Wu et al. found that the heat flow and melt-pool dimensions have a great impact on the final product's residual stress as well as on other mechanical properties during the SLM of AlSi10Mg [40]. The melt-pool size increases as the laser scanning continues and reaches a steady state. Higher beam intensity and slower beam speed have faster melt-pool evolution, while lower intensity with faster beam speed has the opposite effect. A larger melt pool is observed in the subsequent layers. Similar patterns are also observed for other materials. Another study was carried out by Hu et al. on multi-layer SLM of AlSi10Mg material. The gradual increase of temperature and melt-pool were reported with the addition of new layers, which helped in obtaining fine grains for low energy input [41]. A similar numerical study was carried out by Khan et al. [42]. An experimental investigation was performed to measure the residual stress of SLM-manufactured AISI 316L samples. On the top surfaces, higher residual stresses in the scan direction were reported than in the downward direction. However, in the lateral surface, the residual stresses are higher in the perpendicular direction than that of the scan direction. This is due to the temperature gradient and cooling down of the substrate [43]. In another study, it was found that Ti-6A1-4V experiences more residual stress than Inconel 718 material [44]. However, little research is being pursued on a high layer thickness material. As opposed to the general concept, Jingjing et al. found that layer thickness has very little effect on the melt-pool dimensions for a Ti-6Al-4V material by the SLM process [45]. Most of the reported studies concentrated on the very thin layer thickness, which is a limiting factor on the final material addition rate and hence the manufacturing time.

Song et al. presented the effects of scanning patterns on residual stress in an SLM process of Ti-6Al-4V. Even though there is an influence of scanning patterns on the residual stress, no significant change in the melt-pool size was observed [46]. Yang and Wang presented a case study of a repair process by direct laser fabrication (DLF) in ABAQUS software to study the influence of non-linear temperature-dependent properties in a pure nickel material on temperature distribution [47]. It is obvious that the highest peak temperature value is at the point or region where the laser is applied while the second peak value is at the border of the current layer and the previous layer, and the third peak value is at the border of the previous layer and second previous layer. There is a sudden rise in the thermal conductivity and heat transfer at the point where the phase change takes place. Direct metal laser fabrication (DMLF) is designed specifically for metal parts. However, it can be used for non-metal and polymer materials as well [48].

A high layer thickness of an AM process comes with some inherent problems such as an increase in surface roughness, a higher tendency to dimensional distortions and, improper melting. Martínez et al. found that the scan strategy, thermal cycle, and residual stresses affect, in part, distortion, especially on parts where a high strength to weight ratio is considered [49]. Nadammal et al. found that the rotational and alternate scanning pattern results in the least residual stress and distortion [50]. A study by Ventola et al. observed that additively manufactured rough surfaces have enhanced heat transfer and can

be used in electronics cooling [51]. Yang et al. investigated the vertical surface roughness of AlSi10Mg parts manufactured by the SLM process instead of the common research on horizontal surface roughness. The authors determined that the surface roughness can be reduced by about 70% from 15 µm to 4 µm by using the energy density approach [52]. Such inherent problems like the surface roughness can be used to our advantage in applications where enhanced heat transfer is required without much concern regarding the surface roughness of the materials. In such areas, the use of a high layer thickness will improve the manufacturing time.

Ding et al. performed a numerical analysis of heat transfer along with the fluid flow analysis for different laser scanning patterns in an SLM process. In a point laser exposure, a wide melt-pool was observed. In addition to this, there was a longer processing time with multiple thermal cycles, which resulted in finer grains [53]. Another advantage that AM offers is the ability to provide onsite demand and manufacturing of spare parts, which will reduce the manufacturing lead time (MLT), inventory, and transportation cost [54]. By adopting onsite demand, the US Navy was able to reduce the cost by 30% and increase on-demand part production [55,56]. A comparative study of samples is reported based on different manufacturing processes. Chastand et al. investigated different fatigues of Ti-6Al-4V samples produced by electron beam melting (EBM) and the SLM process. It is observed that surface defects have a high impact, followed by un-melted zones and small internal defects [57]. A recent study found that the short-time creep resistance of Inconel 718 manufactured by the SLM process is comparatively the same as that of manufactured by forging process. However, it is far below when compared to a sample manufactured by the casting method [58]. Without denying the importance of these investigations, most of the research concentrates on the comparison of the same material manufactured by different manufacturing processes. Limited information is available that shows a comparative study of two materials viz. Ti and Inconel 718 in terms of temperature distribution and different melt-pool dimensions under the same processing conditions manufactured by the LAM process. Such a study will help in determining which exact material to use in specific conditions or even use both the materials.

However, the AM process faces some major problems that are hindering the mass adoption of this technology on commercial scales. Another major issue is the limited availability of high performance yet light in weight materials. Some of the materials that are available are difficult to process using the AM technique, or it exhibits poor mechanical properties even if it is possible for AM to process those materials. Given the importance of LAM in aerospace and biomedical applications combined with the ever-expanding use of Ti material and Inconel 718 alloy, these two materials are considered in the present study. Another major hindrance is the high manufacturing lead time, which is largely because of the very thin layer thickness. The layer thickness of the most SLM process mentioned in this section is below 100 µm. Manufacturing a whole part with this scale of layer thickness will take a long time to complete. Adopting a higher layer thickness will substantially reduce the MLT of the item. Additionally, limited information is available on the interaction and process information for different materials for additively manufactured parts of high layer thickness materials. Therefore, the present study is focused on the investigation of thermal interaction and change in melt-pool dimensions due to thermal interactions in between the layers and substrates in a high layer thickness multi-layer LAM process of pure Ti and Inconel 718 materials and comparatively analyze the results.

The present paper shows the comparative numerical investigation of laser-based additive manufacturing of high layer thickness materials. A Gaussian distributed disc heat source model is used as the laser heat source model. To simulate the layer addition, the element death and birth feature is employed. It also investigates the effects of laser power and laser scanning speed on the heat flow and melt-pool dimensions. Based on the observed results, it is found that LAM of high layer thickness materials is possible with sufficient process parameters, well under the capability of currently available LAM machines.

#### **2. Numerical Modeling**

A finite element-based numerical model is developed for transient thermal analysis using ANSYS (APDL) 14.5 developed by the ANSYS Inc. Canonsburg, PA, USA. The SOLID70 element having a single degree of freedom (DOF) is chosen during finite element (FE) thermal modeling. Figure 1 shows the FE model of Ti and Inconel 718 materials. The substrate size is 10 mm × 31 mm × 4 mm with a layer size of 1 mm × 31 mm × 0.5 mm. Figure 1b shows the meshed FE model along with a magnified view. Most of the heat transfer and interaction will take place in and around the layers. With an aim to reduce the computational time and cost, fine-mesh is adopted for the layers, and coarse-mesh is adopted for the substrates. To mimic the addition of new layers on top of existing layers, the element birth and death feature is employed. Even though five layers are already modelled, the upper four layers are marked as death elements and do not take part in any physical and thermal interactions. After scanning of the first layer, practically a new powder layer is added, and the 2nd layer is marked as active while the other three upper layers are still marked as death elements. This process is continued until the scanning of the last layer (5th).

**Figure 1.** (**a**) Geometry of the FE model and (**b**) FE model of a five-layer selective laser melting (SLM) for Ti and Inconel 718 alloy material.

The process parameters employed during the LAM process for Inconel 718 and pure Ti are given in Table 1. The layer thickness is kept constant at 0.5 mm for both materials. Temperature-dependent physical material properties of Ti and Inconel 718 are given in Figure 2. The other material properties of the two materials are given in Table 2.

**Table 1.** LAM processing parameters for pure Ti Inconel 718 material.

**Table 2.** Material properties of Ti and Inconel 718 used in the present work [61–63].

**Figure 2.** Temperature-dependent (**a**) thermal conductivity and (**b**) specific heats of Ti and Inconel 718 [44,59–61].

− − − During the SLM process, the energy from the laser beam strikes the metal powders, which melts, and the energy is transferred to subsequent layers. By repeating this process, some layers are subjected to thermal changes several times, thus resulting in phase transformation, grain growth, a final product with non-uniform grain size, shape, and thermal distribution. Moreover, during the SLM process, the object is subjected to convection and radiation heat losses. Figure 3 presents a schematic of thermal boundary constraints of a multi-layered SLM process. − − −

**Figure 3.** Schematic of boundary conditions of a multi-layered SLM process.

A finite 3D model is developed for the laser additive manufacturing process using ANSYS software to determine the non-linearity and temperature variations with respect to time. The 3D heat conduction equation (transient) is represented by [34]

ଶ

 ଶ

$$k\left(\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} + \frac{\partial^2 T}{\partial z^2}\right) + \dot{Q} = \rho c\_p \left(\frac{\partial T}{\partial t}\right) \tag{1}$$

 ଶ

ሶ

 ቆ ଶ ଶ + ଶ ଶ + ଶ ଶ ቇ+ሶ = ൬ ൰ ሶ ሶ *ν ρ* (, , )|௧ୀ = where *k*, *Q*, *ν*, *Cp*, *T*, and *ρ* are thermal conductivity, rate of internal heat generation per unit volume, velocity vector, specific heat, temperature, and density of the material, respectively. The terms on equation 1 represent heat transfers in X, Y, and Z directions with laser heat power supplied for melting of the powder layers. The initial condition at the start of the operation is given by

$$T(x, y, z)|\_{t=0} = T\_0 \tag{2}$$

− −

− − −

− − −

where *T*0 represents ambient temperature (298 K i.e., 25 ◦C).

.

(, , )|௧ୀ = Most of the heat transfer takes place due to phase change, latent heat of conduction in and around the area where laser heat is applied, and melt-pool occurs. Convection and radiation heat transfer are assumed in all the exposed surfaces of the substrate. The natural boundary condition can be represented mathematically, which involves convective heat transfer and radiative heat transfer [64–70]:

$$k\frac{\partial T}{\partial n} - q + q\_c + q\_r = 0 \tag{3}$$

where *q* is the input heat flux, *qc* and *qr* are heat loss due to convection and radiation respectively. The basic equation of convective and radiative heat transfer can be represented as:

$$q\_{\mathcal{C}} = h(T - T\_0) \tag{4}$$

$$q\_r = \sigma \epsilon \left( T^4 - T\_0^4 \right) \tag{5}$$

where *h* is the convective heat transfer co-efficient, *σ* is the Stephan–Boltzmann constant and *ǫ* is the emissivity, *T*0 and *T* are the initial temperature and instant temperature.

The Gaussian heat distribution model is the most common model used in a laserbased additive manufacturing process as the heat distribution, which follows Gaussian distribution. Gaussian distributed disc model is implemented as the heat source to mimic the laser heat source onto the powder layers from the laser source, which is mathematically represented as [32,33,71].

$$q = \frac{3\eta P}{\pi r^2} \exp(\frac{-3\left(x^2 + y^2\right)}{r^2}),\tag{6}$$

where *q, η, P* and *r* represents the rate of laser heat flux, the efficiency of the laser beam absorption, absolute laser beam power, effective radius of the laser beam at the surface of the layer. *x* and *y* depict the position of the centre of the laser beam at a specific time and at the respective layer.

#### **3. Results and Discussion**

The numerical simulation is performed for Ti and Inconel 718, corresponding to the dataset in Table 1, and a detailed analysis of the LAM process is studied. The temperature behavior against time and nature of the melt-pool of Ti and Inconel 718 materials are studied separately. For different datasets, the comparative study of the two materials under the same process parameters are studied and analysed to determine the nature of transient heat transfer and temperature over time. The developed model has been validated with the experimental data available in the literature [45]. First, a single layer FE is developed for Ti-6Al-4V material and is compared with the experimental data available in the literature. As shown in Figure 4, the melt-pool dimensions of computed value are ~0.12 and ~0.13 mm for the experimental data. The pattern and data agree with the computed value and experimental value. The percentage difference in the melt-pool depth is estimated to be 5.38% which is under the acceptable range. This model is further extended into a multi-layer model with the material properties considered in the present paper.

#### *3.1. Melt-Pool Evolution and Temperature Distribution*

The melt-pool dimension increases as the laser power move along the direction of the laser scan. Moreover, the melt-pool size and length increased as the new layers are added. However, there are un-melted powders in some parts of the layer when laser power is 150 W and the laser velocity is 150 mm·s −1 . This is possibly due to the applied laser power is not enough to melt the whole layer thickness. Due to this, the specific dataset is not mentioned in Table 1. Figure 5 represents the 3D view of laser movement along the different layers and evolution of the melt pool. Figure 5a shows the laser movement along the layer at the beginning of the 1st layer. Similarly, Figure 5b–e shows laser movement along the 2nd layer, at the middle of the 3rd layer, at the 4th layer, and at the end of the 5th layer. Figure 5f displays cooling after laser scanning is over for dataset#6 of Table 1. The cross-sectional view of melt-pool alteration is shown in Figure 5g, corresponding to different layers. Moreover, the cumulative effect of the increasing size and length of the

melt-pool can be visually recognized in Figure 5g. The zone above 1941 K denotes part of the layer which is fully melted. The 1400–1941 K zone indicates the sintered area. The other zones do not take part either in melting or sintering.

**Figure 4.** Comparison of (**a**) computed and (**b**) experimental melt-pool shape and size.

− In Figure 5g, it is observed that the melt-pool depth and width increased as the process continue and as layers are deposited on top of one another. The width increases from ~0.42 to ~0.62 mm from 1st layer to the 2nd layer and then to ~0.65 mm for the third, while, fourth and fifth layers have a width of 1 mm or higher. It was observed that the melt pool depth increased from ~0.088 to ~0.41 mm from the 1st layer to the 5th layer. The melt pool depth corresponding to the 2nd layer, 3rd layer, and 4th layer was determined to be ~0.21, ~0.24, and ~0.38 mm, respectively. At the beginning of the 1st layer, it is observed that the whole depth of the layer is not melted. This can be attributed to the fact that at the beginning of the process, the substrate's temperature and layers are at ambient temperature, which prevents it from reaching the melting point. Preheating the powder materials may reduce the improper melting of layers at the beginning of the process. However, as the laser supply and heat transmission from melt pool to substrate continue, the overall temperature of the substrate and the layers increases that enables the laser focus area to attain higher maximum temperatures. With temperature rise, the melt-pool depth increases. This shows that the manufacturing of products by the LAM process is possible. From the 4th to 5th layer, there is a decrease in the rate of increasing melt-pool dimensions when compared to the other layers. This indicates the stagnation point where a further increase in the layers will not affect the melt-pool dimensions significantly. This phenomenon can be attributed to the fact that the temperature of the initial layers is nearing the approximate

substrate temperature. However, the overall temperature of the substrate is increased and remains the principal heat transfer agent. Considering the high layer thickness, it will be of great interest if further research is undertaken for a sloped surface as performed by Xiang et al., where the slope's quality is analysed. Such an analysis by considering different oblique angles under different process parameters will be of great interest as a higher layer thickness may produce more extreme results in increasing or decreasing the quality of slope on the surfaces [72].

**Figure 5.** Laser movement and cooling over different layers (**a**–**f**) and changing melt-pool dimensions of laser scanning during a laser AM process of 5 layers for pure Ti for dataset#6 (**g**).

Figure 6 represents the time-temperature graph at the midpoint of each layer when power is 250 W and speed is 300 mm·s −1 . The maximum temperature obtained at the middle of the 1st layer is 2195 K, 2342 K for the 2nd layer, 2475 K for the 3rd layer, 2552 K for the 4th layer, and 2622 K for the 5th layer. This confirms the general prediction that the maximum peak temperature increases with each increasing layer number. Thereby, the melt-pool size is increased, and it is above the melting temperature of the Ti material.

Theoretically, there should be five and four decreasing peak temperatures corresponding to the 1st and 2nd layer. Similarly, three, two, and one peak temperature corresponding to the 3rd layer, 4th layer and 5th layer are observed. The same phenomenon is also observed in the present case, and it can be identified from Figure 7a,b. However, Figure 6 has only 4 visible peaks due to low laser power. This shows that when the laser is in the 5th layer, the temperature at the 1st layer hardly has any effect. However, there is a rapid decrease in temperature after the laser is applied. After the rapid decline in the temperature, it is gradually reduced as cooling takes place.

−

**Figure 6.** Time-temperature history (**a**) full view, (**b**) zoomed view considering only up to 0.7 s of scanning time, at the centre of each layer for dataset#6.

−

− **Figure 7.** Time-temperature history (**a**) full view, (**b**) zoomed view at the centre of 1st layer, (**c**) full view, (**d**) zoomed view at the end of 5th layer at 200 W laser power and at a scan speed of 150 and 200 mm·s −1 .

*3.2. Effects of Scanning Speed on the Melt-Pool and Temperature Distribution*

As the laser scan speed increases with constant laser power, the depth as well as the width of the melt-pool decreases. Time-temperature history in the middle of the 1st layer is shown in Figure 7a,b. It can be identified that at a scan speed of 150 mm·s −1 , a maximum temperature of 2640 K is attained, while at a scan speed of 200 mm·s −1 , the highest temperature is 2287 K. Similar trend is also observed in the case of 5th layer (Figure 7c,d). At a scan speed of 150 mm·s −1 , the maximum peak temperature is 3722 K,

while at a scan speed of 200 mm·s −1 , the peak temperature is 3154 K. This indicates that the current LAM machines have the capability to produce high layer thickness parts.

Figure 8 shows the decreasing depth of melt-pool corresponding to the 1st layer, 3rd layer, and 5th layer at different scan speeds. The depth of the melt-pool decreases from ~0.31 to ~0.12 mm for 1st layer, from ~0.45 mm to ~0.36 mm for the 3rd layer, and for the 5th layer, it decreases from ~0.55 to ~0.41 mm. Similarly, the width of the melt-pool decreases from ~0.87 to ~0.5 mm for the 1st layer, from ~1 to ~0.7 mm, for the 5th layer. It is evident that for both the processing conditions, melting of the powder material over the whole layer thickness is incomplete in the 1st layer. However, subsequent layers are fully melted. Moreover, a further study on increasing layer thickness will provide extensive information to determine the optimal parameters. −

**Figure 8.** Changing melt-pool shapes for the changing scanning speed for the constant power source of 200 W and scanning speed of (**a**) 150 mm·s −1 and (**b**) 200 mm·s −1 .

#### *3.3. Effects of Laser Power on the Melt-Pool and Temperature Distribution for Pure Ti*

Laser power is directly proportional to the temperature at any point during the LAM process, provided all other parameters are kept constant. Figure 9 shows the increasing final maximum temperature for increasing laser power at constant laser scan speed. The temperature variation at different laser power and at a constant scan speed of 200 mm·s −1 is shown in Figure 9. As discussed above, during the process, there are five major peaks in the 1st layer. The maximum temperature obtained at the centre of the 1st layer is 2288 K when laser power is 200 W and 2685 K when laser power is 250 W. Figure 10 represents the difference in melt-pool profiles corresponding to different laser power and at a constant scanning speed of 200 mm·s −1 . A similar trend of Figure 7 is observed in Figure 9 wherein, 1st layer is not fully melted. However, as the process continues with new layers are being deposited, the temperature keeps increasing. Thereby, a fully melted pool is obtained across the whole cross-section of the layer.

−

− −

−

− **Figure 9.** Effect of laser power in the middle of the 1st layer when laser power is 200, 250 W and scan speed is 200 mm·s −1 (**a**) full view and (**b**) magnified view.

− **Figure 10.** Evolution of melt pool dimensions for (**a**) *P* = 200, and (**b**) 250 W, *v* = 200 mm·s −1 in the 1st, 3rd and 5th layer.

The decreasing nature of peaks represents the gradual decrease of the impacts of laser power on the preceding layers as new layers are being deposited. In Figure 9b, the 5th peak has the lowest temperature in the 1st layer, and it is just above the temperature before cooling starts. This shows the negligible significance of laser in the 5th layer on the maximum temperature in the 1st layer. Figure 9 has overlapping peaks, but their peak values are different since both have the same scanning speed and different laser power. Figure 10 displays the evolution of melt-pool shape as new layers are added. It is evident that the width of the melt-pool increases faster than the depth of the melt-pool. This is due to the larger surface width area interaction with the laser. The increase in depth of melt-pool is significant and should not be discarded.

−

−

#### *3.4. Comparative Study of Pure Ti and Inconel 718 Alloy*

The pure Ti and Inconel 718 have different mechanical and thermal properties. It is self-evident that the melt-pool dimensions and temperature distribution of the two materials will be different for the same process parameters. Since the main influencing factors viz. laser power and laser scanning speed are the same for the two materials, a quantitative analysis is performed. Such an analysis will give more details about the intensity of temperature distribution and the melt-pool nature. This helps in choosing the right material under different circumstances where cost-saving, or safety may be the driving factor. It will be quite beneficial when multi-material manufacturing is being carried out and the difference in temperature and melt-pool becomes very important for the two materials to be fused in a homogenous way. This is especially very interesting concerning the printing of functionally graded materials. In such cases, there is a need to know if the different materials will melt and interact at the time at a given set of process parameters.

It is observed that the pure Ti material has a lower temperature and melt-pool dimensions than the Inconel 718 alloy for the same process parameters. It indicates that Inconel 718 requires lesser laser power to attain the same temperature as pure Ti material. Figure 11a shows the cross-sectional view of the variation of melt-pool of the two materials at 1st layer, 3rd layer, and 5th layer when the laser power is 250 W and laser scanning speed is 200 mm·s −1 . The difference in the melt-pool dimensions can be attributed to the difference in material properties. From Figure 2, it is observed that the Inconel 718 has higher thermal conductivity as temperature increases while pure Ti has higher specific heat as the temperature increases. This shows that the specific heat outweighs the thermal conductivity whenever the maximum temperature of a layer is concerned. Higher specific heat means a longer time to attain a higher temperature. The melt-pool depths for the first layer are ~0.28 and ~0.38 mm for pure Ti and Inconel 718 alloy, respectively. For the third layer, the melt-pool depths are ~0.46 and ~0.54 mm for pure Ti and Inconel 718 alloy, respectively. The melt-pool shape of the fifth layer is almost the same as flat for both cases. However, there is a difference in the melt-pool thickness, which is ~0.56 and ~0.87 mm for pure Ti and Inconel 718.

Figure 11b represents the difference of melt-pool dimensions between pure Ti and Inconel 718 alloy when laser intensity is 200 W, and scan speed is 200 mm·s −1 . The depth of melt-pool in the first layer is ~0.14 and ~0.28 mm for pure Ti and Inconel 718 alloy, respectively. For the third layer, the depth of the melt-pool is ~0.38 and ~0.47 mm for Ti and Inconel 718, respectively. In the 5th layer, the depth of melt-pool is ~0.42 and ~0.59 mm for Ti and Inconel 718 alloy, respectively.

Figure 12a,b shows the corresponding time-temperature history. Figure 12a is the time-temperature history considering the whole manufacturing time, while Figure 12b is the magnified view where peak temperature is represented. The maximum temperatures achieved by the laser power at the centre of the 1st layer are 2684 and 2732 K for pure Ti and Inconel 718, respectively. Figure 12c,d shows the temperature profile at the middle point of the 3rd layer over time. A similar trend is found in this case also. The peak temperature attained at the centre of the third layer in the case of pure Ti is 2599 K, while for Inconel 718 alloy, the peak temperature is 2644 K. Another interesting observation is the nature of the changing shape of melt-pool for both materials as the process continues. At first, the cross-sectional melt-pool shape is semi-circular, but it gradually changes to the shape of a ship's hull. This shows that the melt-pool width has a higher sensitivity of change than that of the melt-pool depth.

**Figure 11.** The difference of melt-pool dimensions for pure Ti and Inconel 718 alloy for the (**a**) dataset#4 and (**b**) dataset#3.

**Figure 12.** Time-temperature history of pure Ti and Inconel 718 alloy (**a**,**b**) at the centre of the 1st layer for dataset#4 and (**c**,**d**) at the centre of the 3rd layer for dataset#3.

#### **4. Conclusions**

A 3D finite-element model of laser-based additive manufacturing is developed to investigate melt-pool complexity and temperature behavior during the laser application throughout the model. One of the peculiar features of the model is the consideration of a high layer thickness as opposed to the general consideration of very thin layer thickness. The five-layer FEM simulation is performed to understand the effects of laser power and laser scan velocity on heat flow, melt-pool shape, and temperature distribution of the Ti and Inconel 718 materials. With the current study, the following conclusions can be drawn:

**Author Contributions:** Conceptualization, S.N.S.; S.C.; and Y.N.; Software, S.N.S.; S.C.; and Y.N.; validation, S.N.S.; S.C.; and Y.N.; formal analysis, S.N.S.; S.C.; Y.N.; A.K.D. and C.P. (Chander Prakash); investigation, S.N.S.; S.C.; Y.N.; H.Y.Z.; and S.S.; resources, Y.N.; C.P. (Chander Prakash); C.P. (Catalin Pruncu), and S.S.; data curation, S.N.S.; S.C.; A.K.D.; and L.Y.W.; writing—original draft preparation, S.N.S.; S.C.; and Y.N.; writing—review and editing, S.N.S.; S.C.; Y.N.; A.K.D., C.P. (Chander Prakash); L.Y.W.; H.Y.Z.; S.S. and C.P. (Catalin Pruncu); visualization, Y.N.; L.Y.W. and H.Y.Z.; supervision, Y.N.; S.S.; and C.P. (Catalin Pruncu); project administration, Y.N.; H.Y.Z.; and S.S.; funding acquisition, Y.N.; C.P. (Chander Prakash) and C.P. (Catalin Pruncu). All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by TEQUIP II grant at the North Eastern Regional Institute of Science and Technology, Itanagar, Arunachal Pradesh, India.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Conflicts of Interest:** There exists no conflict of interest.

#### **References**

1. Facchini, L.; Magalini, E.; Robotti, P.; Molinari, A.; Hoges, S.; Wissenbach, K. Ductility of a Ti-6Al-4V alloy produced by selective laser melting of pre-alloyed powders. *Rapid Prototyp. J.* **2010**, *16*, 450–459. [CrossRef]

## *Article* **Numerical Study on Thermodynamic Behavior during Selective Laser Melting of 24CrNiMo Alloy Steel**

#### **Xiangpeng Luo , Minghuang Zhao, Jiayi Li and Chenghong Duan \***

College of Mechanical and Electrical Engineering, Beijing University of Chemical Technology, North Third Ring Road 15, Chaoyang District, Beijing 100029, China<EMAIL_ADDRESS>(X.L<EMAIL_ADDRESS>(M.Z<EMAIL_ADDRESS>(J.L.)

**\*** Correspondence<EMAIL_ADDRESS>Tel.: +86-010-6443-6678

Received: 4 December 2019; Accepted: 18 December 2019; Published: 20 December 2019 -

**Abstract:** In this paper, a multi-layer and multi-track finite element model of 24CrNiMo alloy steel by selective laser melting (SLM) is established by using the ABAQUS software. The distribution and evolution of temperature field and stress field and the influence of process parameters on them are systematically studied. The results show that the peak temperature increases from 2153 ◦C to 3105 ◦C and the residual stress increases from 335 MPa to 364 MPa with increasing laser power from 200 W to 300 W; the peak temperature decreases from 2905 ◦C to 2405 ◦C and the residual stress increases from 327 MPa to 363 MPa with increasing scanning speed from 150 mm/s to 250 mm/s; the peak temperature increases from 2621 ◦C to 2914 ◦C and the residual stress decreases from 354 MPa to 300 MPa with increasing preheating temperature from 25 ◦C to 400 ◦C. Far away from scanning area, far away from starting point, and the adjacent areas with vertical scanning direction, resulting in a uniform temperature distribution, help to reduce the residual stress. Due to the remelting effect, the interlayer scanning angle changing helps to release the residual stress of the former layer causing a smaller residual stress after redistribution.

**Keywords:** selective laser melting; finite element analysis; thermodynamic behavior; substrate preheating; scanning strategy; 24CrNiMo alloy steel

#### **1. Introduction**

As an academic term for 3D printing, rapid prototyping, and layer manufacturing, additive manufacturing (AM) combines materials processing and forming technology, computer-aided design, and so on. Based on the principle of discrete-stacking, this technology stacks metal materials or non-metal materials by layers to directly produce three-dimensional solid parts through software and control systems, by means of sintering, melting, spraying, photocuring, etc. Compared with the traditional subtractive manufacturing of cutting raw materials, AM is a manufacturing method that is able to process three-dimensional complex structural parts by adding materials point by point, line by line, and surface by surface [1–3]. Moreover, AM technology has the advantages of flexible processing, short production cycle, and high material utilization, and can manufacture any complex shape structure parts in theory [4–6]. Selective laser melting (SLM) is a technique, which utilizes a high-energy laser beam with a planned scanning strategy, used to scan pre-placed metal powders to make them melt rapidly. The powders are then cooled and solidified rapidly, and finally formed into solid components layer by layer [7,8].

SLM, one of the most important means of metal laser additive manufacturing, has attracted considerable attention in recent years, and its numerical simulation research has also become a hot issue in the industry. Due to the rapid movement of the laser heat source, the temperature of the material rapidly rises and then shows an extremely fast material solidification cooling rate. The temperature history of a locally fabricated area is extremely complicated, and the molten pool has a very short lifetime in a SLM process [9]. It is difficult to observe and record the transient temperature field, stress field, and molten pool morphology through experimental methods. Numerical simulation is an effective way to solve this problem.

To date, many scholars have carried out numerical simulation research on a metal powder SLM process. Chen et al. [10] established a multilayer finite element (FE) model to study the temperature field during a SLM process of TiB2/Ti6Al4V multi-material parts under various processing parameters. The simulation results showed that the maximum temperature gradient increased from 24.920 ◦C/µm to 37.754 ◦C/µm with increasing the laser power from 300 W to 450 W, but the maximum temperature gradient decreased from 33.884 ◦C/µm to 31.478 ◦C/µm with increasing the scanning speed from 400 mm/s to 1000 mm/s. Woo et al. [11] developed a three-dimensional FE model to investigate the thermal behavior during the SLM process of WC-reinforced H13 steel composite powder. The molten pool geometry under different parameters was analyzed based on the temperature field obtained by numerical simulation. The results showed that the distribution factor, packing efficiency, and absorption coefficient are the main factors affecting the molten pool structure. Ali et al. [12] developed a modeling approach to simulate the temperature field during a SLM process of Ti6Al4V powder. The validity of the model was validated by comparing the width and depth of the molten pool obtained by finite element analysis and experimental measurement. Based on this model, the effects of process parameters on cooling rates and temperature gradients inducing the accumulation of residual stress build-up was studied. Foroozmehr et al. [13] used a three-dimensional FE model to simulate the size of the molten pool in the SLM process. The model considered the penetration characteristics of laser beam on powder bed, and the depth depended on the thickness of powder. The temperature distribution, depth, width, and length of the molten pool of each track were studied, and the influence of scanning speed on them was analyzed. Wang et al. [14] developed a three-dimensional FE model to research the thermal behavior and residual stress during the SLM process of AlSi10Mg powder. The simulation results showed that the stress gradually increased during the SLM process due to the effect of heat accumulation, and the temperature gradient affected the final distribution of the residual stress. However, numerical studies have not yet been reported on the temperature field and stress field of 24CrNiMo alloy steel, an alloy steel material commonly used for processing brake discs for high-speed rail, fabricated by SLM, and the application of SLM technology in high-speed train and rail industry is rarely studied, which greatly restrict a wider application of this technology in the high-speed train and rail industry. Moreover, there are few researches on the influence of SLM scanning strategy on the temperature field and stress field.

In this paper, the distribution and evolution of temperature field and stress field of 24CrNiMo alloy steel by SLM are studied by finite element analysis method. The influence of different process parameters on temperature field distribution, temperature change rate, thermal stress evolution, and residual stress distribution is clarified. The influence rules and mechanisms of laser power, scanning speed, preheating temperature of substrate, subarea scanning strategy, and interlayer scanning angle changing on temperature field and stress field during a SLM process are revealed.

#### **2. Modeling**

#### *2.1. Mathematical Model*

According to the basic theory of heat transfer, heat conduction, heat convection, and heat radiation are the basic modes of heat transfer. In a SLM process, metal powders melt rapidly and then solidify rapidly. The analysis of temperature field in this process is a non-linear transient thermal analysis, as shown in Figure 1.

**Figure 1.** Schematic diagram of heat transfer during selective laser melting (SLM) process.

For transient heat issues, based on Fourier heat transfer law and energy conservation law, and taking material anisotropic into account, the three-dimensional non-linear transient heat transfer control equation is

$$
\rho c \frac{\partial T}{\partial t} = \frac{\partial}{\partial x} (k\_x \frac{\partial T}{\partial x}) + \frac{\partial}{\partial y} (k\_y \frac{\partial T}{\partial y}) + \frac{\partial}{\partial z} (k\_z \frac{\partial T}{\partial z}) + \mathbf{Q}.\tag{1}
$$

where *kx*, *ky*, *kz* are the thermal conductivity in *x*, *y*, *z* direction, *T* is the powder temperature, Q is the heat flux density, ρ is the density, and *c* is the specific heat capacity.

*ρ* Heat transfer between powder surface and ambient environment is heat convection and radiation. It can be described as follows:

$$-k\frac{\partial T}{\partial n} = h(T\_a - T\_s) + \sigma \varepsilon (T\_a^4 - T\_s^4),\tag{2}$$

 where *k* is the thermal conductivity, *n* is the normal vector to the powder surface, *Ta* is the powder temperature, *Ts* is the ambient temperature, *h* is the convection heat transfer coefficient, σ is the Stephen-Boltzmann constant (5.67 × 10 −8 W/m2 ·K 4 ), and ε is the thermal emissivity.

#### *2.2. Boundary Conditions*

Considering the radiation impact of the laser on the powder, it is used as the correction coefficient of the boundary heat transfer. Moreover, the Equation (3) can be obtained by mathematical transformation of the Equation (2).

∙K

−

$$-k\frac{\partial T}{\partial t} = \beta \left[ h + \sigma \epsilon \left( T\_a{}^3 + T\_a{}^2 T\_s + T\_a T\_s{}^2 + T\_s{}^3 \right) \right] \times \left( T\_a - T\_s \right). \tag{3}$$

 Total heat transfer coefficient is defined by:

$$H = \beta \left[ h + \sigma \varepsilon (T\_a{}^3 + T\_a{}^2 T\_s + T\_a T\_s{}^2 + T\_s{}^3) \right]. \tag{4}$$

 According to the experimental results of the temperature field from Reference [14], *H* at lower temperature is set to be thousands of times of that at steady state, and *H* at higher temperature is set to 80 times of that at steady state in this paper. Furthermore, at steady state, β = 1.

*H* The boundary condition is set to be three-point constraint [15], that is the three vertex constraints on the bottom of the substrate are *Ux* = *Uy* = *Uz* = 0, *Uy* = *Uz* = 0, *Uz* = 0, respectively.

#### *2.3. Heat Source Model*

The double ellipsoidal heat source model used in this paper can be described as follows [16]:

$$q(x,y,z) = \frac{6\sqrt{3}P\eta}{\pi\sqrt{\pi}abc}e^{\left(-3\frac{y^2}{a^2} - 3\frac{y^2}{b^2} - 3\frac{z^2}{c^2}\right)},\tag{5}$$

where *P* is the laser power, η is the laser absorptivity, *a*, *b*, and *c* are the shape parameters of the heat source, *x*, *y*, and *z* are the local coordinates.

#### *2.4. FE Model*

In this paper, two models are used for analysis in ABAQUS (version 6.14.4, Dassault Systèmes, Paris, France), both of them include the substrate and the powder bed. As shown in Figure 2a, the dimensions of the substrate in FE model 1 are 2.0 mm × 1.2 mm × 0.3 mm, and the dimensions of the powder bed are 1.4 mm × 0.6 mm × 0.1 mm with two layers, the height of each layer is 0.05 mm. As shown in Figure 2b, the dimensions of the substrate in FE model 2 are 1.80 mm × 1.80 mm × 0.5 mm, and the dimensions of the powder bed are 1.2 mm × 1.2 mm × 0.10 mm with two layers, the height of each layer is 0.05 mm. Considering the computational efficiency and accuracy, the powder bed is meshed by DC3D8 element, which is an eight-node linear heat transfer brick element, with dimensions of 0.02 mm × 0.02 mm × 0.02 mm, and the substrate is gradually coarsely meshed away from the powder layer. The C3D8R element, an eight-node linear brick element, is used to calculate the stress field by applying the indirect coupling method based on the temperature field.

**Figure 2.** Finite element (FE) model: (**a**) model 1; (**b**) model 2.

#### *2.5. Material Properties*

In this paper, the substrate material is 45 steel whose specific material properties are given in Reference [17]. The metal powder is 24CrNiMo alloy steel whose chemical composition is listed in Table 1.

**Table 1.** Chemical composition of 24CrNiMo alloy steel powder.

– The physical properties of 24CrNiMo alloy steel vary significantly with temperature, which should be considered in the simulation. In this paper, the temperature-dependent physical properties of 24CrNiMo alloy steel in solid state are obtained by the commercial software JMatPro (version 9.0, Sente Software Ltd., Surrey, UK), which is a powerful and integrated software for material properties simulation [18–20], as shown in Figure 3.

It is known that the temperature-dependent physical properties of 24CrNiMo alloy steel in powder state are quite different from those in solid state, including density, thermal conductivity, elastic modulus, and thermal expansion coefficient.

The effective thermal conductivity of the powder bed can be calculated by the Yagi-Kunii model [21]. It is described as follows:

$$\frac{k\_{\varepsilon}}{k\_{\mathcal{S}}} = \frac{\beta(1-\varphi)}{\gamma \binom{k\_{\mathcal{S}}}{k\_{\mathcal{S}}} + \frac{1}{\frac{1}{\varphi} + \frac{D\_{p}h\_{\mathcal{V}}}{k\_{\mathcal{S}}}}} + \varepsilon \beta \frac{D\_{p}h\_{\mathcal{V}\mathcal{V}}}{k\_{\mathcal{S}}},\tag{6}$$

where ϕ is the porosity of the powder, *Dp* is the average diameter of the powder particles, γ is the ratio of the solid effective length to the solid average diameter related to heat conduction, β is the ratio of the average length to average stacking diameter between two adjacent particles in the direction of heat flux, *ke* , *kg*, and *ks* are the effective thermal conductivity of the powder bed, the gas in the pores, and the solid material, *hrs* is the thermal emissivity between adjacent particle surfaces, and *hrv* is the thermal emissivity between adjacent gases.

oisson's **Figure 3.** (**a**) Thermal conductivity and specific heat, (**b**) density and elastic modulus, (**c**) Poisson's ratio and thermal expansion coefficient, and (**d**) yield limit of 24CrNiMo alloy steel.

The density of the powder bed can be calculated by Equation (7). It is described as follows:

$$
\rho\_p = (1 - \varphi)\rho\_{\text{s}\prime} \tag{7}
$$

where ρ*p* is the density of the powder material, ρ*s* is the density of the solid material.

 In the actual SLM process, Marangoni convection exists in the molten pool, resulting in the intensification of energy transfer, which has a significant effect on temperature and stress distribution. Therefore, the thermal conductivity above the melting point is modified by an enhancement factor to approximately consider the effects of Marangoni convection on heat transfer in the molten pool [22,23]. The modified thermal conductivity can be expressed as

$$k^\*(T) = \begin{cases} \begin{array}{c} k(T) \\ ak(T) \end{array} & T \le T\_m \\\end{array} \tag{8}$$

where *k(T)* is the actual thermal conductivity, *k \* (T)* is the modified thermal conductivity, and *Tm* is the melting temperature.

#### *2.6. Latent Heat of Phase Transformation*

*ρ ρ*

 In order to improve the calculation accuracy, the phase transformation latent heat of 24CrNiMo alloy steel during the SLM process is considered by applying the equivalent specific heat method.

In the temperature range of phase transformation, the specific heat of the material can be modified by using the phase transformation latent heat [24]:

$$\mathbf{C}\_P^\* = \mathbf{C}\_P + \frac{L}{T\_L - T\_s} \,'\tag{9}$$

where *L* is the phase transformation latent heat, *TL* is the liquidus temperature, *TS* is the solidus temperature, *CP* is the actual specific heat, and *CP \** is the modified specific heat.

#### **3. Results and Discussion**

Firstly, it should be noted that the results of Sections 3.1 and 3.2 are based on FE model 1 (Figure 2a) and the results of Section 3.3 is based on FE model 2 (Figure 2b).

#### *3.1. Distribution and Variation Rules of Temperature Field and Stress Field*

Figure 4 shows the temperature distribution contour of the whole model and the top surface and cross section of the molten pool under P = 250 W and v = 200 mm/s when the laser beam reaches the center of the first layer. It demonstrates that the peak temperature of the molten pool is 2621 ◦C and the isotherms on the front of the heat source are denser than those in the back, showing that the temperature gradient on the front of the heat source is larger. The main reason is that the front material of the heat source is still in powder state, and the heat cannot be transferred quickly because of its lower thermal conductivity, which results in a larger temperature gradient and a denser isotherm. The powder in the back of the heat source was transformed into solid, which increases the thermal conductivity and makes a faster heat transfer. The dotted line is the area where the temperature is higher than the melting point of the material (1435 ◦C), which can be used to characterize the structure of the molten pool. The length of the molten pool is about 296 µm, the width is about 177 µm, the depth is about 66 µm, the ratio of length to width is about 1.7, and the shape of the molten pool is similar to that of water droplets. gth of the molten pool is about 296 μm, the width is about 177 μm, the depth is about 66 μm, the ratio of length to width is about 1.7, and the

**Figure 4.** Temperature field distribution contour when the laser beam reaches the center of the first layer.

Figure 5a shows the schematic diagram of the midpoint (P1–P6) on the top surface of each scanning tracks. The peak temperatures at the midpoint of the three tracks in the first layer are 2466 ◦C, 2621 ◦C, and 2722 ◦C, respectively, and those of the three tracks in the second layer are 2605 ◦C, 2725 ◦C, and 2818 ◦C, respectively, as shown in Figure 5b. As the laser scanning progresses the peak temperature increases with the increase of scanning tracks and scanning layers, but the increase amplitude decreases gradually.

–

–

– **Figure 5.** (**a**) Schematic diagram of the midpoint (P1–P6) on the top surface of each scanning tracks; (**b**) peak temperature at the midpoint of each scanning tracks.

first scanning track are 236 μm, 162 μm and 59 μm, Figure 6 shows the three dimensions of the molten pool at the midpoint of each scanning track. The solid lines represent the length of the molten pool at the midpoint of each scanning track, the dashed lines represent the width of the molten pool at the midpoint of each scanning track, and the dotted lines represent the depth of the molten pool at the midpoint of each scanning track. As demonstrated, with the increase of scanning tracks, the length, width, and depth of the molten pool increase gradually. Furthermore, the three dimensions of the second layer molten pool are larger than those of the first layer to a certain extent. Taking the first layer as an example, the length, width, and depth of the molten pool at the midpoint of the first scanning track are 236 µm, 162 µm, and 59 µm, respectively. The length, width, and depth of the molten pool at the midpoint of the second scanning track are 25.4%, 9.3%, and 11.9% larger than those at the midpoint of the first scanning track, respectively. Moreover, the length, width, and depth of the molten pool at the midpoint of the third track are 14.9%, 7.3%, and 10.6% larger than those at the midpoint of the first scanning track, respectively. However, the increase amplitude of the three dimensions of the molten pool decreases gradually with the increase of the scanning tracks, as shown in Figure 7. Taking the second track of the two layers as an example, the length, width, and depth of the molten pool at the midpoint of the second track in the first layer are 23.6%, 13.0%, and 13.6% larger than those at the midpoint of the second track in the second layer, respectively. Combining with the temperature field, it is found that the three dimensions of the molten pool with different scanning tracks and layers increase in accordance with the variation of the peak temperature of the molten pool (see Figure 5), which indicates that the three dimensions of the molten pool are greatly affected by the temperature distribution of the molten pool. The reason for the decrease of the increase is that the heat transfer is slowed down with the increase of scanning tracks and layers. first scanning track are 236 μm, 162 μm and 59 μm,

**Figure 6.** Three dimensions of the molten pool at the midpoint of each scanning tracks.

**Figure 7.** Increase amplitude of the molten pool size.

molten pool begins to solidify gradually. The material shrinks due to "thermal expansion and contraction", and is bound by the solidified metal around it. The large temperature When the laser beam scans the powder, the irradiated area of the spot absorbs a large amount of heat so that the temperature increases rapidly. After reaching the melting point, the powder state changes to a liquid state and then a molten pool is formed. At this time, the liquid phase is purely plastic, and the Mises stress is small and is approximately considered to be zero, as shown in Figure 8. When the laser beam is far away from this area, the temperature of the position decreases rapidly and the metal of the molten pool begins to solidify gradually. The material shrinks due to "thermal expansion and contraction", and is bound by the solidified metal around it. The large temperature gradient results in the thermal stress increasing gradually. When the thermal stress is higher than the yield limit of the material, the solidified area is plastically deformed. As the molten pool moves continuously, the scanning area cools gradually. When the temperature tends to be stable, the thermal stress redistributes and remains in the SLMed parts. molten pool begins to solidify gradually. The material shrinks due to "thermal expansion and contraction", and is bound by the solidified metal around it. The large temperature

**Figure 8.** Stress field distribution contour when the laser beam reaches the center of the first layer.

Figure 9 shows the evolution of stress at the center of the first layer. When the laser beam scans the center of the first layer, the high temperature gradient results in a larger thermal stress before and after the molten pool, reaching more than 800 MPa. Moreover, the stress stabilizes at about 400 MPa with the cooling process at the end of the first layer. When the second layer is scanned, the position undergoes a similar temperature evolution with the first layer, but the temperature gradient decreases so that the peak stress decreases. Due to material shrinkage, the stress slightly increases during the cooling processing. The residual stress is released by a post-thermal effect and finally stabilizes at about 350 MPa.

Figure 10 shows the residual stress distribution contour after cooling. The maximum Mises stress is about 355 MPa, which appears at the joint edge of the substrate and the formed layer because of the large temperature gradient between them and the difference in thermal expansion coefficients of the materials. The high stress area is mainly concentrated in the formed layer, and the substrate stress is relatively low. It can be seen from Figure 11b,c that the residual tensile stress mainly occurs in the formed layer, and the X-direction residual stress is slightly higher than the Y-direction residual stress because the X-direction is the scanning direction, and the large cooling rate causes the stress to be parallel to the scanning direction. As can be seen from Figure 10d, the Z-direction residual stress is mainly concentrated between the substrate and the formed layer, which tends to cause warping and cracking.

**Figure 9.** Evolution of stress at the center of the first layer.

**Figure 10.** Residual stress distribution contour: (**a**) Von Mises stress, (**b**) X-direction stress, (**c**) Y-direction stress, and (**d**) Z-direction stress.

**Figure 11.** (**a**) Temperature distribution; (**b**) stress distribution under different laser powers.

#### *3.2. E*ff*ects of Process Parameters on Temperature Field and Stress Field*

Figure 11a shows the temperature distribution along the second scanning track under different laser powers when the laser beam scans the center of the first layer. The temperature distribution tends to follow the same rules, showing characteristics of high in the middle and low on both sides. The temperature and temperature gradient near the molten pool are relatively high in the middle area. When the laser power increases from 200 W to 300 W, the peak temperature of the molten pool increases accordingly, and the central temperature increases from 2153 ◦C to 3105 ◦C because the laser energy density and the heat input increases. Figure 11b shows the residual stress distribution of the second scanning track under different laser powers when scanning the center of the first layer. It can be seen that the Mises stress distribution rules are similar, and the stress in the middle of the scanning track is close to each other. As the laser power increases from 200 W to 300 W, the maximum of Mises stress increases from 335 MPa to 364 MPa. The main reason is that the increase of laser power has a great influence on the temperature gradient of the molten pool so that the growth rate increases from 6.9 × 10 3 ◦C/mm to 1.2 × 10 4 ◦C/mm during the cooling process.

Figure 12a shows the temperature distribution along the second scanning track under different scanning speeds when the laser beam scans the center of the first layer. When the scanning speed increases from 150 mm/s to 200 mm/s, the peak temperature of the molten pool decreases accordingly, and the central temperature decreases from 2905 ◦C to 2405 ◦C because the laser energy density and the heat input per unit time decreases. Figure 12b shows the residual stress distribution of the second scanning track under different laser speeds when the laser beam scans the center of the first layer. As the scanning speed increases from 150 mm/s to 200 mm/s, the maximum of Mises stress increases from 327 MPa to 363 MPa. The main reason is that the increase of scanning speed has a great influence on the temperature gradient of the molten pool so that the growth rate increases from 7.7 × 10 3 ◦C/mm to 1.1 × 10 4 ◦C/mm during the cooling process.

**Figure 12.** (**a**) Temperature distribution; (**b**) stress distribution under different scanning speeds.

Figure 13a shows the temperature distribution along the second scanning track under different preheating temperatures when the laser beam scans the center of the first layer. When the preheating temperature increases from 25 ◦C to 400 ◦C, the peak temperature of the molten pool increases accordingly, and the central temperature increases from 2621 ◦C to 2914 ◦C because of the increase of heat accumulation. Figure 13b shows the residual stress distribution of the second scanning track under different preheating temperatures when the laser beam scans the center of the first layer. As the preheating temperature increases from 25 ◦C to 400 ◦C, the maximum of Mises stress decreases from 354 MPa to 300 MPa. The main reason is that preheating of the substrate helps to reduce temperature gradient. It also can be seen that the increase of the preheating temperature in a certain range makes the overall distribution of residual stress show a significant downward trend, and the high stress range of the formed area is gradually reduced, indicating that the preheating of the substrate helps to reduce the residual stress and the cracking tendency of SLMed parts.

**Figure 13.** (**a**) Temperature distribution and (**b**) stress distribution under different preheating temperatures.

*3.3. E*ff*ects of Scanning Strategy on Temperature Field and Stress Field*

and 4 represent the scanning sequence, "start" Some differences exist in the temperature field under different subarea scanning strategies in the SLM process. The specific subarea scanning strategies are shown in Figure 14, and the scanning area is divided into four areas in which 1, 2, 3, and 4 represent the scanning sequence, "start" represents the starting point of scanning, and points A, B, C, and D are the area centers. and 4 represent the scanning sequence, "start"

**Figure 14.** Schematic diagram of subarea scanning strategies.

Figure 15a shows the peak temperatures of points A, B, C, and D under different subarea scanning strategies. The temperature of strategies 1, 2, 3, and 4 gradually increases due to the heat accumulation effect. Comparing Strategy 1 with Strategy 2, Strategy 2 has a lower temperature in Area 2 and 4, which indicates that the diagonal scanning can make the scanning area as far as possible to reduce the temperature increase caused by the thermal influence of the scanned area. Comparing Strategy 2 and Strategy 3, the temperature in Area 3 and 4 of Strategy 3 slightly decreases, indicating that the method of scanning from the edge to the center can also reduce the preheating effect. Comparing Strategy 3 and Strategy 4, Strategy 4 has a lower temperature in Area 3 and 4, indicating vertical scanning direction of adjacent areas that can reduce the influence of thermal accumulation from adjacent areas. In summary, far away from the scanning area, far away from the scanning starting point and adjacent areas with vertical scanning direction are the scanning strategies, which could result in a more uniform temperature distribution and a lower average temperature (as shown in Figure 15b), and help to reduce the residual stress caused by temperature difference.

**Figure 15.** (**a**) Peak temperature of the area center and (**b**) average temperature under different subarea scanning strategies.

Figure 16 shows the schematic diagram of the interlayer scanning angle changing. They have the same scanning starting point, the same scanning length of each tracks, and the same number of tracks. Figure 17 shows the residual stress distribution contour for scanning only the first layer after cooling. It demonstrates that the maximum Mises stress is about 366 MPa, and the stress distribution of the formed layer is relatively uniform, basically above 300 MPa. The substrate stress is lower, less than 200 MPa. The maximum tensile stresses in the X-direction, Y-direction, and Z-direction are 435 MPa, 415 MPa, and 371 MPa, respectively. The maximum compressive stresses in the X-direction, Y-direction, and Z-direction are 337 MPa, 444 MPa, and 190 MPa, respectively. Moreover, a large stress concentration occurs in the place where the formed layer is in contact with the substrate, which may cause cracking and warping.

**Figure 16.** Schematic diagram of (**a**) no interlayer scanning angle and (**b**) 90 ◦ interlayer scanning angle.

**Figure 17.** *Cont*.

**Figure 17.** Residual stress distribution contour for scanning only the first layer: (**a**) Von Mises stress, (**b**) X-direction stress, (**c**) Y-direction stress, and (**d**) Z-direction stress.

Figure 18 shows the residual stress distribution contour for scanning two layers after cooling with no interlayer scanning angle and 90 ◦ interlayer scanning angle. It can be seen that the maximum Mises stress with no interlayer scanning angle is 332 MPa, and that of 90 ◦ interlayer scanning angle is 328 MPa. The maximum tensile stresses in the X-direction, Y-direction, and Z-direction with no interlayer scanning angle are 392 MPa, 376 MPa, and 392 MPa, respectively; the maximum compressive stresses in the X-direction, Y-direction, and Z-direction with no interlayer scanning angle are 329 MPa, 446 MPa, and 201 MPa, respectively; the maximum tensile stresses in the X-direction, Y-direction, and Z-direction with 90 ◦ interlayer scanning angle are 374 MPa, 398 MPa, and 398 MPa, respectively; the maximum compressive stresses in the X-direction, Y-direction, and Z-direction with 90 ◦ interlayer scanning angle are 459 MPa, 317 MPa, and 207 MPa, respectively. Meanwhile, by analyzing the residual stress values of the first layer, it is found that the stress with no interlayer scanning angle is lower than that with 90 ◦ interlayer scanning angle. The interlayer remelting under the 90 ◦ interlayer scanning angle causes the residual stress of the first layer to be released multiple times so that the stress of the first layer is reduced after redistribution. Therefore, the interlayer scanning angle changing helps to reduce the tendency of cracking by reducing the residual stress of the formed layer.

**Figure 18.** *Cont*.

**Figure 18.** Residual stress distribution contour for scanning two layers with (**a**) no interlayer scanning angle and (**b**) 90 ◦ interlayer scanning angle.

#### *3.4. Experimental Verification*

half of the average molten pool width obtained by experiments are 76.5 μm and 111.5 μm, respectively, and those by numerical simulations are 79.5 μm and 109.5 μm, with errors of 5.8% and Figure 19 shows the experimental and numerical molten pool morphology on the cross section of SLM processed specimens under P = 250 W and v = 200 mm/s. The average molten pool depth and half of the average molten pool width obtained by experiments are 76.5 µm and 111.5 µm, respectively, and those by numerical simulations are 79.5 µm and 109.5 µm, with errors of 5.8% and 2.9%, respectively (as shown in Table 2). It can be seen that the results of numerical simulation and experimental measurements are consistent with each other, which proves that the reliability and accuracy of the numerical analysis is good.

**Figure 19.** Comparisons of experimental (**a**) and numerical (**b**) morphology on the cross section of the molten pool.

#### **4. Conclusions**

In this paper, the distribution and evolution of temperature field and stress field of 24CrNiMo alloy steel by SLM are studied by numerical simulation. The influence of process parameters (laser power, scanning speed, preheating temperature, and scanning strategy) on temperature field distribution, temperature change rate, thermal stress evolution, and residual stress distribution is analyzed, and the relevant experimental verification is carried out. The following conclusions are drawn:

is about 296 μm, the width is about 177 μm, the depth is about 66 μm, the aspect ratio is about 1.7, (1) The peak temperature at the center of the first layer is 2621 ◦C, the length of the molten pool is about 296 µm, the width is about 177 µm, the depth is about 66 µm, the aspect ratio is about 1.7, and the shape is similar to that of water droplets. The increase of thermal accumulation leads to the increase of the peak temperature with the increase of scanning tracks and scanning layers, but the increase of that decreases gradually. The temperature field of the molten pool has great influence on the molten pool size. Temperature gradient results in large thermal stress around the molten pool, which reaches more than 800 MPa at the center of the first layer and stabilizes at about 400 MPa after the first layer is scanned. When the second layer is scanned, the temperature gradient decreases, and the residual stress is released post-thermally and finally stabilizes at about 350 MPa.

(2) When the laser power increases from 200 W to 300 W, the peak temperature of the molten pool increases from 2153 ◦C to 3105 ◦C, the maximum of temperature gradient increases from 6.9 × 10 3 ◦C/mm to 1.2 × 10 4 ◦C/mm during the cooling process, and the Mises stress increases from 335 MPa to 364 MPa. When the scanning speed increases from 150 mm/s to 200 mm/s, the peak temperature of the molten pool decreases from 2905 ◦C to 2405 ◦C, the maximum of temperature gradient increases from 7.7 × 10 3 ◦C/mm to 1.1 × 10 4 ◦C/mm during the cooling process, and the maximum of Mises stress increases from 327 MPa to 363 MPa. When the preheating temperature increases from 25 ◦C to 400 ◦C, the peak temperature of the molten pool increases from 2621 ◦C to 2914 ◦C, and the maximum of Mises stress decreases from 354 MPa to 300 MPa. Therefore, using appropriate process parameters help to reduce the residual stress.

(3) Far away from scanning area, far away from the scanning starting point and adjacent areas with vertical scanning direction are the scanning strategies, which could result in a more uniform temperature distribution, and help to reduce the residual stress caused by temperature difference. The interlayer remelting under the 90 ◦ interlayer scanning angle causes the residual stress of the first layer to be released multiple times so that the stress of the first layer is reduced after redistribution. Therefore, the interlayer scanning angle changing helps to reduce the tendency of cracking by reducing the residual stress.

**Author Contributions:** Methodology, X.L. and M.Z.; software, M.Z. and J.L.; validation, M.Z.; investigation, M.Z. and X.L.; resources, C.D.; data curation, M.Z. and J.L.; writing—original draft preparation, X.L. and M.Z.; writing—review and editing, X.L. and C.D.; visualization, M.Z. and J.L.; supervision, X.L. and C.D.; project administration, C.D.; funding acquisition, C.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Key Research and Development Program of China, grant number 2016YFB1100202.

**Acknowledgments:** The authors gratefully acknowledge the financial support from the National Key Research and Development Program of China (No.2016YFB1100202).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Tri-Planar Geometric Dimensioning and Tolerancing Characteristics of SS 316L Laser Powder Bed Fusion Process Test Artifacts and Effect of Base Plate Removal**

**Baltej Singh Rupal 1,2 , Tegbir Singh 3 , Tonya Wolfe 3 , Marc Secanell 2 and Ahmed Jawad Qureshi 1,\***

**Abstract:** The precision of LPBF manufactured parts is quantified by characterizing the geometric tolerances based on the ISO 1101 standard. However, there are research gaps in the characterization of geometric tolerance of LPBF parts. A literature survey reveals three significant research gaps: (1) systematic design of benchmarks for geometric tolerance characterization with minimum experimentation; (2) holistic geometric tolerance characterization in different orientations and with varying feature sizes; and (3) a comparison of results, with and without the base plate. This research article focuses on addressing these issues by systematically designing a benchmark that can characterize geometric tolerances in three principal planar directions. The designed benchmark was simulated using the finite element method, manufactured using a commercial LPBF process using stainless steel (SS 316L) powder, and the geometric tolerances were characterized. The effect of base plate removal on the geometric tolerances was quantified. Simulation and experimental results were compared to understand tolerance variations using process variations such as base plate removal, orientation, and size. The tolerance zone variations not only validate the need for systematically designed benchmarks, but also for tri-planar characterization. Simulation and experimental result comparisons provide quantitative information about the applicability of numerical simulation for geometric tolerance prediction for the LPBF process.

**Keywords:** laser powder bed fusion (LPBF); benchmark test artifact; numerical simulations; dimensional metrology; geometric dimensioning and tolerancing (GD&T)

#### **1. Introduction and Background**

According to ISO/ASTM 52900:2015 [1], additive manufacturing (AM) is defined as the "process of joining materials to make parts from 3D model data, usually layer upon layer, as opposed to subtractive manufacturing and formative manufacturing methodologies." AM is also commonly known as "3D printing". AM was developed in the early 1980s and has shown great promise and the ability to produce complex and custom geometrical shapes from a wide range of materials [2]. Common AM processes are material extrusion, vat photopolymerization, directed energy deposition, and laser powder bed fusion (LPBF) [3]. The LPBF process for metals uses a laser as a source of energy to fuse layers of metal powder. The laser melts a defined path on each layer of the deposited metal powder. The bed then moves down, and another layer of metal powder with a thickness of 20–100 µm is deposited. This process is repeated until the part is completely manufactured. No binders are used in this process. The process can produce fully dense metal parts ready for industrial use and has limited post-processing needs. It is a widely used metal AM process with various applications in the automotive, aerospace, and biomedical

**Citation:** Rupal, B.S.; Singh, T.; Wolfe, T.; Secanell, M.; Qureshi, A.J. Tri-Planar Geometric Dimensioning and Tolerancing Characteristics of SS 316L Laser Powder Bed Fusion Process Test Artifacts and Effect of Base Plate Removal. *Materials* **2021**, *14*, 3575. https://doi.org/10.3390/ ma14133575

Academic Editor: Mika Salmi

Received: 29 April 2021 Accepted: 17 June 2021 Published: 26 June 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

industries [4]. Although AM has made the transition from research labs to industry in the last decade, various challenges, such as geometric tolerance control of manufactured parts, low repeatability, and controlling deviations due to residual stresses still need to be addressed [2]. To define the challenges, the output characteristics of AM parts must be understood and can be categorized as follows:

These output characteristics are dependent on various process parameters, such as layer thickness, scan strategy, and part orientation. Standardized procedures have already been established for mechanical, material, and surface characteristic testing and quantification [5–7]; however, standardized methods for quantification and assessment of geometric characteristics are still in their infancy for metal AM [8,9]. Like any other manufacturing process, additively manufactured parts also have deviations and errors compared to the input CAD data. Understanding these deviations or variations is critical in engineering design and manufacturing. For example, a higher frequency of part rejections is typical in precision applications, as a high degree of geometric control is challenging. Variations in a final part's geometry occur due to process physics, various process parameters, and manufacturing conditions. Resulting "geometric deviations" or "geometric errors" need to be quantified and assessed in advance to ensure the required dimensions and geometric tolerances of the AM part are met.

To date, methods for geometric tolerance assessment of AM processes are not yet completely defined or standardized. Experimental methods based on geometric benchmark test artifacts, or GBTAs [10,11], aim at providing quantitative information about various geometric tolerance characteristics. A brief comparison of common GBTAs available in the literature is presented from a geometric tolerance perspective in Table 1. The features of the manufactured GBTAs are used to characterize different dimensional and geometric tolerances [12–15]. The GBTA experiments are followed by ranking and optimizing manufacturing parameters that influence the geometric tolerances, and this information is used to optimize these parameters for the actual manufacturing. For example, Shahrain et al. [16] varied 13 process parameters of a fused deposition modeling printer and, based on the experimental results for flatness and cylindricity, the parameters were ranked and optimized to meet the required geometric tolerance of subsequent prints. References [12,13,17–22] provide similar studies, where the geometric tolerances of manufactured GBTAs are characterized.

Even though these studies provided a great starting point for further study, their application in predicting geometric tolerances for other parts manufactured on the same machine is questionable. This is due to the lack of features in the GBTA to quantify certain geometric dimensioning and tolerancing (GD&T) characteristics as per ISO 1101 [23]. Such as step cylinders for concentricity, parallel flat features for parallelism, and so on. The inability of available GBTAs to provide accurate and reliable information about the geometric tolerance of actual parts makes them unsatisfactory for geometric quality characterization. A comparative study of various GBTAs tested on LPBF and the corresponding geometric tolerances is shown in Table 1. The comparison shows that each GBTA has characterized only some of the geometric tolerances, and those characteristics are not quantified in all three principal planar directions. The removal of support structures and the base plate is also not considered during GBTA design or measurements. Moreover, numerical simulation tools were not used to conduct geometric tolerance predictions for the GBTAs to be manufactured.

**Table 1.** Comparison of selected GBTAs according to geometric tolerance characteristics.

The comparative study highlights state-of-the-art GBTA design limitations to characterize critical GD&T, as well as other crucial geometric quality parameters, such as the minimum feature size and fit for assembly. Most of these experimental methods are not conducted on systematically designed benchmarks, lack proper design for the experiments, are based directly on application geometry, and are trial-and-error based. As such, multiple repetitions are required with various parametric changes, some of which do not actually add to any geometric information and eventually add up to the increasing costs. Thus, for very costly metals and large build volumes, repeated benchmark experimentation is not feasible. Significant limitations of the various benchmark artifacts present in the literature are:

The solution is to systematically design GBTAs and conduct only minimal required experimentation for geometric tolerance characterization purposes to obtain useful data for quality characterization of the metal AM process and for prediction purposes. A "featurebased methodology" [29], which links primitive geometric features to GD&T characteristics, and that enables straightforward and systematic design should be used. The AM standard ISO 17296-3 [30] outlines the geometric characteristics that need to be measured, quantified, and controlled to define the geometric properties of an AM part:

The above-mentioned geometric characteristics are further standardized by geometric dimensioning and tolerancing (GD&T). The ISO 1101: Geometrical Product Specifications [23] standard defines GD&T in detail. GD&T characteristics enable the systematic quantification of form, location, and orientation tolerances of the features of a part. The 14 GD&T characteristics in ISO 1101 are explained briefly along with their drawing symbols in Table A1 of Appendix A. The generic guidelines outlined in ISO/ASTM 52902:2019 [31] for test artifact design should be followed carefully. Any new GBTA should quantify all the major GD&T characteristics in the tri-planar directions. Further, to minimize material and manufacturing time, GD&T estimation should be conducted using numerical simulations instead of experimental GBTA fabrication and characterization. Numerical simulation tools are rarely used to estimate GD&T and, as a result, the reliability of these tools to predict GD&T has not yet been assessed. Most research work is focused on deviation simulations, residual stress simulations, microstructure simulations, and topology optimization [32–34]. There is little to no research on the use of macro-scale finite element simulations to predict the geometric tolerances of LPBF parts according to the ISO 1101 standards. Thus, along with experimental datasets, a framework for simulation-based geometric tolerance prediction and analysis is also required.

This article aims to present a new GBTA design with a "feature-based methodology" [29], linking primitive geometric features to the GD&T characteristics and quantifying all the major GD&T characteristics in the tri-planar directions. GBTA will be used, not only to quantify GD&T, but also to assess the reliability of the proposed methodology to quantify GD&T based on numerical simulation tools. The aim is that, in the future, GD&T can be assessed using numerical simulations with the proposed GBTA being used for model calibration and verification. The detailed design process is explained in Section 2. It enables a generic quality characterization of the LPBF process under consideration from a GD&T perspective. The corresponding experimental plan and the measurement procedures are explained in Section 3. Section 4 outlines the numerical simulation process, which is used to extract deviated geometries, with and without a base plate, for a virtual GD&T characterization for comparison with the experimental results. Finally, the experimental and simulation results are presented in Section 5, followed by conclusions in Section 6.

#### **2. Geometric Benchmark Test Artifact Design**

The geometric benchmark test artifact (GBTA) was designed to fulfill two major objectives:

To achieve the first objective, all major GD&T characteristics were quantified on a range of features and sizes on the GBTA. Also, the feature orientation was selected to enable the three principal planar directions for the tri-planar normative quantification of the AM process in consideration. Given the orthotropic, layer-by-layer fabrication of the AM process, and the coupled process physics, it is essential to consider tri-planar repeatability as the mere assumptions of tolerance band applicability across different axes is not valid. The features on GBTA are selected according to the feature-based GBTA design methodology [29], which gives systematic guidelines for selecting features according to the geometric tolerance characterization requirement. The ability to manufacture minimum feature sizes and overhangs was also considered. To fulfill the second objective, i.e., to characterize the effect of removing the base plate, GD&T quantifiers were measured before and after removing the base plate.

Features of the GBTA were selected based on the GD&T requirements for the normative quantification of the geometric quality characteristics of the metal AM process. The bounding box size of the GBTA was decided based on the build volume of the LPBF system on which it had to be manufactured. Since the build volume was 250 × 250 × 300 mm, the size of the GBTA base was kept at 200 × 200 mm and then features were spread on that surface. In the case of LPBF, the raster direction changes with a change in orientation of the part in the AM machine. Therefore, the orientation of the part has a significant effect on the geometric properties of the features. There are two different ways that this variation can be studied and characterized:

The former method is used in this study because, for the latter method, the support structure design for the features in different orientations can vary significantly and, as a result, it would not allow for a robust measurement and comparison of the benchmark artifacts samples. Therefore, the GBTA used in this study was built by printing features in different orientations on a common base. The features to be present on the GBTA base are shown in Figure 1 and are explained below:

**Figure 1.** Nominal GBTA design and corresponding features. (**Left**) Top view and (**Right**) isometric view.

In addition to the GD&T specifications and the other geometric quantifiers, the design needed to take into account the metal AM process constraints. The GBTA features were placed such that the maximum area on the base plate was covered to understand the spatial variations. The effect of variations in terms of feature size on the geometric tolerances is also an important aspect to consider, as the size tolerances significantly influence the design of metal AM in precision applications. The features are shown and explained in greater detail in Figure A1 and Table A2 of Appendix B, showing the numbering of the features on the GBTA, and the relevant geometric tolerances of the features. Complete drawings with size dimensions, location dimensions, and geometric tolerances are also provided in Supplementary Data.

#### **3. Experimental Procedure**

#### *3.1. GBTA Manufacturing*

Three newly designed GBTAs were manufactured using an AM250 LPBF machine (Renishaw PLC, Wotton-under-Edge, Gloucestershire, UK) [35]. The STL file of the GBTA was converted to a sliced file by specifying the process parameters, such as layer height, hatch style, and support structure, using the manufacturer-provided software (Renishaw QuantAM 2018). The process parameters were decided as per previous experience and manufactured using best practices. The process parameters for the manufactured parts were kept constant to investigate the variations in the process and are listed in Table 2.

**Table 2.** Machine parameters and manufacturing parameters for the experimentation.

The build chamber was sealed, and argon gas was introduced to maintain an inert environment for laser-based manufacturing. Throughout the build process, the oxygen level was kept at less than 0.1%. The constant argon gas flow acted to keep the laser lens clean, reduce any oxygen or nitrogen entrapment, and moderate the vapor flow of the processed metal powder. Stainless steel (SS 316L) grade powder from RenishawTM (Wotton-under-Edge, Gloucestershire, UK) was used as a raw material for manufacturing. Upon completion of the build, the part was left in the chamber to cool down to room temperature for approximately 2–3 h and then removed. One of the manufactured samples, as manufactured and attached to the build plate, is shown in Figure 2. To understand the as-built geometric properties of the GBTA, the manufactured samples were assessed without any kind of post-processing.

**Figure 2.** Example of manufactured sample: (**a**) Isometric view of the GBTA, (**b**) top view of the manufactured GBTA showing the "front side" of the LPBF system, gas flow direction, and recoater direction, and (**c**) side view of the manufactured GBTA showing the depicting and the base plate.

#### *3.2. Measurement Procedure*

The features on the manufactured samples were measured for various GD&T characteristics using a Mitutoyo Crysta-Plus M443 (Mitutoyo, Kawasaki, Japan) coordinate measuring machine (CMM). The CMM has a resolution of 0.5 µm. For measurements with the base plate, the GBTA was stationed on the CMM table with fixtures to restrict its movement. The measurements were conducted keeping in mind the tight tolerance zones of the LPBF process under consideration, so reducing measurement variability was a priority. For each characteristic measurement, at least ten data points were taken using the CMM and each measurement was repeated thrice to achieve repeatable readings. For one flatness tolerance zone of a feature, ten data points were collected from the surface to calculate it. The measurement process for this study was divided into four major geometric categories,

i.e., circle, cylinder, line, and surface. The procedure adopted for the measurement for each geometry is listed below [36]:

The schematics of the measurement strategies are shown in Figure 3. The red dots represent the locations where the CMM probe recorded the measurement data.

**Figure 3.** Measurement strategies for different features. The red dots represent the locations where the CMM probe recorded the measurement data.

> The method of least squares was used to define planes and cylinders in the CMM for computing the GD&T tolerance zones. Two coordinate systems were defined to perform the measurements of the GBTA in the CMM. One is the coordinate system of the CMM itself, which defines the motion of the CMM probe in three directions, referred to as the X, Y, and Z directions. The second is the part of the coordinate system that is defined using the GBTA. It is the orthogonal frame of reference that defines the orientation of the features with respect to each other and is used for computing the orientation- and location-based geometric tolerances. The part coordinate system is shown in Figure 2. To eliminate ambiguity, both frames were aligned with each other on the same axes (X–X, Y–Y, and Z–Z) with each other. In the CMM, the surface–line–line method was used to set the part coordinate system [37]. The part coordinate system is depicted in Figure 2. The top surface of the base of the GBTA, on which most of the features are built, is defined as the XY plane. The features categorization for measurements, as per the GD&T, is shown in Table 3. The results are discussed in Section 5 according to the GD&T characteristic.

**Table 3.** Feature categorization for measurements based on GD&T characterization.

For the features with support structures, such as features 1–8, the area covered by the support structures was excluded from the measurements. The supports were kept intact to make sure that the features were hinged on the base plate when the measurements were performed. For the second round of measurements without the base plate, first, the base plate was removed from the GBTA using a bandsaw. The support structures were also removed manually using hand tools. The GBTA, after the removal of the base plate and support structures, is shown in Figure 4. In addition, for fixing the GBTA after the removal of the base plate on the CMM table, special fixtures were used. These fixtures were designed according to the GBTA dimensions and manufactured using polymer 3D printing.

**Figure 4.** GBTA after the removal of the base plate: (**a**) Isometric view and (**b**) side view showing warped features.

#### **4. Numerical Simulation**

A numerical simulation of the GBTA was conducted to understand the effects of temperature and stress fields on the specific planar GD&T characteristics, as well as to assess the reliability of the thermo-elastic finite element model implemented in Netfabb Local Simulation (Autodesk Inc., San Rafael, CA, USA) for GD&T quantification [38]. First, the part and the support structures were imported into Netfabb Local Simulation. Then, a process parameter file (PRM) was generated by conducting a micro-scale simulation using the experimental parameters for the SS 316L material. The process parameters used were the same as those used in the experimental study and are described in Table 2. The simulation parameters are shown in Table 4. The temperature-dependent material properties of SS 316L were based on data from References [39,40]. The PRM file was used to conduct a macroscale simulation of the GBTA part [41,42]. The boundary conditions for the macroscale model were as follows:

The input STL, along with supports, is shown in Figure 5a and the meshing strategy is shown in Figure 5b. After a solution was obtained, the predicted displacement field was used to construct a deviated GBTA part. The deviated STL files were imported to GOM Inspect (GOM GmBH, Braunschweig, Germany) [44] for extracting GD&T quantifiers for a one-to-one comparison with the experimental results. Figure 6 shows the process of constructing fitted features on the deviated STLs from simulations and extracting the GD&T characteristics. The deviated STL file was first converted into a point cloud. Standard geometric shapes were then fitted into the individual features of the deviated point cloud, such as cylinder or plane. GD&T definitions were then used to find the tolerance zones on these fitted features. The GD&T results from the simulations (both with and without base plate) are discussed alongside experimental results in the next section for analytical comparison and physical interpretation.

**Table 4.** Simulation parameters.

**Figure 5.** (**a**) GBTA with supports (in blue) and (**b**) layer-based adaptive coarsening mesh.

**Figure 6.** Extraction of GD&T: (**a**) construction of fitting feature on deviated STL and (**b**) extraction of GD&T characteristics based on the constructed feature.

#### **5. Results and Discussion**

The measurement data from the experiments and the predicted deformed geometry from simulations are used to extract the GD&T characteristics and are presented in the following sections. The data from the samples after removing the base plate are also presented to have a comparative analysis and discussion.

#### *5.1. Form Tolerances*

#### 5.1.1. Straightness

The straightness tolerance zones were computed for the features and categorized according to the feature's orientation to the reference planes—XY, YZ, and ZX. Results for features parallel to reference plane XY are shown with bars labeled "XY" in Figure 7. A similar approach is used for YZ and ZX. For the experimental measurements, the sample space contained 13 features with a feature axis aligning with the XY plane and 8 for each of the YZ and ZX planes. For example, the first XY bar in Figure 7 shows the experimental results for the average tolerance zone for the 13 features aligned to the XY plane with the base plate intact on the GBTA.

Experimental results showed that the straightness tolerance was anisotropic with respect to the reference planes since the results were different in all three principal planar directions, along with variations in standard deviation. The straightness tolerance was higher in the XY planar direction because the measurements were performed on the asbuilt parts without any post-processing; therefore, the hatching effect cannot be ignored on this plane. The effect is increased by chessboard (or checkerboard) style hatching, in which the laser movement is multi-directional and creates a crisscross waviness on the surface. The hatching effect was maximum on surfaces parallel to the XY plane as it is the plane on which the laser moved while the part was built. In general, the straightness tolerance results increased by 15 to 20 µm in all three planar directions after the removal of the base plate, which was anticipated as the residual stresses were released after the base plate removal, which, in turn, increased the deviations. Even with a larger curvature on the base feature of the GBTA after the removal of the base plate, the form tolerances, such as straightness, were less affected, as they were independent of datums. The largest straightness tolerance zone was observed on a thin sheet (feature 9) on the XY plane. It was 158 µm with the base plate and 183 µm without the base plate. The large tolerance zone resulted due to the low thickness value, i.e., 500 µm, of the sheet, which led to larger deformations during the rapid cooling of the part throughout the process.

**Figure 7.** Straightness tolerance results (µm), with and without the base plate.

Figure 7 shows that the predicted straightness tolerances by numerical simulations. The simulation results closely followed the experimental results in the YZ plane; however, there is a dip in simulation results in the XY plane, which could be because the hatching phenomena was not properly captured in simulations. In all three directions, the overall tolerance band is 40 µm lower for both (with and without base plate) results and follows the same pattern. It is hypothesized that the reason for the major variation in the straightness tolerance of the XY plane was that the surface waviness due to hatching was not captured well by the simulations. The difference in results is in a similar range with the generic surface waviness values for LPBF-manufactured SS 316L parts [5]. The difference in the experimental results in the YZ and ZX planes was also not completely captured by the simulations. Since straightness is a form tolerance and the boundary conditions have a maximum effect on the form tolerances, the "uniform heat loss condition" could be one reason for this similarity in simulation results for the YZ and ZX planes. However, the standard deviations for the XY plane are almost the same for the experimental and numerical results, with and without base plate, i.e., only ±1 µm.

#### 5.1.2. Flatness

The sample space for flatness tolerance contained 20 features for the XY plane, 25 features for the YZ plane, and 24 features for the ZX plane. The flatness results for both experiments and simulations are shown in Figure 8, with a comparison of with and without base plate removal. Much like the straightness results, the anisotropy of the experimental results was observed for the flatness tolerance as well. The largest tolerance bands with and without the base plate were observed for the XY plane and the smallest for the YZ plane. Maximum tolerance bands are observed for the XY plane for both with and without base plate conditions. This is because the XY plane was the building plane, which also bore the effect of in-plane shrinkage during the building of the part. Further, the release of the residual stress with the removal of the base plate also affected the XY plane to the highest degree as the base feature of the GBTA was parallel to the XY plane, on which all the features were mounted. Since flatness tolerance was spread over the complete region of the feature, even minor curvatures and warpage due to the removal of the base plate affected the tolerance zone. A large standard deviation in the results for the ZX plane without the base plate was observed, i.e., a standard deviation of 56 µm. This could be due to the recoater direction, which was perpendicular to the ZX plane and affected the layer edges during the building, hence reducing the surface quality of the ZX walls.

Looking at the simulation results in Figure 8, an overall lower range of flatness tolerance is observed as compared to experimental results, except for the YZ plane. For both experiments and simulations, the standard deviation of the results increased with the removal of the base plate. This shows that with the removal of the base plate, some of the surfaces were warped to a greater extent, leading to a rise in standard deviation. For instance, features 4, 5, 18, and 19 show an approximate increase of 20 µm in flatness for the XY plane after the removal of the base plate as they were closer to the edge and were most affected by the warpage of the GBTA base feature. An interesting result to notice is the standard deviation of the ZX plane with the base plate, which reduces from 26 µm to 16 µm. The possible reasoning behind this could be that the features that had larger flatness tolerance bands experienced warpage in such a way after the base plate removal that the flatness values dropped.

**Figure 8.** Flatness tolerance results (µm) with and without the base plate.

#### 5.1.3. Circularity

Measurements were done for different cylindrical and conical features with their axes aligned to their respective reference axial directions—X, Y, and Z. The tolerance zones were computed for these categories of features, and the same are represented in the bar chart in Figure 9. The sample space contained six features each for the X and Y axes directions

and 26 features for the Z-axis direction. The larger number of features in the Z direction varied in terms of size and volume to get a detailed account of the circularity variation in the principal build axis, i.e., the Z-axis.

For the experimental results, the circularity tolerance zone with the base plate intact was around 104 µm for all three axial directions. However, the standard deviation was highest for the Z-axis, i.e., 40 µm, and without the base plate, the standard deviation increased to 52 µm. The large standard deviation observed in Z-axis was due to the removal of the base plate and because a large number of features were characterized in the Z-axis direction. However, since circularity is measured on features of revolutions, the change in the diametric value of the feature was also correlated to circularity tolerance. Trends for circularity vs. diameter in the Z-axis direction are shown in Figure 10. Similar results were observed for experimental circularity tolerance after the removal of the base plate.

For circularity with the base plate, a clear relationship was observed, i.e., the circularity tolerance zone increased with the increase in diameter. It was also depicted by a linear trend line with an R-squared coefficient value of 0.8272. However, for circularity results after removing the base plate, no particular trend was observed. The most reasonable explanation is the uneven distribution of the residual stress led to variations in the deviation. Since with the change in the diameter, the surface area of the feature changed, which led to a change in residual stress and the resulting deviations or the tolerance zone.

**Figure 9.** Circularity (µm) tolerance results, with and without the base plate.

In the simulation results, an overall mean shift of around 40 µm was observed in all directions for results with and without the base plate. The major reason for this mean shift could be the generic under-prediction observed in the deviation simulation and the inability of the simulation to capture meso-level surface variations. Apart from this mean shift and low standard deviation, the simulation results followed a very similar trend to the experimental results, especially for results after removal of the base plate.

Trendline (With base plate) Linear (With base plate)

**Figure 10.** Diameter vs. circularity (experimental).

#### 5.1.4. Cylindricity

Cylindricity tolerance results are shown in Figure 11. The sample space contained six features each for the X and Y direction and 25 features for the Z direction. The diameter of the cylindrical features varied from 0.5 mm to 30 mm. Unlike circularity, the directional results after the removal of the base plate were not in a similar range for the three principal axial directions. The results in axial direction X showed the highest peak in the experimental cylindricity tolerance zone, as well as a standard deviation hike. One reason for this huge variation is the large support structures, which decreased the dimensional fidelity of the features, and along with the residual stress release, another reason could be the cantilever effect due to the nature of the geometric forms of the feature [45]. The effect of the diameter was also studied for the cylindricity tolerance zones, and the results are shown in Figure 12. A linear trend is observed with the cylindricity tolerance zone, which gets wider with an increase in the diameter of the cylindrical feature. Even with a few outliers with small diameter features, both sets of results (with and without the base plate) showed a similar trend. The trendline (with base plate) has an R-squared coefficient value of 0.7734, and for the trendline (without the base plate) the R-squared coefficient value is 0.5607. The results without the base plate were offset with an additional 40–50 µm.

Simulation results for cylindricity with the base plate intact are close to the experimental results. Unlike the large rise of the cylindricity observed in the X-axis direction for the experimental results without the base plate, the simulation does not show any such anomaly. This could be because the surface defects induced by the removal of the support structures are not captured by simulations. Moreover, a rise in cylindricity for the features in the X direction (such as features 2, 3, and 6) is still observed in the simulation results, similar to experimental results, due to the removal of the base plate and the support structures. However, the rise in the cylindricity tolerance with the removal of the base plate is still on the lower side compared to the tolerance increase seen for other form tolerances. This is because cylindricity tolerance is based on the form of the cylindrical feature, but not on the orientation, and with the removal of the base plate, the maximum effect is seen on the orientation as compared to the form of the cylindrical features.

**Figure 11.** Cylindricity (µm) tolerance results, with and without the base plate.

Trendline (Without base plate) Linear (Without base plate) Trendline (Without base plate) Linear (Without base plate)

**Figure 12.** Diameter vs. cylindricity (experimental).

Overall, analysis of the results for the form tolerances shows a general increase in tolerance zones after the GBTA is removed from the base plate. It can directly be linked to the release of the residual stress within the GBTA. Additionally, the increase in standard deviation suggests a similar reason. Apart from this, the process parameters and lasermaterial interaction have a significant effect, which will become clearer when the results are analyzed for a set of process parametric variations. For now, it can be stated that for the selected process parameters and SS 316L material, the form tolerances are generally in the range of 50 to 130 µm with a few exceptions, such as the spike in cylindricity in the X-axis direction after removal of the base plate.

#### *5.2. Orientation Tolerances*

#### 5.2.1. Perpendicularity

The GBTA contained 16 features for the XY plane and 18 features for both the YZ and ZX planes on which perpendicularity is measured. The perpendicularity tolerance zone results are shown in Figure 13. For experimental perpendicularity, the standard deviation increased by a factor of two when the base plate was removed. It increased to 54 µm from 24 µm. The maximum experimental tolerance bands were observed in the XY plane. The simulation results for perpendicularity were very close to those of the experimental results with few exceptions. The major variation consistently observed in the perpendicularity results was that the perpendicularity was minimum in the YZ plane for the experimental results, but for simulation results it was for the ZX plane. In addition, the simulation results in the YZ plane were higher than the experimental results, which was not the usual case in all other tolerance characterizations and simulation results. Since perpendicularity is an orientation tolerance, the flatness of the datum plane affected the tolerance zone, which was seen in both the experiments and the simulations. The variation in the flatness of the datum planes also propagated the tolerance zone to the perpendicularity results. This could be the major reason for the inconsistencies and variations in the results.

**Figure 13.** Perpendicularity (µm) tolerance results, with and without the base plate.

#### 5.2.2. Parallelism

The sample space for parallelism tolerance contained 15 features for the XY plane and 13 features each for the YZ and ZX planes. Parallelism results from the experiments and simulations are shown in Figure 14. The experimental results show the anticipated increase of the tolerance zone after the removal of the base plate. The standard deviation values are different for each planar direction, but the average standard deviation for the three planes remained similar for both with and without base plate results. The results with the base plate for XY and YZ are comparable; however, there is a rise of around 20 µm in the ZX plane. The results without the base plate show the highest average tolerance zone of 215 µm for the YZ plane. In general, the small-sized features showed a larger parallelism tolerance zone with the base plate intact. However, after removing the base plate, the tolerance zone variations in the small features were less than the tolerance zone variations in the large features. The increase in the average tolerance zone after removing the base plate was due mainly to the larger size features as they are susceptible to more warpage and deformations with the release of stress. The simulation results showed a very similar trend for variations between the planes, especially for results with the base plate. The planar variation follows the same trend as the highest ZX plane tolerance zone with a similar standard deviation. However, the zone is 36 µm smaller than the experimental results. The same variations were not observed in the results without the base plate. In addition, the standard deviation for the results without the base plate increase by 14 µm from the experimental to simulation results.

**Figure 14.** Parallelism (µm) tolerance results, with and without the base plate.

#### 5.2.3. Angularity

Angularity measurements were done for two planar features at 40-degree angles to the XY plane and are shown in Figure 15. The experimental angularity increased after removing the base plate. For simulations, the rise in the tolerance zone after removal of the base plate was similar at 3 µm. However, the average tolerance zone was higher by 8 µm, i.e., at 91 µm with the base plate compared to 83 µm for the experimental value.

**Figure 15.** Angularity (µm) tolerance results, with and without the base plate.

#### *5.3. Location Tolerances*

#### 5.3.1. Concentricity

Concentricity tolerance is an important location tolerance for deciding the location of one cylindrical feature with respect to another and plays a major role during assembly operations. The concentricity results are shown in Figure 16. Experimental concentricity results for the base plate intact and without the base plate follow similar trends with a maximum tolerance zone in the Y-axis and a minimum in the Z-axis. It is worth noting that among all the GD&T characteristics discussed above, concentricity had the largest tolerance zones. This is due to the composite nature of concentricity tolerance, as it also depends on the form of the cylinders and the axial shift of the cylindrical features with respect to each other. Even with two features per axis and three measurements per feature, the standard deviation is large. The simulation results also follow suit with average concentricity tolerances being highest along the Y-axis and minimum along the Z-axis with an increase in the tolerance zone after the removal of the base plate. The standard deviations for the simulation results closely followed the experimental results.

**Figure 16.** Concentricity (µm) tolerance results, with and without the base plate.

#### 5.3.2. Position

The GBTA features were positioned evenly on the base to study the position tolerance both for the planar and axial positions and the results are shown in Figure 17. The planar position variation was highest in the YZ plane for all results. The YZ plane is perpendicular to the recoater direction and the recoater movement and powder spread could be the most significant reason for these large tolerance zones. A similar trend was observed in the simulations as the simulation solver also considered the recoater direction and the recoater interference. The standard deviations also got wider for the YZ planar direction results along with a rise in the tolerance zone. For the axial position tolerance, cylindrical features were used across the entire GBTA and the results are shown in Figure 18. The experimental and simulation results are consistent in terms of variations across the axes. In the axial position, the Y-axis tolerance zone was highest for both experimental and simulation results. Simulation results have underpredicted the position tolerance for both planar and axial features. The standard deviations were much higher than any standard deviations observed for other GD&T characteristics, which is because the tolerance values are quite a bit higher than other tolerance characteristics for some of the positional features. The exact reasoning behind this significant shift is still unknown, but the most logical reason is the recoater direction effect and the micro-mirror orientations governing the laser beam.

**Figure 17.** Position tolerance (planar) results (µm), with and without the base plate.

**Figure 18.** Position tolerance (axial) results (µm), with and without the base plate.

#### *5.4. Runout Tolerances*

Circular runout and total runout tolerance results from both experiments and simulations are shown in Figures 19 and 20, respectively. Circular runout, in theory, is a more precise way of measuring circularity as it considers all the points on the periphery of the circular feature that is measured. This is why almost all the circular runout tolerance zones shown in Figure 19 are 50–100 µm more than the respective circularity tolerance results (Figure 9). The average tolerance band for experimental circular runout is 197 µm with the base plate intact. After the removal of the base plate, the average value reached 217 µm. The standard deviation also increased from 99 µm to 109 µm. The maximum runout was observed for the Y-axis features, and the same trend was observed in the simulation results. However, the simulation results for the circular runout showed a downward mean shift of around 10 µm in average tolerance values and the standard deviation was also reduced by at least 30 µm. The average change was mostly due to the drop in the values in the directions of the Y and X axes. For experimental results, due to the removal of the base plate, surface defects come into play, which is not the case in simulations. This effect is not significant in total runout results, as it considers the complete feature, and the effect diminishes compared to the tolerance zone of the complete feature. As shown in Figure 20, the results for total runout are quite a bit higher than the circular runout and even higher than concentricity results except for the Y-axis features.

**Figure 19.** Circular runout (µm) tolerance results, with and without the base plate.

**Figure 20.** Total runout (µm) tolerance results, with and without the base plate.

For total runout, the experimental and simulation results were quite similar for the with and without base plate results, i.e., 214 µm and 224 µm, respectively. The standard deviation increased from 21 µm to 26 µm. Similarly, for the simulation results, the average tolerance values increased from 214 µm to 219 µm and standard deviation values rose from 18 µm to 25 µm. The trend was similar to the trend observed for circular runout and concentricity and the major reasons for this were the support removal and warpage due to residual stresses.

#### **6. Conclusions and Future Scope**

Geometric tolerance characterization is necessary for AM processes due to the inherent residual stresses during the build process that leads to variations in geometric tolerances. A new feature-based design of a geometric benchmark test artifact (GBTA) for LPBF is presented, which can characterize major geometric tolerance characteristics in three principal planar directions. The GBTA was manufactured using stainless steel (SS 316L) using a LPBF process and subjected to geometric tolerance measurements. The measurements were conducted on the GBTA in two stages: first with the base plate intact and then with the base plate removed. The geometric tolerance zones for features aligned with principal planar and axial directions were presented. The variations in the geometric tolerance zones with orientations and sizes were discussed.

Major conclusions from this research work are summarized below:

However, for specific applications, custom features and analysis are required to ascertain if given tolerance specifications are met. Moreover, since the simulation results are not in 100% agreement with the experimental results, this leads to the conclusion that more research is required to make sure that simulations can precisely predict the geometric tolerances for the LPBF process and can take into account the uncertainty of the process. It is hypothesized that the geometric tolerances will be affected by the selection of process parameters. Therefore, a process parameter optimization for specific geometric tolerances is should be performed after a normative benchmark analysis. The authors' future work will be to create a training database for a machine learning algorithm that can predict variations in geometric tolerances with process parameter changes.

**Supplementary Materials:** The following are available online at https://www.mdpi.com/article/10 .3390/ma14133575/s1, A PDF file containing a set of drawings depicting the size dimensions and geometric tolerances of the geometric benchmark test artifact (GBTA).

**Author Contributions:** B.S.R.: conceptualization, methodology, formal analysis, investigation, data curation, validation, writing—original draft; T.S.: formal analysis, investigation, data curation; T.W.: conceptualization, writing—review and editing, funding acquisition; M.S.: validation, writing review and editing, supervision; A.J.Q.: conceptualization, resources, writing—review and editing, analysis, supervision, project administration, funding acquisition. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC), Government of Canada, under strategic partnership grant number 494158: Holistic Innovation in Additive Manufacturing (HI-AM).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The raw/processed data required to reproduce these findings cannot be shared at this time as the data also form part of an ongoing study.

**Acknowledgments:** Authors acknowledge Innotech Alberta for providing the samples for the experimental work.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A. GD&T Characteristics**

**Table A1.** GD&T characteristics, symbols and corresponding descriptions.

**Appendix B. GBTA Features**

**Figure A1.** GBTA drawing depicting all the features along with their numbering.

**Table A2.** GBTA features description as per the numbering.

#### **References**

## *Article* **Methodology for the Quality Control Process of Additive Manufacturing Products Made of Polymer Materials**

**Grzegorz Budzik 1 , Joanna Wo ´zniak 2 , Andrzej Paszkiewicz 3,\* , Łukasz Przeszłowski 1 , Tomasz Dziubek 1 and Mariusz D ˛ebski 1**

**Abstract:** The objective of this publication is to present a quality control methodology for additive manufacturing products made of polymer materials, where the methodology varies depending on the intended use. The models presented in this paper are divided into those that are manufactured for the purpose of visual presentation and those that directly serve the needs of the manufacturing process. The authors also a propose a comprehensive control system for the additive manufacturing process to meet the needs of Industry 4.0. Depending on the intended use of the models, the quality control process is divided into three stages: data control, manufacturing control, and post-processing control. Research models were made from the following materials: RGD 720 photopolymer resin (PolyJet method), ABS M30 thermoplastic (FDM method), E-Partial photopolymer resin (DLP method), PLA thermoplastic (FFF method), and ABS thermoplastic (MEM method). The applied measuring tools had an accuracy of at least an order of magnitude higher than that of the manufacturing technologies used. The results show that the PolyJet method is the most accurate, and the MEM method is the least accurate. The findings also confirm that the selection of materials, 3D printing methods, and measurement methods should always account not only for the specificity and purpose of the model but also for economic aspects, as not all products require high accuracy and durability.

**Keywords:** additive manufacturing; quality control management; process optimization; computing techniques; ICT systems

#### **1. Introduction**

Quality control is one of the key elements of the manufacturing process, regardless of the number of manufactured products. Depending on the stage of the technological process, methods of quality control include different activities with varying scopes, such as ensuring the correctness of designed 3D CAD models; verifying prepared process data; performing visual product control; and controlling dimensional and shape accuracy, surface geometric structure, and material internal structure, particularly in the case of safetycritical elements of vehicles and aircrafts [1–4]. Quality control processes in manufacturing systems have been the subject of numerous publications. Many of them are related to computing techniques, such as contact coordinate computing [5,6], geometric measurement and analysis using optical computing systems [7–10], and geometric accuracy analyses using volume-based methods, including computed tomography [11–13]. Product research that applies CT can produce comprehensive results that reveal the geometric accuracy of

**Citation:** Budzik, G.; Wo ´zniak, J.; Paszkiewicz, A.; Przeszłowski, Ł.; Dziubek, T.; D ˛ebski, M. Methodology for the Quality Control Process of Additive Manufacturing Products Made of Polymer Materials. *Materials* **2021**, *14*, 2202. https://doi.org/ 10.3390/ma14092202

Academic Editor: Mika Salmi

Received: 31 March 2021 Accepted: 23 April 2021 Published: 25 April 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

both the external and internal surfaces of the product, as well as its material structure. However, it is costly and time-consuming and requires specialized equipment. Therefore, CT is reserved for particular product groups, such as aircraft engine blades [14–16]. Quality control in the manufacturing process can be accelerated by applying gauges, but these instruments provide information relevant to a particular product dimension, for instance, the measurement necessary for the mounting or functioning of an element in a machine set [17]. One of the methods for accelerating computing is the application of automated 3D scanning systems, including hardware and software automation, based on robotized measuring sockets that apply rapid scanning procedures. A perfect solution in this case is the application of blue light 3D scanners [18], which enable the quality control of both small-dimension elements and large-dimension artifacts directly on the production line: for instance, these instruments are useful for ensuring the accuracy of vehicle bodywork.

The applied additive manufacturing models and 3D printing method affect several aspects of product quality control and should be considered when developing quality assessment processes. For the quality control of an additive manufacturing model, it is important to consider its place in the technological process. A model that has the properties of an end product will be subjected to quality control before it can be mounted or sold. Visual models are often indispensable at the stages of product conception or the determination of ergonomic characteristics [19,20], but quality control is not usually particularly strict in such cases. For the additive manufacturing of products made of polymer materials, additional mechanical or thermal-chemical processing is not usually applied. Taking this into account, after finishing 3D printing and post-processing, an element has to be subjected to thorough quality control, including both visual control and the analysis of dimensional and shape accuracy [21]. Additive manufacturing technologies that are currently applied to the elements of metal powders (SLS/SLM/DMLS/PBF) can produce semi-finished products that require further mechanical processing and, frequently, thermal-chemical processing. This results in the need for quality control of both the semifinished product and end product of the additive manufacturing process [22]. Therefore, the material of a product, as well as the additive manufacturing method, can be an important basis for determining the appropriate quality control methodology, which is also defined in particular standards [23–31].

Visual prototype assessment plays a significant role in the quality control of additive manufacturing products made of polymer materials. These assessments include the analysis of model structure continuity, correctness in reference to a 3D CAD model, and the colors of elements made of numerous materials that come in various colors or external color textures [32]. Dimensional and shape accuracy must be analyzed with the appropriate tools, devices, and computing systems [18]. In the majority of cases, the dimensional accuracy of products made of polymer materials does not exceed ± 0.05 mm. For this reason, these products may be effectively evaluated with workshop measuring instruments, such as a caliper or micrometer [33]. For products with complex shapes, blue light 3D scanning systems, such as 3D scanners from the GOM Company (Braunschweig, Germany), can be applied to the computing process [34]. These systems enable the relatively rapid quality controls of products in real-time or offline with the application of, for instance, computing results saved in a data cloud. With this approach, 3D scanners can be ideal measuring instruments that simultaneously perform detailed quality control and geometric analyses, which can significantly accelerate the quality control process, particularly in the case of artifacts with complex shapes. The methodology of such an approach to quality control can be developed based on the principles of Industry 4.0, in which available data are used for multi-level and parallel control computing. The application of 3D scanning as a control tool for additive manufacturing products has yet another aspect relevant to data processing: an additive manufacturing product is frequently manufactured on the basis of a 3D CAD/3D STL model, and the STL format is primarily used in the analysis of product dimensional accuracy. In this case, data in STL format from the computing point cloud are compared with data saved in the form of a nominal STL model based on a 3D CAD model [35]. This is

a significant element of the quality control methodology, a major part of which is analyzing and processing numerical data.

In the literature on this subject, the quality control of products fabricated via incremental manufacturing is most often dominated by technical aspects. However, there is still a lack of research and analysis on the management and systematic ordering of processes [12,36].

In line with the above factors, the principal objective of this publication is to present a quality control methodology for additive manufacturing products made of polymer materials, where the methodology varies depending on the intended use. In this paper, the 3D models used for quality control procedures are divided into those that are manufactured for the purpose of visual presentation and those that directly serve the needs of the manufacturing process. For each group, an algorithm of the developed quality control methodology is presented graphically. The authors also propose a comprehensive control system for the additive manufacturing process to meet the needs of Industry 4.0, which applies to both direct control by a qualified specialist and complete automation, as well as remote supervision.