PSI - Issue 45

Volume 45 - 2023

17th Asia-Paci f c Conference on Fracture and Strength and the 13th Conference on Structural Integrity and Failure (APCFS 2022 & SIF 2022)

Andrei Kotousov Ching Tai Ng Wenyi Yan

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Procedia Structural Integrity 45 (2023) 1–3

17th Asia-Pacific Conference on Fracture and Strength and the 13th Conference on Structural Integrity and Failure (APCFS 2022 & SIF 2022) Preface Andrei Kotousov a, *, Ching-Tai Ng b , Wenyi Yan c

a School of Electrical and Mechanical Engineering, The University of Adelaide, Adelaide, SA 5005, Australia b School of Architecture and Civil Engineering, The University of Adelaide, Adelaide, SA 5005, Australia c Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC 3800, Australia

© 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Prof. Andrei Kotousov Abstract The 17 th Asia-Pacific Conference on Fracture and Strength (APCFS 2022) was joined with the 13 th Conference on Structural Integrity and Failure (SIF 2022) and took place in Adelaide, South Australia, from the 6 th to the 9 th of December 2022. Being globally affected by COVID19, the APCFS/SIF 2022 Conference has been run in a flexible format, i.e., a combination of conventional (face-to-face) presentations as well as online presentations via the Zoom platform in order to guarantee maximum safety as well as benefit for all participants. The conference attracted 181 delegates from around the world from those 148 participated in-person and 33 on-line. 158 presentations, including 5 plenary and 41 invited talks, were delivered during the conference. Besides the excellent technical program, participants had the opportunity to enjoy their stay in Adelaide, which is consistently voted as one of the most liveable cities in the world with its stunning architecture, vibrant cultural life, historical landmarks, and most importantly its beautiful untouched nature. This special issue contains twenty research articles, which have been selected and recommended to publication by the editorial team. © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Prof. Andrei Kotousov Keywords: Structural integrity; failure; strength; fracture The Asia-Pacific Conference on Fracture and Strength (APCFS) is co-organized and sponsored by the Chinese Mechanical Engineering Society, Korean Society of Mechanical Engineers, the Japan Society of Mechanical Engineers and the Australian Fracture Group (AFG). Since it was first held in Sendai, Japan in 1984, the conference has been regularly held every 2-3 years in the three countries - Japan, China and South Korea. In 2014, Australia

* Corresponding author. Tel.: +61-8-83135439. E-mail address: andrei.kotousov@adelaide.edu.au

2452-3216 © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Prof. Andrei Kotousov

2452-3216 © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Prof. Andrei Kotousov 10.1016/j.prostr.2023.05.001

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became the fourth country to host APCFS. This conference succeeds the last, which was hosted at Jeju Island, South Korea in November 2020. The first one-day Conference on Structural Integrity and Failure (SIF) organized by the AFG was in October 1974. The SIF conferences and AFG remained Melbourne-centred until 1985 when the fifth AFG conference was held in Sydney. New Zealand became a member of the AFG in 1997, and the 2010 SIF Conference was held in Auckland. The latest (SIF 12) conference was held in Melbourne in December 2021. The aim of the APCFS/SIF 2022 conference was to facilitate the discussion and collaboration of all aspects relating to fracture, strength and, structural integrity. Furthermore, APCFS/SIF 2022 is intended to continue the legacy of both conferences providing a unique platform for the free exchange of ideas between Chinese, Japanese, Korean and Australian scientists as well as experts, researchers, engineers and PhD students across the world. Several new topics have recently emerged and were included into the conference program, i.e., Structural integrity of energy storage devices, including stand-alone batteries and structural batteries, problems of hydrogen storage/transportation, sustainable design as well as structural integrity aspects of 3D printed components. Articles included in the special issue cover a wide range of topics related to structural integrity including fatigue life evaluation methods (Hughes et al.; Magoga et al.), crystal plasticity simulations (Agius et al.), classical linear elastic Fracture Mechanics (Fujimoto; Vidler et al.), composite materials (Jiang, et al.; Le et al.; Zheng et al.; Chen et al.; Yamauchi et al.), behaviour of nano-composites (Ong et al; Sibtain et al.), failure of rocks and building materials (Guo et al.; Ali et al.; Nguyen et al.), bio-mechanics (Wang et al.), Structural Health Monitoring (Hu et al.; Mogeke and Magoga) and non-destructive defect and damage evaluation techniques (Khanna and Young). The authors of these articles represent a diverse international research community focusing on the understanding of failure mechanisms of materials and ensuring structural integrity and safe operation of engineering components and machines starting from the design stage and throughout their life cycle. References Khanna, A. and Young, A. 2023. Guidelines for the field-based vibration assessment of pressure vessel nozzles. Structural Integrity Procedia. Hu, X., Liang, P., Ng, C.-T. and Kotousov, A. 2023. Nonlinear edge wave generation in aluminum plates with microstructural damage. Structural Integrity Procedia. xx Magoga, T., Aksu, S. and Slater, K. 2023. Implementation of a nominal stress approach for the fatigue assessment of aluminium naval ships. Structural Integrity Procedia. xx Mogeke, M. and Magoga, T. 2023. Towards improved understanding of naval ship structural performance via virtual hull monitoring. Structural Integrity Procedia. xx Hughes, J.M., Wallbrink, C. and Kotousov, A. 2023. Cycle-by-cycle crack closure measurements and fatigue crack growth in CT specimen made of 7075-T7351 aluminium. Structural Integrity Procedia. xx Nguyen, N.T., Phan, D.G., Bennett, T., Bui, H.H., Nguyen, G.D. and Karakus, M. 2023. Modelling localised failure in porous reservoir rocks using a continuum model with an embedded localisation band. Structural Integrity Procedia. xx Ali, A., Karakus, M., Nguyen, G.D. and Amrouch, K. 2023. Quantifying the discrepancies in measuring applied stresses using Tangent Modulus Method. Structural Integrity Procedia. xx Guo, Y., Lei, B., Yu, L., Lin, X. and Li, W. 2023. Investigation on mechanical properties and failure criterion of multi-recycled aggregate concrete under triaxial compression. Structural Integrity Procedia. xx Fujimoto, K. 2023. T-stress evaluation of cracks by means of continuous dislocations model in two-dimensional elasticity. Structural Integrity Procedia. xx Vidler, J., Kotousov, A. and Ng, C.-T. 2003. Residual opening of fatigue cracks due to the wake of plasticity. Structural Integrity Procedia. xx Wang, X., Ghayesh, M.H., Kotousov, A., Zander, A.C. and Psaltis, P.J. 2023. Failure investigation and stresses in abdominal aortic aneurysms fluid-structure interaction biomechanics: Effect of nonlinear material properties and presence of intraluminal thrombus. Structural Integrity Procedia. xx Zheng, Y., Chena, T., Huang, C. and Wud, W. 2023. Numerical simulation of compact-tension specimens repaired by CFRP. Structural Integrity Procedia. xx Chen, H., Li, D., Ma, X., Zhong, Z. and Abd-Elaal, E.-S. 2023. Mesoscale analysis of rubber particle effect on compressive strength of crumb rubber mortar. Structural Integrity Procedia. xx Le, T.D., Karampour, H. and Hall, W. 2023. Design of reinforced thermoplastic pipelines for hydrogen transport. Structural Integrity Procedia. xx Jiang, Q., Takayama, T. and Nishioka, A. 2023. Relationship between interfacial shear strength and impact strength of injection molded short glass fiber-reinforced thermoplastics. Structural Integrity Procedia. xx Yamauchi, K., Shiotani, Y. and Saito, H. 2023. Deviation of the Linear Relation between Adhesion strength and Surface Free Energy on the Low Energy Surface. Structural Integrity Procedia. xx Sibtain, M., Smith, S., Yeganehmehr, A., Ong, O.Z.S. and Ghayesh, M.H. 2023. Vibrations of axially travelling CNT reinforced beams with Agius, D., Cram, D., Hutchinson, C., Preuss, M., Sterjovski, Z. and Wallbrink, C. 2023. An experimental and computational study into strain localisation in beta-annealed Ti-6Al-4V. Structural Integrity Procedia. xx.

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clamped-clamped boundary condition and an elastic support. Structural Integrity Procedia. xx Ong, O.Z.S., Ghayesh, M.H. and and Losic, D. 2023. Dynamical behaviour of CNT reinforced plates with mass imperfections. Structural Integrity Procedia. xx

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Procedia Structural Integrity 45 (2023) 4–11

17th Asia-Pacific Conference on Fracture and Strength and the 13th Conference on Structural Integrity and Failure (APCFS 2022 & SIF 2022) An experimental and computational study into strain localisation in beta-annealed Ti-6Al-4V Dylan Agius a, * , Darren Cram b , Christopher Hutchinson b , Michael Preuss b,c , Zoran Sterjovski a , Chris Wallbrink a

a Platforms Division, Defence Science and Technology Group, 506 Lorimer Street, VIC 3207, Australia b Department of Materials Science and Engineering, Monash University, Clayton, VIC 3800, Australia c Department of Materials, University of Manchester, M13 9PL, UK

© 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Prof. Andrei Kotousov Abstract Recent advances in microstructural characterisation techniques are revealing deeper insight into the plastic behaviour of polycrystalline metals. The use of digital image correlation (DIC) to visualise material deformation through slip band localisation is one such emerging technique. Not only does this technique visualise the contribution of microstructure on strain heterogeneity and strain patterns at the meso-scale, it also provides valuable information for the validation and development of computational models. These experimental techniques enable the development of improved crystal plasticity models with a focus on predicting strain localisation associated with slip traces. In this study, DIC was performed on -annealed Ti-6Al-4V to investigate the strain patterns associated with macrozones (clusters of similar orientated grains). This was done to enhance computational capability into the influence of large prior- grains on damage accumulation through the investigation of strain localisation. Simulations using Fast Fourier Transform crystal plasticity (CP-FFT) models were also conducted on the same experimental regions of interest to assess the ability to predict strain localisation. © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Prof. Andrei Kotousov Keywords: crystal plasticity; digital image correlation; fast Fourier transform; strain localisation; titnanium alloys.

* Corresponding author. Tel.: +61 393442284. E-mail address: Dylan.Agius1@defence.gov.au

2452-3216 © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Prof. Andrei Kotousov

2452-3216 © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Prof. Andrei Kotousov 10.1016/j.prostr.2023.05.002

Dylan Agius et al. / Procedia Structural Integrity 45 (2023) 4–11 Dylan Agius et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction Fatigue crack nucleation sites in titanium alloys have been shown to exist along slip bands (Zhang, Zhang et al. 2018), therefore accurately predicting the accumulation of strain along these bands is vital in the step towards correctly predicting crack initiation. Digital image correlation (DIC) experiments have provided visual representation of the slip behaviour occurring across titanium alloys, and has advanced the current understanding on the influence of microstructural features on material properties. This includes observing how strain localisation is affected by features such as 2 content in bimodal Ti-6Al-4V (Lunt, Xu et al. 2018), volume fractions of primary and secondary in additively manufactured Ti-6Al-4V (Cao, Meng et al. 2022), and transformation phase size in bimodal near- titanium (Dichtl, Lunt et al. 2022). Due to the importance of accurately predicting strain localisation in order to investigate the influence of microstructural features on mechanical properties, the computational approach most utilised in this effort is crystal plasticity modelling (Zhang, Lunt et al. 2018, Ganesan, Yaghoobi et al. 2021, Isavand and Assempour 2021). A common issue with the crystal plasticity predictions is the inability to accurately produce the degree of heterogeneity apparent in the experiments, instead predicting homogeneous strain localisation. This was somewhat overcome through the efforts of Hardie, Thomas et al. (2022) who predicted discrete slip by imposing displacements measured by High Resolution-DIC at the edges of the region of interest (ROI). However, such an approach requires prior knowledge of the local displacements, which limits the models predictive capability. An additional important consideration when investigating strain localisation in + titanium alloys is the possible formation of regions of similarly orientated grains referred to as macrozones. Macrozones can develop during processing and have been shown to impact the local deformation of the material. This includes through the formation of intense transgranular strain banding (Lunt, Thomas et al. 2021) and stress concentrations at hard and soft macrozone boundaries (Xu, Joseph et al. 2020). In this study, slip band interactions in a sample of -annealed Ti-6Al-4V was investigated using DIC. This was undertaken to observe the occurrence of strain banding within and across the macrozones formed from to grain transformation during material processing. A representative nonlocal CP-FFT model is applied to explore the possibility of using computational approaches to investigate the influence of microstructural features on strain localisation. Through a qualitative and quantitative analysis of experimental and simulation results, it is found that the influence of the grain environment on strain localisation is being considered in the simulations, as well as predicting comparable levels of strain heterogeneity. Therefore, the use of a blended experimental and computational approach to rapidly assess material failures is one step closer to fruition. Nomenclature Total displacement gradient

Elastic part of total displacement gradient Plastic part of total displacement gradient Lattice strain Cauchy stress tensor Schmid tensor of slip system s ̇ Increment of shear strain on slip system s Resolved shear stress on slip system s Backstress on slip system s Critical resolved shear stress on slip system s Norton flow rule exponent Norton flow rule coefficient 0 Initial critical resolved shear stress on slip system s Maximum softening on slip system s 0 Parameter used to adjust the rate of slip system softening 0 Backstress parameter with dimensions of stress Backstress parameter with dimensions of length

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2. Experimental analysis 2.1. Sample preparation

Samples were machined from an extra low interstitial (ELI) -annealed Ti-6Al-4V plate into a flat subsize tensile specimen geometry (oriented in the rolling direction). Tensile specimens had a dog bone geometry with a gauge length, width, and thickness of 12mm, 5mm, and 3mm respectively. One side of the tensile specimen surface was first ground up to a 2500 grit finish using SiC paper and then polished to a mirror finish using a solution of 90% OPS and 10% hydrogen peroxide. Various micro-hardness indents in a grid-like pattern were made over the samples to help locate a ROI. Using a novel patterning process described in (Yan, Tasan et al. 2015), silicon oxide (SiO 2 ) particles from OPS solution were deposited over the sample to create a fine speckle pattern suitable for μ -DIC. The quality of the speckle pattern (density and distribution) was checked using a JEOL 7001F FEG Scanning Electron Microscope (SEM). To stabilise the SiO 2 particles from the electron beam a 2nm carbon coating was applied. 2.2. Local strain measurements Prior to deforming the specimen, an initial EBSD map (0.8 μm step size) and low voltage secondary electron imaging (SEM-SEI) capturing the SiO2 particle distribution was undergone of the select area. The tensile test was then conducted on an Instron 5982 using a crosshead speed of 0.02mm/s and 10mm extensometer. The specimen was loaded to 2.5% strain. The EBSD map and SEM imaging was repeated over the selected area. The local strain map was then generated by mapping the SiO 2 markers between the unstrained and strained images using Ncorr (v1.2) (Blaber, Adair et al. 2015). 3. Strain gradient crystal plasticity FFT (CP-FFT) model 3.1. Formulation For this work, the crystal plasticity theory was applied in the context of small deformations. Additionally, only the governing equations for this work are provided. A more complete description of the theory being applied can be found in Gurtin (2002), and Marano, Gélébart et al. (2021). The underlying concept of the work proposed by Gurtin (2002) is that the local rotations (and in this case rotations due to the displacement field) contribute to the kinematic description of deformation (Abu Al-Rub, Voyiadjis et al. 2007). The total displacement gradient can be decomposed into elastic (which represents stretching and rotation of the lattice) and plastic (which is the plastic distortion due to slip) parts: = + (1) The lattice strain is given by the symmetric part of : = 1 2 ( + ) (2 ) The plastic deformation rate evolves according to the following: ̇ =∑ ̇ (3 ) where = ⨂ is the Schmid tensor, is the slip direction and is the slip plane normal of slip system . The flow rule evolves according to the classical Norton flow rule: ̇ = ⟨ | − |− ⟩ sign( − ) ( 4 ) where 〈 〉 are Macaulay brackets, and and are the Norton law exponent and coefficient. is the resolved shear stress:

Dylan Agius et al. / Procedia Structural Integrity 45 (2023) 4–11 Dylan Agius et al. / Structural Integrity Procedia 00 (2019) 000 – 000 = ∶ where is the Cauchy stress tensor. is the backstress which is defined as: = 0 2 curl(curl( )): where 0 and are material parameters with dimensions of stress and length respectively. From the analysis conducted by Marano, Gélébart et al. (2019) into the simulation of slip bands, to allow for these mechanisms to form, it is important a component of softening is added to the constitutive models. This is done through the constitutive equation defining the evolution of critical resolved shear stress ( ): = 0 − [1 − exp (− 0 )] ( 7 ) where ̇ = | ̇ | , 0 is the initial critical resolved shear stress, is the maximum softening, and 0 can be used to adjust the rate of softening. The higher order boundary condition applied in this work is the micro-free condition. In order to enforce this boundary condition, the approach used by Lebensohn and Needleman (2016) was utilised where the boundary voxels were assigned =0 , preventing the evolution of Geometrically Necessary Dislocation (GND) induced backstress in these voxels. 4. Simulation framework In the following sections, the simulation framework for both the calibration and EBSD reconstructed environment is presented. In both cases the numerical integration of the nonlocal model was implemented in the MFRONT code generator (Helfer, Michel et al. 2015). The simulations were then run using AMITEX_FFT (Gelebart, Derouillat et al. 2020). For simulations, the phase was modelled with three prismatic ( {101̅0}, 〈112̅0〉 ), three basal ( {0001}, 〈112̅0〉 ), and 12 pyramidal 〈 + 〉 ( {101̅1}, 〈112̅3〉 ) slip systems. It is important to note that some simplifications were made for the simulations. Firstly, 18 slip systems were considered. Application of this approach is due to crystal plasticity parameter availability in the literature. Since most parameters were selected directly from published work rather than calibration, it was deemed appropriate to conduct the analysis using available data. Additionally, only grains were used in the simulations. However from EBSD, there was a low amount of phase present in the microstructure (<1%). Future work will examine the influence of small amounts of phase on simulation accuracy. 4.1. Calibration simulations The calibration simulations were conducted on a three-dimensional representative volume element of 4×10 6 voxels, with the homogenised simulation results provided in Fig. 1 (a), along with the experimental monotonic tensile data. To generate the RVE representative of the -annealed Ti-6Al-4V microstructures, DREAM.3D (Groeber and Jackson 2014) was used to create the prior grains. A Python function based on the boundary vector calculator developed in (Agius, Mamun et al. 2022) was used to separate the prior grain voxels to form grains. The orientations assigned to the grains were determined based on the prior grain and orientation relationships ( {101} // {0001} and 〈111〉 // 〈2110〉 ). The final calibrated parameters are provided in Table 1. Table 1. Parameters used for the nonlocal model CP-FFT model. ( 6 ) 7 4 ( 5 )

E (GPa) 0 (MPa) (Prismatic,

(MPa) (Prismatic, Pyramidal 〈 + 〉 , Basal)

0 (MPa 1/

) 0

(MPa) (MPa)

Model

Pyramidal 〈 + 〉 , Basal) 315, 565, 325

0.0 0

Nonlocal (micro-free)

119

0.29

-59,-93,-62

0.05 7.41

20

200

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4.2. Region of interest reconstruction The ROI is the area of the microstructure used in the DIC investigation. The simulation domain however must be larger than the ROI, reducing the unrealistic influence of boundary conditions. The region used in the simulation is provided in Fig. 1 (b), with the ROI highlighted by the black square. A thickness was added to the reconstructed region of a size comparable to the average grain size of the microstructure. A substrate layer built using the microstructure statistics extracted from the EBSD scan of the larger area shown in Fig. 1 (b) was also added to the simulation domain. Adding the substrate was aimed at incorporating the local grain environment effects of the subsurface grains. Five layers of Fourier points (assigned infinite compliance) were added to the surface. This was done to ensure a free surface was modelled using periodic boundary conditions. The complete simulation domain is provided in Fig. 1 (c).

c

b

a

Reconstructed region Surface layer

Substrate

Fig. 1 (a) The homogenised stress-strain response obtained from calibration simulations and the experimental monotonic tensile results; (b) the reconstructed volume (where colours represent different grains) with the ROI outlined; (c) the complete simulation domain including the top surface Fourier points. 5. Experimental results and discussion The measured effective shear strain ( ) map calculated using the DIC approach over the ROI is provided in Fig. 2 (a). Two different grain boundaries are highlighted: grain boundaries (solid grey lines) and prior grain boundaries (black dotted lines). is calculated from the total strain tensor ( ): =√( − 2 ) 2 + 2 (8) a

b

100µm

From the DIC results, it is evident that significant slip bands have formed during deformation. These include both intergranular and transgranular slip banding. The transgranular slip banding is expected due to the grain clusters of similar crystallographic orientation within prior grains. When considering the three large prior grains, the one in the top left corner has the most activity. This is confirmed from analysis of the magnitude of strain across the Fig. 2. (a) The mapped to the ROI, measured using DIC; (b) the simulated ROI, with grain boundaries (solid grey lines) and prior grain boundaries (black dotted lines) highlighted.

Dylan Agius et al. / Procedia Structural Integrity 45 (2023) 4–11 Dylan Agius et al. / Structural Integrity Procedia 00 (2019) 000 – 000 microstructure where the top left prior grain has an average strain per grain of 0.0264 and standard deviation of 0.00819, compared to the top right and bottom prior grain which have an average strain per grain of 0.0256 and 0.0248 respectively and a standard deviation of 0.00727 and 0.00516 respectively. The results suggest that on average, grains within the top left prior grain accumulate the most strain in addition to having more grains accumulating higher magnitudes of strain than the other two large prior grains. To examine the slip banding further, two grains were extracted (Grain 1 in Fig. 3 (a) and Grain 2 in Fig. 3 (b)). In these grains, the DIC results show intense slip band formation. Using SSLIP developed by (Vermeij, Peerlings et al. 2023), the active slip systems contributing to the localisation observed from the DIC results were identified. For Grain 1 and Grain 2, the slip systems contributing most significantly to this localisation are basal ((1 1 -2 0)[0 0 0 1]) and pyramidal 〈 + 〉 ((-1 -1 2 -3)[0 1 -1 -1]) in Grain 1 and pyramidal 〈 + 〉 ((-1 0 1 1)[-1 -1 2 -3]) in Grain 2. The orientation of these slip systems is provided next to each grain in Fig. 3 (as a combination of a red line for the slip plane and an arrow for the slip direction). This initial slip trace analysis indicates for the two grains studied, the local slip system activity does not correspond to the slip mode with the most favourable Schmid factor. This suggests that the local environment is influencing the slip system activity, which supports the findings of Lunt, Thomas et al. (2021). These observations are valuable for computational model development as they provide a means of validating the capability of the model to capture the interactions between neighbouring grains. 9 6

b

a

Fig. 3 Selected grains (Grain 1 (a) and Grain 2(b)) from the microstructure used to examine the slip systems contributing the localisation observed from the DIC results. The slip system orientation and direction contributing to this localisation is indicated by the red lines and arrows. 6. Simulation results and discussion The simulated ROI is provided in Fig. 2(b) and compared against the experimental DIC results. What is initially evident from the simulation is the significant slip band formation. Further examination of the model’s ability to capture the influence of the local environment on slip system activity involved analysing the slip systems contributing to the strain localisation within the simulated results for Grain 2 against experimental results. Using SSLIP (Vermeij, Peerlings et al. 2023), two slip systems were found to be contributing to the localisation apparent in Grain 2. As was the case in the experimental results, the significant localisation was associated with pyramidal 〈 + 〉 ((-1 0 1 1)[-1 - 1 2 -3]) slip. It was the activity of this slip system which had the most influence on the strain localisation in the direction of the black arrow in Fig. 4 (a). The pyramidal 〈 + 〉 ((0 1 -1 -1)[-1 -1 2 -3]) slip system was also identified to be contributing to localisation. The deformation in the direction of the blue arrow in Fig. 4 (a) (not seen experimentally) is not due to slip band formation but instead kink band formation. This is confirmed from Fig. 4 (b) which provides the lattice rotation field across Grain 2. From Fig. 4 (b), the bands of strain localisation in the direction of the blue arrow in Fig. 4 (a) are lattice rotation bands and are therefore associated with kink bands. The same slip system in both the experimental and simulation results contributing to the most significant strain localisation is an encouraging finding. It suggests that the influence of the local grain environment on slip system activity in Grain 2 is being recognised. However, the issue of inaccurate kink band formation still plagues the simulation accuracy, even with the implementation of the mitigation efforts proposed by Marano, Gélébart et al. (2021).

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b

a

Fig. 4 (a) Grain 2 simulation results with the slip systems contributing to the localisation provided by the red lines and arrows; (b) Grain 2 lattice rotation angle field.

The kink band formation will impact the development of slip bands, therefore, it is important to understand how its formation is affecting the strain magnitude in regions of slip band formation. To do this, the strain within Grain 2 was analysed by extracting strain across a line of interest in the simulation and experiment. Results in Fig. 5 show the existence of areas across the grain where the magnitude is very similar, as indicated by the triangles. However, the circles in Fig. 5 highlight the areas within the grain where the simulated magnitude in strain deviates from the experiments. This deviation is caused by the slight difference in slip band orientation which is the consequence of the additional active slip system in the simulation contributing to the localisation. Therefore, future work will include investigating what is causing this additional slip system to activate and to what extent its activity is affecting the formation of slip bands.

a

b

c

7. Conclusion A combined experimental and computational investigation into strain localisation occurring within -annealed Ti 6Al-4V is presented. Through this investigation, the following findings were made:  Using a nonlocal CP-FFT model, intergranular and transgranular slip bands were successfully predicted in locations across the ROI that were comparable with the DIC results.  Initial findings obtained from a deeper analysis of the simulation results suggest that the nonlocal CP-FFT model is capable of recognising the influence of a grain’s local environment on slip system activity within the grain. Additionally, the predicted magnitude of strain at locations across the grain were comparable to that measured experimentally.  Kink band formation remains incorrectly predicted by the model. This resulted in inaccurate locations of strain localisation which could affect the capability of the model to accurately predict crack initiation sites. This area of the crystal plasticity modelling requires further investigation and development. Fig. 5 Comparison of the experimental and simulated across Grain 2 where (a) is the simulated response, (b) is the experimental response and (c) is the value of along the red line traversing the grain as indicated in (a) and (b).

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Acknowledgements The authors would like to acknowledge the funding and support provided by the Australian Defence Aviation Safety Authority, and the use of instruments in addition to the scientific and technical assistance at the Monash Centre for Electron Microscopy (MCEM), Monash University, the Victorian Node of Microscopy Australia. DC and CH gratefully acknowledge the support and advice of Ms J Luo (Monash University) regarding the DIC experiments. References Abu Al-Rub, RK, Voyiadjis, GZ & Bammann, DJ 2007, 'A thermodynamic based higher-order gradient theory for size dependent plasticity', International Journal of Solids and Structures , vol. 44, no. 9,pp. 2888-2923. Agius, D, Mamun, AA, Truman, C, Mostafavi, M & Knowles, D 2022, 'A method to extract slip system dependent information for crystal plasticity models', MethodsX , vol. 9,pp. 101763. Blaber, J, Adair, B & Antoniou, A 2015, 'Ncorr: Open-Source 2D Digital Image Correlation Matlab Software', Experimental Mechanics , vol. 55, no. 6,pp. 1105-1122. Cao, S, Meng, L, Liu, H, Zou, Y, Smith, A, Wu, X, Donoghue, J, Thomas, R, Preuss, M & Lunt, D 2022, 'Role of microstructure heterogeneity on deformation behaviour in additive manufactured Ti-6Al-4V', Materialia , vol. 26. Dichtl, C, Lunt, D, Atkinson, M, Thomas, R, Plowman, A, Barzdajn, B, Sandala, R, da Fonseca, JQ & Preuss, M 2022, 'Slip activity during low-stress cold creep deformation in a near- α titanium alloy', Acta Materialia , vol. 229. Ganesan, S, Yaghoobi, M, Githens, A, Chen, Z, Daly, S, Allison, JE & Sundararaghavan, V 2021, 'The effects of heat treatment on the response of WE43 Mg alloy: crystal plasticity finite element simulation and SEM-DIC experiment', International Journal of Plasticity , vol. 137,pp. 102917. 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Procedia Structural Integrity 45 (2023) 44–51

17th Asia-Pacific Conference on Fracture and Strength and the 13th Conference on Structural Integrity and Failure (APCFS 2022 & SIF 2022) Cycle-by-cycle crack closure measurements and fatigue crack growth in CT specimen made of 7075-T7351 aluminium

James Martin Hughes a,* , Chris Wallbrink b , Andrei Kotousov a a School of Electrical and Mechanical Engineering, The University of Adelaide, SA 5005, Australia b Platforms Division, Defence Science and Technology Group, VIC 3207, Australia

© 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Prof. Andrei Kotousov Abstract In this study, an advanced piezoelectric strain sensor is applied to measure the crack opening loads of a compact tension specimen with a fatigue crack under variable amplitude block loading. The crack opening loads are subsequently utilised to modify the stress intensity factor range by taking into account the proportion of each load cycle for which the fatigue crack remained closed. This effective stress intensity factor is applied to collapse the growth rate curve, which initially displays a strong dependence on stress ratio, into a single master curve where the only variable governing crack extension is the effective stress intensity factor. The findings of this study provide strong evidence for the crack closure concept, which is important for the development of algorithms which can compress/truncate large spectrums. These algorithms rely on a detailed understanding of how much the crack is open or closed during each load cycle. Furthermore, the results indicate that the piezoelectric sensor could be used to study crack closure under realistic spectrum loading conditions, which will be the subject of future investigations. © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Prof. Andrei Kotousov Keywords: Crack closure; fatigue; crack growth; load spectrum

* Corresponding author. E-mail address: james.m.hughes@adelaide.edu.au

2452-3216 © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Prof. Andrei Kotousov

2452-3216 © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Prof. Andrei Kotousov 10.1016/j.prostr.2023.05.012

James Martin Hughes et al. / Procedia Structural Integrity 45 (2023) 44–51 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction Crack closure is a well-known phenomenon in cyclic fatigue whereby a fatigue crack remains closed for a portion of the load cycle, even for tensile-tensile cycles. This phenomenon was first reported by Elber (1970) and has since been the subject of thousands of scientific studies. The overall effect of crack closure is a reduction in the stress intensity factor (SIF) range, which is the driving mechanism for crack growth in the Paris-Erdogan law (Paris and Erdogan, 1963). Elber (1971) subsequently proposed a modified crack growth equation which takes the crack closure effect into account:

da dN



 eff K

m

C  

(1)

where da/dN is the crack extension per load cycle, Δ K eff is the effective SIF range, and C and m are material parameters. If the crack opening/closure loads are known (or measured), the overall SIF range can be related to the effective SIF through Eq. (2):

max P P P P   max

op/cl

(2)

eff K  

K U K

  

min

where P max , P min , and P op/cl are the maximum load, minimum load, and opening/closure load, respectively, and U is often called the opening load ratio. There is typically some small difference between the opening and closure load, but in practice this difference is disregarded (see Fig. 3 and 4 of Ashbaugh et al., 1997). Although there remains some skepticism (Lout et al., 1993; Vasudeven et al., 1994; Vasudeven et al., 2001), it is well agreed that the theory of crack closure provides clear explanations for the short crack effect (Vormwald and Seeger, 1991; Breat et al., 1983; Pippan and Hohenwarter, 2017) and the stress ratio effect (Pippan and Hohenwarter, 2017; Moreno et al., 2019; Okayasu et al., 2006). Closure measurements can therefore be applied to collapse fatigue crack growth rate curves from constant, variable, or random amplitude load sequences into a single master curve. Although a number of studies have used finite element simulations and experimental techniques to investigate the effect of crack closure for simple constant amplitude load sequences (Fleck et al., 1983; de Matos and Nowell, 2009; Ashbaugh et al., 1997; Sehitoglu, 1985) or after overloads (Borrego et al., 2012; Nowell and de Matos, 2010), the on line measurement of crack closure in variable amplitude loading sequences has been met with considerable difficulty. A limited number of studies have extracted closure measurements for a small number of variable amplitude cycles with some success (Moreno et al., 2019), however, the on-line monitoring of large variable amplitude load sequences is yet to be achieved due to sensor limitations and large data. Such an advancement would enable the abovementioned collapsing of the fatigue crack growth rate curve, and provide essential knowledge and data to develop more sophisticated spectrum compression and truncation algorithms. Crack opening/closure loads can be identified using electrical, acoustic, or compliance-based techniques, although compliance techniques are preferred due to their accuracy (Fleck et al., 1983). Compliance-based techniques use the nonlinear load-displacement relationship to identify the closure/opening load. At sufficiently high loads, the crack is fully open, and the compliance of the specimen remains constant. Below the crack opening load, the compliance of the specimen is nonlinear and changes as the crack is incrementally opened. A variety of instruments can be used to measure specimen compliance, such as a back-face strain gauge, surface strain gauge, extensometer, push-rod system, or piezoelectric strain sensor. The compliance technique, originally proposed by Elber (1970), has since been refined to the current load-differential displacement curve method first proposed by Kikukawa (1976). More information regarding the measurement of crack opening using compliance-based methods can be found in the ASTM standards (2009) and other articles (such as Song and Chung, 2010). In this study a piezoelectric strain sensor (see Wallbrink et al., 2023) is used to track the crack closure/opening loads over the full life of a compact tension specimen. A variable amplitude spectrum containing blocks of constant amplitude loading is applied to the fatigue specimen. Fractographic imaging is used to determine the crack growth rate at various crack lengths for the different stress ratios. Additionally, the crack opening loads are measured using the

James Martin Hughes et al. / Procedia Structural Integrity 45 (2023) 44–51 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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piezoelectric strain sensor. These measurements are subsequently incorporated into the crack growth rate curve (see Eq. 2) to remove the dependency between the fatigue crack growth rate and stress ratio, effectively collapsing the data into a single master curve. These results exhibit good correlation with existing data sets, which generally contain only constant amplitude loading extracted over a small portion of the overall fatigue life. This paper is structured as follows: Section 2 presents the experimental methodology and describes the load sequence, instrumentation, specimen geometry, and the data processing techniques used. The main results of the study are presented in Section 3, where the fatigue crack growth rate curve and crack opening loads are discussed. The overall outcome, collapsing the growth rate curve, is then demonstrated, and the results are compared against existing literature. Finally, Section 4 concludes the paper, and future work arising from this research is suggested. 2. Methodology 2.1. Loading Sequence and Instrumentation A 100 kN MTS testing machine was used to load a compact-tension (CT) specimen manufactured from 7075 T7351 aluminium. The length of the specimen (W) was 50.8 mm, the width (B) 12.7 mm, and the initial notch length (a i ) 10.16 mm. A compression-compression pre-cracking load regime was used to nucleate a crack from the notch until the pre-crack length reached 0.75 mm (total length a 0 = 10.91 mm). Following this, continuous sequences of constant amplitude loading blocks were applied to grow the fatigue crack until failure. Each load sequence consisted of an initial 200 cycles of stress ratio R = 0.5 loading, followed by 100 cycle load blocks of descending stress ratios from 0.4 to 0 in increments of 0.1, interspersed with R = 0.5 load blocks (see Fig. 1 below). This specific sequence was originally used in White et al. (2018). The piezoelectric strain gauge was bonded along the centreline of the back side of the CT specimen. The gauge was indented from the top surface to ensure that the maximum strain range of the instrument was not exceeded, as damage can occur for strains greater than 100 με (Piezotronics Model 740B02 Manual, 2021). The specimen was also fitted with a traditional back-face strain gauge and a clip gauge attached to the crack mouth. More information regarding the specimen, loading sequence, and piezoelectric strain sensor can be found in Wallbrink et al. (2023).

4

3

2

Load (kN)

1

0

0

Cycle Number (hundreds) 1 234567891011

Fig. 1. Load sequence applied to the compact tension specimen, indicating the stress ratio.

2.2. Measurement of Crack Growth Rate The growth rate of the fatigue crack was measured using an optical microscope. Images were taken at a number of locations along the fracture surface which correspond to different crack lengths. Specific load blocks can be identified in the fractographic images as different shaded bands. In particular, the R = 0.5 load blocks act as marker bands, which appear darker in colour (see Fig. 3 ahead) and separate the other load blocks. The fatigue crack growth rate was calculated by measuring the progression of the crack front during each of the loading blocks. Several measurements were taken within the same stress ratio band to improve the accuracy of the measurements; the average value was taken as the growth rate and the standard deviation as the error. Macroscopic crack length measurements were estimated with the standard compliance method as documented in the ASTM standards (2009).