Constitutive Model Research on Pure Aluminum Considering Dynamic Recovery and Recrystallization

Transcription

1 3rd International Conference on Mechatronic and Information Technology (ICMIT 06) Contitutive Model Reearch on Pure Aluminum Conidering Dynamic Recovery and Recrytallization Tingting Zhou, a,yang Yang,b and Maobing Shuai,c Science and Technology on Surface Phyic and Chemitry Laboratory, Jiangyou 6908, China a @qq.com, b @qq.com, chuaimaobing@caep.cn Keyword: pure aluminum contitutive model dynamic recovery recrytallization Abtract. The article introduce ome main contitutive model of pure aluminum with regard to mechanical repone, dynamic recovery and recrytallization during the proce of evere platic deformation. Two kind of contitutive model will be introduced in thi paper, becaue there are few model conidering two apect imultaneouly, that i, material deformation dynamic and microtructure evolution. In the cae of deformation dynamic, the JC model, the ZA model, the power exponent function model will be introduced in detail; in view of microtructure evolution, the M. Zhou explicit dynamic contitutive model, a model conidering dynamic recrytallization will be introduced in detail. At lat, thi paper will preent the BCJ contitutive model pecially, which ha uperiority at macro level and micro level, and ha been widely ued abroad. An analyi of the characteritic of thee model, and cope of application of each model, comparion between each model a well a the common problem of thee model will be ummarized. Furthermore, the article will exhibit ome characteritic of pure aluminum and the reaon for electing the BCJ contitutive model to decribe the deformation mechanim of pure aluminum during ingle point diamond cutting. Introduction Pure aluminum exhibit the characteritic of high platicity and low hardne. It eaily ubjected to intene deformation during ingle point diamond cutting. It belong to high-fault-energy FCC metal. It tend to occur eaily cro lip or climb during deformation, followed by dynamic recovery []. Moreover, when the deformation parameter are adjuted appropriately, it platic deformation capacity can be greatly increaed, followed by dynamic recrytallization []. Therefore, it important to etablih a dynamic contitutive relation which can reflect the dynamic recovery and recrytallization of pure aluminum during the deformation. Thi work will be of great ignificance for the mechanim tudy of material deformation and prediction of material deformation trend. At preent, the contitutive model, decribing the material flow tre, can be roughly divided into two categorie. One kind of model are uing mathematical method or are baed on phyic in a certain extent. They are called empirical or emi-empirical model, e.g. the Johnon-Cook model, the power exponent function model and the Zerilli-Armtrong model. Thi kind of model are imple in form and have been widely applied. Another kind of model are phyic-baed, which conider the microtructure evolution, uch a the M. Zhou explicit dynamic contitutive model, the model conidering the dynamic recrytallization and the BCJ model etc. Thi kind of model involve ome information uch a dilocation proliferation or annihilation, tatic or dynamic recovery and recrytallization in the deformation proce, which i helpful to tudy the deformation mechanim for the material. The factor conidered in contitutive model Contitutive equation i a mechanical repone rule, reflecting the mathematical relationhip between flow tre and other factor during deformation proce. The factor, influencing the rheological tre, are train, train rate, temperature and other load condition. They belong to the external caue; Other factor (e.g. material compoition, grain ize, deformation activation energy and the 06. The author - Publihed by Atlanti Pre 747

2 microtructure of material) belong to the internal caue. The two kind of factor influence the magnitude and change trend of flow tre by train hardening and temperature oftening, tatic or dynamic recovery a well a tatic or dynamic recrytallization[3]. Now, however, there are few contitutive model can fully include the influence of the external caue and internal caue, except everal phyic-baed model, e.g. the BCJ model. The article will preent repreentative contitutive model from literature at home and abroad, ued for pure aluminum or aluminum alloy. Repreentative contitutive model Zerilli-Armtrong contitutive model For BCC metal: n 0 + C exp(-c3t + C4Tlnε) C5 ε σ = C + For FCC metal: σ 4 &. () = C + C ε 0 exp(-c3t + C Tlnε) &. () where, the unit of C0, C, C and C5 are MPa ; for C3, C4, the unit are K - ; n denote a material contant; T denote abolute temperature,whoe unit i K[4]. A can be een from the formula () and (), for BCC metal, the dependence of the flow tre on the train i not affected by the change of temperature and train rate, however the influence mechanim of the FCC material i oppoite. Zerilli-Armtrong (Z-A) contitutive model i a emi-empirical contitutive model baed on the dilocation, which can be ued to decribe armco iron, copper and aluminum in elatic-platic deformation. It i fit for a wide range of temperature and train rate, and ha two form to adapt to metal with different lattice tructure [5-7]. But the Z-A model i lacking in the mechanim reflecting tatic or dynamic repone, loading path, and the effect of train rate hitory. Furthermore, it unable to capture the adiabatic effect [8-0]. Johnon-Cook contitutive equation T - T T - T n room m σ = (A + Bε )(+ Clnε)(- & ( ) ). (3) melt room where, T, T room, T melt are deformation temperature, room temperature and material melting point temperature repectively; A i the material yield tre (unit: MPa ); B i the train hardening contant (unit: MPa); C, n, m are the coefficient on material propertie [, ]. The Johnon-Cook (J-C) contitutive equation i imple, ued widely to repreent the contitutive relation of teel, aluminum and their alloy. It applicable to decribe the tre-train relation of ferrou and non-ferrou metal under large train rate [6]. But it i unable to reveal the phyical bai of deformation. In addition, the effect of the train, train rate and temperature on tre are mutually coupled, the equation alo lack decription of elatic deformation [5-7]. Furthermore, the relationhip between tre and the logarithm of train rate, which i een a a linear relationhip, i wrong in many cae [3]. Power-exponent function model σ = Aε& m e -bt. (4) where, A, m, b are material contant; T i the abolute temperature [4]. Thi model i applicable to decribe rheological propertie of high platic material, uch a pure aluminum. But it cannot conider the relationhip between tre and train, and the enitivity of the high temperature i not very well. Some cholar, baed on MARC platform[5], have carried out the econdary development, conidering all material a perfecting olid or fluid, a a reult, the model get ubection correction according to the temperature. But it till cannot make up for the effect of train on the tre and cannot capture the adiabatic effect. 748

3 M. Zhou explicit dynamic recover model ( ε ε&, T ) f ( ε&, ) σ = f, T. (5) m σ = f ( ε&, T ) = C inh [ B( Zε ) ]. (6) Q Z = ε& ε exp. kt (7) = 0( ε = 0) f ( εε, &, T). = ( ε = ε ) (8) when 0 < ε < ε : n f ( ε, ε&, T ) = ( exp( bε ). (9) where, f decribe the ituation under the large deformation condition, that i, the flow tre will tend to be table. And f can be expreed by the hyperbolic function. For ε i aturated train. In the train-hardening tage, f can be repreented a equation (9). b and n are related to Z, which i temperature compenation train rate[6]. The model contain the train hardening effect, train rate hardening effect and temperature oftening effect. Introducing the deformation activation energy, it can capture the dynamic repone proce, and can explain the reaon of tre oftening, that i, recovery and temperature. Thi model i imple, eay to ue. But the model i not fit for imulate tenion and compreion experiment data[6]. Recrytallization model There are a lot of model to imulate the tatic and dynamic recrytallization. Baed on phyical mechanim, DRX model can predict the evolution of the macrocopic tre and grain ize, with the help of the auxiliary of multiphae platicity and grain growth model, it can alo decribe quantitatively typical characteritic of dynamic recrytallization, uch a unimodal form turning to multimodal form; teady-tate convergence of tre and grain ize; the energy relationhip between tre and grain ize, etc. But thi model cannot predict tre oftening phenomenon under high train rate, cannot contain the influence of olid olution and the precipitated phae. Uing the data of pure copper, which ha a lot of commonne with pure aluminum, to find that the fitting curve can reflect the natural development proce converging to a teady tate of tre and train, but the curve coincidence degree i not high[7]. S.P. CHEN et al.[8] propoed a recrytallization-kinetic model baed on phyic. The model take the effect on recrytallization kinetic into account. The imulation of ingle-phae alloy AA050 how that nucleation denity i cloely related to the local train and tre, however, the dependence of the annealing temperature i weak. A lot of model, focuing on the imulation of the recrytallization behavior, involve baically the grain nucleation model, the growth model, and reflect material microtructure change, but the decription of the macro flow tre i not pecific, even lacking. Concluion on repreentative contitutive model In fact, a variety of deformation mechanim often coupled during the deformation proce, the individual decription for a deformation mechanim of one kind of contitutive model can't be uitable for complex rheological behavior, making the application of the contitutive equation limited. Thi paper will detail another contitutive model -- BCJ model, which i not widely ued at home, but it have got many reearche abroad. The applicability of model i wide. It can be adapted to high temperature, large train and train rate of deformation, and can alo capture the deformation 749

4 mechanim of low temperature and low train rate. At the ame time, it i able to conider the macro and micro apect. The BCJ model i good at imulating the rheological tre during the proce of metal cutting and ha great advantage on other type of material and other deformation procee. BCJ contitutive model The Bammann-Chiea-Johnon contitutive model(bcj model) propoed in 984[9], i one of the few model conidering the yield urface theory. Thi model i a unification of macro and micro contitutive model. After year of reearch and development, it theoretical maturity and application range have been improved greatly. In application, it imulation object are from metal material to the ceramic material, and even geological material (uch a Bammann et al. (995), Harley, E.J and Bammann (999), Regueiro and Bammann (00), Chuzhoy, et al. (003), Solanki et al. (007), Tucker et al. (00), Solanki et al. (00 a), Salehghaffari, S et al. (0), Salehghaffari, S et al. (0), Koffi Enakouta et al. (0)). Becaue there are too many model parameter needing to be determined (up to 8 contant), the tudie on fitting parameter of the BCJ model have been promoted (uch a Guo, et al. (005), M.F. Hortemeyer, (009), Salehghaffari, S et al. (0), Salehghaffari(0), Guoheng Wang (0), Tan Yang(05) etc.).bcj contitutive equation are a follow: e e e σ = σ& - w σ + σ w = λtr D I + µ D. (0) ( ) e σ α { R + Y ( T )} σ α D in = f ( T )inh. () α V ( T ) σ α in in = h( T ) D r ( T ) D + r ( T ) α α d 3. () 3 & in in = H ( T ) D Rd ( T ) D + R ( T ) R. (3) R The above equation are baed on the theory of the baic law of thermodynamic. The train of any point in material can be regarded a the um of elatic train and inelatic train. Material mechanic performance are decided by the iotropic hardening variable R and kinematic hardening tate variable α, and thee two variable are conidered a completely independent. Formula (0), (), () and (3) denote the linear elatic contitutive relation, flow rule, the evolution of kinematic hardening internal variable and the evolution of the iotropic hardening variable repectively, equation () and (3) are baed on the evolution of the dilocation dynamic. The BCJ model can not only decribe the dynamic mechanical behavior under iothermal condition, but alo decribe the material deformation conidering the condition of adiabatic temperature rie. There are 9 calar equation covering yield, recovery and hardening a een in table [0, 0]. Table. 9 calar equation V(T) = Cexp(-C/T) r d (T) = C7exp(-C8/ T) (T) = C3exp(-C4/T) R d Y(T) = C3exp(C4/T) h(t) = C9exp(C0/ T) H(T) = C5exp(C6/T) f(t) = C5exp(-C6/T) r (T) = Cexp(-C/T) (T) = C7exp(-C8/T) where, V(T), Y(T) and f ( T) are temperature-dependence parameter of the Arrheniu type, aociated with creep and the platicity. Y(T) denote the rate-independent yield tre, R 750

5 f ( T) determine when the rate dependence affect initial yielding, V(T) determine the magnitude of rate dependence on yielding. H(T) and h ( T) are the hardening moduli, rd (T) and R d (T) decribe the dynamic repone, r (T) and R (T) capture the tatic recovery and heat recovery. Ci (i=~8) i a material contant, which contain uncertainty reflecting indirectly the material microtructure change. All 9 parameter are temperature-dependent, can capture the temperature hitory effect, and can alo be ued a the contact between material microtructure change and the macrocopic mechanic. The BCJ model cover both the macrocopic tre and microtructure, including dynamic mechanical repone, tatic recovery, dynamic recovery and dynamic recrytallization. It can alo capture the adiabatic temperature rie effect. The model retain the yield urface theory of the claical trength theory, whoe fitting range i not limited to experimental data. In addition, BCJ model i uitable for low temperature and low train rate deformation condition, and can alo be applied to high temperature and high train rate deformation condition. In ummary, the BCJ model i fit for capturing and predicting intene deformationa at blade, the adiabatic temperature rie, the dynamic recovery and recrytallization during the cutting proce of pure aluminum. Furthermore, it can alo decribe the influence of the Bauhinger effect [] on the dynamic mechanical propertie of pure aluminum. Concluion In thi paper, the contitutive model applied to imulate pure aluminum or aluminum alloy are claified. After comparing the repreentative empirical, emi-empirical and phyical model, the BCJ contitutive model i propoed, which i much more uitable for imulation of pure aluminum during ingle point diamond turning proce. In ummary, taking the characteritic and diadvantage of the above model, the proceing technologie, the finite element imulation oftware and the development of large numerical calculation oftware into conideration, the future contitutive model will gradually tend to be more comprehenive, more functional and unified. The BCJ model repond to thi trend exactly, and it undoubtedly ha great propect for the development of contitutive model. However, the parameter recognition method of the model i not ufficiently developed, and require further exploration and adjutment. Acknowledgement Thi work wa financially upported by NSAF of National Natural Science Foundation and China Academy of Engineering Phyic (U53000). The upport of tudent in CAMLAB of Tinghua Univerity i appreciated. Reference []. YU, Y.N., Principle of Metal[M]. Metallurgical Indutry Pre, 03. [].Wen, Q., Dynamic Mechanical Behavior. 005, Alabama. [3]. LIU, B.S., et al., A Review of Thermal Medium Forming Contitutive Modeling Method for Aluminum Alloy Sheet. Journal of Platicity Engineering, 0. [4]. Zerilli, F.J. and R.W. Armtrong, Dilocation-Mechanic-Baed Contitutive Relation for Material Dynamic Calculation. Journal of Applied Phyic, (5): p. 86 [5]. Samantaray, D., S. Mandal and A.K. Bhaduri, A Comparative Study on Johnon Cook, Modified Zerilli Armtrong and Arrheniu-Type Contitutive Model to Predict Elevated Temperature Flow Behaviour in Modified 9Cr Mo Steel. Computational Material Science, (): p

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