5th International & 26th All India Manufacturing Technology, Design and Research Conference (AIMTDR 2014) December 12th–14th, 2014, IIT Guwahati, Assam, India
Finite Element Simulation of Temperature and Strain Distribution in Al2024 Aluminum Alloy by Friction Stir Welding Rahul Jain1*, S.K. Pal2, S.B. Singh3 1
Department of Mechanical Engineering, IIT Kharagpur, 721302,
[email protected] 2 Department of Mechanical Engineering, IIT Kharagpur, 721302,
[email protected] 3 Department of Metallurgical and Material science, IIT Kharagpur, 721302,
[email protected] Abstract Friction stir welding (FSW) is a solid state joining process and is handy for welding aluminum alloys. Numerical simulation of FSW is highly complex due to non-linear contact interactions between tool and work piece and interdependency of displacement and temperature. In the present paper a three dimensional finite element model is proposed to study the thermal history, strain distribution and thermo-mechanical process in butt welding of Aluminum alloy 2024 using DEFORM-3D software. Effect of tool rotational speed on plastic strain is studied and insight is given on asymmetric nature of friction stir welding process. Lagrangian incremental technique is used to model FSW process and sticking condition is defined between tool and work piece. Keywords: Friction stir welding, Finite element method, Temperature distribution
1 INTRODUCTION Friction stir welding (FSW) is a solid state joining process invented by TWI England, Thomas et al. (1991). In FSW, the temperature of material remains below the solidus temperature and hence all defects arrested with solidification of the material are eliminated. In FSW a non consumable rotating tool is plunged in a work piece and stirred along welding direction as shown in Figure 1. Heat generation between rotating tool and work-piece is responsible for plasticizing and softening of the material and this softened material is subjected to extrusion by traverse speed and tool pin rotation which leads to formation of weld nugget zone Mishra and Ma (2005). Simulation of FSW process is complex due to highly non linear contact interaction between tool and work piece, unknown boundary conditions and material flow behavior during welding. Still over the last few years finite element analysis of FSW is under radar of several researchers. Chao et al. (2003), Chen and Kovacevic (2003) have modeled FSW, by considering symmetry of the process along weld line and developed a heat flux equation by measuring the temperature in FSW through experiment. They have not considered material deformation during the simulation and only sliding friction has been considered. Yu et al. (2012) have performed a three dimensional finite element analysis of thermal history in FSW by using Johnson cook material and damage model in ABAQUS/Explicit. Because of damage model, mesh nearby pin is deleted and the simulation
does not have any weld nugget zone. They have also studied the plunging and dwelling periods in FSW. Effect of heat transfer from backing plate on temperature distribution is also considered. Schmidt et al. (2004) have developed a mathematical equation for heat generation and validated it by measuring power through experiments. They have considered heat generation through friction (both sticking and sliding friction) only but neglected the heat generation by mechanical deformation. Arora et al. (2009) have developed a three dimensional visco plastic model of FSW to estimate temperature history and material flow and validated the same with experimental data. They have assumed a material as a non newtonian fluid and flow stress as a function of temperature and strain rate. Buffa et al. (2006) have done a three dimensional analysis of FSW in DEFROM 3D to predict temperature history and strain profile during welding. They have used flow stress as function of temperature, strain and strain rate. Regression analysis is used to calculate material constants. Zhang and Zhang (2007) have developed a fully coupled three dimensional analysis to estimate temperature and strain profiles. Material flow is also simulated for different time intervals of the simulation. They have used arbitrary lagrangian and eulerian analyses to simulate FSW in ABAQUS/Explicit. Simple coulomb law of friction is considered for the analysis. Gok and Aydin (2013) have used solid mechanics approach to model FSW for welding magnesium alloy. They have
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Finite Element Simulation of Temperature and Strain Distribution in Al2024 Aluminum Alloy by Friction Stir Welding
simulated the thermal history. Similarly a number of researchers have also developed mathematical expression for heat generation in FSW due to friction either by assuming constant contact pressure or neglecting heat generation due to mechanical deformation of work piece or by simplifying the contact by using coulomb friction law. Also, FSW is simulated by considering symmetry along weld line which is not true in practical situation. In the present paper a fully coupled three dimensional temperature displacement analysis is used with lagrangian incremental technique and to predict the strain and temperature distribution and its variation with rotational speed. Asymmetric nature of the process is also explained with the help of strain distribution.
mesh at the contact region to have better result and this refined mesh window will follow the tool during tool traverse movement. Boundary conditions assigned to FSW model are: bottom surface of work piece is fixed by assigning zero velocity, with this all movements of work piece is restricted. Rotational (Zdirection) and transverse (X-direction) velocities are assigned to the tool.
Tool rotation Retreating side Shoulder
Figure 2 Geometric model of friction stir welding used in this work
Advancing side Welding direction Figure 1 Schematic representation of friction stir welding
Convectional heat transfer coefficient of 20W/m2/oC is defined between work piece-environment and Toolenvironment. Convectional heat transfer coefficient between bottom surface of work piece and environment is defined as 200W/m2/oC, to consider backing plate effect.
2 Model Description
2.2 Finite element formulation
2.1 Geometric Modeling
Finite element formulation of rigid viscoplastic material is based on the variational approach in which admissible velocities, ui should satisfy the conditions of compatibility and incompressibility, and also the velocity boundary conditions, which gives the following functional (function of a function) a stationary value
A three dimensional analysis of FSW is performed in DEFORM-3D. Lagrangian implicit code is used along with adaptive re-meshing technique. Fully coupled temperature-displacement analysis is considered i.e. at every time increment, temperature and displacement are calculated at each node simultaneously. AA2024 aluminum alloy is taken as work piece material and is modeled as rigid viscoplastic. Dimension of work piece is 80×60×5 mm3. Work piece is meshed with 10339 nodes which forms 44730 tetrahedral elements. Tool steel H13 is used as the tool material which is modeled as a rigid body i.e. stress and strain are not calculated on tool but heat transfer from work piece is considered. Since, yield stress of tool steel is much higher than aluminum alloy considering rigid tool is a valid assumption. Tool is meshed with 9181 nodes which form 40247 tetrahedral elements. Shoulder diameter of tool is 24 mm. Tapered cylindrical pin is used with larger diameter of 7 mm and included angle of 40o. Pin height is 4.6 mm. Tool and work piece meshing is shown in Figure 2. Mesh window is used to refine the
(1) where, is a work function and is the surface traction. A penalized form of the incompressibility is added to remove the incompressibility constraint on admissible velocity fields. The actual velocity field is now can be determined from the stationary value of the variation equation which is stated as (2) where, and is the volumetric strain rate. δui is arbitrary variation; and are the variations in the strain rate derived from δui. The
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5th International & 26th All India Manufacturing Technology, Design and Research Conference (AIMTDR 2014) December 12th–14th, 2014, IIT Guwahati, Assam, India
penalty constant, K is a penalty constant with very large positive value. Kobayashi et al. (1989)).
2.3 Material model Flow stress is a function of strain, strain rate, temperature as given in equation 3. Therefore to define flow stress, stress-strain behavior, at different strain rates, temperature from DEFORM material library and isotropic hardening rule are considered.
σ = σ ε , ε ,T .
(3)
where, σ is flow stress, ε is strain, is temperature.
181
149
2.43
2.78
22
11.7
0.33
0.3
3 Results and Discussions 3.1 Temperature profile
.
ε
is strain rate, T
2.4 Thermal and frictional model Temperature generated during FSW is the range of 0.5-0.6 Tm (where, Tm is the melting point in degree centigrade scale), it also changes the mechanical response of the material. Fourier law of heat conduction is used to calculate temperature distribution
k ∇ 2T + q& = ρ c p
(N/mm2) Thermal conductivity (N/soC) Heat capacity (N/mm2oC) Thermal expansion (µmm/mmoC) Poisson’s ratio
∂T ∂t
(2)
where, k is thermal conductivity of material, T is temperature, q& is heat generation, ρ is material density and c p is specific heat capacity. Thermal properties of material are independent of temperature to avoid non-linearity in thermal calculation. Heat generation due to plastic deformation of the material is given by
q& p = λσε&
In FSW certain amount of heat is required to plasticise the material, which allows mixing of material to achieve a good weld. Heat is generated in FSW due to plastic deformation of material and frictional heat generated between tool and work piece. The latter depends on shear friction factor and contact area. Figure 3 shows the calculated temperature distribution along the weld line and top surface of the work piece. Maximum temperature is obtained at the centre of the weld because rotation of shoulder and probe contributes towards highest heat generation in this region. Also temperature profile along the thickness has attained V shape; this is because convection heat transfer between bottom of work piece and backing plate is much higher (high convective heat transfer coefficient due to contact pressure between them) than convection heat transfer between top of work piece and atmosphere. This difference of convective heat transfer coefficient leads to higher cooling at the bottom of work piece and formation of V shaped temperature profile.
(3)
where, λ is inelastic heat fraction and its value is 0.9 Buffa et al. (2006). q& p is the heat generated due to plastic deformation. Contact interaction between tool and work piece is very critical and to simulate this, sticking condition (shear stress at the interaction remains constant) is considered.
τ = mτ max
τ is frictional shear stress at the interface, m is shear friction factor and its value is 1, τ max is where,
equivalent shear stress of material which is 0.577 times of the yield stress of material. Table 1 Physical properties of material (DEFORM manual) Properties
AA2024
Young’s modulus
68900
60 mm
(4)
Tool steel H13 210000
80 mm
Figure 3 Temperature (oC) profile in longitudinal direction and top surface of work piece for 1000 rpm and 60mm/s traverse speed
3.2 Strain profile Plastic deformation of material plays a vital role in material movement and hence in formation of good
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Finite Element Simulation of Temperature and Strain Distribution in Al2024 Aluminum Alloy by Friction Stir Welding
weld. It also affects the microstructure of the weld zone along with thermal history. Therefore it is important to study the strain distribution to understand the deformation of material. Figure 4 shows the effective strain distribution in transverse direction of the weld for 1000 rpm and 60 mm/s traverse speed.
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Figure 4 Strain (mm/mm) profile along y-z section for 1000 rpm and 60 mm/s
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Figure 6 Strain variations in FSW as a function of rotational speed
4 Conclusion A three dimensional fully coupled temperaturedisplacement analysis is done to understand the thermo-mechanical process of FSW process for AA2024 aluminum alloy. Model is capable of calculating temperature, strain, stress and other parameters which give insight on FSW process. Maximum temperature is attained in the nugget zone and temperature profile attains a V shape. Higher strain is observed on the top surface of the work piece as compared to the bottom surface and also strain distribution is not uniform which indicates asymmetrical nature of FSW process. Maximum strain reduces with reduction in tool rotational speed.
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References
Figure 5 Strain (mm/mm) profile along y-z section for 600 rpm and 60 mm/s Figure 4 clearly depicts that strain is higher on the top surface of the material as compared to bottom. This is due to the fact that rotating shoulder contributes to the deformation of material more than the pin. Figure 5 shows the contour plot for 600 rpm rotational speed. Maximum strain value is reduced due to reduction in rotational speed which leads to reduced deformation of material. Figure 6 clearly indicates that strain in the advancing side (A.S.) of the welding is higher as compared with the retreating side (R.S.). This proves the asymmetric nature of the friction stir welding process. Higher strain on advancing side as compared with retreating side is due to positive impact of rotational and traverse velocity of the tool. Similar pattern is obtained for 600 rpm but the values are reduced.
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Arora, A., Nandan, R., Reymolds, A.P. and Debroy, T. (2009), Torque, power requirement and stir zone geometry in friction stir welding through modeling and experiments. Scripta Materialia, Vol. 60(1), pp.13–16. Buffa, G., Hua, J., Shivpuri, R., and Fratini, L. (2006), A continuum based fem model for friction stir welding-model development, Materials Science and Engineering, Vol. 419(1), pp.389–396. Chao, Y.J., Qi, X. and Tang, W., (2003), Heat Transfer in Friction Stir Welding-Experimental and Numerical Studies, Journal of Manufacturing Science and Engineering, Vol. 125(1), pp.138-145. Chen, C.M. and Kovacevic, R., (2003), Finite element modeling of friction stir welding-thermal and thermomechanical analysis, International Journal of Machine Tools and Manufacture, Vol. 43(13), pp.1319–1326. Gök, K. and Aydin, M., (2013), Investigations of friction stir welding process using finite element method. The International Journal of Advanced Manufacturing Technology, Vol. 68(1), pp.775–780. Kobayashi, S., Soo ik oh, Altan, T., (1989), Metal forming and Finite elment method, Oxford series of advance manufacturing, Oxford university press. Mishra, R.S. and Ma, Z.Y., (2005), Friction stir welding and processing. Materials Science and Engineering: R: Reports, Vol. 50(1), pp.1–78. Schmidt, H., Hattel, J. and Wert, J., (2004), An analytical model for the heat generation in friction stir welding. Modelling and Simulation in Materials Science and Engineering, Vol. 12(1), pp.143–157. Wayne M. Thomas, Edward D. Nicholas, James C. Needham, Michael G.Murch, Peter Temple Smith, C.J.D., Patent_FrictionWelding_ThomasTWI.pdf. U. Yu, M., Li, W.Y., Li, J.L. and Chao, Y.J. (2012), Modelling of entire friction stir welding process by
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explicit finite element method. Materials Science and Technology, Vol. 28(7), pp.812–817. Zhang, Z. and Zhang, H.W., (2007), A fully coupled thermo-mechanical model of friction stir welding, The International Journal of Advanced Manufacturing Technology, 37(3), pp.279–293.
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