Siddiq MOM 2008

Mechanics of Materials 40 (2008) 982–1000

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Mechanics of Materials

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Thermomechanical analyses of ultrasonic welding process usingthermal and acoustic softening effects

A. Siddiq *, E. GhassemiehMechanical Engineering Department, The University of Sheffield, Mappin Street, Sheffield, Yorkshire S1 3JD, UK

a r t i c l e i n f o

Article history:Received 1 August 2007Received in revised form 13 June 2008

Keywords:Ultrasonic weldingThermomechanical analysisFriction lawsUltrasonic softening

0167-6636/$ - see front matter � 2008 Elsevier Ltddoi:10.1016/j.mechmat.2008.06.004

* Corresponding author. Tel.: +44 7726467348.E-mail address: [email protected] (A. Siddiq).

a b s t r a c t

Ultrasonic welding process is a rapid manufacturing process used to weld thin layers ofmetal at low temperatures and low energy consumption. Experimental results have shownthat ultrasonic welding is a combination of both surface (friction) and volume (plasticity)softening effects. In the presented work, a very first attempt has been made to simulate theultrasonic welding of metals by taking into account both of these effects (surface and vol-ume). A phenomenological material model has been proposed which incorporates thesetwo effects (i.e. surface and volume). The thermal softening due to friction and ultrasonic(acoustic) softening has been included in the proposed material model. For surface effects afriction law with variable coefficient of friction dependent upon contact pressure, slip, tem-perature and number of cycles has been derived from experimental friction tests. Thermo-mechanical analyses of ultrasonic welding of aluminium alloy have been performed. Theeffects of ultrasonic welding process parameters, such as applied load, amplitude of ultra-sonic vibration, and velocity of welding sonotrode on the friction work at the weld inter-face are being analyzed. The change in the friction work at the weld interface has beenexplained on the basis of softening (thermal and acoustic) of the specimen during the ultra-sonic welding process. In the end, a comparison between experimental and simulatedresults has been presented showing a good agreement.

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1. Introduction

Ultrasonic welding is a process in which ultrasonic en-ergy is used to create a solid-state bond between twopieces of metal. Ultrasonic welding is a versatile and pow-erful joining technique in the microelectronic packagingindustry because of the low temperature, high yield rateand flexibility of the process (Harman, 1997). The mainadvantages of ultrasonic welding include, absence ofliquid–solid transformations, low energy consumption, noatmosphere control required, works for dissimilar metals,low temperature allows embedding of electronics, suchas sensors and actuators and most importantly, it isenvironmental friendly and very fast (Dushkes, 1973;

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Hu et al., 1991; Mayer and Schwizer, 2002; Sheaffer andLevine, 1991).

The mechanism of creation of an ultrasonic weld hasbeen under study since many decades but still not fullyunderstood (Tucker, 2002). A very simple definition ofthe creation of a weld was proposed by Tucker (2002),i.e. creation of the weld is a process in which ultrasonicinterfacial motion between the two mating surfaces breaksand disperse the surface oxides, dirt and other contami-nants leaving clean intimate surfaces which then createbonds. Joshi (1971) has performed studies on ultrasonicwelding of aluminium, copper and gold wires. A series oftests were performed to quantify temperature rise todetermine if there exists localized melting during the weldformation. It was found that interfacial temperature read-ings were less than 70 �C suggesting that localized meltingdoes not occur during ultrasonic welding of wire bonds. Itwas also found that inter-diffusion at dissimilar bond

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A. Siddiq, E. Ghassemieh / Mechanics of Materials 40 (2008) 982–1000 983

interfaces do not occur. Transmission electron microscopystudies of ultrasonic wire bonding were performed byKrzanowski (1990). Transmission electron microscopy(TEM) was performed to examine ultrasonic bonding ofaluminium wire to various metal substrates. There wasno evidence found of inter-diffusion of atoms from sub-strate to the foil or vice versa. Both Joshi (1971) andKrzanowski (1990) found substantial amount of plasticflow around the hard members. Harman (1997) found thatthe plastic deformation is not only seen with in the micro-structure of the weld zones but also at the interface of themating materials. Transmission electron microscopy stud-ies by James (1990) and Kazumasa et al. (2003) showedthat vacancies or voids, debris or surface contaminants oroxides, and dislocations were frequently observed nearthe bonding interface. Harman and Albers (1977) per-formed studies on aluminium and gold wire bonding inmicroelectronics. Their experimental results showed thatultrasonic bonding takes place primarily by means of adeformation mechanism (ultrasonic softening) rather thanheating or sliding mechanism. Schwizer et al. (1999) stud-ied the ultrasonic ball bonding process. It was shown thatstick–slip motion is necessary for high quality bonding.Prieb (1999) performed experimental studies on the ultra-sonic joining of copper–copper, copper–aluminium, cop-per–silver and copper–steel metal pairs. It was foundthat severe plastic deformation of the metal plays anessential role during joining. It was also found that regionof maximum deformation is located below the top surfaceat the foil/sonotrode interface. It was also found that larg-est microstructural changes occur near the upper surfaceat the foil/sonotrode interface. It was proposed that mainmechanisms which lead to the formation of a metallicbond are removal of oxide coatings, metal plastificationand even flow in the boundary region. No evidences werefound of volume melting of the metals, melting of the met-als along the contact interface, diffusion of the metals or al-loy components into each other at the weld interface.

Ultrasonic welding of two different alloys of aluminium,i.e. AA 6061 and AA 3003 was performed by Kong et al.(2003) and Kong et al. (2004a,b). Kong et al. (2003) per-

formed ultrasonic welding of aluminium alloy 6061. Itwas found that a thick oxide film (magnesium oxide) existsalong the weld interface. This oxide film gets compacteddue to the dynamic interfacial stresses, generated duringultrasonic vibration, causing the oxide layer to form brittleceramic bonds at the weld interface. It was also shown thatthe density of metallurgical bond can be increased by asimple cleaning procedure. The cleaning process consistedof simple cleaning with the help of a degreaser (petroleumdistillate) and wiped with a clean cotton cloth to removeoxides and other contaminants. Micro-hardness tests onwelded and un-welded AA 6061 specimens were per-formed in Kong et al. (2004a,b). It was found that hardnessnear the weld interface is larger than the hardness awayfrom the interface. This difference in hardness values de-picted that both, surface effect (friction) at the weld inter-face and ultrasonic softening (acoustic softening) in thematerial, were present during the welding. Similar studieswere performed on aluminium alloy 3003 using ultrasonicwelding (Kong et al., 2004a,b). It was found that unlike AA

6061, AA 3003 does not require cleaning prior to the weld-ing. Gunduz et al. (2005) performed studies on the ultra-sonic welding of zinc and aluminium at elevatedtemperatures (513 K). It was found that at such high tem-peratures, weld interface exhibits structures indicative ofenhanced inter-diffusion and local melting of aluminiumand zinc solid solution.

Cheng and Li (2007) investigated the heat generationand temperature profile during ultrasonic metal weldingusing micro sensor arrays. The materials used for weldingwere copper alloy and nickel substrate. It was found thattemperature ranges from 100 to 250 �C for various loadingcases.

Daud et al. (2006, in press) performed studies (bothexperimental and simulation) on ultrasonic assisted ten-sion and compression behaviour of aluminium alloy1050. All simulations were done using implicit mechanicalanalysis without temperature effects. A phenomenologicalapproach was presented to simulate the deformationbehaviour of aluminium alloy 1050 by reducing the frictionforces when ultrasonic vibration is present. The frictionforce was reduced by assigning a very small friction coeffi-cient. It was concluded that the effect of ultrasonic vibra-tion on bulk properties of metals cannot be explained interms of stress superposition and surface effects. It wasalso proposed that a clear understanding can be developedby studying, how is the ultrasonic energy absorbed by alu-minium microstructure. Doumanidis and Gao (2004) andGao and Doumanidis (2002) performed the mechanicalanalysis of an ultrasonic spot welding process of a metalfoil on a substrate. The mechanical analysis was based onthe definition of frictional boundary conditions at thefoil/substrate interface. The friction boundary conditionwas defined by using the experimentally measured strainon the substrate surface and adjacent to the ultrasonicprobe. A good agreement of time dependent strain wasfound at the foil/substrate.

Although, a number of researchers have performedstudies on ultrasonic metal working and have reportedboth surface and volume effects in ultrasonic processingof materials. But the mechanisms describing these effectsare not fully explained in quantitative manner for the caseof ultrasonic welding. Also, a very few attempts have beenmade to simulate the ultrasonic welding process(Doumanidis and Gao, 2004; Gao and Doumanidis, 2002).In most of the theoretical and simulated works, the effectof ultrasonic vibration is attributed in the frictioncoefficient rather than taking into account both surfaceand volume effects.

In the present paper, a material model based on cyclicplasticity theory has been proposed to take into accountthe volume effects while a kinematic friction model hasbeen proposed to include the contribution of surface ef-fects during the ultrasonic welding. The proposed materialand friction model are discussed in detail in the following.

2. Deformation behaviour of aluminium alloy 6061

Aluminium alloy (AA) 6060/6061 is one of the mostcommonly used aluminium alloy due to its versatile

984 A. Siddiq, E. Ghassemieh / Mechanics of Materials 40 (2008) 982–1000

thermal and mechanical properties. The typical composi-tion of aluminium alloys 6060/6061 in weight percent is:magnesium (0.8–1.2), silicon (0.4–0.8), iron (0.18–0.7),copper (0.15–0.4), zinc (0.2–0.25), titanium (0.001–0.15),manganese (0.1–0.15), chromium (0.04–0.35) and balancealuminium. Due to its good toughness, surface finish, wel-dability and easy workability, AA 6060/6061 has foundmany applications in the industry, such as aerospace com-ponents, marine fittings, automotives, and other electricaland electronics equipments. One of the widely used appli-cations of AA 6060/6061 is in metal–matrix composites. Inall such applications, material has to bear all kinds ofmechanical and thermal loads. In this section a thermome-chanically motivated cyclic plasticity model has been pro-posed to model the deformation behaviour of AA 6060/6061, which takes into account Bauschinger effect, plasticratchetting and shake down along with thermal softeningwith increasing temperature.

Experimental investigations to study the deformationbehaviour of AA 6060/6061 have been performed in thepast (Swearengen, 1972; Sih and Chou, 1989; Yang andWang, 1993; Davis, 1993; Hopperstad et al.,1995a,b; Srivat-san et al., 1997; Lee et al., 2000). Swearengen (1972) hasperformed experimental studies on the deformationbehaviour of AA 6061. Swearengen (1972) showed thatthermally activated flow stress in AA 6061 arises fromthe simultaneous contributions of two parallel processes,which are, dislocation intersection and shear of the glideplanes. It was also found that at high strain rates the roomtemperature behaviour may begin to incorporate one orboth of the thermally activated processes. Sih and Chou(1989) studied the uniaxial tension behaviour of AA 6061at elevated temperature. They found out the non-equilib-rium thermal/mechanical response of AA 6061 at elevatedtemperatures. It was shown that at a specific surroundingtemperature, during the uniaxial tension loading, temper-ature of the specimen decreases locally due to expansionand then after some duration of time the temperature be-comes the same as surrounding with reversal in heat flux.Yang and Wang (1993) studied the cyclic fracture behav-iour of AA 6061 over and extensive range of positive meanstress. It was shown that secondary-stage creep rate andfracture process are slowed down by decreasing meanstress values for low cycle stress amplitude.

Hopperstad et al. (1995a,b) studied the deformationbehaviour of AA 6060 at room temperature. The main focusof the work was to investigate the factors, such as the shapeof the hysteresis loops, cyclic hardening and softening alongwith the memory of prior strain histories, during deforma-tion. It was found that AA 6060 exhibited cyclic hardeningwith stress range increasing in an exponential mannerduring the first cycles and eventually saturates to a stabi-lized stress amplitude range after a certain number ofcycles. Fig. 1 shows 1st cycle and 40th cycle during defor-mation of AA 6060 at room temperature (Hopperstadet al., 1995a,b). Srivatsan et al. (1997) studied the effect oftemperature on the cyclic response and fracture character-istics of AA 6061. It was found that AA 6061 shows softeningat all test temperatures. Lee et al. (2000) studied the dy-namic response of the AA 6061 material at high strain rateimpact loading. It was found that the impact response of

AA 6061, strongly depends upon applied strain rate, whichresults in the variation of work hardening rate and strainrate sensitivity. It was also shown that rate of work harden-ing decreases with decreasing strain and strain rates.

For the presented work, the data presented in Davis(1993) about the monotonic deformation behaviour of AA6061 is used along with the experimental uniaxial cyclicstress–strain curves of Hopperstad et al. (1995a,b).

3. Material model

3.1. Isothermal cyclic plasticity model

The thermomechanical cyclic plasticity model proposedin this work is based on the combined nonlinear isotropic/kinematic hardening model for time independent cyclicplasticity presented by Chaboche and coworkers (Chaboche,1977, 1979, 1986, 1989; Chaboche and Rousselier, 1981,1983; Lemaitre and Chaboche, 1990; Chun et al., 2002;Freed and Chaboche, 1989).

The basic constitutive equations of the model for uniax-ial loading case are summarized below:

The total strain tensor during deformation is the sum ofelastic strain tensor and plastic strain tensor, given by

e ¼ eel þ epl ð1Þ

Stresses are computed using the elastic stress strainrelation

r ¼ Ceel ¼ Cðe� eplÞ ð2Þ

Yield function (criterion) is given by

F ¼ jr� aj � ðr0 þ RÞ ¼ 0 ð3Þ

with a being the back stress tensor due to kinematic hard-ening, R is the isotropic hardening term and r0 being theinitial yield stress.

Plastic strain during deformation is given by

depl ¼ dkoFor

ð4Þ

with dk being the plastic multiplier which satisfy the fol-lowing consistency conditions (Kuhn–Tucker type)

F 6 0; dk P 0 dk � F ffi 0 ð5Þ

The nonlinear isotropic hardening rule adopted here waspresented in Lemaitre and Chaboche (1990), Huber andTsakmakis (1999), and Chun et al. (2002). The isotropichardening (R) which describes the expansion of the yieldsurface is defined as an exponential function of accumu-lated plastic strain (i.e. isotropic hardening is dependenton the plastic strain history), which is given by

R ¼ Q 1� e�b�epl� �

ð6Þ

where �epl is the equivalent plastic strain, while Q and b arematerial parameters to be identified by inverse modelling.Q is the maximum change in the size of the yield surface,and b is the rate at which the size of the yield surfacechanges with changing plastic strains.

A nonlinear kinematic hardening proposed byArmstrong and Frederick (1966) has been used to capture

-250

-200

-150

-100

-50

0

50

100

150

200

250

-1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6

1st cycle (Hopperstad et al., 1995a, b)

40th cycle (Hopperstad et al., 1995a, b)

-250

-200

-150

-100

-50

0

50

100

150

200

250

-1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6

Strain (%)

Stre

ss (M

Pa)

1st cycle (Hopperstad et al., 1995a, b)

40th cycle (Hopperstad et al., 1995a, b)

Fig. 1. Experimental cyclic stress–strain curves of AA 6060 for 1st and 40th cycle (Hopperstad et al., 1995a,b).


nonlinear hardening behaviour and smooth transition fromelastic to plastic deformation (Chaboche, 1977, 1979, 1986,1989; Chaboche and Rousselier, 1981, 1983; Ohno andWang, 1993a,b; Lemaitre and Chaboche, 1990; Jiangand Kurath, 1996; Wang and Barkley, 1998, 1999; Abdeland Ohno, 2000; Geng and Wagoner, 2000, 2002). Theevolution of back stress (a) is given by

_a ¼ C1r0 ðr� aÞ_�epl � ca_�epl ð7Þ

where r0 = ry + R with ry being the yield stress at zeroplastic strain, while C and c are the material parameterswhich can be identified from cyclic testing. The c termdetermines the rate at which the saturation value of kine-matic hardening decreases with increasing plastic defor-mation. C is the kinematic shift of the yield surface.

The calibration of C and c is performed using the stressstrain data of stabilized cycle. The evolution law of backstress in Eq. (7) when integrated for a uniaxial case is givenby (ABAQUS, 2006)

a ¼ Cc

1� e�c�epl� �

þ a1 � e�c�epl ð8Þ

where a1 is obtained from stabilized cycle and is given by

a1 ¼ r1 � rs

with r1 is the stress at the start of the stabilized cycle andrs is the stabilized size of the yield surface, which is givenby

rs ¼ ðr1 þ rnÞ2

ð9Þ

with r1 and rn are the stress at the start and end of the sta-bilized cycle.

3.2. Cyclic plasticity model with thermal softening

Many metals that exhibit aging processes have shownstrong temperature path history dependence (Swearengen,1972; Sih and Chou, 1989; Srivatsan et al., 1997). The ther-momechanical plasticity theories have been under studysince many years. Many researchers have proposed differ-ent models to describe inelastic behaviour for metals un-der different thermal and mechanical loading conditions.The thermomechanical coupling term used in the presentstudy is adopted from Johnson and Cook (1985). A similarapproach was proposed by McDowell (1992), in which thetemperature terms were only included in the descriptionof isotropic and kinematic hardening rules. This procedureimplicitly takes into account any nonisothermal responseas temperature path history-dependent. In the presentstudy, the thermomechanical term is adopted fromJohnson and Cook (1985) hardening model. The inclusionof such thermomechanical coupling term is quite straightforward. This was done by embedding the temperatureterm (1 � hm) in the nonlinear isotropic and kinematichardening model. The modified nonlinear isotropic hard-ening law is given by

Rth ¼ Q 1� e�b�epl� �

� ð1� hmÞ ð10Þ

where m is the material parameter and h is the nondimen-sional temperature given as

h ¼ h� htransition

hmelt � htransitionð11Þ

htransition is the transition temperature, at or below whichthere is no temperature dependence on yield stress, andhmelt is the melting temperature.


Similarly, the modified nonlinear kinematic hardeninglaw is given by

ath ¼Ccð1� e�c�epl Þ þ a1 � e�c�epl

� �ð1� hmÞ ð12Þ

3.3. Cyclic plasticity model with thermal and acoustic(ultrasonic) softening

Acoustic (ultrasonic) softening is defined as the de-crease in the plastic (yield) limit of a material under in-tense ultrasonic vibration. Acoustic softening has beenunder investigation since many decades (Dawson et al.,1970; Green, 1975; Hansson and Tholen, 1978; Langenecker,1966; Mordyuk, 1975; Severdenko et al., 1973; Winsperand Sansome, 1968).

Langenecker (1966) performed the studies on the effectof ultrasonic vibration on the deformation behaviour ofaluminium and zinc metals. It was found that yield stressof metals reduces significantly when intense ultrasonicstress waves are applied during deformation. It was alsofound that amount of reduction of yield stress is directlyproportional to the acoustic energy input to the specimen.It was also found that as long as ultrasound energy appliedis below a critical value, typical for the different materials,no permanent changes appear in the properties of metals.These results also revealed that the ultrasonic energy den-sity required to produce deformation in aluminium wasroughly 107 times less than the thermal energy.Langenecker (1966) proposed that this difference in ener-gies is due to the fact that the absorption of ultrasonic en-ergy is localized, i.e. in the vacancies, dislocations andgrain boundaries while thermal energy is absorbed uni-formly in the material. Winsper and Sansome (1968) per-formed studies on the deformation behaviour of differentmaterials, such as mild steel, stainless steel, hard copper,and hard and soft aluminium, in the presence of ultrasonicvibration. It was found that the reduction in stress can beexplained by a mechanism of superposition of static andoscillatory stresses. It was also reported that ultrasonic en-ergy in the elastic region does not affect the stress/straincurves of the material. Dawson et al. (1970) presented anoverview of the effect of ultrasonic vibration in the defor-mation of different metals. Green (1975) proposed a theo-retical model which takes the behaviour of the material asnonlinear elastic. Using this nonlinear elastic behaviour, areduction in Young’s modulus has been calculated.Hansson and Tholen (1978) studied the deformationbehaviour of commercial aluminium in the presence ofultrasonic energy. It was proposed that the local heatingdue to the absorption of ultrasonic energy at internal de-fects (e.g. dislocations) dissipates fast due to the relativelyhigh thermal conductivity of aluminium giving only aslight overall increase in the specimen temperatures (al-most negligible). It was also proposed that the acousticsoftening explanations presented by previous researchersdo not take into account the effect of static stress in lower-ing the necessary ultrasonic energy transferred to thematerial for dislocation generation, interaction and mobil-ity. Green (1975), Mordyuk (1975), and Severdenko et al.

(1973) carried out experiments on many metals (zinc, cad-mium, aluminium, copper, steel, and tungsten). It wasfound that a decrease in plastic (yield) limit is proportionalto the intensity of oscillations and independent of their fre-quency in the range of 15–80 kHz. Mordyuk (1975) alsofound that the value of this decrease in yield limit doesnot depend on the degree of preliminary deformation inthe rang of residual elongations below 16% and on the tem-perature within the range 30–500 �C. Gilman (2001) pro-posed a model to describe the contraction of an extendeddislocation. It was proposed that a critical speed exists atwhich an extended dislocation will have a higher total en-ergy than a unit dislocation minus the energy of its stack-ing fault. At this critical velocity, the extended dislocationsin the material will contract into unit dislocations. As theextended dislocations have contracted, screw dislocationswill cross-glide freely without the aid of the thermal acti-vation. It was also shown that critical velocity for contrac-tion is about one-third the velocity of shear waves in thematerial. Rusynko (2001) proposed a generalized theoryof plasticity for the case of plastic deformation of metalsin the presence of ultrasonic vibrations.

In the present work a simple phenomenological ap-proach has been used to include the acoustic (ultrasonic)softening during deformation of the material. The mainassumption for this approach comes from the above dis-cussion (Green, 1975; Langenecker, 1966; Mordyuk,1975; Severdenko et al., 1973). The main assumptionsare the decrease in plastic (yield) limit is proportional tothe ultrasonic intensity. Also, the decrease in plastic (yield)limit is independent of the frequency (in the range of15–80 kHz), temperature (in the range of 30–500 �C) andpreliminary deformation.

A phenomenological softening term dependent uponthe ultrasonic energy density per unit time has been intro-duced in the relations of isotropic and kinematic hardeningterms (Eqs. (10) and (12)). The modified equations of iso-tropic and kinematic hardening are given by

Rultrasonic ¼ Rth � ð1� d � EultrasonicÞ2 ð13Þaultrasonic ¼ ath � ð1� d � EultrasonicÞ2 ð14Þ

where Rth is the isotropic hardening rule with thermal soft-ening, defined in Eq. (10), d is ultrasonic softening param-eter which has to be identified from experiments ofdeformation behaviour of the material in the presence ofultrasonic energy. Eultrasonic is the ultrasonic energy densityper unit time transferred from the sonotrode to the mate-rial. ath is the kinematic back stress term with thermalsoftening, defined in Eq. (12).

The above discussed hardening models, Eqs. (10)–(14),are implemented in ABAQUS user subroutine UHARD(user-defined hardening subroutine). This user subroutineis called at all material integration points of elements forwhich the material definition includes user-defined isotro-pic or cyclic hardening for metal plasticity (ABAQUS, 2006).This user subroutine can be used to define a material’s iso-tropic yield behaviour, the size of the yield surface in acombined hardening model or material behaviour depen-dent on field or state variables. The implementation is verystraight forward. The UHARD user subroutine requires

Table 1Thermal and mechanical properties of AA 6060/6061

Thermal properties Elastic properties

Thermal conductivity 235 W/m K Young’s modulus 66.24 GPaThermal expansion

coefficient23.4e�6/�C Poisson’s ratio 0.33

Specific heat 896 J/kg K Yield stress 50 MPaDensity 2700 kg/m3


three quantities to be defined, i.e. Hardening model (Eqs.(10)–(14)), rate of change of hardening rule with respectto the accumulated plastic strain �epl, which is given by

dRultrasonic

d�epl ¼Q �b �e�b�epl ð1� hmÞ � ð1�d �EultrasonicÞ2 ð15Þ

daultrasonic

d�epl ¼ Ce�c�epl �a1 �c �e�c�epl� �

ð1�hmÞ � ð1�d �EultrasonicÞ2

ð16Þ

And rate of change of hardening rule with respect to thetemperature, which is given by

dRultrasonic

dh¼ � Q �m � ð1� e�b�epl Þ

h

� ðhm�1Þðhmelt � htransitionÞ

#� ð1� d � EultrasonicÞ2 ð17Þ

daultrasonic

dh¼ �

"Ccð1� e�c�epl Þ þ a1 � e�c�epl

� �

� ðhm�1Þðhmelt � htransitionÞ

#� ð1� d � EultrasonicÞ2 ð18Þ

The above discussed nonlinear isotropic/kinematic harden-ing law requires the identification of six parameters(Q, b, C, c, m, d) from cyclic stress–strain data, thermal soft-ening data and acoustic (ultrasonic) softening data.

It should be noted that the presented plasticity modelhas been used in the framework of finite deformation the-ory based on spatial configuration (ABAQUS, 2006). Selec-tion of the infinitesimal strain or finite strainformulation, which requires the selection of appropriatework conjugate stress and strain measures (Green andNaghdi, 1965; Hill, 1970; Simo and Miehe, 1992), is basedon the keyword NLGEOM available in ABAQUS (2006).Detailed discussion about the formulation is available inABAQUS (2006), which is not repeated here for brevity.

Also, the theory presented in this work is a particulartype of thermomechanical Mises plasticity theory withanalytical forms of the hardening law. Thermodynamicalconsistency of such theories for infinitesimal and finitedeformation cases has been discussed in detail in Simoand Miehe (1992), Abed and Voyiadjis (2007), Ristinmaaand Vecchi (1996), and Chaboche (1989). It should benoted that current plasticity theory has an additional inde-pendent state variable (ultrasonic energy, Eultrasonic). Thismeans that the Helmholtz free energy function is a func-tion of elastic strain ðeel

ij Þ, internal state variables (harden-ing rule bn; n = 1,2, . . . n), temperature (h), gradient oftemperature (rih) and additionally ultrasonic energy(Eultrasonic). The modified Helmholtz free energy functionis given by

w ¼ wðeelij ;bn; h;rih; EultrasonicÞ

This potential when substituted in thermodynamicinequality obtained from the conservation of energy andthe Clausius–Duhem inequality (refer to Chaboche, 1989)ends up with an additional term which involves partialderivative of the Helmholtz free energy function with re-spect to the ultrasonic energy (Eultrasonic) times the time

derivative of ultrasonic energy (Eultrasonic). This additionalterm is given by ow

oEultrasonic� _Eultrasonic. Similar to _eel

ij and _h(Chaboche, 1989), Eultrasonic is also an observable variableand for the validity of the inequality ow

oEultrasonic¼ 0. Therefore,

the rest of the dissipation inequality preserves the form ofChaboche (1989).

Using the presented approach in Chaboche (1989) andSimo and Miehe (1992), one can obtain a similar free en-ergy function which is a function of thermal potential,themomechanical coupling potential, elastic potential andhardening potential (Simo and Miehe, 1992).

It should also be noted that term phenomenological hasbeen used in the sense that hardening and softening rulesare defined as analytical functions and does not take intoaccount basic physical mechanisms involved which couldbe the outlook of this research area. For example, usingmicromechanics based material models which take intoaccount activation of slip systems or dislocations due tothermal and acoustic energies. These models could bebased on crystal plasticity framework (Siddiq et al., 2007)or discrete dislocation models (Hartmaier et al., 2005).

3.4. Material parameter identification

The material model discussed above with nonlinear iso-tropic and kinematic hardening rules along with thermo-mechanical coupling and ultrasonic softening, involvessix material parameters (Q, b, C, c, m, d). The role of thesematerial parameters has been discussed in the previoussection. The identification of these material parameters isperformed using inverse modelling method. In this methodexperimental stress–strain curves are compared with thesimulated stress–strain curves for each set of parametersand the difference between the experimental and simu-lated stress–strain curves is minimized by the variationof these parameters. The process is repeated until a goodagreement is achieved between experimental and simu-lated stress–strain curves. To identify large number ofparameters, such as for the case of crystal plasticity theory,when number of unknown parameters ranges between 7and 30, an automatic identification procedure has beenproposed in Siddiq and Schmauder (2005) and Siddiq(2006). In the present study there were only six parame-ters involved, therefore, the identification of these param-eters has been performed manually.

The thermal and mechanical properties, taken fromDavis (1993), Kong (2005), are given in Table 1.

The identified set of isothermal material parameters(Q, b, C, c) are given in Table 2 and the comparison of theexperimental and simulated stress–strain curves is shownin Fig. 2.

Table 2Identified nonlinear isotropic/kinematic hardening parameters

Q (MPa) b C (GPa) c

100 20.0 15.0 60.0

0

10

20

30

40

50

60

0 50 100 150 200 250 300 350Temperature (deg. C)

Initi

al Y

ield

ing

(MPa

)

Experimental (J.G. Kaufman,1999)Simulated

Fig. 3. Comparison between experimental and simulated initial yieldingas a function of temperature.

0

10

20

30

40

50

60

0.0E+00 1.0E+05 2.0E+05 3.0E+05 4.0E+05 5.0E+05 6.0E+05Ultrasonic Energy (W/m2)

Yiel

d St

ress

(MPa

)

Experimental (Langenecker, 1966)Simulated

Fig. 4. Effect of ultrasonic energy per unit time on initial yielding.


The experimental fit for the temperature dependent ini-tial yielding has been performed using the experimentaldata obtained from Kaufman (1999) and Davis (1993) foraluminium alloy 6061. The best fit to the experimentaltemperature dependent initial yielding is shown in Fig. 3,with m = 1.642081.

The ultrasonic softening parameter (d) has been identi-fied by comparing the experimental results of ultrasonicsoftening (Langenecker, 1966) of aluminium. The value ofultrasonic softening parameter (d) is found to be1.3 � 10�6 m2/W. The experimental and simulated initialyield stress as a function of ultrasonic energy density perunit time is plotted in Fig. 4. The results in figure show agood agreement.

The final set of six material parameters for aluminiumalloy 6061 is given in Table 3.

4. Friction model

Friction and wear plays an important role during thesliding of two surfaces under cyclic loading, such as highcycle fatigue in turbine blades and ultrasonic processes,etc. In this work a friction law has been proposed whichcomprises of static and kinematic friction components.

A time dependent friction coefficient was proposed inGao and Doumanidis (2002), ultrasonic welding processwas analyzed using finite element methods. It was as-sumed that friction coefficient is uniform at all locations

-250

-200

-150

-100

-50

0

50

100

150

200

250

-1.6 -1.2 -0.8 -0.4 0

Strain

Stre

ss (M

Pa)

Fig. 2. Comparison between experimental and simulat

of the unbonded foil–substrate interface surface. Atime dependent friction coefficient was defined using the

0.4 0.8 1.2 1.6

(%)

Initial Cycle (Experiment)Initial Cycle (Simulation)40th Cycle (Experiment)40th Cycle (Simulation)

ed stress–strain curves of initial and 40th cycle.

Table 3Final set of parameters for aluminium alloy 6061

Q (MPa) b C (GPa) c m d

100 20.0 15.0 60.0 1.642081 1.3 � 10�6 m2/W

Contact Pressure = 50 MPa

0

0.2

0.4

0.6

0.8

1

1.2

1.4

10 210 410 610 810Number of Cycles

Coe

ffici

ent o

f Fric

tion

Max. Cyc. Stress 169 MPa Max. Cyc. Stress 193 MPa Max. Cyc. Stress 217 MPaMax. Cyc. Stress 243 MPa Max. Cyc. Stress 265 MPa

Fig. 5. Coefficient of friction as a function of number of cycles (Naidu andRaman, 2005).


experimentally measured strain on the substrate surfaceand adjacent to the ultrasonic probe. It was shown thatfriction coefficient increases almost linearly until a specifictime and then remains the same and then starts decreasingas time progresses. Fretting fatigue behaviour of AA 6061was studied experimentally in Naidu and Raman (2005).The effect of different parameters, such as contact pres-sure, stress amplitude and number of cycles, on coefficientof friction was studied. It was found that coefficient of fric-tion decreases with the increasing contact pressure. It wasalso found that, as the number of cycles increases, the coef-ficient of friction also increase and after a certain numberof cycles it saturates to a steady value. Effect of ultrasonicon upsetting of a model paste was analyzed in Huang et al.(2002). A constant coefficient of friction was used based onCoulombs friction model. As soon as the ultrasonic vibra-tion is applied on the specimen, the friction coefficientwas reduced to simulate the experimental behaviour. Thelimitations of a constant coefficient of friction in Coulomb’sfriction model have been studied in Naboulsi and Nicholas(2003). A non-classical Coulomb’s friction model wasdeveloped which allow the coefficient of friction to be afunction of local contact pressure and local slip magnitude.It was shown that with different combinations of the pro-posed model parameters provide better comparison withexperimental stress states. Effect sliding velocity and tem-perature on coefficient of friction of aluminium alloy wasstudied in Zhang et al. (2006). It was found that velocityhas no effect on the friction coefficient while friction coef-ficient increases as the temperature increases until 150 �Cand then starts decreasing. A phenomenological model ofvariable friction coefficient, for the 2D cases, in fretting fa-tigue process has been proposed in Cheikh et al. (2006).The proposed model is based on kinematic and isotropichardening of the coefficient of friction as a function ofaccumulated slip between the contacting surfaces. Thefriction model consisted of three parts static friction coef-ficient, isotropic friction behaviour and kinematic frictionbehaviour. In other studies, such as (Cheikh et al., 2006;Dick and Cailletaud, 2006; Petiot et al., 1995; Stromberg,1999), coefficient of friction has always been assumed tobe constant. On the other hand, as discussed above, exper-imental studies performed in Cheikh et al. (2006), Gao andDoumanidis (2002), Huang et al. (2002), Naboulsi andNicholas (2003), Naidu and Raman (2005), and Zhang etal. (2006), found that the coefficient of friction is not a con-stant. It was also found (Cheikh et al., 2006; Gao andDoumanidis, 2002; Huang et al., 2002; Naboulsi andNicholas, 2003; Naidu and Raman, 2005; Zhang et al.,2006) that the coefficient of friction depends upon slip mag-nitude, contact pressure, number of cycles and temperature.In the following, a friction model based on Coulomb’s stick/slip formulation has been proposed by taking into accountphysical quantities, such as, slip magnitude, contact pres-sure, number of cycles and temperature.

4.1. Description of the friction model

The friction model proposed in this work is based on thedependence of coefficient of friction l, on number of cyclesN, temperature T, and parameters a and b which dependupon magnitude of slip and contact pressure.

The friction model proposed in this work is based on thefriction experiments performed in Cheikh et al. (2006), Gaoand Doumanidis (2002), Huang et al. (2002), Naboulsi andNicholas (2003), Naidu and Raman (2005), Zhang et al.(2006). As discussed before, Naidu and Raman (2005)found that coefficient of friction increases with increasingnumber of cycles and after a certain number of cycles, coef-ficient of friction saturates to a steady value (Fig. 5).

A simple logarithmic correlation has been used to de-fine the experimental friction behaviour. The correlationis given by

liso ¼ ls þ ls � ða � logðNÞ þ bÞ ð19Þ

where a and b are friction parameters depend upon themagnitude of the slip amplitude and contact pressure,while ls is the initial static coefficient of friction, and N isnumber of cycles. The values of a and b are determinedfrom the experimental results of AA 6061 presented inNaidu and Raman (2005). For the case of contact pressureof 50 MPa and stress amplitude of 193 MPa (equivalentto a slip magnitude of 8.4 mm for the case of AA 6061)are found to be a = 0.323 and b = �0.1. The comparison ofthe model with the experimental result for this case isshown in Fig. 6.

The values of a and b are identified for other contactpressure and displacement amplitudes. The values identi-fied are given in Table 4. In order to implement the valuesof a and b as a function of contact pressure and displace-ment amplitude, a correlation has been deduced. The cor-relation is of the form:

a ¼ a1 � a2 � P ð20Þ

and

b ¼ b1 � b2 � P ð21Þ

The values of a1, a2, b1, and b2 are identified from thealready given values of a and b for different contact

0

0.2

0.4

0.6

0.8

1

1.2

1.4

10 110 210 310 410 510 610 710 810 910Number of Cycles

Co

effi

cien

t o

f F

rict

ion Experiment (Naiduand Raman, 2005 )

Friction Model

Contact Pressure = 50 MPa

Displacement amplitude = 8.4 μm

a = 0.323; b = -0.1

Fig. 6. Comparison between friction model and experiments (Naidu andRaman, 2005) for a contact pressure = 50 MPa and stressamplitude = 193 MPa.

Table 5Identified values of a1, a2, b1, and b2 for different displacement amplitudes

Displacementamplitude (lm)

a1 a2 b1 b2

8.4 0.362 0.000827 �0.07303 0.00059210.4 0.25 �0.00033 �0.1447 0.00031312.4 0.2924 0.00054 �0.18218 0.0001514.4 0.2192 0.0000854 �0.2157 0.000015

Table 6Friction parameters for temperature dependent friction coefficient

p q r S t

8.485e�10 �8.842e�7 1.969e�4 �9.762e�3 1.12

Fig. 7. Coefficient of friction as a function of temperature (experimentsand friction model).


pressures. The values are given in Table 5 for different dis-placement amplitude values.

The temperature dependence of coefficient of friction isintroduced using the experimental observation in Zhang etal. (2006). Zhang et al. (2006) studied the friction behav-iour of aluminium allow at different temperatures. It wasfound that coefficient of friction increases with the increas-ing temperature until a specific temperature and then de-creases. This temperature dependence has been taken intoaccount by including an additional fourth order polyno-mial as a function of temperature. The modified coefficientis given by

l ¼ liso � ðp � T4 þ q � T3 þ r � T2 þ s � T þ tÞ ð22Þ

The additional friction parameters p, q, r, s, t are identifiedusing the experimental results (Zhang et al., 2006) for alu-minium alloy and are given in Table 6 while experimentaland friction model results are plotted in Fig. 7.

4.2. Implementation of the friction model

The proposed friction model has been implemented inABAQUS user subroutine (FRIC) to define user frictionmodel. The implementation is based on Coulomb’s fric-tion law with stick–slip algorithm (ABAQUS, 2001) withjsfricj 6 l � P, i.e. if jsfric < l � P then stick and if jsfricj = l � P

Table 4Values of a and b identified from experimental results (Naidu and Raman, 2005)

Contact pressure 25 MPa 30 MPa 50 MPa

Amplitude of vibration = 8.4 lma 0.328 0.327 0.323b �0.098 �0.0985 �0.1




then slip. The numerical implementation of simpleCoulomb’s friction law with constant friction coefficienthas been discussed in ABAQUS (2001). In this work, thealready available friction subroutine (ABAQUS, 2001)has been modified by including Eqs. (19)–(22)). Thishad been done by replacing the constant coefficient offriction with a coefficient of friction that is dependentupon temperature, contact pressure, amplitude of vibra-tion and number of cycles.

100 MPa 125 MPa 155 MPa 175 MPa

0.3095 0.2787 0.2267 0.1945�0.1098 �0.1321 �0.17 �0.1933

0.275 0.2825 0.2975 0.32�0.1675 �0.1775 �0.191 �0.21

0.25116 0.2388 0.2091 0.1824�0.1920 �0.196 �0.2054 �0.214

0.2035 0.199 0.188 0.1782�0.217 �0.2172 �0.2176 �0.219


5. Ultrasonic welding model and boundary conditions

Typical ultrasonic metal welding setup is shown inFig. 8. The welding setup consists of three main compo-nents, a foil, a substrate and a sonotrode (attached to theultrasonic welding unit). Substrate is fixed to an anvil atthe bottom surface, a foil is placed at the top surface ofthe substrate and with the help of the sonotrode load is ap-plied in the vertical direction (as shown in Fig. 8). Thesonotrode vibrates at a frequency of 20 kHz in the directionperpendicular to the rolling (welding) direction.

The process parameters during ultrasonic welding areapplied load (Papplied), velocity of sonotrode (V), frequencyof the ultrasonic vibration (f) and amplitude of vibrationwhich are normally varied in order to check the effect ofeach of these parameters on weld quality.

The geometric parameters for the present study arewidth of the specimen (w) 20 mm, thickness of the sub-strate (ts) 1 mm, thickness of the foil (tf) 100 lm. The ra-dius of the sonotrode used in the present study is 25 mm(Kong, 2005). In the present work, effect of the ultrasonicwelding process parameters (applied load, velocity ofsonotrode, and amplitude of ultrasonic vibration) is stud-ied. Frequency of the ultrasonic vibration (f = 20 kHz) is al-ways kept constant during the present study. The appliedload is varied from 25 to 175 MPa. The amplitude of vibra-tion is varied from 8.4 to 14.4 lm while velocity of sono-trode is varied from 27.8 to 38.8 mm/s.

Finite element analyses of the ultrasonic welding spec-imen have been performed using coupled temperature–displacement analysis. The finite element model has beenconstructed for a small region of approximately 2 mm, asshown in Fig. 9. The selected width of the model (2 mm)has been chosen based on the width of the contact areaduring the specific weld cycle (which ranges from 0.133to 0.324 mm depending upon applied loading). This sizeof the model is chosen so that the distance of the weld areais far enough from the boundary. The geometry of themodel from the side view is shown in Fig. 10. As discussedabove, foil has the dimensions of 2 mm � 20 mm � 0.1 mm

ts

Substrate

Foil

S o n o tro d e

w

tf

fV

P a p p lie d

ts

Substrate

Foil

S o n o tro d e

w

tf

fV

P a p p lie d

Substrate

Foil

S o n o tro d e

w

tf

fV

P a p p lie d

Fig. 8. Ultrasonic metal welding setup.

while substrate is of dimensions 2 mm � 20 mm � 1 mm(20 mm is in the direction orthogonal to the side viewshown in Fig. 10). In reality, sonotrode is a solid cylindricalshaped bar (Kong, 2005), however to save computationtime the geometry of the sonotrode during this work hasbeen modelled as hollow with an inner diameter of50 mm and outer diameter of 50.4 mm (Fig. 10). Thechoice of thickness of the hollow sonotrode walls(0.2 mm) is based on heat conducted through sonotrode.The thickness chosen in this work ensures that the heatgenerated at the foil/sonotrode interface does not reachthe inner surface of the hollow sonotrode modelled in thiswork. Process parameters used during the simulations, i.e.velocity of sonotrode, applied load and vibration ampli-tudes, are applied through a reference point associatedwith the sonotrode as shown in Fig. 10. Normal load is ap-plied in the vertical direction; rolling velocity of the sono-trode is applied using the velocity boundary condition inthe rolling direction (as shown in Fig. 10) while ultrasonicvibration is applied orthogonal to the side view in Fig. 10using displacement boundary conditions with a periodicamplitude curve (A = Amaxsinxt). Where A is the ampli-tude of the vibration dependent on time, Amax is the max-imum amplitude of the vibration, x is the angular velocityand t is the total time. The values of the process parame-ters used are already given in the previous paragraph. Thebottom surface of the substrate is fixed in all directions aswas during the real experiments (Kong, 2005). Initial tem-perature of 20 �C has been prescribed to the completegeometry. For the current analyses all the free edges(other than the contact surfaces and left and right edgesin Fig. 10) in the model are under free convection withconvection coefficient of 30 W/m K and ambient tempera-ture of 20 �C. The left and right edge boundaries are as-sumed to be at 20 �C, by prescribing the temperatureboundary condition. These temperature boundary condi-tions have been used, based on the experimental findingsof Cheng and Li (2007), which showed that for differentweld times the temperature away from the weld regionsdecrease as one moves away from the weld area. Also,heat flux has been tracked during all the simulationsand it has also been found that heat flux never reachedthese boundaries as the weld time is very small, i.e. 4–9 ms, which also makes the assumption of temperature(20 �C) valid for left and right edges. The bottom surfaceof substrate and top surface of the sonotrode are also keptat 20 �C. Throughout this work foil and substrate havebeen modelled using material properties of aluminium al-loy 6061 (see Section 3.4) while sonotrode is modelled assteel (elastic) with properties given in Table 7.

Finite element mesh consisted of 31,842 coupled tem-perature-displacement elements (C3D8RT). Thermome-chanical interaction properties between foil/sonotrodeinterface and foil/substrate interface are discussed in thefollowing. The normal contact properties between foil/sonotrode interface and foil/substrate interface are definedusing hard contact formulation available in ABAQUS(2006). In this contact formulation contact constraint is en-forced with a Lagrange multiplier representing the contactpressure in a mixed formulation (ABAQUS, 2006). In thiscase

Foil

Reference Point Associated with Sonotrode

Rolling Velocity of sonotrode

Applied Load

2

0.1

1

R25

R250.2

All dimensions are in millimetres

*Ultrasonic vibration is orthogonal to this plane

Foil

Substrate

Sonotrode

Reference Point Associated with Sonotrode

Rolling Velocity of sonotrode

Applied Load

2

0.1

1

R25

R250.2

Al millimetres

*Ultrasonic vibration is orthogonal to this plane

Fig. 10. Geometry of ultrasonic welding specimen (side view).

ts

Substrate

Foil

Sonotrode

w

tf

fV

Papplied

2 mm2 mm

1 mm

Path, parallel to the direction of vibration

ts

Substrate

Foil

Sonotrode

w

tf

fV

Papplied

2 mm2 mm

1 mm


ts

Substrate

Foil

Sonotrode

w

tf

fV

Papplied

2 mm2 mm

1 mm

ts

Substrate

Foil

Sonotrode

w

tf

fV

Papplied

2 mmts

Substrate

Foil

Sonotrode

w

tf

fV

Papplied

ts

Substrate

Foil

Sonotrode

w

tf

fV

Papplied

Substrate

Foil

Sonotrode

w

tf

fV

Papplied

2 mm2 mm

1 mm


Fig. 9. Finite element model of ultrasonic welding specimen.


p ¼ 0 for h < 0 ðcontact is openÞ;p > 0 for h ¼ 0 ðcontact is closedÞ;

where h is the contact closure.

The friction properties between foil and substrate con-tact surface is defined using the thermomechanical frictionmodel proposed in this work (Section 4). Friction proper-ties used are already discussed in Section 4. The friction

Table 7Thermal and mechanical properties of sonotrode (steel)

Thermal properties Elastic properties

Thermal conductivity 80 W/m K Young’s modulus 200 GPaThermal expansion

coefficient11e�6/�C Poisson’s ratio 0.27

Specific heat 440 J/kg KDensity 7800 kg/m3

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 20 40 60 80 100 120 140 160 180 200Applied Pressure (MPa)

Fric

tion

wor

k (m

J/m

m2 )

8.4 micron10.4 micron12.4 micron14.4 micron

Fig. 12. Friction work at foil/substrate interface, velocity = 34.5 mm/s.


coefficient for sonotrode/foil interface (steel/aluminium) isdefined using a pressure dependent isothermal coefficientfriction in Coulomb’s friction model. The pressure depen-dent coefficient of friction between sonotrode and foil isplotted in Fig. 11. Through out this work it is assumed thatall of the friction energy generated between different con-tacting surfaces is converted into heat energy. This hasbeen achieved by using ‘‘gap heat generation” option al-ready available in ABAQUS (2006). With the help of thisoption, user can define what fraction of the friction energyis converted into heat. For the present study this fraction isset to 1, i.e. all of the friction energy is converted into heatenergy. It is also assumed that the heat energy is equallytransferred to both the contacting surfaces in every inter-face. Results of the thermomechanical ultrasonic weldinganalyses have been discussed in the following.

6. Results and discussion

6.1. Effect of applied load and displacement amplitude onfriction work between foil/substrate interface

The friction work at the interface of foil and substrate isplotted in Fig. 12. These values are obtained when frictionwork saturates (approximately after 22–28 cycles for theapplied loading between 25 and 175 MPa). The resultsplotted in Fig. 12 are for the case when velocity of sono-trode was 34.5 mm/s. It is found that as the applied loadincrease the friction work at the interface of foil and sub-strate decrease. It has been found that this decrease in fric-tion work has two main reasons, friction dissipation at thefoil/sonotrode interface (surface effect) and ultrasonic soft-ening of the foil material (volume effect).

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0 20 40 60 80 100 120 140 160 180 200Contact Pressure (MPa)

Coe

ffici

ent o

f Fric

tion

Fig. 11. Coefficient of friction (measured) between sonotrode (steel) andfoil (aluminium alloy).

Both of these factors are found to decrease the transferof ultrasonic vibration due to softening of the foil material.The softening comprises of two parts, i.e. thermal softening(surface effect) which is due to the friction dissipation atthe interface and ultrasonic softening which is due to theultrasonic energy being transferred to the material. Thefirst factor, i.e. the friction dissipation at foil/sonotrodeinterface causes higher plastic dissipation at the foil/sono-trode interface as the applied load increases. The increasein plastic dissipation in foil at foil/sonotrode interface isdue to the higher thermal softening, i.e. increasing temper-ature because of increasing heat generation. The equiva-lent plastic strain at a point in the middle of the foilsurface which is in contact with the sonotrode is plottedin Fig. 13. The results plotted in Fig. 13 are for the casewhen velocity of sonotrode was 34.5 mm/s and amplitudeof ultrasonic vibration was 8.4 lm. The plot shows that asthe applied loading increases the amount of plastic strainincreases which is due to the increase in friction dissipa-tion at the foil/sonotrode interface. The second factor, i.e.ultrasonic softening of foil material (volume effect) also re-sults in higher plastic deformation as the loading is in-creased. It is found that ultrasonic energy transferred to

0

10

20

30

40

50

60

70

80


Equi

vale

nt P

last

ic S

trai

n

Fig. 13. Equivalent plastic strain in foil at foil/sonotrode interface(amplitude = 8.4 rmum; velocity = 34.5 mm/s).


the foil increases with the increasing load, i.e. making itsofter. The plot of the ultrasonic energy per second trans-ferred to the foil material at different points in the foilalong the thickness direction is plotted in Fig. 14. It canalso be seen that ultrasonic energy transferred in the foilalong the thickness direction decreases as one moves fromsonotrode surface towards substrate surface.

It can also be seen in Fig. 12 that as the amplitude ofultrasonic vibration increase, the friction work at the inter-face of foil and substrate decrease. This shows that theincreasing amplitude of ultrasonic vibration has the similareffect as that of the increasing load. The reasons are theultrasonic softening (volume effects) and thermal soften-ing due to friction (surface effects). As the amplitude ofultrasonic vibration increase the ultrasonic energy trans-ferred per second also increase resulting into higher soft-ening. Ultrasonic energy per second transferred to thefoil at foil/sonotrode interface is plotted in Fig. 15. The plotin Fig. 15 shows that as the amplitude of ultrasonic vibra-tion increases the amount of ultrasonic energy transferredalso increases.

Also, as the amplitude of ultrasonic vibration increasefriction dissipation increase causing higher equivalentplastic strains at foil/sonotrode interface.

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

0 0.02 0.04 0.06 0.08 0.1 0.12Distance along the thickness direction of the Foil (mm)

Ult

raso

nic

Po

wer

(W

/m2 ) 25 MPa

40 MPa 125 MPa 155 MPa 175 MPa

Fig. 14. Ultrasonic energy per second transferred to the foil along thethickness direction.

0

10000

20000

30000

40000

50000

60000

70000

80000

8 10 11 12 13 14 15Amplitude of ultrasonic vibration (μm)

Ultr

ason

ic P

ower

(W/m

2 )

9

Fig. 15. Ultrasonic energy per second transferred to the foil at foil/sonotrode interface (velocity = 34.5 mm/s; applied load = 25 MPa).

6.2. Effect of sonotrode velocity on friction work betweenfoil/substrate interface

Friction work as a function of velocity of sonotrode fordifferent applied loads and constant vibration amplitude(8.4 lm) has been plotted in Fig. 16. It can be inferred fromthe plot that as the velocity of the sonotrode increase, thefriction work also increases. This can be explained on thebasis of higher loading rate of the sonotrode which allowsless number of cycles to reach up to the specific appliedload when compared with smaller velocities of sonotrode,resulting in less thermal softening due to friction dissipa-tion at foil/sonotrode interface. This lesser thermal soften-ing at the foil/sonotrode interface increase the ultrasonicenergy transferred to the foil/substrate interface resultingin higher friction dissipation.

Similar trend of friction work has been found for differ-ent amplitudes of the ultrasonic vibration. Fig. 17 showsthe plot of friction work between foil/substrate interfaceas a function of velocity for different displacement ampli-tudes and constant applied load (155 MPa). It can be seenthat as the amplitude of the ultrasonic vibration increasesthe friction work also increase. The reason is the same as

0

0.01

0.02

0.03

0.04

0.05

0.06

25 30 35 40 45Velocity (mm/sec)

Fric

tion

Wor

k (m

J/m

m2 ) 25 MPa

100 MPa125 MPa155 MPa175 MPa

Vibration amplitude = 8.4 micron

Fig. 16. Friction work between foil/substrate interface as a function ofvelocity of sonotrode (vibration amplitude = 8.4 lm).

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

25 30 35 40 45

Velocity of Sonotrode (mm/sec)

Fri

ctio

n w

ork

(m

J/m

m2 ) 8.4 micron

10.4 micron12.4 micron14.4 micron

Applied load = 155 MPa

Fig. 17. Friction work between foil/substrate interface as a function ofvelocity of sonotrode (applied load = 155 MPa).


explained above, i.e. higher the velocity, higher is the load-ing rate which allow less number of cycles to reach up tothe specific applied load, resulting in less thermal soften-ing due to friction dissipation at foil/sonotrode interface.

6.3. Plastic deformation

As discussed in the previous section, plastic deforma-tion in the specimen is caused by two different phenom-ena, namely surface and volume effects. It was alsoshown in the previous section that as the applied load in-creases the plastic deformation in the foil at foil/sonotrodeinterface increases (Fig. 18). This is due to the increase infriction dissipation (surface effect) at foil/sonotrode inter-face along with the increasing ultrasonic softening (volumeeffect) due to ultrasonic energy transferred from sonotrodeto the foil. Fig. 19 shows the plot of equivalent plasticstrain in the foil at foil/substrate interface. It is found thatas the applied load increases the equivalent plastic strainalso increases until a loading value which is enough tocause plastic deformation in the material without theapplication of ultrasonic vibration and after this loadingequivalent plastic strains saturate.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07


Equi

vale

nt P

last

ic S

trai

n

Fig. 18. Equivalent plastic strain in the foil at foil/substrate interface(amplitude = 8.4 rmum; velocity = 34.5 mm/s).

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0 50 100 150 200Applied Load (MPa)

Eq

uiv

alen

t P

last

icS

trai

n

Fig. 19. Equivalent plastic strain in the substrate at foil/substrateinterface (amplitude = 8.4 rmum; velocity = 34.5 mm/s).

Similar behaviour has been shown by the substrate, asshown in Fig. 19. The plot in Fig. 19 shows that as theamount of applied load increases the plastic deformationalso increases until a loading value which causes plasticdeformation before the ultrasonic vibration has beenstarted.

Comparison of Figs. 13, 18, and 19 shows that the re-gions of the foil near foil/sonotrode interface undergo se-vere plastic deformation. This high plastic deformation isdue to high friction dissipation and ultrasonic energytransferred to the foil near foil/sonotrode interface (Figs.14 and 15). It can also be inferred from Figs. 18 and 19 thatamount of plastic deformation in foil near the foil/sub-strate interface is almost twice as high as the plastic defor-mation in the substrate. As explained before the reason forhaving larger plastic deformation in foil is due to the dualeffect, i.e. surface (friction dissipation at foil/substrateinterface) and volume (ultrasonic softening) effects. Onthe other hand the substrate has only the surface effects,i.e. friction dissipation at the foil/substrate interface, tocause plastic deformation.

6.4. Temperature at the interfaces

As discussed in Section 1, temperature of the specimendue to the friction dissipation at the interface is found to beonly 15–55% of the melting temperature (650 �C) of AA6061 for various applied loads. Figs. 20–22 show the plotsof the temperature profile at foil and substrate surfaces atfoil/sonotrode and foil/substrate interface. The tempera-ture profile is plotted along the path which is parallel tothe direction of sonotrode vibration and orthogonal tothe sonotrode rolling direction (see Fig. 9).

The plot in Fig. 20 shows that as the amount of appliedload increases the temperature of the foil surface at foil/sonotrode also increases and this causes larger thermalsoftening as discussed in the previous sections. It shouldalso be noted that temperatures are well below the metingtemperature of AA 6061, i.e. 650 �C.

Fig. 21 shows the plot of temperature profile at foil sur-face at foil/substrate interface along the path parallel to thedirection of the vibration of sonotrode. The plot shows thesimilar trend as discussed above, i.e. the increase of tem-perature with increasing applied load. The temperature isagain found to be well below the melting temperature ofAA 6061.

The plot of temperature profile at substrate surface atfoil/substrate interface is shown in Fig. 22. The tempera-ture is again found to be increasing with increasing appliedload. Also, the temperature is found to be 10–37% of themelting temperature of the AA 6061. The results are inagreement with the experimental results of Cheng and Li(2007), it was found that temperature for the case of cop-per and nickel were found to be in the range of 100–250 �C,i.e. copper and nickel never reach to the melting tempera-ture during ultrasonic welding.

One of the most important conclusion which can be in-ferred from Figs. 20–22 is, there exists a temperature gra-dient from sonotrode to the foil and then to the substrate.This can be identified from Figs. 20–22 that highest tem-perature is at foil/sonotrode interface then it starts

0

50

100

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250

300

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400

0 4 8 10 12 14 16 18 20Distance along the path in the direction of sonotrode vibration (mm)

Tem

pera

ture

(deg

. C)

25 MPa

100 MPa

125 MPa

155 MPa

175 MPa

2 6

Fig. 20. Temperature of foil surface at foil/sonotrode interface (amplitude = 8.4 rmum; velocity = 34.5 mm/s).

0

50

100

150

200

250

300

350

0 10 12 14 16 18 20Distance along the path in the direction of sonotrode vibration (mm)

Tem

per

atu

re (

deg

. C)

25 MPa

100 MPa

125 MPa

155 MPa

175 MPa

2 4 6 8

Fig. 21. Temperature of foil surface at foil/substrate interface (amplitude = 8.4 rmum; velocity = 34.5 mm/s).


decreasing as the one move towards the foil/substrateinterface. This important conclusion justifies the argumentgiven in many experimentalists, that friction only plays asecondary role during ultrasonic welding, i.e. it is only re-quired to break and disperse the surface impurities and

oxide layers. The main bonding mechanism is mechanicalinterlocking of atoms when two surfaces are in contact atatomic scale, i.e. the clearance between the two surfacesis in atomic distances. This small atomic distance is thenenough for the surface atoms to form a bond.

0

50

100

150

200

250

300

0 4 8 10 12 14 16 18 20Distance along the path in the direction of sonotrode vibration (mm)

Tem

pera

ture

(deg

.C)

25 MPa

100 MPa

125 MPa

155 MPa

175 MPa

2 6

Fig. 22. Temperature of substrate surface at foil/substrate interface (amplitude = 8.4 rmum; velocity = 34.5 mm/s).


6.5. Friction stress at the foil/substrate interface

Kumar and Hutchings (2004) performed experimentalstudies on the friction behaviour of metals under longi-tudinal and transverse ultrasonic vibration. The materials

0

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60

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160

180

8 10 11Amplitude of Ultras

Fric

tion

Stre

ss a

tFoi

l/Sub

stra

te In

terf

ace

(MPa

)

175 M

25 MPa

9

Fig. 23. Friction stress at foil/substrate

studied were aluminium, brass, copper, and stainlesssteel. They found that the as the amplitude of the ultra-sonic vibration increases the friction stresses decrease.The reduction in friction observed was in the range of60–80%. Fig. 23 shows the plot of friction stress at foil/

12 13 14 15onic Vibration (μm)

Pa

interface (velocity = 34.5 mm/s).


substrate interface as a function of amplitude of ultra-sonic vibration of sonotrode. The results are plotted fortwo different applied loads, i.e. 25 and 175 MPa. It canbe inferred from the plot in Fig. 23 that as the amplitudeof ultrasonic vibration increases the amount of frictionstress decreases and the decrease for these two loadcases is found to be 48% and 57.5%, respectively. Thereduction of friction stresses under ultrasonic vibrationshow similar behaviour as was observed during theexperiments (Kumar and Hutchings, 2004). As explainedin the previous sections, this reduction in friction stres-ses is due to the ultrasonic and thermal softening ofthe material.

6.6. Comparison with experimental results

In order to compare the simulated results with theexperiments, peel tests are performed on the AA 6061specimen welded at an applied load of 155 MPa and avelocity of sonotrode equals to 34.5 mm/s. Using the peeltest force–displacement curves, fracture energies havebeen computed using the procedure described in Korn etal. (2002), Siddiq and Schmauder (2005, 2006), and Siddiqet al. (2007).

Friction work between foil/substrate interface andfracture energies computed from peel test curves areplotted in Fig. 24 as a function of amplitude of ultrasonicvibration for an applied load of 155 MPa. It can be in-ferred from Fig. 24 that as the amplitude of ultrasonicvibration increase the experimental fracture energy ob-tained from peel tests decrease. Similar trend can be seenin Fig. 24 for friction work at the foil/substrate interface,i.e. as the amplitude of ultrasonic vibration increase fric-tion work at the foil/substrate interface decrease. The rea-son for the decrease in experimental fracture energy can

0.005

0.0055

0.006

0.0065

0.007

0.0075

0.008

0.0085

8.4 10.4Amplitude of ultraso

Fri

ctio

n w

ork

(m

J/m

m2 )

Experimental Fractu

Simulated Friction work

Fig. 24. Friction work and fracture energy as a function of amplitude

be explained on the basis of decreasing friction work. Asexplained in the previous sections, the friction energyserves a secondary purpose for welding, i.e. it is requiredto break and disperse the oxide layers and other impuri-ties to bring the two contacting surfaces closer to eachother (approx. atomistic distances). Therefore, as the fric-tion work at the foil/substrate interface decreases the dis-persion of the oxide layer and other impurities alsoreduce, causing less number of bonds at the Foil/substrateinterface. This lower density of bonds ultimately resultsinto a lower fracture energy as exhibited by the weldedspecimen of AA 6061 specimen during experiments (Fig.24).

Similar trends can be seen for other applied loadings,see Fig. 25. It is found that as the applied loading or ampli-tude of ultrasonic vibration increase the experimental frac-ture energy decrease, similar trends have been shown bythe friction work at the weld interface during thermome-chanical analyses. The reason for this decrease in frictionwork has been explained before.

7. Conclusion

A thermomechanical analyses of ultrasonic welding ofaluminium alloy has been presented in this work. Both vol-ume and surface effects have been incorporated in the pro-posed cyclic plasticity model with thermal and acousticsoftening along with a friction law with variable coefficientof friction depending upon the contact pressure, amount ofslip, temperature and number of cycles. Results show that:

– Friction plays a secondary role during ultrasonic weld-ing. Results suggest that, in real experiments, frictionwork only breaks up the oxide layer at the weld inter-face and disperse it along and near the interface.

12.4 14.4nic vibration (m)

800

900

1000

1100

1200

1300

1400

Fra

ctu

re E

ner

gy

(J/m

2 )

re Energy

of ultrasonic vibration (velocity = 34.5 mm/s; load = 155 MPa).

800

900

1000

1100

1200

1300

1400

1500

1600

1700

8 10 11 12 13Amplitude of ultrasonic vibration (ηm)

Frac

ture

Ene

rgy

(J/m

2 )135 MPa 155 MPa 175 MPa

0.002

0.004

0.006

0.008

0.01

0.012

0.014

8 10 11 12 13Amplitude of ultrasonic vibration (ηm)

Fric

tion

wor

k (m

J/m

m2 )

135 MPa 155 MPa 175 MPa

9 9

Fig. 25. Experimental fracture energy (left) and simulated friction work (right) as a function of amplitude of ultrasonic vibration (velocity = 34.5 mm/s).


– The maximum temperature reached during the ultra-sonic welding is well below melting temperatures ofthe joining materials which is in agreement with theexperimental results.

– Our three-dimensional simulations showed that mate-rial immediately next to the sonotrode receives theultrasonic energy which introduces the pre-softeningof the material before the sonotrode has moved on it.This pre-softening of material keeps on moving aheadof the sonotrode in the rolling direction of sonotrode.This could be one of the reasons why it has beenobserved during the ultrasonic consolidation of fibreembedding experiments that material immediatelyflows around the fibre as soon as the load is applied.

– It is also found that friction stresses at the weld inter-face reduce due to thermal and acoustic softeningwhich is in conjunction with the experimental results.

– Comparison with the experimental results shows agood agreement between simulated and experimentalresults.

– The microstructural and finite element analyses at sub-micron level is necessary to further understand thedeformation phenomena involved during ultrasonicwelding process which is planned in near future usingcrystal plasticity theory with ultrasonic softeningeffects.

Acknowledgements

The authors thankfully acknowledge the financial sup-port of EPSRC (Engineering and Physical Sciences ResearchCouncil) and MOD (Ministry of Defence through the grant(GR/T19988) and the collaborative support of the SolidicaLtd.

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