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The Conference Proceedings of the Society for Experimental Mechanics Series presents early findings and case studies from a wide range of fundamental and applied work across the broad range of fields that comprise Experimental Mechanics. Series volumes follow the principle tracks or focus topics featured in each of the Society’s two annual conferences: IMAC, A Conference and Exposition on Structural Dynamics, and the Society’s Annual Conference & Exposition and will address critical areas of interest to researchers and design engineers working in all areas of Structural Dynamics, Solid Mechanics and Materials Research. ii
Garrett Pataky· John Kolinski · Thomas Berfield· Nicholas Bachus · Rosa De Finis · Suhasini Gururaja Editors Fracture, Fatigue, Failure, Damage Evolution and Thermomechanics & Infrared Imaging, Vol. 4 Proceedings of the 2025 Annual Conference on Experimental and Applied Mechanics River Publishers
Published, sold and distributed by: River Publishers Broagervej 10 9260 Gistrup Denmark www.riverpublishers.com ISBN 97887-438-0830-5 (Hardback) ISBN 97887-438-0835-0 (eBook) https://doi.org/10.13052/97887-438-0830-5 Conference Proceedings of the Society for Experimental Mechanics An imprint of River Publishers © The Society for Experimental Mechanics, Inc. 2025 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, or reproduction in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Preface Fracture, Fatigue, Failure, Damage Evolution and Thermomechanics & Infrared Imaging represents one of five volumes of technical papers presented at the SEM 2025 SEM Annual Conference & Exposition on Experimental and Applied Mechanics organized by the Society for Experimental Mechanics and held in Milwaukee, WI, June 2-5, 2025. The complete Proceedings also includes volumes on: Dynamic Behavior of Materials; Challenges in Mechanics of Time-Dependent Materials; Advancement of Optical Methods & Digital Image Correlation in Experimental Mechanics; Mechanics of Biological Systems and Materials and the Mechanics of Composite, Hybrid & Multifunctional Materials; and Mechanics of Additive & Advanced Manufacturing, Inverse Methods and Machine Learning. Each collection presents early findings from experimental and computational investigations on an important area within Experimental Mechanics, Fracture and Fatigue being one of these areas. Fatigue and fracture are two of the most critical considerations in engineering design. Understanding and characterizing fatigue and fracture has remained as one of the primary focus areas of experimental mechanics for several decades. Advances in experimental techniques, such as digital image correlation, acoustic emissions, and electron microscopy, have allowed for deeper study of phenomena related to fatigue and fracture. This volume contains the results of investigations of several aspects of fatigue and fracture such as microstructural effects, the behavior of interfaces, the behavior of different and/or complex materials such as composites, and environmental and loading effects. The collection of experimental mechanics research included here represents another step toward solving the long-term challenges associated with fatigue and fracture. In recent years the applications of infrared imaging techniques to the mechanics of materials and structures has grown considerably. The expansion is marked by the increased spatial and temporal resolution of the infrared detectors, faster processing times, much greater temperature resolution and specific image processing. The improved sensitivity and more reliable temperature calibrations of the devices have meant that more accurate data can be obtained than were previously available. Editors: Garrett Pataky-Clemson University, USA; John Kolinski-EPFL, Switzerland; Thomas Berfield, University of Louisville, KY, USA; Nicholas Bachus, University of California Davis, CA, USA; Rosa De Finis, University of Salento, Italy; Suhasini Gururaja, Auburn University, AL, USA v
Contents 1 Rapid Fatigue Characterisation of AlSi10Mg-AM using Energy-based approaches 1 Rosa De Finis, Davide Palumbo, and Umberto Galietti 2 Effect of Induced Porosity on Fatigue Performance of Additively Manufactured Short-Fiber Thermoplastics Using Infrared Thermography 7 Harsh Gandhi, Pharindra Pathak, and Suhasini Gururaja 3 Fracture Properties Identification using Full-field Measurements: Some Important Concepts and Validation 15 Joa˜o Carlos A. D. Filho, Lukas Wittevrongel, Amar Peshave, Pascal Lava, and Fabrice Pierron 4 Energy Dissipation Measurement Under Cyclic Torsional Loading Using Infrared Thermography 21 Daiki Shiozawa, Motoki Yoshiike, and Takahide Sakagami 5 On the Calculation of the Initial Temperature Slope: Key Considerations for the Fatigue Limit Estimation 25 Mohammad Zaeimi, Ali Mahmoudi, Rosa De Finis, Davide Palumbo, Michael M. Khonsari, and Umberto Galietti 6 Investigation of Failure in Unidirectional Adhesively-Bonded Composite Joints via Infrared Thermography 35 Nithinkumar Manoharan and Suhasini Gururaja 7 Effect of Loading Frequency on Fatigue Behavior of Additively Manufactured Short Fiber Thermoplastics via Infrared Thermography 39 Pharindra Pathak, Kaniz Fatema Bristy, Vipin Kumar, and Suhasini Gururaja 8 Analytical Generalization of the T and A-theta Integrals for the Study of Cracking in Three-dimensional Orthotropic Medium 47 Lo¨ıc Chrislin Nguedjio, Rostand Moutou Pitti, Benoit Blaysat, Pierre Kisito Talla, Fre´deric Dubois, and Naman Recho vii
Chapter 1 Chapter 1 On the Detection and Quantification of Nonlinearity via Statistics of the Gradients of a Black-Box Model Georgios Tsialiamanis and Charles R. Farrar Abstrac t Detection and identification of nonlinearity is a task of high importance for structural dynamics. On the one hand, identifying nonlinearity in a structure would allow one to build more accurate models of the structure. On the other hand, detecting nonlinearity in a structure, which has been designed to operate in its linear region, might indicate the existence of damage within the structure. Common damage cases which cause nonlinear behaviour are breathing cracks and points where some material may have reached its plastic region. Therefore, it is important, even for safety reasons, to detect when a structure exhibits nonlinear behaviour. In the current work, a method to detect nonlinearity is proposed, based on the distribution of the gradients of a data-driven model, which is fitted on data acquired from the structure of interest. The data-driven model selected for the current application is a neural network. The selection of such a type of model was done in order to not allow the user to decide how linear or nonlinear the model shall be, but to let the training algorithm of the neural network shape the level of nonlinearity according to the training data. The neural network is trained to predict the accelerations of the structure for a time-instant using as input accelerations of previous time-instants, i.e. one-step-ahead predictions. Afterwards, the gradients of the output of the neural network with respect to its inputs are calculated. Given that the structure is linear, the distribution of the aforementioned gradients should be unimodal and quite peaked, while in the case of a structure with nonlinearities, the distribution of the gradients shall be more spread and, potentially, multimodal. To test the above assumption, data from an experimental structure are considered. The structure is tested under different scenarios, some of which are linear and some of which are nonlinear. More specifically, the nonlinearity is introduced as a column-bumper nonlinearity, aimed at simulating the effects of a breathing crack and at different levels, i.e. different values of the initial gap between the bumper and the column. Following the proposed method, the statistics of the distributions of the gradients for the different scenarios can indeed be used to identify cases where nonlinearity is present. Moreover, via the proposed method one is able to quantify the nonlinearity by observing higher values of standard deviation of the distribution of the gradients for lower values of the initial column-bumper gap, i.e. for “more nonlinear” scenarios. Keyword s Structural health monitoring (SHM) · Structural dynamics · Nonlinear dynamics · Machine learning · Neural networks 1.1 Introduction In the pursuit of making everyday life safer, humans have extensively tried to model the environment around them. Structures are an important part of the environment, in which humans live. They are man-made and should be safe throughout their lifetime. Structures are exposed to numerous environmental factors, which may cause them to fail. Moreover, during operation, structures are subjected to dynamic loads, which, in time, may cause failure. Such failures will most probably result in economic damage to society and may even result in loss of human lives. Therefore, for the purpose of maintaining structures safe, the field of structural health monitoring (SHM) [1] has emerged. G. Tsialiamanis ( ) Dynamics Research Group, Department of Mechanical Engineering, University of Sheffield, Sheffield, UK e-mail: g.tsialiamanis@sheffield.ac.uk C. R. Farrar Engineering Institute, MS T-001, Los Alamos National Laboratory, Los Alamos, NM, USA e-mail: farrar@lanl.gov © The Society for Experimental Mechanics, Inc. 2024 M. R. W. Brake et al. (eds.), Nonlinear Structures & Systems, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-031-36999-5_1 1 Rapid Fatigue Characterisation of AlSi10Mg-AM using Energy-based approaches Rosa De Finis, Davide Palumbo, and Umberto Galietti Abstract The advent of additive manufacturing has transformed the manner in which structural and non-structural materials and components are designed and manufactured. This technology offers the flexibility of manufacturing but also presents a number of challenges concerning the performance of the material itself. One such challenge is the lack of data regarding the structural aspects of the material, including fatigue resistance. This information is crucial for understanding the behaviour of a component under operating loads. A valuable support in such activities aimed at shedding light on dynamic behaviour is provided by the techniques provided by the experimental mechanics. In particular, Infrared thermography is a valuable tool for detecting anomalies in the thermal map of a material or component subjected to cyclic loading. This is achieved using certain indices linked to reversible and irreversible physical processes that characterise the nature of heat sources. Furthermore, conducting rapid fatigue tests allows for the study of material behaviour through the examination of material self-heating. The aim of this study is to present the challenging aspects of studying the fatigue behaviour of aluminium alloys produced by Additive Manufacturing. This is regarding both the behaviour of aluminium from a thermal point of view (it is a highly diffusive material, so temperature variations are very low) and the behaviour from a mechanical point of view (the fatigue limit of some alloys does not present the characteristic “knee” point). The goal is to demonstrate how thermography can support structural evaluations on this material. Introduction Additive manufacturing is a new material production technique that combines several technological advantages such as the ability to build complex-shaped components in a relatively short time using a relatively circular process and, in some cases, no material rework is required [1]. However, there are still many challenges to face like induced anisotropy, residual stresses, surface finish that affect structural integrity and mechanical material properties. Indeed, the characterization of heterogeneous or anisotropic microstructures, along with the presence of residual stresses and induced defects, and the dependence of material properties on building direction and orientation, requires the development of ad-hoc testing and analysis procedures. Specifically, the whole comprehension of the fatigue behavior in these materials remain not fully achieved. This push the research toward new methodologies for studying the fatigue behavior [1–2]. The experimental mechanics provides invaluable support for both structural integrity inspections and material characterization [3–9]. In particular, in the past different thermography-based techniques were developed to carry out the rapid characterization of materials and the early damage detection. These techniques present the advantage of assessing the damage information in relatively short time. Such techniques are mainly adopted during rapid fatigue tests that exploit the self-heating effect of the material. In these tests by fatigue loading the material first at very low and then at very high load levels until failure, the transition between damage regimes can be studied [3–5]. In fact, if a thermal imaging camera monitors the test, it is possible to derive a range of information related to the energy involved in dissipative processes that serve Rosa De Finis( ) Dipartimento di Ingegneria dell’Innovazione, University of Salento, Via per monteroni, 73100 Lecce, Italy e-mail: rosa.definis@unisalento.it Davide Palumbo· Umberto Galietti Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via Orabona, 5-70125 Bari, Italy © The Author(s), under exclusive license to River Publishers 2025 Garrett Pataky et al. (eds.), Fracture, Fatigue, Failure, Damage Evolution and Thermomechanics & Infrared Imaging, Vol. 4, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.13052/97887-438-0830-5 1
2 G. Toledo et al. as a sentinel for early and local detection of damage. This has enabled the development of energy-based approaches and methodologies [10–18]. Energy-based methodologies [6–9], founded upon the evaluation of quantifiable variables such as temperature and strain, have exhibited their efficacy in the identification of damage, even in the presence of small surface defects, and in the separation of inelastic from anelastic material behavior [10, 12, 17]. More in detail, in recent years, the estimation of energy dissipated during fatigue processes through the assessment of temperature fluctuations (second amplitude harmonics, or SAH [7–9]) has demonstrated considerable potential for the precise analysis of material behavior through the assessment of a parameter that is resistant to the influence of numerous disturbing noise factors. This paper presents preliminary results of fatigue characterization of the AlSi10Mg-AM alloy produced by selective laser melting, using rapid methods. The SAH and the area under hysteresis loop are used as damage indices and to study the material behavior. The results will also be analyzed in terms of material specificity: SAH will represent not only dissipative but also thermoelastic effects [11, 18]. This significantly complicates the assessment of material behavior. Moreover, an ad-hoc procedure for the evaluation of material fatigue strength taking into account the specific thermal behavior of the material is also provided. Materials and Methods The present study dealt with AlSi10Mg alloy produced by selective laser melting additive manufacturing process [2]. The samples were built in vertically direction and heat-treated (age-hardening for 6 hours-T6). Moreover, the surface of the samples was matt black coated to enhance and uniform the surface emissivity. All fatigue tests were performed on a servo-hydraulic MTS 647 loading machine with a 100kN load cell. The samples were addressed to a stepwise loading procedure in order to study the self-heating material behaviour [3–10]. It consists of a sequence of load blocks, each with the same duration of load cycles and fixed values for load frequency and stress ratio. The sequence of blocks is defined by incrementally increasing the applied stress level. Three acquisitions were carried out at each load step at 1000 and 15000 cycles respectively at a loading frequency of 15hz which is sufficiently high to avoid loss of adiabatic conditions. To acquire thermal data the Flir X6540SC Infrared camera was adopted. In particular, this camera has a cooled detector with 640×512 pixels matrix and a NETD lower than 25 mK. The adopted frame rate to obtain IR sequences was 200Hz. An extensometer MTS 634 (clip-on type with 25 mm gage length) acquired the strain data at 500 frame per second. The setup and equipment are reported in Fig. 1. Fig. 1 Experimental setup (1:sample, 2:clamps, 3:dummy specimen;4: extensometer, 5:mirror, 6: cover sheet; 7:microbolometer camera; 8:cooled camera FLIR X6540SC).
Effective Structural Health Monitoring of Rotating Propellers using Asynchronous Neuromorphic Tracking 3 Referring to the signal processing a signal reconstruction algorithm based on the least squares method [7] is adopted. The algorithms are implemented in the software IRTAR⃝. The mathematical model describing the temeprature evolution and fluctuation is: T (t)=T0 +a×t +T1×sin[2πfL t +φ1] +T2 ×sin[4πfL t +φ2] (1) where T0 is the mean value, a is the mean rate, T1 and T2 the two amplitudes, and φ1 and φ2 the two phases and fL is the loading frequency. The processing was performed pixel by pixel but the identified indicator for the damage was the 95◦ percentile value in a region of interest (ROI) coinciding with the gage volume of the sample, was considered to represent the T2 field. The T2 maps were addressed to a double-dimension filter using a gaussian kernel in order to filter out the noise. The strain data from extensometer were used to study the hysteresis loop behaviour and in general the energy involved in fatigue processes. Results Fig. 2 shows the maps of assessed second amplitude harmonics (SAH) referring to the gage volume. The analysis of the SAH maps reveals an increase in signal from the first load levels to the last for all specimens. The damage appears to be widespread, affecting the entire useful section. However, it is only in the final loading steps that circumscribed areas with a markedly higher signal can be identified, which are indicative of the damage sites. Fig. 2 Maps of SAH for samples as provided (right) and heat-treated (left). Fig. 3 shows two exemplary charts with the hysteresis loops related to a sample in ‘as provided’ condition and a sample after heat treatment. The curves show that in both conditions the material behaviour is characterized by limited plastic Fig. 3 Hysteresis loops curves for sample 3, as provided (right) and heat treated (left).
4 G. Toledo et al. deformation and general brittle behaviour. The dissipation increases markedly only in the last loading levels where the hysteresis loops are wider than those at the beginning of the test. Fig. 4 shows the curves of SAH (Fig. 4a) and the area under the hysteresis loop-Wp (Fig. 4b) for the specimens built in the vertical direction. (a) (b) Fig. 4 Curves for samples realized in z-direction with and without heat treatment (ht=heat treatment), (a) SAH , (b) area under hysteresis loop (Wp). As can be seen from Fig. 4a, there is no real cut-off point in the thermal behaviour of the material as would be expected from the reference parameter (Fig. 4b). This may be due to the superposition of reversible and irreversible effects in the thermal behaviour of the material. It should also be noted that aluminum does not have a knee point [16], but rather it is necessary to refer to fatigue strength at a given number of cycles. This will require future testing to better understand how to separate the two reversible and irreversible thermal contributions, as well as ad hoc processing procedures. To estimate the material fatigue strength, a new procedure was identified to be applied to each specimen to select the stress level at which the series trend deviates significantly from the initial trend representing undamaged material. The procedure is summarized as follows: - Starting from the SAH values of the last 3 stress levels, consider the (stress amplitudes, SAH) pairs and calculate the R2 coefficient;
Effective Structural Health Monitoring of Rotating Propellers using Asynchronous Neuromorphic Tracking 5 - Adding another pair of data (stress amplitudes, SAH) and calculate the R2 coefficient; - Continuing until the value of R2 differs by more than 5% from the previous values. The methodology has been applied to SAH data and produced an estimation of the fatigue limit of 97±10 MPa without much difference between heat treated specimens and ’as provided’ specimens. Conclusions In this paper, a comparison between SAH and hysteresis loop area has been presented to study the fatigue behaviour of AlSi10Mg -AM alloy subjected to stepwise testing. The thermal method proves to be a comprehensive technique, allowing not only the detection of damage from its onset, but also the study of its evolution. All this has the advantage of consistently reducing the duration of the experimental campaign. An additional advantage is the ability to better understand any differences between heat-treated and ‘as provided’ material, which is relevant for the purpose of providing guidelines for the technological process. From the obtained results, there is in fact no difference between the fatigue strength of the material in the two configurations, but the data are certainly less noisy after heat treatment. References 1. Liu, H., Yu, H., Guo, C., Chen, X., Zhong, S., Zhou, L., Osman, A., & Lu, J. (2023). Review on Fatigue of Additive Manufactured Metallic Alloys: Microstructure, Performance, Enhancement, and Assessment Methods. 2. Beretta, S., Gargourimotlagh, M., Foletti, S., du Plessis, A., & Riccio, M. (2020). Fatigue strength assessment of as built AlSi10Mg manufactured by SLM with different build orientations. 3. M.P. Luong, Fatigue limit evaluation of metals using an infrared thermographic technique, Mechanics of Materials, 28 (1998) 155-163. 4. G. Fargione, A. Geraci, G. La Rosa, A. Risitano, Rapid determination of the fatigue curve by the thermographic method, International Journal of Fatigue, 24 (2002) 11-19. 5. T. Boulanger, A. Chrysochoos, C. Mabru, A. Galtier, Calorimetric analysis of dissipative and thermoelastic effects associated with the fatigue behavior of steels, International Journal of Fatigue, 26 (2004) 221-229. 6. F. Maquin, F. Pierron, Heat dissipation measurements in low stress cyclic loading of metallic materials: From internal friction to microplasticity, Mechanics of Materials, 41 (2009) 928-942. 7. R. De Finis, D. Palumbo, U. Galietti, A multianalysis thermography-based approach for fatigue and damage investigations of ASTM A182 F6NM steel at two stress ratios, Fatigue & Fracture of Engineering Materials & Structures, 42 (2019) 267-283. 8. G. Meneghetti, M. Ricotta, Estimating the intrinsic dissipation using the second harmonic of the temperature signal in tension-compression fatigue. Part II: Experiments, Fatigue & Fracture of Engineering Materials & Structures, 44 (2021) 2153-2167. 9. R. De Finis, D. Palumbo, U. Galietti, On the relationship between mechanical energy rate and heat dissipated rate during fatigue for a C45 steel depending on stress ratio, Fatigue & Fracture of Engineering Materials & Structures, 44 (2021) 2781-2799. 10. Doudard C, Calloch S, Cugy P, Galtier A, Hild F. A probabilistic two-scale model for high-cycle fatigue life predictions. Fatigue & Fracture of Engineering Materials & Structures. 2005;28(3):279-288. 11. Wong AK, Sparrow JG, Dunn SA. On the revised theory of the thermoelastic effect. Journal of Physics and Chemistry of Solids. 1988;49(4):395-400. 12. Sakagami T, Kubo S, Tamura E, Nishimura T. Identification of plastic-zone based on double frequency lock-in thermographic temperature measurement. 2013. 13. Meneghetti G, Ricotta M. Evaluating the heat energy dissipated in a small volume surrounding the tip of a fatigue crack. International Journal of Fatigue. 2016;92:605-615. 14. Meneghetti G, Ricotta M. The heat energy dissipated in the material structural volume to correlate the fatigue crack growth rate in stainless steel specimens. International Journal of Fatigue. 2018;115:107-119. 15. Liakat M, Khonsari MM. On the anelasticity and fatigue fracture entropy in high-cycle metal fatigue. Materials & Design. 2015;82:18-27. 16. De Finis R, Palumbo D, Serio LM, De Filippis LAC, Galietti U. Correlation between thermal behaviour of AA5754-H111 during fatigue loading and fatigue strength at fixed number of cycles. Materials. 2018;11(5):719. 17. Lepitre P, Calloch S, Dhondt M, Surand M, Doudard C. Identification of the damage scenarios under cyclic loading of a coated 300M steel by infrared thermography measurements. Physical Sciences Forum. 2022;4(1):30. 18. Di Carolo, F.,De Finis, R., Palumbo, D., Galietti, U. A thermoelastic stress analysis general model: Study of the influence of biaxial residual stress on aluminium and titanium, Metals, 2019, 9(6), 671.
Chapter 2 Chapter 1 On the Detection and Quantification of Nonlinearity via Statistics of the Gradients of a Black-Box Model Georgios Tsialiamanis and Charles R. Farrar Abstrac t Detection and identification of nonlinearity is a task of high importance for structural dynamics. On the one hand, identifying nonlinearity in a structure would allow one to build more accurate models of the structure. On the other hand, detecting nonlinearity in a structure, which has been designed to operate in its linear region, might indicate the existence of damage within the structure. Common damage cases which cause nonlinear behaviour are breathing cracks and points where some material may have reached its plastic region. Therefore, it is important, even for safety reasons, to detect when a structure exhibits nonlinear behaviour. In the current work, a method to detect nonlinearity is proposed, based on the distribution of the gradients of a data-driven model, which is fitted on data acquired from the structure of interest. The data-driven model selected for the current application is a neural network. The selection of such a type of model was done in order to not allow the user to decide how linear or nonlinear the model shall be, but to let the training algorithm of the neural network shape the level of nonlinearity according to the training data. The neural network is trained to predict the accelerations of the structure for a time-instant using as input accelerations of previous time-instants, i.e. one-step-ahead predictions. Afterwards, the gradients of the output of the neural network with respect to its inputs are calculated. Given that the structure is linear, the distribution of the aforementioned gradients should be unimodal and quite peaked, while in the case of a structure with nonlinearities, the distribution of the gradients shall be more spread and, potentially, multimodal. To test the above assumption, data from an experimental structure are considered. The structure is tested under different scenarios, some of which are linear and some of which are nonlinear. More specifically, the nonlinearity is introduced as a column-bumper nonlinearity, aimed at simulating the effects of a breathing crack and at different levels, i.e. different values of the initial gap between the bumper and the column. Following the proposed method, the statistics of the distributions of the gradients for the different scenarios can indeed be used to identify cases where nonlinearity is present. Moreover, via the proposed method one is able to quantify the nonlinearity by observing higher values of standard deviation of the distribution of the gradients for lower values of the initial column-bumper gap, i.e. for “more nonlinear” scenarios. Keyword s Structural health monitoring (SHM) · Structural dynamics · Nonlinear dynamics · Machine learning · Neural networks 1.1 Introduction In the pursuit of making everyday life safer, humans have extensively tried to model the environment around them. Structures are an important part of the environment, in which humans live. They are man-made and should be safe throughout their lifetime. Structures are exposed to numerous environmental factors, which may cause them to fail. Moreover, during operation, structures are subjected to dynamic loads, which, in time, may cause failure. Such failures will most probably result in economic damage to society and may even result in loss of human lives. Therefore, for the purpose of maintaining structures safe, the field of structural health monitoring (SHM) [1] has emerged. G. Tsialiamanis ( ) Dynamics Research Group, Department of Mechanical Engineering, University of Sheffield, Sheffield, UK e-mail: g.tsialiamanis@sheffield.ac.uk C. R. Farrar Engineering Institute, MS T-001, Los Alamos National Laboratory, Los Alamos, NM, USA e-mail: farrar@lanl.gov © The Society for Experimental Mechanics, Inc. 2024 M. R. W. Brake et al. (eds.), Nonlinear Structures & Systems, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-031-36999-5_1 1 Effect of Induced Porosity on Fatigue Performance of Additively Manufactured Short-Fiber Thermoplastics Using Infrared Thermography Harsh Gandhi, Pharindra Pathak, and Suhasini Gururaja Abstract This study explores the influence of induced porosity on the fatigue behavior of additively manufactured shortfiber thermoplastics (AM-SFTs), employing infrared thermography (IRT) as an accelerated characterization method. IRT has emerged as a validated technique for drastically reducing the time required to estimate fatigue limits, offering a more efficient alternative to the conventional stress-life (S-N) method. In a previous study, acquiring the S-N curve for 20% short carbon fiber-reinforced Acrylonitrile Butadiene Styrene (CF/ABS) panels required two weeks of testing with 18 specimens. IRT testing achieved comparable fatigue limit estimates using only three specimens over five hours. This underscores the effectiveness of IRT in providing rapid fatigue assessments [1]. In this research, specimens composed of 80% ABS and 20% chopped carbon fibers were produced via fused deposition modeling (FDM) and subjected to fatigue loading. The study considered 16-layer AM-SFT specimens with artificially induced discrete porosity - 6 mm diameter defects located on the middle layer of the specimen. Additionally, control specimens with no pores have also been tested. A test matrix of 15 specimens consistent with ASTM D638 Type I specifications, with five replicates per configuration, has been tested. Each specimen was tested under both static and cyclic loading conditions. IRT facilitated real-time monitoring of surface temperature changes during fatigue testing, a precursor to fatigue damage initiation. This investigation aims to establish a quantitative relationship between defect size, location, and fatigue performance in AM-SFTs. The findings will provide deeper insights into the role of porosity in fatigue behavior and offer more efficient methodologies for fatigue characterization in AM composites. Keywords Fatigue limit · Engineered defects · AM-SFTs · IRT· Damage Introduction Additive manufacturing has revolutionized material design and production, particularly with its ability to fabricate lightweight, high-performance components with tailored properties [2]. Among the most promising materials in this field are additively manufactured short-fiber thermoplastics, which combine polymer matrices with reinforcing short fibers to achieve improved mechanical properties [2]. These materials are commonly produced using fused deposition modeling, a process that offers manufacturing flexibility but can introduce defects, such as porosity, which significantly impact structural integrity under cyclic loading [1, 3]. Porosity in AM components is a critical concern as it acts as a stress concentrator, promoting damage initiation and propagation, thereby accelerating fatigue failure [4]. Fatigue damage, which progressively accumulates in materials under cyclic loading, can substantially affect the residual stiffness and strength of SFTs. Gaining insight into this damage and its influence on material properties is crucial for accurately predicting the lifespan and structural integrity of SFT-based components [1]. Traditional fatigue characterization using stress-life testing is time-consuming and resource-intensive, requiring numerous specimens and long test durations [5]. To address these challenges, infrared thermography has emerged as an effective alternative, offering rapid, real-time monitoring of damage accumulation by detecting thermal responses during cyclic loading [6, 7]. Harsh Gandhi · Pharindra Pathak· Suhasini Gururaja Department of Aerospace Engineering, Auburn University, Auburn, AL 36849 e-mail: hsg0014@auburn.edu; pzp0057@auburn.edu; suhasini.gururaja@auburn.edu © The Author(s), under exclusive license to River Publishers 2025 7 Garrett Pataky et al. (eds.), Fracture, Fatigue, Failure, Damage Evolution and Thermomechanics & Infrared Imaging, Vol. 4, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.13052/97887-438-0830-5 2
8 H. Gandhi et al. This study investigates the effect of engineered defects on the fatigue behavior of AM-SFTs. The specimens, composed of CF/ABS, were fabricated using FDM with±45◦ fiber orientations following the ASTM D638 Type I standard. Engineered defects of 6 mm diameter were introduced in the 8th layer (middle layer) of select specimens to study the influence of porosity on fatigue performance. A total of 15 specimens were tested under static and fatigue loading conditions and monitored using IRT to capture temperature variations corresponding to fatigue damage initiation. Background Materials To investigate the fatigue performance of AM-SFTs with varying defect configurations, a detailed test matrix was developed, as shown inTable. 1. The specimens, fabricated according to ASTM D638 Type I standards, were composed of 20% chopped carbon fibers and 80% ABS. The samples were printed using a fused deposition modeling (FDM) process with a 0.4 mm nozzle diameter and a printing temperature of 240◦C. A rectilinear infill pattern with 100% sparse infill density was utilized to ensure consistent material properties throughout the specimens. The fine print setting was selected to improve dimensional accuracy and surface quality. The total printing duration for each specimen was approximately 20 min per specimen. The ±45◦ fiber orientation was chosen to mitigate shear failure observed in previous tests with 0◦ laminates, which exhibited premature failure due to shear-dominated loading. This orientation helps distribute the load more effectively across the matrix, improving structural integrity during cyclic loading. Table 1 Test Matrix for 3D Printed Specimens Specimen Material Fiber aspect ratio (L / D) 3DPrinter %Infill Ratio σmin σmax Frequency (Hz) Nozzle Dia (mm) ASTM D638 Type I 80wt.%ABS 20 wt.% Carbon Fiber 5-8 Bambu Lab X1 Carbon 100 0.1 15 0.4 Configuration Specimen ID Orientation (deg) Defect Layer No. of Replicates Specimen Printed Testing Testing Completed Pristine PRIS-STC-ALT45-# ±45 N/A 5 5 Static 5 Pristine PRIS-FTG-ALT45-# ±45 N/A 5 5 Fatigue 5 6 mm Dia on Middle/8th Layer 6D-8L-FTG-ALT45-# ±45 8th 5 5 Fatigue 5 Total Specimens 15 15 15 The ASTM D638 Type I geometry was chosen due to its widespread use in tensile and fatigue testing of polymeric materials, providing reproducible and reliable mechanical property assessments [7]. The specimen geometry, depicted in Fig. 1, included a gauge section measuring 57 mm in length and 13 mm in width, with a thickness of 3.2 mm. Each Fig. 1 ASTM D638 Type I Standard Specimen containing 20% CF and 80% ABS materials: pristine specimen (left), defect specimen (right)
Effect of Induced Porosity on Fatigue Performance of Additively Manufactured Short-Fiber Thermoplastics 9 specimen consists of 16 layers (0.2 mm thick) additively manufactured on top of each other. As shown in Table. 1, two sets of specimens were printed: Pristine specimens and specimens with ‘engineered’ defects. Engineered defect specimens comprised a 6 mm diameter pore region that was not printed, strategically placed on the 8th (middle) layer. IRT Testing Procedure All tests, static tensile and fatigue tests were conducted using an MTS Landmark servohydraulic universal test frame with a 100 kN capacity, as shown in Fig. 2. Quasi-static tensile tests were performed at a 2 mm/min displacement-controlled rate to determine the mechanical properties—stiffness and ultimate tensile strength of the CF/ABS composite specimen. Gage pressure was kept around 325 psi to prevent specimen slippage. The strain was measured using an extensometer with a 5 cm gauge length. Five specimens were tested, yielding an average ultimate tensile strength (σuts) of 27.00±1.49 MPa, failure strain (ϵf) of 4.66%±0.46%, and an elastic modulus (E0) of 2.02±0.16GPa, which served as the baseline for subsequent fatigue testing. Fig. 2 Experimental Setup for Fatigue Testing Tension-tension fatigue tests were conducted under sinusoidal load-controlled conditions with a stress ratio R = 0.1. The maximum and minimum loads were set as percentages of the average σuts. The loading frequency was maintained at 15 Hz, following the approach in [8, 9, 10]. Fig. 3 illustrates the staircase cyclic loading with R = 0.1. Temperature Fig. 3 Staircase loading applied to a specimen to determine fatigue limit rapidly with an early increment of 10%σuts followed by 5%σuts increments to σmax. The stress ratio R =0.1 was maintained throughout the test. The rest period between load steps ensured the specimen cooled down to room temperature after every step load
10 H. Gandhi et al. measurements were obtained in real-time using a Telops Spark M150 MWIR cooled camera (640 ×512 pixels, 20 mK NETD, 3-5.4µm spectral range) at a data acquisition frequency of 100 Hz. Data acquisition was done via Reveal IR software, and surface temperature evolution was analyzed to identify fatigue limits and correlate them with defect location and fatigue performance. The fatigue limit was determined by plotting the stabilization temperature change (∆Tstab) for each step (σmax). The intersection of bi-linear curves fitting the ∆Tstab versus σmax data marked the fatigue onset point, identified by the most significant change in slope. The step size (Nstep) was fixed at 7500 cycles, based on trial tests, to establish the Phase II stabilized steady-state zone. A minimum of five replicates were tested for reliability. Fatigue testing was paused after each load step to allow cooling to room temperature before the next step. The cooling phase called the ‘rest period’ in Fig. 3, ensured specimens started each load step at ambient temperature. Following each rest period, a static test was performed to assess stiffness degradation as a function of load cycles. Results and Discussion The fatigue behavior of both pristine and defected specimens was examined through IRT during cyclic loading at increasing stress levels, as shown in Fig. 4a - 4b. The pristine specimen displayed minimal temperature variations across all stress levels, with only slight increases at 60% and 65% of the ultimate tensile strength (UTS), indicating a more uniform stress distribution and a delayed onset of internal damage (see Fig. 4a). In contrast, the specimen with a 6 mm diameter defect in the middle layer showed notable localized heating at higher stress levels (55%, 60%, and 65% of UTS) (see Fig. 4b). The localized heating observed in the engineered defect specimen suggests stress concentrations around the engineered defect, highlighting the role of porosity in accelerating fatigue damage. However, the overall temperature for both pristine and engineered defect specimens remained almost constant, with the defect specimen showing more localized heating due to stress concentration at higher loading levels. Despite the observed thermal variations, the fatigue limit of the defected specimen, determined through a bilinear plot, was 49.52%±0.99% UTS (see Fig. 5a - 5b), which was only marginally higher than the pristine specimen’s fatigue limit of 49.04%±1.28% UTS (see Fig. 6a - 6b). This suggests that the defect did not drastically reduce the fatigue resistance as initially expected. Several factors contributed to this unexpected outcome. Firstly, the MTS machine used in the testing had a load capacity of 100 kN. Since the failure load of the tested specimens was around 1.08 kN, the applied loads were lower than Fig. 4 Temperature displayed within the region of interest for each step loading for both (a) Pristine and (b) Engineered Defect Specimens
Effect of Induced Porosity on Fatigue Performance of Additively Manufactured Short-Fiber Thermoplastics 11 Fig. 5 For Pristine, (a) Temperature vs. Time plot showing the temperature rise for Specimen 4 and (b) Fatigue Limit calculated from the Bilinear Plot for all the specimen Fig. 6 For 6mm diameter defect on the middle layer, (a) Temperature vs. Time plot showing the temperature rise for Specimen 2 and (b) Fatigue Limit calculated from the Bilinear Plot for all the specimen the resolution of the MTS machine, potentially affecting the accuracy of the applied load. Secondly, although the engineered defect was intended to be placed in the middle layer (the 8th layer out of 16), micro-CT imaging revealed discrepancies in the actual defect size and shape. The analysis showed that the CF/ABS deposited filament over the defect location, effectively eliminating the void. This indicated that material consolidation during printing contributed to partially filling the defect (see Fig. 7), altering its intended geometry, and reducing its influence on fatigue performance. Additionally, due to the defect’s depth within the specimen, the thermal signals detected by the infrared camera might have been lower, limiting the ability to capture conclusive temperature data at lower stress levels. This, combined with the resolution constraints of the MTS machine, may have contributed to the inconclusive temperature readings observed at lower load levels. Although localized heating was observed at 55-65% UTS, corresponding to the onset of fatigue damage around the defect, further investigation is needed to determine the defect’s true impact on damage initiation at lower stress levels. In summary, while the presence of the defect was expected to reduce the specimen’s fatigue performance due to stress concentration, the results indicate that the fatigue resistance of the defected specimen was comparable to the pristine
12 H. Gandhi et al. Fig. 7 Microstructure of engineered defect specimen at 0.6 microns voxel size specimen. This finding emphasizes the influence of testing machine limitations, defect location, and stress redistribution mechanisms in determining the fatigue behavior of specimens with induced defects. Conclusions and Future Work This study demonstrated the impact of engineered defects on the fatigue behavior of AM-SFTs through IRT and fatigue limit estimation. Both pristine and engineered defect configurations were considered, with cyclic step-loading applied during the fatigue tests on each specimen. The results showed that while defects were expected to act as stress concentrators and reduce fatigue limits, the observed fatigue threshold for the defected specimen did not decrease as anticipated. This suggests that the chosen defect did not drastically affect the overall fatigue performance under the tested conditions. Future work will focus on increasing the thickness of the specimen from 16 layers (3.2 mm) to potentially 32 layers (6.4 mm), which will increase the UTS value and ensure that the input loads during step loading remain within the resolution of the testing machine. Additionally, the effects of defect placement will be further explored by assessing the fatigue response of specimens with a 6 mm diameter defect positioned in the third layer. This will provide insights into how defect location influences fatigue life. By exploring these different configurations, future work will enable a better understanding of the mechanisms behind defect-induced fatigue and help refine the design and manufacturing processes for more reliable AM-SFT components. References 1. P. Pathak, S. Gururaja, V. Kumar, D. Nuttall, A. Mahmoudi, M. M. Khonsari, and U. Vaidya. Examining infrared thermography based approaches to rapid fatigue characterization of additively manufactured compression molded short fiber thermoplastic composites. Composite Structures, 351:118610, 2025. 2. A. Brasington, C. Sacco, J. Halbritter, R. Wehbe, and R. Harik. Automated fiber placement: A review of history, current technologies, and future paths forward. Composites Part C: Open Access, 6:100182, 2021. 3. C. Colombo, A. Tridello, A. P. Pagnoncelli, C. A. Biffi, J. Fiocchi, A. Tuissi, L. M. Vergani, and D. S. Paolino. Efficient experimental methods for rapid fatigue life estimation of additive manufactured elements. International Journal of Fatigue, 167, Part B:107345, 2023. 4. M. Ivey, G. W. Melenka, J. P. Carey, and C. Ayranci. Characterizing short-fiber-reinforced composites produced using additive manufacturing. Advanced Manufacturing: Polymer & Composites Science, 3(3):81–91, 2017. 5. W. S. de Carvalho, J. Draper, T. Terrazas-Monje, A. Toumpis, A. Galloway, and S. T. Amancio-Filho. Fatigue life as-sessment and fracture mechanisms of additively manufactured metal-fiber reinforced thermoplastic hybrid structures produced via ultrasonic joining. Journal of Materials Research and Technology, 26:5716–5730, 2023. 6. D. Palumbo, R. De Finis, P. G. Demelio, and U. Galietti. A new rapid thermographic method to assess the fatigue limit in gfrp composites. Composites Part B: Engineering, 103:60–67, 2016.
Effect of Induced Porosity on Fatigue Performance of Additively Manufactured Short-Fiber Thermoplastics 13 7. Z. Jia, M. L. Pastor, C. Garnier, and X. Gong. Fatigue life determination based on infrared thermographic data for multidirectional (md) cfrp composite laminates. Composite Structures, 319:117202, 2023. 8. Y. Yan, M. L. Pastor, E. Abisset-Chavanne, and X. Gong. Rapid identification of fatigue degradation law of composite material based on ir thermography. Composite Structures, 354:118787, 2025. 9. N. Manoharan, P. Pathak, S. Gururaja, V. Kumar, and U. Vaidya. Rapid fatigue characterization via infrared thermography of am-cm composites. In Springer Nature Switzerland, editor, Challenges in Mechanics of Biological Systems and Materials, Thermomechanics and Infrared Imaging, Time Dependent Materials and Residual Stress, volume 2, pages 53–58. 2023. 10. J. Montesano, Z. Fawaz, and H. Bougherara. Use of infrared thermography to investigate the fatigue behavior of a carbon fiber reinforced polymer composite. Composite Structures, 97:76–83, 2013.
Chapter 3 Chapter 1 On the Detection and Quantification of Nonlinearity via Statistics of the Gradients of a Black-Box Model Georgios Tsialiamanis and Charles R. Farrar Abstrac t Detection and identification of nonlinearity is a task of high importance for structural dynamics. On the one hand, identifying nonlinearity in a structure would allow one to build more accurate models of the structure. On the other hand, detecting nonlinearity in a structure, which has been designed to operate in its linear region, might indicate the existence of damage within the structure. Common damage cases which cause nonlinear behaviour are breathing cracks and points where some material may have reached its plastic region. Therefore, it is important, even for safety reasons, to detect when a structure exhibits nonlinear behaviour. In the current work, a method to detect nonlinearity is proposed, based on the distribution of the gradients of a data-driven model, which is fitted on data acquired from the structure of interest. The data-driven model selected for the current application is a neural network. The selection of such a type of model was done in order to not allow the user to decide how linear or nonlinear the model shall be, but to let the training algorithm of the neural network shape the level of nonlinearity according to the training data. The neural network is trained to predict the accelerations of the structure for a time-instant using as input accelerations of previous time-instants, i.e. one-step-ahead predictions. Afterwards, the gradients of the output of the neural network with respect to its inputs are calculated. Given that the structure is linear, the distribution of the aforementioned gradients should be unimodal and quite peaked, while in the case of a structure with nonlinearities, the distribution of the gradients shall be more spread and, potentially, multimodal. To test the above assumption, data from an experimental structure are considered. The structure is tested under different scenarios, some of which are linear and some of which are nonlinear. More specifically, the nonlinearity is introduced as a column-bumper nonlinearity, aimed at simulating the effects of a breathing crack and at different levels, i.e. different values of the initial gap between the bumper and the column. Following the proposed method, the statistics of the distributions of the gradients for the different scenarios can indeed be used to identify cases where nonlinearity is present. Moreover, via the proposed method one is able to quantify the nonlinearity by observing higher values of standard deviation of the distribution of the gradients for lower values of the initial column-bumper gap, i.e. for “more nonlinear” scenarios. Keyword s Structural health monitoring (SHM) · Structural dynamics · Nonlinear dynamics · Machine learning · Neural networks 1.1 Introduction In the pursuit of making everyday life safer, humans have extensively tried to model the environment around them. Structures are an important part of the environment, in which humans live. They are man-made and should be safe throughout their lifetime. Structures are exposed to numerous environmental factors, which may cause them to fail. Moreover, during operation, structures are subjected to dynamic loads, which, in time, may cause failure. Such failures will most probably result in economic damage to society and may even result in loss of human lives. Therefore, for the purpose of maintaining structures safe, the field of structural health monitoring (SHM) [1] has emerged. G. Tsialiamanis ( ) Dynamics Research Group, Department of Mechanical Engineering, University of Sheffield, Sheffield, UK e-mail: g.tsialiamanis@sheffield.ac.uk C. R. Farrar Engineering Institute, MS T-001, Los Alamos National Laboratory, Los Alamos, NM, USA e-mail: farrar@lanl.gov © The Society for Experimental Mechanics, Inc. 2024 M. R. W. Brake et al. (eds.), Nonlinear Structures & Systems, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-031-36999-5_1 1 Fracture Properties Identification using Full-field Measurements: Some Important Concepts and Validation Joa˜o Carlos A. D. Filho, Lukas Wittevrongel, Amar Peshave, Pascal Lava, and Fabrice Pierron Abstract This article studies the effect of Digital Image Correlation uncertainties on fracture parameters obtained from a CT test specimen. It uses synthetic image deformation from finite element simulations to identify such errors. The paper looks at systematic errors from the DIC process as well as the effect of image noise. Keywords Fracture mechanics · Synthetic image deformation· Uncertainty quantification· Digital image correlation Introduction Fracture mechanics is a widely used tool in academia and industry to predict the failure of materials. An important parameter to such models is the fracture toughness in the different modes of fracture, I, II and III. Many techniques have been developed over the years to obtain such parameters, and it is beyond the scope of the present paper to review them. They mostly use the load recorded by the load cell of the test machine together with some (semi-) analytical solutions to derive the fracture properties. In the last twenty years, full-field optical measurements have gradually spread in the experimental mechanics community, providing very dense sets of kinematic data (typically tens of thousands or more), hence the term ‘full-field’. Digital Image Correlation (DIC) is the most widespread [1], with many commercial systems providing turnkey solutions. It is therefore not surprising that many studies have used DIC data to extract fracture parameters, as reviewed in [2]. There are generally two main families of approaches: either fitting the crack-tip displacement field with a Williams series [3] to obtain the stress concentration factor; or using the J-integral [4]. DIC is a complex measurement chain, highly nonlinear and subject to many potential sources of error. As a consequence, while it is easy to process DIC data for stress concentration factors or toughness, it is hard to establish realistic error bars on these quantities. This is the objective of the present contribution. It relies on the technology of synthetic image deformation developed initially in [5, 6] to perform uncertainty quantification in material constitutive model identification with the Virtual Fields Method. It is extended here to the determination of stress concentration factors and J-integrals. Simulation of DIC measurements on CT specimen A finite element (FE) model of a Compact Tension (CT) specimen was developed using Abaqus v.6.6, based on the ASTM standard E399 [7]. Plane stress CPS4R linear elements were used. The dimensions and the mesh are reported in Fig. 1. The bottom and top holes were constrained in all translational degrees of freedom, except the top hole vertical displacement which was left free while a vertical load of 35 N was applied. Large transformations were enabled. The material selected for this study is PMMA with a Young’s modulus of 3260 MPa and Poisson’s ratio of 0.36. The material thickness is 1 mm. Based on the FE model displacements, a numerically-generated speckle pattern was deformed according to the procedure described in [6]. The pattern was generated with the internal speckle pattern generator in the MatchID software. It consists of Joa˜o Carlos A.D. Filho· Lukas Wittevrongel · Amar Peshave · Pascal Lava · Fabrice Pierron MatchID NV, Leiekaai 25A, 9000 Ghent, Belgium e-mail: joao.filho@matchid.eu; lukas.wittevrongel@matchid.eu; amar.peshave@matchid.eu; pascal.lava@matchid.eu; fabrice.pierron@matchid.eu © The Author(s), under exclusive license to River Publishers 2025 15 Garrett Pataky et al. (eds.), Fracture, Fatigue, Failure, Damage Evolution and Thermomechanics & Infrared Imaging, Vol. 4, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.13052/97887-438-0830-5 3
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