PSI - Issue 38

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FATIGUE DESIGN 2021, 9th Edition of the International Conference on Fatigue Design Fatigue Design Preface Fabien Lefebvre* a Cetim, 52 avenue Félix Louat, 60304, Senlis, France FATIGUE DESIGN 2021, 9th Edition of the International Conference on Fatigue Design Fatigue Design Preface Fabien Lefebvre* a Cetim, 52 avenue Félix Louat, 60304, Senlis, France

© 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Fatigue Design 2021 Organizers © 2021 The Authors. Published by ELSEVIER B.V. This is an ope acces article under CC BY-NC-ND license (https://cr ativecommons.org/l c nses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Fatigue Design 2021 Organizers © 2021 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) P r-review under responsibility of the scientific committee of th Fatigue Design 2021 Organizers

* Corresponding author. Tel.: +33 (0)6.87.18.89.42 E-mail address: fabien.lefebvre@cetim.fr * Corresponding uthor. Tel.: +33 (0)6 87.18.89.42 E-mail address: fabien.lefebvre@cetim.fr

2452-3216 © 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Fatigue Design 2021 Organizers 2452-3216 © 2021 The Authors. Published by ELSEVIER B.V. This is an ope acces article under CC BY-NC-ND lic nse (https://cr ativecommons.org/l c nses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Fatigue Design 2021 Organizers

2452-3216 © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Fatigue Design 2021 Organizers 10.1016/j.prostr.2022.03.001

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Fabien Lefebvre et al. / Procedia Structural Integrity 38 (2022) 1–3 Lefebvre / Structural Integrity Procedia 00 (2021) 000 – 000

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Fatigue Design 2021 Group photo On behalf of the Fatigue Design 2021 International Scientific Committee and Organizing Committee, the 9 th edition of Fatigue Design 2021 took place at Cetim, Senlis, France on November 17 & 18 2021. Since 2005, and every two years, the conference takes place at Senlis, the City of culture and history, located at 45km from Paris with more than 2000 years of history. The Notre-Dame Cathedral of 12th century, Saint-Pierre church, Medieval ramparts of 13th - 16th century, the château royal and 4 museums are among the most attractive places to be visited. Organized by Cetim and his partners, the 9 th Fatigue Design 2021 International Conference aims to present the most innovative approaches, scientific and technological progress in design methodologies, testing methods and tools to evaluate and extend the fatigue lifetime of the industrial equipment. The papers are mostly focusing on the industrial applications. After USA in 2015, Italy in 2017, Japan in 2019, Germany has been proposed as th e “partner country” for Fatigue design 2021 in respect to the German advance research works in the area of fatigue and fracture mechanics in the last decade. More than 25% of conference speakers are coming from Germany including 2 plenary key speakers. For this edition, a special focus has been made on the contribution of Big Data and Artificial Intelligence to the fatigue design world. This edition of the conference covered as well the following scientific and technical topics: • additive manufacturing • experimental and numerical design and validation methods, • damage tolerance and fatigue life, • reliability -based approaches and probabilistic methods, • nonlinear behavior and cumulative damage, • fatigue of assemblies (mechanical, welded, adhesive -bonding, multimaterial...), • composite and elastomers, • contact fatigue and vibration fatigue behavior, • complex loadings and thermal and thermo-mechanical fatigue, • taking into account manufacturing process in fatigue analysis (effect of microstructure, welding, stress relief techniques...).

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The presentations focus on the latest development and most recent experimental, numerical simulation techniques and the associated engineering tools applied to the large domain of the industrial applications. The 9th edition of the Fatigue Design International conference is organized in close collaboration with Elsevier editor for the proceedings ’ publication through Structural Integrity Procedia. The papers are published online on ScienceDirect, which makes available worldwide for a better dissemination and maximum exposure. In this respect the selection and peer review of the papers have been done in collaboration with the International Scientific and Organizing Committees. “Fatigue Design” bec omes the reference conference with more than 550 delegates to address the concerns of industrials on fatigue design of structures and components. It is also considered as the trade crossroads between industry and academia: 84 oral presentations are performed with 50% by industry. We hope that the speakers and the delegates would have a fruitful exchange and discussions on technical and scientific developments and issues during the conferences. The poster sessions and exhibition stands are the complementary opportunities to facilitate the exchanges between the Scientists, industry participants, PhD students and the solution providers. The organizing committee wanted to keep the conviviality of a face-to-face conference which is the soul of the Fatigue Design conference since 2005. However, in regarding the current health situation, the conference was also available in a digital version. We would like to thank members of the International Scientific and Organizing Committees for their valuable scientific support for the selection and paper reviews, the authors, delegates for their contributions, exhibitors and sponsors, and SF2M and AFM and the colleagues of Cetim for the organization and to make this conference successful one.

Fabien Lefebvre Chairman Organizing Committee Fatigue Design 2021 Pascal Souquet Co-Chairman Organizing Committee Fatigue Design 2021

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Procedia Structural Integrity 38 (2022) 331–341 Structural Integrity Procedia 00 (2021) 000–000 Structural Integrity Procedia 00 (2021) 000–000

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© 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Fatigue Design 2021 Organizers © 2021 The Authors. Published by Elsevier B.V. his is an open access article under the CC BY-NC-ND license (http: // creativec mmons.org / licenses / by-nc-nd / 4.0 / ). eer-review under responsibility of the Fatigue Design 2021 Or aniz rs. Keywords: Fatigue crack growth simulation; uncertainty quantification; response surface modeling; remaining useful life; 3D finite element modeling; probabilistic structural life assessment; Abstract Runtime e ffi cient models designed for damage tolerant life assessment are desired in Structural Health Management and Digital Twin development. While FEM is commonly used in the industry to assess health of a nominal structure design while in service, in probabilistic assessments, reduced order models are preferred due to lower runtime compared to the deterministic models but at the cost of solution accuracy. Readily available machine learning algorithms coupled with deterministic 3D simulations for modeling fatigue crack growth provide a feasible path to reach a better runtime-accuracy compromise. In this study, a fatigue crack growth testing procedure along with measurement data are used for validation purposes and for laying out details of the modeling process. Accuracy and solution runtime of the 3D FEA based surrogate models are assessed to demonstrate the e ffi ciency of the method. © 2021 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 Fatigue Design 2021 Organizers. Keywords: Fatigue crack growth simulation; uncertainty quantification; response surface modeling; remaining useful life; 3D finite element modeling; probabilistic structural life assessment; FATIGUE DESIGN 2021, 9th Edition of the International Conference on Fatigue Design 3D FEA based surrogate modeling in fatigue crack growth life assessment Adrian Loghin a, ∗ , Shakhrukh Ismonov b a Simmetrix Inc., Clifton Park, NY, USA b Jacobs Technologies Inc., Houston, TX, USA Abstract Runtime e ffi cient models designed for damage tolerant life assessment are desired in Structural Health Management and Digital Twin development. While FEM is commonly used in the industry to assess health of a nominal structure design while in service, in probabilistic assessments, reduced order models are preferred due to lower runtime compared to the deterministic models but at the cost of solution accuracy. Readily available machine learning algorithms coupled with deterministic 3D simulations for modeling fatigue crack growth provide a feasible path to reach a better runtime-accuracy compromise. In this study, a fatigue crack growth testing procedure along with measurement data are used for validation purposes and for laying out details of the modeling process. Accuracy and solution runtime of the 3D FEA based surrogate models are assessed to demonstrate the e ffi ciency of the method. FATIGUE DESIGN 2021, 9th Edition of the International Conference on Fatigue Design 3D FEA based surrogate modeling in fatigue crack growth life assessment Adrian Loghin a, ∗ , Shakhrukh Ismonov b a Simmetrix Inc., Clifton Park, NY, USA b Jacobs Technologies Inc., Houston, TX, USA

Nomenclature Nomenclature

RUL Remaining Useful Life FEA Finite Element Analysis FE Finite Element 3D Three-dimensional CAD Computer Aided Design ADT Airframe Digital Twin RBF Radial Basis Function RS Response Surface RUL Remaining Useful Life FEA Finite Element Analysis FE Finite Element 3D Three-dimensional CAD Computer Aided Design ADT Airframe Digital Twin RBF Radial Basis Function RS Response Surface

∗ Corresponding author. E-mail address: loghin@simmetrix.com ∗ Corresponding author. E-mail address: loghin@simmetrix.com

2452-3216 © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Fatigue Design 2021 Organizers 10.1016/j.prostr.2022.03.034 2452-3216 © 2021 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 u der responsibility of the Fatigue Design 2021 Organizers. 2452-3216 © 2021 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 Fatigue Design 2021 Organizers.

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R Cyclic stress ratio, σ min /σ max DOE Design of Experiment GPR Gaussian Process Regression

K Imax Mode I Stress Intensity Factor at maximum load K IImax Mode II Stress Intensity Factor at maximum load ∆ K I Mode I Stress Intensity Factor range, K Imax − K Imin Y 1

Relative distance between initial notch and the hole feature along Y direction Relative distance between initial notch and test specimen centerline

Y 0

a X , a Y Planar position of sequential crack front increments

1. Introduction

It is commonly believed that remeshing process is man-power intensive and generating fine mesh around the crack front is computationally expensive (Peng, et. al. (2018)). Consequently, any mesh convergence study or uncertainty quantification assessment becomes a burden for the engineer in charge of a structural integrity assignment. Under the assumption that a quick runtime model is needed, closed-form solutions for simple crack representations (i.e. elliptical corner crack at a hole under uniform loading) are still developed and used even though they often provide a lower accuracy solution compared to a 3D finite element structural analysis due to the assumptions made in the modeling process. In a realistic fatigue crack growth assessment, far-field loading is not uniform, crack shape might not be elliptical or straight, geometric features can a ff ect the crack path or, interaction of multiple cracks must be considered. Developing closed-form models for each of the potential scenarios is impractical. Instead of developing a generic model specific to a location susceptible for cracking or already containing a crack, the 3D FEA representation of the structure can be utilized to accurately compute crack driving forces and therefore take into account nominal geometry and the stress gradient that controls crack advancement. This can be achieved with e ffi cient remeshing procedures (Loghin (2018)) transparent to the user at a fraction of the runtime cost compared to the solution time. The assessment is more accurate than the closed form equivalent model, but it comes with a higher runtime cost. The advantage of robust remeshing capabilities can be complemented with machine learning algorithms to satisfy both critical crack propagation life assessment requirements: accuracy and low runtime cost. 3D FEA based surrogate modeling development has been reported in the recent literature by Leser et al. (2017), Loghin and Ismonov (2020a), Spear et al. (2011), Shantz (2010), Loghin and Ismonov (2019). Gaussian Process Regression (GPR) is one technique employed to generate surrogate models for a quick computation of mode I stress intensity factors at one or two locations along the crack front. Calibration of the GPR surrogate model makes use of di ff erent 3D FE models that capture the overall geometry and loading configuration of the part, crack shape and size evolution. This is advantageous since these simulations are detached of each other and therefore can be performed as independent processes (Loghin and Ismonov (2020a)) and, secondly, accuracy of the solution is maintained by using representative 3D FEA instead of reduced order models (based on geometric simplifications and weight functions). Radial Basis Function (RBF) based surface response modeling is another technique for developing surrogate models designed to capture the entire crack path and not only the mode I stress intensity factors for a given crack size and shape. Similar to the GPR surrogate model calibration process, a set of independent simulations are performed but, in this case, each simulation is a 3D FEA crack propagation assessment. The outcome of each deterministic assessment consists of a crack surface evolution and associated loading cycles. The main question is how the damage tolerance design community will accommodate more accurate component level fatigue crack growth representations instead of handbook solutions or reduced order models for crack propa gation life assessments. For a simple corner crack at a hole, the elliptical crack front assumption (commonly used in reduced order models) produces a 36% conservative loading cycles estimation relative to a three-dimensional FE model where no crack front shape constraint is used (Loghin (2021)). Sobotka and McClung (2019) point out another lack of accuracy source in crack propagation life assessment: accuracy of stress intensity factor solution. According to Sobotka and McClung (2019) a 10% error in stress intensity factor calculation may translate into 30% to 50% error in computed loading cycles.

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Fig. 1: Overall nominal model dimensions following Leser et al. (2017).

In order to make use of more accurate deterministic solutions, runtime e ffi cient routines are needed in probabilistic fatigue crack growth studies and Airframe Digital Twin development (Kobryn (2019), Millwater et al. (2019)). A component level surrogate model development is a more accurate representation of the fatigue crack growth conditions (local geometry and stress gradient that acts on the crack plane) than a reduced order model. A machine learning based surrogate model calibrated on accurate 3D FEA simulations can satisfy both conflicting requirements, high accuracy and low runtime cost, at a higher standard than current methodologies. Also, since well established FEA solvers are employed, surrogate modeling as presented in this study can benefit from decades of finite element modeling development. A practical implementation is also desired from a cost perspective. The integrated CAD to FEA modeling process along with remeshing capabilities for simulating fatigue crack growth at component level (Loghin (2018)), allows en gineers to easily employ models developed in the design and analysis process. Machine learning modeling capabilities available to the public in SciPy (Virtanen et al. (2020)) were utilized in this study without any additional functional development. SimModeler Crack as well as batch mode capabilities for modeling crack growth were employed to perform all the 3D FEM based simulations presented in this study. Component level CAD geometries as well as meshes with no underlying geometry can be used to initiate the modeling process. A geometry-mesh compatibility allows continuous and automatic assignment of pre-processing items to the geometric entities and transferred to mesh entities for each 3D model generated in the explicit crack propagation simulation process. More details of the development are provided in Loghin (2018) along with several verification and validation examples (Loghin and Ismonov (2020b)). The experimental procedure presented by Leser et al. (2017) is modeled using a nominal geometry of test specimen and finite element representations that capture loading conditions and crack surface advancement. Three-dimensional nominal geometry used in the numerical assessment is presented in Figure 1. Location of the initial crack relative to the hole feature in the panel specimen is identified through the ” Y 1 ” parameter. A cyclic uniform remote tensile loading with a of maximum value of 41 MPa and a stress ratio R = 0 ( ∆ K I = K Imax , K Imin = 0) was used. Fatigue crack growth simulation is performed via SimModeler Crack using classical Paris-Erdogan relationship and fatigue crack growth rate data for 2024-T62 reported in Farahmand et al. (1997): C = 2.97e-12, n = 3.2, corresponding to ∆ K I [MPa*mm 0 . 5 ] 2. Modeling Procedure 2.1. 3D FEA Procedure - Nominal Configuration

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Fig. 2: Comparison of di ff erent solvers (Ansys, Abaqus, CalculiX) for the same nominal configuration, fatigue crack growth life assessment.

and da / dN [mm / cycle]. An initial edge crack of 2.16 mm is introduced in the model. The plane of the crack is normal to the loading direction and located at 6.07 mm from the center of the hole (see Figure 1). An elasticity modulus of 7.17e4 MPa and a Poisson ratio of 0.33 define the linear elastic constitutive model. The fatigue crack propagation formulation uses maximum tangential stress criteria to define crack growth direction and displacement correlation technique to compute stress intensity factors for all three fracture modes. The 3D fatigue crack growth simulation is performed automatically for the nominal configuration presented above. Figure 2 shows a crack path comparison between experimental measurement and numerical procedure along with computed loading cycles using three di ff erent solvers: ANSYS (2021), ABAQUS (2021) and CalculiX (2021). Based on this comparison it can be concluded that the numerical uncertainty related to the solver is minimal and, the pre dicted crack path is successfully validated against experimental measurement. Both the geometric representation and associated mesh for the last considered step in the fatigue crack growth simulation are presented in Figure 3. As it can be easily observed in Figure 3, the crack surface has a uniform growth across thickness direction and mixed mode conditions develop when crack front reaches the hole location. Once the hole is passed, loading conditions at the crack front become mode I dominant again. A collected crack path digital measurement along the free model boundary (Figure 3, d)) is representative for a comparison against experimental measurements shown in Figure 2. An interaction between crack size and stress concentration factors at the hole is captured in Figure 4. As the crack front advances and reaches locations under the hole, the value of K Imax diminishes due to a load shedding e ff ect. As expected, the stress concentration factors ( K t ) at the two hole side locations show an opposite e ff ect: significant increase as the crack approaches locations under left side or right side of the hole. For the initial crack length it can be noticed that the two K t values are close to a value of 3 (as expected) and for a long crack that passed the hole location, the K t values approach 0 indicating no loading bearing at the hole location. The load shedding e ff ect provides an explanation to the shape of crack length vs. cycles presented in Figure 4 d). Two variability sources are considered for a sensitivity study: o ff -nominal geometry and intrinsic fatigue crack growth scatter. For geometric variability, the vertical position Y 1 of the initial crack relative to the hole was incremen tally modified and, for each o ff -nominal geometry a crack propagation simulation was performed using the modeling procedure described in the chapter above. Using 25 equally incremented discrete values of Y 1 from a minimum value of 5.25 mm and a maximum value of 6.75 mm, the surrogate model training data was collected from 3D FE crack propagation simulations using SimModeler as shown in Figure 5. For each deterministic simulation, the initial and final crack sizes of each run were set at a 0 = 2 . 16 mm and a f = 25 mm. About 220 increments were carried out for the entire crack growth analysis from the initial to the final crack size. The applied loads were the same as in nominal model described in Section 2.1 above. Each of these runs generated numerical data of the mode I and II stress 2.2. Surrogate Modeling - Calibration and Verification

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Fig. 3: (a) Close-up view at crack location site; (b) Crack surface mesh of the last simulated increment; (c) Geometric representation of the simulated crack surface; (d) Data collection for crack length measurement and associated cycles.

Fig. 4: (a) Mode I stress intensity factor ( K I ) at maximum applied load from each crack increment; (b) ( a X , a Y ) planar position of sequential crack front increments, ” a ” instantaneous crack length; (c) Stress concentration factors at the hole, two locations: left and right side; (d) Nominal crack length vs. cycles assessment.

intensity factor values K Imax and K IImax across the crack front, crack length a , crack tip X and Y coordinates at the model boundary [ a X , a Y ] at every crack growth increment. Since the magnitude of K IImax is minimized during the

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Fig. 5: Surrogate model training data set: 25 three-dimensional FEA based fatigue crack growth assessments.

out-of-plane crack growth analysis in SimModeler, it was found that the K IImax values are not needed to calibrate the surrogate model. The automated crack growth results showed nearly uniform crack growth across the front i.e. the initial straight through crack remained as straight-through throughout the entire propagation simulation. For this reason, a single parameter characterizing the crack tip driving force was deemed su ffi cient for the surrogate model. This parameter was taken to be K Imax since R = 0 ( K Imax = ∆ K I ) at model boundary to be consistent with [ a X , a Y ] definition. In addition, the path solutions shown in Figure 5 indicated all crack paths remained to be parallel with no overlaps for the majority of the solutions. This allowed us to use the following three RBF based surrogate model components: 1. K I ( Y 1 , a X , a Y ): mode I SIF as a function of Y 1 , a X and a Y – planar crack tip position (at model boundary) during propagation simulation. 2. a X ( Y 1 , a ): as a function of Y 1 and the instantaneous crack length a . 3. a Y ( Y 1 , a ): as a function of Y 1 and a . To verify the surrogate model performance, a new set of test data was generated by running ten additional automated crack propagation simulations at randomly selected initial crack Y 1 -positions within the calibration Y 1 range. Figure 6 shows the correlation plots between the surrogate model and the FE results of K Imax and a X for both calibration and test data. Because of the underlying RBF interpolation models that were used, the surrogate models are expected to predict the calibration points shown by blue circles perfectly; this is what is observed in the plots. However, the surrogate models also exhibit very good performance with the test data shown in red. The performance of the third surrogate model for a Y was very similar to a X and hence its correlation plot is omitted here for brevity. With the verified surrogate model components in place, a crack propagation routine was developed to incrementally grow the crack from the initial size to the final size. With the predefined initial crack size, the crack location defined by Y 1 and the nominal fatigue crack growth rate parameters C and n , the routine follows these steps: 1. Compute the mode I SIF value for the given crack size using the surrogate model for K I ( Y 0 , a X , a Y ) at maximum load. Consider R = K Imin / K Imax = 0, ∆ K I = K Imax − K Imin = K Imax identical to the deterministic solution. 2. Grow the crack size by the incremental amount da and estimate the corresponding incremental number of cycles dN using the Paris law relationship da / dN = C ( ∆ K I ) n . 3. For the new crack length a , estimate the new crack tip position using the surrogate models a X ( Y 1 , a ) and a Y ( Y 1 , a ). 4. Repeat the loop until the final crack length is reached.

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(b)

(a)

Fig. 6: Verification plots for surrogate model components for (a) mode I SIF at maximum loading and (b) crack tip X location.

The solutions of the constructed surrogate model for crack propagation were verified against ten 3D FEA based crack propagation simulations described above. Figure 7 compares the surrogate model and FE results for di ff erent quantities: loading cycles, K Imax and non-planar crack path. The surrogate model solutions are plotted by solid lines and the FE solutions are given by solid symbols. These plots indicate that the surrogate model is adequately capturing the crack propagation behavior of the 3D FE model within the solution space and therefore reaching verification requirements. Note that only five of the ten verification data sets were included in these plots for clarity. The model performance on the remaining cases were similar. Note also that all of the observed variances of the solutions so far are solely due to the variance of the initial crack position Y 1 . No material variation is added at this point. It is observed that even though the estimated crack paths and the K I values had some reasonable variance, the remaining useful life assessment did not have a variation of practical significance. In the next step, the constructed surrogate model for crack propagation was verified with di ff erent material fatigue crack growth rate properties. FE based deterministic solutions were collected from five additional simulations, this time with varying C and n fatigue crack growth parameters in addition to the varying geometric parameter Y 1 . Figure 8 shows the comparison between the surrogate and FE model assessments. As before, the surrogate model solutions are given by solid lines and the FE solutions are plotted by solid symbols. It is observed that one of the solutions terminate at the crack length of about 15 mm. This was because the crack for this particular case merged into the hole, similar to one of the cases shown in Figure 7c. Figure 8 demonstrates that the surrogate model sensitivity to material variation is consistent with the deterministic FE model.

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(a)

(b)

(c)

Fig. 7: Surrogate model verification: (a) Remaining useful life, (b) K I at maximum loading, (c) Predicted crack path.

Fig. 8: Surrogate model verification against the deterministic model for five di ff erent pairs of { C, n } .

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(a)

(b)

Fig. 9: Correlated C and n data extracted from Virkler’s crack propagation measurements on 2024-T3 Aluminum alloy (Virkler (1978).

2.3. Probabilistic Assessment using Surrogate Modeling

To demonstrate the usage of the surrogate crack propagation model in a probabilistic setting, benchmark crack propagation data published in Virkler (1978) was used. This data shown as “Virkler’s data” in Figure 9a contains crack length versus cycles measurements collected from 68 constant amplitude crack growth tests under mechanical stress σ varying from 0 to 48.26 MPa at constant temperature for 2024-T3 Aluminum alloy. The specimen used for the test was M(T) with the sample width W = 152 . 4mm. In each test, the crack was grown from the initial size of a = 9mm to final size 50mm. Assuming the variation in the crack propagation data is solely due to material variation, Paris curve paired constants C , n were extracted from this data using the procedure similar to the one described in Akkaram et al. (2011). A simple crack propagation side-model was built for M(T) sample using the Paris curve da / dN = C ( ∆ K I ) n , and the K I formulation for the middle crack in a finite sheet under uniform remote tensile loading (Tada et al. (2000)): This side-model was used to determine the best fit parameters { C , n } for each crack propagation data set using the Nelder-Mead optimization routine available in SciPy optimization library (Virtanen et al. (2020)). The solid curves shown in Figure 9a are the best fit curves, and the data plotted in Figure 9b are the corresponding material { C , n } parameters from all 68 curve fits. As one may expect these two material parameters are highly correlated (Annis (2003)). Finally, the collected sample of the material parameters were used along with the normally distributed initial crack position Y 0 = N ( µ = 6.74mm, σ = 0.375mm) in Monte-Carlo simulations. Definition of Y 0 is provided in Figure 2. The crack path variation is shown in Figure 10 while the results of the RUL probabilistic assessment is given in Figure 11. Based on the observation that the Y 1 has little e ff ect on the crack growth life (Figure 7a), it can be concluded that almost all of the variation in RUL is due to the material variability in this model. The orange line plotted on top of the histogram in Figure 11b is the estimate of the probability density function obtained by Kernel Density Estimation method called Gaussian kde available in Python SciPy Library. This density function can be conveniently used for probabilistic RUL assessment. The surrogate model runtime savings are quite substantial when compared to the 3D FEA simulation. The determin istic fatigue crack growth simulation using about 220 increments is solved in under 120 minutes while surrogate model K I = σ G √ π a where G = cos ( π a / W ) − 0 . 5 (1)

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Fig. 10: Crack path probabilistic assessment using the verified surrogate model.

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Fig. 11: RUL probabilistic assessment using the verified surrogate model.

provides a solution in less than two seconds. It is important to mention that verification of the surrogate model against deterministic assessments (not part of training set) is an essential requirement. Validation of the overall modeling procedure against experimental measurements needs to be pursued continuously by the damage tolerance community to provide confidence in the methodology when applied at the component or structure level.

3. Conclusions

An RBF fatigue crack growth surrogate model was developed based on three-dimensional finite element modeling procedures. The surrogate model is specific to an edge crack in a flat panel containing a hole for which experimental measurements are publicly available. Each 3D FE simulation that was used to train the surrogate model computes crack propagation path and corresponding loading cycles for di ff erent o ff -nominal geometry configurations. Once the surrogate model passes verification requirements, runtime e ffi cient and accurate probabilistic damage tolerance assessments can be performed considering experimental fatigue crack growth rate scatter. The surrogate modeling procedure can be extended to a generic geometry containing an edge crack since the remeshing technique-based 3D FE modeling procedure can accommodate any CAD representation.

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Acknowledgements

Authors would like to thank to Dr. Patrick Leser for providing some details related to the deterministic model used in this study.

References

Peng, D., Huang, P., Jones, R., 2018. Practical Computational Fracture Mechanics for Aircraft Integrity. Aircraft Sustainment and Repair, Chapter 4, 67–128. Loghin, A., Ismonov, S., 2020-a. Assessment of crack path uncertainly using 3D FEA and Response Surface Modeling. AIAA SciTech Forum, AIAA 2020-2295, https: // doi.org / 10.2514 / 6.2020-2295. Loghin, A., Ismonov, S., 2020-b. V&V 3D Fatigue Crack Growth Modeling: From Deterministic to Uncertainty Quantification (UQ) assessment. CAASE20, Indianapolis, IN, USA. https: // www.doi.org / 10.13140 / RG.2.2.25123.27680 Wilna du Toit, 2008. Radial Basis Function Interpolation, University of Stellenbosch. Loghin, A., 2018. Life Prediction Modeling Capabilities for FE Applications, CAASE, Cleveland OH. Leser, P.E, Hochhalter, J.D., Warner, J.E., Newman, J.A., Leser, W.P., Wawrzynek, P.A., Yuan, F., 2017. Probabilistic fatigue damage prognosis using surrogate models trained via three-dimensional finite element analysis. Structural Health Monitoring, 16(3), 291-308. Shantz, C.R, 2017. Uncertaintly quantification in crack growth modeling under multi-axial variable amplitude loading. Ph.D. thesis, Vanderbilt University. Loghin, A., Ismonov, S., 2019. Augmenting generic fatigue crack growth models using 3D finite element simulations and Gaussian process mod eling. Proceedings of the ASME Pressure Vessels & Piping Conference, San Antonio TX. Loghin, A., 2021. Quantification of the impact of crack shape constraint assumption onto predicted remaining useful life. Submitted to ASIP 2021, http: // www.asipcon.com / . Spear, A. D., Priest, A. R., Veilleux, M. G., Ingra ff ea, A. R., Hochhalter, J. D., 2011. Surrogate Modeling of High-Fidelity Fracture Simulations for Real-Time Residual Strength Predictions. NASA / TM–2011-216879. Sobotka, J. C., McClung, R. C., 2019. Verification of Stress-Intensity Factor Solutions by Uncertainty Quantification. Journal of Verification, Validation and Uncertainty Quantification, vol. 4, 021003-1, ASME. Millwater, H., Ocampo, J., Crosby, N., 2019. Probabilistic methods for risk assessment of airframe digital twin structures. Engineering Fracture Mechanics, vol. 221, 106674. ANSYS, 2021. www.ansys.com Akkaram, S., Loghin, A., Khan, G., 2011. A Framework for Probabilistic Assessment of Fracture Mechanics Life. AFRL-RX-WP-TP-2011-4390. ABAQUS, 2021. https: // www.3ds.com / products-services / simulia / CalculiX, 2021. http: // www.dhondt.de / Virkler, D.A., Hillberry, B.M., Goel, P.K., 1978. The Statistical Nature of Fatigue Crack Propagation. Air Force Flight Dynamics Laboratory Report AFFDL-TR-78-43. Farahmand, B., Bockrath, G., Glassco, J., 1997. Fatigue and Fracture Mechanics of High-Risk Parts. Chapman & Hall. ISBN 978-0-412-12991-9. Tada, H., Paris, P.C., Irwin G.R, 2000. The Stress Analysis of Cracks Handbook. 3rd ed, ASME press, New York. Kobryn, P.A, 2019. The Digital Twin Concept. Frontiers in Engineering, Winter edition, National Academy of Engineering. Virtanen, P., Gommers, R., Oliphant, T.E., et al, 2020. SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods, 17(3), 261-272. Annis, C., 2003. Probabilistic Life Prediction Isn’t as Easy as It Looks. Probabilistic Aspects of Life Prediction, ASTM STP-1450, W. S. Johnson and B.M. Hillberry, Eds., ASTM International, West Conshohocken, PA, 2003.

Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2021) 000 – 000 Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2021) 000 – 000 ScienceDirect

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Procedia Structural Integrity 38 (2022) 519–525

© 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Fatigue Design 2021 Organizers © 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Fatigue Design 2021 Organizers Abstract itanium alloys have been used extensively in aerospace and medical applications due to their exceptional strength to weight ratio, biocompatibility, and corrosion resistance. While these alloys are known to be difficult to machine, they are typically weldable. Therefore, various titanium-based alloys have been recently considered for production via additive manufacturing technology. Additively manufactured titanium alloys are used to produce a wide range of high-performance comp nents, which are ften under cyclic or periodic loading. While the most commonly used titanium alloy (i.e. Ti-6Al-4V) has been extensively characterized, there is a gap in the literature with regards to the fatigue performance of many other titanium alloys considered for additive manufacturing. This study aims at assessing the microstructural, mecha ical, and fatigue performance of two additively manufactured titanium-based alloys, Ti-5Al-5V-5Mo-3Cr and Ti-5Al-5Mo-5V-1Cr-1Fe, and comparing the results with the ones for the well-studied Ti-6Al-4V. A EOS M290 laser beam powder bed fusion (LB-PBF) additive manufacturing machine is used to fabricate specimens from various titanium alloys for this study. Specimens are characterized and compared side by side for their porosity, microstructure, tensile, and fatigue behavior. © 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Fatigue Design 2021 Organizers FATIGUE DESIGN 2021, 9th Edition of the International Conference on Fatigue Design A Comparative Study on Fatigue Performance of Various Additively Manufactured Titanium Alloys Mohammad Salman Yasin a,b , Arash Soltani-Tehrani a,b , Shuai Shao a,b , Meysam Haghshenas c , Nima Shamsaei a,b,* a Department of Mechanical Engineering, Auburn University, Auburn, AL 36849, USA b National Center for Additive Manufacturing Excellence (NCAME), Auburn University, Auburn, AL 36849, USA c Department of Mechanical, Industrial, and Manufacturing Engineering, University of Toledo, Toledo, OH 43606, USA Abstract Titanium alloys have been used extensively in aerospace and medical applications due to their exceptional strength to weight ratio, biocompatibility, and corrosion resistance. While these alloys are known to be difficult to machine, they are typically weldable. Therefore, various titanium-based alloys have been recently considered for production via additive manufacturing technology. Additively manufactured titanium alloys are used to produce a wide range of high-performance components, which are often under cyclic or periodic loading. While the most commonly used titanium alloy (i.e. Ti-6Al-4V) has been extensively characterized, there is a gap in the literature with regards to the fatigue performance of many other titanium alloys considered for additive manufacturing. This study aims at assessing the microstructural, mechanical, and fatigue performance of two additively manufactured titanium-based alloys, Ti-5Al-5V-5Mo-3Cr and Ti-5Al-5Mo-5V-1Cr-1Fe, and comparing the results with the ones for the well-studied Ti-6Al-4V. An EOS M290 laser beam powder bed fusion (LB-PBF) additive manufacturing machine is used to fabricate specimens from various titanium alloys for this study. Specimens are characterized and compared side by side for their porosity, microstructure, tensile, and fatigue behavior. FATIGUE DESIGN 2021, 9th Edition of the International Conference on Fatigue Design A Comparat ve Study on Fa igue Perfor ance f Various Additively Manufactured Titanium Alloys Mohammad Salman Yasin a,b , Arash Soltani-Tehrani a,b , Shuai Shao a,b , Meysam Haghshenas c , Nima Shamsaei a,b,* a Dep rtment of Mechanical Engineering, Aubur University, Auburn, AL 36849, USA b National Center for Additive Manufacturing Excellence (NCAME), Auburn University, Auburn, AL 36849, USA c Department of Mechanical, Industrial, and Manufacturing Engineering, University of Toledo, Toledo, OH 43606, USA Keywords: Additive manufacturing; Laser beam powder bed fusion; Fatigue; Titanium alloys; Ti-5553; Ti-55511; Ti-64

Keywords: Additive manufacturing; Laser beam powder bed fusion; Fatigue; Titanium alloys; Ti-5553; Ti-55511; Ti-64

* Corresponding author. Tel: +1-334-844-4839 E-mail address: shamsaei@auburn.edu * Corresponding author. Tel: +1-334-844-4839 E-mail address: shamsaei@auburn.edu

2452-3216 © 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Fatigue Design 2021 Organizers 2452-3216 © 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Fatigue Design 2021 Organizers

2452-3216 © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Fatigue Design 2021 Organizers 10.1016/j.prostr.2022.03.052

Mohammad Salman Yasin et al. / Procedia Structural Integrity 38 (2022) 519–525 Author name / Structural Integrity Procedia 00 (2021) 000 – 000

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1. Introduction The good strength to weight ratio, biocompatibility, and high corrosion resistance make titanium alloys appealing as compared to other conventional metals such as aluminum, steel, etc (Joshi, 2006; Sha & Malinov, 2009). However, these alloys are usually difficult to machine due to their high chemical reactivity, low modulus of elasticity, and low thermal conductivity (Khanna and Davim (2015); Pramanik (2014)) This illustrates that the application of such alloys hangs in balance due to the high machining cost, which would reduce as the need for machining decreases. Among the various near-net-shape techniques, additive manufacturing (AM) has become popular for fabricating titanium alloys. However, of all titanium alloys, the majority still leans towards the workhorse of the titanium industry, Ti-6Al-4V (Ti-64), an alpha-beta phase titanium alloy (Lütjering and Williams (2007)). As such, researchers have extensively studied the behavior of Ti-64. The current paper aims to focus on two near beta titanium alloys, Ti-5Al 5V-5Mo-3Cr (Ti-5553) and Ti-5Al-5Mo-5V-1Cr-1Fe (Ti-55511). Ti-5553 is built based on the Ti-alloy Ti-55511 (also known as VT22) and was announced by Titanium Metals Cooperation (Bartus (2009); Jones et al. (2009)). Both alloys present a wide range of mechanical properties due to the prospect of modifying the two-phase microstructure through thermo-mechanical treatments (Clément, 2010; Kolli & Devaraj, 2018; Schwab et al., 2017). This has helped Ti-5553 replace Ti-10V-2Fe-3Al in structural components for the landing gear of Boeing airframes. The objective of the present study is to assess the microstructural and mechanical behavior (such as tensile and fully reversed fatigue behavior) of Ti-5553 and Ti-55511 fabricated using laser beam powder bed fusion (LB-PBF), a powder-based AM technology, and to make a comparison with the Ti-64 counter material. The conducted study used specimens, which were fabricated by an EOS M290 machine using the same process parameters in a vertical orientation and later machined to required geometry based on ASTM standards. In the following sections, the experimental setup is discussed along with the results and discussion. 2. Experimental setup In this study, two near-beta titanium alloys, Ti-5553 and Ti-55511 were investigated. The LB-PBF system used for fabricating the specimens was an EOS M290 and the powders used as feedstock were supplied by AP&C, a GE Additive company. The process parameters used for the fabrications were kept the same for both materials. The infill parameters were 280W laser power, 1200 mm/s scan speed, 140 µm hatch distance, 30 µm layer thickness, and 67° hatch rotation. This yielded an energy density of 55.6 J/mm 3 . The build layouts for AM fabrication were also kept similar and can be seen in Fig 1. Some specimens were not fabricated due to complications during manufacturing. Round bars of 13 mm diameter and 100 mm height were fabricated and later shaped into tensile and fatigue specimens according to ASTM E8 and E466 respectively (ASTM International (2015), (2021)). Some net-shaped fatigue specimens were also fabricated with side support to obtain the fatigue behavior of the materials in the as-built surface condition. Additionally, eight half-built specimens were placed in different locations of the build plate for microstructural analysis. After fabrication, the specimens were taken off of the build plate and some half-built, tensile, and fatigue specimens were stress-relieved at 900°C in an inert (argon) atmosphere for an hour and then furnace-cooled to room temperature. Microstructural characterization of the LB-PBF titanium alloys along the build direction was studied in the non-heat treated (NHT) condition to reveal the melt-pool morphologies obtained during the fabrication. The melt-pools were revealed using a modified Kroll’s reagent (10% HF, 10% HNO 3, and 80% distilled water) and analyzed using a Keyence VHX-6000. To obtain the relative density and overall defect distribution of the fabricated specimens, at least two machined specimens were scanned for X-ray computed tomography (XCT) using a Zeiss Xradia 620 versa machine at 0.4X magnification. The voltage and current used for the analysis under 0.4X magnification were 140 kV and 150 µA respectively. The alignment of the detector and source were changed within the X-ray machine to obtain a resolution of 6 µm voxel size. This would indicate that the minimum feature size that the scan could detect would be 6 µm in size. The resulting images were post-processed using the Scout and Reconstruct software. ImageJ was used to analyze the defect size distribution. However, to account for any noises, volumes less than 525 µm 3 (equivalent diameter of 10 µm) were discarded from the analysis.