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Computers and Structures 89 (2011) 977–985

Contents lists available at ScienceDirect

Computers and Structures

journal homepage: www.elsevier.com/locate/compstruc

Numerical simulation of the electron beam welding process

Piotr Lacki a,?, Konrad Adamus b

a b

Faculty of Civil Engineering, Czestochowa University of Technology, Akademicka 3, Czestochowa 42-218, Poland Faculty of Mechanical Engineering and Computer Science, Armii Krajowej 21, Czestochowa 42-201, Poland

a r t i c l e

i n f o

a b s t r a c t

Electron beam welding is a highly ef?cient and precise welding method that is being increasingly used in industrial manufacturing and is of growing importance in industry. Compared to other welding processes it offers the advantage of very low heat input to the weld, resulting in low distortion in components. Modeling and simulation of the laser beam welding process has proven to be highly ef?cient for research, design development and production engineering. In comparison with experimental studies, a modeling study can give detailed information concerning the characteristics of weld pool and their relationship with the welding process parameters (welding speed, electron beam power, workpiece thickness, etc.) and can be used to reduce the costs of experiments. A simulation of the electron beam welding process enables estimation of weld pool geometry, transient temperature, stresses, residual stresses and distortion. However this simulation is not an easy task since it involves the interaction of thermal, mechanical and metallurgical phenomena. Understanding the heat process of welding is important for the analysis of welding structure, mechanics, microstructure and controlling weld quality. In this paper the results of numerical simulation of electron beam welding of tubes were presented. The tubes were made of 30HGSA steel. The numerical calculation takes into consideration thermomechanical coupling (TMC). The simulation aims at: analysis of the thermal ?eld, which is generated in welding process, determination of the heat-affected zone and residual stresses in the joint. The obtained results allow for determination both the material properties, and stress and strain state in the joint. Furthermore, numerical simulation allows for optimization of the process parameters (welding speed, power of the heat source) and shape of the joint before welding. The numerical simulation of electron beam welding process was carried out with the ADINA System v. 8.6. using ?nite element method. ? 2011 Elsevier Ltd. All rights reserved.

Article history: Received 31 May 2010 Accepted 20 January 2011 Available online 4 March 2011 Keywords: Electron beam welding (EBW) Heat-affected zone Numerical simulation 3D conical heat source Thermomechanical coupling analysis

1. EBW characteristics Electron beam welding, EBW, is a fusion welding process that utilizes electrons as a source of energy which is used to join elements. Successful applications of electron in welding processes follow from several of its traits [1]: – Electrons occur in external atom shells, thus they can be easily detached from atom and beam can be created. – Electrons have negative electric charge (?1.6 ? 10?19 C) and they can be accelerated using electric ?eld, the higher the electron speed the higher its kinetic energy which will be used to melt metal. EBW is performed in vacuum. The transport of electrons in vacuum is intended to eliminate electron collisions with much heavier gas particles. The collisions would cause beam defocus and loss of

? Corresponding author. Fax: +48 34 3250609.

E-mail address: piotr@lacki.com.pl (P. Lacki). 0045-7949/$ - see front matter ? 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruc.2011.01.016

electron kinetic energy [2]. Additionally collisions would create air ionization which in turn would destroy cathode [3]. There are also EBW units that operate in atmospheric gases and in partial vacuum. However, due to beam defocus they achieve poorer performance and can be treated as a supplementary method and not as a replacement [4]. The weld creation mechanism during EBW process is not entirely explained. Electron beam allows for achieving high power density (5 ? 108 W/cm2) at a small area (10?7 cm2). Depending on accelerating voltage electrons themselves can penetrate through external layer of material at depth of about 10?2 mm. Although electrons themselves can penetrate only such small distance known fusion zones are much deeper. Possible mechanism behind creation of deep welds is described by Schultz [2]. After electrons penetrate the external layer of element they start to heat the metal. The metal melts and subsequently changes into vapor. The high pressure vapor bubble bursts and destroys the external layer of element. Once the vapor is released the beam is refocused and starts to penetrate through next layers. The cycle repeats and thin deep weld is created.

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Chattopadhyay [5] lists advantages of EBW. EBW is the preferred welding method because of the following reasons: – Application of vacuum allows for welding of materials that react with atmospheric gases, for instance welding of titanium. – Does not require preheating of materials that are characterized by high melting point. – Capability of welding materials that have high thermal conductivity and tend to re?ect laser beam. – Capability of welding both large and small elements since electron beam parameters can be easily controlled and modi?ed. The main drawback of EBW is the size of the welded elements that must ?t into the vacuum chamber. Another factor is the high cost of vacuum generation. 1.1. EBW unit used during experiments Experimental work was performed using polish SE10/60 EBW unit which is presented in Fig. 1. The main components of EBW unit are electron beam gun, working chamber and vacuum pumps. Electron beam gun comprises cathode emitting electrons, anode that attracts electrons and through which beam is transported, and the system focusing electron beam. Working chamber has the shape of cuboid with dimensions 1200 ? 710 ? 850 mm. The chamber is made of acid resistant steel. It is equipped with system that allows for moving welded objects in XY plane and also for their rotation. One of the vacuum pumps is used for empting working chamber and the other for empting chamber containing electron beam gun. Pumps are controlled by system dedicated for measuring pressure. The following parameters can be controlled in the speci?ed ranges: – – – – – – – accelerating voltage: 10–60 kV; beam current: 0–250 mA; cathode heating current: up to 30 A; beam power: up to 15000 W, vacuum in working chamber: 610?5 h Pa; vacuum in chamber containing electron beam gun: 610?5 h Pa; chamber empting time: ca. 30 min.

Fig. 2. EBW welded specimen selected for comparison with numerical analysis results.

Fig. 3. Weld microstructure in the selected specimen.

1.2. Experiment During experimental research a series of welded joints was performed using different input parameters. One of the weldments was selected for the purpose of comparison with numerical calculation results. Fig. 2 presents the selected specimen. The specimen comprises two tubes joined together. Tubes are made of 30HGSA

steel. Specimen dimensions used during numerical simulation are the same as in the actual experiment. The following parameters were used for the selected specimen: accelerating voltage was set to 60 kV, beam current was set to 165 mA, specimen revolution time was set to 10 s. Pulsed mode was selected with pulse width set to 27 ms and pulse pause time set to 111 ms. Sample application of pulsed mode is presented in [6]. In order to determine the size and shape of heat affected zone, HAZ, microsection was created at weld cross section. Fig. 3 presents microsection of the weld joint. The changes resulting from material heating can be seen. Three zones corresponding to different heat change rates during welding process can be distinguished. The parting line can be clearly determined between different zones. The zone in the upper part of weld corresponds to additional post-weld cosmetic pass which was performed with lower values of beam power in order to smooth out the external surface of joint. The two other zones correspond to main pass during which joint was created. The knowledge of size and shape of particular zones and the corresponding zone development conditions can be used to validate numerical model. 2. Heat source models Goldak and Akhlaghi [7] described several basic heat source models that can be used during weld process simulations. Three basic heat source models were presented in Fig. 4. Point heat source is placed on the top surface of the welded object. It is used to model shallow welds. Line heat source which is perpendicular to the top surface of the welded object and occupies space inside object. It is used to model deep welds. Disk heat source is the extension of point heat source. Heat ?ux is assigned to the object top surface represented by a disk. It has uniform or Gaussian distribution. Gaussian distribution is described using the following function which corresponds to Fig. 4a:

q?r ? ? q?0?e?Cr

Fig. 1. EBW unit used for experiments.

2

?1?

where q(r) is the heat ?ux for radius r, q(0) the maximal value of heat ?ux in the center of disk, C the heat ?ux distribution coef?cient

P. Lacki, K. Adamus / Computers and Structures 89 (2011) 977–985

979

(a)

Power density y

z

x

for the purpose of heat distribution description in deep welds occurring during laser welding and electron beam welding. Conical heat source assumes Gaussian heat distribution in radial direction and linear heat distribution in axial direction. Conical heat source model is presented in Fig. 4c. 2.1. Analytical temperature distribution model for EBW processes Ho et al. [8] suggested analytical model describing temperature distribution in cavity created during electron beam welding. The solution presented by authors offers results accuracy similar to the existing analytical models. What distinguishes this model from other is that the predicted temperature at the bottom of the cavity does not approach in?nity. The modi?ed parabolic coordinate system is used to describe heat source:

c

(b)

Power density y a2

z

b x

x?

a1

p?????? 2 ng cos / ; Pe

y?

p?????? 2 ng sin / ; Pe

z?

?n ? g? p??? Pe S

?3?

(c)

Power density y

z

where Pe is the Peclet number and S is the convection coef?cient de?ned as S = a/az. Parameters a, az denote liquid diffusivity and enhanced diffusivity in vertical direction z. Dimensionless temperature H was introduced:

H?

x

hp?????? i T ? T1 exp ng cos / T ? Tm

?4?

where Tm is the melting point temperature and T1 is the ambient temperature. At the walls of cavity the balance between incident ?ux and conduction was assumed:

@H H ? @g 2

s??? n

cos / g

g?g0

p??? p???????? ?3Q S 12ng0 ? exp ng0 cos / ? 2 pPe Pe

?5?

Fig. 4. Heat source models: (a) disk source, (b) double ellipsoid source and (c) conical source [6].

and r is the distance from disk center. Disk heat source is extended by 3D hemi-spherical heat source which is placed beneath the top surface of the welded object. Disk heat source and hemi-spherical heat source assume the symmetry of weld pool with regard to axis going through the middle of heat source. Thus they fail to re?ect the shape of weld pool created by a moving heat source. This problem is solved by double ellipsoid heat source. Initially single ellipsoid was taken into account as the moving heat source produces oval weld pool at the surface of the welded object. Whole power was assigned to the half of ellipsoid beneath the top surface and the half of ellipsoid above the top surface was ignored. Since temperature gradient in the front part of weld pool is lower than in the rear part two different ellipsoids were used to represent heat source. The quarter of one ellipsoid represents heat distribution in front part and the quarter of the other ellipsoid represents heat distribution in rear part. Heat distribution is described by the following equation which corresponds to Fig. 4b:

q?x; y; z; t? ?

p??? 2 ?3?z?v t?2 x2 ?3y 6 3fQ ?32 p???? e a e b2 e c2 abc pp

where Q is the dimensionless electron beam power and g0 is the value of g corresponding to the cavity walls. The temperature predicted by model is the highest at the bottom of cavity, 2200 °C, and decreases linearly toward upper part of the cavity, 1500 °C. At the upper part of cavity temperature is higher than experimental values measured by Schauer and Giedt [9,10]. The discrepancy is probably caused by heat dissipation to ambient air. In the model heat dissipation was ignored as it was assumed that it is negligibly small compared to heat ?ux carried by electrons. Temperature predicted by model at the bottom of cavity is too high and temperature in the middle part of cavity is too low compared to empirical data. The possible explanation of these differences is that the model does not take into account plasma absorption and multiple re?ections. Most of beam power focuses at the bottom of cavity as power has Gaussian distribution. This is the reason for high temperature at cavity bottom. High value of convection parameter S, and thus low value of liquid diffusivity in vertical direction, corresponds to higher temperature at the bottom of cavity and greater cavity depth. Similar effect can be produced by increasing value of Peclet number, increasing beam power or using material that has greater heat absorption. In case of low beam power temperature tends to decrease more rapidly toward the upper part of cavity than in case of high beam power. 2.2. Heat source model generations Goldak and Akhlaghi [7] suggested division of heat source models into ?ve generations. Consecutive generations extend their predecessors. First generation of models uses simple geometric objects like point, line and disk to describe heat sources. Speci?ed amount of

? 2?

where Q is the overall input power, f the fraction of power assigned to ellipsoid quarter, a,b,c the ellipsoid semi-axes, v the heat source speed and t is the time from the beginning of weld process. Double ellipsoid is relatively accurate for description of heat distribution in shallow welds that are produced by electric arc welding process. On the other hand conical heat source is used

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heat is assigned to geometric object and it has uniform distribution and constant value. This approach gives good results for prediction of temperatures that are far from weld pool. Since these models assume constant operating conditions they cannot describe initialization and ?nalization of welding process. Second generation extends heat source description with function representing power density within geometric object. More complex objects are introduced such as double ellipsoid for arc welding and cone for electron beam welding. In case of ellipsoid power is assigned to volume and appropriate function describes power distribution in such a way that power value is highest in the ellipsoid center and decreases to a certain value at ellipsoid border. Shape of weld pool and its temperature distribution are approximation of actual values. If calculated shape of weld pool is signi?cantly different from the actual shape then temperatures in the area of actual weld pool have ?ctitious values. Despite these disadvantages second generation models can relatively accurately predict temperature distribution outside weld pool. In third generation shape of weld pool is a result of calculations and not as it is in case of second generation input data. In order to determine the shape of liquid–solid interface Stefan problem must be solved. The curvature and velocity of liquid–solid interface must be taken into account during de?nition of melting temperature. Additionally, these models include hydrostatic stress in weld pool, pressure on the weld pool surface from the arc, surface tension forces and ?ow of mass into and out of weld pool. From the numerical point of view these methods are moderately more computationally complex than ?rst and second generation models. On the other hand they offer more reliable results. Fourth generation of models extends third generation with equations describing ?uid dynamics inside weld pool. Macroscopic ?uid dynamics is described with Navier–Stokes equations. These equations take into account buoyancy and Lorentz forces acting on the weld pool. Additionally fourth generation models take into account Marangoni effect, arc pressure and shear forces impact on the surface of weld pool. Some of the models take into account also the transport of molten material from electrode but only for currents below 100/150 A. For higher values of current ?uid motion description problems occur. Fifth generation combines the model of electric arc and the model of heat source. This is achieved by introduction of magneto-hydrodynamics equations. Due to high complexity of fourth and ?fth generation models they require complicated mathematical apparatus. Currently it often cannot be proofed that solution exist or it is unique. For these reasons the application of these models to prediction of weld pool geometry in industry is limited. 2.3. Deep penetration welding model Goldak and Kazemi [11] present 3D FEM model describing laser beam welding process. From numerical point of view laser beam welding is similar to electron beam welding. The suggested model produces temperature distribution and shape of weld pool. Heat source comprises surface source and inner source. Surface source is represented by disk model using Gaussian power distribution. Inner source is represented by a line divided into segments. Within one segment the value of produced heat is constant. The amount of heat is the function of segment depth relative to top surface of welded object. Authors used empirical equation suggested by Lankalapalli et al. [12] to determine the amount of heat produced by laser beam at speci?ed depth. This equation de?nes power as a function of thermal conductivity, temperature and Peclet number:

where Pz is the power produced at depth z, k the thermal conductivity, Tv the heat source temperature, T0 the initial temperature and Pe is the Peclet number. It was assumed that cavity created by laser beam has the shape of a cone. Peclet number at a speci?ed depth was de?ned as a function of Peclet number at the top surface of workpiece, penetration depth and distance from top surface:

z Pe ? Pe?0? 1 ? d

?7?

where Pe(0) is the Peclet number at top surface, z the distance from top surface and d is the penetration depth. Based on Lampa and Kaplan work [13] Peclet number at top surface was de?ned as a function of weld width, welding speed and thermal diffusivity:

Pe?0? ?

va 2km

?8?

where v is the welding speed, a the radius of surface source, j the thermal diffusivity of liquid material and m is the user de?ned coef?cient representing multiple of thermal diffusivity. Integrating Eq. (6) and using Eq. (7) to change the variable of integration from z to Pe the authors de?ned the amount of power absorbed by inner source Pl as:

Pl ? t ?akliq ??T v ? T 0 ??2:1995 ? 3:1481Pe?0? ? 0:16647Pe?0?2 ? 0:01152Pe?0?3 ? ?9?

where t is the plate thickness, kliq the liquid metal conductivity, a the user de?ned parameter taking into account impact of welding velocity on thermal conductivity and Pe(0) is the value of Peclet number at top surface. The amount of absorbed power by surface heat source Pc is calculated as product of laser beam power and absorption coef?cient g speci?c to laser welding which was de?ned using Bramson’s formula [14]:

g?T ? ? 0:365

1 3 R 2 R R 2 ? 0:006 ? 0:0667 l l l

?10?

where R is the electrical resistivity of material and l is the is the laser beam wavelength. Whole power absorbed by welded object is de?ned as Pt = Pc + Pl. Thermal conductivity and speci?c heat were assumed to be a function of temperature. The model allows for prediction of weld pool shape. Good results were obtained for prediction of weld width at the top surface and at the bottom of weld. Model fails to predict accurately weld width in depth near the top surface. From calculations it follows that three parameters have the largest impact on the results: Peclet number, thermal conductivity and absorption coef?cient of material used for surface heat source. 3. EBW numerical model EBW numerical model was built using ADINA System v8.6.1 [15,16]. The program utilizes Finite Element Method. The basic ?nite element procedures used in ADINA System were described in [17]. Fourier-Kirchoff equation was used to describe heat propagation:

@T q ? ar2 T ? v @t qc p

?11?

Pz ? k?T v ? T 0 ??2:1995 ? 6:2962Pe ? 0:4994Pe2 ? 0:0461Pe3 ? ? 6?

where a is the thermal diffusivity, q the density, cp the speci?c heat and qv is the ef?ciency of inner volume heat source. The conical heat source model with uniform power distribution was assumed. The assumed shape of heat source follows from penetrative motion of electron beam. As the electron beam penetrates

P. Lacki, K. Adamus / Computers and Structures 89 (2011) 977–985

981

Z Tube 1 Single heat source Tube 2 X

Y

Fixed Surface

Fig. 5. Tubes cross-section with conical heat source.

through material it creates cavity called keyhole. Heat is being generated inside keyhole thus in the model it was assumed that heat is generated in the volume elements. Electron beam produces keyholes of several millimeters to several centimeters deep and heat is generated inside the weld. In order to map the conical heat source to FEM mesh the power assigned to conical heat source was assigned to elements in the shape of prism. The triangle cross-section of prism re?ects the actual cross-section of HAZ in the analyzed specimen. The elongated shape of prism takes into account the movement of heat source along welding trajectory. Geometry of prism is de?ned by its depth, length and ?are angle. The length is the quotient of tube circumference and number of prism elements along tube circumference. The movement of heat source is represented by production of power in the consecutive prism elements. At any time power is produced inside only a single prism element. Two tubes of different thickness were joined using EBW. Butt joint was created. One of the tubes has welding collar which facilitates ?tting tubes to each other. Each of tubes is 50 mm long. Tube external diameter is 31.8 mm which corresponds to circumference of about 100 mm. One of the tubes has walls 5 mm thick the other has walls 3 mm thick. In the vicinity of weld, mesh was thickened and mesh elements were modi?ed so that they re?ect the shape of heat source. Fig. 5 shows mesh representing tubes. It can be seen that mesh elements are thickened near conical heat source. As initial condition temperature of tubes was set to 20 °C. On the tube walls convection coef?cient was set to 0 as welding is performed in vacuum in short time. Calculations were done for three different welding speeds: 6.7, 10 and 20 mm/s which correspond to overall welding time of: 5, 10 and 15 s. Welding time of 10 s corresponds to actual experiment and welding times of 5 and 15 s were used for comparative purposes. Heat is generated in the series of pulses. Compared to continuous beam pulse welding offers higher ratio of fusion zone depth to width and thus enables creating thin welds as explained in [2]. Modeling of pulse welding requires considerably higher number of time steps than modeling of continuous welding. For each welding speed welding time was divided into 72 periods. Each of periods corresponds to 5° rotation of heat source which gives together full 360° rotation. Single pulse lasts 20% of period time and idle time between pulses corresponds to 80% of period time. There are 72 pulses and 72 prism elements. Each of pulses is assigned to the appropriate prism element. For welding speeds 6.7, 10 and 20 mm/s single pulse lasts 0.042, 0.028, and 0.014 s, respectively. One EB pulse is represented by 20 time steps and idle period between pulses is represented by 80 time steps. Power density of heat source during pulse welding is shown in Fig. 6. During active period power density equals 9 ? 1011 W/m3. The actual beam power was 9900 W. Power absorption coef?cient equal to 60% was assumed in the simulation.

1e+12

Heat, W/m 3

8e+11 6e+11 4e+11 2e+11 0 0 0.05 0.1 0.15 0.2 0.25 0.3 Time, s 0.35 0.4 0.45

Fig. 6. Amount of heat generated during pulse EBW for welding speed 10 mm/s.

Tubes were made of 30HGSA steel according to PN-89/H84030/04 standard. This is chromium–manganese–silicon steel with chemical constitution presented in Table 1. 30HGSA steel is used for mills, average machines and high-strength parts. 30HGSA steel has limited weldability especially for thick cross-sections. During welding processes allowable hardness is often exceeded. For large elements it is advisable to apply intermediate annealing. Immediately after end of welding process it is advisable to apply soft annealing or toughening. In case of materials that had undergone heat treatment prior to welding it is possible that within HAZ strength properties will deteriorate. In order to restore these properties in HAZ appropriate heat treatment should be applied. The following material properties were assumed for 30HGSA steel: – – – – – – thermal conductivity speci?c heat density Young’s modulus Poisson ratio yield stress 50 W/mK 472 J/kgK 7850 kg/m3 210 GPa 0.3 850 MPa for 20 °C 150 MPa for 1350 °C 85 MPa for 20 °C 0 MPa for 1350 oC, 11 ? 10?6 K?1

– strain hardening modulus – coef?cient of thermal expansion

4. Modeling results Finite element method program ADINA allows for convenient modeling of pulse EBW process. Theoretical model representing physical process allows us to estimate changes occurring in welded tubes. Modi?cation of welding speed enables us predict how this change will impact temperature distribution. Temperature range will depend on welding speed and the assumed material

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Table 1 Chemical constitution of 30HGSA steel according to PN-89/H-84030/04. Fe Min Residue Ni Min 0 Max 0.3 Max C Min 0.28 Mo Min 0 Max 0.1 Max 0.34 Mn Min 0.8 W Min 0 Max 0.2 Max 1.1 Si Min 0.9 V Min 0 Max 0.05 Max 1.2 p Min 0 Ti Min 0 Max 0.05 Max 0.025 S Min 0 Cu Min 0 Max 0.3 Max 0.025 Cr Min 0.8 Al Min 0 Max 0.1 Max 1.1

a)

b)

c)

d)

TEMPERATURE

1350. 1260. 1170. 1080. 990. 900. 810. 720. 630. 540. 450. 360. 270. TIME 0.3056 180. MAXIMUM 90. 4833. NODE 25803

TIME 0.58333 MAXIMUM 4947. NODE 26991

TIME 0.86111 MAXIMUM 5011. NODE 28179

TIME 1.4167 MAXIMUM 5042. NODE 30555

Fig. 7. Development of HAZ in numerical model of tube welding process: (a) time 0.3056 s, (b) time 0.58333 s, (c) time 0.86111 s and (d) time 1.4167 s.

properties. According to [18] temperature of 25,000 °C can be achieved during EBW. Hai-Xing and Chen [19] analyzed plasma temperature during laser beam welding, which offers beam power similar to EBW, show that keyhole temperature can reach about 13000 °C. During simulation the maximal temperature of 6216 °C was reached within 2.125 s for welding speed of 6.7 mm/s. Changes of temperature distribution in HAZ were presented in Fig. 7. Within about 2 s from beginning of the process HAZ develops in non-stationary way. Subsequently stationary stage is achieved for HAZ. During stationary stage HAZ does not change its shapes and it merely changes its position relative to its initial position moving along welding trajectory. Fig. 8 presents temperature values as a function of time for points at the same distance from heat source in normal direction to welding trajectory and at different depths, for welding speed of 10 mm/s. Initially as the depth increases temperature signi?cantly decreases. After period of 1 s for all points temperature approaches 250 °C and starts to linearly decrease. It can be seen that during ?rst second temperature values have tendency to create wave which re?ect pulse character of electron beam. Fig. 9 presents temperature values as a function of time for points at the same depth and different distances from heat source in normal direction to welding trajectory, for welding speed of 10 mm/s. Only for two points closest to the heat source pulse character of heat source can be seen. After the period of about 1 s temperature for all points stabilizes. Fig. 10 presents changes of temperature values as a function of time for point P2 and different welding speeds. Plot analysis shows that as welding speed increases maximal temperature decreases for point P2. Also temperature amplitude of consecutive pulses decreases.

As the welding speed increases the amount of power generated in weld decreases. Smaller amount of power results in lower keyhole temperature and smaller size of HAZ. Fig. 11 presents three material volumes for temperatures above 500 °C and for different welding speeds. It can be seen that as welding speed increases the volume of material above 500 °C decreases and temperature in center of volume also decreases. HAZ for welding speeds of 10 and 6.7 mm/s has shape of solid of elliptic base that decreases in one direction. For welding speed of 20 mm/s HAZ has the shape of half-ellipsoid with growing cone that represents heat generated by EB pulse. The assumed heat source model allows for distinction between solid and liquid phase based on temperature calculated for 3D solid elements. Due to the assumed kind of ?nite elements the processes occurring in HAZ cannot be analyzed for temperatures above melting point. 4.1. Thermomechanical analysis Thermomechanical coupled, TMC, analysis was used to determine the magnitude of thermal stresses. Similar approach was applied in [20]. Thermal elasto-plastic material model was assumed in the numerical model. Martensitic phase transformation that may occur during cooling period was neglected. The face of thicker tube shown in Fig. 5 was ?xed. All degrees of freedom were taken away for the mesh nodes in the surface corresponding to the tube face. Fig. 12 shows results of TMC numerical analysis. Temperature distribution and the corresponding effective stress distribution are presented in Fig. 12. Fig. 12a presents distribution corresponding to half of pulse duration, Fig. 12b presents distribution

P. Lacki, K. Adamus / Computers and Structures 89 (2011) 977–985

983

600

4 mm

1.55 mm

P0 P1 P2 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P3 P4

800

welding speed = 6.7 mm/s

700 600

500

welding speed = 10 mm/s welding speed = 20 mm/s

Temperature [°C]

400

Temperature,[°C]

0 0.2 0.4 0.6 0.8 Time [s] 1 1.2 1.4 1.6

500 400 300 200 100

300

200

100

0

0

Fig. 8. Temperature values as a function of time for points P0–P4 at constant distance from heat source axis. Welding speed of 10 mm/s.

Time,[s]

Fig. 10. Temperature value changes for point P2 and different welding speeds.

600

1 mm 15.18 mm

P0 P1 P2 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P3 P4

500

Temperature [°C]

400

300

(a)

TIME 0.70833 MAXIMUM 3448. NODE 30555

200

100

0 0 0.2 0.4 0.6 0.8 1 Time [s] 1.2 1.4 1.6

Fig. 9. Temperature values as a function of time for points P2, P5–P14 at the same depth. Welding speed of 10 mm/s.

corresponding to the end of pulse and Fig. 12c presents distribution corresponding to the end of idle period between pulses. The impact of temperature on effective stress ?eld can be inferred from the plots. The lowest values of effective stress occur in the area of molten pool. High values of effective stress surround welding pool. The highest values equal to 370 MPa occur beneath welding pool at the end of idle period. As it was shown in [21] the yield stress is the key mechanical property in welding simulation. The yield stress dependency on temperature must be considered in a welding process simulation to obtain correct result. Young’s modulus and thermal expansion coef?cient have small impact on the residual stress and distortion in welding deformation simulation. 4.2. Model assessment In order to asses numerical model isotherm calculated by the model were put onto macrostructure picture of weld (Fig. 13). For temperatures above 1200 °C isotherms are close to each other

TIME 1.4167 MAXIMUM 5042. NODE 30555

(b)

(c)

TIME 2.1250 MAXIMUM NODE 30555

Fig. 11. Volume of material above 500 °C for welding speeds: (a) 20 mm/s, (b) 10 mm/s and (c) 6.7 mm/s.

which indicates that high temperature gradient occurs. Isotherm in bottom part of weld is in 95% consistent with lines observed in macrostructure.

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Y

a) TIME 0.01389 s

MAX TEMPERATURE 2552 oC

Z

X

o

TEMPERATURE, C 1500 1300 1100 900 700

b) TIME 0.02778 s

MAX TEMPERATURE o 4110 C

500 300 100

EFFECTIVE STRESS, MPa 373 320 266 213 160 106 53 0

c) TIME 0.1389 s

MAX TEMPERATURE o 2435 C

Fig. 12. Temperature and effective stress distribution for: (a) half of pulse duration, (b) end of pulse and (c) end of idle period between pulses.

5. Conclusions

0 TEMPERATURE TIME 1.4167 3000. 2400. 1800. 1200. 600. 0. 5mm

Numerical calculation results and empirical results allowed for validation of assumed model of EBW process. The model was created using ADINA System. The following conclusions can be drawn from the analysis of results: – After period of 1 s for points P0–P4 that are 1 mm from heat source axis the temperature oscillations due to pulse welding tend to stabilize. – As welding speed increases maximal temperature decreases for point P2. Also temperature amplitude due to pulse welding decreases. – Temperature gradient in the area corresponding to heat source causes increase of effective stresses. Maximal values of thermal stresses occur in specimen area beneath heat source. The magnitude of thermal stresses is dependent on yield stress of welded material at given temperature. – Comparison of calculated isotherms and weld macrostructure allowed for validation of the model accuracy. The suggested numerical model produced results that are satisfyingly consistent with empirical data.

MAXIMUM 5042. NODE 30555

Fig. 13. Comparison of numerical calculation results and actual results.

In upper part of weld isotherms are consistent with actual macrostructure areas to a lesser extent. This is caused by the fact that after welding ?nished specimen underwent additional heat treatment with low power electron beam in order to smooth weld face. The impact of additional low power heat source can be seen in macrostructure. Second heat source slightly extends HAZ in upper part and causes discrepancy between calculated isotherms and macrostructure lines. Further research will focus on including second low power heat source in numerical model in order to predict HAZ shape more accurately.

Acknowledgments Financial support of Structural Funds in the Operational Programme – Innovative Economy (IE OP) ?nanced from the European

P. Lacki, K. Adamus / Computers and Structures 89 (2011) 977–985

985

Regional Development Fund – Project ‘‘Modern material technologies in aerospace industry’’, No. POIG.01.01.02-00-015/08-00 is gratefully acknowledged. References

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