Modelling of heat transfer process in non-vacuum electron beam additive manufacturing with CuSi3 alloy wire

Materials Today: Proceedings xxx (xxxx) xxx

Contents lists available at ScienceDirect

Materials Today: Proceedings journal homepage: www.elsevier.com/locate/matpr

Modelling of heat transfer process in non-vacuum electron beam additive manufacturing with CuSi3 alloy wire Dmitrii Mukin a,⇑, Ekaterina Valdaytseva a, Thomas Hassel b, Georgii Klimov b, Svetlana Shalnova a a b

Peter the Great St. Petersburg Polytechnic University, 195251 St. Petersburg, Russian Federation Gottfried Wilhelm Leibniz Universität, 30167 Hannover, Germany

a r t i c l e

i n f o

Article history: Received 24 December 2019 Accepted 30 December 2019 Available online xxxx Keywords: Direct metal deposition Additive manufacturing Non-vacuum electron beam Filler wire Temperature field Surface tension

a b s t r a c t Non-vacuum electron beam wire feed deposition is a new technology in the family of additive technologies. It has some advantages in comparison with the laser one, especially for materials with great reflection ability, such as copper alloys. The suggested model is for assist determination of the optimal modes of processing. It considers heat transfer processes in the substrate and wire and also surface formation of the deposited layers. A wire can be feed along the process direction as well as from a side position. The equation of the liquid phase equilibrium in the gravity field is used to analyze the mechanism of formation of the bead surface profile. The proposed method allows determining the shape of the wall surface of the product with satisfactory accuracy. The position of the wire tip greatly affects both the shape and the size of the melt pool and its temperature. Increasing the wire feed rate leads not only to an increase in the cross-sectional area and the height of the deposited layers but also to a decrease in the width of the wall. Therefore, special attention should be paid to the selection of the wire feed rate. Ó 2020 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of the scientific committee of the Materials Science: Composites, Alloys and Materials Chemistry.

1. Introduction Currently, modern electron beam processing technologies, which began their development more than 60 years ago [1], are quite common tools for processing materials. This is primarily welding, cutting, surfacing and heat treatment [2]. One of the original types of electron beam processing is electron beam welding in an open atmosphere (non-vacuum electron beam welding - NVEBW), which is used in various fields of production [2,3], for example, in the automotive industry for welding of exhaust systems, transmission parts and other components [4]. This process is also used quite successfully in welding dissimilar materials, such as steel and aluminum [5] and others. The main advantages of NVEBW in comparison with conventional EBW in vacuum are the absence of the need to create a vacuum in the working chamber, high welding speed, small duty cycle, good overlap of the gap of welded edges by the beam, high efficiency of the equipment [6]. The disadvantages of the process include a small working distance,

⇑ Corresponding author.

the formation of x-rays and ozone, which require radiationprotected rooms with a ventilation system. In addition to welding, non-vacuum processes are also used for coating various purposes, for example, to improve the wear resistance of titanium [7], steel [8–12], as well as their corrosion resistance [13]. All studies show that the non-vacuum electron beam surfacing is characterized by high-quality coatings and ease of introduction of alloying elements. Additive technologies have been actively developed in recent decades [14]. Laser, electron beam, plasma and arc are used as the main heat source, and the filler material can be used both in the form of powder and in the form of wire. Particularly significant progress has been made in the field of laser additive technologies [15–18]. A wide range of materials can be used: steel, aluminum, titanium and Nickel alloys [19–22]. However, there is also a need to explore the potential use of copper and its alloys for additive manufacturing. Moreover, non-vacuum electron-beam sources look preferable, because they do not have the disadvantages inherent in laser radiation. As is known, copper has a low absorption capacity of laser radiation with a wavelength of 1 mm and above. At this wavelength, the absorption coefficient is about 5% [23,24], this leads to inefficient heating and melting of the copper material.

E-mail address: [email protected] (D. Mukin). https://doi.org/10.1016/j.matpr.2019.12.380 2214-7853/Ó 2020 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of the scientific committee of the Materials Science: Composites, Alloys and Materials Chemistry.

Please cite this article as: D. Mukin, E. Valdaytseva, T. Hassel et al., Modelling of heat transfer process in non-vacuum electron beam additive manufacturing with CuSi3 alloy wire, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.380

2

D. Mukin et al. / Materials Today: Proceedings xxx (xxxx) xxx

This study aims to consider a model that can be used to determine the optimal modes for production of samples by non-vacuum electron beam wire-feed deposition. 2. Methods Wire Feed Deposition as a part of Direct Metal Deposition is a process where a high-energy heat source, in this case, an electron beam, is used to form a molten pool in a solid metal substrate. Filler material in the form of a wire is fed into the molten pool. When the wire enters the molten pool, it melts. It leads to an increase in the volume of the molten material and the formation of the cladding bead. Then the process is repeated, but the melt pool is formed in subsequent layers, capturing previously deposited layers. In the developed model, the heat conduction problem and the free surface formation problem will be solved by the functionalanalytical methods. This is due to the fact that functionalanalytical methods are more computationally efficient than numerical methods. The following physical assumptions are made:
The physical properties of the substrate and the filler wire material (specific heat capacity c, density q, thermal conductivity k, thermal diffusivity v) are temperature-independent
Boundary effects at the beginning and end of the deposited layer are not considered
Heat transfer with the environment is not considered
Heat flux distribution of the electron beam qe [Wmm2] is presented as a surface normally distributed heat source
The wire feeding rate w is constant
The stable metal-transfer mode is considered

v

2

@ T @ T @ T þ þ @x2 @y2 @z2

!

þV

@T ¼0 @x

ð1Þ

where v – thermal diffusivity, V – the speed of cladding. Boundary conditions on the front surface of the computational domain:

k

p  R2E

sinb  exp 

ðxsinbÞ þ y2

! ð4Þ

R2E

where Q – electron beam power, g – heat efficiency, RE – effective radius of the electron beam; b – tilt angle. A distributed source can be represented as a combination of point (infinitesimal) sources. Then the temperature increment at the point with coordinates x, y, z from the point source acting at the point xs, ys is equal to dT:   qeðxs;ysÞ V dTðx;y; z; xs; ysÞ ¼ exp  ðRðx; y;z;xs;ysÞ þ x  xsÞ 2pkRðx; y;z;xs;ysÞ 2v

ð5Þ Temperature field due to normally distributed elliptical heat source qe(x, y) can be found by integrating all the infinitesimal sources over the deposited layer surface or the substrate surface subjected to electron beam heating. 2.2. Wire heating During the wire-feed deposition process, the filler wire absorbs part of the heat of the electron beam source, heats up and melts. Fig. 1 shows the scheme of overlapping part of the heat source by a wire and creating a ‘‘shadow” on the substrate or on the deposited wall. This effect must be taken into account when calculating the temperature field. The total temperature increment Ts (x, y, z), taking into account the overlapping part of the source, can be calculated as the difference of two integrals. The first is the temperature increment from the heat source in the absence of wire, the second is the temperature increment from the absorbed part of the heat by the wire.

Z1 Z1 dTðx; y; z; xs; ysÞdxsdys 1 1

In order to obtain the temperature field in the substrate and the deposited layers it is necessary to solve the following linear quasistationary heat conduction problem in a Cartesian coordinate system x, y, z: 2

2

Tsðx; y; zÞ ¼

2.1. Substrate heating

2

qe ðx; yÞ ¼

Q g

@T ¼ qðx; yÞ @n

ð2Þ

where q(x, y) is the heat flux density. To solve the heat transfer problem it is possible to use the fundamental solutions to the heat equation. Consider a moving source of heat on the surface of a semi-infinite body. Then the solution of the quasi-stationary heat equation for a point source associated with the origin of the coordinate system and moving translationally in positive x-direction has the form:

  q V DTðx; y; zÞ ¼ ðRðx; y; zÞ þ xÞ exp  2pkRðx; y; zÞ 2v

ð3Þ

where DT(x,y,z) – temperature increment at the point with coordinates x, y, z respectively, q – heat source power, k – thermal conductivity of the material, R – distance from the heat source to the body point in question, V – speed of cladding, v – thermal diffusivity, equal to v = k/(cq), c – specific heat capacity, q – density. Heat flux distribution of electron beam qe is presented as a surface normally distributed elliptical heat source [3].

ZRw Z1 

ð6Þ

dTðx; y; z; xs; ysÞdxsdys Rw X 0

where Rw – wire radius, X’ – the coordinate of the tip of the wire along the x-axis (see Fig. 1). To determine the overlap parameter of the source X’, we use the wire melting model presented in [25]. In the first approximation, we assume the parameter X’ at the time when the tip of the wire has completely reached the melting point. The equation for calculating the temperature field in the wire due to the normally distributed elliptical heat source qe (h, z) in the cylindrical coordinate system (the reference frame associated with the wire tip) is as follows:

DTðr; h; z; tÞ ¼

qgsinc

Zp þ1 Z

"

exp  cqp2 Rw wR2E 0 1   X  w exp  z  zj  2v j¼1;1 

1 X

cosnðh  h0 Þ

1 X

ðz0 sincÞ þ ðRw cosðh0 ÞÞ

2

2

#

R2E

l2n;m

J ðl2n;m  n2 Þ  J n ðln;m Þ  Bn;m n n¼0 m¼1       wz  zj  r 1 : exp  ln;m Bn;m  U Rw 2 2v sffiffiffiffi !        z  zj  w t  w z  zj  1 Bn;m  exp  pffiffiffiffiffiffiffi  Bn;m  U 2 v 2 2v 2 vt sffiffiffiffi !)    z  zj  w t  dz0 dh0 Bn;m  pffiffiffiffiffiffiffi þ ð7Þ 2 v 2 vt

Please cite this article as: D. Mukin, E. Valdaytseva, T. Hassel et al., Modelling of heat transfer process in non-vacuum electron beam additive manufacturing with CuSi3 alloy wire, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.380

D. Mukin et al. / Materials Today: Proceedings xxx (xxxx) xxx

3

Fig. 1. The scheme of overlapping part of the heat source by wire.

where c – the angle between the wire and the beam axis, zj = j (z0 + z’ + wt), z0 – coordinate of the beam axis, w – wire feed rate, rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  Ru u2 2l v 2  2ffiffiffi p U ðuÞ ¼ 1  p e du, Bn;m ¼ 1 þ Rwn;mw , mn,m – the positive 0

roots of

dJn ðlÞ dl

¼ 0, t* – the time of action of the infinitesimal source

with z’ coordinate. Wherein

( t ¼

0

t  z0wz ;

if z0 þ z0 < 0;

t;

if z0 þ z0 P 0;

2.3. Determination of the wall borders Due to the assumption that there is no heat transfer with the environment, in order to find the temperature field of the deposited wall, it is necessary to take into account the influence of its boundaries. For this, virtual sources q’ and q” are introduced that are located symmetrically with respect to the lateral boundaries of the wall [26] (Fig. 2). The power of virtual sources will be considered equal to the power of the true source. In this case, the wall material mentally continues to the right and left to infinity. Taking into account the linearity of the thermal problem, we will find a solution as a superposition of thermal fields from a true

source q moving in a medium and virtual sources q’ and q” moving symmetrically to the true source relative to the lateral boundaries of the wall. Then, the temperature field Tw(x, y, z, h) from the true and virtual heat sources for a given wall width h can be written as:

Twðx; y; z; hÞ ¼ Tsðx; y; zÞ þ Tsðx; y  h; zÞ þ Tsðx; y þ h; zÞ

ð8Þ

where Ts(x,y,z) – temperature field created by a true heat source; Ts (x,y–h,z) and Ts(x,y + h,z) –temperature fields created by virtual sources on the right and left, respectively. After the first layer has been deposited, the problem arises of determining the width of the wall, taking into account the boundaries of the layer during heating. Obviously, the wall width coincides with the minimum point of the function Tw(x, y, z, h), and also coincides with the point of maximum removal of the isotherm Tliq from the X-axis. This problem can be represented as a system

(



Twðx ; y ; z; h Þjy !h ¼ minTwðx; y; z; hÞ 

2

Twðx ; y ; z; h Þjy !h ¼ T liq

ð9Þ

2

where h* – optimal wall width. 2.4. Layer formation To describe the formation process of the surface profile of the deposited bead, the equilibrium equation is applied for the liquid phase in the gravity field, which relates the curvature of the bead profile and the surface tension with hydrostatic pressure [27]:

r R

¼ g  Dq  z  C 0

ð10Þ

where r – the surface (interfacial) tension; R – the curvature radius of the surface at the point in question; g – the gravity acceleration; Dq – the density difference of the contacting phases; z – the coordinate of the considered surface point; C0 – a constant depending on the choice of the origin. To obtain an analytical solution to equation (10), we use the approach presented also in [27]. Thus this equation must be reduced to a dimensionless form, while the capillary constant is taken as the scale factor

rffiffiffiffiffiffiffiffiffiffiffiffiffi a¼

Fig. 2. The layout of virtual sources to account for the influence of wall boundaries.

r

g  Dq

Taking the origin at the point with zero pressure (Fig. 3) and expressing the curvature of the layer surface profile at the point in question through the derivatives of the function z = f(x), we obtain

Please cite this article as: D. Mukin, E. Valdaytseva, T. Hassel et al., Modelling of heat transfer process in non-vacuum electron beam additive manufacturing with CuSi3 alloy wire, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.380

4

D. Mukin et al. / Materials Today: Proceedings xxx (xxxx) xxx

Fig. 3. Calculation scheme for determining the shape and size of the bead surface during deposition.

h

d2 z dx2

1þ

dz2 i3=2 ¼ z þ z0

ð11Þ

dx

In the general case, the exact solution of equation (11) in the parametric form is presented as

z2 ¼ z0 2 þ 2ð1  cosuÞ Zu x¼ 0

cosudu pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 z0 þ 2ð1  cosuÞ

ð12Þ

ð13Þ

where the parameter is the angle between the Z-axis and the normal to the curve describing the shape of the deposited layer. According to a given mode, it is possible to determine the area F and width of the deposited layer B by calculation. Using equations (12) and (13), we can calculate the basic geometric parameters of the deposited bead, such as the height of the deposited bead, curvature radius of the bulge at the vertex.

Due to the arched contour of the deposited layer, a new layer cannot simply be applied to the previous layer. Therefore, the optimal wall width calculated according to equation (9) will be considered the boundary of the fastening of the deposited bead. The optimization problem is solved by the iterative method, the convergence condition is to achieve the specified accuracy of the temperature at the point of local minimum. The area of deposited metal per unit time F0 is calculated from the condition that the amount of molten and deposited filler metal is equal:

F0 ¼ p 

2

d w  4 V

ð14Þ

where d – wire diameter; w – wire feed rate; V – the speed of cladding. According to the known values of the width and area of the bead, the theoretical form of the free surface of the liquid metal is constructed. The temperature field in this deposited layer is calculated. Then it is necessary to calculate the height of the formation of a new layer. This value is determined by the intersection

Fig. 4. The temperature fields of the substrate with front feed (a), side feed (b), without wire (c).

Please cite this article as: D. Mukin, E. Valdaytseva, T. Hassel et al., Modelling of heat transfer process in non-vacuum electron beam additive manufacturing with CuSi3 alloy wire, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.380

D. Mukin et al. / Materials Today: Proceedings xxx (xxxx) xxx

Fig. 5. Temperature fields of the substrate surface at various values of the parameter X’ or Y’ (solid line for front feed; dashed line for side feed).

5

of the material were assumed according to [28]. The substrate was heated in the following mode: electron beam power q = 2600 W, effective radius RE = 0.65 mm, V = 3 m/min, wire radius 0.6 mm. According to the research [3] the efficiency of the electron beam is g = 0.87. The actual process efficiency is less because there is a power loss due to energy loss through inelastic scattering. Fig. 5 shows the temperature fields in the section x = 0 mm at different values of the parameter X’ or Y’, where, as mentioned earlier, X’ is the coordinate of the wire tip along the x-axis in the case of front feed (see Fig. 1), Y’ is the coordinate of the wire tip along the y-axis in the case of side wire feed. The position of the wire tip (X’ for front feed or Y’ for side feed) greatly affects both the shape and the size of the melt pool and its temperature. The more the wire overlaps the heat source and absorbs heat, the more real the temperature distribution on the surface of the substrate. The displacement of the center of the melt pool along the y-axis must be taken into account for side feed of the wire. Therefore, special attention should be paid to the selection of the wire feed rate. 3.2. Temperature field in the wire

point of the melting isotherm and the shape of the bead surface. After that, the process is repeated, but the cross-sectional area of the new layer consists of the sum of the cross-sectional area of the penetration of the previous layers and the filler metal deposited per unit time.

3. Results and discussion

Fig. 6 shows the temperature fields longitudinal section of the filler wire, obtained by equation (7) for the CuSi3 copper alloy. The shape of the melting surface depends on the feed rate w. At a slow feed rate, a more uniform heating of the wire over the cross section occurs. The higher the feed rate, the greater the inclination angle of the melting surface and the farther the wire tip will pass through the electron beam axis. It means that other things being equal, there is a greater overlap of the heat source.

3.1. Temperature field in the substrate 3.3. Shape of the layer surface Fig. 4 shows the temperature fields of the substrate in the x0y plane, obtained by equation (6) for front feed and similar to it for side feed, for the CuSi3 copper alloy. The thermophysical properties

Consider the process of wire feed non-vacuum electron beam deposition using CuSi3 wire. The process parameters are as follows:

Fig. 6. The temperature fields of the filler wire longitudinal section at feed rate w = 3.7 m/min and w = 5 m/min (the solid line is the axis of the electron beam, the dashed line is the radius).

Please cite this article as: D. Mukin, E. Valdaytseva, T. Hassel et al., Modelling of heat transfer process in non-vacuum electron beam additive manufacturing with CuSi3 alloy wire, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.380

6

D. Mukin et al. / Materials Today: Proceedings xxx (xxxx) xxx

Fig. 9. The graph of the melt pool width and the layer height as a function of the wire feed rate. Fig. 7. Experimental wall cross-section (left) and calculated cross-sectional shape and temperature field of the deposited wall (right).

electron beam power q = 2600 W, effective radius RE = 0.65 mm, V = 3 m/min, wire feed rate w = 3.7 m/min, wire radius Rw = 0.6 mm, wire angle to the horizon is 20°. The average value of the surface tension for liquid CuSi3 alloy in the temperature range of 1200–1300 °C was assumed to be 1.28 N/m [29]. Fig. 7 shows the result of comparing the calculated and experimental forms of the deposited wall, and also shows the temperature field obtained in the deposition process. Comparing the experimental and calculated results, it can be established that the method of calculating the temperature field and the shape of the deposited beads satisfactorily describes the heat transfer process during the wire-feed electron beam deposition process. This calculation method can be used to pre-select process parameters.

Fig. 8 shows the modelling result of the wall deposition process at a wire feed rate w = 5 m/min. By increasing the wire feed rate, one can notice that an increase in the wall height is associated not only with an increase in the metal deposited per unit time but also with a decrease in the size of the melt pool, which results in a decrease in the wall width. This is due to the fact that by increasing the wire feed rate, the size of the ‘‘shadow” increases, the amount of absorbed energy by the surface of the layer decreases. Fig. 9 shows a graph of the melt pool width and the layer height as a function of the wire feed rate. 4. Conclusions As a result of the theoretical study of the wire-feed electron beam deposition process, calculations were made to establish the relationship between the parameters of the process mode and the geometric characteristics of the deposited layers. The proposed method for solving the system of equations of heat conduction and equilibrium of the liquid phase in the gravity field allows determining with satisfactory accuracy the surface shape of the deposited wall. This calculation method can be used to pre-select process parameters. The position of the wire tip greatly affects both the shape and size of the melt pool and its temperature. It is necessary to take into account the displacement of the melt pool along the y-axis when side wire feed. At the same time, an increase in the wire feed rate leads not only to an increase in the cross-sectional area and height of the deposited layers but also to a decrease in the width of the melt pool, which leads to a decrease in the wall width. Consequently, special attention should be paid to the selection of wire feed rate. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement

Fig. 8. Temperature field and cross-sectional shape of the deposited wall at a wire feed rate w = 5 m/min.

The study was carried out with the financial support of the RFBR in the framework of the scientific project 19-51-12010 NNIO_a ‘‘Investigation of a novel additive manufacturing process

Please cite this article as: D. Mukin, E. Valdaytseva, T. Hassel et al., Modelling of heat transfer process in non-vacuum electron beam additive manufacturing with CuSi3 alloy wire, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.380

D. Mukin et al. / Materials Today: Proceedings xxx (xxxx) xxx

for copper alloys based on the non-vacuum electron beam technology”.

References [1] C. Süsskind, Introduction to electron beam technology, Proc. IEEE 51 (4) (1963) 648. [2] M.S. Wȩglowski, S. Błacha, A. Phillips, Electron beam welding – techniques and trends – review, Vacuum (2016). [3] T. Hassel, N. Murray, R. Konya, A. Beniyash, F.W. Bach, Nonvacuum electron beam cutting and welding – two partnering processes for fast and highly efficient metal working, Weld. World (2013). [4] F.W. Bach, A. Szelagowski, R. Versemann, M. Zelt, Non vacuum electron beam welding of light sheet metals and steel sheets, Weld. World (2003). [5] D.E. Powers, B.W. Schumacher, Using the electron beam in air to weld conventionally produced sheet metal parts, Weld. J. (Miami, Fla) (1989). [6] F.W. Bach, A. Beniyash, K. Lau, R. Versemann, Joining of steel-aluminium hybrid structures with electron beam on atmosphere, Adv. Mater. Res. (2005). [7] U. Dilthey, A. Gumenyuk, H. Masny, Non-vacuum electron beam welding, Adv. Mater. Res. (2005). [8] O. Lenivtseva, L. Chuchkova, D. Krivezhenko, Structure and wear resistance of Ti-TiC-TiB layers obtained by non-vacuum electron beam cladding, in: MATEC Web of Conferences, 2017. [9] A.A. Losinskaya, E.A. Lozhkina, A.I. Bardin, Structure and properties of steel case-hardened by non-vacuum electron-beam cladding of carbon fibers, in: IOP Conference Series: Materials Science and Engineering, 2018. [10] I.A. Bataev, A.A. Bataev, M.G. Golkovski, D.S. Krivizhenko, A.A. Losinskaya, O.G. Lenivtseva, Structure of surface layers produced by non-vacuum electron beam boriding, Appl. Surf. Sci. (2013). [11] I.A. Bataev et al., Structure and tribological properties of steel after nonvacuum electron beam cladding of Ti, Mo and graphite powders, Mater. Charact. (2016). [12] I.A. Bataev et al., Non-vacuum electron-beam carburizing and surface hardening of mild steel, Appl. Surf. Sci. (2014). [13] R. Alexey, G. Mikhail, S. Vitaly, K. Pavel, B. Ivan, B. Anatoly, Corrosion resistance of multilayer Ti-Ta coatings obtained by electron beam cladding in the atmosphere, Adv. Mater. Res. (2014).

7

[14] T. DebRoy et al., Additive manufacturing of metallic components – process, structure and properties, Prog. Mater. Sci. (2018). [15] G.A. Turichin, V.V. Somonov, K.D. Babkin, E.V. Zemlyakov, O.G. Klimova, Highspeed direct laser deposition: technology, equipment and materials, in: IOP Conference Series: Materials Science and Engineering, 2016. [16] L.A. Magerramova et al., Peculiarities of additive technologies application in the production of gas turbine engine parts, J. Phys. Conf. Ser. (2018). [17] G.A. Turichin et al., Technological aspects of high speed direct laser deposition based on heterophase powder metallurgy, Phys. Procedia (2015). [18] G. Turichin, E. Zemlyakov, K. Babkin, S. Ivanov, A. Vildanov, Analysis of distortion during laser metal deposition of large parts, in: Procedia CIRP, 2018. [19] A.D. Ahmetov, M.O. Sklyar, R.S. Korsmik, I.A. Tsibulskiy, Features of the structure formation at laser and laser-arc deposition from aluminum wire, Solid State Phenom. (2018). [20] G. Turichin, E. Zemlyakov, K. Babkin, S. Ivanov, A. Vildanov, Laser metal deposition of Ti-6Al-4V alloy with beam oscillation, in: Procedia CIRP, 2018. [21] O. Klimova-Korsmik, G. Turichin, E. Zemlyakov, K. Babkin, P. Petrovsky, A. Travyanov, Technology of high-speed direct laser deposition from Ni-based superalloys, Phys. Procedia (2016). [22] O. Klimova-Korsmik, G. Turichin, E. Zemlyakov, K. Babkin, P. Petrovsky, A. Travyanov, Structure formation in Ni superalloys during high-speed direct laser deposition, Mater. Sci. Forum (2017). [23] A. Hess, R. Schuster, A. Heider, R. Weber, T. Graf, Continuous wave laser welding of copper with combined beams at wavelengths of 1030 nm and of 515 nm, Phys. Procedia (2011). [24] A. Blom, P. Dunias, P. van Engen, W. Hoving, J. de Kramer, Process spread reduction of laser microspot welding of thin copper parts using real-time control, in: Photon Processing in Microelectronics and Photonics II, 2003. [25] D.V. Mukin, S.Y. Ivanov, E.A. Valdaitseva, G.A. Turichin, A.E. Beniash, An analytical model for filler wire heating and melting during wire feed laser deposition, Key Eng. Mater. (2019). [26] N.N. Rykalin, Calculations of thermal processes in welding (Ripol Klassik), 2013. [27] B.M. Berezovskii, V.A. Stikhin, Effect of surface tension on the formation of weld reinforcement, Svar. Proizv. 1 (1977) 51–53. [28] W. Reimann, M. Dobler, M. Goede, M. Schmidt, K. Dilger, Three-beam laser brazing of zinc-coated steel, Int. J. Adv. Manuf. Technol. (2017). [29] M. Adachi, M. Schick, J. Brillo, I. Egry, M. Watanabe, Surface tension and density measurement of liquid Si-Cu binary alloys, J. Mater. Sci. (2010).

Please cite this article as: D. Mukin, E. Valdaytseva, T. Hassel et al., Modelling of heat transfer process in non-vacuum electron beam additive manufacturing with CuSi3 alloy wire, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.380