**5. Peculiarity of metal structure formation in hybrid welding**

To reduce the constructions weight new high-strength steels are applied. Characteristics of these steels are determined by parameters of ensembles of ultrafine inclusions. New technol‐ ogies for car bodies are based on tailored blanks. Weight reduction without decreasing the strength is achieved by using high-strength steels and alloys in the production blanks. However, it is necessary to ensure satisfactory plastic weld characteristics.

This requires the use of welding technique, which provides the required level of ductility of weld seams and the same quality as laser welding process provides. Using a high-speed thermal cycling is the one of most promising techniques for getting good microstructure and mechanical properties [33]. This may be accomplished by welding two heat sources following one after another, for example, tandem laser welding [34]. However, from an economic standpoint it is advisable to use cheap local sources of heating as the second source, such as a powerful lamp.

To select treatment regimes, which provide the requisite microstructure and properties of the alloy, it is necessary to have a quantitative definition of the effect of temperature cycling on phase and structural transformations in the material. Modern concepts of phase transforma‐ tions mechanisms under the laser exposure on Fe-based alloys [35], which became the basis of thermodynamics of phase transitions, do not take into account the nonequilibrium character‐ istics of fast transformation processes that result in the appearance of nonequilibrium micro‐ structures in laser processing treatment. Thermodynamic characteristics do not allow to predict the temperature mutations for both transformations depending on the rate of heating and do not provide results for the nonstationary leak diffusion process. A quantitative description of the structural components is impossible without these factors. They can be formulated using only the kinetic theory of phase transformations, which has been made for the case of welding steels [36], and will be discussed in more detail in the example.

Phase transformations in Fe alloys under the beam treatment are defined as the metal structure consisting of two components. The first one is connected to decay (or formation) of solid solution of carbon in iron and formation (decay) of ferric carbide. The second process involves the conversion of FCC-BCC upon cooling after heating. A kinetic model was developed to determine the parameters of the formation and growth of the carbide inclusions.

The ratio between the surface area and the volume of the carbide inclusions depends on its shape. For the growth process, it can be considered as a point source. Concentration field around inclusion has a spherical symmetry. The inclusion can be considered as a sphere with an effective radius *a*. The nonequilibrium growth of new phase carbide inclusions is described using kinetic equation of the chemical reaction:

$$\frac{da}{dt} = K\_1(T) \cdot C - K\_2(T) \tag{3}$$

1 2 () () *r a*

The admixture concentration far from the growing inclusion is determined by its average value

The solution of this problem has been obtained by standard methods of mathematical physics:

*D K*


p

( 10 2 )

*D a*

3

<sup>4</sup> . <sup>3</sup>

p

(293)

where *a*lim is a limit size of the growing inclusion. Then the equation for inclusion radius can

3 10 2 1 0 2

3 1

p

Euler's method is used for solving the equations of growth of carbides. According to the results, *a*lim should be included in the equation. Preliminary value of *a*lim should be introduced, which

1

*D a*

To determine a value of the parameter *n*, it is possible to connect the *n* value with a solubility limit, which can be determined from the thermodynamic phase diagram. Having denoted the

1 1.56 . <sup>1</sup> *KC K*

Pay attention to the mutual influence in the carbide inclusions ensemble and having denoted the carbon concentration in the cementite as C' (for Fe3C C' ≅ 0.25) and inclusion number


*C C <sup>r</sup>*®¥ ® <sup>0</sup> (7)

Laser and Hybrid Laser-Arc Welding http://dx.doi.org/10.5772/64522

(9)

¢ (10)

(8)

149

(11)

*<sup>C</sup> D KT C KT <sup>r</sup>*

<sup>=</sup>

*r a*

=

0

density as *n*, the ensemble of spherical inclusions can be obtained as:

0 0

solubility limit as *C*lim(*T*), one can get from a substance conservation condition:

*C C <sup>n</sup>*


0 lim 3 lim

p*a C*

4 1.56


æ ö ç ÷ - =- - - ¢

*da KC K K C nC a <sup>K</sup>*

*dt D K*

p

4 3

*C C nC a* = - ¢

*C C*

¶

¶

*C*0:

be rewritten as:

where *K*1(*T*) and *K*2(*T*) is a constant forward and reverse reactions, *C*is the carbon concentration on the surface of the inclusions, and *T* and *t* are the local temperature and time. The reaction speed constants are given by the Arrhenius formula:

$$K\_{1,2}(T) = K\_{1,2} \, ^{(0)}\exp\left(\begin{matrix} U\_{f,s} \\ \nearrow kT \end{matrix}\right),\tag{4}$$

where *Uf* , *Us* are activation energy of the direct and reverse reaction, *K*<sup>1</sup> (0), *K*<sup>2</sup> (0) are frequency factors.

The superficial concentration is determined by a solution of the diffusion equation:

$$\frac{dC}{dt} = D\Delta C = D \frac{1}{r^2} \frac{\partial}{\partial r} \left( r^2 \frac{\partial C}{\partial r} \right) \tag{5}$$

The boundary condition on the surface of the growing inclusion (at *r* = *a*) is the condition of the solute flux continuity:

Laser and Hybrid Laser-Arc Welding http://dx.doi.org/10.5772/64522 149

$$\left. -D \frac{\partial C}{\partial r} \right|\_{r=a} = K\_1(T) \cdot C \Big|\_{r=a} - K\_2(T) \tag{6}$$

The admixture concentration far from the growing inclusion is determined by its average value *C*0:

tions mechanisms under the laser exposure on Fe-based alloys [35], which became the basis of thermodynamics of phase transitions, do not take into account the nonequilibrium character‐ istics of fast transformation processes that result in the appearance of nonequilibrium micro‐ structures in laser processing treatment. Thermodynamic characteristics do not allow to predict the temperature mutations for both transformations depending on the rate of heating and do not provide results for the nonstationary leak diffusion process. A quantitative description of the structural components is impossible without these factors. They can be formulated using only the kinetic theory of phase transformations, which has been made for

the case of welding steels [36], and will be discussed in more detail in the example.

determine the parameters of the formation and growth of the carbide inclusions.

1 2 () () *da KT C KT*

where *K*1(*T*) and *K*2(*T*) is a constant forward and reverse reactions, *C*is the carbon concentration on the surface of the inclusions, and *T* and *t* are the local temperature and time. The reaction

> (0) , 1,2 1,2 ( ) exp , *<sup>U</sup> f s KT K kT* æ ö <sup>=</sup> ç ÷

> > 2

 ¶

> ¶

, *Us* are activation energy of the direct and reverse reaction, *K*<sup>1</sup>

The superficial concentration is determined by a solution of the diffusion equation:

2 *dC* <sup>1</sup> *<sup>C</sup> DC D r dt rr r*

æ ö =D= ç ÷

¶

¶

The boundary condition on the surface of the growing inclusion (at *r* = *a*) is the condition of

*dt* = ×- (3)

è ø (4)

è ø (5)

(0), *K*<sup>2</sup>

(0) are frequency

using kinetic equation of the chemical reaction:

speed constants are given by the Arrhenius formula:

where *Uf*

148 Joining Technologies

the solute flux continuity:

factors.

Phase transformations in Fe alloys under the beam treatment are defined as the metal structure consisting of two components. The first one is connected to decay (or formation) of solid solution of carbon in iron and formation (decay) of ferric carbide. The second process involves the conversion of FCC-BCC upon cooling after heating. A kinetic model was developed to

The ratio between the surface area and the volume of the carbide inclusions depends on its shape. For the growth process, it can be considered as a point source. Concentration field around inclusion has a spherical symmetry. The inclusion can be considered as a sphere with an effective radius *a*. The nonequilibrium growth of new phase carbide inclusions is described

$$\left.C\right|\_{\cdot \to \circ} \to C\_0 \tag{7}$$

The solution of this problem has been obtained by standard methods of mathematical physics:

$$C = C\_o - \frac{1.56}{D\sqrt{\pi}} \frac{(K\_1 C\_o - K\_2)}{\left(\frac{K\_1}{D} - \frac{1}{a}\right)}.\tag{8}$$

Pay attention to the mutual influence in the carbide inclusions ensemble and having denoted the carbon concentration in the cementite as C' (for Fe3C C' ≅ 0.25) and inclusion number density as *n*, the ensemble of spherical inclusions can be obtained as:

$$C\_0 = C\_0 - nC'\frac{4}{3}\pi a^3. \tag{9}$$

To determine a value of the parameter *n*, it is possible to connect the *n* value with a solubility limit, which can be determined from the thermodynamic phase diagram. Having denoted the solubility limit as *C*lim(*T*), one can get from a substance conservation condition:

$$m = \frac{C\_0 - C\_{\text{lim}}(293)}{\frac{4}{3}\pi a\_{\text{lim}}^3 C'} \tag{10}$$

where *a*lim is a limit size of the growing inclusion. Then the equation for inclusion radius can be rewritten as:

$$\frac{da}{dt} = K\_1 \left( C\_0 - nC' \frac{4}{3} \pi a^3 - \frac{1.56}{\sqrt{\pi D}} \frac{K\_1 C\_0 - K\_2}{\frac{K\_1}{D} - \frac{1}{a}} \right) - K\_2 \tag{11}$$

Euler's method is used for solving the equations of growth of carbides. According to the results, *a*lim should be included in the equation. Preliminary value of *a*lim should be introduced, which provides the same final value of the inclusion radius *a*. The values of parameters, used for calculation in this article for low carbon steel, are given by the next list: *K*<sup>1</sup> (0) = 45 m/s, *K*<sup>2</sup> (0) = 2.2 m/s, *Uf* = 1.26⋅10–19 J/atom, *Us* = 1.60⋅10-19 J/atom, *D*0 = 2⋅10-6 m2 /s, *Ud* = 1.38⋅10-19 J/atom.

thickness of the diffusion layer, the problem is seen as univariate. Simultaneous solution of the related tasks about kinetics of new phase grains growth and the diffusion of carbon allow us to calculate the amount of a new phase at any point in the cycle. The result is a self-consistent system of equations, which describe material microstructure formation at the high-speed heating and cooling. The original structure adopted by the initial size of the carbide inclusions and initial grain sizes affect the diffusion coefficient. The thermal cycle is an input parameter, the parameters of which are determined by the technological cycle. The solution allows to

Laser and Hybrid Laser-Arc Welding http://dx.doi.org/10.5772/64522 151

**Figure 26.** Calculation results for carbide nanoinclusions sizes for steel 08U (solid line – laser processing, dotted line –

**Figure 27.** Calculation results for carbide nanoinclusions sizes for steel 08U (solid line – laser processing, dotted line –

Changing the form of a temperature cycle, which can be realized not only by HLAW, but also by another hybrid technologies, such as laser-light, dual beam, and others, it is possible to

hybrid processing). Delay between temperature peaks 1 s.

hybrid processing). Delay between temperature peaks 2 s.

calculate the evolution of the phase composition of the steel in the treatment zone.

**Figure 24.** Temperature cycle for steel 08U (solid line – laser processing, dotted line – hybrid processing). Delay be‐ tween temperature peaks 1 s.

**Figure 25.** Temperature cycles for steel 08U (solid line – laser processing, dotted line – hybrid processing). Delay be‐ tween temperature peaks 2 s.

Eventually, the kinetic model for the transformation α − *γ* should be formulated on the same principles as the model of nucleation and growth of inclusions. The interphase border movement rate in this case is that the diffusion Peclet number is not small, the diffusion equation, as against a problem about carbides growth, has been solved considering a convec‐ tive term. On the other hand, since growing grain sizes are significantly greater than the thickness of the diffusion layer, the problem is seen as univariate. Simultaneous solution of the related tasks about kinetics of new phase grains growth and the diffusion of carbon allow us to calculate the amount of a new phase at any point in the cycle. The result is a self-consistent system of equations, which describe material microstructure formation at the high-speed heating and cooling. The original structure adopted by the initial size of the carbide inclusions and initial grain sizes affect the diffusion coefficient. The thermal cycle is an input parameter, the parameters of which are determined by the technological cycle. The solution allows to calculate the evolution of the phase composition of the steel in the treatment zone.

provides the same final value of the inclusion radius *a*. The values of parameters, used for

**Figure 24.** Temperature cycle for steel 08U (solid line – laser processing, dotted line – hybrid processing). Delay be‐

**Figure 25.** Temperature cycles for steel 08U (solid line – laser processing, dotted line – hybrid processing). Delay be‐

Eventually, the kinetic model for the transformation α − *γ* should be formulated on the same principles as the model of nucleation and growth of inclusions. The interphase border movement rate in this case is that the diffusion Peclet number is not small, the diffusion equation, as against a problem about carbides growth, has been solved considering a convec‐ tive term. On the other hand, since growing grain sizes are significantly greater than the

(0) = 45 m/s, *K*<sup>2</sup>

/s, *Ud* = 1.38⋅10-19 J/atom.

(0) = 2.2

calculation in this article for low carbon steel, are given by the next list: *K*<sup>1</sup>

= 1.26⋅10–19 J/atom, *Us* = 1.60⋅10-19 J/atom, *D*0 = 2⋅10-6 m2

m/s, *Uf*

150 Joining Technologies

tween temperature peaks 1 s.

tween temperature peaks 2 s.

**Figure 26.** Calculation results for carbide nanoinclusions sizes for steel 08U (solid line – laser processing, dotted line – hybrid processing). Delay between temperature peaks 1 s.

**Figure 27.** Calculation results for carbide nanoinclusions sizes for steel 08U (solid line – laser processing, dotted line – hybrid processing). Delay between temperature peaks 2 s.

Changing the form of a temperature cycle, which can be realized not only by HLAW, but also by another hybrid technologies, such as laser-light, dual beam, and others, it is possible to achieve both size reduction and enlargement of the carbide inclusions in comparison with a temperature cycle, which is typical for laser action without an additional heat source (**Figures 24**–**29**).

alloys. Later on Quench factor analysis was applied for investigation possibility of predicting steel's mechanical properties during heat treatment [38], but in these works, processes of carbide formation and their influence on actual position of austenite decay C-curves were not considered. As was shown in [36], the nonequilibrium kinetics of new phase nucleus formation and nonstationary diffusion are influence by phase condition formation in practical welding conditions. Such point of view was used for logical design of quantity precipitate calculation for low-carbon steel welding, and realized as a computer program for the estimation of thermal field, which was used in the model described above. The calculation was carried out for steel 08U, the comparison of results and experimental data revealed their acceptable coincidence

Laser and Hybrid Laser-Arc Welding http://dx.doi.org/10.5772/64522 153

**Figure 30.** Comparison of calculation results of phase combination with experiment, low carbon steel 08U – laser fre‐ quency 5 Hz, pulse duration 7 ms, radiation power – 2.25 kW, lamp electric power – 5.16 kW, welding speed 2 m/s.

**Figure 31.** Comparison of calculation results for phase combination with experiment, low carbon steel 08U – laser fre‐ quency 10 Hz, pulse duration 3.5 ms, radiation power – 4.5 kW, lamp electric power – 5.726 kW, welding speed 4

(**Figures 30** and **31**).

mm/s.

**Figure 28.** Microstructure after hybrid action, the maximal heating temperature is 1200 K, field width 50 μm. Delay between temperature peaks 1 s.

**Figure 29.** Microstructure after hybrid action, the maximal heating temperature is 1200 K, field width 50 μm. Delay between temperature peaks 2 s.

Influence of processing parameters for the delay between the first and second peaks of the cycle is shown in **Figures 24**–**29**. As obtained by theoretical studies, decrease in the time delay between the peaks results in a significant reduction in the size of carbide inclusions.

Microhardness distribution analysis showed that the welds obtained by hybrid welding have significantly less variation in the values of microhardness versus laser welding samples. Decrease of martensite part in weld metal allows raising its plasticity by more than 40%. So it can be concluded that hybrid welding technology suggests an additional possibility to control phase structure parameters in comparison with laser welding as it has been shown in the example of hybrid laser-light process.

As stated above, the carbides precipitation and nature of thermal cycles influence the process of phase composition formation. For estimation of steels phase composition, the timetemperature transformation diagrams of austenite decay together with curves corresponding to thermal cycles are usually used. The method of phase composition quantitative assessment based on Quench factor analysis was described in [37] and successfully tested on aluminum alloys. Later on Quench factor analysis was applied for investigation possibility of predicting steel's mechanical properties during heat treatment [38], but in these works, processes of carbide formation and their influence on actual position of austenite decay C-curves were not considered. As was shown in [36], the nonequilibrium kinetics of new phase nucleus formation and nonstationary diffusion are influence by phase condition formation in practical welding conditions. Such point of view was used for logical design of quantity precipitate calculation for low-carbon steel welding, and realized as a computer program for the estimation of thermal field, which was used in the model described above. The calculation was carried out for steel 08U, the comparison of results and experimental data revealed their acceptable coincidence (**Figures 30** and **31**).

achieve both size reduction and enlargement of the carbide inclusions in comparison with a temperature cycle, which is typical for laser action without an additional heat source

**Figure 28.** Microstructure after hybrid action, the maximal heating temperature is 1200 K, field width 50 μm. Delay

**Figure 29.** Microstructure after hybrid action, the maximal heating temperature is 1200 K, field width 50 μm. Delay

Influence of processing parameters for the delay between the first and second peaks of the cycle is shown in **Figures 24**–**29**. As obtained by theoretical studies, decrease in the time delay

Microhardness distribution analysis showed that the welds obtained by hybrid welding have significantly less variation in the values of microhardness versus laser welding samples. Decrease of martensite part in weld metal allows raising its plasticity by more than 40%. So it can be concluded that hybrid welding technology suggests an additional possibility to control phase structure parameters in comparison with laser welding as it has been shown in the

As stated above, the carbides precipitation and nature of thermal cycles influence the process of phase composition formation. For estimation of steels phase composition, the timetemperature transformation diagrams of austenite decay together with curves corresponding to thermal cycles are usually used. The method of phase composition quantitative assessment based on Quench factor analysis was described in [37] and successfully tested on aluminum

between the peaks results in a significant reduction in the size of carbide inclusions.

(**Figures 24**–**29**).

152 Joining Technologies

between temperature peaks 1 s.

between temperature peaks 2 s.

example of hybrid laser-light process.

**Figure 30.** Comparison of calculation results of phase combination with experiment, low carbon steel 08U – laser fre‐ quency 5 Hz, pulse duration 7 ms, radiation power – 2.25 kW, lamp electric power – 5.16 kW, welding speed 2 m/s.

**Figure 31.** Comparison of calculation results for phase combination with experiment, low carbon steel 08U – laser fre‐ quency 10 Hz, pulse duration 3.5 ms, radiation power – 4.5 kW, lamp electric power – 5.726 kW, welding speed 4 mm/s.

Finally, it is possible to conclude that the use of hybrid welding instead of laser one allows to increase the melting efficiency and to provide stability of weld formation at welding metals in large variety of thickness. Also, hybrid welding technology provides additional possibility to control phase structure parameters, allowing to decrease the level of welding stress and distortion, and increasing welding productivity. Present level of technology development allows to design reliable and cost-effective technological equipment for hybrid laser-arc welding on the basis of high-power fiber lasers.

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Laser and Hybrid Laser-Arc Welding http://dx.doi.org/10.5772/64522 155

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