Ti- however, the clustered fiber distributions lead to a rogeneous microstructure providing local stress con- n interfaces. The deformation behavior of Ti-MMCs e heterogeneous microstructures during the consoli- een calculated, and the results obtained are shown in 4(a) shows the predicted spatial variation of effective Fig. 4(b) is loading direction strain under the same respectively. By comparison with experimental data, mizati behavi shows ent mi pressu tutive micros densifi ted spatial variations of: (a) effective stress from 0.01 to 20.4 MPa (dark to bright), MMCs obtained from mechanisms-based non-uniform microstructural evolution mo rocess with experimental data, further consolidation s been analyzed in terms of the relative density. Fig. 5 parison of density evolution with time for the differ- ructural evolution models. As can be seen, increasing ds to increasing densification rate so as to the consti- el coupled with the mechanisms-based non-uniform tural evolution may provide better predictions of the n behavior. and (b) loading direction strain from −0.553 to +0.445 (dark to del at 900 ◦C under pressure of 30 MPa. 168 T.-W. Kim / Materials Science and Engineering A 462 (2007) 164–168 Fig. 5. Comparison between experimental (symbols: circle for 30 MPa, rectan- gle for 50 MPa) and predicted (lines) relative density for Ti-MMCs at 900 ◦C. Solid lines are obtained by using non-uniform microstructural evolution model, whereas broken lines are obtained by using only grain growth model. 5. Conclusion Heterogeneous microstructures of Ti-MMCs have been ana- lyzed in consolidation processes, and the relations to densifi- cation together with the deformation behavior investigated. As the consolidation proceeds, dramatic changes of the microstruc- tures including equiaxed �, transformed � and Widmansta¨tten � are obtained depending on the fiber arrangement. The depen- dence of microstructures on the consolidation then has been explained in terms of the change in mechanisms such as grain growth kinetics and recrystallization. Dynamic recrystalliza- tion occurs at high levels of stress–strain fields, particularly around the fibers, whereas at a relatively uniform stress field, the format recrystalliz microstructure is important since it affects mechanical prop- erties, and can lead to inhomogeneity of deformation, which results eventually in material failure. The constitutive model coupled with the mechanisms-based non-uniform microstruc- tural evolution therefore may provide better knowledge of the densification behavior. 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