2. Technological parameters

temperature required can be mentioned. Furthermore, the formation of environmental pollution due to the use of chemicals and the need that the materials must be conductors can also be

The electrical discharge machining process is another method which is used for manufacturing of the materials. This technique is based on the removing of the material using electrical discharge. Series of rapidly recurring current discharge between two electrodes were applied which are responsible for the removal of the material. The method is often used for prototype production and manufacturing of parts, especially for the needs of the automotive and aircraft industries. However, the slow rate of the material removal and the requirement of conductive materials that can be manufactured by the discussed method are of the major drawbacks [2]. Promising techniques for fabrication of new materials with unique properties and for modification of their structure are the additive manufacturing technologies. They are based on layerby-layer fabrication of components [3]. The additive technologies include several techniques for materials' treatment, such as ultrasonic processes, electron beam processes, laser beam processes, etc. The ultrasonic processing is a revolutionary processing technology widely used for welding and joining. It is based on the scrubbing together with ultrasonic vibrations under controlled pressure or normal load. Nevertheless, this technique is not capable to melt the treated area and operates at a temperature significantly lower than the melting point of the manufactured materials. Thus, although the discussed technique is a revolutionary process for welding and joining, it is not suitable for processes such as surface alloying, cladding, etc. [4]. The methods of a surface treatment by high energy fluxes (HEFs), which are a part of the additive technologies, are intensively used for formation of surface alloys, as well as for modification of the surface structure of different materials. Their main advantage is the precise control of the energy input, which alloys the controlling of the structure and properties of the treated materials. Furthermore, in comparison to traditional manufacturing, some benefits of

• The use of high energy fluxes alloys manufacturing at comparatively low cost in compar-

• Single tools can be fabricated in much shorter time by using high energy flux technologies

• Materials and other products with a complex geometry can be manufactured by additive techniques, while using traditional technologies, many different parts have to be

• High energy fluxes are useful for a surface modification and hardening and allow design changes of the surfaces. The application of the traditional technologies for these purposes

The processes used for surface manufacturing of the materials are treatment by fluxes of photons (laser radiation) or accelerated electrons (electron beam). During this process, the manufactured material is irradiated by electron or laser beam. When the flux of the photons or accelerated electrons interacts with the treated surface, the work-piece is heated and forms thermal distribution from the surface to the bulk [6–9]. After the irradiation, the sample

considered as limitations [1].

70 Advanced Surface Engineering Research

the additive technologies can be mentioned [5]:

in comparison to the traditional methods.

manufactured separately and after that assembled.

is too expensive and time ineffective for the discussed purposes.

ison to the traditional processes.

For both types of techniques (i.e., electron and laser beam), the beam power and power density are of the important process parameters. In the case of laser beam, it can be set directly, while for e-beam it is a product of the accelerating voltage and the beam current. For example, typical values for the accelerating voltage are from 50 to 150 kV. With an increase of the beam power, the kinetic energy of the electrons also increases, which causes an increase in the penetration depth of the beam. The beam power density is an important parameter for the alloying operation since it affects the forces acting in the molten material [16].

The speed of the specimen motion during the process is also a basic parameter. As a result of this movement, the heat is transferred to the volume of the material. It is responsible for the heating and cooling rate as well as for the solidification speed. With an increase of the speed of the specimen motion, the heat input decreases. The beam power and the speed of the specimen motion are responsible for the volume of the manufactured zone, the thickness, and the width [5].

methods are time- and effort-consuming, and the results are not always reliable. For that reason, the numerical approaches are more appropriate and widely used for evaluating the thermal field and modeling the thermal processes. The heat transfer equation for the case of treatment by high energy fluxes (i.e., electron and laser beams) can be described for homogeneous and isotropic material whose thermophysical properties are temperature-independent

<sup>T</sup><sup>¼</sup> f rð Þ ;<sup>t</sup>

<sup>c</sup><sup>r</sup> is the thermal diffusivity; λ is the thermal conductivity, c is the specific heat, and r

ð

G r,tjr<sup>0</sup> ð Þ , τ

� � � � � � τ¼0

R

, z<sup>0</sup> ð , τÞ ¼ G1 x,tjx<sup>0</sup> ð Þ� , τ G2 y,tjy<sup>0</sup> ð Þ� , τ G3 z,tjz<sup>0</sup> ð Þ , τ (3)

exp � <sup>x</sup> � <sup>x</sup><sup>0</sup> ð Þ<sup>2</sup>

" # !

4αð Þ t � τ !

<sup>þ</sup> exp � <sup>z</sup> <sup>þ</sup> <sup>z</sup><sup>0</sup> ð Þ<sup>2</sup>

4αð Þ t � τ

4αð Þ t � τ

!

The solution T(r,t) of Eq. (1) for the case of three-dimensional transient, nonhomogeneous heat

G r,tjr<sup>0</sup> ð Þ ,t f r<sup>0</sup> ð Þ ; τ dv<sup>0</sup> þ

where F(r') describes the initial temperature distribution. In orthogonal coordinates, the

In Eq. (3), each of the Green's functions (i.e., G1, G2, and G3) depends on the boundary conditions and the regions (i.e., finite, semi-infinite, or infinite). For the case of infinite region,

exp � <sup>z</sup> � <sup>z</sup><sup>0</sup> ð Þ<sup>2</sup>

By substituting G1(x,t|x',τ) and G2(y,t|y',τ) from Eq.(4) and G3(z,t|z',τ) from Eq.(5) in Eq.(3),

, <sup>z</sup><sup>0</sup> <sup>ð</sup> <sup>¼</sup> <sup>0</sup>, <sup>τ</sup>Þ ¼ 2 4½ � παð Þ <sup>t</sup> � <sup>τ</sup> �1:<sup>5</sup> � exp � <sup>x</sup> � <sup>x</sup><sup>0</sup> ð Þ<sup>2</sup> <sup>þ</sup> <sup>y</sup> � <sup>y</sup><sup>0</sup> ð Þ<sup>2</sup> <sup>þ</sup> <sup>z</sup><sup>2</sup>

By substituting x' = x-r.cosθ and y' = y-r.sinθ and G(r,t|r',τ) from Eq.(6) in Eq.(2), the distribution

4αð Þ t � τ

!

<sup>λ</sup> (1)

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F r<sup>0</sup> ð Þdv<sup>0</sup> (2)

, (4)

(5)

(6)

from the following field equation of heat conduction [19–22]:

Here, <sup>α</sup><sup>¼</sup> <sup>λ</sup>

we obtain:

G x, y, z,tjx<sup>0</sup>

, y<sup>0</sup>

of the temperature is the following:

is the density of the specimen.

T rð Þ¼ ;t

Green's function can be written as follows:

G x, y, z,tjx<sup>0</sup>

the Green's function is the following:

k λ ð t

τ¼0

, y<sup>0</sup>

G z,tjz<sup>0</sup> ð Þ¼ ,<sup>t</sup> ½ � <sup>4</sup>παð Þ <sup>t</sup> � <sup>τ</sup> �1=<sup>2</sup>

dτ ð

R

G x,tjx<sup>0</sup> ð Þ¼ , <sup>τ</sup> ½ � <sup>4</sup>παð Þ <sup>t</sup> � <sup>τ</sup> �1=<sup>2</sup>

and for semi-infinite, when the boundary is at z' = 0, the Green's function is:

1 α ∂T <sup>∂</sup><sup>t</sup> �∇<sup>2</sup>

conduction problems can be expressed by three-dimensional Green's function:

Figure 1. Different types of scanning electron beam: (a) sinusoidal dithering; (b) ellipsoidal rotating; (c) circular rotating with higher specimen movement velocity; and (d) circular rotating with slower specimen movement velocity (the figure is drawn by the authors).

The application of the electron beam for additive manufacturing has a major advantage in comparison to the laser beam, namely beam deflection. Since the electrons are charged particles, they can be deflected from the normal axis by application of electrical and electromagnetic fields. This allows a realization of different scanning approaches which affects the solidification processes and can control further the processes occurring during the abovementioned operations. For example, when applying the e-beam techniques, a scanning can be realized using regime of circular geometry. In this case, the trajectory of the beam is overlapping and maintaining the lifetime of the melt pool further. This is important for the alloying operation since the alloying elements can be distributed significantly more homogeneous [17]. Possible electron beam scanning geometries are shown in Figure 1.

Another difference between electron and laser beam processes is the working pressure. When applying electron beam technique, high vacuum state is absolutely required. The presence of some atoms and gas molecules on the way of the beam can result in loss of its power due to absorption and electron scattering. Typically, the pressure should be at least 5<sup>10</sup><sup>4</sup> mbar or lower. The laser beam processes are usually realized in atmospheric medium. In order to prevent oxidation of the manufactured area, argon is blown over the surface of the manufactured material [16, 18].

#### 3. Heat processes

As already mentioned, the work-piece is heated on the surface and form thermal distribution. The rapid heating and cooling lead to structural transformations, changes in the chemical composition, melting the surface, etc., and therefore the rate of these processes is of major importance. There exist experimental and numerical approaches to examine the temperature field and, thus, the rates of heating and cooling, which will give us information related to the final microstructure and functional properties of the treated material. The experimental methods are time- and effort-consuming, and the results are not always reliable. For that reason, the numerical approaches are more appropriate and widely used for evaluating the thermal field and modeling the thermal processes. The heat transfer equation for the case of treatment by high energy fluxes (i.e., electron and laser beams) can be described for homogeneous and isotropic material whose thermophysical properties are temperature-independent from the following field equation of heat conduction [19–22]:

$$\frac{1}{\alpha} \frac{\partial T}{\partial t} - \nabla^2 T = \frac{f(r, t)}{\lambda} \tag{1}$$

Here, <sup>α</sup><sup>¼</sup> <sup>λ</sup> <sup>c</sup><sup>r</sup> is the thermal diffusivity; λ is the thermal conductivity, c is the specific heat, and r is the density of the specimen.

The solution T(r,t) of Eq. (1) for the case of three-dimensional transient, nonhomogeneous heat conduction problems can be expressed by three-dimensional Green's function:

$$T(r,t) = \frac{k}{\lambda} \int\_{\tau=0}^{t} d\tau \left[ G(r,t|r',t) f(r',\tau) d\upsilon' + \left. \int\_{\mathbb{R}} G(r,t|r',\tau) \right|\_{\tau=0} F(r') d\upsilon' \right] \tag{2}$$

where F(r') describes the initial temperature distribution. In orthogonal coordinates, the Green's function can be written as follows:

$$\mathbf{G}(\mathbf{x}, y, z, \mathbf{t}|\mathbf{x}', y', z', \mathbf{\tau}) = \mathbf{G1}(\mathbf{x}, \mathbf{t}|\mathbf{x}', \mathbf{\tau}) \times \mathbf{G2}(y, \mathbf{t}|y', \mathbf{\tau}) \times \mathbf{G3}(z, \mathbf{t}|z', \mathbf{\tau}) \tag{3}$$

In Eq. (3), each of the Green's functions (i.e., G1, G2, and G3) depends on the boundary conditions and the regions (i.e., finite, semi-infinite, or infinite). For the case of infinite region, the Green's function is the following:

$$\mathbf{G}(\mathbf{x},t|\mathbf{x}',\mathbf{\tau}) = \left[4\pi\alpha(t-\tau)\right]^{-1/2} \exp\left(-\frac{\left(\mathbf{x}-\mathbf{x}'\right)^2}{4\alpha(t-\tau)}\right),\tag{4}$$

and for semi-infinite, when the boundary is at z' = 0, the Green's function is:

The application of the electron beam for additive manufacturing has a major advantage in comparison to the laser beam, namely beam deflection. Since the electrons are charged particles, they can be deflected from the normal axis by application of electrical and electromagnetic fields. This allows a realization of different scanning approaches which affects the solidification processes and can control further the processes occurring during the abovementioned operations. For example, when applying the e-beam techniques, a scanning can be realized using regime of circular geometry. In this case, the trajectory of the beam is overlapping and maintaining the lifetime of the melt pool further. This is important for the alloying operation since the alloying elements can be distributed significantly more homogeneous [17]. Possible

Figure 1. Different types of scanning electron beam: (a) sinusoidal dithering; (b) ellipsoidal rotating; (c) circular rotating with higher specimen movement velocity; and (d) circular rotating with slower specimen movement velocity (the figure is

Another difference between electron and laser beam processes is the working pressure. When applying electron beam technique, high vacuum state is absolutely required. The presence of some atoms and gas molecules on the way of the beam can result in loss of its power due to absorption and electron scattering. Typically, the pressure should be at least 5<sup>10</sup><sup>4</sup> mbar or lower. The laser beam processes are usually realized in atmospheric medium. In order to prevent oxidation of the manufactured area, argon is blown over the surface of the manufactured

As already mentioned, the work-piece is heated on the surface and form thermal distribution. The rapid heating and cooling lead to structural transformations, changes in the chemical composition, melting the surface, etc., and therefore the rate of these processes is of major importance. There exist experimental and numerical approaches to examine the temperature field and, thus, the rates of heating and cooling, which will give us information related to the final microstructure and functional properties of the treated material. The experimental

electron beam scanning geometries are shown in Figure 1.

material [16, 18].

drawn by the authors).

72 Advanced Surface Engineering Research

3. Heat processes

$$\mathbf{G}(\mathbf{z},\mathbf{t}|\mathbf{z}',\mathbf{t}) = \left[4\pi\alpha(\mathbf{t}-\mathbf{r})\right]^{-1/2} \left[\exp\left(-\frac{(\mathbf{z}-\mathbf{z}')^2}{4\alpha(\mathbf{t}-\mathbf{r})}\right) + \exp\left(-\frac{(\mathbf{z}+\mathbf{z}')^2}{4\alpha(\mathbf{t}-\mathbf{r})}\right)\right] \tag{5}$$

By substituting G1(x,t|x',τ) and G2(y,t|y',τ) from Eq.(4) and G3(z,t|z',τ) from Eq.(5) in Eq.(3), we obtain:

$$\mathbf{G}(\mathbf{x}, y, z, \mathbf{t} | \mathbf{x}', y', z' = \mathbf{0}, \tau) = \mathbf{2} [4\pi\alpha(t - \tau)]^{-1.5} \times \exp\left(-\frac{(\mathbf{x} - \mathbf{x}')^2 + (y - y')^2 + z^2}{4\alpha(t - \tau)}\right) \tag{6}$$

By substituting x' = x-r.cosθ and y' = y-r.sinθ and G(r,t|r',τ) from Eq.(6) in Eq.(2), the distribution of the temperature is the following:

$$T(\mathbf{x}, y, z, t) = \left. T\_0 + \frac{2\alpha}{\lambda} \right[ \left| \int\_0^{\pi} \right[ \left| f(\mathbf{x} - r\cos\theta, y - r\sin\theta, \tau) \times \left[ 4\pi\alpha(t - \tau) \right]^{-1.5} \times \exp\left( -\frac{r^2 + z^2}{4\alpha(t - \tau)} \right) \right| \quad \text{(7)} $$

Here, t is the time of temperature calculating, r and θ are the polar coordinates. In Eq. (7), f(x-r. cosθ,y-r.sinθ) is the beam intensity distribution. For a beam with Gaussian distribution which moves along a straight line, the beam intensity is:

$$f(\mathbf{x} - r\cos\theta, y - r\sin\theta, \tau) = \frac{\mathbf{3Q}}{\pi r\_0^2} \times \exp\left\{-\mathbf{3}\left(\frac{(\mathbf{x} - -r\cos\theta - v\tau)^2 + (y - r\sin\theta)^2}{r\_0^2}\right)\right\} \tag{8}$$

In Eq. (8), r0 is the beam radius, Q is the power transferred to the irradiated material, and v is the speed of the beam along moving line. For a dithering beam, the intensity distribution is the following:

by a deposition of a coating material on the substrate and subsequent treatment by laser or electron beam and by direct injection of the coating material into the melt pool. Figure 3a

Figure 2. (a) Solid-state HEF processing of metals and alloys; (b) HEF melting and processing of metals and alloys (the

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In the case of preliminary deposition of the coating, material is applied on the coated substrate in the form of slurry consisting of powder of the coating material mixed with a binder. The material is melted together with a thin layer of the surface substrate, and after the subsequent solidification, a clad track is formed [23]. However, this approach (a deposition of a coating material on the substrate and subsequent treatment by high energy flux) presents some drawbacks: the application of a slurry powder is taking too much time; it is too difficult to deposit a uniform film on complex surfaces. Also, this approach presents significantly lower productivity and high cost in comparison to direct injection of the coating material into the melt pool [24]. At the direct injection of the coating material, the clad track rises above the surface of the coated substrate. The injected alloying material is usually in the form of powder or wire. According to the authors of [25], at a constant beam power and scanning speed (i.e., scanned distance per second), the main parameter is the powder feed rate. Low powder feed rates correspond to lower input energy needed for melting of the incoming powder. This means that

Figure 3. (a) Cladding; (b) alloying by HEFs (the figure is drawn by the authors).

shows the cladding technique.

figure is drawn by the authors).

$$f(\mathbf{x} - r\cos\theta, y - r\sin\theta, \tau) = \frac{\mathbf{3Q}}{\pi r\_0^2} \exp\left(-\mathbf{3}\frac{\left(\mathbf{x} - \cos\theta - \nu\tau\right)^2 + \left(y - r\sin\theta - l\_{\text{max}}\cos\left(\frac{2\pi\tau}{\tau}\right)\right)^2}{r\_0^2}\right) \tag{9}$$

where lmax is the amplitude and τ\* is the period for each cycle. In the case of rotating beam, the beam intensity is the following:

$$\begin{aligned} &f(\mathbf{x} - r\cos\theta, y - r\sin\theta, \tau) \\ &= \frac{3Q}{\pi r\_0^2} \times \exp\left\{-3\left(\frac{(\mathbf{x} - r\cos\theta - v\tau - a\sin\left(\frac{2\pi r}{\tau^\*}\right))^2 + (y - r\sin\theta - I\_{\text{max}}\cos\left(\frac{2\pi r}{\tau^\*}\right))^2}{r\_0^2}\right)\right\} \end{aligned} \tag{10}$$

In Eq. (10), a is the diameter of the rotation along the moving line.

#### 4. Characteristics of the HEFs processes

The processes of surface modification of metals and alloys by using HEFs can be roughly divided into two groups depending on whether the HEFs act on the material in a solid (Figure 2a) or a liquid (Figure 2b) phase. Both types of techniques have found practical applications. In recent years, and in view of developing novel materials, the alloying with HEFs processing techniques has been widely used [5]. These techniques include additional alloying in the zone treated, which has a significant effect on the physical and mechanical properties of the materials processed [7–9].

#### 4.1. Cladding and alloying

Cladding techniques are used for a coating of a substrate by different materials in order to improve the functional properties of the surface. It can be realized by two different approaches:

T xð Þ¼ ; y; z;t T<sup>0</sup> þ

74 Advanced Surface Engineering Research

following:

<sup>¼</sup> <sup>3</sup><sup>Q</sup> πr<sup>2</sup> 0 2α λ ðt

�rdrdθdτ

f x<sup>ð</sup> � <sup>r</sup> cos <sup>θ</sup>; <sup>y</sup> � <sup>r</sup> sin <sup>θ</sup>; <sup>τ</sup>Þ ¼ <sup>3</sup><sup>Q</sup>

f x<sup>ð</sup> � <sup>r</sup> cos <sup>θ</sup>; <sup>y</sup> � <sup>r</sup> sin <sup>θ</sup>; <sup>τ</sup>Þ ¼ <sup>3</sup><sup>Q</sup>

beam intensity is the following:

f xð Þ � r cos θ; y � r sin θ; τ

� exp �3

0

ð π ð ∞

f x<sup>ð</sup> � <sup>r</sup> cos <sup>θ</sup>; <sup>y</sup> � <sup>r</sup> sin <sup>θ</sup>; <sup>τ</sup>Þ � ½ � <sup>4</sup>παð Þ <sup>t</sup> � <sup>τ</sup> �1:<sup>5</sup> � exp � <sup>r</sup><sup>2</sup> <sup>þ</sup> <sup>z</sup><sup>2</sup>

Here, t is the time of temperature calculating, r and θ are the polar coordinates. In Eq. (7), f(x-r. cosθ,y-r.sinθ) is the beam intensity distribution. For a beam with Gaussian distribution which

In Eq. (8), r0 is the beam radius, Q is the power transferred to the irradiated material, and v is the speed of the beam along moving line. For a dithering beam, the intensity distribution is the

where lmax is the amplitude and τ\* is the period for each cycle. In the case of rotating beam, the

The processes of surface modification of metals and alloys by using HEFs can be roughly divided into two groups depending on whether the HEFs act on the material in a solid (Figure 2a) or a liquid (Figure 2b) phase. Both types of techniques have found practical applications. In recent years, and in view of developing novel materials, the alloying with HEFs processing techniques has been widely used [5]. These techniques include additional alloying in the zone treated, which has a significant effect on the physical and mechanical

Cladding techniques are used for a coating of a substrate by different materials in order to improve the functional properties of the surface. It can be realized by two different approaches:

τ∗ � � � � <sup>2</sup> <sup>þ</sup> <sup>y</sup> � <sup>r</sup> sin <sup>θ</sup> � lmax cos <sup>2</sup>πτ

> r2 0

( ) !

� � � �

� exp �<sup>3</sup> ð Þ <sup>x</sup> � �<sup>r</sup> cos <sup>θ</sup> � <sup>v</sup><sup>τ</sup> <sup>2</sup> <sup>þ</sup> ð Þ <sup>y</sup> � <sup>r</sup> sin <sup>θ</sup> <sup>2</sup>

r2 0

( ) !

ð Þ <sup>x</sup> � cos <sup>θ</sup> � <sup>v</sup><sup>τ</sup> <sup>2</sup> <sup>þ</sup> <sup>y</sup> � <sup>r</sup> sin <sup>θ</sup> � lmax cos <sup>2</sup>πτ

!

r2 0 4αð Þ t � τ

τ∗

τ∗

� � � � <sup>2</sup>

� � � � <sup>2</sup>

(7)

(8)

(9)

(10)

0

�π

moves along a straight line, the beam intensity is:

πr<sup>2</sup> 0

πr<sup>2</sup> 0

In Eq. (10), a is the diameter of the rotation along the moving line.

4. Characteristics of the HEFs processes

properties of the materials processed [7–9].

4.1. Cladding and alloying

exp �3

<sup>x</sup> � <sup>r</sup> cos <sup>θ</sup> � <sup>v</sup><sup>τ</sup> � <sup>a</sup> sin <sup>2</sup>πτ

Figure 2. (a) Solid-state HEF processing of metals and alloys; (b) HEF melting and processing of metals and alloys (the figure is drawn by the authors).

by a deposition of a coating material on the substrate and subsequent treatment by laser or electron beam and by direct injection of the coating material into the melt pool. Figure 3a shows the cladding technique.

In the case of preliminary deposition of the coating, material is applied on the coated substrate in the form of slurry consisting of powder of the coating material mixed with a binder. The material is melted together with a thin layer of the surface substrate, and after the subsequent solidification, a clad track is formed [23]. However, this approach (a deposition of a coating material on the substrate and subsequent treatment by high energy flux) presents some drawbacks: the application of a slurry powder is taking too much time; it is too difficult to deposit a uniform film on complex surfaces. Also, this approach presents significantly lower productivity and high cost in comparison to direct injection of the coating material into the melt pool [24]. At the direct injection of the coating material, the clad track rises above the surface of the coated substrate. The injected alloying material is usually in the form of powder or wire. According to the authors of [25], at a constant beam power and scanning speed (i.e., scanned distance per second), the main parameter is the powder feed rate. Low powder feed rates correspond to lower input energy needed for melting of the incoming powder. This means that

Figure 3. (a) Cladding; (b) alloying by HEFs (the figure is drawn by the authors).

the melt depth of the substrate is too high, which corresponds to low built-up material on the surface and low contact angle between the substrate surface and the tangent to the track surface at the contact edge (α) (Figure 4).

With an increase of the powder feed rate, the input energy needed for melting of the incoming powder also increases and the melt depth of the surface decreases. The clad height and angle α increase as well. After passing a certain value of the powder feed rate and α, the cladded material loses adherence and porosity between the tracks can be formed due to the shadowing of the substrate. The angle α is a good indicator for the quality of the cladded material. The optimal values for α are in the range from 45 to 80� [25]. By overlapping of the clad tracks, a large area can be coated. Important merits of the cladded coatings are the good adhesion between the coating and the substrate, low porosity, and absence of cracking. The typical thicknesses of the coatings formed by cladding technique are in the range from 0.5 mm to 5 mm.

For realizing of alloying mechanism (Figure 3b), the manufactured parts are treated by high energy fluxes and built by melting the surface, forming a melt pool. The melt pool is formed due to the energy input of the flux on the manufactured part. During the melting of the surface of the manufactured part, the alloying elements are simultaneously added into the melt pool in the form of powder or wire or are deposited onto the surface as a layer with uniform thickness. Interdiffusion processes between the substrate and the alloying elements occur. The melt pool solidifies rapidly, and after the solidification, the surface alloy is formed [6–9, 12]. The distribution of the alloying elements is based on the Marangoni convection which is caused by the high temperature gradient in the melt pool [26–28]. The influence of the convection on the homogenization process is evaluated by the surface tension number, which is given in Eq. (11):

$$S = \frac{\left(\frac{d\sigma}{dT}\right)\eta d}{\mu u\_0 k} \tag{11}$$

scanning speed; and k is the thermal conductivity. When the value of the surface tension number is low (S ≤ 45,000 [27]), the convection is negligible and the melt homogenization will be too slow. For high values of the surface tension number, the convection takes a leading role in the transport mechanism of the melt pool. In this case, the convection speed in high, as this leads to extremely fast homogenization. Therefore, in order to obtain homogeneous surface alloys with attractive functional properties, it is very important to optimize the technological parameters, included in Eq. (1), and the amount of the alloying elements. To achieve the required characteristics of the surface alloys, the dimension and lifetime of the melt pool

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Beside for alloying and cladding technologies, the high energy fluxes are often used for a

The purpose of such techniques is to increase the hardness and wear resistance of the materials as a result of the processes occurring during the heating and cooling. The hardening is a technological process, in which the metals and alloys are heated to a certain temperature, followed by a rapid cooling which results in formation of metastable structures as well as finer microstructure, leading to an increase in the hardness and wear resistance [29–34]. The high cooling rate required for the structural transformations occurring during the self-quenching process strongly depends on the thermophysical properties of the hardened material. This hardening technique has received attention only in the metallurgical industry since it offers the advantages of low hardening distortion and low energy consumption. The application of a hardening by means of high energy fluxes provides the metallurgist an additional option to

should be controlled accurately and kept stable during the alloying process.

surface hardening of the materials (Figure 5a and b).

conventional hardening techniques [29].

Figure 5. Surface hardening is (a) solid and (b) liquid HEFs treatment.

4.2. Hardening

In Eq. (11), S is the surface tension number; dσ/dT is the temperature coefficient of the surface tension; q is the net heat flow; d is the diameter of the beam; μ is the viscosity; u\_0 is the

Figure 4. Cross section of cladding tracks: (a) low powder feed rate; (b) optimal powder feed rate; (c) high powder feed rate [24].

scanning speed; and k is the thermal conductivity. When the value of the surface tension number is low (S ≤ 45,000 [27]), the convection is negligible and the melt homogenization will be too slow. For high values of the surface tension number, the convection takes a leading role in the transport mechanism of the melt pool. In this case, the convection speed in high, as this leads to extremely fast homogenization. Therefore, in order to obtain homogeneous surface alloys with attractive functional properties, it is very important to optimize the technological parameters, included in Eq. (1), and the amount of the alloying elements. To achieve the required characteristics of the surface alloys, the dimension and lifetime of the melt pool should be controlled accurately and kept stable during the alloying process.

#### 4.2. Hardening

the melt depth of the substrate is too high, which corresponds to low built-up material on the surface and low contact angle between the substrate surface and the tangent to the track

With an increase of the powder feed rate, the input energy needed for melting of the incoming powder also increases and the melt depth of the surface decreases. The clad height and angle α increase as well. After passing a certain value of the powder feed rate and α, the cladded material loses adherence and porosity between the tracks can be formed due to the shadowing of the substrate. The angle α is a good indicator for the quality of the cladded material. The optimal values for α are in the range from 45 to 80� [25]. By overlapping of the clad tracks, a large area can be coated. Important merits of the cladded coatings are the good adhesion between the coating and the substrate, low porosity, and absence of cracking. The typical thicknesses of the coatings formed by cladding technique are in the range from 0.5 mm to 5 mm. For realizing of alloying mechanism (Figure 3b), the manufactured parts are treated by high energy fluxes and built by melting the surface, forming a melt pool. The melt pool is formed due to the energy input of the flux on the manufactured part. During the melting of the surface of the manufactured part, the alloying elements are simultaneously added into the melt pool in the form of powder or wire or are deposited onto the surface as a layer with uniform thickness. Interdiffusion processes between the substrate and the alloying elements occur. The melt pool solidifies rapidly, and after the solidification, the surface alloy is formed [6–9, 12]. The distribution of the alloying elements is based on the Marangoni convection which is caused by the high temperature gradient in the melt pool [26–28]. The influence of the convection on the homogenization process is evaluated by the surface tension number,

S ¼

dσ dT qd

In Eq. (11), S is the surface tension number; dσ/dT is the temperature coefficient of the surface tension; q is the net heat flow; d is the diameter of the beam; μ is the viscosity; u\_0 is the

Figure 4. Cross section of cladding tracks: (a) low powder feed rate; (b) optimal powder feed rate; (c) high powder feed

<sup>μ</sup>u0<sup>k</sup> (11)

surface at the contact edge (α) (Figure 4).

76 Advanced Surface Engineering Research

which is given in Eq. (11):

rate [24].

Beside for alloying and cladding technologies, the high energy fluxes are often used for a surface hardening of the materials (Figure 5a and b).

The purpose of such techniques is to increase the hardness and wear resistance of the materials as a result of the processes occurring during the heating and cooling. The hardening is a technological process, in which the metals and alloys are heated to a certain temperature, followed by a rapid cooling which results in formation of metastable structures as well as finer microstructure, leading to an increase in the hardness and wear resistance [29–34]. The high cooling rate required for the structural transformations occurring during the self-quenching process strongly depends on the thermophysical properties of the hardened material. This hardening technique has received attention only in the metallurgical industry since it offers the advantages of low hardening distortion and low energy consumption. The application of a hardening by means of high energy fluxes provides the metallurgist an additional option to conventional hardening techniques [29].

Figure 5. Surface hardening is (a) solid and (b) liquid HEFs treatment.
