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The second European Conference on the Structural Integrity of Additively Manufactured Materials

ScienceDirect Structural Integrity Procedia 00 (2019) 000–000 Structural Integrity Procedia 00 (2019) 000–000 Available online at www.sciencedirect.com Available online at www.sciencedirect.com ScienceDirect Available online at www.sciencedirect.com ScienceDirect

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Procedia Structural Integrity 34 (2021) 1–5

© 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Esiam organisers Abstract Additive manufacturing (AM) offers the potential to economically fabricate customized parts with complex geometries in a rapid design-to-manufacture cycle. However, the basic understanding of the fracture behavior of AM materials must be substantially improved at all scale levels before the unique features of this rapidly developing technology can be used in critical load bearing applications. This ambitious target can be reached solely via adventurous interdisciplinary research. The virtual event ESIAM21, held from the 5 th to the 8 th of September 2021, constituted the second conference in the ESIAM series, where we continued to gather the strengths of materials science, technological processes, structural integrity assessment methodologies, and advanced design practices to innovate the area of AM materials. The conference featured 16 topics, where fatigue of AM metals, AM in aerospace and lightweight design, characterization of ceramic, polymeric and metallic materials as well as fracture of AM polymers and metals received the highest number of submissions. The conference had 105 participants distributed over 20 countries. Italy, Austria, and Belgium were the most represented countries. The present special issue comprises 38 papers centered around Fracture and Fatigue of AM metals and polymers as well as on simulation and design. The second European Conference on the Structural Integrity of Additively Manufactured Materials Preface Filippo Berto, a* Brecht van Hooreweder, b Francesco Iacoviello, c Jürgen Stampfl, d Luca Susmel, e Jan Torgersen, a† a Department of Mechanical and Industrial Engineering, Norwegian University of Science and Technology, Richard Birkelands Vei 2B, 7034 Trondheim, Norway b Department of Mechanica Engineering, Katholieke Universiteit Leuven, Celestijnenlaan 300, 3001 Leuven, Belgium c Department of Civil and Mechanical Engineering, University of Cassino and Southern Lazio, via G. Di Biasio 43, 03043 Cassino (FR), Italy d Department of Mechanical Engineering, Vienna University of Technology, Getreidemarkt 9 BE, 1060 Vienna, Austria e Department of Civil and Structural Engineering, Sheffield University, Sir Frederick Mappin Building (Broad Lane Building), Mappin Street, Sheffield S1 3JD, United Kingdom Abstract Additive manufacturing (AM) offers the potential to economically fabricate customized parts with complex geometries in a rapid design-to-manufacture cycle. However, the basic understanding of the fracture behavior of AM materials must be substantially improved at all scale levels before the unique features of this rapidly developing technology can be used in critical load bearing applications. This ambitious target can be reached solely via adventurous interdisciplinary research. The virtual event ESIAM21, held from the 5 th to the 8 th of September 2021, constituted the second conference in the ESIAM series, where we continued to gather the strengths of materials science, technological processes, structural integrity assessment methodologies, and advanced design practices to innovate the area of AM materials. The conference featured 16 topics, where fatigue of AM metals, AM in aerospace and lightweight design, characterization of ceramic, polymeric and metallic materials as well as fracture of AM polymers and metals received the highest number of submissions. The conference had 105 participants distributed over 20 countries. Italy, Austria, and Belgium were the most represented countries. The present special issue comprises 38 papers centered around Fracture and Fatigue of AM metals and polymers as well as on simulation and design. The second European Conference on the Structural Integrity of Additively Manufactured Materials Preface Filippo Berto, a* Brecht van Hooreweder, b Francesco Iacoviello, c Jürgen Stampfl, d Luca Susmel, e Jan Torgersen, a† a Department of Mechanical and Industrial Engineering, Norwegian University of Science and Technology, Richard Birkelands Vei 2B, 7034 Trondheim, Norway b Department of Mechanica Engineering, Katholieke Universiteit Leuven, Celestijnenlaan 300, 3001 Leuven, Belgium c Department of Civil and Mechanical Engineering, University of Cassino and Southern Lazio, via G. Di Biasio 43, 03043 Cassino (FR), Italy d Department of Mechanical Engineering, Vienna University of Technology, Getreidemarkt 9 BE, 1060 Vienna, Austria e Department of Civil and Structural Engineering, Sheffield University, Sir Frederick Mappin Building (Broad Lane Building), Mappin Street, Sheffield S1 3JD, United Kingdom

* Filippo Berto. Tel.: +47-485-00-574. E-mail address: filippo.berto@ntnu.no † Jan Torgersen. Tel.: +47-939-66-576. E-mail address: jan.torgersen@ntnu.no * Filippo Berto. Tel.: +47-485-00-574. E-mail address: filippo.berto@ntnu.no † Jan Torgersen. Tel.: +47-939-66-576. E-mail address: jan.torgersen@ntnu.no

2452-3216 © 2020 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Esiam organisers 2452-3216 © 2020 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Esiam organisers

2452-3216 © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Esiam organisers 10.1016/j.prostr.2021.12.001

Author name / Structural Integrity Procedia 00 (2019) 000–000

2 © 2020 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Esiam organisers Keywords: Fracture, Fatigue, Additive Manufacturing, Polymer, Metals, Simulation Filippo Berto et al. / Procedia Structural Integrity 34 (2021) 1–5

1. Introduction Innovative product design is believed to constitute the future revenue in the field of Additive Manufacturing (AM), where the ability to produce complex shaped parts facilitates light-weighting and other performance driven design opportunities. The phenomena leading to the failure of AM materials are extremely complex, not only driven by the intricate geometry but also by inherent process-property relationships. The inherent nature of the AM technology and the strong link between the evolving topology and the evolving mechanical properties is both an opportunity and a dilemma. On the one hand, this unique feature makes it possible to tune a variety of properties beyond just the macroscopic appearance. On the other hand, it leads to unprecedented complexity in manufacturing and resulting properties are difficult to be addressed in standards and recommendations that allow compliant design. Accordingly, the material and key mechanical properties of the fabricated parts are not necessarily generalizable, as they are strongly entangled with the size and geometry of the part, in addition to the specific technology employed. This limits both the theoretical understanding and structural applications and calls for thorough guidelines that are utilizable for practitioners, not necessarily involved in the particularities of the AM processes. To promote the utilization of this technology and to infuse product innovation in sectors such as automotive, biomedicine and aerospace, to facilitate shorter lead times and safer products at lower costs, the European Conference on the Structural Integrity of Additively Manufactured Materials, in short, ESIAM, was founded in 2017 and first held in Trondheim, Norway 2019. Since then, many advances have been made to a large extend by the ESIAM community, allowing us to be better at utilizing the enormous potential of the AM technology for end user applications. ESIAM21 constituted the second conference in the ESIAM series, where we could see several advances in fatigue design and lifetime prediction for AM metals, both on the test geometry as well as on the component level. Moreover, the field of polymer AM was significantly strengthened in 2021, where both aspects on fatigue and fracture were captured in presentations. The event was planned to be held in Vienna, Austria, where Vienna University of Technology would have been kind enough to serve as hosts. However, it was decided in July 2021, two months before the event, that it had to be organized as virtual event due to the impact of the delta variant. We thank our Austrian friends and contributors for their hard work that was unfortunately not made visible due to this decision, which we all regret. However, despite it being held as virtual event, ESIAM21 could motivate 105 participants from 20 countries to present their work. 2. Topics The number of submissions to the 5 most prominent topics represented in the conference can be seen in Figure 1. In total, there were 15 topics to be selected at the conference, which were  Fatigue of AM Metals  AM in Aerospace and Lightweight Design  Characterization of Ceramic, Polymeric and Metallic Materials  Fracture of AM Polymers  Fracture of AM Metals  Computational Property and Process Prediction  Topology Optimization  AM for Biomedical Applications  Post Processing  Non-Destructive Testing and Health Monitoring in AM  Wear and Corrosion of AM Materials

Filippo Berto et al. / Procedia Structural Integrity 34 (2021) 1–5 Author name / Structural Integrity Procedia 00 (2019) 000–000

 AM for Electronics and Photonics  Metamaterials

Figure 1: The 5 most prominent topics of the ESIAM21 conference in terms of the number of abstract submissions per topic

As in 2019, the fatigue of AM metals remained the most prominent topic of the conference with 28 submissions, followed by application-oriented submission towards Aerospace and Lightweight design as well as the characterization of AM materials. This shows the interest and importance of lifetime prediction and extension for AM materials, particularly metals, which will remain one of the most important issues to tackle by the ESIAM community. Yet, the area of AM polymers also experienced a significant increase in representation, where both advances in fatigue and fracture assessment was presented. On the fracture aspect, submissions to AM polymers even exceeded those on metals.

Filippo Berto et al. / Procedia Structural Integrity 34 (2021) 1–5

Author name / Structural Integrity Procedia 00 (2019) 000–000

3. Participating countries The national distribution of participants can be seen in Figure 2. The increased attendance of participants from countries near Vienna, Austria, shows that the event was initially planned as physical event with Vienna as location. People in close proximity had the lowest risk of being restricted in travelling by COVID. Austria is leading the ranks with 21% of the total participants at the conference (22 abstract submissions) and Italy is on the second place (18%, 19 submissions). We are also pleased about the large interest from Belgium (13%, 14 submissions), where excellent contributions originated. The distribution is however heavily biased by the pandemic and does not give any indication of the leading countries in the field. The total number of participants and the spread would be different if the event would have been planned as virtual event to begin with.

Figure 2: Distribution of the contributions to ESIAM21 per country

4. The Special Issue The present special issue contains invited papers from the conference that were subjected to the standard peer review process performed through the Procedia Structural Integrity Editorial board. It contains articles representing the following topics

 Fracture of AM metals (8 submissions)  Fracture of AM polymers (9 submissions)  Fatigue of AM metals (10 submissions)  Fatigue of AM polymers (4 submissions)  Property simulation and design (7 submissions)

The focus of the special issue is fracture mechanics and fatigue, microstructure, and defect analysis of AMmaterials under different loading scenarios as well as the prediction of properties through simulation and the effective design for performance.

Filippo Berto et al. / Procedia Structural Integrity 34 (2021) 1–5 Author name / Structural Integrity Procedia 00 (2019) 000–000

5. Concluding remarks As guest editors, we want to express our acknowledgement to the authors, the reviewers and the editorial office staff that made this issue possible. We hope that the present issue provides a useful state of the art for engineers, academicians and industries involved in the challenges of producing high performance AM materials, from the test geometry level to the final parts. Within 2022, we will determine, where the next conference, ESIAM 23 will be held, on which, we will be very pleased to welcome you again, in person! Sincerely yours,

The editors Filippo Berto, Norwegian University of Science and Technology Brecht Van Hooreweder, University of Leuven Francesco Iacoviello, University of Cassino Jurgen Stampfl, Vienna University of Science and Technology Luca Susmel, Sheffield University Jan Torgersen, Norwegian University of Science and Technology

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Procedia Structural Integrity 34 (2021) 13–19

* Corresponding author. E-mail address: claire.gong@utt.fr

Claire Gong et al. / Procedia Structural Integrity 34 (2021) 13–19 C. Gong et al./ Structural Integrity Procedia 00 (2019) 000 – 000

1. Introduction The many advantages brought by additive manufacturing (AM) open new possibilities in creating complex parts and structures. It is possible to reduce the waste and to optimize the cost-effectiveness [Ngo et al. (2018)]. Thanks to these valuable assets, the popularity of AM leads to develop multiple process. Generally, polymeric and metallic materials are respectively used in material extrusion, such as fused filament fabrication (FFF) and powder bed-based processes. The AM of metals proposes itself multiple technics: laser beam melting (LBM), electron beam melting (EBM) and laser metal deposition (LMD) [Herzog et al. (2016)]. However, the main concern with AM is the anisotropy brought by the temperature gradient from the addition of successive layers [Carroll et al. (2015)]. One of the solution is to treat the material after the printing process. The 17-4PH stainless steel is a material combining high-strength and good corrosion resistance. This precipitate hardening strength material is generally found in nuclear power plants [Bai et al. (2021)] or in marine environments [Murr et al. (2012)]. The treatment or functionalization of material surface can help to improve the mechanical properties like fracture initiation [Olugbade and Lu (2020)]. For example, Surface Mechanical Attrition Treatment (SMAT) gives a nanocristallized surface and enhance hardness and tensile strength [Portella et al. (2020)]. The recent AM machine “Metal X” developed by Markforged Inc. combines the metal injection molding (MIM) with FFF [Metal AM (2017)]. The specimen obtained from this technic will be SMATed and characterized in order to evaluate the mechanical capacities of this process. Moreover, it is challenging to characterize the crack initiation and thus studying the impact of SMAT on the material. The continuous progress made in electron beam lithography (EBL) in creating fine structures, capable of reaching the size of 10 nm [Tseng et al. (2003)], have opened new opportunities in material characterizations at local scale. Previous studies [Allais et al. (1994); Clair et al. (2011); Marae Djouda et al. (2017)] have exploited this progress by applying nanoparticles (NPs) periodic gratings on metallic substrates. During in-situ mechanical test under a scanning electron microscope (SEM), images are recorded, depicting the evolution of the NPs displacements in order to analyze microsctructure feature. In this article, a comparison between two types of metallic single edge notched tension (SENT) samples is presented: a SMATed sample and an as-fabricated (AF) sample, both under an in-situ tensile test in a SEM. Local crack initiation and propagation are observed and compared, exposing the influence of the post-treatment on the material properties. 2. Method 2.1. Specimen fabrication and preparation Based on metal injection molding (MIM), the Atomic Diffusion Additive Manufacturing (ADAM) from Markforged combines the FFF technic with the washing and sintering process. Indeed, a polymerous binder is mixed with the metallic powder into a filament, which is then extruded with heat to print layer by layer the wanted part. To remove the majority of the binder, the as-printed piece is placed into a solvent. Then, the metallic part is sintered near its melting point, to eliminate any remain of the binder and to fuse the powder. Two SENT samples were printed with a Metal X System from Markforged, with a width of 300 μm and a layer of 50 μm for the post-sintered filament. The geometry of the specimens is detailed in Fig. 1(a) and the filament trajectory follows a 45°/-45° orientation, see Fig. 1(b). The notch geometry was conceived in accordance with the ASTM E1820 standard and the different lengths of the sample were designed following the NF EN ISO 6892-1 standard.

Fig. 1 a) Geometry of the sample printed, all dimensions are in mm. b) Trajectory of the nozzle, following a 45°/-45° orientation.

Claire Gong et al. / Procedia Structural Integrity 34 (2021) 13–19 C. Gong et al./ Structural Integrity Procedia 00 (2019) 000 – 000

The samples were then polished thoroughly with a mechanical polishing until obtaining a mirror finish with a diamond paste of 1μm , in order to remove the surface roughness, and thus to easily apply the nanogauges grating. The final thickness of the samples is equal to 1.2 mm in order to guaranty the fracture apparition for both samples during the test, since the maximum load applicable is 5000 N. One of the sample was SMATed after polishing and since this technic is based on plastic deformation induced by spherical shots, many parameters can have an influence on the surface outcome. The chosen parameters correspond to a SMAT High (30 minutes of treatment, 3 mm spherical shots, 20 kHz frequency, generator power at 27%) and are in accordance with the study of Portella et al. (2020). This choice ensures a satisfying modification of the surface structure but also the smoothest roughness among all the SMAT parameters studied. Portella et al. (2020) demonstrated a decrease of 94% of Ra with a SMAT High, from 11 μm to 0.66 μm. In the present study, the average roughness Ra is 0.47 μm for the SMATed sample. The observation of crack initiation and propagation at the surface of the samples is quite challenging since the tip of the notch is 0.2 mm wide and the location of the crack is unknown until its appearance. Even if the method of the nanogauges gratings by EBL was used before, the area of deposition was however limited, in the range of a few micrometers. The EBL process is composed by several steps [Corbierre et al. (2005)]. After preparing the surface of the sample through polishing, a resin is deposited by spin coating and then exposed to a controlled electron beam, in order to have the pattern previously defined by the user. The exposed resin is removed, creating a mask for the gold layer to attach on the raw surface and on the resin. The last step, called lift-off, consists of dissolving the resin with a solvent, only leaving the gold particles on the substrate. Gold is a widespread material in the nanofabrication field for application at room temperature, as it is a conductive material and thus can offer a good image quality with a SEM [Khan et al. (2017)]. It is essential to obtain a large grating in order to cover the tip of the notch and to monitor the crack initiation. The deposition was realized by the Raith e-LiNE Electron Beam Lithography with a Polymethyl methacrylate (PMMA) resin and a new design of gratings was made to follow the crack. Indeed, a 400 x 400 μm² was deposited on the surface, divided into sixteen 100 x 100 μm² s ubgratings, separated by 1 μm basic shapes particles (circles, triangles, squares and semi-circles). This innovative design is a response to a previous difficulty to locate correctly the area of observation when capturing images during the loading. Furthermore, this solution improves the tracking of the crack propagation through the test. In every subgratings, the NPs present a 200 nm diameter, a 50 nm height and a periodic distance of 400 nm between NPs centers. These parameters were chosen following the studies of Marae Djouda et al. (2017), (2018) and (2019). It has the advantage to ensure a good spatial resolution and a good following of the NPs. Both samples show satisfying results regarding to the quality of the deposition, see Fig. 2 a) and b), demonstrating the capacity of EBL to apply a remarkably distinctive grating over an irregular surface. 2.2. Nanogauges gratings

Fig. 2 a) Nanogauges gratings deposited on AF sample. b) Nanogauges gratings deposited on SMATed sample.

2.3. In-situ tensile test

After the deposition, the samples were put into a tensile test machine, inside a FEI Nova NanoSEM 450, see Fig. 3 a). Due to the delay for taking one picture with the SEM, the test has to be briefly stopped regularly, every 125 N,

Claire Gong et al. / Procedia Structural Integrity 34 (2021) 13–19 C. Gong et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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in order to capture alternatively the whole grating, then each 100 x 100 μm² s ubgratings in order to follow the crack evolution and its surrounding until the failure of the sample. Each image has a resolution of 4096 x 3775 pixels, ensuring a good quality of the nanogauges observation. A number is assigned for each subgrating in order to follow their evolutions. The numbers are detailed in Fig. 3 b).

Fig. 3 a) Setup for the in-situ tensile test under the SEM. b) The assigned numbers for identifying each subgratings.

3. Results and discussion 3.1. Macroscopic stress-strain curves

The macroscopic stress-strain curves are presented in Fig. 4 a) for both samples. A magnification is available in Fig. 4 b) order to evidence the serration due the Portevin - Le Chatelier effect (PLC). Since the notch leads to a stress concentration in the middle of the samples, a stress concentration factor K t is assumed to be equal to 3 for the calculation of the stress [Pilkey et al. (2020)]. The macroscopic stress-strain curves in Fig. 4 a) enable to evidence the effect of SMAT regarding to the final elongation. The post-treated sample achieves a fracture elongation of 2.04 % while the AF sample reaches 2.79 %. The strain hardening induced by the multiple impacts of the shots reinforces the surface and thus, the hardness of the sample [Portella et al, 2020]. However, the ultimate tensile strength (UTS) of the SMATed sample should be higher, as it was demonstrated in Portella et al. (2020) and Meng et al. (2018). The maximum stress applied for AF sample is 1919.8 MPa against 1838.8 MPa for the SMATed sample. It is worth noting that the macroscopic curves presented in this study are not from a continuous loading, as the test has to be paused in order to capture the SEM images, the macroscopic behavior of the sample can be influenced and the defects inherent to the fabrication process.

Fig. 4 a) Macroscopic stress-strain curves for both samples. b) Magnification of the area selected in a).

Claire Gong et al. / Procedia Structural Integrity 34 (2021) 13–19 C. Gong et al./ Structural Integrity Procedia 00 (2019) 000 – 000

3.2. SEM images analysis for as-fabricated sample The SEM images showed in Fig. 5 for AF sample are focusing on the subgrating number 3, as it depicts an insight of the crack initiation. Multiple cracks appeared on the image at 993 MPa but not all cracks are at the root of the notch. During the loading, the cracks n°2 and n°3 present a more important growth at 1470 MPa and 1602 MPa, as crack n°4 is slowly closed. At this moment, it can be difficult to predict which crack will be the cause of the sample failure. The presence of the porosity near the notch – framed in a red rectangle in Fig. 5 – , displays a first crack inside at 1470 MPa and a second one at 1602 MPa. At 1638 MPa, a fifth crack appeared but the progression of crack n°2 leads to the failure of the sample. After 1752 MPa, it is evidenced that crack n°2 was greatly influenced by the presence of the nearest porosity. The same observation can be made for crack n°5 at 1752 MPa in Fig. 6, where four visible porosities were circled in red and judging by the crack trajectory, it appears that these defects served as a guide for crack up to the fracture.

Fig. 5 Stress-strain curve and SEM images of the subgrating number 3 for the AF sample during the cracks evolutions.

Fig. 6 SEM image of the subgrating number 3 at 1752 MPa and a magnification of the fifth crack following the multiple porosities.

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3.3. SEM images analysis for SMATed sample For SMATed sample in Fig. 7, the gradual crack initiation is inconspicuous, due to the topography after SMAT, leading to a more difficult examination of the crack evolutions. The plastic deformation, induced by the treatment, could have generated a material aggregation at the end of the notch. These accumulations areas will be called overlaps and can be seen in the red rectangles at 0 MPa in Fig. 7. As opposed to the previous observations with AF sample, the SMATed sample has only two observed cracks, located at material overlaps. Their different location is difficult to introduce in only one subgrating, the choice was made to follow the first line of subgratings, from n°1 to n°4.

Fig. 7 SMATed sample stress-strain curve and SEM images of the cracks evolutions until failure.

The first crack appeared at 1152 MPa and at 1355 MPa for the second crack. The compressive residual stress induced by SMAT hinders the crack initiation as already observed in other studies [Coules et al. (2018)], delaying its apparition. The slow progression for both cracks is replaced by the crack n°2 sudden propagation at 1829 MPa. At the end of the loading, the crack n°2 is the cause of the failure of the sample, as shown in the last SEM image in Fig. 7 at the bottom right. The overlap may create stress concentration at their intersection, increasing the probability to create cracks at the surface. The behavior of the cracks showed during the loading leads to conclude that it may be possible to predict the location of the cracks by observing the overlap of the material near the notch. However, other tests should be conducted in order to completely validate this assumption. 4. Conclusion In this study, an advanced method was used to characterize the crack initiation and propagation from a notch made by ADAM process. The EBL technic allows the deposition of the nanogauges gratings, and the in-situ tensile test under a SEM allows the observation at a local scale. The roughness of the surface did not impact the quality of the deposition, demonstrating the robustness of the procedure. The influence made by SMAT on final elongation and fracture evolution has been evidenced. The unique observations with SEM images bring more details and information on crack initiation and propagation, especially about their location and progression near the notch. This method is a great solution for observing any specific areas for local characterization and in the future, predict possible crack initiation and optimize any parts or structures made by additive manufacturing.

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References

Allais L., Bornert M., Bretheau T., Caldemaison, D., 1994. “ Experimental characterization of the local strain field in a heterogeneous elastoplastic material ” . Acta metallurgica et Materialia 3865 – 3880. Bai, Bing, Rong Hu, Changyi Zhang, Jing Xue, and Wen Yang. “ Effect of Precipitates on Hardening of 17-4PH Martensitic Stainless Steel Serviced at 300 °C in Nuclear Power Plant” . Annals of Nuclear Energy 154, p. 108123. https://doi.org/10.1016/j.anucene.2020.108123. Carroll, Beth E., Todd A. Palmer, and Allison M. Beese. “ Anisotropic Tensile Behavior of Ti – 6Al – 4V Components Fabricated with Directed Energy Dep osition Additive Manufacturing” . Acta Materialia 87, p.309-320. https://doi.org/10.1016/j.actamat.2014.12.054. Clair, A., M. Foucault, O. Calonne, Y. Lacroute, L. Markey, M. Salazar, V. Vignal, and E. Finot. “ Strain Mapping near a Triple Junction in Strained Ni-Based Alloy Using EBSD and Biaxial Nanogauges s” . Acta Materialia 59, no 8, p. 3116-3123. https://doi.org/10.1016/j.actamat.2011.01.051. Corbierre, Muriel K., Jean Beerens, and R. Bruce Lennox. “ Gold Nanoparticles Generated by Electron Beam Lithography of Gold(I)−Thiolate Thin Films” . Chemistry of Materials 17, no 23: 5774-79. https://doi.org/10.1021/cm051085b . Coules, H. E., G. C. M. Horne, K. Abburi Venkata, and T. Pirling. “ The Effects of Residual Stress on Elastic-Plastic Fracture Propagation and Stability” . Materials & Design 143: 131-40. https://doi.org/10.1016/j.matdes.2018.01.064 . Herzog, Dirk, Vanessa Seyda, Eri c Wycisk, and Claus Emmelmann. “ Additive Manufac turing of Metals” . Acta Materialia 117: 371-92. https://doi.org/10.1016/j.actamat.2016.07.019 . Khan, Ibrahim, Khalid Saeed, and Idrees Khan. “ Nanoparticles: Properties, Applications and Toxicities” . Arabian Journal of Chemistry 12, no 7: 908-31. https://doi.org/10.1016/j.arabjc.2017.05.011 . Marae Djouda, Joseph, Yazid Madi, Fabrice Gaslain, Jeremie Beal, Jerome Crepin, Guillaume Montay, Lea Le Joncour, Naman Recho, Benoit Panicaud, and Thomas Maurer. “I nvestigation of Nanoscale Strains at the Austenitic Stainless Steel 316L Surface: Coupling between Nanogauges Gratings and EBSD Techni que during in Situ Tensile Test” . Materials Science and Engineering: A 740-741. 315-35. https://doi.org/10.1016/j.msea.2018.10.059 . Marae Djouda, Joseph, Guillaume Montay, Benoit Panicaud, Jeremie Beal, Yazid Madi, and Thomas Maurer. “ Nanogaugess Gratings for Strain Determination at Nanoscale” . Mechanics of Materials 114, p. 268-78. https://doi.org/10.1016/j.mechmat.2017.08.014. Marae Djouda, Joseph, Benoit Panicaud, Fabrice Gaslain, Jeremie Beal, Yazid Madi, Guillaume Montay, Lea Le Joncour, and al. “ Local Microstructural Characterization of an Aged UR45N Rolled Steel: Application of the Nanogauges Grating Coupled EBSD Technique” . Materials Science and Engineering: A 759: 537-51. https://doi.org/10.1016/j.msea.2019.05.059 . Meng, Xiangchen, Bei Liu, Lan Luo, Yan Ding, Xi-Xin Rao, Bin Hu, Yong Liu, and Jian Lu. “ The Portevin-Le Chatelier Effect of Gradient Nanostructured 5182 Aluminum Alloy by Surface Mechanical Attrition Treatment” . Journal of Materials Science & Technology 34, no 12: 2307-15. https://doi.org/10.1016/j.jmst.2018.06.002. Murr, Lawrence E., Edwin Martinez, Jennifer Hernandez, Shane Collins, Krista N. Amato, Sara M. Gaytan, and Patrick W. Shindo. “ Microstructures and Properties of 17-4 PH Stainless Steel Fabrica ted by Selective Laser Melting” . Journal of Materials Research and Technology 1, no 3: 167-77. https://doi.org/10.1016/S2238-7854(12)70029-7 . Ngo, Tuan D., Alireza Kashani, Gabriele Imbalzano, Kate T. Q. Nguyen, and David Hui. “ Additive Manufacturing (3D Printing): A Review of Materials, Method s, Applications and Challenges” . Composites Part B: Engineering 143: 172-96. https://doi.org/10.1016/j.compositesb.2018.02.012 . Olugbade, Temitope Olumide, and Jian Lu. “ Literature Review on the Mechanical Properties of Materials after Surface Mechanical Attrition Treatment (SMAT)” . Nano Materials Science, Special Issue: Nanostructured metals and alloys, 2, no 1: 3-31. https://doi.org/10.1016/j.nanoms.2020.04.002 . Pilkey, Walter D., Deborah F. Pilkey, and Zhuming Bi. “ Peterson's stress concentration factors ” . John Wiley & Sons, 2020, p. 105. Portella, Q., M. Chemkhi, and D. Retraint. “ Influence of Surface Mechanical Attrition Treatment (SMAT) Post-Treatment on Microstructural, Mechanical and Tensile Behaviour of Additive Manufactured AISI 316L” . Materials Characterization 167, p. 110463. https://doi.org/10.1016/j.matchar.2020.110463 . “THE MAGAZINE FOR THE METAL ADDITIVE MANUFACTURING INDUSTRY ‘METAL AM,’” Inovar Communications Ltd, vol. 3, no. 2, 2017. Tseng, Ampere A., Kuan Chen, Chii D. Chen, and Kung J. Ma. “ Electron Beam Lithography in Nanoscale Fabricatio n: Recent Development” . IEEE Transactions on Electronics Packaging Manufacturing, 2003, 141-49.

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Procedia Structural Integrity 34 (2021) 99–104

* Corresponding author. E-mail address: clarissa.becker@utc.fr

C. Becker et al. / Procedia Structural Integrity 34 (2021) 99–104

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Author name / Structural Integrity Procedia 00 (2019) 000–000

component geometries, as reviewed by van de Werken et al. (2020) and Brenken et al. (2018). A known approach to exploit the anisotropic material properties is load-optimized fiber placement, in which the fiber direction is aligned with the computed stress field, as reviewed by Li et al. (2021). This can be further combined with established geometry optimization methods within a unified design approach (Li et al. (2020)). Both are based on numerical models, which are used to simulate the component behavior. Therefore, the predictive capability of numerical models directly impacts the quality of the derived optimized components and thus influences how well the superior material properties of composites are exploited. A well-known issue with 3D printing is the occurrence of various uncertainties, including variability of physical (geometry) or material properties, which are likely to increase as technology is moving towards non-planar 3D printing (Boroujeni et al. (2021), Tam et al. (2018)). Multiple research works addressed the accuracy of 3D printing as reviewed by Turner and Gold (2015). Nath et al. (2020) reported an optimization method to reduce geometric variability in 3D printed parts. The effect of 3D printing material pretreatment and 3D printing process parameters on mechanical properties was widely studied, for instance, by Li et al. (2016) and Chacón et al. (2019). However, a rarely discussed problem of 3D printing is the high level of variability of mechanical properties. For the determination of mechanical properties by material testing, general test standards for polymers or fiber composites are often used (e.g., ASTM 3039/3039M and ASTM D3039/D3039M), as there is a lack of more specific test standards for 3D printed fiber composites. Hence, most studies only use 3-5 test specimens to determine mechanical properties, which leads to an insufficient quantification of material variability (e.g., in Hao et al. 2018). When the mechanical properties determined by material testing are subsequently used for numerical modeling purposes, the variability of the mechanical properties, if at all considered, cannot be accurately represented. This reduces the quality and robustness of the optimized structures, with respect to 3D printing related uncertainties. In addition to the required improvement of material testing standards, we propose a novel approach to take physical and material variabilities into account, in the numerical modeling. Using this approach, the influence of variability on structural behavior can be investigated. On the one hand, the influence of well-quantified variability on the structural behavior can be studied. On the other hand, a broader study of the influence of various variability levels on the structural behavior can be conducted, when the occurring variability is not sufficiently quantified. In the following sections, we first explain the computationally economical Certain Generalized Stresses Method (CGSM), which is used in our approach. Then, we apply the CGSM to compare the sensitivity of (almost) equally optimum cantilever trusses to the variability of mechanical properties. It is an uncoupled approach as the influence of variability is studied after optimization. Considering variability in numerical modeling improves the predictive capabilities of the numerical model and directly impacts the quality of results obtained by numerical optimization. 2. Numerical modeling of variability The CGSM is based on a stochastic finite element analysis. It makes it possible to consider material and physical variability within the numerical modeling. The method can be used, for instance, to study the variability of displacement, at a point of a structure depending on uncertain material parameters such as the Young’s modulus. Lardeur et al. (2012) first proposed the CGSM formulation for static analysis of bar trusses, which is used here. Fig. 1 shows a flowchart of the CGSM for bar trusses. The CGSM assumes, that the generalized stresses are independent of the uncertain material and physical parameters. As a result, only two finite element analyses (with nominal values of the uncertain parameters) are needed to calculate the strain energy for any number of uncertain parameters. This makes the method fast and computationally inexpensive. The use of the Castigliano’s theorem leads to the CGSM metamodel, by means of which the quantity of interest (e.g., the displacement) can be calculated. With a Monte Carlo Simulation, the quantity of interest is obtained for any values of the uncertain parameters, without the need of additional finite element analyses. Then the mean value and the standard deviation of this quantity of interest can be calculated. The CGSM method can be used for any statistical distribution of uncertain parameters and is suitable for large-sized problems due to the reduced number of finite element analyses.

C. Becker et al. / Procedia Structural Integrity 34 (2021) 99–104 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Fig. 1. Flowchart of the CGSM

3. Design Study: comparison of almost equally optimum designs The influence of uncertain material and physical properties on the behavior of the structure can be studied using the CGSM, which was described in the previous section. In this work we studied the behavior of structures, which are almost equally optimum for a defined optimization problem. This investigation is of interest because optimization of a structure does not automatically lead to a robust structure. The Young’s modulus of the truss members is the selected uncertain parameter, used to study and compare the variability of the maximum displacement of different structures. The truss structures are created using the minimum volume layout optimization tool LayOpt by Fairclough et al. (2020). The optimization objective is to minimize the volume of the structure, with the cross-sectional area of the members as optimization variables. Fig. 2 shows the specification of the design domain, the loads and supports to define the optimization problem. The layout optimization involves the discretization of this design domain by a regular grid of nodes. In the most extreme case, the design contains as many truss members as necessary so that each node is connected to all other nodes. However, such a fully connected ground structure would be far from optimum. Within the layout optimization, a subset of potential members is identified. Fig. 3 shows a fully connected ground structure with different distances between the nodes, leading in a) to 15 and b) to 105 potential members (including overlapping members). Depending on the optimization settings, such as the distance between the nodes, almost equally optimal designs with quite different numbers of truss members and cross-sectional areas can be obtained.

Fig. 2. Design domain and boundary conditions for the cantilever structure with two loads.

Fig. 3. Fully connected ground structure of the design domain. Distance between the nodes in a) is L and in b) 0.5 L.

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Fig. 4. Equally optimum truss designs for the cantilever structure with two loads (the line thickness corresponds to the cross-sectional area).

In our case, we define a threshold of 2%, within which all designs are considered equally optimum. A maximum compression to tension stress ratio of 1:2 is assumed, which roughly corresponds to the mechanical properties of a continuous carbon fiber composite. The domain size is 16x8 and the magnitude of the loads is 1. Fig. 4 shows the obtained optimized structures, in which members under tensile stress are red and members under compression stress are blue. The designs differ significantly in the number of members, which range from 12 to 161. The lowest obtained structure volume is V = 61.958, and the largest volume is V = 63.136. The CGSM is used to investigate the variability of displacement for all designs, at point P where the maximum displacement of the cantilever truss occurs. As described previously, only two finite element analyses are required, in the nominal configuration. Then uncertain displacements are obtained for a large number of trials, using a metamodel. The metamodel is built with the CGSM assumption and the nominal axial member forces extracted from the two finite element analyses. For each trial, the metamodel is used to calculate the displacement, instead of re-studying the entire structure using one finite element analysis each time. This makes the method computationally inexpensive in comparison to the direct Monte Carlo simulation (direct MCS), which requires one finite element analysis per trial. Due to the assumptions of the CGSM, the method is not exact for statically indeterminate structures. However, experience has demonstrated the high quality of the method compared to the direct MCS, even for truss structures with up to 120 bars (see Lardeur et al. (2012)). Still, the use of an error indicator with 10 trials, as proposed by Yin et al. (2018), is helpful to estimate the error level of the obtained results. The error indicator compares the results obtained by the CGSM and direct MCS, using identical values for the uncertain parameters, in both methods. The level of variability is given by the coefficient of variation (c.o.v.), which is the ratio of standard deviation to mean value. For a c.o.v. of 10% of the Young’s modulus, we obtain errors below 0.1% for the mean value and standard deviation of the displacement U at point P. This demonstrates the quality of the results achieved by the CGSM.

C. Becker et al. / Procedia Structural Integrity 34 (2021) 99–104 Author name / Structural Integrity Procedia 00 (2019) 000–000

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The CGSM is valid for low and high variability levels of the input parameters. A Gaussian distribution (± 3σ) of the uncertain parameter is considered. A range of values for the c.o.v. from 5% to 30% is also considered. A c.o.v. of 30% corresponds to an extremely high variability of the Young’s modulus, which then ranges from 10% to 190% of the nominal value. A Young’s modulus value of E = 60GPa is used for a continuous carbon fiber composite in the longitudinal direction. The finite element analyses are performed with Abaqus, one finite element being used for each truss member, as the axial force is considered to be constant in a given member. We further assume that the Young’s modulus of the truss members varies, but stays constant within each member. In general, different cases for the correlation between the uncertain parameters can be considered. The uncertain parameters can be assumed as independent, partially correlated or completely dependent. Here, a fully independent case is considered, leading to a number of uncertain parameters equal to the number of truss members in a given design. For the optimized structures, which we compare here, the number of uncertain parameters ranges from 12 to 161. The variability of the displacement at point P, which depends on the uncertain Young’s modulus, is evaluated using Matlab. Once the uncertain parameters are introduced, the influence on the displacement can be evaluated using the CGSM. Almost no difference is found between the designs for the mean value of the displacement, for all levels of variability. In contrast to the mean value, the standard deviation shows a clear difference between the designs. Fig. 5 shows the variability of displacement c.o.v.(U) for all studied designs. For a c.o.v.(E) of 10%, the variability of the displacement ranges from 1.97% to 3.34%. For an extremely high variability level (c.o.v.(E) = 30%), the variability of displacement ranges from 9.09% to 15.44%. In summary, uncertainty in the material properties (in this case Young’s modulus) affects the variability of the displacement at point P. In all cases, the displacement variability level is smaller than the input parameters variability level. The findings suggest a correlation between the number of cantilever truss members and the variability of the displacement. The lowest value for the output variability is obtained for a truss structure with 161 members, while the four highest values of output variability are obtained for designs with 32 or fewer members. Thus, the designs with more elements are more robust to the variability of the Young’s modulus. This is due to a compensation phenomenon, which often occurs when the number of uncertain parameters increases, which is the case here when the number of members increases.

Fig. 5. Cantilever structure with 2 loads: variability of the maximum displacement for different levels of variability of Young’s modulus.

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