effect of coefficient of friction in finite element modeling sanjeev n k

Int. Journal of Applied Sciences and Engineering Research, Vol. 3, No. 4, 2014 www.ijaser.com

© Copyright 2011 - Integrated Publishing Association [email protected]

Research article ISSN 2277 – 8442

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*Corresponding author (e-mail: [email protected])

Received on Jun. 16, 2014; Accepted on Jun. 20, 2014; Published on August 2014

Effect of Coefficient of Friction in Finite Element Modeling

of Friction Stir Welding and its Importance in

Manufacturing Process Modeling Applications

Sanjeev N.K*1, Vinayak Malik2, H. Suresh Hebbar1

1Department of Mechanical Engineering, National Institute of Technology Karnataka, Surathkal, India

2Department of Mechanical Engineering, Indian Institute of Science, Bangalore, India

DOI: 10.6088/ijaser.030400001

Abstract: Friction Stir Welding (FSW) is a relatively new joining process which is gaining significance in

many joining applications. The development in Finite element (FE) modeling is also aiding in widening the

applicability of FSW by simulating the process for better understanding. The success of modeling of FSW

depends on selection of suitable techniques and models/laws irrespective of FE package used for

simulation. The principal equations that govern modeling of FSW are the material model and the friction

model. This paper aims at discussing the effect of variation in Coefficient of Friction (COF) on simulation

outputs. It also highlights the modification required in friction model to get the realistic results from FSW

simulations using ABAQUS.

Key words: FE modeling; FSW; Coefficient of friction; Coupled Eulerian Lagrangian; ABAQUS

1. Introduction

Friction stir welding (FSW) is a relatively new joining process invented at The Welding Institute

(Cambridge, UK) in 1991. It involves the joining of metals without fusion or filler materials. It was

initially applied to aluminum alloys. Since then FSW has rapidly evolved and has opened up multiple

research channels. It is being touted as the most significant development in metal joining in the last decade

(Mishra and Ma, 2005, Mishra and Mahoney, 2007). Many alloys, including most aerospace Al alloys (e.g.,

Al 7xxx) and those regarded as difficult to weld by fusion processes (e.g., Al 2xxx), may be welded by

FSW (Uyyuru and Kailas, 2006, Kumar et al., 2008). The basic process of FSW is that, a rotating

cylindrical tool is plunged into the plates to be welded and moved along joint line as illustrated in Figure 1.

During the welding, heat is generated by contact friction between the tool and workpiece due to which the

material gets plasticized within a narrow zone while transporting metal from the leading face of the pin to

its trailing edge. The processed zone cools without solidification, as there is no liquid. Hence, a defect-free

re-crystallized fine grain microstructure is formed and welding is achieved between plates. Since FSW is

solid state joining process, i.e., without melting, high quality weld can generally be fabricated with absence

of solidification cracking, porosity, oxidation, and other defects typical to traditional fusion welding

(Prasanna et al., 2010). The significant advantage of FSW is that it is an environment friendly process,

which does not make use of flux and consumable electrodes thereby minimizing and avoids the generation

of fumes, formation of slag and ultra-violet radiation thus minimizing the level of health hazards

(Kandasamy et al., 2011).

Effect of Coefficient of Friction in Finite Element Modeling of Friction Stir Welding and its Importance in


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Figure 1: Schematic of friction stir welding process (Deplus, 2014)

Use of Finite Element (FE) simulations is adding the FSW process to a better understanding of its physics,

observing the influence of input parameters on the obtained joints, and optimizing the overall process for a

large range of tools, process conditions and materials and also in lowering development costs (Assidi et al.,

2010). Simulations require the modeling of friction, mechanical and thermal behavior and kinematics to

solve all field equations (Lorrain et al., 2009). However, the difficulty arises when one needs to implement

accurate friction characteristics (Contact condition) using a particular FE formulation. In this study, a

Coupled Eulerian Lagrangian finite element formulation is used to simulate FSW of 2024-T3 aluminium

alloy. The effects of using various tool-work interface contact conditions on the simulations are

investigated. Experimentally measured temperature in the work piece, force on the tool and macro

structural findings for defects are utilized in investigation and evaluation of the results for the friction

models (different values of variables in models are also checked). The results depict that the use of various

tool-work interface friction models and COF has appreciable influence in predicting temperature, force and

mainly defect formation.

2. Contact condition

When modeling the FSW, the contact condition between workpiece and tool is a critical part of the FE

model. In FE packages the contact conditions are defined using available friction laws or with user defined

laws. The friction models available in ABAQUS are:

• Isotropic and anisotropic Coulomb friction model: In its general form allows the COF to be

defined in terms of slip rate, contact pressure, average surface temperature at the contact point and

field variables. It also provides the option to define a static and a kinetic COF with a smooth

transition zone defined by an exponential curve (Steen, 2007).

• Softened interface model for sticking (no slip) friction (modified Coulomb friction model): Here,

the shear stress is a function of elastic slip, which can be implemented with a stiffness (penalty)

method, a kinematic method or a Lagrange multiplier method depending on the contact algorithm

used (Steen, 2007).

Sticking condition: The matrix surface will stick to the moving tool surface segment, if the friction shear

stress exceeds the yield shear stress of the underlying matrix. In this case, the matrix segment will

accelerate along the tool surface, until equilibrium state is established between the contact shear stress and

the internal matrix shear stress. At this point, the stationary full sticking condition is fulfilled (Schmidt et



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al., 2004). In ABAQUS, friction law used in solid mechanics and that suite for FSW modeling is modified

Coulomb friction law (Lorrain et al., 2009, Schmidt et al., 2004). According to Coulomb friction law, the

shear stress of the contacting interface is expressed as:

fricpµτ = (1)

where fricτ is the friction shear stress, µ the COF and p the normal contact pressure (Li et al., 2012).

Figure 2: Modified Coulomb law (Zhang and Chen, 2007)

The COF could be a variable dependent on the interface temperature, relative slipping rate between the two

surfaces and normal pressure. However, for FSW, the conventional Coulomb friction law will be only

applied at the very beginning of welding when interface temperature is relatively low. As the interface

plasticized material is formed in larger volumes at elevated temperatures, the friction behavior will be

dominated by viscoplastic friction. Therefore, heat generation is dependent on intense plastic deformation

of the thin shear layer at the interface (i.e. all heat generated in the whole FSW process is attributed solely

to the significant plastic deformation in the shear layer of certain thickness (Li et al., 2011)). A modified

Coulomb friction law is then applied (Figure 2), where the equivalent flow stress of the material is used as

follows:

3fric shear sτ τ σ= = (2)

Where shear

τ is the flow shear stress calculated from the equivalent flow stress s

σ (Li et al., 2012).

Hatzenbichler et al. (2009) have stated that the COF which is true for one software package cannot be

transferred directly into another one. So, COF has to be calibrated for each process and software package

used for simulation by the user. This is because contact in conjunction with plastic material behavior leads

to highly nonlinear equations in the FEM algorithms, which may cause problems in numerical convergence.

Some FEM software providers handle this problem by automatic contact damping or similar algorithms.

However, the user has mostly no detailed information about adjustments and prediction accuracy. The only

possibility for the user to have an impact on the contact behavior is to set a COF and to choose a friction

model appropriate to the investigated process and model availability in software package. Friction factors



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are often measured by standard tests like the ring compression test which should be valid for all used

software packages (Hatzenbichler et al., 2009). The COF (µ) between tool and work-piece is an input

parameter in FE model and used in heat generation formulations. Different values of COF have been used

in literature. Tutunchilar et al. (2012) used COF values of 0.4, 0.5, and 0.6, under 100 mm/min transverse

speed and 900 rpm rotational speed. According to investigations made by Kumar et al. (2009), the COF

and temperatures do have a synergic influence on each other. The COF in FSW condition was found to be

as high as 1.2 to 1.4 in temperature range of 400-450°C. Therefore, simulations were performed by varying

the COF values from 0.1-2.0 to see the effects on results and to choose the right value.

3. FE modeling details

FE model is developed in the commercial code ABAQUS/Explicit using the Coupled Eulerian-Lagrangian

Formulation, the Johnson-Cook material law, and Coulomb’s law of friction.

Figure 3: Geometry of tool employed (Malik et al., 2014)

The tool with shoulder, frustum shaped pin made of material of Hot die steel (HDS) is considered. The

Figure 3 shows schematic representation of tool geometry. The work-piece of 200X100 mm area and

thickness of 5 mm is considered in simulation. In FE model the Eulerian domain is meshed with

multi-material thermally coupled 8-node (EC3D8RT) Eulerian elements (Merzoug et al., 2010, Al-Badour

et al., 2013) and the void region thickness is taken as 1 mm. The simulation and experimental welding

conditions considered are; Plunge velocity of 10 mm/min, Dwell Time of 10 sec, Welding speed of 60

mm/min, Plunge depth is 0.2 mm, tool tilt angle of zero degree and varying the rotational speed.

4. Results and discussion

Initially model was developed referring to results of temperature and macrographs obtained from

experiment conducted on aluminium 2024-T3 alloy. Further by changing the workpiece material,

validation of model was carried out using temperature results and macrographs published by Merzoug et al.

(2010) and Hirasawa et al. (2010). Here the effects of COF on material AA2024-T3 are discussed in detail.

The simulation results show that the COF has a major effect on void formation. The lower the COF is

applied, larger is the void formed. The Figure 4 shows the effect of COF on void size at a tool rotational

speed of 950 rpm. As the friction between tool and the workpiece increased the formation of void and

moment of material was closer to that of experimental conditions. It can be seen that any value of 1µ <

resulted in unrealistic prediction of results. Also considering 1.2µ > lead to over softening of material,



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which in turn showed the defect as shown in Figure 5.

Figure 4: Effect of COF (µ) on void size (Top view): (a) µ = 0.2, (b) µ = 0.4, (c) µ = 0.6,

(d) µ = 0.8, (e) µ = 1

Figure 5: Effect of high COF (Top view): (a) µ = 1.4, (b) µ = 1.6

For a sound weld, it is found from literature that the working temperature in FSW should be in the range

of 80 to 90% of melting temperature (Tmelt) of the welding material (Qian et al., 2013, Chao et al., 2003).

Table 1 indicates that with µ=1, the maximum temperature predicted in simulation is in the 80 to 90% of

Tmelt range. Here, the percentage of error is calculated by considering the maximum temperature of



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404.36°C, recorded by thermo-couple during the experiment. The resulted simulation temperature at µ=1 is

in close agreement with thermocouple reading with an error of 6.46% (which is of acceptable range). The

error could be because of considering tool as a discrete rigid body. Considering µ=1 and Johnson-Cook

model, the Figure 6 shows the capability of model in accurate simulation of FSW process.

Table 1: Simulation temperature with respect to COF

COF (µ) Temperature (°C)

[Simulation]

Error (%)

0.2 140.86 -61.28

0.4 180.62 -52.03

0.6 260.54 -33.45

0.8 367.46 -8.58

1 432.14 6.46

1.2 460.57 13.07

14 470.23 15.32

1.6 475.15 16.46

1.8 477.48 17.00

2 478.34 17.20

Figure 6: Comparison of (i) experimental and (ii) FE model simulated FSW process

(After retracting tool)

5. Conclusions

Based on the analysis carried out and the results obtained, following conclusions can be made:

(1) A COF of 1.0 has to be considered with sticking condition while using Columbus law of friction in

modeling of FSW and its variants.

(2) Based on the comparison of the simulation and experimental results, under the no slip condition

(µ=1) and Johnson-Cook material model in ABAQUS/Explicit environment, the proposed model

is capable of predicting right processing parameters.



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Acknowledgements

Authors wish to thank Department of Mechanical Engineering, Indian Institute of Science, Bangalore, for

providing research facilities and National Institute of Technology Karnataka, Surathkal, for constant help

and encouragement.

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effect of coefficient of friction in finite element modeling sanjeev n k

Engineering

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new joining process

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