Modeling of LPBF Scanning Strategy and its Correlation with the Metallic 316 L, 321, and Alnico Magnets Samples Structure

*Pavel Kuznetsov, Anna Mozhayko, Ivan Shakirov, Vitaliy Bobyr, Mikhail Staritsyn and Anton Zhukov*

## **Abstract**

This chapter presents the influence of powder bed laser scanning strategy on the crystallographic structure of the fused specimens 316 L, 321 stainless steel, and Alnico magnets. The main parameters affecting structure are as follows—laser power, stripe width, number of repeated passes with different power, and type of scanning (circle, bidirectional or interlaced, etc.). Changes in the crystallographic structure are studied with regard to melt pool geometry, surface temperature, and surface heat transfer. The correlation is shown between stripe width and laser beam focal spot diameter. Depending on the ratio between stripe width and laser beam focal spot diameter one can see growth elongated and oriented grains or quasi-equiaxed non-oriented grains. The influence of the energy input on the melt pool size and the microstructure of the sample is studied. The influence of the scanning mode (bidirectional and circular) on the temperature distribution in the sample and the microstructure of the sample made of Alnico alloy is considered. All these experimental and model examples clearly demonstrate that it is possible to produce a controllable structure during LPBF process building for advanced additive manufacturing.

**Keywords:** Laser powder bed fusion, finite element modeling, scanning strategy, melting pool geometry, crystallographic structure

## **1. Introduction**

Laser powder bed fusion (LPBF) is one of the additive manufacturing (AM) techniques in which a metal powder bed is selectively melted by a laser beam using a layer-by-layer method based on the designed scanning strategy to produce final parts [1, 2]. In general, AM enables to control the microstructure of metals by changing various values of the process parameters that cannot be achieved by traditional metal parts manufacturing technologies due to their inability to control heat transfer conditions on a very limited scale [3].

The microstructure of the sample obtained by the LPBF method depends on many parameters, such as laser power, scanning speed, hatch spacing, stripe width, and scanning strategy. Alteration of scanning parameters leads to a change in the geometry of the melt pool. In turn, when the geometry of the melt pool changes, the thermodynamic conditions of crystallization will change, which will lead to the formation of various structures. Thus, thanks to the ability to select various scanning parameters, it becomes possible to control the microstructure of products [4].

Currently, different numerical models of LPBF are available. Some of them evaluate and predict the temperature distribution and melt pool size during the selective laser melting process [5–12]. Others investigate the influence of various LPBF parameters on temperature distribution [13–16] and the sample's microstructure [3, 17, 18]. For instance, Yingli Li et al. developed a model, which incorporates a phase function to differentiate powder phase, melting liquid phase, dense solid phase, and vaporized gas phase to determine the melt pool size [6]. Zhichao Dong et al. investigated the effects of hatch spacing on the temperature field, microstructure and melt pool size, overlap rate, surface quality, and relative density during the selective laser melting of 316 L SS [16]. They found that increasing the hatch spacing reduced maximum temperature and heat accumulation. The change in the melt pool size when the laser beam moves from the center of the first layer to the center of the second layer was studied by Yali Li et al. [13].

Besides, the research studies the influence of process parameters on the structure of fused steels or alloys. For example, as shown in [19, 20], various scanning strategies can make for a clear epitaxial growth along the heat flow with an orientation <100>, which can enhance isotropy. It was also shown that the change in yield strength was mainly due to different grain sizes, and the improved plasticity was associated with a changed grain structure based on different scanning [20].

Despite a large number of studies in the field of LPBF, the relationship between fabrication and microstructure has not been fully studied. There are many process parameters whose influence on temperature fields and microstructure needs to be studied.

In this chapter, we focus on understanding the effect of LPBF parameters on the microstructure of the fused specimens. The chapter discusses the influence of energy input, ratio of stripe width, and various scanning strategies (circle, bidirectional or interlaced, and so on) on the microstructure of the sample.

Austenitic stainless steels AISI 316 L and AISI 321 and hard magnetic alloy Alnico were selected as investigated materials. Section 2 contains a detailed description of the LPBF model and the physical properties of the austenitic steel AISI 316 L selected as the modeled material since this steel is widely used in additive manufacturing. Sections 3 and 4 provide an investigation of the stripe width and generalized energy input effect on microstructure. Thermal fields and microstructure of austenitic steels AISI 316 L and AISI 321 are studied in these sections. Austenitic steels do not have phase transitions in the entire temperature range under study, therefore, they make it possible to study directly the influence of LPBF parameters on the structure being formed. Research on the influence of the scanning strategy on the metal quality is necessary for such labor-intensive materials in additive manufacturing as the two-phase Alnico alloy. The high-stress level leading to cracking creates many difficulties in the way of additive production of permanent magnets. It is shown that with the help of a favorable change in the distribution of thermal fields by means of applying an optimized scanning strategy, it is possible to manufacture Alnico alloy permanent magnet with a good structure.

## **2. Modeling**

#### **2.1 Model description**

In general, heat transfer can be described by the heat conduction equation:

*Modeling of LPBF Scanning Strategy and its Correlation with the Metallic 316 L, 32… DOI: http://dx.doi.org/10.5772/intechopen.102073*

$$
\rho \mathbf{C}\_p \left( \frac{\partial T}{\partial t} + \left( \overrightarrow{u} \bullet \overrightarrow{\nabla} T \right) \right) = \overrightarrow{\nabla} \bullet \left( k \overrightarrow{\nabla} T \right), \tag{1}
$$

where *ρ* is the density of the material, *Cp* is the heat capacity, *T* is the temperature, *u* ! is the velocity vector of the liquid, and *k* is the thermal conductivity.

It is assumed that the distribution of the surface heat flux *Qin* over the powder layer represents Gaussian distribution, which mathematically can be rendered as:

$$Q\_{\rm in} = \frac{2PA}{\pi r^2} \exp\left(-\frac{2\left(\mathbf{x} - \nu t\right)^2 + y^2}{r^2}\right),\tag{2}$$

where *P* is the laser power, *A* is the laser energy absorption coefficient, *r* is the radius of the laser beam, and *v* is the speed of the laser beam. The scanning direction is set by replacing of *x* by ð Þ *x* � *vt* .

The initial conditions of the model include a uniform temperature field along the full sample before the heat source is supplied, which can be described as:

$$T(x, y, z, t)\_{t=0} = \mathfrak{B}\mathfrak{B} \, K \tag{3}$$

Heat exchange between the sample and ambient occurs on the upper surface of the model.

$$-k\frac{\partial T}{\partial \mathbf{z}} = Q\_{in} - a(T\_w - T\_0) - \sigma \varepsilon \left(T\_w^4 - T\_0^4\right) - Q\_{nup},\tag{4}$$

where α is the heat transfer coefficient, *Tw* is the surface temperature, and *T*<sup>0</sup> is the ambient temperature, *σ* is the Stefan-Boltzmann constant, ε is the surface absorption coefficient, and *Qvap* is the vapor flow.

On the right side of Eq. (4) all the input and output heat fluxes on the upper surface of the model are described. Heat losses due to convection, radiation, and evaporation are described in the succession.

When the evaporation temperature is reached, a vapor flow appears in the model, which is given in the formula [21]:

$$Q\_{vap} = L\_v(1 - \beta) \sqrt{\frac{M}{2\pi RT}} P\_{amb} \exp\left[\frac{ML\_v}{RT\_v} \left(1 - \frac{T\_v}{T}\right)\right],\tag{5}$$

where *Lv* is the specific heat of evaporation, *β* is the rate of re-condensation, *R* is the universal gas constant, *M* is the molar mass, *Pamb* is the ambient pressure, and *Tv* is the evaporation temperature.

β is the fraction of evaporated particles that re-condenses upon the interaction with the surrounding gas.

The melting phase transition is taken into account by the enthalpy method [22]. Latent heat of fusion is taken into account in the heat capacity equation.

$$\mathbf{C}\_p^q = \mathbf{C}\_p + D\_m L\_m,\tag{6}$$

where *Lm* is the latent heat of fusion,*Cp* is the heat capacity, *Dm* is the Gaussian function normalized around the melting temperature *Tm*:

$$D\_m = \frac{\exp\left(-\frac{(T - T\_m)^2}{\Delta T}\right)}{\sqrt{\pi \Delta T^2}},\tag{7}$$

where ΔT is the smoothing interval equal to 50 K.

## **2.2 Numerical methods**

Numerical modeling is widely used to determine the optimal scanning strategies in the LPBF process. FEM is the most commonly used numerical approach to analyze the temperature profile and the size of the melt pool during the melting and solidification of materials. Commercial software Comsol Multiphysics 5.4. was used to create models of the LPBF process. The present model involves "Heat Transfer" module that is solved with a time-depended solver. The mesh elements are triangular in shape. The upper part is of relatively higher importance where many phenomena are involved at relatively high temperature. The meshing of this part is done with extra fine mesh with a maximum element size of 25 microns. The mesh is relatively coarse at the remaining parts of the model with a maximum element size of 0.2 mm. The results change by less than 1% when a smaller grid is used. Such size of the grid elements was chosen as optimal because it provides maximum accuracy at the lowest calculation speed.

The temperature dependence of the heat capacity of 316 L steel is shown in **Figure 1**. The physical properties of the modeling material are shown in **Table 1**.

#### **Figure 1.**

*Equivalent heat capacity of 316 L steel.*


#### **Table 1.**

*Physical properties of 316 L steel [14, 16].*

*Modeling of LPBF Scanning Strategy and its Correlation with the Metallic 316 L, 32… DOI: http://dx.doi.org/10.5772/intechopen.102073*

## **3. Investigation of stripe width effect on the microstructure**

LPBF technology is conditioned that the sample in its volume is built from a set of melt pools. Consequently, the geometry of the melt pool and the rate of metal crystallization has a decisive influence on the formed structure of the sample. The geometry of the melt pool and the crystallization rate directly depend on all parameters of fusing the surface of the powder layer with a laser beam—the described beam trajectory, the speed, the laser power, the geometry of a specific section of the part when scanning a specific layer. The stripe width is one of the key parameters that affect the geometry of the melt pool and the conditions of metal crystallization.

The printing process on most LPBF installations is carried out by fusing the part section in the form of blocks with a certain width. The thermal pattern of the distribution of temperature fields depends on the width of the block, therefore, this has a direct effect on the rate of metal crystallization in the melt pool and the structure created.

It is of interest to study the influence of such paint parameters as the stripe width on the formation of the melt pool and the metal structure.

The main objective of the present study was to get a deeper understanding of the correlation between LPBF process parameters and microstructure evolution. The temperature field close to the solid–liquid interface determines the morphology and grain size, as well as the crystallographic structure of each track of the material obtained by LPBF. The solidified microstructure depends on local solidification conditions at the trailing edge of the melt pool. Hence, the melt pool geometry (i.e., size and shape) and thermal profile need to be first predicted as a function of the process parameters. Further, taking the solidification theory as a basis and calculating the profile of the melt pool on the basis of numerical modeling, it is possible to establish a connection with the microstructure of the experimentally obtained product.

#### **3.1 Modeling of the LPBF process with different stripe widths**

Three modes of the LPBF process with various stripe widths (1 mm, 2.5 mm, and 5 mm) were considered. The model parameters are shown in **Table 2**. The diameter of the focal beam of the laser was equal to 100 microns and did not change. Thus, in the first case, 10 focal spot diameters fit the stripe, 25 in the second, and 50 in the third (**Figure 2**).


**Table 2.** *The model parameters.*

#### **Figure 2.**

*Schematic representation of different stripe widths (1 mm, 2.5 mm, and 5 mm).*

Based on the simulation results, the dimensions of the melt pool were measured in three directions. The melt pool was measured at the midpoint of the track with a step equal to the hatch. The melt pool dimensions (length, width, and depth) were observed from the tracks temperature distribution results and considered from the melting point to the peak temperature along the scanning direction.

**Figures 3**–**5** show the dependences of the width, length, and depth of the melt pool on the number of the laser beam track.

It can be seen in F**igures 3**–**5** that for the first pass of the laser, the melt pool dimensions differ insignificantly. This is explained by the fact that the initial

**Figure 3.** *Dependence of the melt pool width on the track number.*

**Figure 4.** *Dependence of the melt pool length on the track number.*

**Figure 5.** *Dependence of the melt pool depth on the track number.*

## *Modeling of LPBF Scanning Strategy and its Correlation with the Metallic 316 L, 32… DOI: http://dx.doi.org/10.5772/intechopen.102073*

parameters for the three modes are identical (the substrate temperature is equal to room temperature), as a result of which heating occurs at the same temperature. With an increase of the stripe width, the width and depth of the melt pool decrease. Since the rest of the process parameters remain unchanged, the time of one laser pass increases, with an increase of the stripe width, but the cooling rate does not change. Thus, the next pass of the laser starts after a longer period, and heating occurs at a lower temperature.

Melt pool profiles were described for 1, 5, and 9 laser passes at the midpoint of the track (**Figures 6**–**8**). The melt pool profiles differ insignificantly for the first laser pass. However, the melt pool rotates already at the fifth pass for a stripe width of 1 mm, the center of the melt pool shifts toward the beginning of the hatching (**Figures 6**–**8**). The side of the sample from which the hatching starts is heated to a higher temperature for all passes except for the first one than the other side (**Figure 9**). This leads to an increase in the melt pool width from the beginning of the hatching. Therefore, the melt pool becomes asymmetric about the straight line along laser movement, with rotation around its symmetry axis. The most significant rotation of the molt pool about the beam path is observed for a stripe width of 1 mm.

**Figure 6.** *Melt pool for 1, 5, and 9 track numbers (1 mm).*

**Figure 7.** *Melt pool for 1, 5, and 9 track numbers (2.5 mm).*

**Figure 8.** *Melt pool for 1, 5, and 9 track numbers (5 mm).*

#### **Figure 9.**

*Temperature profile for 10 laser track (1 mm stripe width, 12.35 ms).*

During LPBF the grain morphology and crystallographic structure are determined by a characteristic epitaxial grain growth at the solid–liquid interface of the melt pool. Grain growth occurs mainly in specific material-dependent crystallographic directions, along the maximum temperature gradient [17, 23]. Grains grow epitaxially from the previously deposited layer to be partially re-melted. A decrease in the stripe width increases the molten pool depth and penetrates deeper into the previous layers. Such conditions may lead to an increased grain elongation degree, considerable epitaxial growth, and thus an increased morphological and crystallographic texture.

### **3.2 Investigation of LPBF samples**

The experimental samples are cubes with a side of 10 mm, made of 316 L steel. To study the effect of the width of the paint block on the resulting structure, LPBF samples were produced in accordance with the previously selected modes (see **Table 2**), which were modeled. LPBF samples were manufactured on the EOSint M270.

**Figures 10**–**12** show the microstructure of the samples in the vertical plane (in the direction of sample growth). The boundaries of the former melt pools and grains grown epitaxially through several layers of deposited metal are clearly visible.

#### **Figure 10.**

*Microstucture of sample 1: (a) is the general plan, (b) is the view of the melt pool and single grains (the direction of growth of the sample is shown by an arrow).*

*Modeling of LPBF Scanning Strategy and its Correlation with the Metallic 316 L, 32… DOI: http://dx.doi.org/10.5772/intechopen.102073*

#### **Figure 11.**

*Microstucture of sample 2: (a) is the general plan, (b) is the view of the melt pool and single grains (the direction of growth of the sample is shown by an arrow).*

**Figure 12.**

*Microstucture of sample 3: (a) is the general plan, (b) is the view of the melt pool and single grains (the direction of growth of the sample is shown by an arrow).*

According to the study results obtained by optical microscopy methods, the structure of all the three samples at a first glance is identical with no obvious differences in the modes.

Based on the EBSD analysis of the vertical plane of samples 1–3, maps of crystallite orientations were obtained (see **Figure 13**).

It should be noted that the morphology of the crystallites of the first sample (**Figure 13a**) is characterized by epitaxial growth. The contours of the crystallites freely extend over the several printed layers of metal, the outlines of the boundaries of the melt pools are not traced on the EBSD map. The phenomenon of epitaxial growth of crystallites is also observed in the second sample, but at the same time, crystallites boundaries take the form of the boundaries of the printed layers.

The morphology of the crystallites of sample 3 indicates that epitaxial growth is strongly reduced and the structure is fragmented, the boundaries of the printed layers are easily traced, while sample 1 has a pronounced line structure.

For the purpose of quantitative analysis of the detected EBSD structure, pole figures of orientation densities were constructed (**Figure 14**).

**Figure 14** shows the pole figures of the orientation densities of the crystallographic planes {100}, {110}, and {111}. The polar figures of samples 1 and 2 have a similar appearance, that is, a symmetrical intensity distribution (**Figure 14a** and **b**), whereas in sample 3 (**Figure 14c**) the pole figure is not symmetrical.

Based on the numerical modeling results (**Figure 6**), a feature of the geometry of the melt pool is established for the stripe width of 1 mm—a significant rotation of the melt pool with relation to the trajectory of the beam.

The crystal lattice of individual grains is characterized by preferential orientation. Since the pole figures show a set of orientation densities of all crystallographic planes in the examined area, the observed symmetrical image of these areas is

**Figure 13.** *EBSD sample cards no.: (a) – 1, (b) – 2, (c) – 3.*

associated with the characteristic morphology of the grains revealed in **Figure 13a** and **b**. The structure of sample 3 is represented by smaller vertically oriented grains shown in the pole figure (**Figure 14c**) as a difference between the structure of samples 1 and 2.

The structure of samples 1 and 2 with different stripe widths of 1 mm and 2.5 mm, respectively, is represented by a set of symmetrical crystallites elongated in the growth direction of the sample and rotated at different angles around the normal to the plane. The structure of sample 3 does not have a pronounced symmetry of the crystallographic in the vertical plane. Thus, it was found that the stripe width affects the morphology of the structure of the generated LPBF sample.

## **4. The generalized energy input**

In this section, to analyze the influence of LPBF parameters on thermal fields, microstructure and mechanical properties of AISI 321 austenitic steel, the LPBF process was simulated and a series of samples was created to combine various combinations of LPBF technological modes, such as scan speed, laser power, and scanning strategy. The possibility of controlling the structure formation of steel in the LPBF process in order to obtain a specific crystallographic texture, grain size, and morphology is evaluated. The relationship between the resulting anisotropic

*Modeling of LPBF Scanning Strategy and its Correlation with the Metallic 316 L, 32… DOI: http://dx.doi.org/10.5772/intechopen.102073*

**Figure 14.** *Pole figures of samples no.: (a) – 1, (b) – 2, (c) – 3.*

structure and mechanical properties is investigated. The aim is to understand the influence of the scan speed on the microstructure with the same energy input. The generalized energy input parameter is calculated as a ratio of laser power to the scan speed on the irradiated surface. In addition, the study is aimed at understanding whether there is additivity of power with the number of passes.

In Section 2, the effect of the stripe width on the microstructure of the samples was studied. The stripe width is selected 5 mm and remains constant for all modes studied in this section. To study the dependence of the melt pool size and microstructure on the energy input, nine modes of the LPBF process were selected. The laser speed varies in the range of 800–1013 mm/s, the laser power varies in the range of 75–190 W. The modes were chosen in such a way to study three models with an energy input of 0.188 Ws/mm, taken as 100%, three more ones with an energy input of 0.141 Ws/mm (50%), and the others with an energy input of 0.094 Ws/mm (75%), with each mode being different in power and scanning speed. In addition, various scan modes are used: the first three models go with one scan, the rest use double scan (**Table 3**).


## **Table 3.**

*LPBF Parameters.*

The experimental samples are cylinders with a diameter of 4 mm and a height of 7 mm. The thickness of the powder layer was 40 microns.

## **4.1 Modeling**

The melting pool size (length, width, and depth) was observed from the tracks temperature distribution results considered from the melting point to the peak temperature along the scanning direction.

The dependences of the length, width, and depth of the melt pool on the laser power are shown in **Figures 15**–**17**.

**Figures 15**–**17** show that the increase in energy input extends the width, length, and depth of the melt pool. Comparing 1 and 4 scanning modes, where the input power was doubled, it was found that the melt pool width increased from 160 μm to 210 μm, the melt pool length increased from 190 μm to 530 μm, and the melt pool depth increased from 20 μm to 54 μm. For modes 4–6, the melt pool depth is less than the depth of the powder layer (40 μm). Thus, lack of fusion can be suggested with these process parameters. The melt pool width increased 1.3 times, while the length and depth increased 2.8 and 2.7 times, respectively. Therefore, it can be concluded that a change in energy input has a greater effect on changes in length and depth of the melt pool, while the width changes insignificantly.

**Figure 15.** *Dependence of the melt pool width on the power.*

*Modeling of LPBF Scanning Strategy and its Correlation with the Metallic 316 L, 32… DOI: http://dx.doi.org/10.5772/intechopen.102073*

**Figure 16.** *Dependence of the melt pool length on the power.*

**Figure 17.** *Dependence of the melt pool depth on the power.*

Comparing the modes with the same energy input (laser's speed and power may vary, but their ratio remains unchanged). For example, in modes 1, 2, and 3, the melt pool width and depth practically remain invariable, while the length grows with raising speed and power. To assume this case the laser scanning speed affects the change in the melt pool length largely. A high scanning speed leads to a longer tail of the melt pool in the x-y plane, thereby increasing its length. Modes 1–3 correspond to the greatest melt pool depth (**Figure 17**) with deeper penetration into the previous layers. These conditions might represent a more considerable epitaxial growth. Modes 7–9 correspond to the smallest melt pool depth (**Figure 17**), which might favor the grinding of the microstructure, since upon multiple scans, previous layers of the sample will not be melted.

### **4.2 Investigation of LPBF samples**

#### *4.2.1 Density*

The results of density measurement depending on the LPBF modes are shown in **Figure 18**. It demonstrates that at the values of energy input of 100 and 75% with

#### **Figure 18.**

*Dependences of the sample density on the laser power.*

single or double scanning, respectively, it is possible to achieve a density of 7.8 g/cm<sup>3</sup> , which corresponds to porosity of 1% or less. At an energy input of 50%, the sample density decreases to 7.2 g/cm<sup>3</sup> , which corresponds to a porosity of about 10%.

Thus, we can conclude that the energy input at the level of 100 and 75% for single or double scanning is sufficient to melt the powder layer and form a highquality melt pool. This enables to achieve a high density.

#### *4.2.2 Vickers hardness*

The measured values of the samples hardness on a plane parallel to the direction of construction are shown in **Figure 19**. It can be seen that with a single scan at 100% of energy input, the hardness values are a bit less than with a double scan at 75% of energy input and are 230 and 250 HV, respectively.

**Figure 19.**

*Samples hardness dependences on laser power.*

*Modeling of LPBF Scanning Strategy and its Correlation with the Metallic 316 L, 32… DOI: http://dx.doi.org/10.5772/intechopen.102073*

The measured hardness values enable to evaluate strength properties of the samples. Thus, for the samples obtained at 100% of the energy input, the time resistance is 800 MPa, whereas for the samples obtained at 75% of the energy input the time resistance is 750 MPa. This indicates a significant hardening of the samples, which is consistent with other authors' works [16], where such hardening factors as dislocation, dimensional, and dispersed particles are mentioned.

#### *4.2.3 Microstructure*

**Figure 20** shows the microstructure obtained by optical metallography of all nine samples.

A large number of pores is observed on samples 4–6, which corresponds to reduced density values (**Figure 20d–f**).

The micrographs in **Figure 20** show the effect of various modes (**Table 3**) on the solidification structure. The merge lines are clearly visible. Grains consist of colonies of hardened cells with the same orientation. The grains grow parallel to the construction direction and pass through several layers of powder melted by a laser. According to the simulation results, the melt pool depth was obtained for samples No. 4–6 with power values of 75, 85, and 95 W (see **Figure 17**). As you can see, the estimated melt pool depth is not enough to melt a powder layer of 40 microns.

The structure of samples 1–3 in **Figure 21** is formed by grains elongated in the direction of sample growth extending through several layers that indicates their epitaxial growth. From the first to the third sample, a proportional increase in power and speed occurred. In general, this accelerates the thermokinetic process of structure formation, hence a change is observed from large columnar grains, similar to those

**Figure 20.** *Optical microscopy. Sample no.: (a) – 1, (b) – 2, (c) – 3, (d) – 4, (e) – 5, (f) – 6, (g) – 7, (h) – 8, (i) – 9.*

**Figure 21.** *EBSD maps for sample numbers: (a) – 1, (b) – 2, (c) – 3, (d) – 4, (e) – 5, (f) – 6, (g) – 7, (h) – 8, (i) – 9.*

formed at casting with directional solidification, to grains with morphology that is similar to the outlines of melt pools. Lower rates of formation of the deposited metal contribute to the growth of crystallites, the appearance of grain boundaries changes with increasing speed, the shape of the grains acquires the appearance of crystallized melt pools; the grain structure is crushed since the crystallization conditions do not favor epitaxial growth. The grains are mainly oriented along the growth axis (building direction) and the length of these grains approaches 1 mm, which is much larger than the thickness of the layer used in the construction (40 microns).

Double scanning leads to the structure grinding. Samples 7–9 (see **Figure 21g–i**), in comparison with the structure of samples 1–3, have a structure with smaller grains of 100 μm in length order, with a drop-shaped morphology. In the future, double scanning can be applied for the structure grinding to obtain a favorable one with functional gradient properties of the part as a whole, or on a separate site.

In this section, the change in the parameters of the LPBF process, like scanning speed and the number of repeated scans was evaluated in terms of the effect on melt pool size, density, hardness, and microstructure. The use of experimental methods with computer modeling methods contributed to a better fundamental understanding of the correlation between process, microstructure, and properties.

## **5. Scanning strategy**

The laser beam scanning strategy in the LPBF process has a direct impact on the formed sample structure. The forming metal structure strongly depends on the

*Modeling of LPBF Scanning Strategy and its Correlation with the Metallic 316 L, 32… DOI: http://dx.doi.org/10.5772/intechopen.102073*

thermokinetic conditions of crystallization. In the previous sections, the effect of stripe width (Section 3) and energy input (Section 4) on temperature fields and microstructure was considered. In this section, with a constant stripe width equal to 5 mm, as well as a fixed speed of 800 mm/s and a power of 190 W, the influence of the scanning strategy on temperature fields and microstructure is studied. The scanning strategy of the powder layer with a laser beam in each section of the part being created can change the nature of the distribution of temperature fields and, as a consequence, the formed structure. It is shown that it is possible to eliminate the process of cracking in the Alnico alloy by applying an optimized scanning strategy developed on the basis of modeling. The magnetic hard alloy alnico was chosen as the material, which is characterized by a difficult-to-process in the LPBF.

#### **5.1 Modeling**

In this section, several modes of selective scanning are investigated—1) bidirectional; 2) circular from the center; 3) circular to the center. The model parameters for different scanning modes are shown in **Table 4**. Here L is the sample length, W is the sample width, H is the sample height, and R is the radius of the cylindrical sample.

Using the created model, it is possible to obtain the temperature distribution at any time during the entire considered LPBF process within the entire volume of the sample. In order to study the history of temperature distribution under different scan modes, temperature distributions for all models were analyzed at the end of the LPBF process (**Figure 22**). The melting zone is shown in burgundy. It was observed that the nature of the scan mode has little effect on the size of the melt pool, and the temperature gradient is relatively high near the melt pool.

The scan strategy has a significant impact on the temperature distribution. As can be seen from **Figure 22**, different scan strategies lead to different temperature


**Table 4.**

*Model parameters for different scan modes.*

#### **Figure 22.**

*Temperature distribution on the upper surface of the sample after the LPBF process for (a) bidirectional; (b) circular from the center; (c) circular to the center mode.*

distributions in the sample. The circular scan mode from the center provides a temperature distribution with approximately diagonal symmetry (**Figure 22b**). The circular scan mode in the center provides a temperature distribution with circular symmetry (**Figure 22c**).

The stresses generated in the longitudinal direction of the laser beam are higher than in the transverse direction due to non-uniform compression during cooling [24–26]. Since the longitudinal direction of the laser does not change from pass to pass in bidirectional scan mode, the stresses in the longitudinal direction are higher than in the transverse one. This might lead to the formation of cracks in the sample. When the bidirectional scanning mode changes to a circular one, the residual stresses become more directional, which in turn can lead to a reduction in cracks in the manufactured sample.

Temperature dependences were plotted for 10 laser beam passes for 1–3 scanning modes. The cross-sectional distributions x = 2.5 mm (**Figure 22a**) and y = 0 mm (**Figure 22b** and **c**) were considered.

**Figure 23** illustrates that in the bidirectional scan mode, heating occurs asymmetrically in cross-section. If we consider the first pass of the laser (indicated in blue in **Figure 23a**), it can be seen that the temperature on one side reaches about 2500 K, while the other side of the sample remains almost in equilibrium with a temperature of 300 K. During the circular scan mode from the center, heating occurs from the center along small radiuses, so the time of one laser pass is very short. This leads to the fact that the initial temperatures of the next pass will be greater. From the graph of the temperature distribution over the cross-section of the sample (**Figure 23b**), it can be observed that during the circular scan from the center, the temperatures are distributed more evenly than for the circular to the center and bidirectional modes.

Thus, the circular mode from the center is optimal, since the temperature distribution in this mode is more uniform. This corresponds to the residual stresses directions are pointed to the center, and, together with the cylindrical shape of the sample, contributes to the proper distribution of stresses and prevents cracking. These considerations will be verified in the next section.

#### **5.2 Investigation of LPBF samples**

In accordance with the scanning modes selected for modeling (**Figure 24**; **Table 4**), samples from the Alnico alloy were obtained. The samples were obtained using the equipment "Russian SLM Factory," which allows for more detailed configuration of scanning modes.

The standard technology of the bidirectional scanning strategy (mode 1) in LPBF with the microstructure is shown in **Figure 25**. A directional grid of cracks permeates the entire volume of the resulting sample, which changes its appearance from the center to the surface.

Since the morphology of multiple cracks has a clearly expressed anisotropy associated with the sample's geometry and the growth direction under LPBF, the crack formation process is apparently associated with the distribution of thermal stresses in the volume of the fused sample.

Based on the modeling data, when studying the structure of the obtained samples to rearrange the thermal stresses during the sample's construction, the samples were obtained by two types of ring scanning. The laser-scanned section of a cylindrical sample in each powder layer with a beam from the generatrix to the center and vice versa with 75 μm scanning step, 800 mm/s speed, and a power of 190 W (**Table 4**). This experiment allowed us to evaluate the effect of scanning strategy on *Modeling of LPBF Scanning Strategy and its Correlation with the Metallic 316 L, 32… DOI: http://dx.doi.org/10.5772/intechopen.102073*

**Figure 23.**

*Temperature distribution in cross-section: (a)* bidirectional scan mode, *x = 2.5 mm; (b)* circular from the center mode, *y = 0 mm; (c)* circular to the center mode, *y = 0 mm.*

thermal stresses in LPBF samples and lead to cracks formation. The structure of the samples corresponding to mode 2 and mode 3 (**Figure 24c**; **Table 4**) is shown in **Figures 26** and **27**, respectively.

The structure of sample 3 has no cracks in its volume, with only a grid of cracks found in the radial direction into a depth of about 300 μm from the surface, and the presence of many pores distributed over the sample volume.

Based on numerical modeling, the distribution of temperature fields in cylindrical-shaped LPBF samples was estimated under various scanning modes of the sample—bidirectional, ring-centered. This experiment allowed us to evaluate

**Figure 24.**

*Scanning modes: (a) bidirectional; (b) circular from the center; (c) circular to the center.*

**Figure 25.** *Mode 1 (bidirectional). (a) – vertical direction, (b) – horizontal direction.*

**Figure 26.** *Mode 2 (circular from the center). (a) – vertical direction, (b) – horizontal direction.*

the influence of the scanning strategy under LPBF on the thermal stresses in the sample volume and lead to the formation of the crack.

Comparative analysis of temperature fields and microstructure of LPBF samples revealed that the scan strategy (bidirectional or circular) had an intense effect on the distribution of thermal fields and, consequently, on the microstructure of

*Modeling of LPBF Scanning Strategy and its Correlation with the Metallic 316 L, 32… DOI: http://dx.doi.org/10.5772/intechopen.102073*

**Figure 27.** *Mode 3 (circular to the center). (a) – vertical direction, (b) – horizontal direction.*

samples produced by LPBF. The structure of the specimens produced by the circular scan method had no cracks in the sample volume.

## **6. Conclusions**

In this chapter by computer modeling and experimental investigations, we revealed that the type of scanning has an essential effect on microstructure. Energy input was constant 0.188 Ws/mm, but speed and power were changed in such a way: 800, 906, 1013 mm/s, 190, 170, 159 W, respectively. Additionally, energy input was reduced by 25 and 50% by decreasing laser power, but at the same time, there was double scanning to estimate the influence of repeated heat input.


Double scanning does not have a summing effect, that influences the physicomechanical properties of the obtained specimens. Double scanning leads to shredding of the structure. In the future, double scanning can be used for structure grinding to obtain a favorable structure with functional gradient properties of the part as a whole, or on a separate site.

## *Advanced Additive Manufacturing*

The low depth of penetration into the melt pool, high-temperature gradients, and high solidification rates stimulate the grinding of the microstructure and reduced intensity of texture due to a partial change in the solidification mode from columnar to equiaxed.

The density of 321 steel depends directly on the energy input as a ratio of laser power to scan speed at the level of 100 and 75% with single or double scanning, which is enough to melt the powder layer and form a high-quality melt pool.

3.Uneven temperature distribution under LPBF, a sharp temperature gradient in the melt pool and thermal influence zone lead to cracking. The fused metal and the heated part of the sample expand and cause stresses in the rest of the sample, which leads to characteristic cracks and their directed growth during layer-by-layer sample creation. The casting shrinkage of the molten Alnico alloy amount to 3%; this leads to internal stresses and cracking. Thus, a typical selection of modes for selective laser fusion of the Alnico alloy does not provide proper effect.

Ring scanning has a positive effect on the redirection of thermal stresses and cracking. Topological optimization of the sample's geometry scanning for thermal stress control enabled us to reduce cracking.

It was found that the LPBF fusion mode had a strong influence on the structure of the sample (especially the Alnico alloy); the scanning strategy is of great importance. Therefore, good sample's quality cannot be achieved merely by changing scanning power and speed. As stated above, the selection of LPBF modes for some materials refers to a scanning strategy for a specific 3D model of the sample.

## **Acknowledgements**

This work was supported by the Russian Science Foundation under Grant No. 21-73-30019. Experimental studies were performed on the equipment in the Shared Use Center entitled "Composition, structure, and properties of structural and functional materials" of the NRC "Kurchatov Institute" – CRISM "Prometey" with the financial support of the state represented by the Ministry of Education and Science of the Russian Federation under the Agreement No. 13.CKP.21.0014 (075-11- 2021-068). The unique identifier is RF——2296.61321X0014.

## **Author details**

Pavel Kuznetsov\*, Anna Mozhayko, Ivan Shakirov, Vitaliy Bobyr, Mikhail Staritsyn and Anton Zhukov NRC "Kurchatov Institute" – CRISM "Prometey", St. Petersburg, Russia

\*Address all correspondence to: prometey\_35otdel@mail.ru

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Modeling of LPBF Scanning Strategy and its Correlation with the Metallic 316 L, 32… DOI: http://dx.doi.org/10.5772/intechopen.102073*

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## **Chapter 10**
