Sequential Transient Numerical Simulation of Inertia Friction Welding ...

Proceedings of IMECE2008 2008 ASME International Mechanical Engineering Congress and Exposition October 31-November 6, 2008, Boston, Massachusetts, USA

IMECE2008-67570 SEQUENTIAL TRANSIENT NUMERICAL SIMULATION OF INERTIA FRICTION WELDING PROCESS Mohammad S. Davoud, Professor Georgia Southern University [email protected]

Medhat Awad El-Hadek Suez Canal University Port-Said, Egypt [email protected]

ABSTRACT Inertia friction welding processes often generate substantial residual stresses due to the heterogeneous temperature distribution during the welding process. The residual stresses which are the results of incompatible elastic and plastic deformations in weldment will alter the performance of welded structures. In this study, threedimensional (3D) finite element analysis has been performed to analyze the coupled thermo-mechanical problem of inertia friction welding of a hollow cylinder. The analyses include the effect of conduction and convection heat transfer in conjunction with the angular velocity and the thrust pressure. The results include joint deformation and a full-field view of the residual stress field and the transient temperature distribution field in the weldment. The shape of deformation matches the experimental results reported in the literature. The residual stresses in the heat-affected zone have a high magnitude but comparatively are smaller than the yield strength of the material. Keywords Inertia Friction Welding, Finite Element Analysis, Sequential Analysis, Elasto-Plastic modeling. INTRODUCTION Inertia Friction Welding (IFW) is a solid state joining process that can produce high quality joints among similar and dissimilar materials [1]. High quality welds are needed to meet performance specifications for products where temperatures, stresses and life requirements are ever more challenging. Inertia welding is a subset of friction welding. In friction welding energy is converted into frictional heat at the interface of the two weldments as they are forced together to obtain a bond without fusion. The energy input may be in the form of forced rotation (e.g. continuous drive rotational friction welding and 1

friction stir welding), forced linear displacement (e.g. linear friction welding) or a flywheel’s inertia. This latter mechanism is the one being exploited in angular velocity inertia friction welding otherwise known as inertia welding [2]. Typically, axisymmetric parts are welded using inertia welding. Examples are solid and hollow shafts and relative assemblies. The process has 5 basic stages ; initial energizing of the flywheel followed by the disconnecting of the drive, the application of the forge pressure at a predetermined rpm to create contact between weldments, the generation of thermal heat via friction at weld interface causing plastic flow, axial shortening as the joint material is extruded as flash while the flywheel’s velocity reduces as its energy is consumed and, finally, cool-down where the forge pressure is maintained for a few seconds after the flywheel is stationary. The main attractions of inertia welding are the combination of high integrity welds in alloys difficult or impossible to weld using fusion welding techniques, consistent weld quality, and ease with which the process can be controlled once the tooling and weldments have been designed correctly for the process. The process also allows dissimilar materials to be joined together, even materials which are impossible to weld using conventional welding techniques due to greatly different metallurgical behavior near to or at the individual alloy’s liquids and solids temperatures. When welding dissimilar metals by friction welding, problems arise not only from the different hardnesses and melting points of the materials, but also from the possibility of interaction producing either brittle intermetallic phases or low melting- point eutectics [3]. In the aluminum/steel system, intermetallic compounds are a major problem, in general the formation of intermetallic phases being considered undesirable. Dawes [4] has introduced a relationship between the properties of joints of dissimilar materials which form brittle intermetallic compounds and the time available for the formation of the compounds; concluding that satisfactory welds could be made if the welding conditions were such that the incubation period was longer than the weld time. However, the existence of an incubation period for Copyright © 2008 by ASME

intermetallic formation is questionable and control should be based on limiting the intermetallic thickness rather than on using an incubation period. In the past 10 years, a few numerical models were developed, assuming a coupling between the thermal and mechanical effects. Sluzalec [6] followed by Moal [7], developed a Finite Element Analysis (FEA) code computing the strain and stress fields in the welded components [8-10]. More recently, Fu and Duan [5] carried out a coupled deformation and heat flow analysis by FEA. These approaches are clearly more in agreement with the physical aspects of the process. Concerning friction welding between dissimilar materials, the number of FEA studies is very limited. One of the rare references in the literature is Balasubramanian et al. [8], who presented the results of numerical simulations to compute the temperature distribution in the case of dissimilar welding. However, this study consists of a pure thermal calculation. A number of 2D Finite Element simulations of inertia welding of dissimilar materials were carried out [9-11] by coupling the thermal and mechanical effects, the temperature distribution was obtained and was comparable to the experimental ones. The deviation was related to the various assumptions in the 2D models. More recently, Bennett [12] used commercially available modeling software (Deform) for simulating the IFW process but due to the software limitation the deformations were only the focus of the analysis. In the present study, simulation of IFW for 36CrNiMo4 is covered using the commercially available finite element software ANSYS. The number of parameters involved in IFW is quite large; most of the previous studies were restricted in the examination of the more variable parameters, which always led to approximated results. Therefore, in the current work the following main parameters were studied: 1- Elastic-plastic material properties were used in the model 2- Contact elements were used at the contact surface with consideration of heat generated by friction and the heat flux at contact 3- Heat conduction is included 4- Implicit FEA transient 3D axisymmetric quarter hollow cylinder with Sequential Thermal – Structural finite element analysis

mechanical problem can be expressed by the non-linear partial differential equation shown below [5]: 1 ∂ ⎛ ∂T ⎞ 1 ∂ ⎛ ∂T ⎞ ∂ ⎛ ∂T ⎞ ∂T ⎜⎜ kr ⎟⎟ + ⎜ k ⎟ + q = ρC ⎜ kr ⎟+ 2 r ∂r ⎝ ∂r ⎠ r ∂φ ⎝ ∂φ ⎠ ∂z ⎝ ∂z ⎠ ∂t where ρ, k, and C are the density, thermal conductivity, and

specific heat of the welded material, respectively. q is the internal energy rate and the coupling factor for the thermomechanical action. It is a function of plastic work, and can be expressed as

q = a σ ε where σ refers to the equivalent stress, ε

is the equivalent strain rate, and α is the thermal efficiency of plastic deformation. Here we take α = 90% [5]. The total welding time in the inertia process is usually very short and the contacting surfaces are not exposed to surroundings, the heat loss through convection and radiation can be neglected. Thus, the boundary condition of the temperature field can be determined as follows:

∂T ∂z

z =0

∂T ∂r

r = r1 or r = r2

∂T ∂z

z =l

=

1 q(r, T ) k =0

=0

( M ax . Heat ) ( Surface Conditions ) ( free end )

where q(r,T) refers to heat flow density at frictional surface.

r2

X Z Y

l

r1

METHODS Heat flux equation and model description: Figure 1 shows the schematic of the weldment and the finite element model used for analysis. The radius of its outer circle is r2, the radius of its inner circle is r1 and the length of both workpieces is l each. Due to symmetry only half the length and a quarter of the section will be used in FE analysis as shown in Fig. 1. The fundamental non-steady state equation of the heat conduction with variable thermal properties in the coupled thermo-

2

Figure 1. Schematic of welded pipes and FE mesh Inertia welding differs essentially from continuous drive friction welding by the rate of energy input. Since the rotational speed varies in inertia friction welding, the rate of heat generated at the interface due to the frictional force is a Copyright © 2008 by ASME

2

n(t) = at + bt + N By using the initial and final conditions, and one additional point selected from the actual speed curve during inertia welding, the parameters a, b, and N (initial rotation speed of the flywheel) can be evaluated. So, the rate of heat input going into both parts is linearly proportional to r at a given instant and can be expressed by:

500

400

Yeild Stress, MPa

function of the distance from the center and the rotational speed. It can be seen that the frictional coefficient depends on the thrust pressure acting on the workpiece and rubbing speed, which, in turn, vary with radius r and the time t. In view of the complex and correlated transient phenomena occurring at the interface during a very short period of time, the experimental data indicates that the speed-time history can be represented as follows:

300

Y = -0.305256 * X + 405.565

(4) 200

100

(b) 0 0.00

2

1.8* J * N * n(t ) q = 3.6 *10−4 * r * ( ro − ri )3 * t (2at 2 + 3bt + 6 N )

400.00

800.00

(5)

1200.00

1600.00

Temp, C

240 220

Materials Properties: Thermal properties of the 36CrNiMo4 alloy extracted from multiple pages of Handbook of Physical quantities [13] and another reference [14] are shown in Figure 2 (a, b, c, d), which (a) includes the stress – strain curve at different temperatures varying from 25 °C – 900 °C, (b) the yield stress varying with temperature (softnability), (c) the elastic modulus varying with temperature, and finally (d) the plastic modulus varying with temperature.

200

Elastic Modulus, GPa

where J is the polar moment of inertia of the rotating mass (1.34112 lb-in.-s2), N is the initial speed (1050 rpm), and t is the time (as a time increment of 0.1 sec for a total time of 16 sec). Thus, the heat flow is assumed to flow equally into the stationary as well as the rotating parts. Where the applied thrust of the rotating hollow cylinder (P = 13 MPa).

180 160 140 Y = -0.103137 * X + 197.298

120 100 80 60

(c)

40 20 0 0

400

800

1200

1600

2000

Temp, C 6 5.5 5

Plastic Modulus, GPa

500

(a)

Stress, MPa

400

300

4.5 4 Y = -0.00397866 * X + 5.28287

3.5 3 2.5 2 1.5 1

200 SS vs Temp

25 C

0

300 C

100

(d)

0.5 0

700 C

400

800

1200

1600

Temp, C

800 C

Figure 2 (a, b, c, d). Thermal properties of the 36CrNiMo4 alloy

900 C

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

Strain %

Note the linear relations in the last three graphs varying with temperature. The alloy’s density is 7800 kg/m3, the 3

Copyright © 2008 by ASME

thermal conductivity is 530 W/m.°K, the thermal expansion coefficient is 17.3 * 10-6 K-1. The stress and strain distribution and distortion of a weld is strongly dependent on the plastic yield strength of the material. As the hot zone is moving and generating rapid temperature changes, the plastic properties of the plate also change. The plastic properties were classified in three different zones: parent, Heat Affected Zone (HAZ) and weld zones, for a more accurate prediction of the residual stress. The plastic flow properties in the three zones of a weld were defined by testing the relevant material from those regions. In the stress analysis, the commercial software ANSYS was utilized, and has been employed to deal with the material property changes during the modeling process. It was assumed that (temperature corrected) parent metal properties could be used for those regions of the plate that did not experience temperatures above 1200°F. HAZ properties were used for those regions that went above 1200°F but remained below 2200°F. Beyond this temperature the material starts to melt and weld nugget properties were used. However, the maximum temperature remains below the solidus (i.e. 2200°F) [5]. Finite element modeling: To determine or predict the residual stress field in a weldment, the mechanical properties of the material and their temperature dependence, the transient temperature field during the entire welding process, the geometry of, and mechanical and thermal restraint conditions for the weldment and all pertinent governing equations should be know. In open literature, several references exist for modeling the inertia and continuous friction welding process where energy based thermal models [1, 8], sequentially coupled and fully coupled [5,6,7] analysis techniques have all been utilized. As the process involves the conversion of mechanical energy into heat and large plastic deformation at the joint interface under a mechanical load, a fully coupled non-linear formulation is required to capture the essential physics of the process and deliver a realistic solution. While several methodologies have historically been used to numerically model different aspects of the inertia welding process, the main emphasis early on was on mechanical modeling of tooling concepts since the right tooling design is the key to exploiting the inertia welding process’s inherent consistency. If the process interactions rather and the effects of 3D tooling features are of interest, the process lends itself to quarter model axisymmetric models for both the thermal and mechanical solutions. The fact that the rotational movement of the modeled plane is vital for the correct representation of the process requires that an element formulation with an out of plane twist [ANSYS] is used where the dynamic (variation with time) mechanical loads derived from the flywheel’s motion can be incorporated into the force matrix. While this allows the 4

process to be adequately represented in sequential thermal and mechanical (structure) terms, the hoop stress component in the circumferential joint can influence operational life of rotating structures, especially ones under high loads at deferent temperature. The sequential analysis refers to starting the calculations with solving one sub-step in thermal then switching to structural analysis then incorporating the structural results in the second solution step in thermal and then switching to structural analysis again, and so on, each sub-step requires remeshing and keeping track with the elements deformation from one sub-step to the other. The estimation of this out of plane stress is enabled by the use of the generalized plane strain elements. Thereby, a representative model capturing all the important behaviors of the component and tooling has been developed as a numerical formulation in space. A number of user subroutines are used to implement features such as; the flywheel, friction laws which represent the complex behavior as a function of relative interfacial velocity and thrust pressure, termination of analysis when a preselected hold time has been achieved following the flywheel coming to rest, heat convection through the surrounding air of the model and plastic material behavior. To simplify the implementation of alloy specific material visco-elasticity laws to include the complex rheological behavior at high temperatures, for a large range of deformation rates (0.1-20+s-1) and large strain deformation, this feature was implemented in ANSYS. This allows the size of the yield surface to be specified for a material rather than having to implement the whole behavior of a material in terms of all physics. Also, it is used in conjunction with a mathematical package with good symbolic and numerical calculation capabilities and output, in the form of function visualization and APDL code. This programming feature in ANSYS has proved very useful in developing and incorporating the sequential analysis, as well as the material properties based on experimental testing. By using physics and metallurgical based material yield formulations, the extrapolation of behavior can be readily made with some confidence and the gradient of the non-linearity at any given point is visible to the solver. From what has been described and discussed so far, it is clear that the problem requires a robust remeshing scheme incorporating numerical error estimators to initiate the remesh operation. Multiple re-zoning or remeshing stages are required for the completion of the analysis. A function has been implemented where an analysis terminates when an element has reached the selected threshold value of distortion or error estimation, Computer Aided Engineering (CAE) is used to extract the deformed shape and create a new analysis job to continue the simulation from where the previous analysis stopped. All remeshed jobs utilized in ANSYS refer to transfer state variables from the old to the new mesh/analysis job. An overall controlling Python script is used to control the analysis sequence holistically through the remesh operations


including model building, job submission and determination of completion status. The interface is basically built around modules which the user can activate and are brought up by the launch script. The modules cater for the following functionality; inertia welding model building, IW post processing, post-weld heat treatment, heat treatment post processing and temporary use of the full /Viewer functionality to interrogate the results beyond the routine requirements. This is intended to cater for the requirements of an integrated modeling environment where the user only needs to specify the process aspects to undertake what is a series of complex analyses with a high degree of consistency and confidence. Figure 1 outlines the schematics to show how the process starts in Computer Aided Design (CAD) software, showing also the fine mesh at contact between the two hollow pipes. The input concept is built around a proposed tooling and component design combination which is available in the CAD system. From this, a drawing where contact interfaces and interactions with the external boundary conditions such as flywheel connections and forge force application area, are indicated with the use of tag names on the relevant entities of the component outline.

Figure 4 shows the experimental validation of deformation for the same material at the same welding conditions. It should be noticed that the experimental image was obtained at the completion of the welding process and after material cool down, where as the numerical simulation images were taken at the end of the actual welding process (just at the end of the rotation (time = 16 sec)).

RESULTS, COMPARISONS, AND DISCUSSIONS The multi-body finite element code described in this paper is able to simulate the shortening and the consequent appearance of flash during welding. The predicted values are compared to the experimental data, with the aim of validating the numerical tool. The trials were undertaken to measure, the same materials and operating parameters. Figures 3 and 4 show both the numerical simulation of the deformation in comparison with the experimental deformation [5] of the same material. The deformation of the meshed elements for a quarter model and a close view of the contact deformation are shown in Figure 3.

Figure 3. Deformation of the quarter model; and a close view of the deformation at the contact surfaces

5

Figure 4. Experimental validation of deformation for the same material at the same actual welding conditions The numerical model shows substantial deformation in both the upper and the lower lip of the hollow pipes, note the elongation ratio of the element at the edge that is approximately 1:14 of it original size. Figure 5 and Figure 6 show both the residual stress in the model as well as the temperature rise at the peak of the friction. The maximum temperature rise in the weldment was below the 1900 °F (less than solidus) that last for 0.8 second during the numerical analysis.

Figure 5. Residual stress at the end of the process


Figure 6. HAZ and the temperature (◦F) rise at the peak of friction The temperature distribution was homogenous across the pipe length, but it was noticed that the temperatures at the upper lip of the hollow cylinder were relatively higher than its counterparts at the lower lip through the process. The HAZ size was found to be less than 3.5 mm as represented in Figure 6 around the contact of the pipes. The deformations of pipe at contact were not homogenous, upper part deformation is relatively larger than the lower part. But beyond the contact area (HAZ) the heat is dissipated smoothly as the pipes lengths are 1m in the Z-axis. The residual stress shown in Figure 5 tend to be relatively high and can be reduced with the use of model pre-heating. The residual stresses values are very high at the most deformed region shown in red at the upper and lower lip of the model in Figure 5. Conclusion: Through the results presented, the numerical model was proved numerically efficient in terms of multi-body contact and experimentally validated. The numerical tool developed is therefore predictive and general enough to be applied at other conditions. An original methodology was used to deduce the friction law and its parameters upon the basis of experimental acceleration curves. The numerical analysis was sufficient to predict the deformations, peak temperature distribution, and residual stresses due the IFW process. The model can also be used to minimize the residual stresses by preheating of the weldment base materials.

[3] N. I. Fomichev, “The friction welding of new high-speed tool steels to structural steels”, Svar Proiz, Vol. 27 (4), pp 2628, (1980). [4] C. J. Dawes, “Micro-friction welding aluminum studs to mild steel plates”, Jounrnal of Metal Construction, 9 (5), pp 196-197, (1977). [5] L. Fu, and L. Y. Duan, "The coupled deformation and heat flow analysis by finite element method during friction welding”, Welding Journal, Vol. 77(5), pp. 202 - 207, (1998). [6] A. Sluzalec, “Thermal effects in friction welding”, Intentional Journal Mech. Sci., Vol. 32 (6), pp. 467–478, (1988). [7] A. Moal, and E. Massoni, "Finite element simulation of the inertia welding of two similar parts", Engineering Computations, Vol. 12 (6): pp. 497–512, (1995). [8] V. Balasubramanian, L. Youlin, T. Stotler, J. Crompton, N. Katsube, O. Winston, W. Soboyejo, "Numerical simulation of inertia welding" Recent Advances in Solids/Structures and Application of Metallic Materials, Vol. PVP-369, ASME, pp. 289– 295, (1997). [9] K. Lee, A. Samant, W.T. Wu, S. Srivatsa, "Finite element modeling of inertia welding processes", Proceedings of the NUMIFORM Conference, Japan, pp. 1095–1100, (2001). [10] Z. Liwen, L. Chengdong, Q. Shaoan, Y. Yongsi, Z. Wenhui, Q. Shen and W. Jinghe, "Numerical simulation of inertia friction welding process of GH4169 alloy", Journal de Physique IV France, Vol. 120, pp 681-687, (2004). [11] M. Sahin, “Simulation of friction welding using a developed computer program", Journal of Materials Processing Technology, Vol. 153-154 (10), pp 1011-1018, (2004). [12] C. J. Bennett, T. H. Hyde, and E. J. Williams, "Modelling and simulation of the inertia friction welding of shafts", Journal of Materials: Design and Applications, Vol. 221(4), pp. 275-284, (2007). [13] I. S. Grigoriev, E. Z. Meilikhov, “Handbook of Physical quantities” Kurchatov Institute of Moscow in Russia. English edition by CRC Press 1997. [14] M.S. Abu-Haiba, A. Fatemi, M. Zoroufi, “Creep deformation and monotonic stress-strain behavior of Haynes alloy 556 at elevated temperatures” Journal of Materials Science, Vol 37, pp 1-9, (2002).

REFERENCES [1] K. K Wang, “Friction Welding”, WRC Bulletin, Vol. 204, pp.1-22, (1975). [2] D.E. Spindler, “What industry needs to know about friction welding”, Welding Journal, (1994). 6
