Microsoft Word - numero_73_art_17_5444.docx D. Leonetti, Fracture and Structural Integrity, 73 (2025) 256-266; DOI: 10.3221/IGF-ESIS.73.17 256 An experimental study into the net cross-sectional failure of damaged plates with holes for different steel grades and temperatures Davide Leonetti, Bo van Schuppen, Maryam Jahanian, Sumya Mobder, H.H. (Bert) Snijder Eindhoven University of Technology, Eindhoven, The Netherlands d.leonetti@tue.nl, https://orcid.org/0000-0002-7436-3977 b.v.schuppen@student.tue.nl, m.jahanian@student.tue.nl, s.mobder@student.tue.nl, h.h.snijder@tue.nl KEYWORDS. Capacity design, Tensile strength, Structural steel, Failure Assessment Diagram. Citation: Leonetti, D., van Schuppen, B., Jahanian, M., Mobder, S., Snijder, H. H., An experimental study into the net cross- sectional failure of damaged plates with holes for different steel grades and temperatures, Fracture and Structural integrity, 73 (2025) 256-266. Received: 29.03.2025 Accepted: 09.05.2025 Published: 15.06.2025 Issue: 07.2025 Copyright: © 2025 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. INTRODUCTION he EN 1993-1-1 [1] provides design rules against various failure modes in steel structures, which are applicable to plain and notched components, and structural connections for steel grades up to S460 under ambient temperature conditions (~ 20°C). Clause 6.2.3 provides a design rule concerning the cross-sectional resistance of steel elements subjected to tension. In the presence of a notch, like a bolt hole in the case of a bolted connection, which can be made by either drilling and reaming or by punching, stress concentration occurs due to a reduction in cross-section, causing a redistribution of internal stresses in the net area. This stress concentration, and specifically the reduced cross-section, may result in a failure of the structural element at a load smaller than that required to yield the gross cross-sectional area [2]. This is undesirable because it hinders not only the ductility of the structural element but can also lead to a sudden redistribution of the force flow within the structure. The addition to the Eurocode, EN 1993-1-12 [3], includes the design rules for steel grades ranging from S460 up to S700. For structures in service at temperatures below 0°C, an additional T https://youtu.be/cPjZ4VqYq_k D. Leonetti, Fracture and Structural Integrity, 73 (2025) 256-266; DOI: 10.3221/IGF-ESIS.73.17 257 fracture toughness verification may be necessary, which is ensured in terms of maximum allowable thickness, mainly depending on the steel grade. For components loaded in tension, independent of the steel grade or geometry, the design value of the applied tension force NEd shall satisfy: Ed t Rd N N , 1.0 (1) where Nt,Rd is the design tension resistance of the element, which in this case contains holes and is equal to the governing (lowest) resistance, either the design plastic resistance of the gross cross-section Npl,Rd, or the design ultimate resistance of the net cross section Nu,Rd:   y pl Rd M Af N 0 , (2)   net u u Rd M A f N 2 , 0.9 (3) where A is the gross cross-sectional area, fy is the nominal value of the yield strength, fu is the characteristic value of the ultimate tensile strength, Anet is the net cross-section area, and γM0 and γM2 are partial factors. The EN 1993-1-12 [3] formulates the net cross-sectional resistance of steel plates of steel grade S460 up to S700 similar to the one presented in Eqn. 3, with the only difference being the substitution of γM12 instead of γM2. However, this part of the Eurocode also recommends using the same value for γM12 as for γM2, so γM12 = γM2. When a structural element is required to fail in a predictable and controlled manner such that it warns before failure hence, when a capacity design is requested, the design plastic resistance of the gross cross-section should be lower than the ultimate resistance of the net cross-section at the hole: Npl,RdN>105 cycles) in order to avoid elastic-plastic shakedown at the notch root and, at the same time, reduce testing time. The loading cycles differ for each specimen type and are applied at a frequency of between 4 and 7 Hz, mainly depending on the load levels. Crack initiation is detected using a broken wire electronic binary sensor method [11], which enables the identification of relatively small cracks, generally smaller than 1 mm. In this method, a thin copper wire having a diameter of 0.1 mm is glued as close as possible to the hole using cyanoacrylate. The wires are glued at both sides of every bolt hole, both at front and back of the plate as shown in Fig. 3. A 5V potential is applied between the two ends of the circuit and a resistor placed in series with the wires to limit the electrical current. When a crack initiates, and grows through the copper wire, the crack causes it to break, hence the circuit opens and the measured potential across the wire drops to 0 V. The voltage is monitored by the controller and a drop of the measured potential causes the cyclic loading to stop. Checking across each of the lead terminals shown in Fig. 3 whether the circuit is open or closed, allows for immediate detection of the crack location. The accuracy and the resolution of the sensor detecting relatively small cracks is highly dependent on the installation quality and wire diameter. According to the experience of the authors, the crack is required to grow across the wire location and D. Leonetti, Fracture and Structural Integrity, 73 (2025) 256-266; DOI: 10.3221/IGF-ESIS.73.17 261 extend over it for a few times the wire diameter for the wire to break. Hence, considering the diameter of the selected wire and the error in the positioning of the wire, the minimum detectable crack size is expected to be in the order of 0.5 mm. However, no systematic study is conducted to characterize the error in wire positioning and the effect of the load level and wire diameter on the minimum detectable crack size.       Figure 3: Setup for pre-cracking procedure including setup of the broken wire electronic binary sensors. During the monotonic tensile tests, three quantities are recorded:  The applied force measured by the loadcell,  The displacement of the actuator, or equivalently the crosshead displacement for the tests conducted in the Instron universal testing machine,  The specimen average elongation measured by an LVDT with initial gauge length equal to the plate width, installed across the holes and spanning the center of the plate.  For cooled specimens, the temperature is recorded in the vicinity of the pre-crack. The failure assessment diagram The Failure Assessment Diagram (FAD) is an approach used to evaluate the failure behavior of metal structures that contain crack-like flaws. It visualizes the type of failure graphically, where the placement of an assessment point with respect to the failure line indicates the type of failure that may occur in the assessed structural element. The FAD considers two competing failure modes, namely brittle fracture and plastic collapse. Brittle fracture is assessed using linear elastic fracture mechanics theory by means of the Stress Intensity Factor (SIF) K, which allows the estimation of the brittle fracture ratio, Kr, calculated as the ratio between K and Kmat, i.e. the material fracture toughness. Plastic collapse, instead, is assessed through a limit load analysis applied to the cross-section containing the defect. Hence, the plastic collapse ratio, Lr, is obtained as the ratio between the applied load and the plastic collapse load. Equivalently, the reference stress approach can be used in which the ratio between the reference stress, σref, and the yield strength, fy, is used to obtain the plastic collapse ratio. The interaction between the failure modes is considered through a failure line, which is material dependent. In the British Standard BS7910 [17] the failure line can be constructed according to three options. In this work, Option 2 is considered. To obtain it, the full stress-strain curve of the material is used. This ensures a more realistic and less conservative assessment as compared to Option 1, which is crucial for safety standards. In order to obtain the SIF and the reference stress, existing solutions in BS7910 [17] have been used for corner cracks at holes, in which the crack sizes are obtained D. Leonetti, Fracture and Structural Integrity, 73 (2025) 256-266; DOI: 10.3221/IGF-ESIS.73.17 262 from the fracture surface. The approach is only employed here for the specimens in steel grade S700MC and type A. This is because of two reasons: (1) FAD has been shown to be successful for S275JR in previous research work [9, 18], and (2) stress intensity factor and reference stress solutions for other hole configurations do not exist, and their derivation is outside of the scope of this work. The procedure to estimate the material fracture toughness is the same as adopted in [18]. The material fracture toughness in terms of stress intensity factor including constraint correction, Kcmat is estimated through correlation with the Charpy impact energy, using the following Master Curve:                         mat k f K T T T B P 0.25 0.5 0 25 1 20 11 77exp 0.019 ln 1 (5) where T is the temperature at which Kmat is to be determined, T0 = T27J − 18 is the temperature for a median toughness of 100 MPa m0.5 in 25 mm thick specimens, Tk = 25˚C describes the scatter in the Charpy vs, fracture toughness correlation, B [mm] is the thickness for which an estimation of the toughness is required, and Pf is the probability level for Kmat [MPa m0.5]. To correct Kmat for low constraint level, i.e. for Tstress < 0, a correction formula is provided in [17], which is based on the Master Curve method:                 c stress mat mat T K K MPa 20 20 exp 0.019 10 (6) where Tstress is the second-order expansion of the Williams series describing the stress field in the vicinity of the crack tip, calculated using the formula reported in [17]. In both equations, 20 MPa m0.5 corresponds to the minimum value of the fracture toughness. RESULTS total of 51 tests are conducted, the results are reported in Tab. 4 for each specimen type and material. In this table, Nu,exp is reported for each specimen, whereas Nu is calculated considering the measured dimensions of the specimens. The reported value is the average for all the specimens of the same type and the coefficient of variation, i.e. the ratio between the standard deviation of the sample and the average value, is smaller than 1%. It should be noted that the computation of the net area depends on the hole layout and it is not trivial for specimen type D, further reference is given to relevant standards [1] and early works [19]. Generally, three types of cracks have been induced, namely corner cracks, semi elliptical surface breaking cracks, and through the thickness cracks. Through the thickness cracks often result from two corner cracks coalesced together. Semi elliptical surface breaking cracks have been found in conjunction with corner cracks and considered as through the thickness cracks for the purpose of conducting the assessment according to the FAD, in accordance with the crack interaction rules in [16]. The cracks generated are generally smaller than 2 mm, with the majority being in the range 0.5-1.0mm. In the majority of cases, a single corner crack is found at the edge of the hole however, in some cases, two corner cracks nucleate at the same side of the hole and coalesced forming a through the thickness crack. The size of the crack generated by this pre- cracking procedure turned to be highly sensitive to the positioning of the copper wire used for the broken wire sensor method. In the case of corner cracks, the average pre-crack induced is characterized by an average characteristic length of 0.85 mm, with a standard deviation equal to 0.23 mm. Corner cracks are of semicircular shape. For through the thickness cracks, the average pre-crack induced is characterized by an average characteristic length of 1.64 mm, with a standard deviation equal to 0.39 mm. The type of test is recognizable from the specimen ID, as indicated in the previous section. Fig. 4a shows a typical load- elongation plot resulting from the tests for both steel grades and for both non pre-cracked and pre-cracked specimens. From this, it can be seen that the presence of cracks marginally affects the failure load and the deformation capacity of the specimen, however the number of test data for each specific testing condition is not deemed sufficient to draw statistically relevant conclusions. Fig. 4b shows the unity check resulting from the ratio between the failure load obtained experimentally and the ultimate load predicted by the design rule, i.e. Nu,exp/Nu. The figure highlights the scatter of this ratio for each specimen type and material. All the performed tests are above unity, meaning that the design rule predicts A D. Leonetti, Fracture and Structural Integrity, 73 (2025) 256-266; DOI: 10.3221/IGF-ESIS.73.17 263 an ultimate load which is on the safe side even in the presence of cracks and at relatively low temperatures. It should be noted that for the considered specimen configurations and loading conditions, there is no significant effect of neither the steel grade, nor of the pre-crack on the ultimate resistance. Moreover, despite the limited number of tests conducted on cooled specimens, there is also no evidence of reduction of ultimate resistance due to lower temperature. Fig. 5a shows an example of fracture surface, namely specimen S700MC-A1-C-T. It can be observed that despite the presence of the crack, the failure mechanism of the cross-section is mainly ductile. In the vicinity of the crack, lateral contraction is inhibited due to local stress triaxiality induced by the notch and the crack. This can be observed by looking at the lateral contraction at the two sides of the hole, where the thickness at the side without the crack is significantly reduced. However, lateral contraction is largely present in the failure region demonstrating a ductile failure mode. Fig. 5b shows the type and the size of the crack induced by the pre-cracking procedure. Type A Type B Type C Type D Specimen ID Nu,exp Specimen ID Nu,exp Specimen ID Nu,exp Specimen ID Nu,exp [kN] [kN] [kN] [kN] S700MC S700MC-A1-C-T* 238 S700MC-B1-C-T* 231 S700MC-C1 195 S700MC-D1-C-T* 188 S700MC-A2-C-T* 236 S700MC-B2-C 237 S700MC-C2 198 S700MC-D2-C-T* 176 S700MC-A3-C 235 S700MC-B3-C-T* 235 S700MC-C3 199 S700MC-D3-C 220 S700MC-A4-C 237 S700MC-B4 244 S700MC-C4 192 S700MC-D4-C 220 S700MC-A5-C 241 S700MC-B5 242 S700MC-C5-C 191 S700MC-D5 218 S700MC-A6 244 S700MC-B6 242 S700MC-C6-C 201 S700MC-D6 222 S700MC-C7-C 200 S700MC-D7 222 S700MC-C8-C 198 Nu [kN] 172 Nu [kN] 175 Nu [kN] 169 Nu [kN] 170 S275JR S275JR-A1 327 S275JR-B1 312 S275JR-C1 275 S275JR-D1 293 S275JR-A2 325 S275JR-B2 313 S275JR-C2 276 S275JR-D2 291 S275JR-A3 326 S275JR-B3 313 S275JR-C3 273 S275JR-D3 293 S275JR-A4-C 322 S275JR-B4-C 309 S275JR-C4-C 272 S275JR-D4-C 277 S275JR-A5-C 319 S275JR-B5-C 307 S275JR-C5-C 274 S275JR-D5-C 293 S275JR-C6-C 273 S275JR-D6-C 290 S275JR-C7-C 274 S275JR-D7-C 230 Nu [kN] 285 Nu [kN] 285 Nu [kN] 231 Nu [kN] 269 *S700MC-A1-C-T fractured at 0˚C; S700MC-A2-C-T fractured at 10˚C S700MC-B1-C-T fractured at 10˚C; S700MC-B3-C-T fractured at -10˚C S700MC-D1-C-T fractured at 0˚C; S700MC-D2-C-T fractured at 10˚C Table 4: Summary of experimental results grouped by specimen geometry. (a) Example of Load-Elongation curve (b) Summary of Results Figure 4: Overview of experimental results grouped by steel grade and specimen geometry. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0 5 10 15 N or m al iz ed F or ce [- ] Elongation [mm] S275JR-C1 S275JR-C5-C S700MC-C1 S700MC-C5-C N u ,e xp / N u 0.6 0.8 1 1.2 1.4 1.6 1.8 2 S700MC-A S700MC-B S700MC-C S700MC-D S275JR-A S275JR-B S275JR-C S275JR-D D. Leonetti, Fracture and Structural Integrity, 73 (2025) 256-266; DOI: 10.3221/IGF-ESIS.73.17 264 (a) Fracture surface of specimen S700MC-A1-C-T (b) Corner crack in specimen S700MC-A1-C-T Figure 5: Assessment using the Failure Assessment Diagram. FAILURE ASSESSMENT DIAGRAM nly the specimens made of steel grade S700 have been assessed also using the FAD. The results are depicted in Fig. 6. In particular, the failure assessment point is reported for each pre-cracked specimen of type A. All the assessment points fall in the plastic collapse region, hence brittle failure is not deemed to occur despite the high steel grade, which is in line with the experiments. All the assessment points fall in the unacceptable region outside of the line, implying that the ultimate load that is predicted by the Failure Assessment Diagram is generally conservative. The predicted failure load by the FAD is 0.86 times smaller than the experimental failure load. This ratio is characterized by a coefficient of variation of 0.02. Considering the typical scatter in the FAD [14], this is significantly small. It appears that the FAD can be used to predict the failure load of notched specimens containing relatively small cracks, also for relatively high steel grades with reasonable accuracy, provided that solutions for Stress Intensity Factor and reference stress are provided. The use of the FAD is bounded by the availability of reference stress and stress intensity factor solutions for the considered crack configuration and load applied. Numerical methods, such as finite element analyses can be used to obtain these solutions and extend the use of the FAD to other relevant geometries. Figure 6: Assessment using the Failure Assessment Diagram. 0 0.2 0.4 0.6 0.8 1 1.2 0 0.2 0.4 0.6 0.8 1 1.2 K r [- ] Lr [-] FAD - Option 2 S700MC-A1 to A5 O D. Leonetti, Fracture and Structural Integrity, 73 (2025) 256-266; DOI: 10.3221/IGF-ESIS.73.17 265 CONCLUSIONS n this work, several experiments were conducted to assess the applicability of the net cross-section design rule of EN1993-1-1 for the design of notched elements in tension. Particularly, in this study a relatively high steel grade was used, as compared to previous work. This study is conducted on specimens with and without relatively small fatigue cracks, i.e. generally shorter than 1mm. These cracks have been induced by a pre-cracking procedure involving cyclic loading. The termination of the pre-cracking procedure is controlled by the broken wire method, which is able to detect such small cracks. The experiments indicate that the failure load is not practically affected by the presence of relatively small cracks. This result is valid for both considered steel grades, namely S275JR and S700MC. Moreover, the failure load appears to be also marginally affected by low temperatures. The Failure Assessment Diagram has been adopted to predict the failure load of pre-cracked specimens for S700MC steel grade. The prediction is in line with the experimental data, and suggests that the failure is mainly ductile, as confirmed by an examination of fracture surfaces and the load-displacement behavior recorded during the tests. Considering the experiments carried out in this and previous work, it appears that for the considered geometry and loading conditions, the considered design rule leads to predictions which are on the safe side. Hence, future tests should be conducted in loading and temperature conditions promoting a brittle behavior, in order to verify the prediction of the design rule in these circumstances. Given its reliable predictions, the FAD can be of help in identifying such conditions. REFERENCES [1] EN 1993-1-1 (2005) Eurocode 3: Design of steel structures – Part 1-1: General rules and rules for buildings, CEN, Brussels. [2] Može, P., Beg, D., Lopatič, J. (2007). Net cross-section design resistance and local ductility of elements made of high strength steel, J. Constr. Steel Res., 63(11), pp. 1431–1441. DOI: 10.1016/j.jcsr.2007.01.009. 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