Microsoft Word - numero_42_art_22.docx M. Peron et alii, Frattura ed Integrità Strutturale, 42 (2017) 205-213; DOI: 10.3221/IGF-ESIS.42.22 205 Local strain energy density for the fatigue assessment of hot dip galvanized welded joints: some recent outcomes M. Peron, S.M.J. Razavi ,F. Berto, J. Torgersen, F. Mutignani Department of Mechanical and Industrial Engineering, Norwegian University of Science and Technology (NTNU), Richard Birkelands vei 2b, 7491, Trondheim, Norway. mirco.peron@ntnu.no, javad.razavi@ntnu.no, filippo.berto@ntnu.no, jan.torgersen@ntnu.no ABSTRACT. Since in literature only data about the effect of the hot-dip galvanizing coating on fatigue behavior of unnotched specimens are available, whereas very few for notched components and none for welded joints, the aim of this paper is to partially fill this lack of knowledge comparing fatigue strength of uncoated and hot-dip galvanized fillet welded cruciform joints made of structural steel S355 welded joints, subjected to a load cycle R = 0. 34. The results are shown in terms of stress range Δσ and of the averaged strain energy density range W in a control volume of radius R0 = 0.28 mm KEYWORDS. Hot-dip galvanized steel; High cycle fatigue; Fillet welded cruciform joint; SED. Citation: Peron, M., Razavi, S.M.J., Berto, F., Torgersen, J., Mutignani, F., Local strain energy density for the fatigue assessment of hot dip galvanized welded joints: some recent outcomes, Frattura ed Integrità Strutturale, 42 (2017) 205-213. Received: 15.07.2017 Accepted: 31.07.2017 Published: 01.20.2017 Copyright: © 2017 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 orrosion is one of the main issue affecting metallic materials such as iron and steel, and several technique to prevent corrosion are available in literature, especially surface treatments. Among all, hot-dip galvanizing has been widely used, with great successes in a large amount of worldwide applications. Hot-dip galvanization involves the coating of the base material with a zinc layer and several works investigate the influence of different bath composition on mechanical properties [1, 2] and the effect of this protective film on static and fatigue behavior. Whilst tensile properties are not greatly affect, except for the yield stress, fatigue strength is reported to be reduced when the coating thickness exceed a threshold value [3], calculated employing the Kitagawa–Takahashi diagram. Moreover, Bergengren and Melander [4], found an increase in the detrimental effect on fatigue life increasing the zinc layer thickness, but, nevertheless, contrasting results were obtained by Browne et al., [5], and Nilsson et al., [6], that did not find any correlation in terms of loss of the fatigue strength due to the coating thickness. Furthermore, hot-dip galvanization is still an attractive topic, as proved by several recent studies, such as [7-10]. However, the works just mentioned refer to unnotched specimens and very few results are available for notched components. In fact, at the best of author’s knowledge the only data available in literature for notched components are due to Huhn and Valtinat [11], that examined S 235 JR G2 plates with holes and bearing-type connections with punched and drilled holes. Besides this lack of C M. Peron et alii, Frattura ed Integrità Strutturale, 42 (2017) 205-213; DOI: 10.3221/IGF-ESIS.42.22 206 experimental results on notched components, that represents a great gap since notches greatly affect the mechanical behavior [12–15] , the detrimental effect of the zinc layer on the fatigue strength cannot be quantified yet, neither in [11], since a direct comparison between uncoated and hot-dip galvanized notched specimens was not performed. Furthermore, though hot-dip galvanization is widely used to enhance the corrosion resistance of welded joints, none researchers have interested in assessing the effect of this surface treatment on their fatigue behavior. Thus, the aim of this work is to fill these lacks, by means of experimental fatigue tests on uncoated and hot-dip galvanized fillet welded cruciform joints made of structural steel S355. The results report the harmful effect of the presence of zinc layer on fatigue strength both in terms of stress range Δσ and of the averaged strain energy density range W in a control volume of radius R0 = 0.28 mm. Figure 1: Geometry of the fillet welded cruciform specimen and typical fracture surface. EXPERIMENTAL DETAILS he steel plates used to fabricate the samples were 10 mm in thickness, while the complete specimen had a global length of 250 mm. The complete geometry of the specimen can be seen in Fig. 1. Fatigue tests have been conducted on transverse non-load carrying fillet welded joints, made of S 355J2+N structural steel. Welding beads have been made by means of automatic MAG (Metal Active Gas) technique. One of the two series of welded joints has been later hot dip galvanized. Tests have been performed on a servo-hydraulic MTS 810 test system with a load cell capacity of 250 kN at 10 Hz frequency, in air, at room temperature. All samples have been tested using a sinusoidal signal in uniaxial tension (plane loading) and a load ratio R = 0, under remote force control. Regarding the galvanized series, the coating treatment has been carried out at a bath temperature of 452 oC and the immersion time was kept equal to 4 minutes for all the specimens. As a consequence, the coating thickness resulted in a range between 96 and 104 μm. RESULTS atigue tests results are here presented in terms of the stress range Δσ = σmax - σmin versus the number of cycles to failure, in a double logarithmic scale. The stress range is referred to the nominal area (400 mm2). Failure has always occurred at the weld toe, as expected, with a typical fracture surface as that shown in Fig. 1. The results from the tests were statistically elaborated by using a log-normal distribution. The ‘run-out’ samples, over two million cycles, were not included in the statistical analysis and are marked in the graphs with an arrow. Fig. 2 refers to uncoated and coated series, while Fig. 3 shows all the data elaborated together: in addition to the mean curve relative to a survival probability of Ps = 50%, (Wöhler curve) the scatter band defined by lines with 10% and 90% of probability of survival (Haibach scatter band) is also plotted. The mean stress amplitude values corresponding to two million cycles, the inverse slope k value of the Wöhler curve and the scatter index Tσ (the ratio between the stress amplitudes corresponding to 10% and 90% of survival probability) are provided in the figure. For the complete listing of the results of the fatigue tests, please refer to Tab. 1. T F M. Peron et alii, Frattura ed Integrità Strutturale, 42 (2017) 205-213; DOI: 10.3221/IGF-ESIS.42.22 207 It can be noted, comparing the uncoated and coated series (Fig. 2), that the scatter index reduces from 1.6 to 1.3. This value is reasonably low both for the uncoated series and the galvanized one. Moreover also in terms of fatigue strength the effect of the galvanization is found to be negligible with a reduction, at N = 2×106 and Ps = 90%, from 83 to 82 MPa. Furthermore, from the data summarised in Fig. 3, it is possible to see that the fatigue strength at N = 2×106 and Ps = 90% is 75 MPa: this value is comparable with the fatigue stress range (from 71 to 80 MPa) given for the corresponding detail category in Eurocode 3. Figure 2: Fatigue behaviour of bare (left) and galvanized (HDG, right) welded steel at R = 0. Figure 3: Fatigue behaviour of both uncoated and galvanized welded steel at R = 0. STRAIN ENERGY DENSITY APPROACH n averaged strain energy density (SED) criterion has been proposed and formalized first by Lazzarin and Zambardi ([16]), and later has been extensively studied and applied for static failures and fatigue life assessment of notched and welded components subjected to different loading conditions [17]. According to this volume- based criterion, the failure occurs when the mean value of the strain energy density over a control volume with a well-W A M. Peron et alii, Frattura ed Integrità Strutturale, 42 (2017) 205-213; DOI: 10.3221/IGF-ESIS.42.22 208 defined radius R0 is equal to a critical value WC, which does not depend on the notch sharpness. The critical value and the radius of the control volume (which becomes an area in bi-dimensional problems) are dependent on the material [17]. Figure 4: Polar coordinate system and critical volume (area) centered at the notch tip. UNCOATED SPECIMENS COATED SPECIMENS Δσ [MPa] N [cycles] W [N.mm/mm3] Δσ [MPa] N [cycles] W [N.mm/mm3] 260 168750 0.5692 140 494000 0.1650 320 81500 0.8622 120 1079000 0.1212 260 181484 0.5692 100 4800000 Run out 0.0842 220 445750 0.4075 260 85000 0.5692 180 572333 0.2728 140 436500 0.1650 140 5000000 Run out 0.1650 120 978200 0.1212 160 803000 0.2155 220 96820 0.4075 160 523983 0.2155 120 905500 0.1212 140 804960 0.1650 110 1125546 0.1019 140 556990 0.1650 100 3800000 Run out 0.0842 160 645140 0.2155 110 1500000 0.1019 320 45000 0.8622 110 4500000 Run out 0.1019 120 5000000 Run out 0.1212 110 4000000 Run out 0.1019 220 173000 0.4075 260 101200 0.5692 220 205616 0.4075 170 195000 0.2433 170 250000 0.2433 110 1940000 0.1019 320 42000 0.8622 220 115000 0.4075 Table 1: Fatigue results from uncoated and coated (HDG) welded specimens. The SED approach was formalized and applied first to sharp, zero radius, V-notches ([16]), considering bi-dimensional problems (plane stress or plane strain hypothesis). The volume over which the strain energy density is averaged is then a circular area Ω of radius R0 centred at the notch tip, symmetric with respect to the notch bisector (Fig. 4), and the stress M. Peron et alii, Frattura ed Integrità Strutturale, 42 (2017) 205-213; DOI: 10.3221/IGF-ESIS.42.22 209 distributions are those by Williams [18], written according to Lazzarin and Tovo formulation ([19]). Dealing with sharp V- notches the strain energy density averaged over the area Ω turns out to be: 1 2 2 2 1 1 2 2 1 1 0 0 e K e K W E R E R                (1) Where E is the Young’s modulus of the material, λ1 and λ2 are Williams’ eigenvalues [18], e1 and e2 are two parameters dependent on the notch opening angle 2α and on the hypothesis of plane strain or plane stress considered. Those parameters are listed in Tab. 1 as a function of the notch opening angle 2α, for a value of the Poisson’s ratio ν = 0.3 and plane strain hypothesis. K1 and K2 are the Notch Stress Intensity Factors (NSIFs) according to Gross and Mendelson [20]:         1 2 1 1 0 1 2 0 2 lim , 0 2 lim , 0 r r r K r r K r r                       (2) The SED approach was then extended to blunt U- and V-notches ([21,22]), by means of the expressions obtained by Filippi et al. [23] for the stress fields ahead of blunt notches, and to the case of multiaxial loading [24], by adding the contribution of mode III. Table 2: Values of the parameters in the SED expressions valid for a Poisson’s ratio ν = 0.3 (Beltrami hypothesis) It is widely demonstrated that the SED criterion is a reliable approach for the strength determination in a wide range of materials and notch geometries [25-28], in particular it has been successfully applied to the fatigue assessment of welded joints and steel V-notched specimens. Considering a planar model for the welded joints, the toe region was modelled as a sharp V-notch. A closed form relationship for the SED approach in the control volume can be employed accordingly to Eq. (1), written in terms of range of the parameters involved. In the case of an opening angle greater than 102.6o, as in transverse non-load carrying fillet welded joints (Fig. 4), only the mode I stress distribution is singular. Then the mode II contribution can be neglected, and the expression for the SED over a control area of radius R0, centred at the weld toe, can be easily expressed as follows: 1 2 1 1 1 0 e K W E R          (3) The material parameter R0 can be estimated by equating the expression for the critical value of the mean SED range of a butt ground welded joints, / 2C AW E   , with the one obtained for a welded joint with an opening angle 2α > 102.6o. The final expression for R0 is as follows [16]: 1 1 1 1 1 0 2 A A e K R          (4) 2α [rad] γ [rad] λ1 λ2 λ3 e1 Plane strain e2 Plane strain e3 Axis-sym. 0 π 0.5000 0.5000 0.5000 0.13449 0.34139 0.41380 π/6 11π/12 0.5014 0.5982 0.5455 0.14485 0.27297 0.37929 π/3 5π/6 0.5122 0.7309 0.6000 0.15038 0.21530 0.34484 π/2 3π/4 0.5445 0.9085 0.6667 0.14623 0.16793 0.31034 2π/3 2π/3 0.6157 1.1489 0.7500 0.12964 0.12922 0.27587 3π/4 5π/8 0.6736 1.3021 0.8000 0.11721 0.11250 0.25863 M. Peron et alii, Frattura ed Integrità Strutturale, 42 (2017) 205-213; DOI: 10.3221/IGF-ESIS.42.22 210 In Eq. (4) 1 AK is the NSIF-based fatigue strength of welded joints (211 MPa.mm0.326 at NA = 5×106 cycles with nominal load ratio R = 0) and ΔσA is the fatigue strength of the butt ground welded joint (155 MPa at NA = 5×106 cycles R = 0) [29]. Introducing these values into Eq. (4), R0 = 0.28 mm is obtained as the radius of the control volume at the weld toe for steel welded joints. For the weld root, modelled as a crack, a value of the radius R0 = 0.36 mm has been obtained by [29], re-writing the SED expression for 2α = 0. Therefore it is possible to use a critical radius equal to 0.28 mm both for toe and root failures, as an engineering approximation [29]. It is useful to underline that R0 depends on the failure hypothesis considered: only the total strain energy density is here presented (Beltrami hypothesis), but one could also use the deviatoric strain energy density (von Mises hypothesis) ([30]). The SED approach was applied to a large bulk of experimental data: a final synthesis based on 900 fatigue data is shown in Fig. 5 [17], including results from structural steel welded joints of complex geometries, for which fatigue failure occurs both from the weld toe or from the weld root. Also fatigue data obtained for very thin welded joints have been successfully summarized in terms of the SED ([31]). Recently, the SED approach has been extended to the fatigue assessment of notched specimens made of Ti-6Al-4V under multiaxial loading [32] and to high temperature fatigue data of different alloys [33]–[35]. A new method to rapidly evaluate the SED value from the singular peak stress determined by means of numerical model has been presented by Meneghetti et al. [36]. Some recent applications to creep are reported in [37]. RESULTS IN TERMS OF SED E analyses of the transverse non-load carrying fillet welded joint have been carried out applying as remote loads on the model the experimental values used for the fatigue tests. A control volume with a radius equal to 0.28 mm was realized in the model, in order to quantify the SED value in the control volume having the characteristic size for welded structural steel. The diagram of the SED range value W versus the number of cycles to failure N was plotted in a double logarithmic scale, summarizing the fatigue data for both bare and hot-dip galvanized specimens. With the aim to perform a direct comparison, the scatter band previously proposed for welded joints made of structural steel and based on more than 900 experimental data, Fig. 5, has been superimposed to the results of the present investigation (Fig. 6). For the detailed list of the SED values for both bare and HDG specimens corresponding to the stress ranges used in the fatigue tests, please refer to the last columns of Tab. 1. It can be noted that hot-dip galvanized specimens have a lower fatigue strength than the bare specimens, but both bare and HDG data fall within the scatter band previously proposed in the literature for welded structural steel. Figure 5: Fatigue strength of welded joints made of structural steel as a function of the averaged local strain energy density. F M. Peron et alii, Frattura ed Integrità Strutturale, 42 (2017) 205-213; DOI: 10.3221/IGF-ESIS.42.22 211 Figure 6: Fatigue behaviour of uncoated and galvanized welded steel at R = 0 as a function of the averaged local strain energy density. Scatter band of 900 experimental data of welded joints made of structural steel is superimposed. ACKNOWLEDGMENTS he authors wish to remember with great gratitude Professor Paolo Lazzarin, master of science and life, under whose leadership the research presented in this paper has been planned. Finally they want to express sincere thanks to Ing. Emiliano Guido of Zincherie Valbrenta for his active and valuable collaboration. REFERENCES [1] Di Cocco, V., Sn and Ti influences on intermetallic phases damage in hot dip galvanizing, Frattura ed Integrità Strutturale, 22 (2012) 31-38. 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NOMENCLATURE 2α notch opening angle γ supplementary angle of α: γ = π – α ν Poisson’s ratio Δσ stress range ΔσA fatigue strength in terms of stress range at NA cycles ΔK1,2,3 mode 1, 2 and 3 notch stress intensity factor range ΔK1A fatigue strength in terms of notch stress intensity factor range at NA cycles W averaged strain energy density (SED) CW critical value of the SED range λ1,2,3 mode 1, 2 and 3 Williams’ eigenvalues E Young’s modulus e1,2,3 mode 1, 2 and 3 functions in the SED expression f frequency K1,2,3 mode 1, 2 and 3 notch stress intensity factor (NSIF) k inverse slope of the Wöhler curve N number of cycles Ps survival probability R load cycle ratio R0 radius of the control volume for the calculation of the averaged SED value Tσ scatter index referred to the stress range TW scatter index referred to the SED range << /ASCII85EncodePages false /AllowTransparency false /AutoPositionEPSFiles true /AutoRotatePages /None /Binding /Left /CalGrayProfile (Dot Gain 20%) /CalRGBProfile (sRGB IEC61966-2.1) /CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2) /sRGBProfile (sRGB IEC61966-2.1) /CannotEmbedFontPolicy /Error /CompatibilityLevel 1.4 /CompressObjects /Tags /CompressPages true /ConvertImagesToIndexed true /PassThroughJPEGImages true /CreateJobTicket false /DefaultRenderingIntent /Default /DetectBlends true /DetectCurves 0.0000 /ColorConversionStrategy /CMYK /DoThumbnails false /EmbedAllFonts true /EmbedOpenType false /ParseICCProfilesInComments true /EmbedJobOptions true /DSCReportingLevel 0 /EmitDSCWarnings false /EndPage -1 /ImageMemory 1048576 /LockDistillerParams false /MaxSubsetPct 100 /Optimize true /OPM 1 /ParseDSCComments true /ParseDSCCommentsForDocInfo true /PreserveCopyPage true /PreserveDICMYKValues true /PreserveEPSInfo true /PreserveFlatness true /PreserveHalftoneInfo false /PreserveOPIComments true /PreserveOverprintSettings true /StartPage 1 /SubsetFonts true /TransferFunctionInfo /Apply /UCRandBGInfo /Preserve /UsePrologue false /ColorSettingsFile () /AlwaysEmbed [ true ] /NeverEmbed [ true ] /AntiAliasColorImages false /CropColorImages true /ColorImageMinResolution 300 /ColorImageMinResolutionPolicy /OK /DownsampleColorImages true /ColorImageDownsampleType /Bicubic /ColorImageResolution 300 /ColorImageDepth -1 /ColorImageMinDownsampleDepth 1 /ColorImageDownsampleThreshold 1.50000 /EncodeColorImages true /ColorImageFilter /DCTEncode /AutoFilterColorImages true /ColorImageAutoFilterStrategy /JPEG /ColorACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /ColorImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000ColorACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000ColorImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 300 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /GrayImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000GrayACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000GrayImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict << /K -1 >> /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile () /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False /CreateJDFFile false /Description << /ARA /BGR /CHS /CHT /CZE /DAN /DEU /ESP /ETI /FRA /GRE /HEB /HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. 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