Improved model and 3D simulation of densification process for iron powder

Available online at www.sciencedirect.comTransactions ofPScienceDirectNonferrous MetalsScienceSociety of ChinaELSEVIER PressTrans. Nonferrous Met. Soc. China 20(2010) 1470-1475www.nmsc.cnImproved model and 3D simulation of densification process for iron powderSONG Yi(宋毅), LI Yuan-yuan(李元元), ZHOU Zhao-yao(周照耀),ZHENG Zhen-xing(郑振兴), CHEN Pu-qing(陈普庆)School of Mechanical and Automative Engineering, South China University of Technology, Guangzhou 510640, ChinaReceived 1 September 2009; accepted 2 February 2010Abstract: A new model for describing the compaction process of iron powder was proposed based on the continuum hypothesis andelliptical yield criterion. To simulate the densification behaviour, the constitutive model was implemented in M arc computer program.For the relationship between load and displacement, different models were compared and the influence of the parameters in theconstitutive equations was determined by means of simulation and experiments. The density distribution of a balancer was measuredand simulated. The results show that the parameter ? adopted plays a modification role for the load-displacement curve, andcompared with other models the present model fits better with the experimental data in the later stage of the compaction processmainly due to the different parameters A and B. The friction on the contact surface contributes to the inhomogeneous densitydistribution under large deformation of the workpiece. The comparison between the simulation and experimental data indicates thatthis model can be used to predict the powder compact process precisely and effectively.Key words: powder compaction; simulation; iron; density distribution; constitutive modelare based on the constitutive function of porous material1 Introductionwhich is not in accordance with the properties of thepowder material completely.Powder forming is a highly developed process ofA new constitutive relation under a general form ofmanufacturing ferrous matrix or ceramic matrixthe yield function with an ellipsoidal yield surface for thecomposite material products, which combines the costdensification process of iron powder during the coldand material saving advantages of conventional powdercompaction was reported which was put forward basedmetallurgy with the high production rates and propertyon the speciality of powder. The action mechanisms ofenhancement of forging. So me important factors, such asdifferent parameters in the yield function were analyzedpressure，temperature and strain rate， determine the in detail. And the finite element calculations derivedproduct quality. Therefore, these process factors shouldfrom user-subroutines of Marc were compared withexperimental data.experimental approaches to manufacture high strengthand accuracy parts with homogeneous density2 Constitutive modeldistribution[ 1-5].During the deep exploration of powder formingTaking into account of the influence of porosity andphenomenon, a number of constitutive models werehydrostatic pressure of porous materials, one generalproposed based on the hypothesis that powder wasform of the yield criterion isconsidered as a continuous， elasto-plastic， andcompressible medium With some classical ellipticalAJ2+B.J=ηsζ=s艮(1)yield equations[6- 9], they are commonly integrated withJ2 and J1 are the second invariant of deviatoricfinite element method (FEM) for the investigation ofstress tensor and the first invariant of stress tensor,metal powder. However, most of these models[10-12]respectively. Ss is the yield stress of the dense referenceFoundation item: Project(50325516) supported by the National Natural Science Foundation 0中国煤化工，rted by ChinaEatceanionana Keoearch undcConaond)i Froflet0onsp suporteaby the Natl IMYHCNMH G& Povince, ChinasCorresponding author: SONG Yi; Tel: +86-20-87112933; E-mail: songyi0591 @ gmail.comPgmail.comDOI: 10.1016/S1003-6326(09)60323-XSONG Yi, et al/Trans. Nonferrous Met. Soc. China 20(2010) 1470- 14751471material and SR is the flow stress of the porous material.η=(ρ°-pρ2)/l-ρ?)(8)The parameter ? is a function of relative density ? andrepresents contribution of geometric hardening. A and BIt produced better results with the experimental data. Inare the coefficients of the yield criterion which can bethis work, the elasto-plastic deformation of iron powderpresented as functions of material Poisson ratio vwith low initial density was analyzed and the yieldKUHN and DOWNEY[6], and DORAIVELU et al[8]criterion was put forward as follows:put forward the following functions:(1.86p+1.14)Ji +0.32(1-p)J}=(P -起3n=s民A=2(1+v ), B=(1-2v )/3(21-ρ(9)For the uniaxial stress condition， J1= σ1 ,J2=σ/3 and sp=s， i.e. A and B satisfy theDuring the compaction of powder material, thfollowing relationship :density is closely related to the plastic strain. The densityincreases gradually with the cumulation of plastic strainA/3+B=1(3and the property of material changes simultaneously. TheVarious relationships between V and ? wereevolution of density must follow the mass conservationproposed by many investigators[6, 8, 13]. According toequation and the relationship between relative densitythe experimental data, ZHDANOVICH[ 14] assumed thatand plastic strain is given as follows:v =0.5?"Po462l3ρ+Sp=(4 +?4)(2+?12)(l3+?13)KUHN and DOWNEY[6], and DORAIVELU eal[8] applied n=2 to the yield criterion. W ANG et al[15]Po4213=ρoexp(- eδ;)(10)adopted a linear relationship between V and ? for iron1123 exp(eBδo)powder material[15]:where ?o and (?+? ?) are the relative densities before andv =0.93?- 0.43(5after deformation, l; and (;+?l) are the dimensions of amicro -unit before and after deformation, and ε} is theCompared with KUHN's[6] formula by compactioncumulative logarithmic plastic strain. .experiments of iron powder, Eq.(5) fits better with theexperimental data. Therefore, Marx- Davies function was3 Three-dimensional FEM analysis andadopted in this work for the higher precision.experiments of compaction processWANG[15] et al Submitted Eq.(5) to Eq(2) andscaled the parameter B properly. The yield criterion canThis new constitutive model was employed intobe written asMSC. Marc. User subroutines which used the implicit(1.86ρ+1.14)J2 +0.32(1-ρ)J7=ηsζ=s艮(6code to simulate the compaction process of pure ironpowder and the corresponding experimental data wereIt is noteworthy that when materials are of fullpresented to verify the simulation results.density, i.e. in the state of ?=1 and v =0.5, this yieldIn the following simulations, eight-noded andcriterion reduces to the usual von Mises yield criterion.full-integration solid elements were adopted to build theAlthough when ??1, Eq.(6) does not accord with the3D finite element models. The material parameters wereuniaxial stress condition, Eq.(3). KIM et al[2] mentionedset as: ?c=0.457 9, s=405 MPa， ?o=0.458 and elasticthat Eq.(3) is mandatory for porous materials, but not formodulus E=210? GPa.powder.The foctor ? was introduced via the flow stress in3.1 Comparison of different modelsorder to characterize geometrical and strain hardeningAn uniaxial compaction experiment of a blockwhich is generally considered as the function of relativeworkpiece was conducted on the test machinedensity. DORAIVELU et al[8] assumed thatSANS _CMT5105. Pure iron powders were flled in a dieη=(ρ2→p?)/l←ρ2)(7with a square cross section of 10 mmx 10mm in size, andthe flling height was 19.65 mm. The load on the upperwhere ?c is an experimental parameter that is referred aspunch increased linearly from 0 to 70 kN. The load-the critical relative density for the state of the porousdisplacement curves were recorded by test machine.material without flow stress. The value of ?c should beIn the simu中国煤化工rtia force wasvery close to the initial relative density. Based on theignored becauseTYHCN MH Gssue of theDORAIVELU's formula[8], an expression of the factor ?upper punch actuuly. 1 nc uppul puiui, i lower punch,was proposed by LI et al[16]:and the die were assumed as rigid walls. A coulomb1472SONG Yi, et al/Trans. Nonferrous Met. Soc. China 20(2010) 1470- 1475friction model with an additional stress limit was used.of these two load-displacement curves are almost theThe friction coefficients at the interfaces were supposedame. Although DORAIVELU's modeI[8] fits well withto be 0.1. With relative residual testing, the check forthe experiment in the later densification process, it isconvergence was made whether the largest residual forceobvious that its error is large at the beginning. In onedivided by the maximum reaction force was smaller thanword, ? is overestimated in DORAIVELU' model. Asthe tolerance of 0.1.mentioned above， ? represents geometric hardeningIn Fig.1, the load vs displacement curve obtainedcontribution, so in the prometaphase of compaction, thefrom the experiment is compared with that of theadvance of the flow stress for powder material can be .simulation for the constitutive models of LI et al[16],described more accurately by LI et al[16]. TheDORAIVELU et al[8] and the present model. It can beexpression proposed by LI et al[16], Eq.(8), was adoptedfound that the present model shows a higher accuracy inin the present model.this case. Compared with model in Ref.[8], model ofCompared with the model in Ref.[16], the presentRef.[16] has the same functions of the parameters A andmodel has a similar load-displacement curve with theB and the different expression of the parameter ?, whichdifferent functions of the parameters A and B and themakes the load-displacement cuve 'softer' because of itssame expression of the parameter ?, because Fig.3 and‘softer’relationship between relative density and,Fig.4 show that there is not a great difference betweenshown in Fig.2. Fig .2 suggests that ? of these two models, these two models for the A and B functions of relativeEq.(7) and Eq.(8), all approach to 1.0 as relative densitydensity. Although A and B of all models approach to 3.0approaches to the limit, and the difference of ? increasesand 1.0, respectively, as relative density approaches togradually with the densification process to the maximum1.0， which meets the constraint of von Mises yieldvalue at the relative density of 0.816, then decreasescriterion，the present model fits better with therapidly to zero. These evolution trends are also reflectedexperimental data in the later stage of the compactionon their comparison in Fig. 1, and the start and end pointsmainly due to the more reasonable expression of V，70 r3.0Experimental!一Ref[14]，60-- Ref,[16]2.8-2一Present model- Ref.[8]50 r4一 Present model2.62.4-33020.2 t10/22.02468100.4 0.5 0.60.7 0.8 0.9 1.0Displacement/mmRelative densityFig.1 Load vs displacement curves of experiment and simulationFig.3 Parameter A as function of relative density0.301- Ref:[8]1.0二Ret:16]. Reftia0.350.25 t!二Ref[10.8-40.250.20。0.6-的0.15I卜0.150.40.10-0.1020.2 r0.05 t0.050le中国煤化工).50.6 0.7 0.8 0.9 1.009 1.0fYHCNMH GFig.2 Parameter ? as function of relative densityFig.4 Parameter B as function of relative densitySONG Yi, et al/Trans. Nonferrous Met. Soc. China 20(2010) 1470- 14751473Eq.(5). The parameters A and B can be regarded as nodes and 2 400 hexahedral elements. The calculationweighting factors for deviatoric stress and hydrostaticwas divided into 200 incremental steps. The updatedstress, respectively[1]. So, based on the parameters A andB modified through the experiments of iron powder, thelarge-strain elasticity and plasticity analysis. Thepresent model behaves a more authentic status ofconvergence criterion assumed that the residual forceelasto-plastic stress and strain for this material.should be less than 1% of the reaction force. On acomputer with 1.8 GHz CPU and 2 GB memory, the total3.2 Simulation of density distributiontime steps taked approximately 7h.A balancer used in the piston mechanism is shownFig.7 shows the contour plots of relative density ofin Fig.5. In the compaction process, it is difficult tothe sample. The highest relative density, 0.933 9, is at theachieve a completely homogeneous density distributionupper joint of the ring part and the fan-shaped part. Thebecause of the structure of two levels steps, which means relative density distribution from 0.911 0 to 0.933 9the requirement of the elaborated process scheme. Fig .6appears mainly at the outter upside edge of theshows the schematic illustration of the die, powder andfan-shaped part. The lowest relative density, 0.819 5, ispunches. In this case, the lower punch 2 and the upperat the outter arc edge of the downside of fan-shaped part.punch were movable downwards to compact the powder,The relative density distribution from 0.819 5 to 0.831 0and their velocities were proportional to their finalappears mainly at the outter edge of the downside ofdisplacements. The initial positions of the lower punch 2fan- shaped part. All the large gradients occur around theand the upper punch were set as H=15.23 mm anddie, core rod, and punches where the flow of powders isH2=15.23 mm. The lower punch 1, die and core rod were constrained by the friction at interfaces, especially in thefixed.corners, but the relative density in inner districts presentsa relatively homogeneous distribution.140Relative densityL 0.9339A、. 0.92250.91100.8996器导0.888208767 ，0.8653R32.50.85380.8424区↑0.8310Fig.5 Schematic diagram of balancer (Unit: mm)0.8195-t(a)Core rod -Upper punchDie0.93390.922509882Powder0.8767Lower punch 1Lower punch 2(b)Fig.7 Relative density distributions of simulation: (a) Top;Fig.6 Schematic diagram of die, powder, core rod and punches(b) Bottom中国煤化工The constitutive model described above waAt the verCNMHGders and theimplemented to simulate the densification process. A full die, relative den.AYH3D simulation was conducted using a mesh with 3 398to down. However, the situation is contrary on the axial1474SONG Yi, et al/Trans. Nonferrous Met. Soc. China 20(2010) 1470- 1475interface between powders and the lower punch 2 (i.e.Two parts of the balancer shown in Fig. 9 were splitsurface B marked in Fig.7(b), because the downwardinto sixteen pieces respectively for measuring the relativefriction, with the downward compaction of the lowerdensity distribution by Archimedes’ method. Fig.10punch 2, promotes the movement of powders to theshows the experimental and simulative results of thebottom and densifies these regions. In addition, thsymmetry plane and A- -A section. By comparison, theplaces of lower density in the upside form an annularsimulations are basically consistent with theshape (i.e. A marked in Fig.7(a)), which is the joint effectexperimental results. It is found that the span and theof the horizontal friction from upper punch and themaximum value of relative density on the symmetryvertical friction from die and core rod. Fig .8 reveals theplane are greater than those in the A- -A section. And thedirections of the friction on upper surface and the dashedprediction mentioned above that the relative densityline represents the region A. As shown in Fig.8, thenearby the interfaces is more inhomogeneous than that ofbilateral friction of the regionA is completely reversed inthe inner, is confirmed by the experiment.direction, which causes the diffusion of the intermediatepowders to the both sides and the downward. As a result,Relative densityan annular low density distribution comes into being.09125 a 90800.870237086703。。 。aMgs5o0090350912404 .0.89440.88540.876320.8920270.8673108715250.85830.8492 035 79208495420.8402 0.8617140.8311I 0.822120.82210.8872510.87191008661220873016山(a)0.86 0.86 0.88:0.89 |0.85 0.86 0.86:0.860.86 0.87 0.86:0.85j0.87 j0.86 0.85j0.84Fig.8 Directions of friction on upper surface(b)0.9125 090080.86793I 0.90350.870237/ 0.86556866550D.9124040.89202710°A0.871525' 30°0.8492 08357920.8402 0.861 fi14L0822120.822 1083016870 24(c)0.85 0.85 0.87 0.880.85 0.87:0.87 0.87LA0.85 0.87:0.85 0.840.86 0.86 0.85 0.84(d)Fig.10 Comparison of experimental and simulative results:(a) Sinulative res中国煤化工ExperimentalFig.9 Cutting scheme for measuring relative densityresults on symm;YHCNMHGesultsinA-A.distributionsection; (d) Experimental results in A- A sectionSONG Yi, et al/Trans. Nonferrous Met. Soc. China 20(2010) 1470- 14751475[4] BIER w, HARTMANN s.4 Conclusionsmetal powder compaction using a unique and convex single surfaceyield function [J. European Joumal of Mechanics -A/Solids.2006,25(6): 1009-1030.1) The simulative load vs displacement curve of theLEE S C, KIM K T. A densification model for powder materialsnew model agrees better with the experimental data. Theunder cold isostatic pressing- -ffect of adhesion and friction ofparameters A, B and ? produce different influence on therubber molds []. Materials Science and Engineering A，2008,numerical solutions. The results show that the parameter498(1/2): 359-368.[6] KUHN H A, DOWNEY C L. Deformation characteristics and’adopted plays a mo dification role for the load-plasticity theory of sintered powder materials []. Intemationaldisplacement curve， because of the compaction ofJournal of Powder Mallurgy, 1971, 7(1): 15-25.powder, which describes the increase of the flow stressGREEN R J. A plasticity theory for porous solids [U]. Intermationalmore accurately. In the later stage of the compaction, theJournal of Mechanical Sciences, 1972, 144): 215-224.present model fits better with the experimental dataDORAIVELU s M, GEGEL H L, GUNASEKERA Js, MALASJC,MORGAN J T, THOMAS Jr J E A new yield function forcompared with other models mainly due to the differentcompressible materials []. International Journal of Mechanicalparameters A and B which are based on the moreSciences, 1984, 26(9/10): 527-535.reasonable expression of V for the iron powder.SHIMA S, OYANE M. Plasticity theory for porous metals [].2) In the simulation of a balancer with a 3D finiteInternational Journal of Mechanical Sciences, 1976, 18(6): 285-291.element model, the relative density distribution was10] KANGC s, LEE S C, KIM K T, RDZENBERG Q Densificationobtained by employing the constitutive function intobchavior of iron powder during cold stepped compaction [J].Materials Science and Engineering A 2007, 452/453: 359-366.MSC. Marc. User subroutines. The simulative resultsshow that the friction on the contat surfaces contributes[11] CHUNGS H, KWON Y, PARK S J, GERMAN R M Sensitivityanalysis by the adjoint variable method for optimization of the dieto the inhomogeneous density distribution of thecompaction process in particulate materials processing [J]. Finiteworkpiece under large deformation. For the relativeElements in Analysis and Design, 2009, 45(11): 836-844.density distribution, the simulation data are basicallycriterion for compressible sintered powder materials [J]. Journal ofconsistent with the experimental results. Some errorsMaterials Processing Technology, 2006, 180(1/3): 174- 178.exist because the simulation data are obtained from[13] HUANG C, CHEN P, SHAO M, LI Y Numerical simulation innodes of the specified plane but the experimental data arepowder compaction of metallurgy component []. Transactions offrom the solid entities.Nonferrous Metals Society of China, 2006, 16(6): 1353-1357.14] ZHDANOVICH G M. 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