Modeling of microstructural evolution and flow stress of aluminium alloy during thermomechanical pro

Vol. 14 No. 3Trans. Nonferrous Met. Soc. ChinaJun.2004Article ID: 1003 - 6326(2004)03 - 0491 - 05Modeling of microstructural evolution and flow stress ofaluminium alloy during thermomechanical process"SHEN Jian(沈健)' , G. Gottstein?(1. General Research Institute for Nonferrous Metals, Beiing 100088, China;2. Institut fur Metallkunde und Metallphysik, RWTH-Aachen, Germany)Abstract: The evolution of microstructural variables , including the densities of mobile dislocation, immobile dislo-aluminium alloy during thermomechanical processing were simulated based on a three-internal-variables model(3IVM) involving dislocation elimb and interaction. Optimization was carried out to fit the calculated stress- straincurves to the experimental data of the Al-Mg-Si alloy with minimum mean deviation. Precipitations were taken intoconsideration of modeling. The stress- strain curves predicted by the kinetic equations of state in the 3IVM have agood agreement with the experimental data.Key words : aluminium alloy; microstructure evolution; dislocation; modelingCLC number: TG146. 2; TG111.7Document code: A1 INTRODUCTIONbetween neighboring subgrains during steady statedeformation were taken into consideration. TheModeling of materials processing has been onemicrostructure development under plastic deforma-of the most significant research fields in materialstion up to large strains was modelled by Seefeldtscience and technology over the world in recentand Klimanek8J by means of a four-component re-years, whilst modeling of microstructure evolutionaction kinetic for the density of mobile and immo-of advanced materials during deformation and re-bile dislocations and disclinations. A relationshipcrystallization processes, which is necessary in thebetween the density of sessile disclinations and theprediction of as-deformed microstructure and in op-flow stress was proposed using a Hall-Petch typetimization and controlling of the accordingly poten-relation for subgrain-size strengthening. An meth-tial mechanical properties of the finished products,od to the modeling of work hardening during plas-is one of the most interest topics. Basic under-tic deformation of pure FCC metals was proposedstanding of computer modeling of testa- and micro-by Marthinsen and Neso], which is based on a sta-structures evolution is a direct element in the pre-tistical approach to the problem of athermal stor-cise microstructure and property prediction andage of dislocations. By combining the solution forcontrol of advanced materials, where modelingthe dislocation storage problem with the models forbased on interaction of dislocation is very impor-dynamic recovery of network dislocations and sub-tant. Unfortunately, as indicated by Morris fromboundary structures, a general internal state varia-UC Berkeleyl, this is still somewhat less inte-ble description was obtained. Effects due to the el-grated so far.ements in solid solution and the presence of non-A large number of investigations have beendeformable precipitate particles were also includedcarried out to simulate the evolution of flow stres-in the model, named AL-FLOW, proposed by theses and microstructural features during hot work-authors. Semi empirical microstructural modelsing processes of many kinds of materialsC2-8] ，suchbased on dislocation climb and interaction betweenas subgrain size, dislocation density, misorienta-dislocations were implemented into FEM programstion among subgrains, etc. Flow stress and recrys-by Brand et al4] and Roters et a15,6] to simulatetallization behaviors of aluminum-magnesium alloymicrostructure evolution at imposed starting condi-during hot rolling process were simulated and pre-tions of microstructure during multistage forgingdicted by Sellars and his co-workers[2,0), where theand multi-pass hot rolling operations.variation of the subgrain size, dislocation densityThe evolution of densities of mobile disloca-in the interior of subgrains and the misorientationtions,, immobile dislocations in the cell interiors中国煤化工①Foundatlon item: Project(59701007) supprted by the National Natural Sciene|YHCN M H G3085) sppored bythe International Coorperating Research Program of the National Natural Science rounation ot ChinaRecived date: 2003 -09 - 25; Accepted date: 2003-12 -29Correspondence: SHEN Jian, Professor, PhD; Tel; +86-10-82241261; E-mail jshen@mail. grinm. com. cn●492●Trans. Nonferrous Met. Soc. ChinaJun. 2004and immobile dislocations in the cell walls for anpolycrystalline materials for the imposed strainAl-Mg- Si alloy during hot compression was simula-path, and b the magnitude of the Burgers vector.ted in the present work by a three internal varia-The average glide velocity of mobile disloca-bles model of dislocations ( 3IVM) proposed bytions V is calculated asRoters et alCs.6.10]. The variation of flow stressesv=Xvexp(-号)sinh(\)(3)of the alloy predicted by modelling was analyzedand compared with the experimental data. Onlywhere λ is the jump width of dislocation, i.e. theclimb of dislocation are taken into consideration inmean spacing of obstacles (the immobile forest dis-dynamic recovery process at elevated temperatureslocation)，Uo the attack frequency, Q the effectiveand consideration to cross slip of screw segments isactivation energy for dislocation glide, kg Boltzmanlimited.constant, V the activation volume, and T the de-formation temperature. Then the effective shear2 THREE INTERNAL VARIABLES MODEL OFstress tell can be calculated by substituting Eqn. (3)DISLOCATIONS(3IVM)into Eqn. (2).As the forest dislocation spacing is differentIn dynamic recovery process, an inhomoge-between the cell interiors and the cell walls, twoneous cellular dislocation arrangement composed ofdifferent values for the effective stress, elt in thecell walls with high dislocation density develops incell interiors and T.w in the cell walls are ob-most commercial aluminum alloys, which enclosetained. The necessary resolved shear stress in thecell interior of low dislocation density. Such a dis-cell interior τ and in the cell walls tw can be derivedlocation network has significant influence on theashardening behavior and evolution of microstructurei{m = Tl,i(w) +aGb√pikw)(4)of the material during severe plastic deformation.where a is a constant and G the temperature de-Precipitations and dynamic precipitating also playpendent shear modulus.important roles in thermomechanical processes ofThe required external stress can then be calcu-commercial aluminum alloys， which has to belated astaken into account in modeling of microstructure e-σel= M(rer,;+qw ted,wn)(5)volution of aluminum alloys.The current multi-parameter dislocation modelwhere 9n and Pw are the volume fractions respec-tively. The Taylor factor for polycrystalline mate-distinguishes the aforementioned two regions with-rial can be calculated for arbitrary strain paths as ain the material. The spatial distribution of disloca-function of the total strain.tions within each region is still treated as beinghomogeneous. This is due to the fact that the large2.2 Mobile dislocation densitynumber of dislocations do not allow an analyticThe mobile dislocations are assumed to pene-treatment of individual dislocations. On the othertrate through both dislocation walls and cell interi-hand, there is no simple analytical formula availa-ors. Each mobile dislocation is supposed to glide able which describes the evolution of the dislocationmean free effective path Fe before it is immobilizeddistribution during the deformation of dislocationby one of the three processes described below. Thenetwork.externally imposed strain rate E is found to have arelationship with the increscent rate of mobile dis-2.1 Kinetic equation of stateThe 3IVM distinguishes three dislocation cat-locations pπ asegories, namely, mobile dislocation(pm), immobileε=p# bF.(6)dislocations in the cell interiors(p), and immobileThe mean effective path Fu is determined bydislocations in the cell walls(p.). For each class ofthree obstacle spacing: the average free spacing ofdislocations, an evolution law of the form will bemobile dislocation in the cell walls Fw and in thederived :interiors F, the grain size K and the distance between precipitates Lp as:where ρ+ and ρ~ represent one or more produc-号+卡+k+z。(7)tion terms and reduction terms, respectively.The mobile dislocation density is decreased byWithin the 3IVM model, the Orowan equationis used as kinetic equation of state to calculate the中国煤化二-rmation of disloca-- nd dislocation anni-applied stress of the material during thermome-hlbability can be de-chanical process:ter.YHC N M H Gbabilit跳iuuutiuns ates for the disloca-j=ε●M=pmbu(2)tion density are:where r is the shear rate, M the Taylor factor offormation of dipoles:Vol.14 No. 3Modeling of microstructural evolution and flow stress●493.walls resulting from enhancement of dislocationpm.=2(d.-d.-)M.t.pm(8)glide resistance. On the other hand, the precipita-tions enlarge the activation energy for glide andformation of locks;lead to a larger glide resistance. Meanwhile, they2=4d●iM.n-1.pm(9)also increase the yield stress by the Orowan stress:annihilation;o=Gbv中r(14)p_..-2d-. sM.1.p(10)where 4 is the volume fraction of precipitatesand r the average precipitate radius. The ripeningwhere n is the number of active glide systems,of precipitations during deformation at elevatedand ds, d, d.-. the critical distances for the indi-temperatures cannot be neglected for it has effectscated processes, respectively.on the precipitation radius, volume fraction andfree spacing between neighboring precipitations.2.3 Dislocation density in cell interiorsThe increased hardening rate is taken by incorpora-The increase of dislocation density inside theting the precipitation spacing in the effective slipcells is equal to the decrease of mobile dislocationslength:due to the formation of the locks:(15)ρt=pm,=4d.M.n-1.p(11)For precipitate coarsening, the change of pre-Since locks can not glide, the only process tocipitate radius with time is given bydecrease the immobile dislocation density is annihi-r=c(t+t)/*(16)lation by dislocation climb. The rate equation forwhere k=3 for ideal Ostwald ripening.this process is given byThe above equations are coupled and can be utilized to calculate the dislocation densities for eachpr =2v.d_g°j°ptime step. One can calculate the evolution of threewhere d, 。is the critical distance of the two dis-populations of dislocation density from Eqn. (6) tolocations with antiparallel Burgers vectors whenEqn. (14). The external stress required to arrive atthey are close enough to be annihilated along dislo-the imposed strain rate and at the given initial av-cation gliding direction, and V。is the climb velocityerage dislocation density can be modeled by itera-controlled by thermal activation process.tion from the Orowan equation, with the help ofve is calculated ascalculations of general dislocation density and thev。= tAD/(kgT)variation of effective shear stress in both cell inte-where D is the diffusion cofficient, r the shearriors and cell walls. The stress-- strain curves canstress and A the activation area.then be derived out as a coupled constitutive equa-tion in FEM simulation of thermomechanical2.4 Dislocation density in cell wallsprocess of the materials'5].The population of dislocations, named immo-bile dislocations in the cell walls Pm，undergo the3 MODELLING OF HOT DEFORMATION OF Alsame processes as those inside the cells, exceptMg-Si ALLOYthat contributed to the increase of the dislocationdensity. To calculate the rate of increase of dislo-The physics based models require relevant da-cations in the cell walls, the assumption that allta, which of most can economically obtained fromdislocation dipoles accumulated in the cell wallsphysical simulation tests. In order to validate theshould be taken into consideration. As dipoles arecurrent model, hot compression tests were per-generated in the whole volume, but stored in theformed at 450 and 500 C with a constant strainwalls only, the rate of increased dislocations can berate of 0. 001 s-+ on an Al-Mg-Si alloy ( Al-derived as0.62Mg-0. 70Si-0. 20Mn-0. 03Cr). The experimen-p:=tp-2(d-d_>M.1.p (13)tal stress- -strain curves were obtained from com-pression testing on Gleeble-1500 thermomechanicalsimulation machine. The experimental stress-2.5 Precipitationsstrain curves of the Al-Mg-Si alloy exhibit a char-Concerning dislocation motions in heterogene-acteris中国煤化工ning of deform-ous commercial alloys, solid solution and precipita-ationhe imposed lowtion hardening have to be taken into account. ThestrainfYHCNMHGimplyingalessnon-deformable precipitations act as dislocation ob-strain hardening than dynamic restoration'stacles and affect the free spacing of the mobile dis-shown in Fig. 1. This is caused by more thermallocations both in the cell interiors and in the cellactivation events and the possibleripening of pre-494 .Trans. Nonferrous Met. Soc. ChinaJun.2004creation of dislocation locks are set to about 5- 2018times of the magnitude of dislocation Burgers vec-■一Calculatedtor[0l. For a dipole to form, the distance between16●由一Experimentaltwo dislocations has to exceed the critical distance. 14for annihilation d-c, but has to be small enough to_450 C, 0.001s-1have the involved dislocations trap.12The remaining parameters were optimized by品1(500 C, 0.001 slthe means of random walk optimization algorithmwithin 10 000 iteration steps to obtain the lowestpossible value for the mean square deviation of ex-6perimental and simulated stress- -strain curves.The formation of textures during hot deformation0.20.40.60.8is ignored in the modelling process. The optimizedTrue strainvalues are also outlined in Table 1, giving quiteFig. 1 Measured and computed stress- strainreasonable values of activation energies for com-curves of AI-Mg-Si alloymercial aluminium aloysl14.15]. For the fittingprocess, the experimental data were used only upcipitates in the matrix. During hot compression,to a true strain of 0.7, because at larger strains thedissolution of the precipitates leads to less precipitateinfluence of friction became dominate, which wasvolume fraction and finer particle size.not accounted in the modelling. It can be seen fromThe 3IVM was adopted in the hot compressionFig.1 that the computed stress- strain curves atof the alloy. The physical constants in above equa-different temperatures are in very good agreementtions were set before the fitting process. Some ma-with the experimental curves, where the mean de-terial constants were chosen for pure alumin-viation ratio is less than 5%.iun[5.6] and some special ones for the Al-Mg-Si al-Fig. 2 ilustrates the evolution of the disloca-loy, as listed in Table 1. The volume fraction oftion densities with the strain computed from thecell interiors and cell walls were set to qn=0.9 and3IVM model. The curves of the total ( average)φw=0.1. The minimum distance for dislocationdislocation densities at different temperatures areannihilation and climb, and the critical spacing forquite similar to those of the experiment, implyingTable 1 Material parameters for 3IVM computation on Al-MgSi alloyConstantGiven valueOptimized valueElastic modulusl1] /GPa69.0Shear modulus at 300 K/GPa25.9Diffusion coefficient/(m2 ● s~')1.3X10-*Initial grain size/m1.0X10-+Burgers vector of dislocation/m2. 86X10-10Constant of dffusion(Mg in A1D)13)/(m2●s5-')2. 83X10-10Constant of dffusion(Si in ADC)/(m2 .851)3.74X10-10 .Taylor factor for polyerytalline materials3. 06Starting dislocation density at cell interior/m“1.0X10*Starting mobile dislocation density/mi - 21. 0X10*Starting dislocation density at cell walls/m 21.0X10Minimum distance in glide direction/m(1.0-5.0)X10-94. 17X10~9Minimum distance for dislocation annihilation/m2.35X10-9Critical spacing for creation of dislocation locks/m(1.0-5. 0)X10~92.71X10-9Constant for ripening1. 05X10-*Activation energy for glide/eV0.9-1.91. 60Activation energy for climbl4/eV1.47Number of active glide systems中国煤化工5Volume fraction of precipitateMHCNMHG0. 05Attack frequency of dislocations/s-(6.8-7.8)X10*7.14X10°Decrease of shear modulus with temperature/(MPa. K-')0.1-0.50.17Vol. 14 No.3Modeling of microstructural evolution and flow stress1014■- 450C，0.001s5-!REFERENCES●- 500 C, 0.001s-1[1] Li Y Y. Summary on material science and engineeringzAl cll wllsdevelopment[ A]. Symposium of the 81* Xiangshan1013Academic Conference on Science[C]. Xiangshan, Bei>Totaljing: 1997. 9-11.yIn cell iteriors2] Zhu Q, Sellars C M. Microstructural evolution of alu-minium-magnesium alloys during thermomechanical1012processing[J]. Materials Science Forum, 2000, 331 -337: 409 - 420.[3] Marthinsen K, Nes E. The ALFLOW-model; A mi-crostructureal approach to constitutive plasticity mod-1011.20.elling of aluminium alloys[J]. Materials Science Fo-True strainrum, 2000, 331 - 337: 1231 - 1242.4] Brand A J, Kalz S, HenningsenP, et al. 3D simula-Fig.2 Computed dislocation densities oftion of closed pass rolling with intergrated microstruc-Al-Mg Si alloy at different temperaturestural simulation[A]. Beynon J H, Ingham P, et al.Proc. of the 2nd Inter. 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