Quantification and analysis of residual stresses in braking pedal produced via laser-powder bed fusion additive manufacturing technology

Citation: Fojtík, F.; Potrok, R.; Hajnyš, J.; Ma, Q.-P.; Kudrna, L.; Mˇesíˇcek, J. Quantification and Analysis of Residual Stresses in Braking Pedal Produced via Laser–Powder Bed Fusion Additive Manufacturing Technology. Materials 2023,16, 5766. https://doi.org/10.3390/ma16175766 Academic Editors: Thomas Niendorf and Chih-Chun Hsieh Received: 3 July 2023 Revised: 11 August 2023 Accepted: 21 August 2023 Published: 23 August 2023 Copyright: © 2023 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/). materials Article Quantification and Analysis of Residual Stresses in Braking Pedal Produced via Laser–Powder Bed Fusion Additive Manufacturing Technology František Fojtík1, Roman Potrok 1, JiˇríHajnyš 2, Quoc-Phu Ma 2, Lukáš Kudrna 3and Jakub Mˇesíˇcek 2,* 1 Department of Applied Mechanics, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 70800 Ostrava, Czech Republic 2Department of Machining, Assembly and Engineering Metrology, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 70800 Ostrava, Czech Republic; [email protected] (J.H.) 3 Department of Machine and Industrial Design, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 70800 Ostrava, Czech Republic *Correspondence: [email protected]; Tel.: +420-596-999-146 Abstract: This study focuses on the experimental verification of residual stress (RS) in a 3D-printed braking pedal using the Powder Bed Fusion (PBF) method with SS316L material. The RS was measured at two representative locations using the hole drilling method (HDM) and the dividing method, which are semi-destructive and destructive methods of RS measurement, respectively. The finite element method (FEM) was used with Ansys Workbench 2020R2 and Simufact Additive 2021 software to determine the magnitude of RS. The results provide insights into how RS is incorporated into metal 3D-printed components and the available tools for predicting RS. This information is essential for experts to improve the accuracy and functionality of SLM parts when post-subtractive or additive manufacturing processes are used. Overall, this study contributes to the advancement of knowledge on the effects of RS on 3D-printed metal components, which can inform future research and development in this area. Keywords: powder bed fusion; SS316L; residual stress; hole drilling method 1. Introduction Metallic 3D printing has shown its capability in producing parts with complex geometries [ 1 – 5 ], revolutionizing the design and optimization of functional metallic components [ 6 – 9 ]. However, 3D-printed metal parts manufactured through Powder Bed Fusion (PBF) encounter two primary challenges: surface texture resulting from layer stacking [10–12] , and residual stress (RS) caused by the rapid heating and cooling process [ 13 , 14 ]. In terms of surface texture, numerous studies have aimed to reduce the roughness of 3D-printed metal parts for both functional and aesthetic purposes, employing mechanical abrasive approaches [ 15 , 16 ]. Moreover, water jet peening has been explored to modify the surface texture, enabling improved cell growth for implant applications [ 17 ]. Additionally, this technology can create a desirable layer of hardened surface with RS on the component [ 18 ]. Recent studies have focused on the surface treatment of 3D-printed metal components, demonstrating that with suitable treatment methods, it is possible to enhance not only the surface texture, but also the RS profile on the component’s surface. Surface improvement is for functional and aesthetic purposes, while changing the RS profile can strengthen the part and prolong the lifetime if utilized appropriately. As opposed to the RS introduced by mechanical work with surface treatment, a major source of RS in 3D-printed metal components is from the thermal process the manufacturing method endures. RS is a significant factor that affects the structural properties and performance of components produced through additive manufacturing [ 19 , 20 ]. These stress Materials 2023,16, 5766. https://doi.org/10.3390/ma16175766 https://www.mdpi.com/journal/materials Materials 2023,16, 5766 2 of 18 states can have a pronounced impact on the mechanical properties and behavior of printed parts, making them an important aspect that needs to be thoroughly investigated and analyzed [ 21 ]. This article focuses on the experimental verification of RS in a 3D-printed braking pedal using the Powder Bed Fusion (PBF) method with SS316L material. Under working conditions, the component is highly stressed and may undergo severe deformation under dynamic loading. Therefore, for the 3D-printed replica, it is necessary to determine the RS distribution for subsequent strength analyses and computational model tuning. The main objective of this study is to measure the RS at two representative locations of a braking pedal using the hole drilling method (HDM) and the slicing method, which are semi-destructive and destructive methods of RS measurement, respectively. The finite element method (FEM) was employed using Ansys Workbench 2020R2 and Simufact Additive 2021 software to determine the magnitude of these stress states. The results of this study provide detailed insights into how RS is incorporated into 3D-printed metal components and the available tools for predicting these stress states. The distribution and magnitude of RS in the 3D-printed braking pedal were determined through experimental measurements and numerical analysis. The experimental measurement of RS was performed using a semidestructive drilling method following the methodology outlined in ASTM E837-20 [ 22 ]. Additionally, a destructive cutting method was employed. The two methods were chosen because of their availability at the authors’ institution and their expertise in performing the measurements for research and industry applications. The numerical simulation of the RS distribution on the braking pedal was performed using the Simufact Additive 2021 computational software and the Ansys Workbench 2020R2 software environment. 2. Materials and Methods The braking pedal was developed based on the basis of a previous study conducted by the team. The Renishaw-AM400 3D printer (Renishaw plc., Great Britain, Wotton-underEdge) used using PBF printing technology, and the printing parameters can be found in [ 23 ]. The manufacturing process and the strength testing procedure were extensively documented in the same paper. In this paper, the authors report a comprehensive analysis of the RS in the printed pedal through physical tests and numerical simulations, which are discussed in detail in the subsequent subsections. 2.1. Residual Stress Analysis in the Braking Pedal Using the Hole Drilling Method HDM is a semi-destructive drilling method, according to the procedure outlined in the ASTM E837-20 standard [ 22 ], requiring the attachment of strain gauges to the surface of the measured component. Therefore, the selection of measurement locations must allow their seamless installation. For the RS analysis, the two locations in Figure 1are chosen. Materials 2023, 16, x FOR PEER REVIEW 3 of 19 Figure 1. Selected locations for measuring residual stress in the braking pedal. Point (1) and (2) are for RS measurements. The locations of the selected points are where the strain gauges can be well positioned. Furthermore, these locations are sufficiently distant from shape changes on the pedal. They are two distinct points in the printing strategy. Point 1 is close to the supports during printing, and these supports, when removed, can influence the redistribution of RS. On the other hand, point 2 is not affected by supports. These locations are suitable for comparing computational methods with experimental results. The RS in the braking pedal was evaluated up to a depth of 1 mm, considering both uniform and non-uniform RS. The measurement and subsequent evaluation of RS in the braking pedal were performed according to the methodology specified in the ASTM E83720 standard. For the experimental measurement of RS using the drilling method, strain gauges CAE-06-062UL-120 [24] were utilized along with the appropriate accessories. The drilling was carried out to the desired depth using equipment compliant with the ASTM E837-20 standard. Prior to attaching the strain gauge to the desired location, the surface roughness of the pedal was carefully modified using fine manual grinding to ensure that the values of the surface RS were not influenced by the surface roughness of the measured component [25]. After attaching the strain gauge, the drilling setup is established. The strain gauges at the selected measurement locations on the braking pedal are shown in Figure 2. Figure 2. Attached strain gauges on the braking pedal at the selected measurement locations. Measurement point (1) and (2) can be observed with drilled holes from HDM. Before each measurement, it is necessary to set the null depth for each strain gauge. The drilling of the hole into the pedal is performed intermittently in specified steps [26– Figure 1. Selected locations for measuring residual stress in the braking pedal. Point (1) and (2) are for RS measurements. Materials 2023,16, 5766 3 of 18 The locations of the selected points are where the strain gauges can be well positioned. Furthermore, these locations are sufficiently distant from shape changes on the pedal. They are two distinct points in the printing strategy. Point 1 is close to the supports during printing, and these supports, when removed, can influence the redistribution of RS. On the other hand, point 2 is not affected by supports. These locations are suitable for comparing computational methods with experimental results. The RS in the braking pedal was evaluated up to a depth of 1 mm, considering both uniform and non-uniform RS. The measurement and subsequent evaluation of RS in the braking pedal were performed according to the methodology specified in the ASTM E83720 standard. For the experimental measurement of RS using the drilling method, strain gauges CAE-06-062UL-120 [ 24 ] were utilized along with the appropriate accessories. The drilling was carried out to the desired depth using equipment compliant with the ASTM E837-20 standard. Prior to attaching the strain gauge to the desired location, the surface roughness of the pedal was carefully modified using fine manual grinding to ensure that the values of the surface RS were not influenced by the surface roughness of the measured component [ 25 ]. After attaching the strain gauge, the drilling setup is established. The strain gauges at the selected measurement locations on the braking pedal are shown in Figure 2. Materials 2023, 16, x FOR PEER REVIEW 3 of 19 Figure 1. Selected locations for measuring residual stress in the braking pedal. Point (1) and (2) are for RS measurements. The locations of the selected points are where the strain gauges can be well positioned. Furthermore, these locations are sufficiently distant from shape changes on the pedal. They are two distinct points in the printing strategy. Point 1 is close to the supports during printing, and these supports, when removed, can influence the redistribution of RS. On the other hand, point 2 is not affected by supports. These locations are suitable for comparing computational methods with experimental results. The RS in the braking pedal was evaluated up to a depth of 1 mm, considering both uniform and non-uniform RS. The measurement and subsequent evaluation of RS in the braking pedal were performed according to the methodology specified in the ASTM E83720 standard. For the experimental measurement of RS using the drilling method, strain gauges CAE-06-062UL-120 [24] were utilized along with the appropriate accessories. The drilling was carried out to the desired depth using equipment compliant with the ASTM E837-20 standard. Prior to attaching the strain gauge to the desired location, the surface roughness of the pedal was carefully modified using fine manual grinding to ensure that the values of the surface RS were not influenced by the surface roughness of the measured component [25]. After attaching the strain gauge, the drilling setup is established. The strain gauges at the selected measurement locations on the braking pedal are shown in Figure 2. Figure 2. Attached strain gauges on the braking pedal at the selected measurement locations. Measurement point (1) and (2) can be observed with drilled holes from HDM. Before each measurement, it is necessary to set the null depth for each strain gauge. The drilling of the hole into the pedal is performed intermittently in specified steps [26– Figure 2. Attached strain gauges on the braking pedal at the selected measurement locations. Measurement point (1) and (2) can be observed with drilled holes from HDM. Before each measurement, it is necessary to set the null depth for each strain gauge. The drilling of the hole into the pedal is performed intermittently in specified steps [ 26 – 29 ]. In each step, the deformation released from each strain gauge is recorded. As part of the analysis, the distribution of uniform and non-uniform stress was assessed according to the relevant ASTM E837-20 standard. 2.2. Residual Stress Analysis in the Braking Pedal Using the Sectioning Method The sectioning method belongs to the destructive RS measurement methods [ 30 ]. The measurement of RS in a specimen is based on dividing the examined body into sections or creating various arranged grooves within it. When the sample is sectioned, RS is released, resulting in the deformation of the cut sections. Depending on the type of RS, the cut sections move apart or come closer to each other. The magnitude of RS is calculated from the resulting deformations of the test sample. The FEM can be employed to determine the magnitude of RS. In this case, the computational software Ansys Workbench 2020R2 was used. This method is commonly used as a quick comparative test for quality control in material production. Furthermore, this method can be utilized for assessing RS in thin-walled tubes [30–33] and other mechanical components. Materials 2023,16, 5766 4 of 18 2.3. Simulation of Residual Stress in the Braking Pedal Using Computational Methods The values and distribution of RS in the printed part can be determined through experimental measurements or, alternatively, by conducting a simulation of 3D printing using computational software. One of the options is to perform a 3D printing simulation within the Ansys Workbench computational program. The goal of the 3D printing simulation is to predict the deformation of the printed part and to estimate the magnitude and distribution of RS. Knowledge of deformation and RS helps prevent the destruction of the printed part during operation, thus reducing prototyping costs. The Ansys Workbench software 2020R2 incorporates the Additive Manufacturing system module, which allows the creation of a simulation workflow for additive manufacturing. The Additive Manufacturing system (AM) module [ 34 ] combines thermal analysis with structural analysis. It includes component orientation, support structure generation, and simulation of the entire printing process. This module needs to be added to the Ansys Workbench software as an extension through the Additive Wizard. Alternatively, the Ansys Additive software can be utilized for 3D printing simulation. This software is suitable for predicting RS and deformation after printing or optimizing the printing process [35]. Simufact Additive 2021 is software developed for simulating metal-based additive manufacturing processes. The program includes a database of commonly used metals, ranging from titanium and stainless steel 316L to aluminum. Users can manually input materials into the program’s database. In addition to the material database, the software also provides a database of 3D printers. It allows the simulation of four different manufacturing processes: Metal PBF, Metal binder jetting, Geometry inspection, and Machining. Simufact Additive 2021 enables the simulation of 3D printing technologies such as Selective Laser Melting, Selective Laser Sintering, and Direct Metal Laser Sintering. At the end of the 3D printing simulation, the deformation of the printed part can be evaluated. Furthermore, the software enables the prediction of the distribution and magnitude of RS introduced into the printed part during the 3D printing simulation [36]. 3. Results 3.1. Resulting Values of Residual Stress in the Braking Pedal Using the Hole Drilling Method HDM allows us to determine uniform or non-uniform stress in the body. 3.1.1. Calculation of Uniform Stress From the measured deformation values, it is possible to determine the magnitude and direction of the principal stresses σ1 and σ2 , as well as the von Mises equivalent stress σVMS for uniformly distributed RS throughout the depth of the drilled hole for both measurement points identified as numbers 1 (74 mm) and 2 (57.5 mm). As aforementioned, these are the suitable locations for installing the strain gauge rosette. Location 1 is on a part of the pedal that is constrained by supports during printing. The dimensions mentioned, 74 mm and 57.5 mm, resulted from the precise position of the installed strain gauges and were transferred to the computational model for evaluation. Furthermore, it is possible to calculate the axial stress based on the orientation of the strain gauge. Table 1presents the values of normal stresses σa (1) corresponding to the normal stress in the direction of strain gauge 1 and σc (3) in strain gauge 3 of the strain gauge rosette (as per the orientation indicated in Figure 2), along with the magnitude of the equivalent stress σVMS for both measurement points. Materials 2023,16, 5766 5 of 18 Table 1. Calculated values of uniform stress at both measurement points. Uniform Stress Drilling Depth (mm) Measurement Point No. 1 (74 mm) Measurement Point No. 2 (57.5 mm) σa(1) (MPa) σC(3) (MPa) σVMS (MPa) σa(1) (MPa) σC(3) (MPa) σVMS (MPa) 0.1 261 749 659 490 420 525 0.2 235 686 604 472 416 522 0.3 209 643 569 440 389 496 0.4 194 618 548 414 365 473 0.5 187 602 534 394 346 451 0.6 183 589 522 375 329 432 0.7 180 577 512 358 315 414 0.8 181 570 505 346 307 402 0.9 182 564 499 336 301 391 1.0 186 560 494 327 298 384 3.1.2. Calculation of Non-Uniform Stress In real bodies, non-uniform stress is commonly present. To determine non-uniform stress, a blind hole is drilled, and its depth is gradually increased in increments of 0.05 mm. Several methods can be used for calculation [ 37 ]. In order to determine the values of nonuniform stress from the released deformations, the procedure specified in ASTM E837-20 was employed. The resulting values for non-uniform RS at both measurement points are presented in Table 2. Table 2. Calculated values of non-uniform stress at both measurement points. Non-Uniform Stress Drilling Depth (mm) Measurement Point No. 1 (74 mm) Measurement Point No. 2 (57.5 mm) σa(1) (MPa) σC(3) (MPa) σVMS (MPa) σa(1) (MPa) σC(3) (MPa) σVMS (MPa) 0.05 290 797 699 491 407 510 0.10 235 693 611 490 436 543 0.15 197 622 550 457 415 523 0.20 170 578 515 416 378 491 0.25 154 551 494 379 341 455 0.30 143 533 479 345 306 419 0.35 137 521 468 316 274 384 0.40 134 510 458 288 246 351 0.45 134 501 449 263 220 321 0.50 136 493 441 239 199 294 0.55 140 485 433 217 181 271 0.60 147 479 425 197 168 250 0.65 155 474 418 179 159 233 0.70 165 470 413 161 152 218 0.75 175 467 408 142 148 206 0.80 187 465 405 123 144 197 0.85 203 467 405 105 143 192 0.90 223 474 410 90 147 190 0.95 250 488 423 79 156 193 1.00 285 509 442 73 169 200 3.2. Residual Stress Analysis in the Braking Pedal Using the Sectioning Method The second experimental method used to measure RS in the braking pedal was the sectioning method. The length of each cut was such that it passed through the selected measurement locations. As a result of RS, the cut halves of the braking pedal experienced Materials 2023,16, 5766 6 of 18 deformation. Figure 3illustrates the deformation of the braking pedal caused by RS after making a cut at measurement location No. 2 (57.5 mm). Materials 2023, 16, x FOR PEER REVIEW 6 of 19 0.65 155 474 418 179 159 233 0.70 165 470 413 161 152 218 0.75 175 467 408 142 148 206 0.80 187 465 405 123 144 197 0.85 203 467 405 105 143 192 0.90 223 474 410 90 147 190 0.95 250 488 423 79 156 193 1.00 285 509 442 73 169 200 3.2. Residual Stress Analysis in the Braking Pedal Using the Sectioning Method The second experimental method used to measure RS in the braking pedal was the sectioning method. The length of each cut was such that it passed through the selected measurement locations. As a result of RS, the cut halves of the braking pedal experienced deformation. Figure 3 illustrates the deformation of the braking pedal caused by RS after making a cut at measurement location No. 2 (57.5 mm). Figure 3. Deformation of the braking pedal after cutting it at measurement location No. 2 (red point). The calculation of RS σa was performed using the FEM in the Ansys Workbench computational program. The calculation of RS was carried out as a reverse problem. Boundary conditions were applied to each half of the pedal arm to achieve the same opening displacement as measured after cutting. The gap between the halves in Ansys had to match the measured gap on the actual braking pedal. Subsequently, the stress σa was evaluated at both measurement locations. The values of stress σa for both measurement locations as a function of the depth from the outer surface are provided in Table 3. Table 3. Values of stress σa(1) at measurement location No. 1 and measurement location No. 2 obtained using the sectioning method in the Ansys Workbench program environment. Depth (mm) Measurement Point No. 1 (74 mm) Measurement Point No. 2 (57.5 mm) σa(1) (MPa) σa(1) (MPa) 0 51 469 0.1 49 447 0.2 46 424 0.3 44 401 0.4 42 378 0.5 40 355 0.6 38 332 0.7 35 309 Figure 3. Deformation of the braking pedal after cutting it at measurement location No. 2 (red point). The calculation of RS σa was performed using the FEM in the Ansys Workbench computational program. The calculation of RS was carried out as a reverse problem. Boundary conditions were applied to each half of the pedal arm to achieve the same opening displacement as measured after cutting. The gap between the halves in Ansys had to match the measured gap on the actual braking pedal. Subsequently, the stress σ a was evaluated at both measurement locations. The values of stress σa for both measurement locations as a function of the depth from the outer surface are provided in Table 3. Table 3. Values of stress σa (1) at measurement location No. 1 and measurement location No. 2 obtained using the sectioning method in the Ansys Workbench program environment. Depth (mm) Measurement Point No. 1 (74 mm) Measurement Point No. 2 (57.5 mm) σa(1) (MPa) σa(1) (MPa) 0 51 469 0.1 49 447 0.2 46 424 0.3 44 401 0.4 42 378 0.5 40 355 0.6 38 332 0.7 35 309 0.8 33 286 0.9 31 263 1.0 29 240 3.3. Analysis of Residual Stress in the Braking Pedal Using the Ansys Workbench 2020R2 Computational Program The Ansys Workbench 2020R2 computational program features a database of commonly used materials for 3D printing. For the production of the braking pedal, recycled powder material of stainless steel 316L was chosen because it is the most common 3D-printed material with a well-established knowledge base regarding the printing and treatment, as reviewed in the Introduction. Therefore, it was necessary to determine the corresponding material parameters of the recycled material before simulating the 3D print- Materials 2023,16, 5766 7 of 18 ing process and adjust them in the Ansys Workbench 2020R2 program. A tensile test was performed on the original and recycled powder material of stainless steel 316L, revealing differences in the values of yield strength and ultimate tensile strength. Tensile tests were performed at room temperature and are shown in Figure 4[23]. Materials 2023, 16, x FOR PEER REVIEW 7 of 19 0.8 33 286 0.9 31 263 1.0 29 240 3.3. Analysis of Residual Stress in the Braking Pedal Using the Ansys Workbench 2020R2 Computational Program The Ansys Workbench 2020R2 computational program features a database of commonly used materials for 3D printing. For the production of the braking pedal, recycled powder material of stainless steel 316L was chosen because it is the most common 3Dprinted material with a well-established knowledge base regarding the printing and treatment, as reviewed in the Introduction. Therefore, it was necessary to determine the corresponding material parameters of the recycled material before simulating the 3D printing process and adjust them in the Ansys Workbench 2020R2 program. A tensile test was performed on the original and recycled powder material of stainless steel 316L, revealing differences in the values of yield strength and ultimate tensile strength. Tensile tests were performed at room temperature and are shown in Figure 4 [23]. Figure 4. Stress–strain curves of the original and recycled powder material of stainless steel 316L during the tensile test [23]. The data were taken from the average of five tests. Tensile samples were vertically distributed in the center of the building platform, where the braking pedal was to be printed following the same setup. The virgin powder was first used for printing, and then it was filtered to eliminate the melted, but unsintered particles. Then, it was mixed with virgin powder in a 1:1 ratio. This is one cycle of recycling. The braking pedal in this study was printed with powder recycled five times. The yield modulus of elasticity (E) was determined from the stress–strain curve of the tensile test for the recycled powder material of stainless steel 316L. Its value was used to construct a bilinear isotropic hardening model. The assembled bilinear hardening model for the recycled powder material of stainless steel 316L at a temperature of 22 °C is shown in Figure 5. 0 100 200 300 400 500 600 700 800 0 0.05 0.1 0.15 0.2 Stress [MPa] Strain [1] RECYCLED VIRGIN Figure 4. Stress–strain curves of the original and recycled powder material of stainless steel 316L during the tensile test [23]. The data were taken from the average of five tests. Tensile samples were vertically distributed in the center of the building platform, where the braking pedal was to be printed following the same setup. The virgin powder was first used for printing, and then it was filtered to eliminate the melted, but unsintered particles. Then, it was mixed with virgin powder in a 1:1 ratio. This is one cycle of recycling. The braking pedal in this study was printed with powder recycled five times. The yield modulus of elasticity (E) was determined from the stress–strain curve of the tensile test for the recycled powder material of stainless steel 316L. Its value was used to construct a bilinear isotropic hardening model. The assembled bilinear hardening model for the recycled powder material of stainless steel 316L at a temperature of 22 ◦C is shown in Figure 5. Materials 2023, 16, x FOR PEER REVIEW 8 of 19 Figure 5. Bilinear isotropic hardening model of the recycled powder material of stainless steel 316L. The analysis of RS distribution in the printed braking pedal was performed using the inherent strain method. In contrast to Simufact Additive 2021 software, the Ansys Workbench 2020R2 program does not require specific values of inherent strain. Instead, a strain scaling factor (SSF) needs to be set [38], which can be understood from Equation (1), where σY represents the yield strength (MPa) and E is the tensile modulus of elasticity (MPa). Additionally, the layer thickness was set to 50 µm. 𝜀 = 𝑆𝑆𝐹 ∙𝜎𝑌 𝐸, (1) Prior to simulating the printing process in the Ansys Workbench 2020R2 software, a calibration procedure is necessary, as detailed in the software manual [38]. The goal of calibration is to ensure that the simulated printing of the component in the software corresponds to the actual printed part. Calibration is performed by physically printing a cantilever specimen. Simultaneously, the same cantilever is simulated using Ansys Workbench 2020R2 software. After printing, the test specimen is cut at a height of 3 mm from the build plate, and the height of the cut end relative to the build plate along the Z-axis is measured, representing the deformation caused by RS (Figure 6). Subsequently, the measured value is compared with the deformation value of the cantilever obtained from the simulation of the test specimen printing. Figure 6. Measurement of the deformation of the test specimen [31]. Ten test cantilevers were printed for calibration, and they were placed at various locations on the build plate. Subsequently, the distance between the end of each cantilever and the build plate was measured for all test specimens (Figure 7). The distance of the deformed ends of the cantilevers in the Z-axis ranged from 10.09 mm to 10.91 mm. 0 100 200 300 400 500 600 0 0.002 0.004 0.006 0.008 0.01 Stress [MPa] Strain [1] Bilinear Isotropic Hardening Material Model Figure 5. Bilinear isotropic hardening model of the recycled powder material of stainless steel 316L. Materials 2023,16, 5766 8 of 18 The analysis of RS distribution in the printed braking pedal was performed using the inherent strain method. In contrast to Simufact Additive 2021 software, the Ansys Workbench 2020R2 program does not require specific values of inherent strain. Instead, a strain scaling factor (SSF) needs to be set [ 38 ], which can be understood from Equation (1), where σY represents the yield strength (MPa) and Eis the tensile modulus of elasticity (MPa). Additionally, the layer thickness was set to 50 µm. ε=SSF · σY E, (1) Prior to simulating the printing process in the Ansys Workbench 2020R2 software, a calibration procedure is necessary, as detailed in the software manual [ 38 ]. The goal of calibration is to ensure that the simulated printing of the component in the software corresponds to the actual printed part. Calibration is performed by physically printing a cantilever specimen. Simultaneously, the same cantilever is simulated using Ansys Workbench 2020R2 software. After printing, the test specimen is cut at a height of 3 mm from the build plate, and the height of the cut end relative to the build plate along the Z-axis is measured, representing the deformation caused by RS (Figure 6). Subsequently, the measured value is compared with the deformation value of the cantilever obtained from the simulation of the test specimen printing. Materials 2023, 16, x FOR PEER REVIEW 8 of 19 Figure 5. Bilinear isotropic hardening model of the recycled powder material of stainless steel 316L. The analysis of RS distribution in the printed braking pedal was performed using the inherent strain method. In contrast to Simufact Additive 2021 software, the Ansys Workbench 2020R2 program does not require specific values of inherent strain. Instead, a strain scaling factor (SSF) needs to be set [38], which can be understood from Equation (1), where σY represents the yield strength (MPa) and E is the tensile modulus of elasticity (MPa). Additionally, the layer thickness was set to 50 µm. 𝜀 = 𝑆𝑆𝐹 ∙𝜎𝑌 𝐸, (1) Prior to simulating the printing process in the Ansys Workbench 2020R2 software, a calibration procedure is necessary, as detailed in the software manual [38]. The goal of calibration is to ensure that the simulated printing of the component in the software corresponds to the actual printed part. Calibration is performed by physically printing a cantilever specimen. Simultaneously, the same cantilever is simulated using Ansys Workbench 2020R2 software. After printing, the test specimen is cut at a height of 3 mm from the build plate, and the height of the cut end relative to the build plate along the Z-axis is measured, representing the deformation caused by RS (Figure 6). Subsequently, the measured value is compared with the deformation value of the cantilever obtained from the simulation of the test specimen printing. Figure 6. Measurement of the deformation of the test specimen [31]. Ten test cantilevers were printed for calibration, and they were placed at various locations on the build plate. Subsequently, the distance between the end of each cantilever and the build plate was measured for all test specimens (Figure 7). The distance of the deformed ends of the cantilevers in the Z-axis ranged from 10.09 mm to 10.91 mm. 0 100 200 300 400 500 600 0 0.002 0.004 0.006 0.008 0.01 Stress [MPa] Strain [1] Bilinear Isotropic Hardening Material Model Figure 6. Measurement of the deformation of the test specimen [31]. Ten test cantilevers were printed for calibration, and they were placed at various locations on the build plate. Subsequently, the distance between the end of each cantilever and the build plate was measured for all test specimens (Figure 7). The distance of the deformed ends of the cantilevers in the Z-axis ranged from 10.09 mm to 10.91 mm. Materials 2023, 16, x FOR PEER REVIEW 9 of 19 Figure 7. Placement of the test specimens on the build plate and their deformations. In Ansys Workbench 2020R2, a computational model of the cantilever was created, with the same dimensions as the physically printed cantilever. Subsequently, a 3D printing simulation was conducted using inherent strain. Calibration was achieved with multiple cantilevers distributed at different positions on the building platform to record the average inherent strain. In addition, the tensile specimens and the braking pedal were printed and loaded in the same direction, ensuring that the strength analysis was valid. After cutting the cantilever from the build plate, the deformation of the printed cantilever was compared to the simulated deformation (Figure 8). The goal was to determine the optimal value of the strain scaling factor (SSF) parameter. If the deformations do not match, new values of the SSF parameter need to be set [38]. Due to the wide range of actual measured deformations, finding the exact value of the SSF parameter was computationally demanding. This is because for the calibration of the cantilevers to obtain inherent strains, we had to prescribe ten values of z deformation in correspondence with ten cantilevers at the exact position on the build plate, as in reality. Then, the software will have to find one set of inherent strains to satisfy the deformation of ten such values. Figure 8. Deformation of the cantilever end after the 3D printing simulation in Ansys Workbench. Point a and point b distort in Oz direction 1.3446 mm and 1.4906 mm, respectively. For the 3D printing simulation of the braking pedal, the value of SSF was set for anisotropic material. The SSF parameters used for each direction are listed in Table 4. Figure 7. Placement of the test specimens on the build plate and their deformations. Materials 2023,16, 5766 9 of 18 In Ansys Workbench 2020R2, a computational model of the cantilever was created, with the same dimensions as the physically printed cantilever. Subsequently, a 3D printing simulation was conducted using inherent strain. Calibration was achieved with multiple cantilevers distributed at different positions on the building platform to record the average inherent strain. In addition, the tensile specimens and the braking pedal were printed and loaded in the same direction, ensuring that the strength analysis was valid. After cutting the cantilever from the build plate, the deformation of the printed cantilever was compared to the simulated deformation (Figure 8). The goal was to determine the optimal value of the strain scaling factor (SSF) parameter. If the deformations do not match, new values of the SSF parameter need to be set [ 38 ]. Due to the wide range of actual measured deformations, finding the exact value of the SSF parameter was computationally demanding. This is because for the calibration of the cantilevers to obtain inherent strains, we had to prescribe ten values of z deformation in correspondence with ten cantilevers at the exact position on the build plate, as in reality. Then, the software will have to find one set of inherent strains to satisfy the deformation of ten such values. Materials 2023, 16, x FOR PEER REVIEW 9 of 19 Figure 7. Placement of the test specimens on the build plate and their deformations. In Ansys Workbench 2020R2, a computational model of the cantilever was created, with the same dimensions as the physically printed cantilever. Subsequently, a 3D printing simulation was conducted using inherent strain. Calibration was achieved with multiple cantilevers distributed at different positions on the building platform to record the average inherent strain. In addition, the tensile specimens and the braking pedal were printed and loaded in the same direction, ensuring that the strength analysis was valid. After cutting the cantilever from the build plate, the deformation of the printed cantilever was compared to the simulated deformation (Figure 8). The goal was to determine the optimal value of the strain scaling factor (SSF) parameter. If the deformations do not match, new values of the SSF parameter need to be set [38]. Due to the wide range of actual measured deformations, finding the exact value of the SSF parameter was computationally demanding. This is because for the calibration of the cantilevers to obtain inherent strains, we had to prescribe ten values of z deformation in correspondence with ten cantilevers at the exact position on the build plate, as in reality. Then, the software will have to find one set of inherent strains to satisfy the deformation of ten such values. Figure 8. Deformation of the cantilever end after the 3D printing simulation in Ansys Workbench. Point a and point b distort in Oz direction 1.3446 mm and 1.4906 mm, respectively. For the 3D printing simulation of the braking pedal, the value of SSF was set for anisotropic material. The SSF parameters used for each direction are listed in Table 4. Figure 8. Deformation of the cantilever end after the 3D printing simulation in Ansys Workbench. Point a and point b distort in Oz direction 1.3446 mm and 1.4906 mm, respectively. For the 3D printing simulation of the braking pedal, the value of SSF was set for anisotropic material. The SSF parameters used for each direction are listed in Table 4. Table 4. Values of the SSF parameter for the 3D printing simulation of the braking pedal. SSFXSSFYSSFZ 0.98 0.98 0.997 To simulate the 3D printing of the braking pedal, it is necessary to create a corresponding computational model represented by voxels. The resulting computational model has the parameters listed in Table 5, and a visual representation of the computational model can be seen in Figure 9. Table 5. Parameters of the computational model of the braking pedal. Number of Voxels Number of Nodes 152,057 178,462 Materials 2023,16, 5766 16 of 18 from the numerical solution. The gradient of non-uniform equivalent stress is higher up to a depth of 0.8 mm from the surface of the braking pedal. From a distance of 0.8 mm to a depth of 1 mm, the value of non-uniform equivalent RS remains nearly constant. On the other hand, it can be observed that the gradient of uniform equivalent stress and the gradients of the equivalent stress from the Simufact Additive and Ansys Workbench programs are very similar (the slopes of the lines are very close). In the case of these stresses, there is a gradual reduction in the mutual differences, and the smallest difference of 33.53 MPa was achieved at a depth of 1 mm. Figure 15a,b show the profiles of normal stresses in the direction of strain gauge 1 at measurement point 1 (74 mm) and measurement point 2 (57.5 mm), respectively. The results obtained from the HDM for both the uniformly and non-uniformly distributed RS up to a depth of 1 mm from the outer surface are presented. Additionally, the results of normal stress obtained in this direction and the measurement point using the sectioning method are shown. Furthermore, the results of the normal RS obtained by simulation in Ansys Workbench and Simufact Additive 2021 are included. For measurement point 1 in direction 1, the stress results obtained from the sectioning method correlate well with the computed stress profile in Ansys Workbench. The results of the normal stress obtained in Simufact Additive 2021 exhibit a non-standard profile, which does not correlate with the resulting reduced stress indicated in Figure 14a. Higher RS values were obtained from the drilling method. Compared to the reduced stress values according to von Mises theory, which are comparable to the calculations, this indicates a different stress redistribution in the measured region. From a quantification perspective, the sectioning method is in better agreement with computational methods in this region. However, it should be noted that the sectioning method provides average stress values derived from the deformation of half the thickness of the crankshaft at the respective location, whereas the HDM obtains values corresponding to the specific measured depths for both methods of RS evaluation. For measurement point 2 in direction 1, both experimental methods show relatively good agreement compared to the results obtained from both computational methods. Figure 15c,d present the results of normal RS in the direction of strain gauge 3. The results obtained from the HDM and the results obtained from numerical simulations in both software programs are shown. The sectioning method was not used in this direction. For measurement point 1, there is a very good agreement between the experimentally determined stress and the numerical simulations from a depth of 0.2 mm onward. The normal stresses obtained from HDM on the surface up to a depth of 0.2 mm are higher, which corresponds to the trend observed in 3D printing on the surface with the SLM method. For measurement point 2 in direction 3, the values of residual normal stresses obtained from the HDM are greater than the stresses obtained from numerical simulation. This difference is likely due to stress redistribution, taking into account the results of reduced stresses according to von Mises theory, as shown in Figure 14b. The results of RS obtained through measurements and computational modeling in the form of VMS stress, as shown in Figure 14, exhibit relatively good agreement. It is essential to consider that the computational models were set up based on bridge calibration. When this calibration setup is applied to a real component, it shows a reasonably good match, despite the shape differences between the calibration bridges and the actual component, the pedal. 4. Conclusions From the results, it can be concluded that at the measurement point farther from the build plate or supports during printing, there is a better correlation between the calculated and experimentally determined RS profiles. This could be because of different heat dissipating efficiency at the measured points. It should be noted that the material model and the printing parameters are based on the deformation methodology of cantilevers, which are significantly smaller in size and volume compared to the printed pedal. The calibration results shown in Figure 7indicate that the deformation of individual cantilevers varies depending on their position on the measurement substrate, indicating the influence of Materials 2023,16, 5766 17 of 18 printing parameters, powder flow in the printing chamber, and other factors. However, in the settings of the individual programs, only the average value of this parameter is taken into account, which affects the results of both numerical simulations. The information obtained in this study is essential for experts striving to improve the accuracy and functionality of components produced through PBF when post-subtractive or additive manufacturing processes are employed. Overall, this study contributes to advancing knowledge regarding the effects of RS on 3D-printed metal components, which can inform future research and development in this field. Given the increasing interest in additive manufacturing and the need to enhance the properties of printed components, it is crucial to gain a comprehensive understanding of the influence of RS on these complex structural arrangements. We hope that the findings of this study will contribute to improving evaluation techniques and optimizing 3D-printed metal components, thereby fostering further development in this promising field. Author Contributions: Conceptualization, J.M., F.F. and L.K.; methodology, J.M., Q.-P.M. and F.F.; software, R.P.; validation, F.F., R.P. and J.M.; formal analysis, J.M. and J.H.; investigation, L.K., J.H. and J.M.; resources, J.M.; data curation, F.F., J.M. and J.H.; writing—original draft preparation, R.P., F.F., Q.-P.M., J.M. and J.H.; writing—review and editing, Q.-P.M., J.M. and J.H.; visualization, R.P.; supervision, J.M.; project administration, J.M. and F.F.; funding acquisition, J.H. All authors have read and agreed to the published version of the manuscript. Funding: This paper was completed in association with the project “Innovative and additive manufacturing technology—new technological solutions for 3D printing of metals and composite materials”, reg. no. CZ.02.1.01/0.0/0.0/17_049/0008407, financed by the Structural Funds of the European Union. The study was conducted in connection with the project “Students Grant Competition” SP2023/027 and SP2023/088, financed by the Ministry of Education, Youth, and Sports and the Faculty of Mechanical Engineering VŠB-TUO. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data available on request. Acknowledgments: The authors would like to thank MSC. Software s.r.o., a Hexagon company, for support in the analysis of the printing process study. Conflicts of Interest: The authors declare no conflict of interest. References 1. Janek, M.; Žilinská, V.; Kovár, V.; Hajdúchová, Z.; Tomanová, K.; Peciar, P.; Veteška, P.; Gabošová, T.; Fialka, R.; Feranc, J.; et al. Mechanical testing of hydroxyapatite filaments for tissue scaffolds preparation by fused deposition of Ceramics. J. Eur. Ceram. Soc. 2020,40, 4932–4938. [CrossRef] 2. 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