doi:10.1016/j.ijfatigue.2019.105227

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Contents lists available atScienceDirectInternational Journal of Fatiguejournal homepage:www.elsevier.com/locate/ijfatigueMixed-mode I and II fatigue crack growth retardation due to overload: Anexperimental studyKristen Rege⁎, Jørgen Grønsund, Dimitrios G. PavlouDepartment of Mechanical and Structural Engineering and Materials Science, University of Stavanger, P.O. Box 8600 Forus, NO-4036 Stavanger, NorwayARTICLE INFOKeywords:Fatigue crack growthMixed modeOverloadsRetardationStainless steelABSTRACTEnvironmental loads acting on structures usually cause fatigue crack propagation under variable amplitudemixed-mode conditions. In order to better estimate the remaining fatigue life, the fatigue crack growth beha-viour under these conditions needs to be studied. In this paper, an experimental study where mixed-mode I and IIoverloads are applied to a fatigue crack propagating under mixed-mode I and II constant amplitude loading, ispresented. The overloads are found to cause fatigue crack growth retardation, lasting over a length which ismore than two times longer than the overload crack tip plastic zone extent estimated using a linear elasticsolution.1. IntroductionDue to thefluctuating behaviour of environmental loads, offshorestructures are subjected to variable amplitude fatigue. The fatigueloading may lead to the initiation and propagation of cracks, especiallyat critical spots, such as welded tubular joints in jacket structures. Asenvironmental loads are also multi-directional in nature, the fatiguecracks may propagate under mixed-mode conditions[1–5]. Accuratemodelling of the fatigue crack propagation life is important whenevaluating detected fatigue cracks, and when planning inspection in-tervals[5–8] for these structures. However, there is a lack of modelsand experimental studies for mixed-mode variable amplitude fatiguecrack propagation.The qualitative behaviour of variable amplitude fatigue crack pro-pagation under pure mode I conditions, i.e. tensile opening, is wellknown from experimental studies. A single tensile overload in anotherwise constant amplitude load history causes a retardation in theproceeding crack propagation, while a single underload causes an ac-celeration[9]. As any loading history in principle can be represented asa sequence of overloads and underloads[10], these simple load casesform the basis for developing models for variable amplitude fatigue.Most of these models may be divided into two groups; those whichassume that residual stresses in the plastic zone in front of the crack tipare responsible for the load interaction effects[11–17], and thosewhich assume plasticity-induced closure due to plastic stresses in thewake of the crack tip to be responsible[18–22]. The latter type ofmodel typically requires time-consuming elastic-plasticfinite elementcomputations to be carried out, while the former employs analytical orsemi-analytical expressions for the crack tip plastic zone size to predictthe retardation and acceleration. A number of models emphasizingother mechanisms, e.g. the strain hardening effect on the crack growthretardation[23], do also exist. An overview of the different mechanismswhich have been proposed to contribute to fatigue crack growth re-tardation may be found in[10].Some experimental studies have considered the application of amixed-mode I and II (combination of tensile opening and in-planeshear) overload to an otherwise purely mode I constant amplitude loadhistory. Richard[24]demonstrated that a pure mode II overload re-sulted in very little retardation of the proceeding mode I fatigue crackpropagation in an aluminium alloy, compared to the application of amode I overload. This was further demonstrated by Sander and Richard[25], who applied mixed-mode I and II overloads. They showed that byincreasing the ratio of the mode I to the mode II overload stress in-tensity factor, the retardation effect on the proceeding mode I fatiguecrack propagation was increased. In order to compare the appliedoverload under different mode mixity ratios, they kept Richard'sequivalent stress intensity factor[26]equal for all the overloads.Sander and Richard'sfinding was confirmed by similar experimentscarried out by Mohanty, Verma and Ray[27]. Meanwhile, Decreuseet al.[28] found that applying 10 or 50 cycles of overload in pure modeII actually accelerated the proceeding mode I fatigue crack propagationinS355NL steel.Mokhtarishirazabad et al.[29]applied an overload to a crack pro-pagating through a carbon steel cylinder subjected to non-proportionalhttps://doi.org/10.1016/j.ijfatigue.2019.105227Received 12 June 2019; Received in revised form 2 August 2019; Accepted 5 August 2019⁎Corresponding author.E-mail addresses:kristenrege@hotmail.com(K. Rege),jorgen.gronsund@uis.no(J. Grønsund),dimitrios.g.pavlou@uis.no(D.G. Pavlou).International Journal of Fatigue 129 (2019) 105227Available online 06 August 20190142-1123/ © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/BY/4.0/).T

Kristen Rege

constant amplitude tensile and torsional cyclic loading, and observedretardation. Gates and Fatemi[30]subjected aluminium cylinders tonon-proportional variable amplitude tensile and torsional cyclicloading, and found the fatigue crack propagation lives to be longer thanthose predicted using mode I models. However, due to the complexityof non-proportional multiaxial fatigue, it is challenging to use theseresults in the early development of a predictive model.Some models for variable amplitude fatigue crack propagationunder mixed-mode conditions have been proposed. Sander and Richard[25]simulated the influence of mixed-mode overloads on mode I crackpropagation quite well by considering plasticity-induced closure. Aframework for non-proportional mixed-mode plasticity at the crack tiphas been presented by Fremy et al.[31], but further development isneeded in order to apply it to variable amplitude mixed-mode fatiguecrack propagation. Boljanovićand Maksimović[32,33], and Dirik andYalçinkaya[34] have directly applied the Wheeler[11] and Willenborg[12]models to mixed-mode conditions, implicitly assuming that theplastic zone is circular, with its centre at the crack tip. It is evident thatthe crack tip plastic zone is not circular for general mode I, mode II, ormixed-mode I and II loading[35–38], and the crack growth retardationeffects are therefore still worth studying. Other models have also beenproposed[39,40], but further comparison with experimental results isclearly necessary.Experimental results for proportional mixed-mode fatigue crackpropagation after a mixed-mode overload are found in the work by Leeand Choi[41]. However, they did only consider a single overload ratio.In the present paper, the effect of a single mixed-mode I and II overloadon proceeding mixed-mode I and II constant amplitude fatigue crackpropagation is studied for two different overload ratios. Fatigue crackpropagation tests are carried out using tubular specimens made ofaustenitic stainless steel, subjected to proportional (in-phase) tensileand torsional cyclic loading. Thefinite element method (FEM) is used toobtain the stress intensity factor of the propagating crack, in order torelate it to the crack propagation rate. The observed retardation fol-lowing the overload is compared to estimates of the crack tip plasticzone size, which forms the basis of most of the existing models forpredicting the retardation.2. Material and methods2.1. Specimen and materialIn this study, tubular specimens are subjected to proportional tensileand torsional cyclic loading. Tubular specimens are often used to studyfatigue crack propagation under biaxial loading[24,42,43]. Their mainadvantages are the possibility of continuously adjustable mode mixity,and the possibility to apply non-proportional biaxial loading.The geometry of the specimen is shown inFig. 1. It consists of awelded austenitic stainless steel tube according to ASTM A269/A270,and two custom-made steel plugs which facilitate the installation of thespecimen into the fatigue testing machine. Twelve equal specimenswere made from a single tube. The average diameter over the cross-section of the tube was measured at three points along the length of thetube, using a coordinate measuring machine. The outer diameter wasmeasured to be 63.609 ± 0.005 mm, while the inner diameter wasmeasured to be 60.055 ± 0.006 mm, where the deviations refer to themaximum difference between the three cross-sections. This means thatthe mean radiusRm≈30.9 mm, while the wall thicknesst≈1.78 mm.The diameter was chosen to be this large, in order to allow observationof macroscopic crack propagation, while the thickness was kept low, inorder to minimize the through-thickness variation of shear stress.The tubing material is 316L austenitic stainless steel, satisfying bothEN 10088 grade 1.4404 and ASTM A269/A270 grade TP316L. Thissteel grade is commonly used in topside process facilities on offshoreplatforms, and as a structural material in power plants[44]. The che-mical composition and mechanical properties obtained from the 3.1.Bmaterial certificate for the tube are given inTables 1 and 2.A notch was prepared in each specimen to facilitate crack initiation,as shown inFig. 1. The notch was made directly opposite of the long-itudinal welding seam, in order to avoid crack propagation through theheat-affected zone, using die-sinking electrical discharge machining.The plugs shown inFig. 1were made for installing the larger tubeinto the 1 in. grip of the fatigue testing machine. They were machinedfrom a round bar of 520 M carbon steel (a variant of S355J2), andwelded to the stainless steel tube.2.2. Experimental setupThe 12 specimens were loaded using a servohydraulic MTS 809axial/torsional test system, model 319.25. All specimens were pre-cracked in cyclic tension withPmax,PC= 28 kN and load ratioR= 0.1,except specimen I-A, whosePmax,PCwas increased stepwise from 20 to25 to 30 kN. The pre-cracking load was applied as a tapered sinusoidalwave with a frequency of 10 Hz. The pre-cracking was stopped whencracks of approximately 2 mm length were observed at each side of thenotch shown inFig. 1. This corresponds to an initial crack length2a0≈17 mm. The exact pre-crack length for each specimen is given inTable 3.In this study, four different load cases were studied; the applicationof cyclic tension only, the application of cyclic tension and torsion, theapplication of cyclic tension and torsion following a 25% ten-sion + torsion overload, and the application of cyclic tension and tor-sion following a 50% tension + torsion overload. The overload wasapplied immediately after the pre-cracking. Three specimens weretested for each load case. The detailed loading of each specimen isdocumented inTable 3. All torsion loads were applied in the negativeFig. 1.Specimen geometry. All dimensions are given in mm.Table 1Chemical composition (wt%) of the steel tube. The balance is Fe.CSiMnPSCrNiMo0.0230.400.880.0270.00617.3911.122.04K. Rege, et al.International Journal of Fatigue 129 (2019) 1052272