Local strain energy density for the fatigue assessment of hot dip galvanized welded joints : some recent outcomes

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

Local strain energy density for the fatigue assessment of hot dip galvanized welded joints: some recent outcomes 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][8][9][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 experimental results on notched components, that represents a great gap since notches greatly affect the mechanical behavior [12][13][14][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 R 0 = 0.28 mm.

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 o C 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 mm 2 ).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 T σ (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
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 = 2×10 6 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 = 2×10 6 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.

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 volumebased criterion, the failure occurs when the mean value of the strain energy density over a control volume with a well-W A 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].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 R 0 centred at the notch tip, symmetric with respect to the notch bisector (Fig. 4), and the stress distributions are those by Williams [18], written according to Lazzarin and Tovo formulation ( [19]).Dealing with sharp Vnotches the strain energy density averaged over the area Ω turns out to be: Where E is the Young's modulus of the material, λ 1 and λ 2 are Williams' eigenvalues [18], e 1 and e 2 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]: 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.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][26][27][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 102.6 o , 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 R 0 , centred at the weld toe, can be easily expressed as follows: 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, / 2 , with the one obtained for a welded joint with an opening angle 2α > 102.6 o .The final expression for R 0 is as follows [16]: In Eq. ( 4) is the NSIF-based fatigue strength of welded joints (211 MPa.mm 0.326 at N A = 5×10 6 cycles with nominal load ratio R = 0) and Δσ A is the fatigue strength of the butt ground welded joint (155 MPa at N A = 5×10 6 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 R 0 = 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 1 :
Figure 1: Geometry of the fillet welded cruciform specimen and typical fracture surface.

Figure 3 :
Figure 3: Fatigue behaviour of both uncoated and galvanized welded steel at R = 0.

Figure 5 :
Figure 5: Fatigue strength of welded joints made of structural steel as a function of the averaged local strain energy density.

FFigure 6 :
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.

Table 1 :
Fatigue results from uncoated and coated (HDG) welded specimens.

Table 2 :
Values of the parameters in the SED expressions valid for a Poisson's ratio ν = 0.3 (Beltrami hypothesis) ΔσA fatigue strength in terms of stress range at NA cycles ΔK1,2,3 mode 1, 2 and 3 notch stress intensity factor range ΔK 1A fatigue strength in terms of notch stress intensity factor range at N A cycles W  averaged strain energy density (SED)