Effect of viscosity on material behavior in friction stir welding process

Available online at www.sciencedirect.comSCIENCEdoIREcT.Transactions ofNonferrous MetalsSociety of ChinaScienceTrans. Nonferrous Met. Soc. China 16(2006) 1045-1052Presswww.csu.edu.cn/ysxb/Effect of viscosity on material behavior in friction stir welding processZHANG Hong-wu(张洪武)，ZHANG Zhao(张昭)，BIE Jun(别俊), ZHOU Lei(周雷), CHEN Jin-tao(陈金涛)State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics,Dalian University of Technology, Dalian 116024, ChinaReceived 25 November 2005; accepted 8 May 2006Abstract: Temperature dependent elastic viscoplastic material model was used for the numerical simulation of the friction stirwelding process. The non-elastic response of the rate-dependent material in the large deformation problems was calculated by usingthe closest point algorithm. The numerical results show that the shape of the equivalent plastic strain looks like onion rings and thespacing of the rings is approximately equal to the forward movement of the tool in one rotation. The equivalent plastic strain isincreased with the increase of viscosity coefficient due to the increase of friction stress in the pin-plate interface. The region which isinfluenced by the rotating tool is decreased with the decrease of viscosity coefficient. The radial and circumferential stresses in frontof the pin are greater than the ones behind the pin. This difference can be reduced with the decrease of viscosit.Key words: rate-dependent model; constitutive relationship; radial return mapping algorithm; friction stir weldingfracture location characterizations in friction stir welds1 Introductionand the friction stir welding characteristic of aluminumalloy plates with different thicknesses.Friction stir welding(FSW) is a new solid-stateAs a solid-state joining technique, the materialjoining process invented by TWI, in which joining ofaround the pin will generate great thermal plastic strainmaterial is achieved without melting. The usual flawsduring FSW. The mechanical properties of the material atsuch as slag-inclusions and porosity can be minimized orhigh temperature can be related to time. Thus, theeven can be eliminated in friction stir welds. This newunderstanding of the mechanism of FSW can betechnique is successfully being applied to the aerospace,improved by use of the visco-plasticity model.automobile and ship-building industries. NumericalA time-continuous model normally forms the basissimulation is important for investigating the mechanismfor the constitutive equations in the modeling of theand even optimizing the process parameters of frictionelasto-plastic material behavior. In this time-continuousstir welding. DENG et al[1] used solid-mechanics basedmodel the relation between strain and stress in thefinite element method with adaptive meshing to simulateinelastic domain is defined in a rate formulation. So inthe friction stir welding process. Two different interfacethe numerical solution procedure, it becomes necessarymodels with rate-independent material were used toto integrate the constitutive equation to obtain thstudy the material flow. SANTIAGO et al[2] simulatedincremental formulation. It is recognized that the returnthe 3D thermally coupled FSW process and presented themapping algorithm is very efficient for large scaletemperature field distribution using a general finiteinelastic computations[7]. This integration scheme iselement code. The strain hardening and texture evolutionboth inexpensive and accurate[8]. In order to preservein the friction stir welds of stainless steel has beenthe quadratic rate of asymptotic convergence, it is crucialstudied by CHO et al[3]. Recently, ZHANG et al[4]to ensure the consistency between the tangent modulusstudied the stress and strain distributions in FSW byand the integration algorithm especially for the widelyfinite element method. LIU et al[5, 6] studied the tensileused iterative schemes based on Newton' s method.中国煤化工Foundation item: Porjects( 10225212; 10421002; 10302007) supported by the National Natural s: spprted by theProgram of Changjiang Scholars and the Innovative Research Team in UniveMHC N M H G2005CB321704)supported by the National Basic Research Program of ChinaCorresponding author: ZHANG Hong-wu; Tel/Fax: +86-411-84706249; E-mail: zhanghw@dlut.edu.cn.1046ZHANG Hong-wu, et al/Trans. Nonferrous Met. Soc. China 16(2006)ZHANG[9] presented a method whereby an explicit.30mm小30mmexpression for the tangent moduli consistent with aRetreatingAdvancingclosest point return mapping algorithm may besideuideveloped for generalized pressure-dependent elasto-plasticity models. One significant advantage of thisWeldingmethod is that no matrix inversion is necessary in the; lineconsistent tangent modulus expression. SERCOMBE etal[10] investigated the consistent returm mappingalgorithm for chemo-plastic constitutive laws withinternal couplings. A closest point project algorithm wasdeveloped to preserve the quadratic rate of convergenceR,=3. mm0of the Newton-Raphson iteration scheme.dO)rIn the high temperature state, the effect of the↓Dlviscosity on material behavior becomes important. IFSW, the temperature near the pin is high enough toFig.1 Sketch of friction stir weldingmake the material soft, and it is believed that thetemperature ranges 80%-90% of the melting point of thetion and causes the solving difficulty of double non-material[11]. So the effect of the viscosity on materiallinearity[12]. In order to solve this problem thebehavior becomes more obvious. The study of the effecttemperature field from experiment[13] is used. In theof the viscosity becomes useful and interesting in theexperimental test, the angular velocity of the rotating toolFSW process.is 0=400 r/min and the translational velocity v=2 mm/s.The return mapping algorithm is implemented forFig.2 shows the history of temperature. In the FSWthe massive computations on the flow properties aroundprocess, the friction force between rotating tool and thethe pin in the FSW process. Two methods are used towelding plates cannot grow without limit. Therefore thereduce the computational costs and to complete themodified Coulomb law is used to describe the contactsimulation in a reasonable short time. One is the use ofbehavior. The limited critical friction stress in thethe experimental temperature field which is applied topin-plate interface is defined as follows:the friction stir welds. The temperature field in thesimulation keeps the same as the one in the experimentsTmx =σ/√3.(1)at any instant. The other method is to increase thewhere σs is the current yield stress.loading speeds. The combination of the two methods will700reduce the computational costs dramatically. The codesdeveloped are combined with the explicit solver in00 tABAQUS to model the friction stir welding process as auser subroutine (VUMAT).500A160014002 Finite element model of FSW process300Fig.1 shows the sketch of the FSW model used in200this research. The translational velocity v=2 mm/s isapplied to the boundaries of the welding plates, which isequal to the translational velocity of the tool in FSW. Thetool is rotated with a certain angular velocity o= 400255075100 125r/min. The dimensions of the welding plates are 100 mmTime/sin length and 30 mm in width. The plate material to beFig.2 Experimental data used in FSW modelingwelded is 1018CR steel. The diameter of the rotating pinis Ro=3 mm. Roθ is a polar coordinate fixed on the pin.The material properties depend on the temperatureThe weld can be divided into two parts: the advancingand are shown in Fig.3[14]. So the material around theside and the retreating side according to the rotatingin is so中国煤化工ess continuedirection of the pin and to the travel direction.successfully.2018CR steelIn the FSW process, the rotating pin is in contactσ(20, 0)=478 .TYHCNMHGIusatroomwith the welding plates, which produces heat transforma-temperature E(20)=210 GPa..ZHANG Hong-wu, et al/Trans. Nonferrous Met. Soc. China 16(2006)1047less than or equal to the yield stress. The loading1.2(a)function based on von Mises condition can be defined asg(σ)=δ-σo(T)(4)where σ =√(3/2)σ':σ' is the equivalent stress.. 1018 CR steelFor Perzyna model, the flow law is given by0.6gp=y2g(σ)(5)dσ昌0.4-Al 6061-T6where” is the slip rate and0.2r=(g()》/η .(6)-Ti-6A1-4Vwhere (》denotes Macauley brackets which is defined100200300400500 600oy (x)=1/2(x +x) .Temperature/CThe plastic strain has no influence on elastic1.0 rcharacteristic tensor, considering thermal strain the stress(b)广can be expressed as0.9食0.8-\ 1018 CR steeldoσ; =Cjxu(dεx -deR - dEk -- aσn)dTdCjkl(7)where Cjxu is a material elastic constant tensor, for heat昌0.7-transfer problems in high temperature, Cjk=Cj(T) is afunction of temperature， dE represents the plastic0.6-Ti-6AI-4Vstrain and dEkl is the thermal strain.4 Return mapping algorithm0.5200 300500 600For elastic perfectly viscoplastic model, theFig.3 Properties of materials used in FSW modeling: (a) Varia-gcometric interpretation of the closest point projectiontion of yield stress with temperature; (b) Variation of elasticalgorithm in stress space is ilustrated in Fig.4[16, 17]. Inmodulus with temperaturethe state of plastic loading,Oγ= pt>0(8)3 Material constitutive modelo盟The generalization of the classic von Mises criterionfor the rate dependent material can be expressed as[8]f=σ-σo(T)-η(EP)"(EP)”=0(2)where σ0 is the initial yield stress, m is the viscosityexponent, n is the strain hardening exponent, and η is theviscosity coefficient.σ件|_The equation can be transformed to idealizeelastic-plastic model when n=0. If n=0, the strain ratehardening/softening model can be obtained as follows:f =σ-σo(T)-η(ER)"=0(3)Ewhere η> 0 represents the state of strain rate hardeningand n<0 strain rate softening. Strain rate softening has aFig.4 Geometric interpretation of closest point projectionremarkable influence on the material distortion in finitealgorithm in stress spaceelement solution. In the same case, plastic strain in thesoftening model is greater than that in the hardeningThe plasticl中国煤化工d asmodel[15].In contrast to the case of rate-independent plasticity,:MYHCNMHG(9)the effective stress is no longer constrained to remainwhere.1048ZHANG Hong-wu, et al/Trans. Nonferrous Met. Soc. China 16(2006)fi+1= f(σπn+)(10)loading speed is increased. The relation of strain rate andslip rate is linear from Eqn.(5). According to Eqn.(3),Since the total strain is fixed during thincreasing the strainrate by N times and reducingelastic- predictor stage, it followsviscosity coefficient by N times do not affect the materialbehavior when m=1.0oe:41 =-C-1 :Oo{k)(11)Linearization of Eqns.(9) and (10) gives6 Benchmark examplesaR.+Jo[Cc-. ++D25.]+ 0/[vr+t❽Vf+]1) Example 1The side of the plane is 1 mx1 m, as shown in Fig.5.(12)The elastic modulus is 70 GPa. The Poisson's ratio is 0.1.f4)+ Vf):0σH4 =0(13)The initial yield stress is 200 MPa. The viscosityexponent is m=1 and the viscosity coefficient is n1=51.8Hessian matrix can be given byMPa. The right side of the plane is subjected to auniform load of 300 MPa.Solving the linearized problem, one can obtain theincrement of the viscoplastic strain:E1m300 MPaOεR'=c+:[mxH +0/nVfR @V罪T :R品. (15)So the plastic strain εYP can be updated until th|Eresidual is less than a specific tolerance.AAA5 Computational costsFig.5 Plate subjected to uniform loadFig.6 shows the stress-strain curve in x direction asFor the themo-elasto-viscoplastic coupling problem,the results of the code developed and ANSYS. The goodthe time increment is given byagreement of the two curves demonstrates the validity ofLminthe model established. This means that the closest pointOt=c2(16)return mapping algorithm developed is available in thewhere C2 is a constant, Lmin is the smallest elementelastic viscoplastic problems.dimension, a is the thermal diffusivity of the material,3.5and3.0(17)2.5 |where k is the heat exchange coefficient, C is the唱2.0specific heat, and ρ is the density. The iteration number n1.54●- ABAQUS/VUMATis defined by the time period of the event being■- ANSYSsimulated (the natural time) t and the time increment Ot:1.0n=t/ Ot = tmax1 λ+2μ(18)云.V- ρ0.050.100.150.20Strainpresent coupled thermal stress calculation the mechanicalFig.6 Stress-strain relation of plate subjected to uniform loadresponse will govern the stability limit. The estimate ofthe time increment is only approximate and in most cases2) Example 2not conservative.The side of the plane is 1 mX1 m. as shown inIncreasing the loading speed will reduce the naturalFig.7 and the (中国煤化工rhe Poisson'stime of the event being simulated and then reduce theratio is 0.1.lYHCN MH G8 MPa. Thecomputational costs. The viscosity must be reduced toviscosity exponent is m=1 and the vIScosIty coefficient isbalance the influence of strain rate increment when the .n=152.8 MPa. The displacement of the right side in the.ZHANG Hong-wu, et al/Trans. Nonferrous Met. Soc. China 16(2006)1049natural time t is 0.005 m, the stress distribution of thet is 0.1 s for the case in which the loading speed isplane is calculated when t is different.increased by 10 times. In the elastic domain, the errorranges from 0.047% to 0.469%. In the initial stage of theplastic state, the error decreases to 0.02% and then0.005 m .1mdecreases to zero with the increase of the plastic strain.This means that the error caused by increasing theloading speeds can be neglected in large deformationproblems.2Table 1 Comparison of history resultsoσ,/MPaWithoutWithA6T/sus/momError/%computational computationalFig.7 Tension of plate under different load ratesacceleration acceleration0.1t 5.0X10 4106.0106.50.469Fig.8 shows the stress under different loading.2t 1.0X103212.0212.20.094speeds. The displacement of the right side of the plane is0.3t 1.5X10-3318.0318.10.005 m in x direction at the end of the natural time t.0.4t 2.0X 10-3423.8424.00.047Whent=l s, σx is 502.3 MPa. In another case t=0.1 s in x0.5t2.5X 10 3502.3502.40.020direction which means that the simulation is accelerated).6t 3.0X10-3by 10 times, the stress in x direction is 502.3 MPa. The .0.7t 3.5X10-30results obtained in the two cases can agree with each0.81 4.0X 10-3other very well. But the calculation time can be reduced).9t 4.5X10-3ofrom 34 s without considering any computational acce.0t 5.0X10-3leration to 3 s in the case in which the loading speed isincreased by 10 times. So this method is very essential to7 Numerical results of FSWreduce the computational costs when the rate dependentconstitutive model is used.By using the codes developed, the FSW process issimulated. The results obtained are described as follows.Figs.9(a) and (b) show the equivalent plastic straindistribution when the viscosity coefficients are 50.3 MPaand 22.9 MPa respectively. As can be seen from thefigures, the equivalent plastic strain distribution lookslike onions, which shows the nature of the materialdeformation behavior in the FSW process. Around thepin, the value of the equivalent plastic strain distributionis greater and the maximum value does not occur inwelding line but on the advancing side near the welding(a)line. This shows that the material flow on the advancingside and the one on the retreating side are different[18- -20], which causes that the deformation of materialnear the welding line is not strictly symmetric. At thesame time the value of equivalent plastic strain aroundthe pin is increased when the viscosity η is increased.Due to the increase of viscosity coefficient, the yieldstress in the pin-plate interface is also increased and thenthe friction stress in the interface is increased. So thedeformation of the material near the pin is increased(b)when the viscosity is increased. Fig.9(c) shows theFig.8 Numerical results of tensile plate with given displace-texture of onion rings in friction stir welds which ismentscaused by the rotation and the forward movement of thepin. It is noted t中国煤化工is equal to theTable 1 shows the history results of the casesforward movemYH.CN MH Gtion[21]. Thementioned above. t represents the natural time. t iscomparison of +1gs.n(a), 0) allui 心SIIOWs that the1 s for the case without computational acceleration, andeformation of the material shapes like onion ring when.1050ZHANG Hong-wu, et al/Trans. Nonferrous Met. Soc. China 16(2006)the material is slightly away from the pin in the weld.interface is increased. This is the reason for the increaseThe deformation is not strictly symmetric along theof the velocity near the pin when the viscosity iswelding line. The spacing of the rings is equal to theincreased. It should be noticed that the velocities atforward movement of the tool in one rotation.different radii in Fig.10 when 1=50.3 MPa are verysimilar. This means a thicker fluid bed exists around thepin when the viscosity coefficient is greater. The materialflow velocity at R=3.15 mm is reduced more obviouslyPROthan that at R=3.05 mm when n=22.9 MPa, which meanssmaller viscosity coefficient causes the decrease of theinfluence range of the pin. The material flow in theregion)f 120°< θ< 250°which means that the material flow on the retreating side|(a一n=22.9 MPa0)一1-50.3 MPa(a)二stPERO0|60 120 180 240 300 3600/(°)25(6)20一n7=50.3 MPa三0- 60 120~ 180 240 300 360(C)/(° )Fig.9 Distribution of equivalent plastic strain and texture ofonion rings in friction stir weld: (a) n=50.3 MPa; (b) n=22.92S[cMPa; (c) Texture of onion rings in friction stir welds一n=22.9 MPa .20一n=50.3 MPaFig.10 shows thmaterial flow near the pin.Loading speeds, including the translational velocity andthe angular velocity of the pin, are accelerated by 1000times to increase the moving velocity and the rotation复10velocity in order to accelerate the solving process. It canbe seen that the difference of the viscosity coefficient haseffect on the material flow. The maximum material flowvelocity when n7 22.9 MPa in Fig. 10(a) is about 18 m/s,while the maximum flow velocity when n=50.3 MPa in中国煤化工300 360Fig. 10(a) reaches 22 m/s. When the viscosity is increased,CNMHGthe current yield stress in the pin-plate interface is alsoFig.10 Material flow near pun: (a) K=5.US mm; (b) R=3.1 mm;increased and then the friction stress in the pin-plate(c) R=3.15 mm.ZHANG Hong-wu, et al/Trans. Nonferrous Met. Soc. China 16(2006)1051is faster than that on the advancing side.weak. This is the reason for the slower material flow onFig.11 shows the distributions of the radial stressthe advancing side. The increase of the shear stress onaround the pin. As can be seen, the radial stress in thethe retreating side with the increase of the viscosity is thefront area (θ=0°-180°) of the pin is larger than thatreal cause for the increase of the material flow, as shownbehind the pin (0= 180*- 360* ). This is because that in thein Fig.10. .FSW process the rotating pin moves forward withrotating, which causes the material in front of the pin tobe extruded and to be rotated around the pin. Therefore,--n22.9MPathe radial stress in front of the pin is greater while the后-1一n=50.3MPaone behind the pin is smaller. The maximum of the radialstress is reduced from 3.86 GPa to 3.78 GPa with thedecrease of viscosity coefficient. The radial stress behind喜-2个the pin (0= 180° - -360) is also increased with the increaseof viscosity cofficient.-0.5- - n=22.9MPa. n7=50.3 MPa60120180 240 300 3608-1.5-0/(°Fig.12 Circumferential stress distributions around pin at circleof R=0.1mm-2.5-0.3-3.5-0.2- n=22.9 MPa... η=50.3 MPa， 0.1号6180240 30036000/°)Fig.11 Radial stress distributions around pin at circle of号-0.1R=0.1mm美-0-0.3stress around the pin with different viscosity coefficients.The maximum of circumferential stress occurs in front of6(120 180 240 300 360the pin while the minimum behind the pin. The decrease0/(C°)of viscosity coefficient causes that the circumferentialFig.13 Shear stress distributions around pin at circle ofstress is decreased from 3.68 GPa to 3.37 GPa. ThisR=0.1mm .means the increase of viscosity coefficient may cause theincrease of the radial stress and the circumferential stress,8 Conclusionsalthough the amplitude is small. But the increase of thestresses behind the pin is greater than the one in front ofA two-dimensional model of the FSW process isthe pin. ZHANG et al[18] used the model ofdeveloped by using the elastic-viscoplastic constitutiverate-independent aluminum alloy to investigate threlationship and the return mapping algorithm. The stressrelationship between the distribution of stress and timet and deformation of the material around the pin arearound the pin when n=0. The calculating result showsinvestigated. The effect of the viscosity coefficient onthe stress distribution aroundthe pin is morematerial behavior and stress distribution is also analyzed.homogeneous. Compared with this result, increasing theThe results demonstrate the validity of the numericalviscosity coefficient may cause the differences of themodel developed. The main results obtained areradial stress and the circumferential stress in front of thesummarized below.pin and behind the pin become more obvious.1) The distribution of equivalent plastic strain looksFig.13 shows the shear stress distributions near thelike onion ring中国煤化工。: equal to thepin-plate interface. It can be seen that the shear stressforward movem-e rotation.around the pin is increased with the increase of the2) The incYHCNMHGntcausestheviscosity. In the region near θ=0° the shear stress is veryincrease of the equivalent plastic strain..1052ZHANG Hong-wu, et a/Trans. Nonferrous Met. Soc. China 162006)3) The influence range of the rotating tool can beaccount for rate-dependent efets in fictional contact anddecreased with the decrease of the viscosity ceofficient.visco-plasticity [0] J Mater Process Technol, 1998, 80- -81:628- 6344) The radial stress and the circumferential stress in[9] ZHANG Z L Explicit consistent tangent modulus with a returnmapping algoritm for pressure dependent eatplasticity models pfront of the pin are greater than those behind the pin.Comput Meth Appl Mech Eng, 1995, 121:29 -44.5) The material flow on the retreating side is faster[10] SERCOMBE J, ULM F J, MANG H A. Consistent retum mapping，than that on the advancing side.algorithm for chemoplastic constitutive laws with internal couplings小Int J Num Meth Eng, 2000, 47: 75-100.[川TANG W, GUO x, MCCLURE J C,et al. Heat input and .Acknowledgementstemperature distribution in friction stir welding []. 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An extension of the nadial returm algorithm to(Edited by YUaN Sai-qian)中国煤化工MHCNMH G ..