PSI - Issue 51

ScienceDirect Structural Integrity Procedia 00 (2021) 000–000 Structural Integrity Procedia 00 (2021) 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 51 (2023) 1–2

© 2023 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 ICSID 2022 Organizers © 2023 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 ICSID 2022 Organizers Keywords: Preface; fatigue; fracture; structural integrity 1. Preface The 6 th International Conference on Structural Integrity and Durability, ICSID 2022, was organized by the Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, and the Croatian National Group of the European Structural Integrity Society (ESIS), in Dubrovnik in Croatia from September 20 to 23, 2022. Due to the Covid-19 pandemic situation, ICSID 2022 was organized as the Hybrid Conference i.e, a combination of on-site and online participation to provide safety and convenience for participants. The Conference was held in the Centre for Advanced Academic Studies (CAAS) of the University of Zagreb, in the city of Dubrovnik. The magnificent old building of CAAS is situated in the center of Dubrovnik on the Croatian Adriatic Coast, in the vicinity of the most prominent historical places of the Old Town (http://icsid2022.fsb.hr/). Online presentations were held © 2023 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 ICSID 2022 Organizers Keywords: Preface; fatigue; fracture; structural integrity 1. Preface The 6 th International Conference on Structural Integrity and Durability, ICSID 2022, was organized by the Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, and the Croatian National Group of the European Structural Integrity Society (ESIS), in Dubrovnik in Croatia from September 20 to 23, 2022. Due to the Covid-19 pandemic situation, ICSID 2022 was organized as the Hybrid Conference i.e, a combination of on-site and online participation to provide safety and convenience for participants. The Conference was held in the Centre for Advanced Academic Studies (CAAS) of the University of Zagreb, in the city of Dubrovnik. The magnificent old building of CAAS is situated in the center of Dubrovnik on the Croatian Adriatic Coast, in the vicinity of the most prominent historical places of the Old Town (http://icsid2022.fsb.hr/). Online presentations were held 6th International Conference on Structural Integrity and Durability (ICSID 2022) Preface Željko Božić a, *, Siegfried Schmauder b , Katarina Monkova c , George Pantazopoulos d , Sergio Baragetti e , Francesco Iacoviello f a University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Ivana Lu č i ć a 5, 10000 Zagreb, Croatia b University of Stuttgart, Institute for Materials Testing, Materials Science and Strength of Materials (IMWF), Pfaffenwaldring 32, Stuttgart, Germany c Technical University of Kosice, Faculty of Manufacturing Technologies, Sturova 31, 080 01 Presov, Slovakia d ELKEME - Hellenic Research Centre for Metals S.A., Athens – Lamia National Road , 32011 Oinofyta Viotias, Greece e University of Bergamo, Department of Management, Information and Production Engineering, Viale Marconi 5, Dalmine 24044, Italy f Università di Cassino e del Lazio Meridionale, via G. DI Biasio 43, 03043, Cassino (FR), Italy 6th International Conference on Structural Integrity and Durability (ICSID 2022) Preface Željko Božić a, *, Siegfried Schmauder b , Katarina Monkova c , George Pantazopoulos d , Sergio Baragetti e , Francesco Iacoviello f a University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Ivana Lu č i ć a 5, 10000 Zagreb, Croatia b University of Stuttgart, Institute for Materials Testing, Materials Science and Strength of Materials (IMWF), Pfaffenwaldring 32, Stuttgart, Germany c Technical University of Kosice, Faculty of Manufacturing Technologies, Sturova 31, 080 01 Presov, Slovakia d ELKEME - Hellenic Research Centre for Metals S.A., Athens – Lamia National Road , 32011 Oinofyta Viotias, Greece e University of Bergamo, Department of Management, Information and Production Engineering, Viale Marconi 5, Dalmine 24044, Italy f Università di Cassino e del Lazio Meridionale, via G. DI Biasio 43, 03043, Cassino (FR), Italy

* Corresponding author. Tel.: +385 1 6168 536; fax: +385 1 6156 940. E-mail address: zeljko.bozic@fsb.hr * Corresponding author. Tel.: +385 1 6168 536; fax: +385 1 6156 940. E-mail address: zeljko.bozic@fsb.hr

2452-3216 © 2023 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 ICSID 2022 Organizers 2452-3216 © 2023 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 ICSID 2022 Organizers

2452-3216 © 2023 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 ICSID 2022 Organizers 10.1016/j.prostr.2023.10.058

Željko Božić et al. / Procedia Structural Integrity 51 (2023) 1 – 2

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using a commercial meeting platform. In total 62 on-site and online presentations were given, including five plenary lectures. The objective of the ICSID 2022 Conference was to bring together scientists, researchers, and engineers from around the world to discuss how to analyze, predict and assess the fatigue and fracture of structural materials and components. The Conference provided a forum for discussion of contemporary and future trends in experimental, analytical, and numerical fracture mechanics, fatigue, failure analysis, structural integrity assessment, and other important issues in the field. A wide range of topics was covered such as: Failure investigation and analysis; Multiscale materials modeling; Mixed-mode and multiaxial fatigue and fracture; Durability and life extension of structures and components; Structural integrity of 3D-printed structures; Models, criteria and methods in fracture mechanics; Finite element methods and their applications; Effect of residual stresses; Fatigue and fracture of weldments, welded components, joints and adhesives; Reliability and life extension of components; Corrosion, environmentally enhanced degradation and cracking, corrosion fatigue; Fracture and damage of cementitious materials; Fatigue and fracture of polymers, elastomers, composites and biomaterials; and others. Prior to the ICSID 2022 Conference a two-day Summer School with the topic “Fatigue and fracture modelling and analysis” was organized for graduate students, researchers, and engineers from industry. Those participants who came to Dubrovnik, besides the excellent technical program, had the opportunity to enjoy their stay in Dubrovnik, one of the most famous Mediterranean cities, world celebrated symbol of historical heritage and beauty, which has found its place in the UNESCO World Heritage List. As the Guest Editors of this Conference Proceedings, we wish to thank all authors for their contributions. Guest Editors of the Procedia Structural Integrity ICSID 2022 Conference Proceedings: Željko Božić, University of Zagreb, Croatia Siegfried Schmauder, University of Stuttgart, Germany Katarina Monkova, Technical University in Kosice, Slovakia George Pantazopoulos, ELKEME - Hellenic Research Centre for Metals S.A., Athens, Greece Sergio Baragetti, University of Bergamo, Italy Francesco Iacoviello, Università di Cassino e del Lazio Meridionale – DICeM, Italy

Available online at www.sciencedirect.com Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2022) 000–000 Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2022) 000–000

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ScienceDirect

Procedia Structural Integrity 51 (2023) 51–56

© 2023 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 ICSID 2022 Organizers Abstract Pitting corrosion is a common cause of concern for steel structures in an offshore environment. As geometric stress concentrating features, corrosion pits can potentially act as fatigue crack initiation sites. The severity of a pit can be analyzed based on its geometric characteristics, and the loading and boundary conditions of the component. In this study, the stress distribution in and around a semi-ellipsoidal pit in a plate subjected to (remote) uniaxial tension is investigated using finite element analysis. The investigated characteristics include the width, length and depth of semi ellipsoidal pits ( 2 , 2 and , respectively); the remote load acts parallel to the pit length. A parametric study was conducted with a focus on normalized parameters , and , and their effect on the stress concentration factor (SCF). The considered value ranges for , and were 0.1 to 1, 0.01 to 0.2 and 0.125 to 1.5, respectively. Within the range of values for each parameter, SCF did not vary significantly with changes in and increases for increasing and values. The maximum value of SCF is obtained for the sharpest pit with a circular mouth ( = 1.5 and = 1). © 2023 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 ICSID 2022 Organizers Keywords: Stress concentration; pitting corrosion; linear elastic study; finite element analysis 6th International Conference on Structural Integrity and Durability (ICSID 2022) A numerical study on tensile stress concentration in semi-ellipsoidal corrosion pits F. Mehri Sofiani a, * , S. Chaudhuri b , S. A. Elahi a , K. Hectors a , W. De Waele a a Ghent University, Department of Electromechanical, Systems and Metal Engineering, Soete Laboratory, Technologiepark-Zwijnaarde 46, 9052, Zwijnaarde, Belgium b Bundesanstalt für Materialforschung und -prüfung (BAM), Berlin, Germany Abstract Pitting corrosion is a common cause of concern for steel structures in an offshore environment. As geometric stress concentrating features, corrosion pits can potentially act as fatigue crack initiation sites. The severity of a pit can be analyzed based on its geometric characteristics, and the loading and boundary conditions of the component. In this study, the stress distribution in and around a semi-ellipsoidal pit in a plate subjected to (remote) uniaxial tension is investigated using finite element analysis. The investigated characteristics include the width, length and depth of semi ellipsoidal pits ( 2 , 2 and , respectively); the remote load acts parallel to the pit length. A parametric study was conducted with a focus on normalized parameters , and , and their effect on the stress concentration factor (SCF). The considered value ranges for , and were 0.1 to 1, 0.01 to 0.2 and 0.125 to 1.5, respectively. Within the range of values for each parameter, SCF did not vary significantly with changes in and increases for increasing and values. The maximum value of SCF is obtained for the sharpest pit with a circular mouth ( = 1.5 and = 1). © 2023 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 ICSID 2022 Organizers Keywords: Stress concentration; pitting corrosion; linear elastic study; finite element analysis 6th International Conference on Structural Integrity and Durability (ICSID 2022) A numerical study on tensile stress concentration in semi-ellipsoidal corrosion pits F. Mehri Sofiani a, * , S. Chaudhuri b , S. A. Elahi a , K. Hectors a , W. De Waele a a Ghent University, Department of Electromechanical, Systems and Metal Engineering, Soete Laboratory, Technologiepark-Zwijnaarde 46, 9052, Zwijnaarde, Belgium b Bundesanstalt für Materialforschung und -prüfung (BAM), Berlin, Germany

* Corresponding author. Tel.: +32-9-331-0489 E-mail address: farid.mehrisofiani@ugent.be * Corresponding author. Tel.: +32-9-331-0489 E-mail address: farid.mehrisofiani@ugent.be

2452-3216 © 2023 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 ICSID 2022 Organizers 2452-3216 © 2023 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 ICSID 2022 Organizers

2452-3216 © 2023 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 ICSID 2022 Organizers 10.1016/j.prostr.2023.10.066

F. Mehri Sofiani et al. / Procedia Structural Integrity 51 (2023) 51 – 56 F. Mehri Sofiani et al. / Structural Integrity Procedia 00 (2022) 000–000

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1. Introduction The global world population is expected to increase by 20% until the year 2040 based on the Stated Policies Scenario (IEA, 2019). Consequently, the energy demand may rise by 26% by 2040 (IEA, 2019). The crucial effect of climate change and the detrimental impact of air pollution on the Earth’s ecosystems, are the major reasons to deploy renewable energy resources. Among these, offshore wind turbines (OWTs) represent promising technology for energy generation which convert wind energy into electricity. As the number of offshore wind farms rises, concerns regarding the OWT’s structural integrity (Shittu et al., 2020) rise as well. The OWT support structures are subject to corrosion due to seawater and humidity (Adedipe et al., 2016). There are multiple types of corrosion (Ahmad, 2006) and pitting corrosion is one of the most insidious forms of localized corrosion. Additionally, OWT support structures undergo fatigue loads due to wind and waves. The combination of these damage mechanisms is generally categorized as corrosion-fatigue (Ahn et al., 1992; Zhang et al., 2018). The high cycle fatigue regime is applicable to OWT structures (Kolios et al., 2014). For such applications, stress-life (S-N) plots are used to assess the fatigue life. Fatigue life of structural components is affected by several factors such as their geometry, loading type, surface condition and environment. As corrosion pits act as stress raisers, fatigue cracks most likely initiate at pits (Farhad et al., 2021), though the influence of degraded material properties due to corrosion cannot be discounted (Vukelic et al., 2022). This study is part of the MAXWind project with the main goal of rendering optimized inspection and maintenance plans for OWT structures. Hereto, an integrated corrosion-fatigue numerical model is being developed. The present study focuses on the pit-to-crack transition stage by investigating the stress concentration factor (SCF) for different pit configurations. The SCF can be used to quantify the stress raising effect of a pit, effectively allowing quantification of the severity of the pit geometry with respect to fatigue cracking. Cerit et al. (2009) studied the stress distribution in pits with circular mouth in a plate subject to tensile and torsional (Cerit, 2013) loads. They reported SCF values according to the absolute size of the pit depth and the ratio of pit depth over pit mouth diameter. Further, they studied the effect of a secondary small pit at the bottom of a hemispherical pit. Huang et al. (2014) performed a similar study without considering the plate thickness effect on the stress concentration factor, but focusing on the effect of the pit mouth aspect ratio. An et al. (2019) conducted a numerical analysis of tensile stress concentration in a semi-ellipsoidal pit by taking the plate thickness into account in addition to pit depth over pit length ratio. However, they have not studied the effect of pit mouth aspect ratio on SCF. Shojai et al. (2022) have performed a probabilistic modelling of pitting corrosion to assess its influence on SCF in OWT structures. They evaluated the effect of interaction between two pits on SCF, and also reported SCF values for a few single pit configurations considering absolute pit depth size and pit half-length over depth ratio. Liang et al. (2019) investigated the effects of absolute pit depth size and half-length of pit on SCF. They located the pit at the centre of the top plate surface as well as the edge of the plate. None of these last two works have incorporated pit mouth aspect ratio in the model. In a preceding study (Mehri Sofiani et al., 2023), the effect of pit depth over pit length, pit mouth aspect ratio, local thickness loss and loading direction on SCF was studied. Also, the most critical regions within semi-ellipsoidal pits as the potential locations for crack initiation were identified. However, the effect of local thickness loss lower than 0.1 is not explored. Adding to the state-of-the-art, the present work considers the combined effects of pit mouth aspect ratio, the pit depth over pit length ratio, and the plate thickness effect on SCF. Also, response of the material for local thickness loss lower than 0.2 is studied which is another novelty of the work.

Nomenclature a

pit depth

b c L

pit mouth half width pit mouth half length

plate length

t plate thickness OWT offshore wind turbine SCF stress concentration factor ������� nominal stress applied to the pitted plate principal stress at pit

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2. Finite element model For the linear elasto-static stress analysis, commercial software ABAQUS ® v2021 was used. The finite element model consists of a square plate with a central pit at its top surface, see Fig. 1.

A

2c

A

2c

L

2b

a

t

z

x

L

L

y

x

A-A

Fig. 1. Schematic representation of the pitted plate: top view of the plate (left) and through-thickness view of the plate (right).

As exhibited in Fig. 2, the 3D pitted plate is generated in ABAQUS ® and exported as a .sat file containing three dimensional geometry information. The exported file is then imported into the commercial meshing software Coreform Cubit ® 2020.2 to mesh the pitted plate. Due to the rather complex geometry of the pits, the quadratic tetrahedral element type was adopted for meshing. Fig. 3 shows a cross-sectional view of a semi-spherical pit ( �� � ��� and � � 1.0) where = = = 3 mm and a fine mesh size of 0.01 mm was applied to the concave surface of the pit. In order to maintain a smooth transition from this fine to the global coarser mesh, a cubic partition is created at the vicinity of the pit and its edges are meshed with relatively larger mesh size of 0.5 mm. A global, coarser mesh size of 12 mm was also applied to the plate edges to reduce the computational costs. An .inp file consisting of the meshed 3D part is next exported from Coreform Cubit ® and imported into ABAQUS ® .

Coreform Cubit®

ABAQUS®

ABAQUS®

Material properties

3D plate

Boundary conditions

3D ellipsoid/hemisphere

Finite element meshing

Cut/Assembly

Stress analysis

3D pitted plate

Stress extraction in the region of interest

Python®

Fig. 2. Modelling and implementation process.

F. Mehri Sofiani et al. / Procedia Structural Integrity 51 (2023) 51 – 56 F. Mehri Sofiani et al. / Structural Integrity Procedia 00 (2022) 000–000

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At this stage, the load and boundary conditions are added to the model. The pitted plate is subjected to a uniform axial tensile stress at one side and fixed at the opposite side; see Fig. 1. For the elastic material used in the simulations, a Young’s modulus of 205 GPa and a Poisson ratio of 0.29 are used (Igwemezie et al., 2019). Ultimately, the stress analysis is performed and the output files are post-processed using Python. The post-processing extracts the principal stresses from the pit region to calculate the SCF which is defined as: SCF = �� �� � ��� ������� (1) where ���� � � is the maximum value of the principal stresses extracted from the region containing the pit and ������� is the nominal stress applied to the pitted plate. The entire modelling and implementation process shown in Fig. 2 was automated using ABAQUS scripting with Python.

Fig. 3. FE mesh at semi-spherical pit. This study investigates the effect of normalized geometric parameters of a corrosion pit on its SCF. This includes the ratio of pit semi-width over pit semi-length ( ), the ratio of pit depth over pit length ( ), and the effect of localized thickness loss ( ). Normalized parameters have been used to avoid being constrained to absolute dimensional values. Values of equal to 0.125, 0.5, 1, and 1.5 were considered to address both wide and narrow shapes of a corrosion pit. Additionally, the pit mouth aspect ratio was considered to be 0.1, 0.5, and 1.0. The value of 0.5 for represents a hemispherical pit at = 1. The model also incorporates values of 0.01, 0.05, 0.1, 0.15, and 0.2. 3. Results and discussions Fig. 4, exemplarily, shows the distribution of maximum principal stress for a plate with two different pit configurations. One having normalized dimensions = 0.2, = 1, and equal to 0.125 and the second one having equal to 1.5 whilst the other normalized dimensions remained the same. The wider pit shown in Fig. 4 (a) causes lower values of stress in comparison to the sharper pit presented in Fig. 4 (b). Also, the effect of the pit dissipates in the immediate surrounding of the wider pit whereas around the sharper pit, still a significant range of stress is evident. Concentrated regions of minimum and maximum stress can be observed for the sharper pit; in contrast to the wider pit for which the stresses are more homogeneously distributed over the entire pit wall.

y z x

(a) (b) Fig. 4. Maximum principal stress (MPa) for a plate having a pit with = 0.15, = 1.0: (a) = 0.125 and (b) = 1.5.

F. Mehri Sofiani et al. / Procedia Structural Integrity 51 (2023) 51 – 56 F. Mehri Sofiani et al. / Structural Integrity Procedia 00 (2022) 000–000 5 Fig. 5 shows the SCF values versus ranging from 0.01 to 0.2 for between 0.125 and 1.5 at = 0.1 and = 1. Changes in yield no significant variations in the SCF when � 0.2. This means that the effect of the localized plate thickness loss is negligible for these shallow pits, which is in agreement with Liang et al. (2019). Similarly, Shojai et al. (2022) have observed negligible SCF variations versus absolute size of pit depth. 55

(a) (b) Fig. 5. SCF vs. for a range of values where (a) = 0.1 and (b) = 1.0. Both Fig. 5 and Fig. 6 reveal that the SCF increases as the value of increases. For the widest pits ( = 0.125), the SCF is not significantly different for pits with different pit mouth aspect ratios. The increase in SCF with is more pronounced for pits with = 1.0. A much smaller increase in SCF is seen for pits with = 0.1; the corresponding SCF curve on Fig. 6 converges to a value of 1.2. On the other hand, the SCF curves do not approach a constant value for = 0.5 and 1.0 within the studied range of . The limited effect of a pit with an extremely narrow mouth ( = 0.1) on SCF is most probably the consequence of the loading being parallel to the major axis ( 2 ) of the semi-ellipsoidal pit.

Fig. 6. SCF vs. a/2c for a range of b/c values.

4. Conclusion A parametric study was carried out to explore the effect of different pit configurations on stress concentration for a plate containing a hemispherical or semi-ellipsoidal pit. Within the studied ranges of geometrical parameters, the results show that the effect of localized plate thickness loss on SCF is negligible for ≤ 0.2. On the other hand, it was evident that and significantly affect the SCF. The SCF increases as and increase. A pit with an elliptical mouth ( = 0.1), causes minimum stress concentration even when it is narrow ( > 0.5). Quantifying the stress concentration factor for different pit configurations assists in identifying critical pit shapes and their

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susceptibility in transiting into crack(s). As future work, this study will be extended to a wider range of values for each parameter. Further, the effect of the angle between the pit’s length and the loading direction will be quantified. Acknowledgements The authors would like to acknowledge the financial support of the Belgian Federal Government through the Energy Transition Fund (ETF). References Adedipe, O., Brennan, F., Kolios, A., 2016. Review of corrosion fatigue in offshore structures: Present status and challenges in the offshore wind sector. Renewable and Sustainable Energy Reviews 61, 141–154. Ahmad, Z., 2006. Principles of Corrosion Engineering and Corrosion Control. Elsevier Ltd. Ahn, S. ‐H, Lawrence, F. V., Metzger, M. M., 1992. Corrosion Fatigue of an Hsla Steel. Fatigue & Fracture of Engineering Materials & Structures 15(7), 625–642. An, L. S., Park, Y. C., Kim, H. K., 2019. A Numerical Study of the Tensile Stress Concentration in a Hemi-ellipsoidal Corrosion Pit on a Plate. International Journal of Steel Structures 19(2), 530–542. Cerit, M., 2013. Numerical investigation on torsional stress concentration factor at the semi elliptical corrosion pit. Corrosion Science 67, 225–232. Cerit, M., Genel, K., Eksi, S., 2009. Numerical investigation on stress concentration of corrosion pit. Engineering Failure Analysis 16(7), 2467– 2472. Farhad, F., Smyth-Boyle, D., Zhang, X., 2021. Fatigue of X65 steel in the sour corrosive environment—A novel experimentation and analysis method for predicting fatigue crack initiation life from corrosion pits. Fatigue and Fracture of Engineering Materials and Structures 44(5), 1195– 1208. Huang, Y., Wei, C., Chen, L., Li, P., 2014. Quantitative correlation between geometric parameters and stress concentration of corrosion pits. Engineering Failure Analysis 44, 168–178. IEA. (2019). World Energy Model. IEA Paris. https://www.iea.org/reports/world-energy-model/stated-policies-scenario Igwemezie, V., Mehmanparast, A., Kolios, A., 2019. Current trend in offshore wind energy sector and material requirements for fatigue resistance improvement in large wind turbine support structures – A review. Renewable and Sustainable Energy Reviews 101, 181–196. International Energy Agency, 2019. Offshore Wind Outlook 2019 – Analysis - IEA. https://webstore.iea.org/download/direct/2886?fileName=Offshore_Wind_Outlook_2019.pdf%0Ahttps://www.iea.org/reports/offshore-wind outlook-2019 Kolios, A., Srikanth, S., Salonitis, K., 2014. Numerical simulation of material strength deterioration due to pitting corrosion. Procedia CIRP 13, 230–236. Liang, X., Sheng, J., Wang, K., 2019. Investigation of the mechanical properties of steel plates with artificial pitting and the effects of mutual pitting on the stress concentration factor. Results in Physics 14, 102520. Mehri Sofiani, F., Chaudhuri, S., Elahi, S. A., Hectors, K., De Waele, W., 2023. Quantitative Analysis of the Correlation between Geometric Parameters of Pits and Stress Concentration Factors for a Plate Subject to Uniaxial Tensile Stress. Theoretical and Applied Fracture Mechanics, 104081. Shittu, A. A., Mehmanparast, A., Shafiee, M., Kolios, A., Hart, P., Pilario, K. (2020). Structural reliability assessment of offshore wind turbine support structures subjected to pitting corrosion-fatigue: A damage tolerance modelling approach. Wind Energy 23(11), 2004–2026. Shojai, S., Schaumann, P., Brömer, T., 2022. Probabilistic modelling of pitting corrosion and its impact on stress concentrations in steel structures in the offshore wind energy. Marine Structures 84, 103232. Vukelic, G., Vizentin, G., Ivosevic, S., Bozic, Z., 2022. Analysis of prolonged marine exposure on properties of AH36 steel. Engineering Failure Analysis 135, 106132. Zhang, J., Hertelé, S., De Waele, W., 2018. A Non-Linear Model for Corrosion Fatigue Lifetime Based on Continuum Damage Mechanics. MATEC Web of Conferences 165, 1–5.

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Procedia Structural Integrity 51 (2023) 199–205

© 2023 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 ICSID 2022 Organizers Abstract This paper presents DIC-based experimental verification of topology optimization of the 3D printed cantilever plate load-bearing element. Test samples were 3D printed from ABS and PET-G materials using FDM technology. A 3D geometrical parametric model was created and FEA and topology optimization were performed using computer program Autodesk Inventor. In order to successfully define the optimization problem and obtain reliable results, it is extremely important to properly define the analysis input parameters, such as material parameters and boundary conditions. Young’s moduli of ABS and PET-G were determined experimentally on samples which were made using 3D printing technology with identical settings as cantilever plate samples. Stresses and strains in optimized samples were determined using FEA. To verify the FEA and topology optimization results, an experimental setup for holding and loading of 3D printed samples was prepared and displacements were measured using digital image correlation system ARAMIS. Results obtained experimentally were compared with the results obtained by finite element analysis of optimized cantilever plate sample and show very good agreement for both ABS and PET-G samples, with deviation of around 4 % and 11 % respectively. © 2023 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 ICSID 2022 Organizers Keywords: Topology optimization; digital image correlation; finite element analysis 1. Introduction Development of technology and market puts ever-increasing requirements to products being developed. To enable development of better and optimized products, new methods and procedures such as topology optimization based on 6th International Conference on Structural Integrity and Durability (ICSID 2022) Application of Digital Image Correlation method for verification of topology optimization of 3D printed load-bearing element Daniel Ivaničić a , Tea Marohnić b, *, Robert Basan b a Gaj 6, 51211 Matulji, Croatia b University of Rijeka, Faculty of Engineering., Vukovarska 58, 51000 Rijeka, Croatia Abstract This paper presents DIC-based experimental verification of topology optimization of the 3D printed cantilever plate load-bearing element. Test samples were 3D printed from ABS and PET-G materials using FDM technology. A 3D geometrical parametric model was created and FEA and topology optimization were performed using computer program Autodesk Inventor. In order to successfully define the optimization problem and obtain reliable results, it is extremely important to properly define the analysis input parameters, such as material parameters and boundary conditions. Young’s moduli of ABS and PET-G were determined experimentally on samples which were made using 3D printing technology with identical settings as cantilever plate samples. Stresses and strains in optimized samples were determined using FEA. To verify the FEA and topology optimization results, an experimental setup for holding and loading of 3D printed samples was prepared and displacements were measured using digital image correlation system ARAMIS. Results obtained experimentally were compared with the results obtained by finite element analysis of optimized cantilever plate sample and show very good agreement for both ABS and PET-G samples, with deviation of around 4 % and 11 % respectively. © 2023 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 ICSID 2022 Organizers Keywords: Topology optimization; digital image correlation; finite element analysis 1. Introduction Development of technology and market puts ever-increasing requirements to products being developed. To enable development of better and optimized products, new methods and procedures such as topology optimization based on 6th International Conference on Structural Integrity and Durability (ICSID 2022) Application of Digital Image Correlation method for verification of topology optimization of 3D printed load-bearing element Daniel Ivaničić a , Tea Marohnić b, *, Robert Basan b a Gaj 6, 51211 Matulji, Croatia b University of Rijeka, Faculty of Engineering., Vukovarska 58, 51000 Rijeka, Croatia

* Corresponding author. Tel.: +385-51-651-531; fax: +385-51-651-416. E-mail address: tmarohnic@riteh.hr * Corresponding author. Tel.: +385-51-651-531; fax: +385-51-651-416. E-mail address: tmarohnic@riteh.hr

2452-3216 © 2023 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 ICSID 2022 Organizers 2452-3216 © 2023 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 ICSID 2022 Organizers

2452-3216 © 2023 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 ICSID 2022 Organizers 10.1016/j.prostr.2023.10.089

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Finite Element (FE) method are constantly being improved. Topology optimization finds its application in numerous fields such as aeronautics, transport and mobility, as well as in some very specific areas of research such as shape optimization of weld orientation in simple plate structure (Larsen, Arora, Clausen (2021)). Benefits of topology optimization are multiple – optimal designs are easier to find, time required for product development is reduced, lightweight designs with maintained rigidity of individual parts are developed, and reduced weight consequently reduces the amount of energy used. Numerical simulations are often performed during the product development. To obtain reliable results, input information i.e. material properties, boundary conditions (loading scenario etc.) must be defined properly. Since these information are often unknown or unavailable at a given time, assumptions must be made and verified. Recently, Digital Image Correlation (DIC), a nondestructive method for measurement of displacements and deformations, i.e. the behavior of a product is widely used as a tool for verification of various models and numerical analysis results (i.e. evaluation of true stress-stress diagrams for welded joints, Milosevic et al. (2021), determination of material parameters from measurements, Gerbig et al. (2016), levelling FE analysis data, Lava et al. (2020) etc.). Within this work, the topology optimization on the selected design of the cantilever plate load-bearing element was performed. To verify the obtained results, experimental verification of 3D printed samples was performed. Displacements were measured using Digital Image Correlation system (DIC) and compared to the results obtained by FE analysis to verify the design and performed FE-based optimization and analysis.

Nomenclature b e

cross-section width [mm] Young's modulus [MPa]

E L

arm force [mm] loading force [N] yield stress [MPa] displacement [mm]

Q e R e w ʹ

cross-section height [mm] Poisson number [ − ]

δ e

ν

2. Materials and methods 2.1. Experimental setup for holding and loading of samples The load-bearing element chosen for this investigation is a cantilever plate element, clamped on one side and loaded on the free end (Fig. 1).

Fig. 1. Schematic of the loading setup.

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Holding and loading assembly had to ensure quality and reliable clamping of the sample so a custom holding and loading device assembly is designed and manufactured, consisting of a load-bearing frame, L-profile 40x40x4, clamping plate, hexagonal socket M6 bolts and corresponding washers and nuts. An existing 10 mm thick steel plate served as a base for the device mounting. A shackle was placed through the hole on the free end of the sample which enabled the loading of the sample with existing 5 kg weight. The whole assembly is shown in Fig. 2 (Ivaničić (2020)).

Fig. 2. Custom holding and loading assembly.

2.2. Young's modulus determination In order to perform reliable FE analysis, Young’s modulus ought to be determined. The Young's modulus E of polymer material depends on manufacturing method, humidity, loading duration and other factors which is why different literature sources provide different values of Young's moduli E of ABS and PET-G, materials that will be used for 3D printing of optimized samples. The Young’s modulus can be determined by tensile or compressive loading of the sample, as well as by loading the sample by pure bending. For the purpose of Young’s moduli determination, a simple pure bending device was used. The schematic representation of the pure bending device is shown in Fig. 3.

Fig. 3. Schematic representation of pure bending device, Lovrin (2001).

Young’s modulus can be calculated using the following expression: 2 e 2 e e e 3 2   ⋅ ⋅ = −   ′ ⋅ ⋅ ⋅   Q L L E ν b δ w b .

(1)

For this purpose, beam elements with rectangle cross-section ( b e = 10 mm, δ e = 20 mm) have been 3D printed using Prusa i3 MK3 FDM 3D printer. Printed samples from both ABS and PET-G filament were loaded with 5 kg weights placed at the distance L from the supports. Deflection was measured in 3 points for each sample, both for unloaded and loaded condition to compensate printing imperfections. Using measured values of deflection in each point,

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deflection on central part of the beam is calculated and inserted in Eq. (1) which resulted in Young’s moduli of ABS and PET-G material, 2347,37 MPa and 2160,5 MPa respectively. Obtained results show good agreement with values found in literature, MatWeb (2020), and Autodesk Inventor’s materials database, as seen in Table 1. Experimentally obtained values were then used as input parameters in FE analysis.

Table 1. Young’s modulus of PET-G and ABS.

Young’s modulus, E [MPa] Values from catalogue, MatWeb (2020)

Material

Experimental value

Autodesk Inventor

ABS

2347,37 2160,5

1500 – 2600 2010 – 2110

2240 N/A

PET-G

2.3. Topology optimization of the load-bearing element Topology optimization was performed using Autodesk Inventor software, i.e. Stress Analysis module. The goal of the topology optimization of the initial volume, i.e. initial size and shape of the cantilever load-bearing element (Fig. 4. (a)), was the reduction of the overall mass while maintaining the load-bearing capability.

a)

b)

Fig. 4. (a) Initial volume of the cantilever plate load-bearing element with boundary conditions; (b) Meshed model with boundary conditions.

As was mentioned in subsection 2.2, for successful FE analysis, material parameters have to be assigned properly. PET-G material that will be used, along with ABS, for 3D printing of the optimized cantilever sample, is not available in Autodesk Inventor so its parameters ought to be determined. Yield stress R e and Poisson number ν are taken from the literature, MatWeb (2020). The Young’s modulus E is experimentally determined as explained in subsection 2.2. Since R e is given in range, the lowest value of 24 MPa is adopted to obtain conservative calculations. Further step is to exclude the areas for which the optimization will not be performed. Here that are the clamping and the loading area, as marked green in Fig. 4. (a). Clamping of the cantilever plate is set on the rectangular part with two holes that corresponds with clamping that will be obtained on the real sample. Loading force in vertical direction is set on the hole on the free end of the cantilever plate, as shown in Fig. 4. (a). Topology optimization depends on mesh density that depends on finite element size. These should be optimized in order to obtain the best ratio of details and analysis duration. Average and minimal element size are set to 0,01, mesh resolution is set to 1.00, while the percentage of the removed volume is set to 50 %. In Fig. 4. (b) the meshed model is shown, while Fig. 5. (a) represents the optimized shape obtained for the given parameters and boundary conditions. Based on the obtained results, parametric 3D model is made in Autodesk Inventor, Fig. 5. (b). In following sections it will be seen that the free end of cantilever load-bearing element, where the maximum deflection is expected, was redesigned when compared to optimization results to a rectangular-like shape in order to allow better raster application and easier recognition and definition of facets with GOM Correlate software used for processing of the experimental measurements using DIC. Optimized sample volume was reduced by 50,5 % when compared to initial volume resulting in mass reduction of 13,46 g (initial mass 27,081 g, end weight 13,261 g).

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a)

b)

Fig. 5. (a) Results of the topology optimization; (b) Parametric 3D model of the optimized shape.

2.4. FE analysis of the optimized sample Prior to experimental verification, FE analysis of the optimized shape stress distribution was made to verify the design for both PET-G and ABS assigned 3D models. Material properties and loading force were set identically as for topology optimization, however, clamping scenario was modified in order to solve convergence issues. Analysis with modified boundary conditions converged within 5 % when considering Von Mises stresses. Fig. 6. shows y axis displacement distribution for 3D models with assigned ABS and PET-G properties.

a)

b)

Fig. 6. y axis displacement distribution according to FEA for 3D models with assigned (a) ABS material properties; (b) PET-G properties.

2.5. Verification of the topology optimization using Digital Image Correlation An experimental verification i.e. Digital Image Correlation measurements were performed on the optimized shape cantilever plate load-bearing elements using the ARAMIS system and GOM Correlate software. Optimized test samples were 3D printed using Prusa i3 MK3 FDM printer with the same printing settings as for beam samples used to determine Young’s moduli values, one ABS (Fig. 7) and two PET-G samples.

Fig. 7. 3D printed ABS optimized cantilever plate load-bearing element.

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Prior to experimental measurements, sensors were set, ARAMIS system was calibrated, samples were prepared by applying a stochastic pattern of paint and the quality of the raster was checked. Each sample was then clamped to a holding and loading device and loaded with 5 kg weight, as shown in Fig. 8. Two separate measurements were performed for each sample in order to obtain more reliable results.

Fig. 8. Experimental measurements using ARAMIS system.

3. Results and discussion Results used for comparison and verification were values of displacement along the y axis. Fig. 9 shows first experimental measurement of displacement along y axis on ABS sample and corresponding results obtained using FE analysis.

a)

b)

Fig. 9. Results of (a) experimental measurement and (b) FEA results of ABS sample.

For easier comparison of the results, the values of y axis displacement measured using ARAMIS system and FE analysis results, along with the relative deviation of the average experimentally obtained value from the value obtained by FE analysis are given in Table 2 for ABS and Table 3 for two PET-G samples. Table 2 shows good agreement of the results obtained experimentally and using FE analysis with maximum deviation for ABS cantilever sample being 6,193 %. Table 3 shows good agreement of the results obtained experimentally and using FE analysis with maximal deviation for the 1st PET-G cantilever plate sample being 4,416 %, while maximal deviation for the 2nd PET-G cantilever plate sample is somewhat higher, 11,797 %. Larger

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measurement errors could have occurred due to insufficient tightening of the sample which caused imperfect clamping, or due to errors in the material that could have occurred during the 3D printing of the samples.

Table 2. Comparison of y axis displacements obtained experimentally and using FE analysis, ABS cantilever sample. Point Average value of measurements [mm] FEA result [mm] Relative deviation [%] 1 1.6145 1.526 5.799 2 1.6105 1.521 5.884 3 1.614 1.522 6.045 4 1.6152 1.521 6.193 5 1.609 1.527 5.370

Table 3. Comparison of y axis displacements obtained experimentally and using FE analysis, PET-G cantilever samples.

1 st PET-G sample

2 nd PET-G sample

Point

Average value of measurements [mm]

FEA result [mm]

Relative deviation [%]

Average value of measurements [mm]

FEA result [mm]

Relative deviation [%]

1 2 3 4 5

1.7265 1.7235 1.7225

1.658 1.653 1.654 1.653 1.658

4.131 4.265 4.141 4.416 4.131

1.841 1.848

1.658 1.653 1.654 1.653 1.658

11.037 11.797 11.699 11.162 11.037

1.8475 1.8375

1.726

1.7265

1.841

4. Conclusion Based on the comparison of the results obtained using the finite element method, and the results obtained by experimental measurement using the ARAMIS system, it can be concluded that the appropriate method was applied when determining the Young’s modulus and that applied boundary conditions well represented the real component loading scenario. The applicability of the Digital Image Correlation method for checking the results obtained by the finite element method is confirmed. The measurement results coincide well with the results obtained by analysis using the finite element method. Acknowledgements This work was supported in part by Croatian Science Foundation under the project IP-2020-02-5764, by University of Rijeka under the project number uniritehnic-18-116 and University of Rijeka, Center for Advanced Computing and Gerbig, D., Bower, A., Savic, V., Hector, L. G., 2016. Coupling digital image correlation and finite element analysis to determine constitutive parameters in necking tensile specimens. International Journal of Solids and Structures 97–98, 496–509. Ivaničić, D. Numerical analysis and topology optimization of load-bearing element , (Master thesis in Croatian). University of Rijeka, Faculty of Engineering, 2020. Larsen, M.L., Arora, V., Clausen, H.B., 2021. Finite element shape optimization of weld orientation in simple plate structure considering different fatigue estimation methods. Procedia Structural Integrity 31, 70–74. Lava, P., Jones, E.M.C., Wittevrongel, L., Pierron, F., 2020. Validation of finite-element models using full-field experimental data: Levelling finite element analysis data through a digital image correlation engine. Strain 56, 1–17. Lovrin, N. Analiza nosivosti evolventnog ozubljenja s velikim stupnjem prekrivanja profila , (Doctoral dissertation in Croatian). University of Rijeka, Faculty of Engineering, 2001. MatWeb Material Property Data. http://www.matweb.com, accessed: October, 2020. Milosevic, N., Younise, B., Sedmak, A., Travica, M., Mitrovic, A., 2021. Evaluation of true stress–strain diagrams for welded joints by application of Digital Image Correlation. Engineering Failure Analysis 128, 105609. Modelling. References