PSI - Issue 74

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Procedia Structural Integrity 74 (2025) 106–113

© 2025 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 the responsibility of Libor Pantělejev Abstract In material science, especially when analyzing SEM and TEM images, the measurement of microstructural features has traditionally relied on manual methods. These methods are slow and prone to human error. A framework employing the BIRCH clustering algorithm and thresholding techniques was developed to automatically segment and categorize microstructural features. The framework can extract quantitative parameters such as cell diameter, aspect ratio, major and minor axis lengths, etc. While cell diameter can be measured using traditional methods like the line-intercept technique, obtaining other parameters manually is significantly more difficult. By utilizing the automated framework, results are more consistent. However, while this framework substantially reduces manual effort and accelerates analysis, challenges remain when addressing highly complex or anomalous images. In such cases, artificial neural networks (ANN) offer a more adaptive and robust solution. Yet, preparing the extensive well-labeled datasets required for ANN is time-consuming and resource-intensive. Semi-automated data preparation strategies are being explored, to minimize these demands by reducing manual input and enhancing the efficiency and scalability of the analysis pipeline. In this work, the cellular structure present in additively manufactured 316L steel was evaluated using the above-mentioned tools to enable potential correlation of the microstructural features with mechanical properties. © 2025 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 the responsibility of Libor Pan tě lejev Keywords: Addtive manufacturing; Machine learning; austenitic steel 316L; Dislocation substructure; Deep learning 1. Introduction Austenitic stainless steel 316L is a widely used engineering material known for its exceptional corrosion resistance, weldability, and biocompatibility (Shih et al., 2004). However, its ability to be strengthened by traditional heat treatment methods is limited due to its stable austenitic structure (Saeidi et al., 2015). Enhancing its strength through Eleventh International Conference on Materials Structure and Micromechanics of Fracture Advanced Semantic Segmentation of Cellular Substructure in Selectively Laser Melted 316L Stainless Steel Tomáš Vražina 1, 2*, Jaromír Brůža 1, 2 , Alice Chlupová 1 , Ivo Šulák 1 , Libor Pantělejev 2 , Tomáš Kruml 1 , Jiří Man 1 1 Institute of Physics of Materials, Czech Academy of Sciences, Žižkova 22, 61600 Brno, Czech Republic 2 Institute of Materials Science and Engineering, Brno University of Technology, Technická 2896/2, 61669 Brno, Czech Republic

2452-3216 © 2025 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 the responsibility of Libor Pant?lejev

2452-3216 © 2025 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 the responsibility of Libor Pantělejev 10.1016/j.prostr.2025.10.041

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alloying additions, such as carbides or intermetallic precipitates, often compromises ductility and poses a trade-off in mechanical performance (Liu et al., 2018). Laser powder bed fusion (LPBF), an additive manufacturing technique, introduces an alternative approach to strengthening the 316L austenitic stainless steel by promoting the formation of dislocation structures during rapid solidification (Hu et al., 2022). Specifically, the high thermal gradients and cooling rates in LPBF lead to the development of dislocations organized into a shape of hexagonal prism-like structures in 3D (when sliced, the 2D structure is composed of cells) (Kong et al., 2021). These dense dislocation structures act as a barrier to dislocation motion. Therefore higher stresses must be attained for dislocation movement. The resulting strength of the material is increased while maintaining reasonable ductility (Liu et al., 2018; Riabov et al., 2021). Process parameters such as laser power and layer thickness influence the size and morphology of these dislocation cells, allowing microstructural refinement through process control (Kong et al., 2021). However, these finely structured dislocation network is destabilized when an increased temperature is introduced. In-service conditions involving elevated temperatures or cyclic mechanical loads can cause coarsening, annihilation, or rearrangement of the dislocation network, leading to a reduction in yield strength and a drop in fatigue life as investigated by Babinský and Chen (Babinský et al., 2023; Chen et al., 2022). Therefore, rapid and reliable quantification of cell or prism size and density is essential for monitoring microstructural changes during heat treatment and for predicting the performance of additively manufactured parts. (Kong et al., 2021; Wang et al., 2025). Traditionally, techniques based on the line-intercept method have been employed for dislocation cell size assessment. Although considered reliable, these methods are fully manual and extremely time- and labor-intensive. More automated thresholding-based approaches have been explored to reduce manual effort. However, these methods often require extensive tuning of parameters for each image due to differences in brightness, contrast, or image content. Slight variations in image quality may lead to inconsistencies or incorrect results, making such methods unreliable for processing larger datasets without constant user intervention (Stuckner et al., 2022). Recent developments in deep learning have introduced more robust alternatives. Convolutional neural networks (CNNs), particularly U-Net architectures, first proposed by Ronnenberger (Ronneberger et al., 2015), have demonstrated excellent performance in segmenting complex features in medical and materials science imaging (Chaurasia et al., 2023; Mikmeková et al., 2023; Zhou et al., 2024). However, applying them to microstructural features such as dislocation cells in LPBF-processed 316L presents practical challenges. Preparing a training dataset is time consuming, and variations in image contrast can still affect segmentation quality. This study proposes a hybrid image segmentation approach that combines automatic thresholding with deep learning using U-Net. The key idea is to use thresholding-based segmentation as an initial step, which is later manually refined to create accurate training masks. It allows for more efficient preparation of training data without starting annotation from the ground up. The trained model is then used for automated segmentation of new images. This combined approach should reduce annotation time while ensuring high-quality output for complex microstructures.

Nomenclature ANN Artificial Neural Network BIRCH Balanced Iterative Reducing and Clustering using Hierarchies CLAHE Contrast Limited Adaptive Histogram Equalization CNN Convolutional Neural Networks DICE Dice Similarity Coefficient DL Deep Learning EBSD Electron Backscattered Diffraction IoU Intersection over Union LPBF Laser Powder Bed Fusion ReLU Rectified Linear Unit SEM Scanning Electron Microscopy STEM Scanning Transmission Electron Microscopy

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2. Material and methods The 316L stainless steel used in this study was produced from two different powder batches (Table 1) using two distinct additive manufacturing technologies (Table 2). Both Commercially available powders have particle size typical for LPBF processing (15-45 µm). Vertically oriented flat specimens with cross-section dimension 4 mm and heigh 45 mm were fabricated using Renishaw and EOS systems. No postprocessing heat treatment was applied to the specimens. The relative densities were measured by the Archimedes method and found to be 99.2% in the case of Renishaw specimens and 99.4% for the EOS specimens. Small samples were extracted from each set of specimens for microstructural characterization. Scanning electron microscopy (SEM) (Fig. 1a, b) was performed on mechanically prepared samples, which were further polished electrolytically in a 10% oxalic acid solution for 45 seconds at 5 V. The samples were subsequently etched using a BERAHA II solution (800 ml distilled water, 400 ml HCl, and 48 g NH₄FHF) , to enhance the visibility of the cellular boundaries. The etched microstructure of the material is shown in Fig. 1a and 1b, highlighting the distinct features characteristic of the LPBF process. Additionally, thin foils were prepared for scanning transmission electron microscopy (STEM) to enable high-resolution observation of dislocation structures, as presented in Fig. 1c.

Table 1 Chemical composition of 316L powders in wt.% provided by the manufacturers Elements Cr Ni Mo C Si

Mn 1.2 1.9

S

N

Fe

EOS

18.3 18.3

14

2.7 2.2

-

0.47

-

0.1

Bal. Bal.

RENISHAW

11.2

0.02

1.1

0.004

0.03

Table 2. LPBF process parameters for manufacturing the 316L steel. Parameters Laser power [W] Scan speed [mm.s -1 ]

Jump speed [mm.s -1 ]

Scan strategy

Hatch distance [mm]

Layer thickness [mm]

EOS

214.2

928.1

-

Rotation (67°)

0.1

0.04

RENISHAW 0.05 Microstructural characterization was performed using a LYRA 3 XMU field emission SEM equipped with an electron backscatter diffraction (EBSD) system from Oxford Instruments. Grain size measurements were conducted using AZtecCrystal software, applying the Feret diameter method. The EBSD analysis covered an area of approximately 1800 μm × 1200 μm, providing average grain sizes of 49.8 μm for the Renishaw sample and 49.3 μm for the EOS sample. A JEOL JEM-2100F STEM was used to observe the dislocation structure in detail. The microscope is equipped with a bright-field detector, allowing for high-resolution imaging in scanning transmission electron microscopy mode. 200 - 5500 Chess board 0.06

Fig. 1. (a) Representative SEM micrograph of additively manufactured 316L (EOS) capturing the melt pool (b) the cellular substructure inside the melt pools (EOS) - SEM. (c) detail of dislocation cell walls (STEM BF)

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Melt pool tracks visible in Fig. 1a represent regions where the material was locally melted during the processing of individual layers. These tracks encompass several grains, within which near-hexagonal cellular structures are formed, as shown in Fig. 1b. The boundaries of melt pools often serve as sites for irregularities in material flow. A higher magnification STEM micrograph (Fig. 1c) reveals that these cells consist of dislocation networks. Dislocation rich cell structures are attributed to the strengthening of 316L steel. Proper characterization of the dislocation substructures and subsequent correlation with mechanical properties is therefore of great importance. Three different measuring methods were utilized to assess the characteristics of these cell parameters. Namely: a) the line-intercept method b) the adaptive thresholding, and c) the deep-learning U-net method. The diagram in Fig. 2 presents a hybrid segmentation workflow combining image preprocessing with a deep learning model based on a U-Net architecture.

Fig. 2. Simplified diagram of the hybrid workflow for segmenting dislocation cell structures, combining image preprocessing techniques with a U-Net architecture using a ResNet-based encoder. (ReLU – Rectified Linear Unit).

The input to the U-Net model consists of cropped images and microscopy image masks that are generated through a preprocessing pipeline that includes CLAHE (Contrast Limited Adaptive Histogram Equalization), adaptive thresholding, and subsequent morphological post-processing. The processed images are then passed through a modified U-Net network that uses a ResNet34 (He et al., 2015) encoder pretrained on ImageNet (database). Instead of max-pooling, the encoder employs stride convolutions to extract hierarchical features, which are later upsampled through transposed convolutions in the decoder. Skip connections bridge the encoder and decoder stages, preserving spatial detail for accurate segmentation. A final sigmoid activation produces a binary segmentation mask that identifies the dislocation cell regions. The dataset was divided into three subsets for model development and evaluation: 5–10 images were used for training, 2 for validation during model tuning, and 2 for final testing of segmentation performance. The U-Net model was trained for segmentation using the Adam optimizer with a learning rate set to 0.001. Training was conducted for 50 epochs, and binary cross-entropy loss was employed as the loss function. Data was processed in batches, and model performance was monitored through periodic validation loss assessment. 3. Results and discussion 3.1 Image thresholding and classification The etched microstructure in Fig. 3a was segmented using an adaptive thresholding method. The resulting cellular structures were then classified with the BIRCH (Zhang et al., 1996) (Balanced Iterative Reducing and Clustering using

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Hierarchies) algorithm based on two geometric parameters: cell area and the squared ratio of the major to minor axes, which enhances the separation between structural types (Fig. 3b–c). This clustering process distinguished three main categories: clustered cells (Fig. 3d), hexagonal cells (Fig. 3e), and elongated cells (Fig. 3f). Clustered cells typically arise from thresholding artifacts, often due to incomplete or irregular cell boundaries caused by uneven etching. Despite postprocessing efforts, some of these artifacts persist. While structurally distinct, elongated cells are not the focus of the final analysis. Only hexagonal cells, characterized by their regular morphology, were selected for quantitative size and density measurements. Thus, the BIRCH algorithm served as a classification tool to distinguish morphologically distinct cell groups (cluster, hexagonal, elongated), ensuring that measurements were performed exclusively on relevant structures.

Fig. 3 Image processing of 3D printed 316L microstructure (a) raw image, (b) visualization of highlighted distinguished groups in plot, (c) representation of grouped data in the original image, (d) clustered cells, (e) hexagonal-shaped cells, (f) elongated cells

3.2 Introducing U -Net In the case of the EOS-manufactured microstructure, the parameters for adaptive thresholding were carefully fine tuned to achieve precise cell segmentation. However, applying the same parameters to the Renishaw-produced structures resulted in less accurate segmentation. This discrepancy may be attributed to differences in powder composition, printing technology, and processing parameters, all of which may influence the microstructural features and the response of the material during chemical etching. In particular, some cell boundaries in the Renishaw samples were not as distinctly revealed as those in the EOS samples, leading to a reduced number of clearly segmentable cells. Fig. 4 presents the segmentation outcomes using both pretrained and non-pretrained U-Net models. Model performance (see Fig. 4b–g) was evaluated with two widely used metrics: the Dice Similarity Coefficient (DICE) and Intersection over Union (IoU), both of which measure the overlap between predicted and ground-truth masks. The comparison highlights the benefit of using pretrained encoders, especially in cases where thresholding-based preprocessing is challenged by morphological variability (Fig 4a) or suboptimal contrast (Fig. 4b). The highest segmentation accuracy was achieved for the EOS-manufactured structure (Fig. 4g) when the U-Net was trained on ten images and employed a ResNet encoder pretrained on ImageNet. Notably, pretraining (Fig 4c, d) had a more significant impact on performance than simply increasing the number of training images (Fig 4e, f). Similar conclusions were drawn by Stuckner (Stuckner et al., 2022) who showed that high IoU scores can be achieved even with a single training image, and by Sevi and Aydin (Sev ı̇ and Aydin, 2023) who highlighted the effectiveness of U Net for small datasets, contradicting the common assumption that deep learning always requires large amounts of data.

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Bailly (Bailly et al., 2022) further emphasized that larger datasets do not always lead to higher accuracy but contribute to greater model stability; feature engineering and data quality remain critical factors. Nevertheless, while satisfactory performance can be achieved with very limited training data, generalization to new images, especially those acquired with different manufacturing technologies, etching conditions, or microscopy settings may be limited. Ultimately, the required dataset size depends on the specific application, as illustrated by Mikmeková (Mikmeková et al., 2023) where 230 training images were used even with pretraining on ImageNet.

Fig. 4 Comparison of segmentation accuracy and error distribution (Dice: 95.8%, IoU: 91.9%) for dislocation cells in LPBF-produced 316L steel by EOS (left) and Renishaw (right). (a) EOS original cropped image, (b) Renishaw original cropped image, (c), (d) 5 images ImageNet, (e), (f) 10 images No pretrain, (g), (h) 10 images ImageNet. (True positive: green; False positive: blue; False negative: red), Recent studies have tackled the annotation bottleneck in microstructure segmentation using either weak supervision with human-in-the-loop learning (Na et al., 2023) or synthetic dataset generation based on kinetic models (Chaurasia et al., 2023). Each approach has certain advantages: weak supervision can minimize the need for pixel-level labeling, while synthetic data enables the generation of large datasets from limited real examples. Table 3 compares the cell diameter measurements obtained by the traditional line-intercept method, the adaptive thresholding, and the U-Net segmentation. Each value in the Table 3 is based on measurements from approximately 500 individual cells per manufacturing technique and method. The differences between measuring methods are

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relatively small when the standard deviation is considered, indicating that all three approaches provide consistent results for average cell diameter. However, while the line-intercept method is limited to average diameter measurements, both the adaptive thresholding and the U-Net enable the extraction of additional information, such as cell eccentricity, precise area, distribution statistics, and cell count. It is important to note that the adaptive thresholding can be affected by microstructural artifacts, as illustrated in Fig. 3d–f, which may have an impact on the accuracy of the measurement. In contrast, the U-Net approach demonstrates improved robustness to such artifacts, enabling more reliable quantification of individual cell features. Table 3. Comparison of cell diameter (µm) obtained by various measurement methods for different manufacturing techniques. Methodology EOS RENISHAW Line-intercept 0.5 ± 0.11 0.57 ± 0.12 Adaptive thresholding 0.6 ± 0.05 0.47 ± 0.03 U-net 0.62 ± 0.03 0.52 ± 0.03 4. Conclusions Based on the comprehensive analysis of the 316L cellular microstructure using a combination of classical and deep learning-based segmentation methods, the following key conclusions can be drawn: • A hybrid approach combining adaptive thresholding with deep learning (U-Net with a pretrained ResNet34 encoder) enables reliable and efficient segmentation of hexagonal dislocation cells in LPBF-produced 316L austenitic steel, applicable to samples produced by both EOS and Renishaw machines. • All three methods under investigation provided similar results concerning cell diameter. Nevertheless, Adaptive thresholding and U-net were faster and offered additional parameters from analyzed pattern. • U-Net models utilizing ImageNet-pretrained encoders achieved higher segmentation accuracy, with a stronger impact than merely expanding the training set or training without preexisting weights. • The study confirms that, although deep learning models can perform well with small datasets in specific tasks, their generalizability to images acquired under different manufacturing or imaging conditions may require further data augmentation or adaptation. Acknowledgements The authors would like to express their gratitude for the financial support of the Czech Science Foundation within the project No. GA23-05372S. This work has also been supported by the project INTER-COST No. LUC24093 funded by the Ministry of Education, Youth and Sports of the Czech Republic. Support from the Czech Academy of Sciences within the framework of the project Lumina quaeruntur is acknowledged. References Babinský, T., Šu lák, I., Kuběna, I., Man, J., Weiser, A., Švábenská, E., Englert, L., Guth, S., 2023. Thermomechanical fatigue of additively manufactured 316L stainless steel. Materials Science and Engineering: A 869, 144831. Bailly, A., Blanc, C., Francis, É., Guillotin, T., Jamal, F., Wakim, B., Roy, P., 2022. Effects of dataset size and interactions on the prediction performance of logistic regression and deep learning models. Computer Methods and Programs in Biomedicine 213, 106504. Chaurasia, N., Jha, S.K., Sangal, S., 2023. A novel training methodology for phase segmentation of steel microstructures using a deep learning algorithm. Materialia 30, 101803. Chen, Y., Wang, X., shen, J., Peng, Y., Jiang, Y., Yang, X., Leen, S.B., Gong, J., 2022. Deformation mechanisms of selective laser melted 316L austenitic stainless steel in high temperature low cycle fatigue. Materials Science and Engineering: A 843, 143123. He, K., Zhang, X., Ren, S., Sun, J., 2015. Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification, in: 2015 IEEE International Conference on Computer Vision (ICCV). Presented at the 2015 IEEE International Conference on Computer Vision (ICCV), pp. 1026–1034. Hu, Z., Gao, S., Zhang, L., Shen, X., Seet, H.L., Nai, S.M.L., Wei, J., 2022. Micro laser powder bed fusion of stainless steel 316L: Cellular structure, grain characteristics, and mechanical properties. Materials Science and Engineering: A 848, 143345. Kong, D., Dong, C., Wei, S., Ni, X., Zhang, L., Li, R., Wang, L., Man, C., Li, X., 2021. About metastable cellular structure in additively manufactured austenitic stainless steels. Additive Manufacturing 38, 101804.

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Liu, L., Ding, Q., Zhong, Y., Zou, J., Wu, J., Chiu, Y.-L., Li, J., Zhang, Z., Yu, Q., Shen, Z., 2018. Dislocation network in additive manufactured steel breaks strength–ductility trade-off. Materials Today 21, 354–361. Mikmeková, Š., Man, J., Ambrož, O., Jozefovič, P., Čermák, J., Järvenpää, A., Jaskari, M., Materna, J., Kruml, T., 2023. High -Resolution Characterization of Deformation Induced Martensite in Large Areas of Fatigued Austenitic Stainless Steel Using Deep Learning. Metals 13, 1039. Na, J., Kim, S.-J., Kim, H., Kang, S.-H., Lee, S., 2023. A unified microstructure segmentation approach via human-in-the-loop machine learning. Acta Materialia 255, 119086. Riabov, D., Leicht, A., Ahlström, J., Hryha, E., 2021. Investigation of the strengthening mechanism in 316L stainless steel produced with laser powder bed fusion. Materials Science and Engineering: A 822, 141699. Ronneberger, O., Fischer, P., Brox, T., 2015. U-Net: Convolutional Networks for Biomedical Image Segmentation, in: Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F. (Eds.), Medical Image Computing and Computer-Assisted Intervention – MICCAI 2015. Springer International Publishing, Cham, pp. 234–241. Saeidi, K., Gao, X., Zhong, Y., Shen, Z.J., 2015. Hardened austenite steel with columnar sub-grain structure formed by laser melting. Materials Science and Engineering: A 625, 221–229. Sev ı̇, M., Aydin, İl. , 2023. Improving Unet segmentation performance using an ensemble model in images containing railway lines. Turkish Journal of Electrical Engineering and Computer Sciences 31, 739–750. Shih, C.-C., Shih, C.-M., Su, Y.-Y., Su, L.H.J., Chang, M.-S., Lin, S.-J., 2004. Effect of surface oxide properties on corrosion resistance of 316L stainless steel for biomedical applications. Corrosion Science 46, 427–441. Stuckner, J., Harder, B., Smith, T.M., 2022. Microstructure segmentation with deep learning encoders pre-trained on a large microscopy dataset. npj Comput Mater 8, 1–12. Wang, X., Nadimpalli, V.K., Tiedje, N.S., Juul Jensen, D., Yu, T., 2025. Additive-Manufacturing-Induced Cell Structure in Stainless Steel 316L: 3D Morphology and Formation Mechanism. Metall Mater Trans A 56, 506–517. Zhang, T., Ramakrishnan, R., Livny, M., 1996. BIRCH: an efficient data clustering method for very large databases. SIGMOD Rec. 25, 103–114. Zhou, P., Zhang, X., Shen, X., Shi, H., He, J., Zhu, Y., Jiang, F., Yi, F., 2024. Multi-phase material microscopic image segmentation for microstructure analysis of superalloys via modified U-Net and rectify strategies. Computational Materials Science 242, 113063.

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Procedia Structural Integrity 74 (2025) 50–55

© 2025 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 the responsibility of Libor Pantělejev This contribution focusses on the damage assessment of concrete fatigue failure with the whole range of fatigue regimes, i.e. static fracture, low-cycle to high-cycle with more than 1×10 4 loading cycles. The results of the experimental tests are presented in form of a S-N curve, a load-CMOD curve, a damage-CMOD curve and are providing useful information for future structural design. Additionally, acquisition of CMOD during the cyclic loading allowed for evaluation of the fatigue crack growth rate by Paris’ law. © 2025 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 the responsibility of Libor Pantělejev Abstract Concrete structures form an essential part of the local and global infrastructure, and their lifespan is usually measured in decades. Many structures such as highway and railroad bridges, railway sleepers, offshore structures and wind turbine foundations are exposed to repeated load and often fail due to fatigue rupture of concrete. Furthermore, the fatigue design of a structure is considered for the ultimate limit state (ULS), while the serviceability limit state (SLS) is missing, i.e., the assessment of the crack width w c , crack length l , and deflection δ . This missing SLS fatigue consideration in standards may lead to an unoptimized structure, which may eventually result in a visible damage of load-bearing structural components. This contribution focusses on the damage assessment of concrete fatigue failure with the whole range of fatigue regimes, i.e. static fracture, low-cycle to high-cycle with more than 1×10 4 loading cycles. The results of the experimental tests are presented in form of a S-N curve, a load-CMOD curve, a damage-CMOD curve and are providing useful information for future structural design. Additionally, acquisition of CMOD during the cyclic loading allowed for evaluation of the fatigue crack growth rate by Paris’ law. © 2025 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 the responsibility of Libor Pantělejev Eleventh International Conference on Materials Structure and Micromechanics of Fracture Assessment of concrete fracture and fatigue damage across multiple load regimes Petr Miarka a *, Lucie Malíková a , Jose D. Ríos c , Vlastimil Bílek d a Institute of Physics of Materials, Czech Academy of Sciences, Žižkova 22, 616 00 Brno, Czech Republic b Brno University of Technology, Faculty of Civil Engineering, Veveří 331/95, 602 00 Brno, Czech Republ ic c Department of Continuum Mechanics and Structural Analysis, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, Ca mino de los Descubrimientos s/n, 41092, Seville, Spain d VŠB — Technical University of Ostrava, Faculty of Civil Engineering, Ludvíka Podéště 1875/17, 708 00 Ostrava - Poruba, Czech Republic Abstract Concrete structures form an essential part of the local and global infrastructure, and their lifespan is usually measured in decades. Many structures such as highway and railroad bridges, railway sleepers, offshore structures and wind turbine foundations are exposed to repeated load and often fail due to fatigue rupture of concrete. Furthermore, the fatigue design of a structure is considered for the ultimate limit state (ULS), while the serviceability limit state (SLS) is missing, i.e., the assessment of the crack width w c , crack length l , and deflection δ . This missing SLS fatigue consideration in standards may lead to an unoptimized structure, which may eventually result in a visible damage of load-bearing structural components. Eleventh International Conference on Materials Structure and Micromechanics of Fracture Assessment of concrete fracture and fatigue damage across multiple load regimes Petr Miarka a *, Lucie Malíková a , Jose D. Ríos c , Vlastimil Bílek d a Institute of Physics of Materials, Czech Academy of Sciences, Žižkova 22, 616 00 Brno, Czech Republic b Brno University of Technology, Faculty of Civil Engineering, Veveří 331/95, 602 00 Brno, Czech Republ ic c Department of Continuum Mechanics and Structural Analysis, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, Ca mino de los Descubrimientos s/n, 41092, Seville, Spain d VŠB — Technical University of Ostrava, Faculty of Civil Engineering, Ludvíka Podéště 1875/17, 708 00 Ostrava - Poruba, Czech Republic

Keywords: Fatigue; Concrete; S-N field; Cycling loading Keywords: Fatigue; Concrete; S-N field; Cycling loading

* Corresponding author. Tel.: +4-205-322-90430. E -mail address: miarka@ipm.cz * Corresponding author. Tel.: +4-205-322-90430. E -mail address: miarka@ipm.cz

2452-3216 © 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC-BY 4.0 license (https://creativecommons.org/licenses/by/4.0) Peer-review under the responsibility of Libor Pant ě lejev 2452-3216 © 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC-BY 4.0 license (https://creativecommons.org/licenses/by/4.0) Peer-review under the responsibility of Libor Pant ě lejev

2452-3216 © 2025 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 the responsibility of Libor Pantělejev 10.1016/j.prostr.2025.10.033

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Nomenclature δ

deflection

compressive strength flexural strength

f c f ct

fracture energy

G F

N load cycle 3PBT three-point bending test CMOD crack mouth opening displacement FPZ fracture process zone OPC ordinary Portland cement ULS ultimate limit state

1. Introduction Fatigue failure of concrete caused by cyclic loading is unexpected as it has form of cumulative damage, which is often unintentionally omitted, as the main engineering parameters used in the structural design are compressive or flexural strength of the material. In such case, the structural design considers the fatigue assessment Lee and Barr (2004) as a stress reduction in critical locations produced by the external load, with the structural life related to total number of load cycles N . This approach is directly related to ultimate limit state (ULS) and to stress reduction by percentage of measured static compressive or flexural strengths Korte (2014a), respectively. Relation of stress-load cycles is often referred to as S-N curve or as Wöhler’s curve Basquin (1910). The increasing demand for resilient, economical, and long-lasting civil engineering structures highlights the pressing need to advance our understanding of crack initiation and fracture propagation in concrete under cyclic loading Mena-Alonso (2024). Despite ongoing research, the reliable prediction and mitigation of these fatigue-driven damage mechanisms remain unresolved challenges in both scientific inquiry and engineering practice Korte (2014b). This experimental study set its focus on the understanding of fatigue damage initiation and presents wide range data for assessment of fracture and fatigue resistance of concrete. For this, three-point bending test (3PBT) with a notch is used for static fracture, low-cycle and high-cycle experimental tests. The static fracture tests provide information of fracture energy G F . The low-cycle fatigue tests are controlled crack mouth opening displacement (CMOD) providing the information about the damage progress of each load cycle. Lastly, the high-cycle fatigue tests with a runtime set to 2 × 10 6 are of main focus. These experiments provide information of S-N field, Paris’s law proposed by Paris and Erdogan (1963). 2. Experimental details 2.1. Material Within this study ordinary Portland cement (OPC) was selected as a binder. OPC was mixed with three fractions of natural aggregates: sand 0/4 mm, granite 4/8 mm and granite 8/22 mm. A constant dosage of polycarboxylate superplasticizer Glenium 300 (BASF, Germany) was added to the mixture to achieve good workability. The water to cement ration w/c was 0.3. The mixture composition per 1 m 3 is shown in Table 1.

Table 1. Mixture composition per 1m 3 .

CEM I 42.5R [kg]

Water [kg]

Superplasticizer [kg]

Sand 0/4 [kg]

Granite 4/8 [kg]

Granite 8/22 [kg]

450

135

9

866

290

740

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In order to characterise concrete behaviour static compressive strength f c , static flexural strength f ct and modulus of elasticity E were measured at various age. Measured mechanical properties according to European standards are presented in Table 2.

Table 2. Measured mechanical properties at various age.

Age [days]

f c [MPa]

f ct [MPa

E [GPa]

1

49.9 ± 0.5 91.5 ± 4.3 90.4 ± 4.3 109.6 ± 1.0

-

-

28 91

8.1 ± 0.4 9.3 ± 1.1 10.2 ± 0.7

44.2 ± 1.6 44.7 ± 1.6 46.6 ± 1.3

365

2.2. Geometry and test set- up Three-point bending set-up using beam with rectangular cross-section was selected with dimension of L = 240 mm, B = 40 mm, a 0 = 8 mm and 24 mm and W = 80 mm – See Fig. 1(a). Concrete samples were then tested using servo hydraulic testing rig Instron 8872 with a maximum load capacity 25 kN. Static and cyclic test were performed under a CMOD controlled regime, while monotonic tests were done with a testing frequency of 10Hz. The experimental results were obtained at 365 days age. The sample mounted in testing machine is presented in Fig. 1(b).

(a)

(b)

Fig. 1. Geometry of tested concrete sample – (a) and experimental test set-up – (b).

2.3. Loading conditions In order to comprehensively characterise the fracture behaviour of concrete and tackle the fatigue crack growth, we have selected following the loading cases according to Bakheer (2021) under which the material was tested. In total, three loading cases were selected: a) static fracture with CMOD increasing during the test, b) cyclic with CMOD increasing and decreasing with each load step, and c) monotonic cyclic with defined maximum and minimum force P max and P min , respectively. The selected load cases are presented in Fig. 2

Fig. 2. Loading conditions (a) - static, (b) - cyclic and (c) - monotonic loading.

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3. Experimental results 3.1. Static fracture tests

The maximum loads recorded ranged between 2.5 and 3.2 kN, corresponding to CMOD values at peak between 0.15 and 0.25 mm. The descending branch is characterised by a pronounced loss of load-bearing capacity, which is typical of quasi-brittle fracture behaviour. The shaded envelope in Fig. 3(a) reveals that the variability between specimens is moderate, especially in the pre-peak zones and towards the end of the curve. The widening of the envelope at higher CMOD values reflects the stochastic nature of microcracking in the fracture process zone (FPZ). In total ten load cycles were performed for relative notch depths a / W = 0.3. The longer initial notch depth was chosen to reduce the brittleness of the material and allow test to be performed in full length. The results of low cycle test are presented in Fig. 3(b).

(a)

(b)

Fig. 3. Static fracture tests results (a) and (b) - recorded P-CMOD hysteretic loops.

Using experimental data presented in Fig. 3(a) a mean fracture energy G F = 133 ± 18 N/m was obtained according to RILEM-TCM85 (1985). Such value is within the expected range for conventional concretes of similar compressive strength. The obtained cyclic material response is plotted as Load-CMOD curve, in which the shape of each loading and unloading cycles during a characteristic hysteretic loop behaviour can be observed. A static tests had maximum CMOD value of approx. 1.0 mm, while low-cyclic reached nearly half of this value. The low-cycle fatigue tests exhibit maximum force values comparable to those obtained under static loading conditions, while offering enhanced insight into crack propagation mechanisms during individual loading cycles and the progressive stiffness degradation occurring in the post-peak phase. The shape of the load–CMOD curves characterises the energy dissipation behaviour over the 12-cycle loading steps, capturing the cumulative damage evolution under repeated loading. The results of the low-cycle fatigue test are illustrated by a representative hysteresis loop, where each cycle facilitates fracture characterisation through the analysis of unloading stiffness degradation. This degradation is quantified by the damage parameter ω, defined as follows: =1 − 0 , (1) where E 0 is the initial elastic stiffness of the material, and E i is the stiffness corresponding to i -th hysteresis loop of the load-CMOD curve. A detailed characterisation of the concrete’s flexural fracture response under cyclic loading—focusing on stiffness degradation observed at each load step or within individual hysteresis loops—was carried out following the methodology described in Hori (1992) and Baktheer(2021). This parameter quantifies cyclic stiffness degradation over the loading history, with its evolution across loading cycles shown in Fig. 4.

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Fig. 4: Obtained damage parameter ω for low-cycle fatigue tests.

Fig. 4 shows the progressive damage ω evolution during low-cycle loading indicating non-linear behaviour after reaching CMOD of approx. 0.05 mm which corresponds to P max at peak load from fracture static tests as presented in Fig. 3(a). Similar results were obtained by Baktheer (2024) 3.2. High -cycle f atigue tests Material’s fatigue resistance presented by measured S-N curve covers wide range of the data from low-cycle to high-cycle fatigue Fig. 5(a). The following coefficients were obtained: the slope B of -0.017, which could be considered as standard for HPC concrete as the study Miarka et. al. (2022) measured similar value of -0.017. and coefficient A corresponding to static strength of 5.574 MPa.

(a)

(b)

Fig. 5. High-cycle fatigue results – (a) S-N curve and (b) – Paris’ law.

Obtained values are with the expected range, for normal type of concrete with compressive strength f c < 60 MPa coefficient B is ranging from -0.03 to -0.04 see e.g. Šimonová (2021) and Miarka (2025) showing more rapid mechanical degradation due to cyclic load. Experimental results from the S–N curve indicate that a reduction of around 30% in static strength is necessary to attain the fatigue strength limit at 2 × 10 6 load cycles. The obtain Paris’s law constants are slope m with value of 15.036 and constant C with value of -8.067. The parameters characterizing fatigue crack growth rate in concrete are again in previously observed range see Bažant and Schell (1993).

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Conclusions This study re-evaluated the fracture and fatigue behaviour of high-performance concrete (HPC) under static, low cycle, and high-cycle loading at 365 days of age. Notched three-point bending tests were used, using either CMOD controlled mode for static and low-cycle tests or with a loading frequency of 10 Hz for high-cycle fatigue tests. While static loading produced a relatively homogeneous response, cyclic loading revealed greater heterogeneity, reflecting the effects of fatigue damage and meso-structural variability. The static tests provided the fracture energy, while the low-cycle fatigue tests evaluated the damage parameter, and the high-cycle regime was characterised through S–N and Paris law crack growth curves. The obtained experimental results align well with previously published data, confirming the reliability of the testing methodology. The S–N curve revealed that a 30% reduction strength was necessary to reach the fatigue limit of 2 × 10 6 . Acknowledgements This paper was created as a part of project No.CZ.02.01.01/00/22_008/0004631 Materials and technologies for sustainable development within the OP JAK Program financed by the European Union and from the state budget of the Czech Republic as well as the financial support from the Czech Science Foundation under project no. 25-15755S. Data availability The data used in this study are available at: https://doi.org/10.5281/zenodo.15341786 References Basquin, O.H., 1910. The exponential law of endurance tests. Am. Soc. for Test. and Mat. Proceedings 10, 625-630. Bazant, Z.P., Schell W.F., 1993. Fatigue fracture of high-strength concrete and size effect. ACI Mater. J. 90:472. Baktheer, A. Becks, H., 2021. Fracture mechanics based interpretation of the load sequence effect in the flexural fatigue behavior of concrete using digital image correlation. Construction and Building Materials, 307, 124817. Baktheer, E. Martínez-Pañeda, F. Aldakheel, 2024. Phase field cohesive zone modeling for fatigue crack propagation in quasi-brittle materials, Computer Methods in Applied Mechanics and Engineering 422, 116834. RILEM-TCM85, 1985. Determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams Materials and Structures 18(4), 287-290. Horii, H.C. Shin, T.M. Pallewatta, 1992. Mechanism of fatigue crack growth in concrete, Cemement Concrete Composites 14, 83–89. Á. Mena-Alonso, D.C. González, J. Mínguez, M.A. Vicentem, 2024. Size effect on the flexural fatigue behavior of high-strength plain and fiber- reinforced concrete, Construction and Building Materials 411, 134424. S Korte, V Boel, W De Corte, G De Schutter, 2014a. Static and fatigue fracture mechanics properties of self-compacting concrete using three-point bending tests and wedge-splitting tests, Construction and Building Materials 57, 1-8. S. Korte, V. Boel, W. De Corte, G. De Schutter, 2014b. Behaviour of fatigue loaded self-compacting concrete compared to vibrated concrete, Structural Concrete 15 575–589. Lee, M.K., Barr, B.I.G., 2004. An overview of the fatigue behaviour of plain and fibre reinforced concrete. Cement and Concrete Composites 26, 299-305. Miarka, P., Seitl S., Bílek, V., Cifuentes Bulte H., 2022. Assessment of fatigue resistance of concrete: S-N curves to the Paris law curves. Construction and Building Materials 341, 127811. Miarka P., Šimonová H., Kucharczyková B., Seitl S., Poletanovic B., Merta I. 2025. Optimisation of fine RCA content in mortar mixture based on the long-term fracture and fatigue tests. Construction and Building Materials 481, 141371 Paris, P., Erdogan, F., 1963. A Critical Analysis of Crack Propagation Laws, Journal of Basic Engineering, 85, 528-533 Šimonová, H., Kucharczyková, B., Bílek, V., Malíková, L., Miarka, P., Lipowczan, M. 2021. Mechanical fracture and fatigue characteristics of fine-grained composite based on sodium hydroxide-activated slag cured under high relative humidity. Applied Sciences - Basel, 11(1), 1–20.

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Eleventh International Conference on Materials Structure and Micromechanics of Fracture Assessment of the plastic zone magnitude around the crack tip with uniformly distributed, continuous load acting over the crack surface Eleventh International Conference on Materials Structure and Micromechanics of Fracture Assessment of the plastic zone magnitude around the crack tip with uniformly distributed, continuous load acting over the crack surface

Dragan Pustaić a , Martina Lovrenić - Jugović a,b, * a University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Institute of Applied Mechanics, Ivana Lučića 5, 10 000 Zagreb, Croatia b University of Zagreb, Faculty of Metallurgy, Department of Mechanical Metallurgy, Aleja narodnih heroja 3, 44 000 Sisak, Croatia Dragan Pustaić a , Martina Lovrenić - Jugović a,b, * a University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Institute of Applied Mechanics, Ivana Lučića 5, 10 000 Zagreb, Croatia b University of Zagreb, Faculty of Metallurgy, Department of Mechanical Metallurgy, Aleja narodnih heroja 3, 44 000 Sisak, Croatia

© 2025 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 the responsibility of Libor Pantělejev © 2025 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 the responsibility of Libor Pant ě lejev Keywords: Dugdale´s cohesive model; straight crack in the plate; uniformly distributed, continuous loading over the crack surface; isotropic and non-linear hardening of a plate material; strain hardening exponent; stress intensity factor; plastic zone magnitude around a crack tip; exact analytical solution. Abstract The thin, infinite plate contains a discontinuity in form of straight crack of the length, 2 a . The uniformly distributed, continuous loading, p 0 , acts across the crack surface and is successively and gradually increasing. The loading, p 0 , acts in-plane of the plate (same as the crack) and opens the crack. The plane state of stress, ( σ x , σ y , τ xy ), is assumed in the plate. The plate is made of homogeneous and ductile metallic material which is, at the plastic deformation, isotropic and non-linear hardened in accordance with the Ramberg-Osgood´s hardening law. At the crack loading, the small plastic zones around its tips are formed, which are spread with increasing of the load, p 0 . The goal of this article was to investigate the correlation between the increase of loading, p 0 , and the increase of the plastic zone magnitude, r p . The problem was solved fully exactly in analytical way. In order to solve the problem the cohesive Dugdale´s model was used. The original expressions for the stress intensity factors (SIFs) from the external loads, K ext , and from the cohesive stresses, K coh , were derived. The solutions are given through the special Gamma, the Hypergeometric and the inverse trigonometric functions . All numerical computations and diagrams were done by using the mathematical software Wolfram Mathematica. © 2025 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 the responsibility of Libor Pant ě lejev Keywords: Dugdale´s cohesive model; straight crack in the plate; uniformly distributed, continuous loading over the crack surface; isotropic and non-linear hardening of a plate material; strain hardening exponent; stress intensity factor; plastic zone magnitude around a crack tip; exact analytical solution. Abstract The thin, infinite plate contains a discontinuity in form of straight crack of the length, 2 a . The uniformly distributed, continuous loading, p 0 , acts across the crack surface and is successively and gradually increasing. The loading, p 0 , acts in-plane of the plate (same as the crack) and opens the crack. The plane state of stress, ( σ x , σ y , τ xy ), is assumed in the plate. The plate is made of homogeneous and ductile metallic material which is, at the plastic deformation, isotropic and non-linear hardened in accordance with the Ramberg-Osgood´s hardening law. At the crack loading, the small plastic zones around its tips are formed, which are spread with increasing of the load, p 0 . The goal of this article was to investigate the correlation between the increase of loading, p 0 , and the increase of the plastic zone magnitude, r p . The problem was solved fully exactly in analytical way. In order to solve the problem the cohesive Dugdale´s model was used. The original expressions for the stress intensity factors (SIFs) from the external loads, K ext , and from the cohesive stresses, K coh , were derived. The solutions are given through the special Gamma, the Hypergeometric and the inverse trigonometric functions . All numerical computations and diagrams were done by using the mathematical software Wolfram Mathematica.

* Corresponding author. Tel.: +0-385-1-48-54-168; fax: +0-000-000-0000 . E-mail address: dragan.pustaic@fsb.unizg.hr * Corresponding author. Tel.: +0-385-1-48-54-168; fax: +0-000-000-0000 . E-mail address: dragan.pustaic@fsb.unizg.hr

2452-3216 © 2025 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 the responsibility of Libor Pant ě lejev 2452-3216 © 2025 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 the responsibility of Libor Pant ě lejev

2452-3216 © 2025 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 the responsibility of Libor Pantělejev 10.1016/j.prostr.2025.10.036