PSI - Issue 28

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1st Virtual European Conference on Fracture - VECF1

Volume 2 8 • 2020

ISSN 2452-3216

ELSEVIER

1st Virtual European Conference on Fracture - VECF1

Guest Editors: Francesco I acoviello Aleksandar Sedmak L iviu Marsavina Bam b er Blackma n Giuse pp e Andrea Ferro Valer y Shl y annikov P er St å hle Zhiliang Zhang P edro M . G .P. Moreira Ž eljko Bo ž ic L eslie Banks - Sills

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1st Virtual European Conference on Fracture Preface 1st irtual European Conference on Fracture reface

© 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the European Structural Integrity Society (ESIS) ExCo © 2020 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the European Structural Integrity Society (ESIS) ExCo Keywords: Preface, Fracture, Structural Integrity Francesco Iacoviello* a , leksandar Sed ak b , Liviu arsavina c , a ber lack an d , Giuseppe ndrea Ferro e , alery Shlyannikov f , Per Ståhle g , Zhiliang Zhang h , Pedro . . P. oreira i , Željko ožić j , Leslie anks-Sills k a Università di Cassino e del Lazio Meridionale, via G. DI Biasio 43, 03043, Cassino (FR), Italy b University of Belgrade, Kraljice Marije 16, 11000 Belgrade, Serbia c University Politehnica Timisoara, Blvd. M. Viteazu, Nr. 1, Timisoara 300222, Romania d Department of Mechanical Engineering City & Guilds Building Imperial College London South Kensington Campus London SW7 2AZ, UK e Dept Structural Engg & Geotechnics, Politecnico di Torino Corso Duca degli Abruzzi, 24, 10129 - Torino, Italy, Italy f Kazan Scientific Centre, Russian Academy of Science, Lobachevsky Steet, 2/31, 420111. Kazan, Russia g Div. of Solid Mechanics, Faculty of Engineering, LTH, Lund University, Ole Römers väg 1, SE-223 63 Lund, Sweden h NTNU Nanomechanical Lab, Dept. of Structural Engineering, Norwegian University of Science and Technology (NTNU), N-7491 Trondheim, Norway i INEGI - Institute of Science and Innovation in Mechanical and Industrial Engineering, Rua Dr. Roberto Frias 400, 4200-465 Porto, Portugal j Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lu č i ć a 5, 10000 Zagreb, Croatia k School of Mechanical Engineering, Tel Aviv University, Ramat Aviv 6997801, Israel, Israel © 2020 The Authors. Published by ELSE IER 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 European Structural Integrity Society (ESIS) ExCo Keywords: Preface, Fracture, Structural Integrity Francesco Iacoviello* a , Aleksandar Sedmak b , Liviu Marsavina c , Bamber Blackman d , Giuseppe Andrea Ferro e , Valery Shlyannikov f , Per Ståhle g , Zhiliang Zhang h , Pedro M. G. P. Moreira i , Željko Božić j , Leslie Banks-Sills k a Università di Cassino e del Lazio Meridionale, via G. DI Biasio 43, 03043, Cassino (FR), Italy b University of Belgrade, Kraljice Marije 16, 11000 Belgrade, Serbia c University Politehnica Timisoara, Blvd. M. Viteazu, Nr. 1, Timisoara 300222, Romania d Department of Mechanical Engineering City & Guilds Building Imperial College London South Kensington Campus London SW7 2AZ, UK e Dept Structural Engg & Geotechnics, Politecnico di Torino Corso Duca degli Abruzzi, 24, 10129 - Torino, Italy, Italy f Kazan Scientific Centre, Russian Academy of Science, Lobachevsky Steet, 2/31, 420111. Kazan, Russia g Div. of Solid Mechanics, Faculty of Engineering, LTH, Lund University, Ole Römers väg 1, SE-223 63 Lund, Sweden h NTNU Nanomechanical Lab, Dept. of Structural Engineering, Norwegian University of Science and Technology (NTNU), N-7491 Trondheim, Norway i INEGI - Institute of Science and Innovation in Mechanical and Industrial Engineering, Rua Dr. Roberto Frias 400, 4200-465 Porto, Portugal j Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lu č i ć a 5, 10000 Zagreb, Croatia k School of Mechanical Engineering, Tel Aviv University, Ramat Aviv 6997801, Israel, Israel 1. Preface Reading the first lines of the European Structural Integrity Society (ESIS) statutes, we can find that: The aim of ESIS is to develop and extend knowledge in all aspects of Structural Integrity and disseminating that knowledge world-wide with the objective of improving the safety and performance of engineering equipment, individual components and structures. 1. Preface Reading the first lines of the European Structural Integrity Society (ESIS) statutes, we can find that: The aim of ESIS is to develop and extend knowledge in all aspects of Structural Integrity and disseminating that knowledge world-wide with the objective of improving the safety and performance of engineering equipment, individual components and structures.

* Corresponding author. Tel.: +39.07762993681. E-mail address: iacoviello@unicas.it * Corresponding author. Tel.: +39.07762993681. E-mail address: iacoviello@unicas.it

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

Francesco Iacoviello et al. / Procedia Structural Integrity 28 (2020) 1–2 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Specifically: To foster research and collaboration into the prevention of failure of engineering materials, components and structures under mechanical loadings and associated phenomena. To encourage interdisciplinary research into the physical behaviour of engineering components, materials and structures. To develop new testing methods, numerical methods, and engineering estimation methods for structural integrity assessment. To improve engineering designs. To improve manufacturing, inspection and maintenance procedures. To develop methods for interpretation of material property data, probabilistic assessment and tools for failure prevention and management. To disseminate knowledge, by means of scientific publications, procedure documents, and referring developments to national and international code-making bodies where relevant. To educate young engineers and scientists in structural integrity matters. In order to achieve these ambitious goals, ESIS is structured in about thirty National Groups and about twenty Technical Committees, and in the last decades organized dozens of international events, publishing dozens of Proceedings and Technical notes, special issues and about thirty issues on Procedia Structural Integrity as well as YouTube channel with thousands of videopresentations and lectures from the last few summer schools. The main ESIS event is the European Conference on Fracture (ECF): this is a biennial conference that is usually organized by a National Group at beautiful venues in Europe. The previous ECF event was organized in 2018 in Belgrade, Serbia, and in 2020 the ECF23 was scheduled in Funchal, Madeira (Portugal). But, unfortunately … “no one expects the Spanish Inquisition”! … at the beginning of 2020, the problems connected to the Covid 19 forced the ESIS Executive Committee to postpone the ECF23 in Funchal to 2022 and, for the first time in the ESIS history, the ExCo decided to organize a Virtual ECF and a virtual Summer School, using the Google Suite platform. It was necessary to create a new paradigm for the organization of these virtual events. The ExCO decided to: - Organize the largest summer school ever organized by ESIS. All the Technical Committees were encouraged to organize one day on the basics of their topics … eleven TCs accepted the challenge and organized one day of activity each, ranging from Fatigue to Numerical Methods, from Polymers to Concrete. Almost all the presentations were recorded and they are available in the dedicated playlist in the YouTube channel: https://www.youtube.com/playlist?list=PLqdhWx9Ll8U7DJNegq0qoQl0aK8VXqExk Participants were allowed to register to different activities, in a sort of “à la carte” summer school. The result was really exciting: about two hundred and fifty participants were registered to the different activities organized in the frame of the ESIS summer school, the 1 st Virtual ESIS Summer School (VESS1). - Organize a Virtual ECF, trying to improve as much as possible the importance of the discussions. For this reason, all the participants were invited to upload their presentations before the conference and watch the videopresentations of interest before the conference. All the videopresentations are available in the dedicated YouTube playlist: https://www.youtube.com/playlist?list=PLqdhWx9Ll8U7Hrv_Hu-qLFAXE7QM-A2RT Furthermore, in the case of the Virtual ECF, the Technical Committees support was crucial: nine prestigious invited lecturers, twenty sessions, 320 presentations, more than four hundred participants and really interesting and engaging discussions were the final results of the 1 st Virtual European Conference on Fracture (VECF1). The ESIS Ex-Co wishes to warmly acknowledge all the invited lecturers, all the Technical Committees Chairpersons, all the participants, all the sessions chairpersons: without their enthusiastic help, it would not have been possible to organize these two events in a few months. We also thought that publishing Procedia Structural Integrity after VECF1 is a “must do” activity, so we have invited all presenting authors to submit a paper. To our great satisfaction, 274 papers are submitted, proving once again great success of this event. We are all enthusiastic about these great results but … we are looking forward to meeting our community again in presence at the first possible occasion and, the most enthusiastically, in Funchal, in 2022, for the ECF23. The 2018-2022 ESIS Executive Committee

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* Corresponding author. Tel.: +39-02-2399-8630; fax: +39-02-2399-8263. E-mail address: andrea.manes@polimi.it

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Keywords: epoxy resin; high strain rate; fracture mechanism; zero-thickness cohesive elements

1. Introduction During the service life of polymer materials, tensile loading is hard to avoid, especially considering the fracture behaviour evoked by the tensile stress (Ma et al., 2020). However, the investigation of the tensile properties of polymer materials is complex because their mechanical properties varies due to the presence of very influential factors, such as material uncertainty (Li et al., 2020a), strain rate (Li et al., 2020b; Zotti et al., 2020) and inevitable defects (Zhou et al., 2005). The tensile behaviour of RTM-6, known as a highly cross-linked thermoset, commonly applied as coating and matrix of composites due to its high strength and temperature resistance, has been found to be complicated especially under various strain rates. A proper model, which replicates the tensile behaviour of RTM-6, is required. Such a model might be helpful in uncovering the potential mechanism of the strain rate effect on polymer materials. Experimental investigations on the tensile properties of RTM-6 have been widely conducted at various strain rates. In quasi-static tests, RTM-6 epoxy resin presents a nonlinear behaviour after the yield stress (Chevalier et al., 2016; Morelle et al., 2017), but under dynamic conditions the tensile behaviour is totally different according to the work of Gerlach et al. (Gerlach et al., 2008), which focussed on the high strain rate response of RTM-6 epoxy resin using split Hopkinson tensile bar (SHTP) tests. A brittle behaviour, characterised by high strength and Young’s modulus though low failure strain, can be obtained under high strain rates, while dynamic conditions lead to a reduction of nonlinearity. Such behaviour is not unique for thermoset polymers, e.g., PMMA has similar stress-strain curves under tension considering various strain rates (Wu et al., 2004), and therefore the investigation of the strain rate effect on the tensile mechanical property of RTM-6 epoxy resin can help to uncover a more generic mechanism. Usually, during a tensile test, final fracture is preceded by microcracking. The observed stress-strain response is the result of both the materials’ tensile and fracture behaviours. The analysis of the fracture behaviour during tension is thus of great importance, even though it is difficult due to the high speed of the fracturing process. However, with the recent development of detection methods, fracture during tension can be investigated, aided by digital image correlation (DIC) (Li et al., 2020a) and post analysis by microscopy (Morelle et al., 2017). The analysis of microscopy images of the fracture surface revealed that the defects of the brittle polymeric materials, which are inevitable due to the manufacturing process, are the main reason for the different behaviour under various strain rates (Zhou et al., 2005). Even though avoiding the effect of defects in tests on polymer materials is almost impossible, small samples are always used in related experiments to reduce the influence of defects. As for the modelling strategies, a cohesive model is one of the most efficient methods to capture the facture and failure behaviours of materials. Cohesive models have been widely used for the simulation of the delamination in composite materials when applied to cohesive elements (Li et al., 2019) or contact models (Ma et al., 2019). The cohesive models are also usually used to model the interface, which does not physically exist, but has an essential effect on the results. Replication of cracks meets this application: a crack does not exist until a fracture initiates. Consequently, the cohesive model was able to mimic the crack in fracture tests with assistance of common elements (Tabiei and Zhang, 2018). Furthermore, a modified cohesive model can replicate the defected materials as conducted by Zhou et al. (Zhou et al., 2005). However, the drawback of the use of the cohesive model for crack replication is the extensive calculation cost because, considering the random nature of the crack generation, the cohesive model should be inserted between each two adjacent elements, which significantly increases the calculation time. The objective of the present work is to investigate the tensile properties of RTM-6 epoxy resin under different strain rates and to create an in-depth understanding of the potential mechanism behind the strain rate effect through numerical modelling. For this purposes, tensile tests on small samples of RTM-6 epoxy resin with a SHTB facility were conducted in the present work and were monitored by high-speed DIC. This provides reliable experimental data of the strain rate effect, while the fracture behaviour can be captured by the high-speed cameras. Assuming that the strain rate effect can be attributed to activation of defects, a numerical model using zero-thickness cohesive elements was developed with two cohesive models for materials with and without defects assigned. Through controlling the number of defective cohesive elements, the tensile behaviour of RTM-6 epoxy resin under various strain rates can be replicated, which may validate the assumption that the strain rate effect is due to the activation of defects in brittle polymeric materials.

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2. Materials and experimental methods 2.1. Specimen material and geometry

The RTM-6 epoxy resin used in this study was supplied by Hexcel composites. It consists of tetra-functional epoxy resin tetraglycidyl methylene dianiline (TGMDA), two hardeners 4,4′-methylenebis (2,6-diethylaniline) and 4,4′- methylenebis(2-isopropyl-6-methylaniline). Mixed resin and hardener were poured into long cylindrical rods which were then mechanically machined into small dog-bone samples. Threaded aluminum caps were glued on the shoulders of the dog-bone sample, in order to be gripped by the Hopkinson bars during testing. Figure 1 shows the dimensions of the RTM6 epoxy samples used, and a sample with threaded caps.

Figure 1 Dimensions of the tensile sample used (left) and image of the sample with the threaded caps (right)

2.2. Quasi-static and high strain rate setups Referenced quasi-static tensile tests were performed using a Deben micro tensile testing stage. The load was measured using a 1000 N loadcell. Tensile tests were performed at a testing speed of 1mm/min. Local displacements and strains were measured on the surface of the samples using 3D digital image correlation technique. The optical setup consisted of two 5 megapixel cameras equipped with two fixed focus lenses of 100 mm focal length each. Samples were painted with a speckle pattern prior to testing. Figure 2 shows the quasi-static setup used. High strain rate tensile tests were performed using the SHTB facility available at Ghent University. The setup consisted of two long aluminum bars (input and output bars) with the sample fixed in between. The diameter of the input bar was 25 mm while the diameter of the output bar was 12 mm. Small threaded end tabs were provided at the ends of both bars, in order to fix the tensile samples with the threaded caps. The average stress, strain and strain rate in the sample can be calculated from strain signals measured directly on the bars based on the one-dimensional wave propagation analysis. Additional details on the setup, the measurements, and the post processing of the data can be found in a previous work by Elmahdy et al. (Elmahdy and Verleysen, 2019). Similar to the quasi-static tests, local displacements and strains were measured using high speed stereo digital image correlation (high-speed 3D DIC). The system consisted of two Photron Mini AX200 high speed cameras, fitted with two fixed focus lenses of 90 mm focal length. Figure 3 shows the high strain rate setup used. Post processing of the images was performed using MatchID commercial software. The axial tensile strain was extracted from an area of 2x5 mm 2 around the center of the sample. The correlation criterion used for processing of the images was zero normalized sum of square differences (ZNSSD).

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Figure 2 Quasi-static setup used with detail of the speckled sample (bottom left)

Figure 3 Experimental setups and the sample employed (static and dynamic)

2.3. Experimental results Figure 4 shows an example of the engineering stress-engineering strain response of RTM-6 epoxy resin in tension at different strain rates. The solid lines indicate a second-degree polynomial fit, with R 2 values above 0.8. The achieved strain rates were in the range of 0.003 s -1 to 160 s -1 . The RTM-6 epoxy resin was strain rate sensitive in tension. Indeed, an increase of the strain rate led to an increase of the stiffness and strength of the epoxy but decreased the fracture strain. The tensile behavior of RTM-6 epoxy at the quasi-static range showed a highly non-linear response, compared to the nearly linear response at high strain rates. Similar behavior was also reported by Morelle et al. (Morelle et al., 2017) at quasi-static strain rates, and by Gerlach et al. (Gerlach et al., 2008) at high strain rates.

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Figure 4 Experimental engineering stress-strain response of RTM6 epoxy tensile tests at various strain rates

3. Numerical approach 3.1. FE model

The finite element (FE) model used in the present work is presented in Figure 5. The centre of the gauge region of the tensile sample was modelled with a 2D model because the centre of the sample can be regarded as the main region representing the mechanical behaviour of the whole sample. The Belytschko-Tsay shell element was employed in the present model with a linear elastic model. To replicate the fracture behaviour of the RTM-6 epoxy resin, zero-thickness cohesive elements (ELFORM=29 in LS-DYNA) were inserted between each pair of the normal shell elements. In view that the fracture behaviour of the present work is controlled by the cohesive elements, no failure model was assigned to the shell elements for simplification. In the present work, two cohesive models were used for modelling the perfect material and material containing defects with more details provided in Section 3.3. Additionally, the loads applied on the sample was the displacement along y-axial, as shown in Figure 5, identical to the experimental activities and the FEM model was built through LS-DYNA.

Figure 5 FE model for the present work

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3.2. Mesh morphology As presented in Figure 5, the mesh morphology was arbitrary in the model. Three typical mesh morphologies considered in the present work are listed in Figure 6. Cohesive elements were built to consider the effect of defects, which are formed randomly in the material and, hence, an arbitrary mesh was appropriate instead of a regular mesh. However, as the generation of the arbitrary mesh was uncontrollable, two mesh types, denoted as Mesh-A and Mesh B in Figure 6, were obtained. According to the results from the tensile simulations with the two arbitrary mesh morphologies presented in Figure 6, the results on the tensile stress-strain curves with different arbitrary meshes are comparable. However, the more arbitrary mesh, i.e. Mesh-B, can provide better fracture predictions due to the random feature of the defects in polymer materials and, thus, Mesh-B was further employed.

Figure 6 Study of the effect of various mesh morphologies

3.3. Material model To study the relationship between the effect of the strain rate and defects, two different cohesive models were created to replicate the mechanical behaviour of the material without and with defects, as type-I and type-II presented in Figure 7, while the linear elastic material model was applied on the normal shell elements with Young’s modulus and Poisson ratio equal to 2900 MPa and 0.36. Generally, G c and σ f are necessary to determine the shape of cohesive model, while ε f can be calculated accordingly, therefore, only G c and σ f can be regarded as the input data in the present model. In the present work, cohesive models were built through MAT_186 (*MAT_COHESIVE_GENERAL) in LS DYNA. The type-I cohesive model was used to capture the mechanical behaviour of the pure RTM-6 epoxy resin, in perfect condition without defects. The nonlinear behaviour, when �� in Figure 7, was used to capture the nonlinear behaviour of RTM-6 under quasi-static conditions. All related parameters were obtained through fitting of the experimental results with the quasi-static model. The type-II cohesive model is utilized to mimic the material with defects. Defects can always lead to a stress concentration, producing an immediate peak in the material behaviour, which is described as the initial peak in the material model, type-II cohesive model. The comparison of the two models showed that the type-II model has a quicker failure, i.e. � � � � ( � � �� ) in Figure 7, to replicate the accelerated failure process due to the presence of defects. Furthermore, the defected cohesive model, i.e. the type-II cohesive model, did not describe the behaviour of the defect itself, but of the material containing defects without considering the exact amount of defects. Regarding the parameters involved in the present cohesive models: � � �� ⁄ (Gerlach et al., 2008; Tserpes, 2011; Zotti et al., 2020), where τ f is used to describe the shear strength of the cohesive elements and the shear behaviour was reproduced in the same way as tension behaviour. Herein, it is noted that the value of the failure stress, σ f , is large because it is used to model the material in perfect condition, which is difficult to obtain. Therefore, the

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largest value presented in literature under various conditions (Gerlach et al., 2008) was employed. Herein, the proportion of cohesive elements with the type-II cohesive model was altered to obtain the related change on the stress strain curves and the fracture behaviour of the simulated results compared with the experimental results at various strain rates. Thus, the aim to bridge the effect of strain rate and defects can be achieved. Replaced by the proportion of defects, the effect of the strain rate can be estimated in the numerical model, indicating the model in the present work is time independent. As a result, the implicit solver was used to conduct all the calculations in the present study. It took around 10 min for each simulation with the implicit solver (single CPU of I7-875 K 2.93 GHz 4 core/8 threads and 16 GB RAM), which is more efficient and significantly reduces the calculation time compared to the explicit solver usually employed in numerical studies of strain rate.

Figure 7 Cohesive models used in present work to present the material with (Type II) and without (Type I) the defects

4. Results and discussion 4.1. Effect of the proportion of defects

The simulated results of the stress-strain curves under tension with different proportions of the defective cohesive elements are shown in Figure 8. The peak stress and modulus increase with the increase of the proportion of defective cohesive elements. Additionally, the peak stress of the curves is actually smaller than the tensile strength of the cohesive model, indicating the shear failure is the main failure mechanism for the present work. A high proportion can reduce the nonlinearity in the numerical model. Furthermore, the trend of the change in the strength, modulus and nonlinearity with the proportion is identical to the change in those quantities with the strain rate, which provides feasibility to employ the proportion to replace the effect of strain rate in the numerical model. 4.2. Comparison with experimental data No defective element was present in the model of the quasi-static case, i.e. 0% type-II cohesive elements. However, one single defective cohesive element was inserted into the centre to guarantee the crack initiation as the failure of RTM-6 epoxy resin always initiates from defects (Zhou et al., 2005). As presented in Figure 9, the tensile curve from the simulation showed good agreement with the experimental data, including in the nonlinear region. Regarding the fracture behaviour, a stable crack was found in the experiment, which can be replicated through the failure of the cohesive elements, as the crack path marked by the red line in Figure 9. In summary, the numerical results fitted the experimental data well with respects to the stress history and the fracture behaviour.

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Figure 8 Stress-strain curves with different proportions of the defective cohesive elements

Figure 9 Comparison of tensile curves and fracture behaviour between the results from the numerical model and experiments for the quasi-static case

To obtain good agreement with the test results when the strain rate was equal to 133 /s, the proportion of randomly distributed defective cohesive elements should reach 80%. According to our investigation, the distribution only minimally affects the numerical results, so a typical case of the numerical model was selected for the comparison with the experimental data as shown in Figure 10. The tensile curve from the numerical model is comparable with the experimental curve. Considering the fracture behaviour, many discontinuous cracks were identified by the numerical model (marked as red lines in Figure 10). This phenomenon, denoted as “multi-cracks” in the present work, indicates that the failure was so unstable that more than one crack initiated. During the dynamic tests under this strain rate, two failure positions were recorded by the high-speed camera at the peak stress, which were also reported by Gerlach et al. (Gerlach et al., 2008) and can validate the multi-cracks predicted by the numerical model.

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Figure 10 Comparison of the tensile curves and fracture behaviour between the results from the numerical model and experiments at a strain rate of 130 /s

The proportion of the defective cohesive elements should be 94% to fit the tensile curves with the strain rate equal to 160 /s. As presented in Figure 11, the stress-strain curves are in very close resemblance if the oscillations from the experimental data are ignored. Additionally, the phenomenon of multi-cracks was also obtained in the numerical results, see Figure 11. The fragments recorded and marked by red circles in Figure 11 confirmed the presence of the multi-cracks in the experiments. Considering all these comparable results, the present model is considered to be validated.

Figure 11 Comparison of the tensile curves and fracture behaviour between the results from numerical model and experiments under the strain rate of 160 /s

4.3. Discussion of the possible mechanism of the strain rate effect The fracture surface was analysed through optical microscopic inspection (VHX-2000E, KEYENCE). As presented in Figure 12(a), the initiation of the failure of the RTM-6 epoxy resin was due to the existence of defects near the exterior surface, marked by a red circle. Similar phenomena were also reported in (Li et al., 2020b) for tensile tests. The presence of defects cannot be avoided, especially for polymer materials, regardless of the manufacturing process applied. As a result, defects are the key for the failure of the brittle polymeric materials. According to the results presented, the proportion of defects can be used to replicate the effect of the strain rate under tensile loading with respect to the stress-strain curves and the fracture phenomena. The obtained results can also be regarded as a validation

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of the assumption of the relationship between the effect of strain rate and defects. The mechanical response of RTM 6 resin under different strain rates can be attributed to the existing defects: as the strain rate increases, the modulus increases according to the experimental stress-strain curves, indicating more energy absorbed by the material with the same strain level. Based on the present model considering defects, more energy can be absorbed as the increase of the proportion of defects, which fits the results from the experiments. Furthermore, the reduction of the nonlinearity can also correspond to the increasing amount of the activated defects, which may cause a quick failure. All of these indicate that high strain rate may activate more defects. Additionally, multi-cracks obtained from the numerical model, presented as more than one failure position or fragments during experimental tensile loading and observed as a change of the surface roughness shown in Figure 12(b), can also validate the previous explanation.

(a)

(b)

Figure 12 Inspection of the fracture surface: (a) optical microscopy image; (b) roughness analysis

5. Conclusion To bridge the effect of the strain rate and the defects, a numerical model was built in the present work with zero thickness cohesive elements based on the experimental results of tensile tests under static and high strain rates. By changing the proportion of the defective cohesive model, the results from the numerical model can achieve good agreement with experimental data with respect to the stress-strain history and the fracture behaviour. The following main conclusions can be drawn:  The fitting of the experimental curves, by means of the proportion of defective elements, shows that more defects seems to be activated as the test strain rate increases, which leads to more cracks prior to the collapse of the samples under high strain rates.  As the amount of the defective cohesive elements increases, the strength and modulus increase while the failure strain decreases. Again, this is in a good agreement with the experimental results.  The presence of defects seems to be one of the reasons for the strain rate effect of the brittle polymeric material (RTM-6 epoxy). Additionally, to build a comprehensive numerical method, according to the present work further developments are still required to:  Link the proportion of defective elements to physical parameters.  Apply the method to complex loading conditions and large structures in order to check the transferability.

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Acknowledgement The authors would like to thank the Italian Ministry of Education, University and Research, through the project of the Department of Excellence LIS4.0 (Integrated Laboratory for Lightweight and Smart Structures). The experimental work was funded by the European Union’s Horizon 2020 program through the EXTREME project, grant number 636549. Also, thanks are expressed to Dr. Aldobenedetto Zotti, Dr. Anna Borriello, and Dr. Mauro Zarrelli of the Italian Research Council-Institute of Polymers, Composites, and Biomaterials for providing the testing materials. A special thanks goes to Eliseo Hernández Durán, from Ghent University, for his valuable support for the microscopic Chevalier, J., Morelle, X.P., Bailly, C., Camanho, P.P., Pardoen, T., Lani, F., 2016. Micro-mechanics based pressure dependent failure model for highly cross-linked epoxy resins. Eng. Fract. Mech. 158, 1–12. https://doi.org/10.1016/J.ENGFRACMECH.2016.02.039 Elmahdy, A., Verleysen, P., 2019. Tensile behavior of woven basalt fiber reinforced composites at high strain rates. Polym. Test. 76, 207–221. https://doi.org/10.1016/j.polymertesting.2019.03.016 Gerlach, R., Siviour, C.R., Petrinic, N., Wiegand, J., 2008. Experimental characterisation and constitutive modelling of RTM-6 resin under impact loading. Polymer (Guildf). 49, 2728–2737. https://doi.org/10.1016/J.POLYMER.2008.04.018 Li, X., Kupski, J., Teixeira De Freitas, S., Benedictus, R., Zarouchas, D., 2020a. Unfolding the early fatigue damage process for CFRP cross ply laminates. Int. J. Fatigue 140, 105820. https://doi.org/10.1016/j.ijfatigue.2020.105820 Li, X., Ma, D., Liu, H., Tan, W., Gong, X., Zhang, C., Li, Y., 2019. Assessment of failure criteria and damage evolution methods for composite laminates under low-velocity impact. Compos. Struct. 207, 727–739. https://doi.org/10.1016/J.COMPSTRUCT.2018.09.093 Li, X., Saeedifar, M., Benedictus, R., Zarouchas, D., 2020b. Damage Accumulation Analysis of CFRP Cross-Ply Laminates under Different Tensile Loading Rates. Compos. Part C Open Access 100005. https://doi.org/10.1016/j.jcomc.2020.100005 Ma, D., Esmaeili, A., Manes, A., Sbarufatti, C., Jiménez-Suárez, A., Giglio, M., Hamouda, A.M., 2020. Numerical study of static and dynamic fracture behaviours of neat epoxy resin. Mech. Mater. 140, 103214. https://doi.org/10.1016/J.MECHMAT.2019.103214 Ma, D., Manes, A., Amico, S.C., Giglio, M., 2019. Ballistic strain-rate-dependent material modelling of glass-fibre woven composite based on the prediction of a meso-heterogeneous approach. Compos. Struct. 216, 187–200. https://doi.org/10.1016/j.compstruct.2019.02.102 Morelle, X.P., Chevalier, J., Bailly, C., Pardoen, T., Lani, F., 2017. Mechanical characterization and modeling of the deformation and failure of the highly crosslinked RTM6 epoxy resin. Mech. Time-Dependent Mater. 21, 419–454. https://doi.org/10.1007/s11043-016-9336-6 Tabiei, A., Zhang, W., 2018. A Zero Thickness Cohesive Element Approach for Dynamic Crack Propagation using LS-DYNA ®. pp. 1–15. Tserpes, K.I., 2011. Strength Prediction of Composite Materials from Nano- to Macro-scale, in: Attaf, B. (Ed.), Advances in Composite Materials for Medicine and Nanotechnology. IntechOpen, Rijeka. https://doi.org/10.5772/13964 Wu, H., Ma, G., Xia, Y., 2004. Experimental study of tensile properties of PMMA at intermediate strain rate. Mater. Lett. 58, 3681–3685. https://doi.org/10.1016/j.matlet.2004.07.022 Zhou, F., Molinari, J.F., Shioya, T., 2005. A rate-dependent cohesive model for simulating dynamic crack propagation in brittle materials. Eng. Fract. Mech. 72, 1383–1410. https://doi.org/10.1016/j.engfracmech.2004.10.011 Zotti, A., Elmahdy, A., Zuppolini, S., Borriello, A., Verleysen, P., Zarrelli, M., 2020. Aromatic Hyperbranched Polyester/RTM6 Epoxy Resin for EXTREME Dynamic Loading Aeronautical Applications. Nanomaterials 10, 188. https://doi.org/10.3390/nano10020188 inspection. References

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1st Virtual European Conference on Fracture A combined CFD and FEM analysis of pressurized thermal shock applied to the probabilistics of cleavage fracture Casper Versteylen a, *, Heleen Uitslag-Doolaard a , Lorenzo Stefanini a , Frederic Blom a a NRG Petten, Westerduinweg 3, 1755 LE Petten. In a nuclear power plant, the integrity of the pressure vessel which contains the primary water is paramount. In case of an accident involving the guillotine break of primary system piping there can be a sudden loss-of-coolant accident (LOCA). During such an incident, the reactor core needs to be cooled for some period after its shut-down (residual heat removal). The emergency core cooling is achieved by the injection of cold water in the still pressurized reactor pressure vessel (RPV). The combination of pressure and thermal stresses provides a complex stress state in the RPV wall: a pressurized thermal shock (PTS). The RPV material is generally a ferritic steel. The critical stress intensity for brittle cleavage fracture depends on the ductile to brittle transition temperature. This complex combination of stresses, absolute temperatures and temperature gradients in combination with radiation damage requires an integral approach for the evaluation of the probability for the occurrence of cleavage fracture. This problem is simulated with a combined CFD and FEM approach. A quarter of the reactor pressure wall including the cooling nozzle is simulated during the 1000 seconds of the cooling transient. This method can accurately predict the thermal profile and the corresponding stress field. This approach is applied to a reactor pressure vessel containing pre-existing semi-elliptical cracks. The stress intensities for every time step, the temperature, the effects of radiation damage, and the material properties of two types of RPV steel; (SA 508gr.3 and SA-508gr.4N) contribute to the probability for a brittle cleavage crack to form. An estimation of the probability for cleavage fracture is made through the Master Curve approach. These probabilities are calculated for different crack locations, sizes, aspect ratios and for two different grades of RPV steel. The influence of these geometric factors and material properties under the influence of radiation have been analysed. The material just below the nozzle is cooled down further and the thermal gradient is more severe. This is reflected in a higher probability for cleavage fracture. The new generation of RPV steel; SA-508gr.4N is very promising for its resistance to radiation induced embrittlement and for its higher strength, both factors leading to a lower probability of cleavage fracture in the reactor pressure vessel. Increasing the safety of the RPV. 1st Virtual European Conference on Fracture A combined CFD and FEM an lysis of pressurized thermal shock applied to the probabilistics of cleavage fracture Casper Versteylen a, *, Heleen Uitslag-Doolaard a , Lorenzo Stefanini a , Frederic Blom a a NRG Petten, Westerduinweg 3, 1755 LE Petten. Abstract In a nuclear power plant, the integrity of the pressure vessel which contains the primary water is paramount. In case of an accident involving the guillotine break of primary system piping there can be a sudden loss-of-coolant accident (LOCA). During such an incident, the reactor core needs to be cooled for some period after its shut-down (residual heat removal). The emergency core cooling is achieved by he injection of cold wat r in the til pressurized reac or ressu e vess l (RPV). The combinati n of pressure a d thermal stresses provid s a complex stres state n the RPV wall: a pressurized thermal shock (PTS). The RPV material is generally a ferritic steel. The critical str ss int nsity f r brittle cleavage frac ure depends on t ductile to brittl transition temperature. This complex combination of stresses, bsolu e temperatures an t mpe ature gradient in combination with r d ati n damage requir s an in egral a proach for the evaluation of the probability for the occurr nce of c eavage fracture. This problem is simulated with a combin d CFD and FEM approach. A quarter of he reactor pressure wall includi g t cool ng nozzle is simulated during the 1000 econds of the cool ng transi nt. This me hod can ccurately predict he thermal profile and he correspond ng stress field. Thi pproach is lied to a reactor pressure vess l c ntain ng p e-existing s mi-elliptical cracks. Th stre s intensitie for every time step, the temperature, the effects of radiation damage, nd the material properties of two types of RPV teel; (SA 508gr.3 and SA-508gr.4N) contribute to the probability for a brittle leavage c ack o form. An estimation of probability for cleavag fracture is made through the Master Curv approach. These probabiliti s are calculat d for different crack locatio s, izes, asp ct atios and for two diff ent grad s o RPV steel. The influence of these geometric factors and material propertie under the influence of radiation have been analysed. The m ter al just below the nozzle is ooled down further nd the t rmal grad ent is more seve e. This is refl cted in a igher probability for cleavage fracture. The new generation of RPV st el; SA-508gr.4N is v ry promising for its resistance to adiation induced embrittlem nt and for its high r streng h, both factors le ding to a lower probability of cl avage f cture in the reactor pres ure vessel. Increasing the safety of the RPV. © 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-re iew under responsibility of the European Structural Integrity Society (ESIS) ExCo Abstract

* Corresponding author. E-mail address: Versteylen@nrg.eu

2452-3216 © 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the European Structural Integrity Society (ESIS) ExCo 2452-3216 © 2020 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the European Structural Integrity Society (ESIS) ExCo 2452-3216 © 2020 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the European Structural Integrity Society (ESIS) ExCo * Corresponding author. E-mail address: Versteylen@nrg.eu

Versteylen/ Structural Integrity Procedia 00 (2020) 000–000

Casper Versteylen et al. / Procedia Structural Integrity 28 (2020) 1918–1929 © 2020 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the European Structural Integrity Society (ESIS) ExCo Keywords: Cleavage; Reactor pressure vessel; CFD-FEM

1919

1. Introduction

A reactor pressure vessel needs to retain the integrity of the pressure boundary even in the most extreme loading conditions. In the event of a loss of coolant accident (LOCA), cold water can be injected in the still pressurized reactor pressure vessel (RPV). Pressurized thermal shock (PTS) can occur on the wall of a RPV due to the injection of cold cooling water in the still hot and pressurized RPV. The emergency core cooling system (ECCS) causes a temperature gradient in the RPV wall, which in turn causes thermal stresses. According to ASME codes, a postulated crack must be assumed in the RPV with a depth of 1/4 of the wall thickness and a length of 3/2 times the wall thickness. The thermal and hoop stresses are most severe for cracks along the axial direction of the RPV and the dominant fracture mechanism: mode I. The thermal stresses can be approximated for a specific thermal transient, but real thermal transients feature turbulent flows which leads to complex hot and cold spots and thermal gradients. The thermal stresses can therefore fluctuate in a similar fashion. A rigorous multidisciplinary approach is chosen in order to study the PTS under these conditions. Linking computational fluid dynamics analyses to a finite element analysis of stress states and the J integral, provides the input used in the Master Curve approach. Using the Master Curve approach, and under the assumption that only the fracture toughness influence significantly the rupture conditions and the only factor influencing the fracture toughness is the fluence, the probability of fracture under this transient can be approximated. The authors give their outlook about how this approach could be implemented in IAEA and ASME guidelines.

Nomenclature PTS

Pressurized Thermal Shock

NRG

Nuclear Research & Consultancy Group

LOCA

Loss Of Coolant Accident Reactor Pressure Vessel

RPV

ECCS ASME IAEA

Emergency Core Cooling System

American Society of Mechanical engineers International Atomic Energy Agency

SSY BCC

Small Scale Yielding

Body Centred Cubic (crystal structure) Ductile to Brittle Transition Temperature

DBTT

SIF � �

Stress Intensity Factor RPV wall thickness

radius through the cross-section of the RPV

probability for failure

Weibull stress

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