PSI - Issue 76

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ScienceDirect

Procedia Structural Integrity 76 (2026) 1–2

5th International Symposium on Fatigue Design and Material Defects FDMD 2025 Editorial Matteo Benedetti a *, Stefano Beretta b , Mauro Madia c , Giovanni Meneghetti d a University of Trento , Department of Industrial Engineering , via Sommarive, 38123 Trento, Italy b Politecnico di Milano, Department of Mechanical Engineering, Via La Masa 1, 20156 Milano, Italy c Bundesanstalt für Materialforschung und –prüfung (BAM), Unter den Eichen 87, 12205 Berlin, Germany d University of Padova Department of Industrial Engineering, Via Venezia 1 35131, Padova, Italy

Abstract

The fatigue strength and service life of structural components are critically influenced by the presence of defects introduced during manufacturing. These material discontinuities—ranging from pores, inclusions, and surface roughness to microstructural inhomogeneities—act as precursors to fatigue damage, promoting early crack initiation at the microstructural scale. Over the past two decades, the concept of defect-tolerant design has emerged as a powerful framework to bridge the gap between traditional stress-life design methods, conservative safety factors, fracture-mechanics-based residual life assessments, and the limitations of non destructive evaluation (NDE) techniques. This approach is particularly relevant in the context of metal additive manufacturing (AM) , where complex defect populations, anisotropic properties, and novel microstructures challenge conventional fatigue assessment methodologies. Following the successful editions of the Fatigue Design and Material Defects (FDMD) Symposium held in Trondheim (2011), Paris (2014), Lecco (2017), and online in 2021, the 5th FDMD Symposium (FDMD5) was held in Trento, Italy, from May 14 to 16, 2025 . The event attracted an international audience of academic researchers, industry professionals, and

* Corresponding author. Tel.: +39-0461-282457; fax: +39-0461-281977. E-mail address: matteo.benedetti@unitn.it

2452-3216 © 2025 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 FDMD 2025 chairpersons 10.1016/j.prostr.2025.12.279

Matteo Benedetti et al. / Procedia Structural Integrity 76 (2026) 1–2

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practitioners with a shared interest in understanding and mitigating the effects of defects on fatigue performance. The scientific program featured 97 presentations , covering a wide range of topics such as: • Characterization and modeling of defects in metallic materials • Fatigue behavior of AM and cast alloys

• Multiaxial and high-cycle fatigue phenomena • Defect-sensitive design methods and standards • Advanced imaging, computational, and experimental techniques

Lively discussions were stimulated by thematic sessions, keynote and plenary lectures, and industrial contributions focusing on sectors such as aerospace, automotive, biomedical, and energy. This Special Issue of Procedia Structural Integrity includes a selection of 20 full-length papers , which were submitted after the conference and peer-reviewed under the supervision of the Scientific Committee. These contributions reflect the latest advances and diverse approaches to fatigue design in the presence of material defects. We gratefully recognize the support of our plenary and keynote speakers, sponsors, and the technical and administrative staff of the University of Trento for their essential role in the success of FDMD5. Their efforts made it possible to create an engaging, collaborative environment for advancing the field of fatigue design in the presence of material defects. M. Benedetti, S. Beretta, M. Madia, G. Meneghetti

Available online at www.sciencedirect.com

ScienceDirect

Procedia Structural Integrity 76 (2026) 99–106

© 2025 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 FDMD 2025 chairpersons Keywords: Aadditive manufacturing; Polylactic acid (PLA); Voids; Fatigue; Critical distance; Notch Abstract This study presents a novel fatigue life prediction method for plain and notched polylactide (PLA) structures manufactured with di ff erent in-fill levels via additive manufacturing. The proposed method models additively manufactured PLA with internal voids as a continuous, homogeneous, linear-elastic, and isotropic material. The e ff ect of these voids is represented by an equivalent crack, whose size is related to the void size. This approach provides a practical and accurate way to estimate the fatigue life of both plain and notched components, even when manufactured with di ff erent in-fill levels. The predicted fatigue lives agree with the experimental results obtained from specimens in di ff erent raster angles and in-fill levels. Additive manufacturing (AM) makes it possible to create lightweight, complex, and custom parts that are di ffi cult to create using conventional methods. However, as AM is a relatively new technology, further research is required to fully characterise the mechanical performance of printed components, particularly under cyclic loading. Some studies have investigated the fatigue behaviour of PLA components produced by Fused Deposition Model ing (FDM), highlighting the e ff ects of both design and manufacturing parameters. Hassanifard and Behdinan (2022) tested specimens printed flat on the build plate with unidirectional raster orientations (0° or 90°) and found that fil ament direction strongly a ff ected fatigue life. The same study also showed that the raster angle a ff ected the stress concentration around the notch. Ezeh and Susmel (2019) also printed specimens flat on the build plate but applied alternating raster patterns such as 0° / 90° and -45° / 45°. Their results indicated that variations in in-plane raster orien tation had negligible e ff ect on fatigue life. Cerda-Avila et al. (2023) printed parts in di ff erent build orientations. This change in geometric orientation, relative to the layer deposition direction, had a strong e ff ect on fatigue life. It demon- 5th International Symposium on Fatigue Design and Material Defects FDMD 2025 A Homogenised Material Approach to Predict Fatigue Life of Additively Manufactured PLA with Di ff erent In-fill Levels Mehmet F. Yaren a , Luca Susmel b, ∗ a Department of Mechanical Engineering, Sakarya University, 54050, Sakarya, Turkiye b Materials and Engineering Research Institute (MERI), She ffi eld Hallam University, Harmer Building, She ffi eld, S1 1WB, United Kingdom 1. Introduction

∗ Corresponding author. Materials and Engineering Research Institute, She ffi eld Hallam University, Harmer Building, She ffi eld, S1 1WB, UK E-mail address: l.susmel@shu.ac.uk (L. Susmel)

2452-3216 © 2025 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 FDMD 2025 chairpersons 10.1016/j.prostr.2025.12.292

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Fig. 1. Details of the specimens: (a) plain, (b) U-notched with 3 mm root radius, (c) U-notched with 1 mm root radius, (d) V-notched, and (e) experimental setup

strated that global build orientation is important. Regarding loading conditions, studies showed that non-zero mean stresses can significantly reduce fatigue life. PLA was found to be more sensitive to mean stress e ff ects than traditional metals Algarni (2022); Ezeh and Susmel (2019). Manufacturing parameters such as nozzle diameter, printing speed, and extrusion temperature also a ff ect fatigue performance. Lendvai et al. (2025) examined the e ff ect of filament feed rate and showed that higher feed rates create larger internal voids. These voids increase stress concentrations and re duce fatigue strength. Rotating bending fatigue tests performed by Dadashi and Azadi (2023) revealed that decreasing the nozzle diameter and extrusion temperature enhances interlayer bonding, thereby improving fatigue performance. Similarly, Gomez-Gras et al. (2018) examined the e ff ects of nozzle diameter, layer height, and fill density on fatigue performance, reporting that honeycomb in-fill outperforms rectilinear patterns under cyclic loading. Most studies on FDM-printed PLA investigate the e ff ect of manufacturing parameters through experiments, with limited focus on analytical methods. This paper builds on a previous study published in the International Journal of Fatigue by Yaren and Susmel (2025), which used the Theory of Critical Distances (TCD) Tanaka (1983);Taylor (1999) to assess the fatigue behaviour of PLA with di ff erent in-fill levels. That study introduced a method combining TCD with a homogenised cracked material concept to model internal voids. The method is reformulated to predict medium-cycle fatigue life using a simplified model: a homogenised continuous plate containing a central crack. The specimens were manufactured flat on the build plate using an Ultimaker ® 2 Extended + 3D printer with 2.85 mm white polylactic acid (PLA) filament from NewVerbatim ® . The properties of the filament, as provided in its datasheet, include a density of 1.24 g / cm 3 and a glass transition temperature of 58 °C. The yield strength of the parent material is specified as 63 MPa. Printing was performed using a 0.4 mm brass nozzle. The wall and shell thicknesses were set to 0.4 mm, with a layer height of 0.1 mm, a printing speed of 30 mm / s, a build plate temperature of 60 °C, and an extrusion temperature of 210 °C. Plain and notched specimens, each with a thickness of 5 mm, were fabricated based on the technical drawings presented in Fig. 1a–d. It is worth mentioning that although the notch root radius for the V-notched specimen was defined as zero in the technical drawings, optical measurements revealed that the actual root radius was approximately 0.15mm. Two types of internal geometries were investigated by varying the raster angles ( θ p ) to0° / 90 ° and -45 ° / 45°, each with five di ff erent in-fill levels (100%, 80%, 60%, 40%, 20%). Fig. 2 shows the internal geometries of the specimens corresponding to the di ff erent in-fill levels and illustrates the determination of the e ff ective void size, d v . Fig. 2 shows that d v varies across the specimen, so an average from multiple measurements was used in subsequent calculations. For the notched specimens, d v was generally measured around the notch, as crack initiation typically occurs in this area. Tabs. 1–2 present the measured values of d v for each in-fill level and specimen type. 2. Additive manufacturing, experimental procedure, and results

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Fig. 2. Internal views of specimens by in-fill level (left to right) and raster angle (top to bottom); void size d v is shown in the last column.

Table 1. The experimental results for un-notched specimens manufactured at di ff erent in-fill levels. in-fill level [%] R θ p [°] ∆ σ 0 − 50% [MPa] k T σ

d v [mm]

N. of tests

100 100 100

-1 -1

0

6.3 5.5 3.9 2.8 3.8 2.5 2.4 2.7 1.7 1.3 2.6 0.9 1.6 1.8 0.8

7.0 8.0 8.4 4.0 6.1 7.7 4.2 5.3 6.2 3.8 8.3 4.1 4.6 6.1 4.5

1.40 1.50 1.42 1.42 1.49 1.21 1.46 1.47 1.34 2.05 1.37 1.53 1.53 1.65 1.58

13

- - -

45

7

0.1

0 0

12

80 80 80 60 60 60 40 40 40 20 20 20

-1 -1

9 9 9 9 8 9 8 8

0.30 0.26 0.30 0.40 0.53 0.40 0.75 0.84 0.75 1.62 1.60 1.62

45

0.1

0 0

-1 -1

45

0.1

0 0

-1 -1

45

0.1

0 0

11

-1 -1

9

45

10

0.1

0

9

Plain specimens were printed with two raster orientations, 0 ° / 90 ° and -45 ° / 45 °, and tested under fully reversed loading ( R = − 1), while additional tests were performed on 0 ° / 90 ° specimens under tensile–tensile loading ( R = 0 . 1). Notched specimens were tested at both R = − 1 and R = 0 . 1, but only with the 0 ° / 90 ° raster angle. This decision was based on the observation that raster angle had no significant e ff ect on the fatigue performance of plain specimens, allowing for a reduction in the number of tests with notched specimens. The fatigue tests were conducted at room temperature under constant amplitude axial loading using a shaking table driven by an electric motor. Specimens were fixed to grips with bolts, as shown in Fig. 1e. An axial load cell and a linear variable di ff erential transformer (LVDT) were used to measure and record force and displacement throughout the tests. Each test was terminated either upon specimen failure or upon reaching 2 × 10 6 cycles, which was considered as run-out. A summary of the fatigue results for all test cases is presented in Tab. 1 for un-notched specimens and in Tab. 2 for notched specimens. Further details on the fatigue test data can be found in Ref. Yaren and Susmel (2025). In calculating nominal stress for both notched and un-notched specimens, internal voids were not taken into account. Specifically, for the notched specimens, nominal stress was calculated based on the net cross-sectional area. Tabs. 1 - 2 present the key fatigue parameters: ∆ σ 0 − 50% , which is the stress range at the endurance limit for a 50% survival probability ( P S = 50%), extrapolated at 2 × 10 6 cycles; the negative inverse slope ( k ) of the S–N curve; and the scatter ratio ( T σ ). The scatter ratio is defined as the ratio of endurance limits at P S = 90%and P S = 10%, assuming a log-normal distribution and estimated with a 95% confidence level. As summarised in Tabs. 1-2, increasing the in-fill level consistently led to a higher endurance limit across all combinations of load ratio, raster orientation, and geometry. Meanwhile, the negative inverse slope ( k ) remained approximately constant at around 5, regardless of the testing configuration.

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Table 2. The experimental results for di ff erent type of notched specimens printed at di ff erent in-fill levels for θ p = 0. Notch Type [%] in-fill Level [%] R ∆ σ 0 n , 50% [MPa] k n T σ

N. of tests

d v [mm]

V-notched V-notched V-notched V-notched V-notched V-notched V-notched V-notched V-notched V-notched

100 100

− 1 0.1 − 1 0.1 − 1 0.1 − 1 0.1 − 1 0.1 − 1 0.1 − 1 0.1 − 1 0.1 − 1 0.1 − 1 0.1 − 1 0.1 − 1 0.1 − 1 0.1 − 1 0.1 − 1 0.1

2.5 2.2 2.7 2.0 1.8 1.6 1.4 1.1 1.5 1.5 3.3 2.6 2.6 1.9 1.5 1.5 1.3 1.2 1.2 1.0 4.6 2.8 2.6 2.4 2.7 1.4 1.9 1.4 1.6 1.0

3.9 5.6 5.6 6.5 4.8 5.4 4.4 5.1 5.4 7.6 4.7 6.8 5.0 5.7 3.7 5.5 4.5 6.4 5.7 6.4 5.8 5.4 4.0 6.1 7.9 4.1 6.5 6.2 5.8 5.2

1.17 1.64 1.55 1.22 1.31 1.71 1.76 1.44 1.59 1.33 1.43 1.27 1.20 1.39 1.80 1.60 1.47 1.27 1.28 1.14 1.29 1.53 1.36 1.69 1.24 1.50 1.41 1.31 1.19 1.63

8 8 8 8 8 9 8 9 8 6 7 8 8 8 8 7 8 7 8 8 8 8 8 9 9 8 8 8

-

80 80 60 60 40 40 20 20 80 80 60 60 40 40 20 20 80 80 60 60 40 40 20 20

0.20

0.39

0.73

1.57

U-notch, 1 mm root radius U-notch, 1 mm root radius U-notch, 1 mm root radius U-notch, 1 mm root radius U-notch, 1 mm root radius U-notch, 1 mm root radius U-notch, 1 mm root radius U-notch, 1 mm root radius U-notch, 1 mm root radius U-notch, 1 mm root radius U-notch, 3 mm root radius U-notch, 3 mm root radius U-notch, 3 mm root radius U-notch, 3 mm root radius U-notch, 3 mm root radius U-notch, 3 mm root radius U-notch, 3 mm root radius U-notch, 3 mm root radius U-notch, 3 mm root radius U-notch, 3 mm root radius

100 100

- -

0.23

10

0.38

0.75

1.66

100 100

10

- -

0.23

0.42

0.77

1.66

3. Fatigue life estimation of additively manufactured plain and notched specimens

The approach proposed in this section to estimate the fatigue life of AM PLA structures is based on some assump tions based on experimental findings on previous studies Ezeh and Susmel (2019), Ahmed and Susmel (2019). First, since the e ff ect of raster angle on fatigue life is considered negligible for specimens printed flat on the build plate, the material behaviour can be assumed homogeneous and isotropic. Additionally, the stress–strain behaviour of the PLA specimens is assumed to be linear-elastic, and the e ff ect of superimposed static stresses on fatigue performance is accounted for by the maximum stress in each loading cycle.

3.1. Life estimation on un-notched specimen

As shown in Tab. 1, a decrease in in-fill density reduces the fatigue strength of 3D-printed PLA, making void size an important factor in fatigue life estimation. Fig 3a illustrates a PLA un-notched structure that contains internal voids of size d v , subjected to cyclic tensile loading. The structure fails after N f cycles. It should be noted here that the internal voids are neglected in stress calculations, meaning that the structure is made from homogeneous and continuous material. Fig. 3b illustrates an infinitely large plate, made of a continuous, homogeneous, isotropic, and linear-elastic ma terial, containing a centrally located through-thickness crack with a half-length a eq , and subjected to cyclic loading. In this context, the equivalent crack length a eq corresponds to the crack size that leads to failure of the plate after N f cycles under the applied maximum stress σ max . Since the configuration shown in Fig. 3b is considered as a central through-thickness crack, the Linear Elastic Fracture Mechanics (LEFM) shape factor is independent of crack length

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Fig. 3. Illustration of the transformation from a plain material with uniformly distributed voids (a) to an equivalent homogenized cracked continuum material (b); process zone (c) and fictitious linear-elastic local stress fields (e) to estimate fatigue lifetime of notched components (d) of AM PLA

and equals 1. Additionally, the structures shown in Figs. 3a and b are assumed to exhibit the same fatigue strength in the case of 100% in-fill and absence of any cracks. To achieve identical fatigue lives ( N f ) under cyclic loading with a maximum stress of σ max for both the plate containing a central through-thickness crack and the un-notched plate with internal voids, a relationship between the equivalent half-crack length ( a eq ) and the internal void size ( d v ) must be established. In Eq. (1), the function f( d v ) transforms the AM plate with internal voids (Fig. 3a) into an equivalent homogeneous, isotropic, linear-elastic plate containing a central crack, as depicted in Fig. 3b. a eq = f ( d v ) (1) The Theory of Critical Distances (TCD), as given in Eqs. (2) and (3), is used to evaluate the fatigue strength of an infinite plate with a through-thickness crack under cyclic tensile loading. ∆ σ 0 n =∆ σ o  1 −    a a + L 2    2 (2) ∆ σ 0 n =∆ σ o  L a + L (3) By replacing the a in Eqs. (2) and (3) with the a eq and using the critical distance L M ( N f ), the PM and LM can be directly expressed as follows for PM (Eq. 4) and LM (Eq. 5). For a detailed definition of critical distance for fatigue loading L M ( N f ), readers are referred to the paper by Susmel and Taylor (2007). σ max =        σ max , 0 ·  N Ref N f  k        100% ·  1 −    a eq a eq + | L M ( N f ) | 100% 2    2 (4) σ max =        σ max , 0 ·  N Ref N f  k        100%     L M ( N f )    100% a eq +    L M ( N f )    100% (5) In Eqs. (4) and (5), σ max , 0 represents the endurance limit at N Ref cycles, and k is the negative inverse slope of the fatigue curve obtained from specimens manufactured with 100% in-fill. Notably, these equations are expressed

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in terms of the maximum stress in the fatigue cycle, as experimental study Ezeh and Susmel (2019) has shown that the maximum stress e ff ectively captures the influence of mean stress on the fatigue performance of additively manufactured PLA. As previously mentioned in Eq. (1), to define the relationship between the equivalent half-crack length a eq and the void size d v in the simplest form, a linear function can be assumed. Accordingly, the relationship can be expressed using a dimensionless transformation constant k t as follows: a eq = k t · d v (6) After directly determining the constant k t from experiments on specimens with less than 100% in-fill, it can be substituted into Eqs. (4) and (5). Now the Point Method (PM) and Line Method (LM) methods in TCD can be applied by using the Eqs. (7) and (8). σ max =        σ max , 0 ·  N Ref N f  k        100% ·   1 −    k t · d V k t · d V +     A · N B f     100% 2    2 (7) In Eqs. (7) and (8), σ max is the maximum stress in the fatigue cycle applied to the un-notched AM component being designed (Fig. 3a). The stress analysis is conducted assuming the material is linear-elastic, continuous, homogeneous, and isotropic (i.e., by neglecting the presence of manufacturing voids). Fatigue constants σ max , 0 (at N Ref cycles to failure), k , A , and B are all determined by testing specimens manufactured by setting the in-fill level equal to 100%. In Eqs. (7) and (8), A and B are material constants that must be determined experimentally. Although the values of A and B for a specific material may vary with changes in the load ratio, they remain una ff ected by variations in the profile or the sharpness of the geometrical feature being assessed Susmel and Taylor (2007). For a detailed definition of critical distance for fatigue loading L M ( N f ), the constants A and B , readers are referred to the paper by Susmel and Taylor (2007). As a result, the PM and LM approaches can be used to estimate fatigue life by solving Eqs. (7) and (8) for N f . The corresponding number of failure cycles can be e ffi ciently computed using conventional numerical methods. Localized stress concentrations within AM structures can compromise structural integrity. To overcome this issue, a combined approach integrating the TCD and the previously introduced equivalent homogeneous material modeling is proposed. This framework enables the fatigue strength of notched AM PLA components to be assessed through simple and reliable design rules. As shown in Fig. 3c, a notched AM component with less than 100% in-fill contains internal voids with an average size of d v and is subjected to uniaxial fatigue loading with a peak cyclic force F max . To accurately estimate the fatigue strength using the TCD, the notched AM component shown in Fig. 3e is modeled as a continuous, homogeneous, isotropic, and linear-elastic body with the same dimensions as the component in Fig. 3d. This approach enables the application of the Point Method (PM) and the Line Method (LM), assuming that the size of the process zone remains constant regardless of internal void size in Fig. 3c. Based on this assumption, the critical distance L M from fatigue tests on plain specimens with 100% in-fill is calculated by using the proposed approach by Susmel and Taylor (2007). Since L M is constant for a given AM material, the influence of manufacturing voids is considered by adjusting the intrinsic static strength of the material using either Eqs. (7) and (8). Assuming the AM component behaves as a continuous, homogeneous, isotropic, and linear-elastic material, the lo cal fictitious stress fields shown in Fig. 3e can be determined using standard Finite Element (FE) analysis or analytical methods. These stress fields are used to calculate the e ff ective stress σ max , ef f using either the PM or LM from TCD. To account for internal voids, the fatigue failure condition at N f cycles is given by: σ ef f , max  N f  = σ max  N f  (9) σ max =        σ max , 0 ·  N Ref N f  k        100%      A · N B f     100% k t · d v +     A · N B f     100% (8) 3.2. Life estimation on notched specimen

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Here, σ max , ef f ( N f ) is the fatigue strength of the plain material, evaluated using Eqs. (7) and (8), both expressed in terms of maximum stress to include mean stress e ff ects. For the PM, the failure condition can be directly obtained by combining the e ff ective stress definition in Eq. (10) with the fatigue strength model in Eq. (7). Similarly, for the LM, it is derived by combining Eq. (10) with Eq. (8). ∆ σ ef f =∆ σ y  θ = 0 , r = L M ( N f ) 2  (10)

1 2 · L M ( N f ) 

2 L M ( N f )

∆ σ y ( θ = 0 , r ) · dr

(11)

∆ σ ef f =

0

· 

f     100% 2  

    A · N B

   2

 1 −  

σ y , max  

k    

 =    

   σ max , 0 · 

N f 

N Ref

 k t · d V k t · d V +    

 θ = 0 , r =

(12)

   100%

f     100% 2

A · N B

·     

f     100%

k    

σ y , max ( θ = 0 , r ) · dr =    

f     100%

2 ·     A · N B

   σ max , 0 · 

N f 

f     100% 

A · N B

N Ref

1 2 ·     A · N B

(13)

f     100%

k t · d V +     A · N B

   100%

0

Eqs. (12) and (13), the unknown is the number of cycles to failure, N f , which appears on both sides of the equations. To find the fatigue life, standard numerical iteration methods can be used by combining the linear-elastic fictitious stress field with the PM and LM formulations in Eqs. (12) and (13), respectively.

4. Model validation with experimental results

Local stress fields for the TCD analysis were obtained using 2D linear-elastic FE models (PLANE182) in ANSYS ® . The notched AM-PLA specimens were modeled as homogeneous, isotropic, and linear-elastic materi als, without explicitly including internal voids. In the simulations, the root radius of V-notch was set to 0.15 mm, matching the average measured value from the actual manufactured specimens. To assess the accuracy and reliability of the Point Method (PM) and Line Method (LM), Eqs. (7) and (8) were employed to estimate the fatigue strength of the un-notched specimens (see Tab. 1). The required constants A and B in these equations, which are used to define the critical distance for fatigue loading L M ( N f ), were derived from fatigue test results of 100% in-fill plain and V-notched specimens Fig. 1a and d. Key parameters of the fatigue curves are presented in Tabs. 1 and 2. The resulting values for A and B were 25.1 and -0.242, respectively. Then, experimental results from plain PLA specimens printed with 80% in-fill and a raster angle of ( θ p ) = 0° under fully reversed loading (R = -1) were used to calibrate the transformation function f( d V ) in Eq. (6). For each data point, the number of cycles to failure ( N f ) was taken from the experiment, and the transformation constant k t was calculated using both the PM and LM approaches defined in Eqs. (7) and (8). The average of the eight calculated k t values gave 9.4 for the PM and 8.2 for the LM. Due to page limits, Fig. 4a and b show PM and LM results for one un-notched and one notched case, respectively, though both methods were validated for all specimen types. In Fig. 4a, the PM predictions using Eqs.(7) and (8) show strong agreement with experimental fatigue lives for un-notched specimens, with most data points falling within the scatter band of the 100% in-fill reference curve. Similarly, Fig. 4b illustrates that the LM predictions from Eqs.(12) and (13) also align closely with the experimental results for notched specimens. These results confirm the accuracy and consistency of the proposed TCD-based framework in predicting fatigue life for both notched and un-notched AM PLA components with various in-fill levels. Since the method relies on linear-elastic FE stress fields using a homogeneous, isotropic material model, it avoids the need to explicitly model internal voids, making it practical for fatigue design of AM components.

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Fig. 4. Accuracy of (a) PM for plain and (b) LM for V-notched specimens in estimating the fatigue life of AM PLA with di ff erent infill levels.

5. Conclusion

This study experimentally and computationally investigates the e ff ect of in-fill level on the fatigue performance of plain and notched AM PLA. A new approach based on the TCD is proposed to estimate the fatigue behaivour of both additively manufactured plain and notched PLA, accounting for internal voids. A strong correlation between internal void size and the fatigue strength of plain AM PLA is established by using an equivalent homogenised material concept within the TCD framework. The proposed approach also yields accurate fatigue life predictions for notched components manufactured with varying in-fill levels. The proposed TCD-based fatigue design method allows the use of standard linear-elastic FE results from homogeneous, isotropic models, removing the need to model manufacturing voids explicitly. Ahmed, A.A., Susmel, L., 2019. Static assessment of plain / notched polylactide (pla) 3d-printed with di ff erent infill levels: Equivalent homogenised material concept and theory of critical distances. Fatigue & fracture of engineering materials & structures 42, 883–904. Algarni, M., 2022. Fatigue behavior of pla material and the e ff ects of mean stress and notch: Experiments and modeling. Procedia Structural Integrity 37, 676–683. Cerda-Avila, S.N., Medell´ın-Castillo, H.I., Cervantes-Uc, J.M., May-Pat, A., Rivas-Menchi, A., 2023. Fatigue experimental analysis and modelling of fused filament fabricated pla specimens with variable process parameters. Rapid Prototyping Journal 29, 1155–1165. Dadashi, A., Azadi, M., 2023. Experimental bending fatigue data of additive-manufactured pla biomaterial fabricated by di ff erent 3d printing parameters. Progress in Additive Manufacturing 8, 255–263. Ezeh, O., Susmel, L., 2019. Fatigue strength of additively manufactured polylactide (pla): e ff ect of raster angle and non-zero mean stresses. International Journal of Fatigue 126, 319–326. Gomez-Gras, G., Jerez-Mesa, R., Travieso-Rodriguez, J.A., Lluma-Fuentes, J., 2018. Fatigue performance of fused filament fabrication pla speci mens. Materials & Design 140, 278–285. Hassanifard, S., Behdinan, K., 2022. E ff ects of voids and raster orientations on fatigue life of notched additively manufactured pla components. The International Journal of Advanced Manufacturing Technology 120, 6241–6250. Lendvai, L., Fekete, I., Rigotti, D., Pegoretti, A., 2025. Experimental study on the e ff ect of filament-extrusion rate on the structural, mechanical and thermal properties of material extrusion 3d-printed polylactic acid (pla) products. Progress in Additive Manufacturing 10, 619–629. Susmel, L., Taylor, D., 2007. A novel formulation of the theory of critical distances to estimate lifetime of notched components in the medium-cycle fatigue regime. Fatigue & Fracture of Engineering Materials & Structures 30, 567–581. Tanaka, K., 1983. Engineering formulae for fatigue strength reduction due to crack-like notches. International Journal of Fracture 22, R39–R46. Taylor, D., 1999. Geometrical e ff ects in fatigue: a unifying theoretical model. International journal of fatigue 21, 413–420. Yaren, M.F., Susmel, L., 2025. A novel critical distance-based homogenised material approach to estimate fatigue lifetime of plain / notched polylactide 3d-printed with di ff erent in-fill levels. International Journal of Fatigue 193, 108750. References

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Procedia Structural Integrity 76 (2026) 3–10

© 2025 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 FDMD 2025 chairpersons Keywords: Ti-6Al-4V; DED-LB/CW; Defects; Microstructure; K-T diagram; Fatigue assessment Abstract This work presents comprehensive fatigue test results utilizing machined specimens extracted horizontally from Ti-6Al-4V blocks manufactured by Direct Energy Deposition using Laser Beam and Coaxial Wire (DED-LB/CW). The experimental results act as basis to establish defect- and microstructure-based models applying the Kitagawa-Takahashi (K-T) approach and the modifications by El Haddad, Murakami and Chapetti. Three batches manufactured in two different DED-LB/CW systems were considered to achieve a variation in microstructure and micropore sizes. Fractographical analyses were executed to examine the size, location and shape of the crack-initiating features. Due to the parameter optimization carried out, Lack of Fusion (LoF) defects were avoided and only shrinkage and keyhole pores were detected. Fatigue Crack Growth (FCG) tests were performed using Compact Tension (CT) specimens to determine the long and effective crack growth thresholds. Kitagawa-Takahashi, El-Haddad, Murakami and Chapetti models were calculated combining fatigue strength, fractographical analysis, as well as fracture mechanics characteristics, achieving good fit with the experimental results. It can be concluded that the interaction between the defects and the microstructure is not negligible. Hence, an application of defect- and microstructure-based models using simplified pore size parameters such as Murakami ’ s √ area, enable a proper assessment of K-T diagrams for life predictions of Ti-6Al-4V manufactured by DED-LB/CW based on FCG behavior. 5th International Symposium on Fatigue Design and Material Defects FDMD 2025 Assessment of Kitagawa-Takahashi diagram for Ti-6Al-4V manufactured by DED-LB/CW: Evaluation of the interaction between defects and microstructure Xabat Orue a, *, Mikel Abasolo b , Eduardo Tabares a , Iban Quintana a a Tekniker, C/ Iñaki Goenaga 5, Eibar 20600 (Gipuzkoa), Spain b University of the Basque Country, Plaza Ingeniero Torres Quevedo 1, Bilbao 48013 (Bizkaia), Spain

* Corresponding author. Tel.: +34 673 748 369. E-mail address: xabat.orue@tekniker.es

2452-3216 © 2025 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 FDMD 2025 chairpersons 10.1016/j.prostr.2025.12.280

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1. Introduction Additive Manufacturing (AM) is a layer-by-layer advanced manufacturing technology that enables great geometrical freedom in part design and production. However, the mechanical properties that are obtained are not as high as in Conventional Manufacturing (CM) due to the limited of control under different factors, such as the process temperature and the layer height. This is true irrespective of the AM technology, but it is more pronounced in the case of Direct Energy Deposition (DED) [1]. Consequently, a process optimization is required to obtain zero-defect components and enhance the final properties [2]. In the case of the variant where a laser beam is used to deposit a coaxial wire (DED-LB/CW), this task becomes more critical due to the interaction between parameters and the importance of the layer height control [3]. Additionally, a proper fatigue assessment is essential to ensure reliability, as most failures of structural components are due to this phenomenon where dynamic loads are involved. This is influenced by many factors such as defects and microstructure among others. One of the procedures to consider the influence of defects is using the Kitagawa-Takahashi (K-T) diagram [4], where the fatigue limit range (Δσ w ) is represented with respect to the crack or equivalent defect size ( a ) according to the following expression: ∆ ( ) = ∆ ℎ, · √ · (1) Where ∆ ℎ, is the long crack growth threshold stress intensity factor range and Y is the geometrical factor taking the crack or defect position and the configuration into account. To consider other aspects apart from the size of defects, modifications of K-T diagram are used. One of them was proposed by El Haddad with a smooth transition between the intrinsic fatigue strength and defect-affected region considering a fictious crack size a + a 0 according to the following expression [5]: ∆ ( ) = ∆ ℎ, · √ · ( + 0 ) (2) Where a 0 is a fictitious intrinsic crack length for long cracks, below which no effect from the defects occurs. Its value is calculated as follows: 0 = 1 · ( ∆ ℎ, · ∆ 0 ) 2 (3) Where ∆ 0 is the intrinsic fatigue strength range in absence of defects. Its value for fully reversal stress ratios ( R = -1) is related with the Vickers hardness ( HV ) of the material as follows [6]: ∆ 0 = 3,2 · (4) To consider the influence of mean stresses ( R ≠ -1), different models are employed, such as Walker’s [7]: , =−1 = · (1 −2 ) = · (1 −2 ) (5) Where R stands for the stress ratio ( σ min /σ max ) and γ is Walker’s exponent which is material dependent with HV [6,7]: = 0,226 + −4 (6) Murakami proposed another modification for the K-T diagram considering the HV of the material and the square root of the projected area of the defect in the plane perpendicular to the principal stresses ( √ ) with the following expression [6]: ∆ ( , √ ) = · ( + 120) · (√ ) 1/6 · (1 −2 ) (7) Where C is a material dependent position factor of the defect [6]. Another model was proposed by Chapetti to consider the microstructural effect of the material on the transition from short to long cracks [8]. This model is interesting especially when the size of defects is small and comparable to microstructural features of the material. ∆ ( , )= ∆ ℎ (∆ , ) · √ · (8)

Xabat Orue et al. / Procedia Structural Integrity 76 (2026) 3–10 5 Where ∆ ℎ (∆ , ) is calculated as follows considering the crack extension Δ a , and a dimensional characteristic of the microstructure l R , as well as the effective crack growth threshold stress intensity factor range ∆ ℎ, [8]: ∆ ℎ (∆ , )=∆ ℎ, +(∆ ℎ, −∆ ℎ, ) · (1− −Δ / ) (9) Fig. 1 presents a schematic illustration of the original Kitagawa – Takahashi diagram, along with the modifications proposed by El-Haddad, Murakami and Chapetti, which serve as the foundational framework for the assessment of K T diagram conducted in this study for Ti-6Al-4V manufactured by DED-LB/CW. Thereby, a safe fatigue assessment is ensured if the equivalent defect size a and the corresponding applied stress range Δσ is below the curves.

log Δσ w

log a

Fig. 1. Schematic illustration of K-T diagram with the modifications by El Haddad, Murakami and Chapetti.

Many authors analyzed the mechanical properties of Ti-6Al-4V obtained by DED-LB/W in different conditions [9 – 11], but very few focused on the interaction between the defects and the microstructure [12,13]. To fill this gap, this work presents the assessment of K-T diagram considering the interaction between defects and microstructure by modified models. For this purpose, microstructural analysis and mechanical characterization with Vickers hardness, tensile, HCF and FCG tests were carried out. 2. Material and Method In this study a 1.20 mm diameter Ti-6Al-6V wire was coaxially deposited with a laser beam in commercially pure titanium (grade 2) plates of dimensions 200 x 200 x 20 mm 3 (substrate). Table 1 shows the chemical composition of the wire used: Table 1. Chemical composition of the Ti-6Al-4V wire. Elem. Al V O Fe C N H Ti Comp. (wt.%) 6.75 4.50 0.20 0.30 0.08 0.05 0.01 Bal. To obtain a variation in the resultant microstructure and defects, the samples were extracted from three batches manufactured in two different DED-LB/CW systems. All of them were manufactured with a set of optimized parameters following a zero-defect philosophy [2]. As a result, Lack of Fusion (LoF) defects were avoided and only shrinkage and keyhole pores were detected in fractographic analysis (see section 3). The selected configuration is shown below: Table 2. DED-LB/CW process parameter configuration. Parameter: P L [W] v w [mm/s] v f [mm/s] d o [mm] h L [mm] Value: 2056.10 25 20 1.80 0.75 Where, P L is the real laser power; v w is the wire feed rate; v f is the forward speed; d o is the overlapping distance; h L is the layer height.

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The DED-LB/CW systems used consist on a 6+2-axis robotic cell, and a 3-axis machine called TITAN which was designed and manufactured by Tekniker for research and development purposes. Both systems are equipped with a continuous wave 4 kW Yb fiber laser (1070 nm) from IPG Photonics and the coaxial wire laser head CoaxPrinter from Precitec GmbH & Co. The deposition was accomplished by a bidirectional strategy alternating 90º in each layer, and an additional contouring to ensure the integrity in height growth. To generate an inert atmosphere, plastic welding chamber of 700 x 700 x 500 mm 3 size filled with commercially pure argon was employed. The oxygen concentration was monitored and maintained below 100 ppm to avoid the formation of any oxides in the deposited Ti-6Al-4V. The samples were extracted in horizontal direction from rectangular solid blocks manufactured in as-built conditions with no heat treatment by Wire-based Electro Discharge Machining (EDM-w). This was executed deep inside the solid blocks to obtain homogeneous material. A safety margin of 10 mm from the surface was considered enough for this purpose. This also ensures to avoid the possible residual alpha-case layer that might have been generated in the surface despite being manufactured in an inert atmosphere. Afterwards, all samples were machined. For microstructural characterization, 12 mm wide and 2 mm thickness specimens were extracted along the height of the blocks. These specimens were metallurgically prepared by grinding with 2500-grit and polishing with colloidal silica suspension 50 nm alkaline, and afterwards Weck's reagent was used for etching. The microstructure, as well as the fractographical analysis of post-mortem specimens, was undergone by the Olympus GX71 Optical Microscope (OM) and ZEISS Ultra Plus Scanning Electron Microscope (SEM). Additionally, the software MountainsMap® was used to postprocess the acquired images and to obtain microstructural characteristics such as the length, the width and the aspect ratio of α -laths. Related to the mechanical characterization, Vickers hardness, tensile, High Cycle Fatigue (HCF) and Fatigue Crack Growth (FCG) tests were executed. Vickers hardness tests were undergone along the height of microstructural samples by FUTURE-TECH FM-700 with 0,5 kg indentation-load. For tensile tests, rectangular specimens of 4 x 6 mm 2 cross-section were tested according to ASTM E8 [14] using the INSTRON 3369 testing system (50 kN). For HCF and FCG tests, INSTRON 8852 servohydraulic biaxial machine (100 kN and 1000 Nm) was used instead. HCF assessment was carried out at R = 0,1 with 16 Hz of frequency ( f ), and a run-out of 10 million cycles was set. Axial force controlled constant amplitude procedure according to ASTM E466 [15] was applied using cylindrical specimens of 6 mm diameter and 12 mm calibrated length. To determine the fatigue limit, the up-and-down method was applied according to Dixon ’s evaluation procedure [16]. Regarding FCG tests, compliance method was applied with a Crack Opening Displacement (COD) gauge of 10 mm length and 4 mm travel. Here, Compact Tension (CT) specimens of 12,5 mm thickness ( B ) and 50 mm width ( W ) extracted in L/T-L/T (H-H) and L/T-S (H-V) directions [17] were used. FCG tests were executed at R = 0,1 and R =0,7with f = 16 Hz applying K-Decreasing procedure according to ASTM E647 [18]. The construction of the K-T diagram was executed considering the experimental results obtained from the above mentioned tests. The prospective fatigue limits were calculated considering the specimens that failed before 10 million cycles (fractures). According to the fatigue design guide of non-ferrous materials for helicopters [19], all data point were moved to 50 million cycles keeping the same Gaussian normalized residual, i.e., extrapolating with the slope of the S-N curve. The intrinsic fatigue limit of the material free of defects was calculated by the relationship (4) for R = -1 [6], and to consider the mean stresses of the tests at R = 0,1 Walker’s model was applied with (5,6) [7]. Based on Linear Elastic Fracture Mechanics (LEFM), the long crack region of the K-T diagram was determined by ΔK th,lc obtained from FCG tests in each direction. Related to the consideration of equivalent defect size, Murakami’ s √ was used and Y was determined accordingly based on the results obtained from fractographic analysis (see section 3). 3. Results and Discussion The microstructural analysis by OM and SEM revealed a columnar prior-beta grains with martensite (Fig. 2). This is in line with other authors due to the fast cooling rates towards the base plate that are common in DED processes [1]. The undergone post-processing by MountainsMap® revealed a length of alpha-lath of 11 µm.

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Fig. 2. Microstructural analysis by OM at 50x (left) and 200x (center), and by SEM at 1500x with SE2 (right). The martensitic microstructure obtained leads to high values of hardness, stiffness and strength, but low ductility (Table 3). This is also in line with the literature [20]. Table 3. Results of Vickers hardness and tensile tests in horizontal direction. HV [kgf/mm 2 ] E [GPa] σ yp [MPa] σ ut [MPa] A t [%] Value: 381,35 ± 8.53 103,45 ± 11,44 997,84 ± 22,37 1096,25 ± 9,16 5,74 ± 1,08 Where, E refers to the Young’s modulus (stiffness), σ yp is the yield strength (stress), σ ut is the ultimate tensile strength (stress) and A t stands for the total percentual elongation (strain). The values correspond to the meansand the standard deviations. Related to the dynamic mechanical performance, S-N curve of HCF tests at R = 0,1 for horizontally extracted samples with no heat treatment (T0) is shown in Fig. 3, where fractures (FR) and run-outs (RO) are distinguished. The fatigue limit range ( Δσ w ) obtained by the up-and-down method according to Dixon [16] is 598,5 MPa and the corresponding knee-point ( N k ) is at 2,18·10 7 cycles.

y = 1640,6x -0,06 R² = 0,6759

FR-T0

RO-T0

Potencial (FR-T0)

1000

800

log Δ σ (MPa)

400

1,00E+04

1,00E+05

1,00E+06

1,00E+07

log N (cycles)

Fig. 3. S-N curve of HCF tests at R = 0,1 of horizontal specimens with no heat treatment. Fractographical analysis of tested samples revealed that all the defects that cause the failure (killer defects) are internal based on the relationship between the size and the position. According to Murakami, a defect is considered internal when the ratio between the equivalent radius of the same area ( R eq ) and the position of its center to the outer surface ( h ) is less than 0,8. In such cases, the geometrical factor Y takes a value of 0,50 [6]. It should be noted that this might be due to the extraction of samples from inside the manufactured solid blocks avoiding the critical zones (see section 2). The defect distribution inside the blocks manufactured by DED-LB/CW is usually very low and homogeneous [2].

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Table 4 shows the results of FCGtests executed by K-Decreasing procedure according to ASTM E647 [18]: Table 4. Results of FCG tests in H-H and H-V directions. Direction ΔK th,eff [MPa·m 1/2 ] ΔK th,lc [MPa·m 1/2 ] C p [-] n p [-] H-H 1,90 ± 0,05 4,14 ± 0,19 (1,80 ± 1,70) ·10 -10 5,76 ± 0,57 H-V 2,00 ± 0,05 2,70 ± 0,07 (2,50 ± 0,71) ·10 -8 3.12 ± 0,20 Where, ΔK th,eff is the effective fatigue crack growth threshold (R0.7), ΔK th,lc is the fatigue crack growth threshold in the long crack regime (R0.1), and C p and n p are Paris fitting parameters (R0.1). The values correspond to the means and standard deviations. The directions analyzed in FCG tests are representative of crack growth direction of horizontally extracted samples. Due to the implemented deposition strategy (see section 2), the obtained properties are orthotropic (L=T≠S) , i.e., the properties in horizontal directions are similar (L=T) and the only difference is in vertical direction (S). Therefore, the notation was simplified with H and V for horizontal and vertical directions respectively. According to the results obtained (Table 4), it could be stated that H-V direction is more critical than the H-H direction, because the long cracks propagation threshold ( ∆ ℎ, ) is lower (being ∆ ℎ, similar) and the Fatigue Crack Growth Rate (FCGR) is higher. This is related to the low distribution of defects [2] and the columnar microstructure obtained (Fig. 2), where the alignment of prior-beta grains with H-V direction facilitates the propagation of cracks. In H-H direction on the other hand, the crack is faced with more grain boundaries that impedes its propagation, and that is why better FCG results are obtained. Considering all these results, the K-T diagram and the modifications by El Haddad, Murakami and Chapetti are presented for each crack growth direction (Fig. 4):

H-H

1000,00

log Δσ w (MPa)

100,00

1,00

10,00

100,00

1000,00

log √area ( µ m)

H-V

1000,00

log Δσ w (MPa)

100,00

1,00

10,00

100,00

1000,00

log √area (µm)

Fig. 4. K-T diagram and de modifications of El Haddad, Murakami and Chapetti in H-H (up) and H-V (down) directions.