Stress Concentration Factor on a Corrosion Pit

SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 23 | NUMBER: 2 | 2023 | DECEMBER © 2023 VSB - TECHNICAL UNIVERSITY OF OSTRAVA FACULTY OF CIVIL ENGINEERING 27 STRESS CONCENTRATION FACTOR ON A CORROSION PIT Lucie MALÍKOVÁ1,2, Anna BENEŠOVÁ2, Mohammad S. AL KHAZALI2, Vít KŘIVÝ3, Stanislav SEITL1,2 1Institute of Physics of Materials, Czech Academy of Sciences, v. v. i.. Žižkova 513/22, Brno, Czech Republic 2Faculty of Civil Engineering, Brno University of Technology, Veveří 331/95, Brno, Czech Republic 3Faculty of Civil Engineering, VŠB - TU Ostrava, Ludvíka Podéště 1875, 708 33 Ostrava, Czech Republic [email protected], [email protected], [email protected], [email protected], [email protected] DOI: 10.35181/tces-2023-0011 Abstract. Phenomenon of corrosion in structural materials is very important, because they very often yield to aggressive environment. Moreover, not inconsiderable effect of fatigue damage via cyclic loading of such engineering structures should be considered as well. Thus, the influence of a corrosion pit (of a circular segment shape) on the stress distribution in a rectangular specimen subjected to remote tensile stress range has been investigated via finite element method. Particularly the stress concentration factor has been calculated for various sizes of the corrosion pit and the results obtained have been discussed. Keywords Corrosion pit, finite element simulations, stress concentration, high-strength steel (HSS). 1. Introduction Steel constructions are very often besides the cyclic loading (fatigue) subjected to aggressive environment during their service life. Thus, when assessing their lifetime, this effect needs to be considered. Corrosion can cause both weakening the specimen/construction crosssection and formation of stress concentrators. These processes are undesirable and have significant effect on the lifetime period. Various protective arrangements are being searched (such as surface coatings and treatments that are more resistant to impact of moist environment). Nevertheless, the corrosion phenomenon is often unavoidable and therefore, it is necessary to investigate its influence on reliability assessment of structures subjected to corrosive environment, see e.g. [1] or [2]. There exist different kinds of corrosion. Some review works dealing with the probably most widespread pitting corrosion can be mentioned, such as [3], [4] or [5]. Moreover, a few papers are devoted directly to combination of corrosion and fatigue damage, see e.g. [6], [7], [8] or [9]. Also in this paper, combination of corrosion and fatigue mechanisms are studied. Particularly, stress concentration on a corrosion pit of various length and depth in a rectangular specimen under tensile cyclic loading is investigated and results obtained from numerical simulations are discussed. 2. Corroded specimen Corrosion pits are created based on the particular conditions of each structure, i.e. their size and shape depend on corrosive environment (its aggressivity, period of its impact etc.), see Fig. 1. Thus, effect of the pit length and depth on the stress distribution was investigated. The dimensions of the specimen for numerical simulations were suggested according to real specimens prepared for fatigue tests under various corrosion levels, see. Fig. 2a. Although the real specimen is cylindrical, the finite element model was created as a two-dimensional rectangular cut of the middle part of the corroded specimen as indicated in Fig. 1. Plane strain conditions were considered to avoid the ring-shaped pit if axisymmetric condition would be applied. The corrosion pit shape is a circular segment considering the relation between its depth and length as LC = 4×D, see Fig. 2. Fig. 1: Example of steel specimens for fatigue experiment without and with various level of corrosion. SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 23 | NUMBER: 2 | 2023 | DECEMBER © 2023 VSB - TECHNICAL UNIVERSITY OF OSTRAVA FACULTY OF CIVIL ENGINEERING 28 (a) (b) Fig. 2: Scheme of the real cylindrical specimen (a) and the analysed rectangular specimen with a corrosion pit subjected to remote tensile cyclic loading. The values of the individual geometrical parameters were set as:  specimen length, L = 24 mm;  specimen width, W = 4 mm;  corrosion pit depth, D = 0.1 to 1 mm;  corrosion pit length, LC = 0.4 to 4 mm;  corrosion pit radius, RC = (LC2+4D2)/8D. Cyclic loading value and properties of the linear elastic material model representing the properties of very popular high-strength steels (HSS) were assumed to be: tensile stress range,   appl = 100 MPa; Young’s modulus, E = 210 GPa; Poisson’s ratio,  = 0.3. Numerical model was created as two-dimensional adopting the plane strain conditions. Due to the symmetry, only the upper half of the specimen was modelled. Elements used in ANSYS computational software for creation of the specimen were quadratic ones, denoted as PLANE183. The size of the smallest element used at the corrosion pit surface as well as in its closest vicinity was 0.001 mm in all configurations under the study. Thus, it was possible to obtain comparable values of the maximum stress at the bottom point of the corrosion pit. The stress distribution at the corrosion pit surface was investigated to find the location of the maximum stress concentration. Further, the stress concentration at the corrosion pit was expressed via the stress concentration factor Kt defined as, see [10]: 𝐾  , (1) where  max represents the maximum stress value (occurring at the corrosion pit bottom) and  avg represents the average stress value (along the ligament of the crosssection ahead of the corrosion pit, as it is indicated by the red “path” in Fig. 2b). Particularly, the von Mises stress values were assessed. 3. Results In the following section, results and their discussion can be found. Particularly, the von Mises stress distribution along the (half of the) corrosion pit obtained from ANSYS computational software can be seen in Fig. 3 and it is obvious that the maximum occurs at the bottom of the corrosion pit (symmetry axis) and the rest of the values decrease towards the edge of the corrosion pit. Additionally, the distribution of selected stress components was investigated ahead of the corrosion pit through the specimen width. The dependences of the  xx,  yy and  vM (von Mises) stresses for various corrosion pit depths (D between 0.1 and 1.0 mm) can be found in Fig. 4. The results are plotted as a function of the relative distance from the corrosion pit x related to the ligament W-D. Fig. 3: Von Mises stress (in MPa) distribution along the upper half of the corrosion pit for the specimen with the corrosion pit 0.5 mm deep and 2 mm long. The last set of results is presented via Tab. 1, where the values of the maximum and average von Mises stress is presented together with the corresponding stress concentration factor and its percentual difference for increasing corrosion pit size. Tab.1: Values of the maximum and average von Mises stress together with the corresponding stress concentration factor and its percentual difference for increasing corrosion pit depth (D = 0.1 to 1.0 mm). D [mm]  max [MPa]  avg [MPa]  t [-]   t-Kt,D=0.1mm)/Kt,D=0.1mm [%] 0.1 202.47 88.84 2.28 - 0.2 204.71 89.18 2.30 0.72 0.3 210.72 89.97 2.34 2.76 0.4 217.67 91.11 2.39 4.83 0.5 228.46 92.74 2.46 7.89 0.6 238.11 94.47 2.52 10.59 0.7 251.55 96.68 2.60 14.17 0.8 266.68 99.16 2.69 18.00 0.9 284.70 102.02 2.79 22.44 1.0 304.92 105.14 2.90 27.25 SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 23 | NUMBER: 2 | 2023 | DECEMBER © 2023 VSB - TECHNICAL UNIVERSITY OF OSTRAVA FACULTY OF CIVIL ENGINEERING 29 (a) (b) (c) Fig. 4: Selected results of the stress distribution along the path overlapping the specimen width ahead of the corrosion pit for various corrosion pit depths (D between 0.1 and 1.0 mm): (a)  xx; (b)  yy; (c)  vM. From the results obtained, the following points can be highlighted:  The stress distribution of  yy component (Fig. 4b) shows the typical singular behaviour when the specimen is loaded via 100 MPa of tension. The stress growth at the corrosion pit is rather gentle when the pit is deeper.  The deeper the corrosion pit, the higher the investigated stress values ahead of the pit.  The previous statement is valid both for maximum and average values of the selected stress components.  Moreover, also the ratio between the maximum and average value (referred to as stress concentration factor, Kt) calculated for von Mises stresses increases with increasing corrosion pit depth.  An increase of about 27 % has been observed when the corrosion pit is ten times larger (D = 1.0 mm vs. D = 0.1 mm)  It means that the level of the corrosion (directly influencing the corrosion pits size) affects the stress distribution/concentration in the specimen and/or structure and consequently can also influence its lifetime.  Comparison with experimental results on corroded specimens is intended to compare the results qualitatively and quantitatively. 4. Conclusion Influence of the presence of a circular-segment-shaped corrosion pit in a rectangular specimen subjected to remote cyclic tensile loading on the stress distribution has been investigated via finite element method for various corrosion pit geometries. Various stress components dependences on the distance from the corrosion pit have been analysed and stress concentration factors for von Mises stress calculated. The results show that depending on the level of the corrosion (corresponding to the corrosion pit size), the stress concentration increases. Particularly, when the corrosion pit is ten times larger (D = 1.0 mm in comparison to D = 0.1 mm), the stress concentration is higher about ca. 27 %. Experimental campaign on corroded specimens is running to be able to compare the results obtained. Then, the numerical simulations will probably enable to predict the lifetime of corroded specimens quickly and reliably. SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 23 | NUMBER: 2 | 2023 | DECEMBER © 2023 VSB - TECHNICAL UNIVERSITY OF OSTRAVA FACULTY OF CIVIL ENGINEERING 30 Acknowledgements Financial support from the Czech Science Foundation (project No. 21-14886S: Influence of material properties of high strength steels on durability of engineering structures and bridges) and Faculty of Civil Engineering, Brno University of Technology (project No. FAST-S-238216: Analysis of fatigue behavior of high-strength steels subjected to various levels of corrosion) is gratefully acknowledged. References [1] KUNZ, L., P. LUKÁŠ and J. KLUSÁK. Fatigue strength of weathering steel. Materials Science (Medziagotyra). 2015, vol. 18, iss. 1, pp. 18–22. DOI: 10.5755/j01.ms.18.1.1335. [2] RAJASANKAR, J. and N. R. A. IYER. A probability-based model for growth of corrosion pits in aluminium alloys. Engineering Fracture Mechanics. 2006, vol. 73, iss. 5, pp. 553–570. DOI: 10.1016/j.engfracmech.2005.10.001. [3] GUO, Y., H. CHEN and G. YAO. Bayesian prediction of the stress concentration effect on high-strength wires with corrosion pits. Engineering Failure Analysis. 2022, vol. 131, paper 105827. DOI: 10.1016/j.engfailanal.2021.105827. [4] SHOJAI, S., P. SCHAUMANN, M. BRAUN and S. EHLERS. Influence of pitting corrosion on the fatigue strength of offshore steel structures based on 3D surface scans. International Journal of Fatigue. 2022, vol. 164, paper 107128. DOI: 10.1016/j.ijfatigue.2022.107128. [5] SINGH, A.K., G. M. REDDY and K. S. RAO. Pitting corrosion resistance and bond strength of stainless steel overlay by friction surfacing on high strength low alloy steel. Defence Technology. 2015, vol. 11, iss. 3, pp. 299–307. DOI: 10.1016/j.dt.2015.06.002. [6] BRENNAN, F. P. A framework for variable amplitude corrosion fatigue materials tests for offshore wind steel support structures. Fatigue and Fracture of Engineering Materials and Structures. 2014, vol. 37, iss. 7, pp. 717–721. DOI: 10.1111/ffe.12184. [7] DUQUESNAY, D. L., P. R. UNDERHILL and H. J. BRITT. Fatigue crack growth from corrosion damage in 7075-T6511 aluminium alloy under aircraft loading. International Journal of Fatigue. 2003, vol. 25, iss. 5, pp. 371–377. DOI: 10.1016/S01421123(02)00168-8. [8] JIANG, C., C. WU and X. JIANG. Experimental study on fatigue performance of corroded highstrength steel wires used in bridges. Construction and Building Materials. 2018, vol. 187, pp. 681–690. DOI: 10.1016/j.conbuildmat.2018.07.249. [9] WANG, S., D. ZHANG, K. CHEN, L. XU and S. GE. Corrosion fatigue behaviors of steel wires used in coalmine. Materials and Design. 2014, vol. 53, pp. 56–64. DOI: 10.1016/j.matdes.2013.06.059. [10] PILKEY, W. D. and D. F. PILKEY, Peterson’s Stress Concentration Factors. New York: John Wiley & Sons, 2008. ISBN 978-0-470-04824-5. About Authors Lucie MALÍKOVÁ was born in Olomouc, Czech Republic. She received her PhD in 2009 in Engineering Mechanics at the Institute of Solid Mechanics, Mechatronics and Biomechanics, Faculty of Mechanical Engineering, Brno University of Technology via defence of her doctoral thesis entitled: Stability assessment of general stress concentrators in layered materials. She is an expert on numerical modelling and various fracture mechanics issues. Anna BENEŠOVÁ was born in Brno, Czech Republic. She is a master student at the Faculty of Civil Engineering, Brno University of Technology under the supervisor assoc. prof. Stanislav Seitl and a member of the FRACTIGUE group at Institute of Physics of Materials, Czech Academy of Sciences with her research interest in civil engineering materials and numerical support for evaluation of their fracture properties. Mohammad AL KHAZALI was born in Al Ramtha, Jordan. He is a Ph.D. student at the Faculty of Civil Engineering, Brno University of Technology under the supervisor assoc. prof. Stanislav Seitl. He has been dealing with evaluation of fatigue and fracture parameters, partially numerical simulations via FEM as a support for experiments. Vít KŘIVÝ was born in Frýdek-Místek, Czech Republic. He is an associate professor at Faculty of Civil Engineering VŠB TU Ostrava. He is interested in corrosion processes on the surface of weathering steel influenced by deposition of chlorides; design of steel structures. Stanislav SEITL was born in Přerov, Czech Republic. He is an associate professor at Faculty of Civil Engineering, Brno University of Technology and a leader of FRACTIGUE group at Institute of Physics of Materials, Czech Academy of Sciences. His research interests consist in fatigue of civil engineering materials and lifetime estimation, two-parameter fracture mechanics, numerical modelling and calculations of fracture mechanics parameters.