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3rd International Workshop on Plasticity, Damage and Fracture of engineering Materials (IWPDF 2023)

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Procedia Structural Integrity 61 (2024) 1–2 Structural Integrity Procedia 00 (2024) 000–000

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3rd International Workshop on Plasticity, Damage and Fracture of Engineering Materials (IWPDF 2023) Editorial Tuncay Yalc¸inkaya a, ∗ a Department of Aerospace Engineering, Middle East Technical University, Ankara 06800, Tu¨rkiye

Keywords: Plasticity; Damage; Micromechanics; Fracture Mechanics

This special issue features a curated selection of research papers presented at the 3rd International Workshop on Plasticity, Damage, and Fracture of Engineering Materials. Hosted by the Middle East Technical University in Istanbul, Tu¨rkiye, from October 4th to 6th, 2023, the workshop welcomed contributions from both in-person and virtual attendees. Alongside the live broadcast of in-person poster and oral presentations to online participants, virtual pre-recorded contributions were uploaded to a YouTube channel prior to the meeting. The workshop primarily centered on three main subjects: plasticity, damage, and fracture. Both computational and experimental studies were presented, with a focus on enhancing the understanding of how material microstructure, loading, and environmental conditions influence the deformation, degradation, and failure of engineering materials. The workshop achieved remarkable success, featuring 6 keynote lectures, 49 oral, 15 poster, 42 pre-recorded presentations, and a total of 110 in-person participants. 301 co-authors from 37 countries submitted over 100 abstracts, contributing to the book of abstracts. Social activities, such as a welcome reception, a private Bosphorus boat tour, and a gala dinner, were arranged to foster a welcoming atmosphere for workshop participants to engage in scientific discussions. Only the papers that are accepted after a peer-review process are published in this special issue. The workshop’s exceptional scientific caliber was established through the outstanding keynote lectures delivered by Prof. Fionn Dunne (Imperial College London, UK) on stress redistribution in dwell fatigue, by Prof. Mingwang Fu (The Hong Kong Polytechnic University, Hong Kong) on damage and fracture in deformation of materials and deformation-based manufacturing, by Prof. Somnath Ghosh (Johns Hopkins University, USA) on parametrically upscaled constitutive model and crack nucleation model for fatigue predictions, by Prof. Anne-Marie Habraken (Uni versity of Lie`ge, Belgium) on the simulations of the directed energy deposition process, by Prof. Benjamin Kluse mann (Leuphana University Lu¨neburg, Germany) on fatigue crack propagation in laser peened materials, and by Prof. Alexander M. Korsunsky (University of Oxford, U.K.) on spatially resolved eigenstrain analysis. We extend our sincere appreciation to all the keynote speakers for their invaluable contributions to the workshop. The workshop organization was greatly facilitated by the kind, attentive, and e ffi cient assistance provided by the members of the organizing committee: ˙Ilbilge Umay Aydiner, Orhun Bulut, Can Erdogan, Tevfik Ozan Fenercioglu, Enes Gu¨nay, Aptullah Karakas, Berkehan Tatli, Izzet Erkin U¨ nsal, and Hande Vural. I would like to express sincere gratitude for the tremendous support from the main workshop sponsor Repkon Machine and Tool Industry and Trade Inc., whose invaluable contributions have made this conference possible. I also extend my thanks to the European

∗ Corresponding author. Tel.: + 90-312-2104258 ; fax: + 90-312-2104250. E-mail address: yalcinka@metu.edu.tr

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Structural Integrity Society (ESIS) for their generous assistance with both the workshop and this special issue. Addi tionally, we would like to acknowledge the support from The European Scientific Association for Material FORMing (ESAFORM) and Borc¸elik C¸ elik Sanayii Ticaret A.S., which is deeply appreciated. Last but certainly not least, I would like to thank the scientific committee for their help in reviewing the articles in this special issue.

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Procedia Structural Integrity 61 (2024) 252–259

* Corresponding author. Tel.: +61-8-83132259. E-mail address: g.nguyen@adelaide.edu.au / giang.nguyen@trinity.oxon.org

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1. Introduction Three-dimensional (3D) concrete printing provides potential opportunities for the construction industry with the benefits of design flexibility and sustainability compared to conventional construction techniques (Hamidi & Aslani 2019; Tay et al. 2017; Wu et al. 2016). The 3D concrete structures are manufactured by stacked 2D planes, inducing weak inter-layer bonds and anisotropic properties (Panda et al. 2017). Interface weakness can cause cold joints or cracking, therefore the improvement of interlayer strength is one of the research topics to ensure technology reliability. The weak interfaces between layers induced challenges in testing, especially in fracture tests for fracture properties. Instability can happen due to abrupt failure of the interface, leading to instant load drop and hence rendering the tests out of control. This is particularly the case for indirect tensile tests using circular shape disc specimens (Brazilian tests). This type of test is appealing thanks to the ease in specimen preparation. It can give us tensile strength and also fracture properties if the tests can be carried out successfully without abrupt failure. Nevertheless, the configuration of the test and the orientation of the interfaces of 3D-printed specimens make it much more challenging than tests on “homogeneous” materials (Gell et al. 2019). Loading direction parallel to the interfaces facilitates fracture of the interface in pure mode I fracture, given maximum tensile stress in such cases is perpendicular to the interfaces. On the other hand, inclined interfaces are subjected to mixed mode conditions and when the angle between the loading direction and interfaces reaches 90 degrees, the effect of weak interfaces can be negligible, given it is subjected to compressive stress perpendicular to the interface. In this paper, the challenges in indirect tensile testing are addressed using our innovative technique in controlling the loading process. The focus is the application of this new technique for controlling fracture in Brazilian disc testing, and the associated benefits for advanced instrumentation. This technique, named AUSBIT (Adelaide University Snap Back Indirect Tensile Test; Verma et al. 2019, 2021a, 2021b; Verma, 2020) uses indirect displacement control, taking the feedback from the lateral expansion of the disc to stabilize the fracturing processes. Given the lateral expansion is a monotonically increasing quantity, its feedback to the loading machine helps control the test and allows capturing snap-back behaviour that is impossible using direct displacement control. In this sense, lateral displacement control in AUSBIT can effectively stabilize the sudden cracking of disc specimens to allow the effective use of Digital Image Correlation (DIC) to capture the full-field strain during testing. Both promising features and challenges in applying this technique to 3D-printed cement materials with weak interfaces are addressed. 2. Experiment program 2.1. Material The cementitious mortar was used in the 3D printed specimen fabrication, including five main ingredients: ordinary Portland cement (OPC), natural sand, superplasticizer and water. The OPC is used as the mixture binder produced by Adelaide Brighton Cement LTD. The sand component is procured from Marion Sand & Metal Pty. LTD, Adelaide and sieved to maintain a maximum grain size of 600 μm. The additive of ViscoCrete 10 as a superplasticizer complied with AS1478.1-2000 helps enhance the mixture fluidity without requiring an increasing amount of water content. Details on the cementitious mortar are summarized in Table 1.

Table 1. Printable mix design composition. Component

Weight ( g )

Concentration ( % )

Sand

7044.50 2555.60 1390.50

63.122 22.903 13.891

Water

Cement

Superplasticizer

9.30

0.085

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2.2. Specimen preparation In this study, a simple wall structure containing nine layers was printed using the Delta WASP 3D clay/mortar printer at the University of Adelaide (UoA). Each layer is about 17mm in height and 400mm in length, printed using a circular plastic nozzle with a diameter of 30mm. The printer parameters were kept the same in all printings to maintain the consistency and repeatability of 3D-printed specimens. All the printed samples were cured for 28 days in the fog room at UoA under the same storage environment conditions to maintain consistency. For each printed wall, three cylindrical specimens of 100mm in diameter were prepared by waterjet cutting equipment as shown in Fig. 1a. The originally textured surfaces of all specimens were then smoothed using a saw, followed by the grinding technique to obtain cylindrical samples with two smooth surfaces for Brazilian disc testing. All disc specimens were air-dried before the application of speckle pattern for instrumentation using Digital Image Correlation (DIC).

(a)

(b)

Fig. 1. (a) Three cylindrical specimens from the printed wall; (b) A cylindrical sample with smooth surface after grinding.

2.3. Test setup using AUSBIT The cylindrical specimens, after 28 days of curing period, were used in indirect tensile tests to examine the interlayer bond between layers. MTS loading frame is used in conjunction with the DIC technique to obtain the full field strain distribution and its evolution during loading. DIC is a non-contact and non-destructive method to measure the strain and deformation on the surface of specimens (Chu et al. 1985). It has been widely used in testing engineering materials, including 3D-printed disc specimens under impact loading (Sharafisafa & Shen 2020). In this study, the disc specimens after surface grinding were painted with black speckles in random patterns on a white background. The camera location and lighting conditions should be suitable for clear image capture and correlation throughout the whole testing procedure. This study applied the VIC-snap 2D Correlation Solutions commercial package (Correlation Solutions 2009). The load and displacement from the MTS loading machine were recorded at a rate of five samples per second, while images captured using the camera were at one frame per two seconds, given a huge amount of image data and the expected long duration of the testing, thanks to the use of AUSBIT (Verma et al. 2021b). The readings obtained from the two systems (MTS and DIC camera) were correlated and synchronized in time during post processing. Fig. 2a presents the overall testing setup.

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Fig. 2. (a) overall testing setup of MTS loading frame and DIC technique; (b) loading direction relative to printing direction.

Adelaide University Snap-Back Indirect test (AUSBIT) was applied in this study, where the indirect lateral displacement control could stabilize the instant cracking under the diametrical compression load (Verma et al. 2019a; Verma et al. 2021a). Compared with the conventional indirect tensile test, AUSBIT enables to capture a complete strain response with the post-peak behaviour (Verma et al. 2021b). In this study, the vertical displacement rate was set as 0.2 mm/min and the load set point is 1 kN for early stage of loading, before switching to lateral control. The lateral deformation was used to control the loading over the cracking period with the lateral displacement rate of 0.5 μm/min . The tensile strength of the material can be obtained using the peak load as per Equation 1 (Verma et al. 2021b): (1) where P is peak load (kN), D is the diameter (mm), and t is the thickness (mm) of the disc specimen. Given the layer-by-layer deposition of cement mortar in 3D printing, the interfaces between layers are usually the weakest link, governing the strength and fracture properties of 3D-printed cement mortar. In this sense, in Brazilian disc testing, loading direction relative to printing direction has strong effects on the results. This also affect the stability and controllability of the tests, given the disc specimen in Brazilian disc testing is expected to be weaker if loading direction is parallel with printing direction (making an angle of zero degree; Fig. 2b). On the other hand, the specimen is expected to be stronger if the angle between the loading and printing direction is 90 degrees. In relation to the above two configurations (0° and 90°, Fig. 2b, right), the obtain strengths in these two cases correspond to strength of the interface (for 0° loading angle) and cement mortar layer (for 90° loading angle). This is one of the advantages of using Brazilian disc testing for investigating the behaviour of 3D-printed cement mortar, given the ease in specimen preparation and also loading condition. The disadvantage is that this kind of test is usually very unstable, with abrupt fracture in a fraction of a second, and therefore it is much more difficult to control the fracturing process in the case of for 0° loading angle. The use of AUSBIT in this case can help stabilise the fracturing process, giving more time for advanced instrumentation based on DIC. 3. Result and discussion 3.1. Discontinuity perpendicular to the applied load (90° loading angle) The AUSIT approach is applied for controlling the lateral deformation for three specimens which are tested under 90 degree loading angle. The evolutions of lateral displacement and vertical displacement with time are shown in Figs. 3a, 3c, 3e, while Figs. 3b, 3d and 3f show the load-displacement curves. The points on the load-displacement curves

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(Figs. 3b, 3d and 3f) correspond to times indicated in the plots of load, and displacements against time (Figs. 3a, 3c, 3e).

Fig. 3. (a, c, e) Evolution of load, vertical displacement and lateral displacement with time; (b, d, f) Load-displacement curves for three tests (90° loading angle).

In Fig. 3b, the load-displacement curve indicates the loading behaviour of point 1 and point 2 are almost linear within the pre-peak stage before reaching the peak load at point 3 under diametrical compression. Meanwhile, the results of Fig. 3a shows the lateral displacement increases linearly under control. The vertical displacement exhibits nonlinear increase before reaching the peak load. After reaching the peak load at point 3, the load starts to drop gradually while the vertical displacement still grows slightly and gradually tend to be stable after 3 hours. Moreover, Figs. 3f and 3e both show that the vertical displacements tend to be stable after reaching the peak load value with lateral control. Therefore, the AUSBIT setting can keep adjusting the vertical loading rate to maintain the predefined constant rate of lateral displacement which can capture post-peak evolution of cracking of 90 loading angle specimen. Overall, the results show that the lateral deformations increase linearly and monotonically at both pre-peak and post-peak stages, as specified in the MTS control feedback. This indicates a steady failure process, given the decrease of both load and vertical displacement in post-peak stage does not lead to decrease of lateral displacement in all three

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tests. While drop of load bearing capacity due to cracking can be observed in all three tests (Figs. 3b, 3d and 3f), strong snap-back can be seen in the last two cases (Figs. 3d and 3f). In these two cases of strong snap-back, the lateral displacements are still increasing steadily, as seen in Figs. 3a, 3c and 3e. This indicates the success of AUSBIT in stabilizing fracturing processes. The duration of all three tests shown in Fig. 3 exceeds 4 hours, allowing the use of advanced instrumentation based on DIC. Therefore, full-field strain measurement can be possible for the whole duration of the tests. Fig. 4 shows contours of lateral strain at five stages of test 2 (Figs. 3c and 3d). The cracking process is well under control, and crack observed on the surface of the specimen seems to grow steadily despite snap-back response. The failure pattern is also indicated, showing non-straight crack path due to the heterogeneity of the specimen. In this case the crack cuts through all six layers and the peak load in this case can be associated with tensile strength of the layer.

Fig. 4. evolution of lateral strain, and failure pattern observed at the end of the test (90° loading angle).

3.2. Discontinuity aligned to the applied load (0° loading angle) Fig. 5 shows the results obtained on specimens tested with loading direction aligned with the interface.

Fig. 5. (a, c) evolution of load, vertical displacement and lateral displacement with time; (b, d) load-displacement curves, for two tests (0° loading angle).

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In Fig. 5b, 5d, point 1 and point 2 indicates the linear stage of load increase, after an initial nonlinear stage due to the overall closure of crack or void throughout the specimen. The lateral displacement control using AUSBIT was applied from the beginning, helping to stabilize the cracking process at least partly, as shown in Fig. 5a and 5c. The predefined rate of lateral displacement is consistent throughout the whole test. The load and vertical displacement increase nonlinearly with time before reaching peak load value. However, due to weak interface between layers, the failure process becomes abrupt slightly after peak load, although snap-back can still be captured before the occurrence of unstable failure. In both tests, the lateral displacement jumps up suddenly due to loss of control at certain stages after peak load. This can be due to the lack of sensitiveness of the loading machine compared to the rate of crack propagation along the weak interfaces. This is the issue that should be investigated and addressed later in the control of the test.

Fig. 6. Evolution of lateral strain, and failure pattern observed at the end of the test (0° loading angle).

Lateral strain obtained from DIC and its evolution during failure are plotted in Fig. 6. Once the load reaches the peak value at point 3, the strain distribution of the DIC contour shows that the highest strain (red region) starts concentrating in the middle vertical loading pathway of the specimen. The failure process becomes unstable beyond point 4, given the control is lost due to low strength and fracture toughness of the interface. As can be seen in the failure pattern, the crack in this case is almost straight, following the interface between two layers in the middle of the specimen. 3.3. Comparison of tensile strengths Based on the results of tested specimen, the peak load and tensile strength of some specified specimens have certain differences with lower values due to the inconsistent printing quality and the cracking paths. Fig. 1(a) shows the layer height and width has variations of the printed wall results in inconsistent printing quality. Therefore, the cracking paths of the fully fractured specimens did not always go through the weak interface between two printed layers. The specimen with lower peak load and strength were obtained from the specimens with cracking path along the whole weaker interface compared with the others were cracked within the layer in vertical direction. The cementitious mortar density of printed specimens is different due to the influence of printing process. The density of specimen has impact on both strength and stiffness of the specimen which eventually affects the tensile strength. The average tensile strengths of specimens underloading at different loading angles (90° and 0°) with similar average density are shown in Table 2. The preliminary results indicate that the tensile strength of specimens with 90° loading angle specimens is stronger than those with 0° loading angle. Although the results are not significantly different due to lack of data, this still shows the effect of weaker interlayer on strength. The results in Table 2 are indicative only, given they are preliminary ones showing both successes and challenges in control cracking processes in Brazilian disc testing. The repeatability of the tests and consistency of test results still

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a challenge, due to difficulties in controlling the cracking, especially for the case of 0° loading angle. Therefore, more tests will be conducted to ensure better reproductivity.

Table 2. Comparison of tensile strength for 90° and 0° loading scenario with average density. Loading Angle Average Density (kg/m 3 ) Average Tensile strength ( MPa )

2175 2130

2.62 2.58

4. Conclusions We have shown the application of AUSBIT to a challenging fracture test, using Brazilian discs made of 3D-printed cement-based mortar in which the effects of printing direction are focused on. Although AUSBIT is able to control the whole fracture process for the case of 90° loading angle, it faces challenges the loading direction induces tensile stress on the weak interface between layers (the case of 0° loading angle). For such cases of 0° loading angle, early snap-back responses can still be successfully captured, and very unstable fracture happens after that due to low fracture toughness of the interfaces compared to the layer. The results show the difference between tensile strengths of the layers and their interfaces. The printing quality should be improved with a more consistent mix design. Nevertheless, due to challenges in carrying out this kind of test even with the control using AUSBIT, the results obtained from a few successful tests are not statistically significant enough to indicate a clear difference between strengths of the layers (90° loading angle) and its interfaces (0° loading angle). In addition, due to challenges in controlling the test for the case of 0° loading angle, it was impossible to obtain the full post-peak curve for the calculation of fracture energy. Better control will be used, and more tests will be carried out in the future for more conclusive outcomes. Acknowledgements Giang D. Nguyen and Murat Karakus acknowledge support from the Australian Research Council (ARC) and OZ Minerals Ltd through Linkage Projects LP200100038 and LP220200792. References Chu, T., Ranson, W., Sutton, M., 1985. Applications of digital-image-correlation techniques to experimental mechanics. Experimental Mechanics 25, no. 3, 232–244. Correlation Solutions., 2009. Vic-2D Reference Manual, pp. 1–59. Gell, E., Walley, S., Braithwaite, C., 2019. Review of the validity of the use of artificial specimens for characterizing the mechanical properties of rocks. Rock Mechanics and Rock Engineering 52 chapter 9, 2949–2961. Hamidi, F., Aslani, F., 2019. Additive manufacturing of cementitious composites: Materials, methods, potentials, and challenges. Construction and Building Materials 281, 582-609. Panda, B., Paul, S., Hui, L., Tay, Y., Tan, M., 2017. Additive manufacturing of geopolymer for sustainable built environment. Journal of Cleaner Production 167, 281-288. Sharafisafa, M., Shen, L., 2020. Experimental Investigation of Dynamic Fracture Patterns of 3D Printed Rock-like Material Under Impact with Digital Image Correlation. Rock Mechanics and Rock Engineering 53 chapter 8 , 3589–3607. Tay, Y., Panda, B., Paul, S., Mohamed, N., Tan, M., Leong, K., 2017. 3D printing trends in building and construction industry: a review. Virtual and Physical Phototyping 12, 261-276. Verma, R., Nguyen, G., Karakus, M., 2019a. Snap back indirect tensile test (AUSBIT) Patent, IP Australia 2019101006. Verma, R., & Fallah, P., Nguyen, G., Bui, H., Karakus, M., Taheri, A., 2020. Analysing localisation behaviour of rocks using Digital Image Correlation technique in 13th International Conference on Mechanical Behaviour of Materials, pp 11-14. Verma, R., Nguyen, G., Bui, H., Karakus, M., 2021. Effect of Specimen Size on Localization using Digital Image Correlation, in Proceedings of the 8th International Conference on Fracture, Fatigue and Wear, Springer Singapore. Singapore, pp. 397–405. Verma, R., Nguyen, G., Karakus, M., Taheri, A., 2021a. AUSBIT: A novel approach to capturing snapback in indirect tensile testing in 55th US Rock Mechanics/Geomechanics Symposium OnePetro. Verma, R., Nguyen, G., Karakus, M., Taheri, A., 2021b. Capturing snapback in indirect tensile testing using AUSBIT - Adelaide University Snap Back Indirect Tensile test International Journal of Rock Mechanics and Mining Sciences (Oxford, England : 1997) 14 7, 104897–. Wu, P., Wang, J., Wang, X., 2016. A critical review of the use of 3-D printing in the construction industry. Automation in Construction 68, 21–31.

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Procedia Structural Integrity 61 (2024) 277–284 Structural Integrity Procedia 00 (2024) 000–000 Structural Integrity Procedia 00 (2024) 000–000

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© 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of IWPDF 2023 Chairman Abstract Magnesium is among the lightest structural metals with a high strength-to-weight ratio. A widespread adoption of magnesium alloys in the industry, however, is impeded by its unorthodox mechanical behavior. The vast di ff erences between activation ener gies of the slip systems in HCP magnesium, combined with profuse (and abrupt) activity of tensile twinning leads to an extreme plastic anisotropy. On top, there is intense strain heterogeneity, primarily, linked to the spatial coordination of twinning that also shows a strong dependence on crystallographic texture. The recent experimental e ff orts target a better understanding of magnesium (and validate polycrystal simulations) largely by investigating its mechanical response. In contrast, this work aims to incorporate temperature measurements of the dissipative response of Magnesium during deformation as well as the usual stress-strain mea surements to infer a thermomechanical description of its plastic deformation. To this end, the temperature of a textured magnesium AZ31 sample is recorded under an IR camera. Then, stress and temperature obtained as a function of strain are compared with the output of a coupled thermomechanical Taylor-type crystal plasticity model, posed in the variational framework. © 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of the scientific committee of IWPDF 2023. Keywords: magnesium; twinning; plastic dissipation; thermomechanical behavior 3rd International Workshop on Plasticity, Damage and Fracture of Engineering Materials (IWPDF 2023) A thermomechanical investigation of textured Magnesium in an e ff ort to validate crystal plasticity simulations Necdet Ali O¨ zdu¨r a , Sefer Can Erman a , Rian Seghir b , Laurent Stainier b , C. Can Aydıner a, ∗ a Department of Mechanical Engineering, Bog˘azic¸i University, Istanbul 34342, Turkey b Research Institute in Civil and Mechanical Engineering, Ecole Centrale Nantes, Nantes 44321, France Abstract Magnesium is among the lightest structural metals with a high strength-to-weight ratio. A widespread adoption of magnesium alloys in the industry, however, is impeded by its unorthodox mechanical behavior. The vast di ff erences between activation ener gies of the slip systems in HCP magnesium, combined with profuse (and abrupt) activity of tensile twinning leads to an extreme plastic anisotropy. On top, there is intense strain heterogeneity, primarily, linked to the spatial coordination of twinning that also shows a strong dependence on crystallographic texture. The recent experimental e ff orts target a better understanding of magnesium (and validate polycrystal simulations) largely by investigating its mechanical response. In contrast, this work aims to incorporate temperature measurements of the dissipative response of Magnesium during deformation as well as the usual stress-strain mea surements to infer a thermomechanical description of its plastic deformation. To this end, the temperature of a textured magnesium AZ31 sample is recorded under an IR camera. Then, stress and temperature obtained as a function of strain are compared with the output of a coupled thermomechanical Taylor-type crystal plasticity model, posed in the variational framework. © 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of the scientific committee of IWPDF 2023. Keywords: magnesium; twinning; plastic dissipation; thermomechanical behavior 3rd International Workshop on Plasticity, Damage and Fracture of Engineering Materials (IWPDF 2023) A thermomechanical investigation of textured Magnesium in an e ff ort to validate crystal plasticity simulations Necdet Ali O¨ zdu¨r a , Sefer Can Erman a , Rian Seghir b , Laurent Stainier b , C. Can Aydıner a, ∗ a Department of Mechanical Engineering, Bog˘azic¸i University, Istanbul 34342, Turkey b Research Institute in Civil and Mechanical Engineering, Ecole Centrale Nantes, Nantes 44321, France

Nomenclature Nomenclature

DIC digital image correlation IRT infrared thermography DIC digital image correlation IRT infrared thermography

∗ Corresponding author. Tel.: + 90 (212) 359 4471 ; fax: + 90 (212) 287 2456. E-mail address: can.aydiner@bogazici.edu.tr ∗ Corresponding author. Tel.: + 90 (212) 359 4471 ; fax: + 90 (212) 287 2456. E-mail address: can.aydiner@bogazici.edu.tr

2452-3216 © 2024 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of IWPDF 2023 Chairman 10.1016/j.prostr.2024.06.035 2210-7843 © 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of the scientific committee of IWPDF 2023. 2210-7843 © 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of the scientific committee of IWPDF 2023.

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1. Introduction

Magnesium has been the subject of an intense research activity that aims to develop an understanding of and to possibly predict the idiosyncrasies in its mechanical attributes. Starting from the crystal scale, the di ff erence between activation energies of slip and twin deformation mechanisms (Agnew and Duygulu (2005)) and the profusely activated tensile twin mechanism (Christian and Mahajan (1995)) yield an extremely anisotropic plastic deformation. On the macroscopic scale, tensile twin is auto-catalytic, causing an avalanche of twinning across the sample. This type of macroscopic localized plastic deformation (Lu¨ders banding) is particularly sharp in rolled Magnesium (Aydıner and Telemez (2014); Kapan et al. (2017); Shafaghi et al. (2020); Erman et al. (2023)). Since twinning completely reorients a portion of the crystal, it has a convoluted interaction with other deformation mechanisms, which further adds to the complexity of the material behavior. Due to the heterogeneous and anisotropic deformation of Magnesium, it is di ffi cult to predict its behavior consis tently in a wide range of environments. Hence, the scope of material models are restricted in terms of physical fidelity. Mean-field, self-consistent formulations like Wang et al. (2013) try match the overall stress-strain behavior by mod eling intra-grain deformation mechanisms and various aspects of twinning. Among full-field modeling attempts with finite elements and spectral solutions, Zhang and Joshi (2012); Mareau and Daymond (2016) employ various phe nomenological treatments of twinning in an attempt to achieve mechanical fidelity, while Homayonifar and Mosler (2012); Chang and Kochmann (2015); Husser and Bargmann (2019) also consider the evolution of the texture. Most models homogenize the abrupt twinning activity with a volume fraction parameter; this treatment of twinning is called ”pseudo-slip”. More recent models with discrete twin implementations (e.g., Cheng and Ghosh (2017)) aim to better capture the morphological details of twinning and local plasticity though they are computationally more expensive. While these crystal plasticity models are able to capture certain aspects of the mechanical behavior of Magnesium, for a large portion of them, thermal behavior (and thus temperature comparisons) is irrelevant, unless they impose a temperature-dependent formulation such as Hollenweger and Kochmann (2022). In fact, most models lack the necessary mathematical structure to produce temperature information. In this context, the main goal of this work is to introduce an additional methodology to validate crystal plasticity models by incorporating temperature measurements. Similar to Eisenlohr et al. (2012), the dissipated energy during the deformation will be measured by an infrared (IR) camera. Synchronously collected stress and strain data allows the calculation of plastic work (and power). The stored and dissipated components of plastic work are thus experimentally obtained, yielding the main comparison point with a thermomechanical model, similar to the in the sense to the thermomechanical analysis done by Seghir et al. (2010). In this study, the model that is employed to make this comparison is a thermo-viscoplastic variational model, cast in the variational framework initially devised by Ortiz and Stainier (1999) for viscoplastic constitutive relations and later revised by Yang et al. (2006); Stainier and Ortiz (2010) to incorporate thermomechanical coupling.

Fig. 1. (a) Experiment setup, components 1-9 are referred to in the text; (b) representation of hot rolled plate and the most prominent unit cell; (c) prepared specimen with dummy sample; (d) pole figure of the plate, indicating sharp rolling texture.

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2. Materials and Methods

2.1. Setup

The experimental setup that is used in deformation and temperature measurements is shown in Fig.1(a). The major component of the experiment, a FLIR A655sc thermal camera equipped with 1.5X close-up IR lens is shown in here with the label 2 . The IR camera is set to record at 640x240 pixel resolution at 100 Hz. It is pointing towards a Kammrath & Weiss 10 kN tension-compression module (labeled 4 ), which is placed on top of a Newport XYZ positioning stage ( 5 ). The stage is used to carry the tension-compression module under the macro-DIC line ( 3 ),which consists of a 1X Edmund Optics zoom inspection microscope (further details in Erman et al. (2023)). The entire setup rests on a vibration isolation table ( 7 ), and is covered with an opaque curtain ( 8 ) to block outside light. Here, all infrared thermography (IRT) measurements with in situ loading are conducted in dark conditions. The micro-DIC camera labeled as 1 is not utilized for this experiment. The dog-bone Mg AZ31 sample is wire-EDM cut from a hot-rolled plate (the same saw material in Erman et al. (2023)) as depicted in Fig. 1(b), so that the rolling direction of the plate coincides the loading axis of the specimen. The HCP unit cell in the same figure also illustrates an abundant orientation observed in rolling texture. The sharp rolling texture of the plate can be seen in the pole figure provided in Fig. 1(d). When compressed along the rolling direction, this type of sharp texture is known to trigger profuse and coordinated activity of { 101¯ 2 }⟨ 1¯ 011 ⟩ tensile twins. To serve as a reference temperature measurement surface, a leftover Mg part is glued to the side of the grip section, with a piece of bakelite in between to act as a thermal insulator. The ensemble of the dog-bone specimen and the stress-free side attachment is sketched in Fig. 1(c). Both surfaces are spray painted matte black for increased surface emissivity. Prior to the experiment, a reference image of the initial specimen surface is captured with the macro-DIC line using external light source (label 9 in Fig. 1). Then the specimen is carried under the thermal camera and the light is turned o ff . The dark conditions are necessary for the thermal measurements but preclude the recording of any other macro-DIC images. Under the IR camera, the dog-bone sample is compressed continuously for 16 seconds with the maximum possible displacement rate the tension-compression module is capable of (20 µ m / s). The IR signal emitted by the specimen (and the dummy sample) is recorded with the thermal camera during loading (and for a brief period 2.2. Sample 2.3. Experimental Procedure

Fig. 2. (a) IR image and; (b) macroscopic image with DIC regions of interest marked with rectangles; (c) comparison of IR-DIC and macro-DIC measurements.

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after). Simultaneously, instantaneous force values are recorded using the analog output of the load cell (label 6 ). At the end of the experiment, the light is turned back on and a final macro-DIC image is recorded to depict the final deformation. Sensor noise in the form of spurious jumps appearing in raw temperature readings are eliminated by subtracting the average temperature change values of the dummy sample. A Savitzky-Golay filter is then applied to smooth the temperature signal. The total strain rate along the gage section does not stay constant throughout the experiment, even though the loading is applied in a displacement-controlled manner. Therefore, the displacement rate could not be assumed constant and inferred directly from the macro-DIC measurement at the end of the loading. Thus, the strain history of the specimen is measured by DIC analysis on IR images themselves, by treating the entire gage section as a single deformation subset. Since the IR images are low resolution, and the surface pattern is sub-optimal due to the matte black paint, IR-DIC measurements are validated by comparing the final strain value to the macro-DIC strain average inside the gage section (Fig. 2). (1) Here, the left-hand side of the equation represents change in thermal energy, div( q ) represents heat losses due to conduction, r is the external heat supply, and D int is the internal (or intrinsic) dissipation. Under the postulate of existence of a Helmholtz free energy function, W ( F , T , Z ), where Z denote a suitable set of internal variables (e.g. plastic deformation, F p , plastic slip on the slip system α , γ α ), the above equation for energy balance can be reformulated into the following local form given in Stainier (2013): − T ∂ 2 W ∂ T 2 ˙ T = D int − div( q ) + r + T ∂ 2 W ∂ F ∂ T : ˙ F + T ∂ 2 W ∂ Z ∂ T · ˙ Z (2) The two newly occurring terms in the right-hand side in Eq. 2 correspond to the thermo-elastic part and thermal couplings for the internal variables, respectively. Following the variational framework of Ortiz and Stainier (1999), the constitutive equations can be written as 2.4. Thermal Modeling The energy conservation in terms of entropy rate, ˙ η , is given by ρ 0 T ˙ η = D int − div( q ) + r where Y k are the thermodynamic driving forces for the internal variables Z k . Here, ∆ ∗ ( ˙ Z ; Z , T ) denotes the dual form of the dissipation pseudo-potential, which incorporates rate dependency relations. Together with rate of Helmholtz free energy, they form the stress power, ˙ W +∆ ∗ . In the variational framework, the minimum (or stationary point) of stress power with respect to internal variables gives the evolution law of internal variables. Furthermore, note that following the work of Taylor and Quinney (1934), the internal dissipation is traditionally related to the total plastic work through a coe ffi cient, β , also referred to as the Taylor-Quinney coe ffi cient. D int = Y · ˙ Z = β S : D p (4) Here, S , and D p denote Mandel stress and plastic flow rate tensors, respectively. Combining Eqs. 3, 4 with Eq. 2, and defining the heat capacity as ρ 0 C = − T ∂ 2 W /∂ T 2 , the local thermal equilibrium equation can be written as ρ 0 C ˙ T = β S : D p − div( q ) + r + T ∂ P ∂ T : ˙ F − T ∂ Y ∂ T · ˙ Z . (5) For the experimental measurements in this work, further simplifications are made to Eq. 5 using the following assumptions: P = ∂ W ∂ F ∂ W ∂ Z k ∂ W ∂ T Y k = − ρ 0 η = − = ∂ ∆ ∗ ∂ ˙ Z k (3)

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• No external heat supply • Small deformations • Negligible thermal couplings of internal variables • Thermoelastic e ff ects limited to isotropic heat expansion • 0D thermal di ff usion

which reduces the local thermal equilibrium equation given in Eq. 5 to the following form ρ 0 C ˙ T + ρ 0 CT τ eq = βσ : ˙ ε p − α T tr( ˙ σ )

(6)

W s + W l = β W a + W is , (7) where W s , W l , W a , and W is denote the energetic contributions related to thermal storage, convectively lost energy, applied plastic work, and thermoelastic e ff ects, respectively. τ eq that appears in the 0D thermal heat loss term, W l , is a measure of characteristic time that describes how quickly the material loses heat to its surroundings both conductively and convectively; it is the only remaining unknown term in Eq. 6 except for β . The definition of τ eq in 0D thermal di ff usion is originally derived by Doudard et al. (2010) as follows: 1 τ eq = 2 h 1 ( e + l ) el + 2 h 2 L (8) Here, e , l , and L correspond to the specimen dimensions of thickness, width, and length; while h 1 and h 2 denote the air-film coe ffi cient and the apparent film coe ffi cient between the grips and the specimen. The aim of the polycrystal plasticity simulation is only to produce a statistical representation of the thermomechan ical response of a large aggregate in the average sense. The simulation is therefore simplistic and is not expected to capture detailed non-local and inter-granular mechanical interactions. To this end, a Taylor-type simulation domain consisting of 172 grains, oriented such that it resembles the rolling texture of the sample is generated, using Neper by Quey et al. (2011). The texture used for the simulation can be seen in Fig. 5(c). The domain is compressed along its ‘rolling direction’ with a strain rate of 0.2% s − 1 for 16 seconds such that it reaches to 3.2% strain at the end of the simulation, in line with the experiment. For the case study, the visco-plastic material model by Chang and Kochmann (2015) is implemented, which is already cast in variational form. Briefly, the model uses a pseudo-slip homogenization approach for tensile twins, 2.5. Crystal Plasticity Simulation

Fig. 3. (a) Stress (blue) and change in temperature (red) with respect to strain. (b) The decay of average surface temperature measured after the end of the experiment. Blue line is an exponential fit to the temperature data. Above the figure is the functional form used in data fitting.

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as introduced by Kalidindi (1998). A Voce-type hardening law governs the evolution of energy storage mechanisms in slip systems. In contrast, a linear hardening law is assumed for tensile twin volume fractions. Rate dependency for plastic slip is introduced through a power-law type dissipation potential, while the twins are assumed to be rate independent. For more model details and model parameters, readers can refer to the original paper of Chang and Kochmann (2015). Variational constitutive updates are calculated implicitly by minimizing the incremental form of the internal energy density. This is iteratively carried out in two nested minimizations in a predictor-corrector fashion. At each time step, first the strain is held fixed, and the incremental change in internal variables (slip and twin volume fraction increments) are predicted by minimizing the internal energy density using a projected gradient method developed by Bertsekas (1982). Then a correction step in the form of a Newton-Raphson iteration is used to update the total strain for the current values of the internal variables, similar to Chang and Kochmann (2015). Fig. 3(a) shows the combined stress and change in temperature ( θ , with respect to the initial temperature) as function of strain. Up until 0.2% strain, the temperature of the specimen sharply increased by 120 mK due to thermoelastic e ff ects. After the yield-point, the twin plateau characteristic to the sharply textured Magnesium (see Lou et al. (2007)) was observed during when the temperature dropped down to about 60 mK above its initial temperature and stabilized. At about 2.5% strain, the material hardens further as the macroscopic shear bands probably encompassed the entire gage section. After 16 seconds, the specimen Mg is loaded by nearly 3.2% strain (Fig. 2(b)). Regarding the temperature loss estimates using Eq. 8, h 1 and h 2 are di ffi cult to characterize individually, despite the fact that the dimensions of the specimen are known. Therefore, τ eq is estimated directly through an exponential fit to the temperature decay following the end of the experiment, which is found to be about 0.95 seconds. This is presented in Fig. 3(b). Fig. 4 shows a decomposition of each energy component given in Eq. 7 as calculated directly from experimental measurements. By rearranging these energy terms, the fraction of plastic dissipation to the applied plastic work, β , can be calculated (the ratio between black and blue curves in Fig. 4). This is separately plotted for the entire duration of the experiment in Fig. 5(a). The value of β is commonly chosen to be about 0.9 for most engineering metals. Here, 3. Results and Discussion

Fig. 4. The energetic contributions obtained from the experimental results. See Eq. 7 for their definitions.

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