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A simplified fatigue assessment method for high quality welded cruciform joints
International Journal of Fatigue 31 (2009) 79–87
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International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
A simplified fatigue assessment method for high quality welded cruciform joints T. Nykänen, G. Marquis *, T. Björk Laboratory of Fatigue and Strength, Lappeenranta University of Technology, P.O. Box 20, FIN 53851 Lappeenranta, Finland
a r t i c l e
i n f o
Article history: Received 21 September 2007 Received in revised form 18 January 2008 Accepted 27 February 2008 Available online 16 March 2008 Keywords: Welded joints Fatigue strength Fatigue crack growth Weld profile Fatigue assessment
a b s t r a c t The primary goal of this study was to develop an equation relating the geometric parameters to fatigue strength which can be used is routine design assessment. To attain this, the influence of local geometrical weld variations on the fatigue strength of non-load-carrying cruciform fillet welded joints were systematically studied using plane strain linear elastic fracture mechanics (LEFM). The effects of weld toe radius, flank angle and weld size were considered. Both continuous weld toe cracks and semi-elliptical toe cracks with alternate pre-existing defect depths were considered. A previously developed experimental crack aspect ratio development curve was used for assessing the growth of the semi-elliptical cracks using 2D FE models. A total of 152 experimental fatigue data points from six published studies of welded cruciform joints were evaluated. Details of the actual weld toe radius, flank angle and weld size were available for these joints. For the high quality welds evaluated, an assumed initial crack depth of 0.05 mm was found to correlate best with the experimental data. Of all the geometric parameters considered analytically, weld toe radius was found to have the most dramatic influence on fatigue life. A simple equation is proposed which relates welded joint fatigue strength to the ratio weld toe radius/plate thickness for high quality welds. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction In current industrial practice, welds and welded joints are an integral part of many complex load-carrying structures. Experience has shown, however, that welds are often the weakest portions of these structures and that the welding process has significant influence on the integrity of a structure. Fatigue strength is known to be closely related to the precise geometrical discontinuity of the welded joint [1–7]. Welding imperfections that may be introduced during fabrication are only generally considered in commonly applied fatigue design rules for welded structures that are based primarily on S–N curves [8,9]. In most cases the S–N curves in design guidance documents are based on laboratory tests of ‘‘normal” quality welds, even though the precise definition of normal quality is not always clearly defined. There is a need to better understand the fatigue behaviour of welded joints with consideration of the geometrical factors that produce locally high stresses. The goal of this study is to quantify the link between weld geometry and fatigue strength. Some fabricators of fatigue loaded structures are able and willing to invest in welds with consistently higher fatigue strength. The ultimate goal, therefore, is to produce welds with known and adequate fatigue design strength at reasonable cost.
* Corresponding author. E-mail address: Gary.Marquis@lut.fi (G. Marquis). 0142-1123/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2008.02.016
For fully reversed loadings in notched members without any initial cracks the fatigue life is dominated by crack initiation, when N = 106–107 cycles, depending on notch severity [10]. However, the existence of crack-like imperfections in welded joints is normally considered to eliminate the so-called crack initiation stage of fatigue life, when the welds are under high tensile residual stresses. Therefore, the emphasis of the fatigue assessment for most welded structures is focused on the crack growth portion of fatigue life which can be assessed within the framework of linear elastic fracture mechanics (LEFM). This is the case when the yield zone at the crack tip is small with respect to both the crack size and the remaining ligament [3]. By characterizing stable macroscopic crack growth using the stress intensity factor range DK, it is possible to predict crack growth rate of a weld during cyclic loading, and hence the number of cycles necessary for a crack to extend from some initial size, i.e. the size of pre-existing crack or crack-like defects, to a maximum permissible size to avoid catastrophic failures. It can be noted that using modern welding practices the crack initiation phase of fatigue life can become significant and this promises to be an area of active research in future years. This current study is concerned with the fatigue behaviour of cruciform fillet welded joints in the as-welded condition and under cyclic tensile loading. The primary goal has been to use both experimental data and analytical methods to develop a equations relating the geometric parameters to fatigue strength which can be used is routine design assessment. In the as-welded condition the fatigue crack initiation period was considered non-existent
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and LEFM was used to calculate fatigue strength for a range of weld geometries. Normally this type of non-load-carrying welded attachment always fails at the weld toe. Fracture mechanics assessment of these weld toe cracks requires accurate stress intensity factor solutions. A particular feature of such solutions is the stress concentration magnification function Mk which takes into account the stress concentration due to the welded joint geometry.
2 3 2x 2x 2x Y u ¼ 1:98 þ 0:36 þ 3:42 ; 2:12 T T T
0<
2x < 0:95 T ð2Þ
In those cases when a correction for the semi-elliptical crack was used, the value of Yu defined by Newman and Raju [13] was used as in Refs. [3–5]. The Mk solution was assumed to apply also at the deepest point of the semi-elliptical crack front.
2. Fracture mechanics analysis 2.3. Calculation of fatigue life 2.1. Introduction In engineering structures, welded joints are normally elements of a more complex structure. Boundary conditions of the structure are also frequently complex and may vary with time. In the current project the fatigue cracks were assumed to propagate under force control because this is considered to provide conservative fatigue strength estimates. The investigated non-load-carrying fillet welded cruciform joint is shown in Fig. 1. The weld throat, a, weld flank angle, b, and weld toe radius, q, were varied. The analysis was carried out for a/T ratios 0.1, 0.3, 0.65 and 1.0, weld flank angles b of 15°, 30°, 45° and 60° and q/T ratios 0.0, 0.01, 0.02, 0.05, 0.1, 0.2, 0.4 and 1.0. 2.2. Stress concentration magnification factor, Mk For an elliptical crack at the toe of a fillet welded joint, the range of the stress intensity factor, DK, can be written as [11] DK ¼
M k Y u pffiffiffi Dr x /0
ð1Þ
In Eq. (1) Mk is the stress concentration magnification factor which is defined as the ratio of the stress intensity factor of a cracked plate with a stress concentration to the stress intensity factor with the same cracked plate without the stress concentration. Dr is the nominal tensile stress range in the plate and x is the crack depth. The geometry factor, Yu = Ms Mt is the product of the free surface correction factor, Ms, and the finite size correction factor, Mt. Ms depends on the crack aspect ratio and position around the crack front while Mt is a correction to allow for the presence of a free surface ahead of the crack and depends on the crack depth to plate thickness ratio and the crack front shape. /0 is a correction term given by the complete elliptic integral of the second kind and depends on the crack front shape. The Mk-function [3–5] used in this study is for continuous edge crack, hence, the crack aspect ratio is zero, x/2c = 0, and /0 = 1. The correction term Yu for a double-edge crack in a plate under tensile loading, Eq. (2), given by Brown and Srawley [12] was applied in Refs. [3–5].
Fig. 1. Joint geometry and the local weld parameters.
In order to predict fatigue crack propagation, numerous empirical or semi-empirical equations have been proposed to relate fatigue crack growth rate data to the parameter DK. Among the proposed equations, the Paris–Erdogan relationship [14] is commonly accepted and used in practice for a wide range of mode I cracks. This relationship is given as dx ¼ CDK m dN
ð3Þ
where dx/dN is the crack growth rate per cycle, C and m are material constants, and DK is the range of the stress intensity factor for the opening mode. Eq. (3) is also recommended by the International Institute of Welding (IIW) [8] for calculating the fatigue crack propagation rate of welded joints made of steel or aluminium. The constants m = 3 and Cchar = 5.21 1013 (dx/dN in mm/cycle and DK in Nmm3/2) recommended by IIW [8] for the assessment of ferrite-pearlite steel welded joints in the as-welded condition and Cmean = 1.7 1013 [15] are used in this study. Cmean is considered to be the mean fatigue crack growth rate coefficient and Cchar is the characteristic value corresponding to 95% survival probability value. The threshold value of the stress intensity factor was not used in this study. If the crack length is normalised by the plate thickness, 2x/T, Eqs. (1) and (3) can be combined and integrated to give the expected number of cycles to failure. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z 2xf !m Z 2xf T 1 T 1 T 2x T 2x T 2x N ¼ 2x DK m d ¼ 2x M k Y u Dr d i i C 2 T C 2 T 2 T T T ð4Þ By separating the constants from the integration NDrm ¼
I
CT
; m=21
where
I¼
Z
2xf T
2xi T
2m=21 M k Y u
sffiffiffiffiffiffiffiffiffiffiffiffi ffi!m 2x 2x d T T ð5Þ
This leads to NðDr Þm ¼
1 ; C
where
Dr ¼
T m=21 I
!1=m Dr
ð6Þ
The term Dr* is the equivalent structural stress range [16] or the generalized stress parameter [17]. This modified stress parameter takes into account the applied stress and the stress gradient resulting from alternate specimen geometries. Geometric size effect is automatically included in Dr* because plate thickness appears in both the computation of the crack growth integral, I, Eq. (5) and in the relationship between I and Dr* Eq. (6). The initial and final crack lengths are xi and xf, respectively. The value of crack growth integral, I, depends on xi and xf. For semi-elliptical cracks, the same Mk-factors were used to model crack growth in the thickness direction as were used for edge cracks. This is expected to give conservative results, because the Mk-factors based on 2D analysis are slightly higher than those based on 3D analysis [18]. The experimental crack aspect ratio curve proposed by Engesvik and Moan [19] is used for the growing semi-elliptical surface
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cracks to take into account the random coalescence of cracks at the weld toe: 8 x < 0:062 mm > < 0:5 x ¼ 1=ð6:43 0:27=xÞ 0:062 6 x 6 3 mm ð7Þ 2c > : 0 x > 3 mm
toe radii studied. For a relatively deep initial edge crack, xi = 0.8 mm, the effect of weld toe radius and weld flank angle vanishes. For a smaller initial edge crack size, the effect of weld toe radius and flank angle is more pronounced thus highlighting the local nature of the stress concentration.
In principle, we need only one common on the equivalent stress range based S–N curve in cases, where the above fatigue assessment procedure is valid, that is the first Eq. (6).
2.5.2. Semi-elliptical crack versus continuous crack Eq. (3) was also integrated from three different initial crack depths, xi equal to 0.05, 0.2 and 0.8 mm, for an assumed semi-elliptical surface crack at the weld toe. As in the case of a continuous crack the final crack size was equal to T/2. The predicted fatigue strengths for the case T = 6 mm and a = 4 mm are presented in Fig. 2b. A comparison of Fig. 2a and b reveals that the expected fatigue strength for a semi-elliptical crack is approximately14% higher than for the corresponding continuous crack, when xi equals to 0.2 or 0.8 mm and 19–31% higher when xi equals to 0.05 mm. The predicted FAT classes are also presented as contour plots in Fig. 3 for both 0.2 and 0.05 mm deep semi-elliptical toe cracks as a function of b and q/T, when a/T = 0.3 and T = 25 mm. It can be seen, that the effect of flank angle on the fatigue strength is small for rounded weld toes. For high quality welds the weld toe radii should be large and the initial crack depth should be much smaller than 0.2 mm as is frequently assumed for normal quality welds.
2.4. Fatigue strength The fatigue strength of a welded joint is normally characterised by its fatigue class, FAT, which identifies the range of stress corresponding to 2 106 cycles to failure with a 95% survival probability [8]. Using the values m and Cchar the cyclic life corresponding to any stress range can be evaluated. The theoretical FAT can then be determined by adjusting the result according to the S–N curve, Eq. (5), so as to give the stress range corresponding to the fatigue life of two million cycles. On the basis of Eq. (5) the corresponding mean fatigue strength is sffiffiffiffiffiffiffiffiffiffiffiffi m C char FAT ð8Þ Drmean ¼ C mean
3. Summary of published experimental data 2.5. Predicted fatigue strengths 2.5.1. Continuous crack Eq. (3) was integrated from three different initial continuous crack depths, xi equal to 0.05, 0.2 and 0.8 mm. The final crack size was equal to T/2. The maximum effect of throat thickness is observed in the case of a small weld toe radius (q = 0), weld angle b = 45°, and the initial edge crack depth was 0.2 mm. In this case, FAT varied by only 11% over the entire range, 0.1 6 a/T 6 1 and 5 mm 6 T 6 50 mm. For rounded weld toes the effect of throat thickness was even smaller. In general, as the throat thickness increases, the fatigue strength tends to decrease. The predicted fatigue strengths for the case T = 6 mm and a = 4 mm are presented in Fig. 2a. For the 0.2 mm initial edge crack case in Fig. 2, the maximum difference between minimum and maximum predicted FAT is approximately 15% over the entire range of weld angles and weld
Most published experimental fatigue data for welded structures does not include full details of the weld geometry. However, several studies have included this information for non-load-carrying cruciform joints failing from cracks at the weld toe [5,20–24]. This section gives some details of the different experimental programs and gives a comparison between the experimental and analytical results. In total 168 experimental data points were available and 152 were used in the analysis. The 16 excluded data points had Nf > 2 106 and were not included so as to avoid any potential threshold effects. Test specimens in Ref. [20] were fabricated from SM50B rolled steel plates (UTS = 570 MPa, ry = 485 MPa) with manual arc welding and with covered electrodes, SMAW, in the flat position, PA (EN ISO 6947, EN 287-2). Tests were carried out for joints with T equal to 9, 20 and 40 mm under load control and zero to tension loading, i.e. stress ratio R = 0. Similar tests were later done using
Fig. 2. Predicted fatigue strengths at Nf = 2 106 cycles for (a) continuous and (b) semi-elliptical toe cracks, when T = 6 mm and a = 4 mm.
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Fig. 3. Predicted fatigue classes, when semi-elliptical toe cracks with initial depths xi of 0.2 and 0.05 mm were assumed. a/T = 0.3 and T = 25 mm.
SMAW and metal active gas welding, MAG, for joints with T = 20 mm [21]. Branco et al. [22] carried out tests on joints welded entirely by tungsten inert gas welding, TIG, or by plasma processes. Joints were fabricated from 3 mm thin Grade 50 C–Mn structural steel plate and fatigue tested with applied loading such that the maximum stress was maintained constant at 300 N/mm2. Weld toe radius and tangent angle were measured with a video monitoring system and the data were treated by statistical analysis. Lindqvist [23] studied 12 mm thick non-load-carrying transverse fillet welded cruciform joints in pure tension. The joints were made of the steel DOMEX 550 MC. DOMEX 550 MC is high strength hot rolled steel with the minimum yield strength 550 MPa and minimum and maximum tensile strengths of 600 MPa and 760 MPa, respectively. MAG welding was used with shielding gas MISON 8 and the filler metal OK12.51. Before the welding the specimens were shot blasted to avoid cold laps. The effective throat thickness was nominally 6 mm. Measurements later showed that the effective throat thickness varied between 6 and 7 mm with an average of 6.5 mm. Altogether sixty measurements were made and the weld toe radius fluctuated between 0.15 and 2 mm. The average radius was 0.62 mm. The reported variation in the weld angle, b, was only a couple of degrees. However, since the reported precision of the measuring system was smaller than the measured variation, the value b = 45 was used. The original aim of the measurements was reportedly to locate the point of crack initiation and measure the initial crack and weld toe radius at this point. Neither initial points nor cracks could be found. So the weld toe radii were just measured at random points along the welds on the specimens. The fatigue specimens were tested with constant amplitude loaded at a stress ratio R = 0 with the frequency 10 Hz. Kuhlmann et al. [24] tested joints in constant amplitude pulsating tension at R = 0.1. The specimens were fabricated from 12 mm thick S 460 steel plate using fully mechanized welding. The widths of the sawed small scale specimens were 40 mm. Manual TIGdressing was performed on all specimens. Fatigue tests at Lappeenranta University of Technology [5] were carried out in constant amplitude pulsating tension and in the as-welded condition. In the first test series, the specimens were fabricated from S 355 steel plates, ry = 355 MPa. Robotized MAG welding with waving was used with shielding gas Mison 8, Mison
18 or 2He and the filler metal PZ6105R. The weld toe geometry, where the fatigue failure later occurred was measured by optical microscope. In the second test series the specimens were fabricated from S 650 steel plates, ry = 650 MPa. Robotized MAG welding with waving was used with shielding gas Mison 18 and Mison 8, and the filler metal Autrod 13.13, Tubrod 14.03 or PZ6105R. The weld toe geometry was measured by optical microscope. In the third test series the specimens were fabricated from S 960 steel plates, ry = 960 MPa. Robotized MAG welding with waving was used with the filler metal X96. Within each of the three test series, i.e., three material strengths, the welding parameters were intentionally varied in order to attain variations in the attained weld quality and fatigue strength. Those welding parameters that were varied included shielding gas, filler wire type, welding current, welding voltage, travel speed, travel angle, nozzle distance and angle, and waving. In this sense the LUT data was unique because other investigations had the goal of producing entire series of fatigue test specimens with similar weld quality. The weld toe geometries of each of the four welds that comprised the cruciform specimens were measured and digitally recorded using a structured light measurement (SLM) system with computer interface [25]. These measurements made it possible to collect statistical information of the weld profiles and consider the profile at the location where fatigue crack was later found to initiate [26]. All experimental data is presented in Fig. 4 and the corresponding average values of geometrical parameters are shown in Table 1. The characteristic curves in Fig. 4 are drawn based on k1 = 1.9 [8], where k1 is the factor relating the measured standard deviation of the sample to the expected standard deviation of the population based on normal statistics. The characteristic values then approximately correspond to the 95% survival probability at a confidence level of 75% of the mean.
4. Results and discussion It is well known that fracture mechanics based computations are extremely sensitive to the initial crack size. In order to compare experimental data with computations, a realistic initial crack size and shape must be assumed. In this study it will be assumed that the best estimate for the initial crack depth and shape can be found
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dard deviation) between predicted and experimental data [3–5]. In Figs. 5 and 6 the experimental data collected from the literature, i.e., data from Fig. 4, is presented in terms of the equivalent structural stress range, Dr*. Figs. 5 and 6 also present the mean regression line for the experimental data and the resulting characteristic S–N curve. In this analysis the slope of the experimental curve was forced to be 1/3. These figures also show the fracture mechanics based mean and characteristic S–N lines based on Eq. (6). A summary of the statistical information from Figs. 4–6 is provided in Table 2. 4.1. Continuous crack case In Fig 5a an initial continuous crack with depth xi = 0.2 mm was assumed while in Fig 5b an initial crack depth xi = 0.05 mm was assumed. The use of Dr* in place of nominal stress reduced the scatter for the 152 failed specimens by 16.8% for a 0.2 mm assumed initial crack, i.e., the standard error in log(1/C), Eq. (6). If Dr* is used with an assumed initial crack size of xi = 0.05 mm, the scatter is reduced by 27.5% with respect to the scatter observed based on nominal stress. Secondary bending stresses due to misalignments could only be considered for only a small number of data points where structural stresses were measured [5].
Fig. 4. Summary of test results for as-welded specimens.
4.2. Semi-elliptical crack case
Table 1 Average values of geometrical parameters used in this study
NIMS 1979 [20] NIMS 1979 [20] NIMS 1979 [20] NIMS 1980 [21] NIMS 1980 [21] Branco et al. 1999 [22] – TIG Branco et al. 1999 [22] – Plasma Lindqvist 2002 [23] Kuhlmann 2005 [24] – As-welded Kuhlmann 2005 [24] – TIG-dressing LUT 2006 [5] a
T (mm)
q (mm)
b (°)
a (mm)
9 20 40 20 20 3 3 12 12 12 6
0.465 0.470 0.546 0.650 0.400 6 6 0.62 1.1 7.0 0.01–3.9a
39.2 50.9 37.4 35.0 43.0 10 7 45 41 41 38–93a
4.59 7.35 8.45 6.93 8.00 2 2 6.5 4 4 5
Variable, values measured for each specimen.
if the mean S–N curve based on analytical calculations equals the mean experimental S–N curve. Previous studies have shown that this method also reduces the standard error of estimation (stan-
In Fig. 6 initial semi-elliptical cracks with depths xi = 0.2 mm or xi = 0.05 mm were assumed. In comparison with the scatter observed in Fig. 4, the scatter in Fig. 6 is reduced by 20.0% for a 0.2 mm assumed initial crack and for a 0.05 mm assumed initial crack the respective reduction is 26.9%. From Fig. 6 it can be noted that if the initial crack size of xi = 0.05 mm is assumed, the mean Dr*–N curve based on the experimental results is practically coincident with analytical curve computed using Cmean = 1.7 1013. In order to achieve coincident curves with an assumed continuous crack, a much smaller assumed initial crack depth would be needed. From the statistical information in Table 2, it is clearly seen that xi = 0.05 mm provides the best fit for the data if a semi-elliptical crack is assumed. In Figs. 7 and 8, the experimental and predicted strengths for each of the 152 data points are compared based on nominal stress ranges in cases of xi = 0.2 and 0.05 mm, respectively. The righthand figure in each case shows the comparison based on the
Fig. 5. Equivalent structural stress range versus N in continuous toe crack case, when xi = 0.2 and 0.05 mm.
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Fig. 6. Equivalent structural stress range versus N in semi-elliptical crack case, when xi = 0.2 and 0.05 mm.
Table 2 Standard deviation in log(1/C), Eq. (6) xi (mm)
Continuous initial crack
Elliptical initial crack
0.025 0.05 0.075 0.1 0.2
0.2226 0.2217 0.2290 0.2324 0.2544
0.2514 0.2236 0.2242 0.2260 0.2446
predicted characteristic fatigue strengths, i.e., using Cchar = 5.21 1013, while the left-hand figure is based on the predicted mean strengths, Cmean = 1.7 1013. 4.3. The effect of local geometry As was seen in Figs. 2 and 3, for high quality welds that have a relatively large q and small xi, the effect of b on fatigue strength is
small as compared to the effect of q. The effect of throat thickness, a, is also small [3]. Others have reported a mild effect of a [27,28]. If the LEFM based predicted fatigue strengths for the test specimens at 2 106 cycles (m = 3) are drawn as a function of q/T, the effects of b and a appear as ‘‘scatter” as seen in Fig. 9a. In this figure xi = 0.05 mm was assumed for all specimens. All fatigue strength values lie on virtually on a single line for all variations of b and a. The increased scatter at low q/T indicates that these geometric features are expected to have an influence of fatigue life for small q/T. The experimental results, presented as fatigue strengths at 2 106 cycles (m = 3) are shown in Fig. 9b as a function of the reported q/T. The scatter in this figure is greater than that observed in Fig. 9a. The reasons for the scatter are, at least partly, the same as for the LEFM based calculations. However, since these points represent actual experimental data, other factors like initial crack depth variation between specimens, actual crack shape, small crack growth behaviour, welding residual stresses and secondary
Fig. 7. Correlation between predicted and experimental fatigue strengths, if semi-elliptical toe crack with xi = 0.2 mm is assumed.
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Fig. 8. Correlation between predicted and experimental fatigue strengths, if semi-elliptical toe crack with xi = 0.05 mm is assumed.
Fig. 9. (a) Predicted fatigue strengths, Dr, at 2 106 cycles as a function of q/T ratio with assumed semi-elliptical toe crack xi = 0.05 mm and (b) experimental fatigue strengths at 2 106 cycles, m = 3.
bending may occur. The degree of penetration may also vary in the test specimens. The LEFM model assumed no penetration. In spite of these experimental uncertainties, the experimental mean curve Drmean = 156.3 (q/T)0.12 at 2 106 cycles is very close to the predicted mean curves Drmean = 159.9 (q/T)0.125 at 2 106 cycles. Also the experimental characteristic curve Drchar = 107.3 (q/T)0.12 at 2 106 cycles nearly coincides to the predicted characteristic curve. In summary, the LEFM assessments have led to a simplified relationship which can be used for high quality fillet welded cruciform joints when q/T P 0.02 and the initial crack depth, xi < 0.05 mm. q0:125 Drmean ¼ 159:9 T
and
q0:125 Drchar ¼ 110:1 T
ð9Þ
These equations are nearly identical to those found by statistical analysis of 152 experimental results from six different studies of
non-load-carrying fillet welded cruciform joints where physical characteristics of the weld geometry were measured and reported and (q/T) P 0.02. q0:12 Drmean ¼ 156:3 T
and
q0:12 Drchar ¼ 107:3 T
ð10Þ
The exponents in Eqs. (9) and (10) are lower than exponents observed in previous studies of the effect of (q/T) on stress concentration factors for welded joints with various geometries [29–31]. These previous studies, however, were concerned with the elastic stress concentration factor, Kt, rather than the fatigue stress concentration factor, Kf, which is conceptually closer to Eqs. (9) and (10). The value Kt is related to the peak stress at the surface of a notch while Eq. (9) relates to the stress and stress gradient just below the surface. The good agreement between analytical and experimental observed relations indicates that the important features of the process have been captured.
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4.4. Relation between the Paris law and equivalent structural stress Based on the left-hand portion of Eq. (6) and with m = 3, the Paris law coefficient Cmean = 1.7 1013 leads to a mean value of the equivalent structural stress range, Dr*, equal to 143.3 MPa mm1/6 at Nf = 2 106 cycles. Note that this value is independent of the crack shape, initial crack depth or joint type because it is based solely on the crack growth rate coefficient. Using the right-hand portion of Eq. (6), an assumed semi-elliptical toe crack with xi = 0.05 mm gives a mean value of Dr* = 141.4 MPa mm1/6 for the published experimental data. This practically coincides to the LEFM based value of Dr* = 143.3 MPa mm1/6. The scatter in Fig. 9b is large, but the characteristic Dr*–N curve of the experimental data is in good agreement with the characteristic Dr*–N curve obtained from Eq. (6), if Cchar = 5.21 1013 recommended by IIW [8] is used. On the basis of the experimental fatigue lives of welded cruciform joints seen in Fig. 6b, Cchar = 1/(1.97 1012) = 5.08 1013 is computed. This value nearly coincides with Cchar recommended by IIW. If the LUT-results [5] are ignored and an initial semi-elliptical toe crack with depth of 0.05 mm is assumed, the computed mean equivalent structural stress range, Dr*, for the experimental data is still near the value 143.3 MPa mm1/6 [2–4]. In this case, however, the predicted characteristic Dr*–N line corresponds to a crack growth coefficient Cchar = 3.0 1013. This is the value proposed by the previous IIW recommendations [32]. In other words, the addition of the LUT data slightly increases the observed scatter in the calculations. It is interesting to note that, for the cases single- or double-edge cracked plates in tension, Dr . Dr* when xi = 0.05 mm and Dr is only slightly dependent on plate width. The resulting fatigue strength is FAT 99 if Cchar = 5.21 1013 is used. This FAT-value is virtually identical to the fatigue strength, FAT 100, of manually thermally cut plate edges recommended by IIW which has been determined by statistical evaluation of a large experimental data base [6]. Therefore, the simple cases of single- or double-edge cracked plates in tension with xi = 0.05 mm further verify the usefulness of the proposed Dr–N curve.
5. Conclusions The influence of local geometric parameters on the fatigue strength of non-load-carrying cruciform fillet welded joint under tensile loading has been studied using linear elastic fracture mechanics calculations and based on previously reported experimental fatigue data. The primary goal has been to use both experimental data and analytical methods to develop an equation relating the geometric parameters to the fatigue strength which can be used is routine design assessment. On the basis of theoretical calculations and comparisons between predictions and experimental results, the following conclusions can be made: (1) Local geometrical variations of the weld and weld throat size have only a small effect on the fatigue strength, if the depth of an initial toe crack is greater than 0.2 mm. As the depth of the initial toe crack increases, the local geometrical effects disappear. (2) The effect of weld angle on the fatigue strength is small when the toe radius is large. For high quality welds, the weld toe radii should be large and the initial crack depth should be very small. According to this study the fatigue strength of joints with large toe radii increases approximately 20– 40% as the initial crack depth decreases from 0.2 mm to 0.05 mm.
(3) If the stress term is presented using the equivalent structural stress range, Dr*, and Cmean = 1.7 1013 is used in Eq. (6), the best fit between predicted and experimental mean fatigue strengths is achieved when an initial semi-elliptical toe crack with depth of 0.05 mm is assumed. (4) If the experimental data is presented using equivalent structural stress range, Dr*, the characteristic Dr*–N curve corresponds to the characteristic Paris law coefficient, Cchar = 1/ (1.97 1012) = 5.08 1013. This is very close to the value recommended by IIW. (5) If the predicted and experimental fatigue strengths at 2 106 cycles (m = 3) are drawn as a function of q/T, the corresponding fitted curves, Eq. (9) and (10) are almost identical, when an initial semi-elliptical toe crack with depth of 0.05 mm is assumed. The results are based on 152 experimental data points. Predicted: q0:125 Drmean ¼ 159:9 T q when P 0:02 T
and
q0:125 Drchar ¼ 110:1 T ð9aÞ
Experimental: q0:12 Drmean ¼ 156:3 T q when P 0:02 T
and
q0:12 Drchar ¼ 107:3 T ð10aÞ
Acknowledgements This study was a part of the weld quality project ‘‘LAATU” which was carried out in the Laboratory of Fatigue and Strength at Lappeenranta University of Technology. The support of Metso Paper Inc., Andritz Oy, KCI Konecranes Oyj, John Deere Forestry Oy, Ruukki, VR, Wärtsilä, Auramo, Ponsse, Bronto Skylift Oy, Stalatube Oy and the National Technology Agency of Finland, are greatly appreciated. Prof. Luca Susmel and the co-editors are thanked for the invitation to contribute to this special publication. References [1] Maddox SJ. Fatigue strength of welded structures. Cambridge: Abington; 1991. [2] Nykänen T, Li X, Björk T, Marquis G. A parametric fracture mechanics study of welded joints with toe cracks and lack of penetration. Eng Fract Mech 2005;72:1580–609. [3] Nykänen T, Marquis G, Björk T. Fatigue analysis of non-load-carrying fillet welded cruciform joints. Eng Fract Mech 2007;74(3):399–415. [4] Nykänen T, Marquis G, Björk T. Effect of local geometrical variations on the fatigue strength of fillet welded joints. In: Proceedings of the IX finnish mechanics days, Lappeenranta University of Technology, Finland; 2006. p. 359–77. [5] Nykänen T, Marquis G, Björk T. Effect of weld geometry on the fatigue strength of fillet welded cruciform joints.In: Marquis G, Samuelsson J, Agerskov H, Haagensen PJ, editors. Proceedings of the international symposium on integrated design and manufacturing of welded structures, March 13–14, 2007. Sweden: Eskilstuna; March 2007. p. 23. ISBN: 978-952-214-363-1, ISSN: 1459-2924. [6] Lazzarin P, Tovo R. A notch intensity factor approach to the stress analysis of welds. Fatigue Fract Eng Mater Struct 1998;21:1089–103. [7] Atzori B, Meneghetti G, Susmel L. Estimation of the fatigue strength of light alloy welds by an equivalent notch stress analysis. Int J Fatigue 2002;24(5): 591–9. [8] Hobbacher A, Recommendations for fatigue design of welded joints and components. International Institute of Welding, XIII-2151-07/XV-1254-07, Paris; 2007. [9] EC3 (2002c). prEN 1993-1-8. Eurocode 3: design of steel structures. Part 1–8, design of joints (draft 26 February 2002). [10] Verreman Y, Limodin N. Fatigue notch factor and short crack propagation. Eng Fract Mech 2008;75(6):1320–35. [11] Maddox SJ. Int J Fract 1975;11:221–43. [12] Brown WF, Srawley JE. Plane strain crack toughness testing of high strength metallic materials. West Conshohocken, PA: ASTM STP 410, ASTM; 1966.
T. Nykänen et al. / International Journal of Fatigue 31 (2009) 79–87 [13] Newman JC, Raju IS. Stress-intensity factor equations for cracks in threedimensional finite bodies. Fracture mechanics. Springer; 1983. [14] Paris PC, Erdogan F. A critical analysis of crack propagation laws. J Basic Eng 1963;85:528–34. [15] VTT Symposium 100. Fatigue design of structures. Technical Research Centre of Finland (VTT), Finland; 1989 (in Finnish). [16] Dong P, Hong JK, et al. Life predictions using mesh-insensitive structural stress method. Fatigue design and evaluation committee of the SAE, spring 2003 meeting, April 15–16, 2003. Hosted by Caterpillar in Peoria, Illinois. http:// www.fatigue.org/Minutes/Spring-2003/contents.html. [17] Gurney TR. Fatigue of welded structures. Cambridge: Cambridge University Press; 1979. [18] Pang HLJ. A review of stress intensity factors for semi-elliptical surface crack in a plate and fillet welded joint. The Welding Institute, Cambridge, England: Abington Publishing; 1990. [19] Engesvik KM, Moan T. Probabilistic analysis of the uncertainty in the fatigue capacity of welded joints. Eng Fract Mech 1983;18(4):743–62. [20] NIMS 1979. Data sheets on fatigue properties of non-load-carrying cruciform welded joints of SM50B rolled steel for welded structure. Effect of specimen size. http://tsuge.nims.go.jp/. [21] NIMS 1980. Data sheets on fatigue properties for non-load-carrying cruciform welded joints of SM50B rolled steel for welded structure. Effect of welding procedure. http://tsuge.nims.go.jp/. [22] Branco CM, Maddox SJ, Infante V, Gomes EC. Fatigue performance of tungsten inert gas (TIG) and plasma welds in thin sections. Int J Fatigue 1999;21: 587–601.
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[23] Lindqvist J. Fatigue strengths thickness dependence in welded constructions. Master thesis. Borlänge, Sweden; 2002. http://hem.passagen.se/johanlindq/ Exjobb.pdf. [24] Kuhlmann U et al. Erhöhung der Ermüdungsfestigkeit von geschweißten höherfesten Baustählen durch Anwendung von Nachbehandlungsverfaren. Stahlbau, Stahlbau, 2005;74: H. 5, S. 358–65. [25] Couweleers F, Skotheim Ø, Tveiten BW. Presented at 8th international symposium on measurement and quality control in production, October 2004. Erlangen, Germany. [26] Nieminen T. Non-destructive measurement of weld surface geometries. MS thesis. Lappeenranta University of Technology, Lappeenranta, Finland; 2006 (in Finnish). [27] Labesse F, Recho N. Geometrical stress level at the weld toe and associated local effects. Weld World 1999;43(1):23–32. [28] Poutiainen I, Marquis G. A fatigue assessment method based on weld stress. Int J Fatigue 2006;28(9):1037–46. [29] Radaj D, Zhang. Multiparameter design optimisation in respect of stress concentrations. Engineering optimisation in design processes. Berlin: Springer; 1991. p. 181–9. [30] Niu X, Glinka G. The weld profile effect on the stress intensity factors in weldments. Int J Fract 1987;35:3–20. [31] Yung JY, Lawrence FV. Analytical and graphical aids for the fatigue design of weldments. Fatigue Fract Eng Mat Struct 1985;8(3):223–41. [32] Hobbacher A. Recommendations for fatigue design of welded joints and components. Cambridge: Abington Publishing; 1996.
Contents lists available at ScienceDirect
International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
A simplified fatigue assessment method for high quality welded cruciform joints T. Nykänen, G. Marquis *, T. Björk Laboratory of Fatigue and Strength, Lappeenranta University of Technology, P.O. Box 20, FIN 53851 Lappeenranta, Finland
a r t i c l e
i n f o
Article history: Received 21 September 2007 Received in revised form 18 January 2008 Accepted 27 February 2008 Available online 16 March 2008 Keywords: Welded joints Fatigue strength Fatigue crack growth Weld profile Fatigue assessment
a b s t r a c t The primary goal of this study was to develop an equation relating the geometric parameters to fatigue strength which can be used is routine design assessment. To attain this, the influence of local geometrical weld variations on the fatigue strength of non-load-carrying cruciform fillet welded joints were systematically studied using plane strain linear elastic fracture mechanics (LEFM). The effects of weld toe radius, flank angle and weld size were considered. Both continuous weld toe cracks and semi-elliptical toe cracks with alternate pre-existing defect depths were considered. A previously developed experimental crack aspect ratio development curve was used for assessing the growth of the semi-elliptical cracks using 2D FE models. A total of 152 experimental fatigue data points from six published studies of welded cruciform joints were evaluated. Details of the actual weld toe radius, flank angle and weld size were available for these joints. For the high quality welds evaluated, an assumed initial crack depth of 0.05 mm was found to correlate best with the experimental data. Of all the geometric parameters considered analytically, weld toe radius was found to have the most dramatic influence on fatigue life. A simple equation is proposed which relates welded joint fatigue strength to the ratio weld toe radius/plate thickness for high quality welds. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction In current industrial practice, welds and welded joints are an integral part of many complex load-carrying structures. Experience has shown, however, that welds are often the weakest portions of these structures and that the welding process has significant influence on the integrity of a structure. Fatigue strength is known to be closely related to the precise geometrical discontinuity of the welded joint [1–7]. Welding imperfections that may be introduced during fabrication are only generally considered in commonly applied fatigue design rules for welded structures that are based primarily on S–N curves [8,9]. In most cases the S–N curves in design guidance documents are based on laboratory tests of ‘‘normal” quality welds, even though the precise definition of normal quality is not always clearly defined. There is a need to better understand the fatigue behaviour of welded joints with consideration of the geometrical factors that produce locally high stresses. The goal of this study is to quantify the link between weld geometry and fatigue strength. Some fabricators of fatigue loaded structures are able and willing to invest in welds with consistently higher fatigue strength. The ultimate goal, therefore, is to produce welds with known and adequate fatigue design strength at reasonable cost.
* Corresponding author. E-mail address: Gary.Marquis@lut.fi (G. Marquis). 0142-1123/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2008.02.016
For fully reversed loadings in notched members without any initial cracks the fatigue life is dominated by crack initiation, when N = 106–107 cycles, depending on notch severity [10]. However, the existence of crack-like imperfections in welded joints is normally considered to eliminate the so-called crack initiation stage of fatigue life, when the welds are under high tensile residual stresses. Therefore, the emphasis of the fatigue assessment for most welded structures is focused on the crack growth portion of fatigue life which can be assessed within the framework of linear elastic fracture mechanics (LEFM). This is the case when the yield zone at the crack tip is small with respect to both the crack size and the remaining ligament [3]. By characterizing stable macroscopic crack growth using the stress intensity factor range DK, it is possible to predict crack growth rate of a weld during cyclic loading, and hence the number of cycles necessary for a crack to extend from some initial size, i.e. the size of pre-existing crack or crack-like defects, to a maximum permissible size to avoid catastrophic failures. It can be noted that using modern welding practices the crack initiation phase of fatigue life can become significant and this promises to be an area of active research in future years. This current study is concerned with the fatigue behaviour of cruciform fillet welded joints in the as-welded condition and under cyclic tensile loading. The primary goal has been to use both experimental data and analytical methods to develop a equations relating the geometric parameters to fatigue strength which can be used is routine design assessment. In the as-welded condition the fatigue crack initiation period was considered non-existent
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and LEFM was used to calculate fatigue strength for a range of weld geometries. Normally this type of non-load-carrying welded attachment always fails at the weld toe. Fracture mechanics assessment of these weld toe cracks requires accurate stress intensity factor solutions. A particular feature of such solutions is the stress concentration magnification function Mk which takes into account the stress concentration due to the welded joint geometry.
2 3 2x 2x 2x Y u ¼ 1:98 þ 0:36 þ 3:42 ; 2:12 T T T
0<
2x < 0:95 T ð2Þ
In those cases when a correction for the semi-elliptical crack was used, the value of Yu defined by Newman and Raju [13] was used as in Refs. [3–5]. The Mk solution was assumed to apply also at the deepest point of the semi-elliptical crack front.
2. Fracture mechanics analysis 2.3. Calculation of fatigue life 2.1. Introduction In engineering structures, welded joints are normally elements of a more complex structure. Boundary conditions of the structure are also frequently complex and may vary with time. In the current project the fatigue cracks were assumed to propagate under force control because this is considered to provide conservative fatigue strength estimates. The investigated non-load-carrying fillet welded cruciform joint is shown in Fig. 1. The weld throat, a, weld flank angle, b, and weld toe radius, q, were varied. The analysis was carried out for a/T ratios 0.1, 0.3, 0.65 and 1.0, weld flank angles b of 15°, 30°, 45° and 60° and q/T ratios 0.0, 0.01, 0.02, 0.05, 0.1, 0.2, 0.4 and 1.0. 2.2. Stress concentration magnification factor, Mk For an elliptical crack at the toe of a fillet welded joint, the range of the stress intensity factor, DK, can be written as [11] DK ¼
M k Y u pffiffiffi Dr x /0
ð1Þ
In Eq. (1) Mk is the stress concentration magnification factor which is defined as the ratio of the stress intensity factor of a cracked plate with a stress concentration to the stress intensity factor with the same cracked plate without the stress concentration. Dr is the nominal tensile stress range in the plate and x is the crack depth. The geometry factor, Yu = Ms Mt is the product of the free surface correction factor, Ms, and the finite size correction factor, Mt. Ms depends on the crack aspect ratio and position around the crack front while Mt is a correction to allow for the presence of a free surface ahead of the crack and depends on the crack depth to plate thickness ratio and the crack front shape. /0 is a correction term given by the complete elliptic integral of the second kind and depends on the crack front shape. The Mk-function [3–5] used in this study is for continuous edge crack, hence, the crack aspect ratio is zero, x/2c = 0, and /0 = 1. The correction term Yu for a double-edge crack in a plate under tensile loading, Eq. (2), given by Brown and Srawley [12] was applied in Refs. [3–5].
Fig. 1. Joint geometry and the local weld parameters.
In order to predict fatigue crack propagation, numerous empirical or semi-empirical equations have been proposed to relate fatigue crack growth rate data to the parameter DK. Among the proposed equations, the Paris–Erdogan relationship [14] is commonly accepted and used in practice for a wide range of mode I cracks. This relationship is given as dx ¼ CDK m dN
ð3Þ
where dx/dN is the crack growth rate per cycle, C and m are material constants, and DK is the range of the stress intensity factor for the opening mode. Eq. (3) is also recommended by the International Institute of Welding (IIW) [8] for calculating the fatigue crack propagation rate of welded joints made of steel or aluminium. The constants m = 3 and Cchar = 5.21 1013 (dx/dN in mm/cycle and DK in Nmm3/2) recommended by IIW [8] for the assessment of ferrite-pearlite steel welded joints in the as-welded condition and Cmean = 1.7 1013 [15] are used in this study. Cmean is considered to be the mean fatigue crack growth rate coefficient and Cchar is the characteristic value corresponding to 95% survival probability value. The threshold value of the stress intensity factor was not used in this study. If the crack length is normalised by the plate thickness, 2x/T, Eqs. (1) and (3) can be combined and integrated to give the expected number of cycles to failure. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z 2xf !m Z 2xf T 1 T 1 T 2x T 2x T 2x N ¼ 2x DK m d ¼ 2x M k Y u Dr d i i C 2 T C 2 T 2 T T T ð4Þ By separating the constants from the integration NDrm ¼
I
CT
; m=21
where
I¼
Z
2xf T
2xi T
2m=21 M k Y u
sffiffiffiffiffiffiffiffiffiffiffiffi ffi!m 2x 2x d T T ð5Þ
This leads to NðDr Þm ¼
1 ; C
where
Dr ¼
T m=21 I
!1=m Dr
ð6Þ
The term Dr* is the equivalent structural stress range [16] or the generalized stress parameter [17]. This modified stress parameter takes into account the applied stress and the stress gradient resulting from alternate specimen geometries. Geometric size effect is automatically included in Dr* because plate thickness appears in both the computation of the crack growth integral, I, Eq. (5) and in the relationship between I and Dr* Eq. (6). The initial and final crack lengths are xi and xf, respectively. The value of crack growth integral, I, depends on xi and xf. For semi-elliptical cracks, the same Mk-factors were used to model crack growth in the thickness direction as were used for edge cracks. This is expected to give conservative results, because the Mk-factors based on 2D analysis are slightly higher than those based on 3D analysis [18]. The experimental crack aspect ratio curve proposed by Engesvik and Moan [19] is used for the growing semi-elliptical surface
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cracks to take into account the random coalescence of cracks at the weld toe: 8 x < 0:062 mm > < 0:5 x ¼ 1=ð6:43 0:27=xÞ 0:062 6 x 6 3 mm ð7Þ 2c > : 0 x > 3 mm
toe radii studied. For a relatively deep initial edge crack, xi = 0.8 mm, the effect of weld toe radius and weld flank angle vanishes. For a smaller initial edge crack size, the effect of weld toe radius and flank angle is more pronounced thus highlighting the local nature of the stress concentration.
In principle, we need only one common on the equivalent stress range based S–N curve in cases, where the above fatigue assessment procedure is valid, that is the first Eq. (6).
2.5.2. Semi-elliptical crack versus continuous crack Eq. (3) was also integrated from three different initial crack depths, xi equal to 0.05, 0.2 and 0.8 mm, for an assumed semi-elliptical surface crack at the weld toe. As in the case of a continuous crack the final crack size was equal to T/2. The predicted fatigue strengths for the case T = 6 mm and a = 4 mm are presented in Fig. 2b. A comparison of Fig. 2a and b reveals that the expected fatigue strength for a semi-elliptical crack is approximately14% higher than for the corresponding continuous crack, when xi equals to 0.2 or 0.8 mm and 19–31% higher when xi equals to 0.05 mm. The predicted FAT classes are also presented as contour plots in Fig. 3 for both 0.2 and 0.05 mm deep semi-elliptical toe cracks as a function of b and q/T, when a/T = 0.3 and T = 25 mm. It can be seen, that the effect of flank angle on the fatigue strength is small for rounded weld toes. For high quality welds the weld toe radii should be large and the initial crack depth should be much smaller than 0.2 mm as is frequently assumed for normal quality welds.
2.4. Fatigue strength The fatigue strength of a welded joint is normally characterised by its fatigue class, FAT, which identifies the range of stress corresponding to 2 106 cycles to failure with a 95% survival probability [8]. Using the values m and Cchar the cyclic life corresponding to any stress range can be evaluated. The theoretical FAT can then be determined by adjusting the result according to the S–N curve, Eq. (5), so as to give the stress range corresponding to the fatigue life of two million cycles. On the basis of Eq. (5) the corresponding mean fatigue strength is sffiffiffiffiffiffiffiffiffiffiffiffi m C char FAT ð8Þ Drmean ¼ C mean
3. Summary of published experimental data 2.5. Predicted fatigue strengths 2.5.1. Continuous crack Eq. (3) was integrated from three different initial continuous crack depths, xi equal to 0.05, 0.2 and 0.8 mm. The final crack size was equal to T/2. The maximum effect of throat thickness is observed in the case of a small weld toe radius (q = 0), weld angle b = 45°, and the initial edge crack depth was 0.2 mm. In this case, FAT varied by only 11% over the entire range, 0.1 6 a/T 6 1 and 5 mm 6 T 6 50 mm. For rounded weld toes the effect of throat thickness was even smaller. In general, as the throat thickness increases, the fatigue strength tends to decrease. The predicted fatigue strengths for the case T = 6 mm and a = 4 mm are presented in Fig. 2a. For the 0.2 mm initial edge crack case in Fig. 2, the maximum difference between minimum and maximum predicted FAT is approximately 15% over the entire range of weld angles and weld
Most published experimental fatigue data for welded structures does not include full details of the weld geometry. However, several studies have included this information for non-load-carrying cruciform joints failing from cracks at the weld toe [5,20–24]. This section gives some details of the different experimental programs and gives a comparison between the experimental and analytical results. In total 168 experimental data points were available and 152 were used in the analysis. The 16 excluded data points had Nf > 2 106 and were not included so as to avoid any potential threshold effects. Test specimens in Ref. [20] were fabricated from SM50B rolled steel plates (UTS = 570 MPa, ry = 485 MPa) with manual arc welding and with covered electrodes, SMAW, in the flat position, PA (EN ISO 6947, EN 287-2). Tests were carried out for joints with T equal to 9, 20 and 40 mm under load control and zero to tension loading, i.e. stress ratio R = 0. Similar tests were later done using
Fig. 2. Predicted fatigue strengths at Nf = 2 106 cycles for (a) continuous and (b) semi-elliptical toe cracks, when T = 6 mm and a = 4 mm.
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Fig. 3. Predicted fatigue classes, when semi-elliptical toe cracks with initial depths xi of 0.2 and 0.05 mm were assumed. a/T = 0.3 and T = 25 mm.
SMAW and metal active gas welding, MAG, for joints with T = 20 mm [21]. Branco et al. [22] carried out tests on joints welded entirely by tungsten inert gas welding, TIG, or by plasma processes. Joints were fabricated from 3 mm thin Grade 50 C–Mn structural steel plate and fatigue tested with applied loading such that the maximum stress was maintained constant at 300 N/mm2. Weld toe radius and tangent angle were measured with a video monitoring system and the data were treated by statistical analysis. Lindqvist [23] studied 12 mm thick non-load-carrying transverse fillet welded cruciform joints in pure tension. The joints were made of the steel DOMEX 550 MC. DOMEX 550 MC is high strength hot rolled steel with the minimum yield strength 550 MPa and minimum and maximum tensile strengths of 600 MPa and 760 MPa, respectively. MAG welding was used with shielding gas MISON 8 and the filler metal OK12.51. Before the welding the specimens were shot blasted to avoid cold laps. The effective throat thickness was nominally 6 mm. Measurements later showed that the effective throat thickness varied between 6 and 7 mm with an average of 6.5 mm. Altogether sixty measurements were made and the weld toe radius fluctuated between 0.15 and 2 mm. The average radius was 0.62 mm. The reported variation in the weld angle, b, was only a couple of degrees. However, since the reported precision of the measuring system was smaller than the measured variation, the value b = 45 was used. The original aim of the measurements was reportedly to locate the point of crack initiation and measure the initial crack and weld toe radius at this point. Neither initial points nor cracks could be found. So the weld toe radii were just measured at random points along the welds on the specimens. The fatigue specimens were tested with constant amplitude loaded at a stress ratio R = 0 with the frequency 10 Hz. Kuhlmann et al. [24] tested joints in constant amplitude pulsating tension at R = 0.1. The specimens were fabricated from 12 mm thick S 460 steel plate using fully mechanized welding. The widths of the sawed small scale specimens were 40 mm. Manual TIGdressing was performed on all specimens. Fatigue tests at Lappeenranta University of Technology [5] were carried out in constant amplitude pulsating tension and in the as-welded condition. In the first test series, the specimens were fabricated from S 355 steel plates, ry = 355 MPa. Robotized MAG welding with waving was used with shielding gas Mison 8, Mison
18 or 2He and the filler metal PZ6105R. The weld toe geometry, where the fatigue failure later occurred was measured by optical microscope. In the second test series the specimens were fabricated from S 650 steel plates, ry = 650 MPa. Robotized MAG welding with waving was used with shielding gas Mison 18 and Mison 8, and the filler metal Autrod 13.13, Tubrod 14.03 or PZ6105R. The weld toe geometry was measured by optical microscope. In the third test series the specimens were fabricated from S 960 steel plates, ry = 960 MPa. Robotized MAG welding with waving was used with the filler metal X96. Within each of the three test series, i.e., three material strengths, the welding parameters were intentionally varied in order to attain variations in the attained weld quality and fatigue strength. Those welding parameters that were varied included shielding gas, filler wire type, welding current, welding voltage, travel speed, travel angle, nozzle distance and angle, and waving. In this sense the LUT data was unique because other investigations had the goal of producing entire series of fatigue test specimens with similar weld quality. The weld toe geometries of each of the four welds that comprised the cruciform specimens were measured and digitally recorded using a structured light measurement (SLM) system with computer interface [25]. These measurements made it possible to collect statistical information of the weld profiles and consider the profile at the location where fatigue crack was later found to initiate [26]. All experimental data is presented in Fig. 4 and the corresponding average values of geometrical parameters are shown in Table 1. The characteristic curves in Fig. 4 are drawn based on k1 = 1.9 [8], where k1 is the factor relating the measured standard deviation of the sample to the expected standard deviation of the population based on normal statistics. The characteristic values then approximately correspond to the 95% survival probability at a confidence level of 75% of the mean.
4. Results and discussion It is well known that fracture mechanics based computations are extremely sensitive to the initial crack size. In order to compare experimental data with computations, a realistic initial crack size and shape must be assumed. In this study it will be assumed that the best estimate for the initial crack depth and shape can be found
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dard deviation) between predicted and experimental data [3–5]. In Figs. 5 and 6 the experimental data collected from the literature, i.e., data from Fig. 4, is presented in terms of the equivalent structural stress range, Dr*. Figs. 5 and 6 also present the mean regression line for the experimental data and the resulting characteristic S–N curve. In this analysis the slope of the experimental curve was forced to be 1/3. These figures also show the fracture mechanics based mean and characteristic S–N lines based on Eq. (6). A summary of the statistical information from Figs. 4–6 is provided in Table 2. 4.1. Continuous crack case In Fig 5a an initial continuous crack with depth xi = 0.2 mm was assumed while in Fig 5b an initial crack depth xi = 0.05 mm was assumed. The use of Dr* in place of nominal stress reduced the scatter for the 152 failed specimens by 16.8% for a 0.2 mm assumed initial crack, i.e., the standard error in log(1/C), Eq. (6). If Dr* is used with an assumed initial crack size of xi = 0.05 mm, the scatter is reduced by 27.5% with respect to the scatter observed based on nominal stress. Secondary bending stresses due to misalignments could only be considered for only a small number of data points where structural stresses were measured [5].
Fig. 4. Summary of test results for as-welded specimens.
4.2. Semi-elliptical crack case
Table 1 Average values of geometrical parameters used in this study
NIMS 1979 [20] NIMS 1979 [20] NIMS 1979 [20] NIMS 1980 [21] NIMS 1980 [21] Branco et al. 1999 [22] – TIG Branco et al. 1999 [22] – Plasma Lindqvist 2002 [23] Kuhlmann 2005 [24] – As-welded Kuhlmann 2005 [24] – TIG-dressing LUT 2006 [5] a
T (mm)
q (mm)
b (°)
a (mm)
9 20 40 20 20 3 3 12 12 12 6
0.465 0.470 0.546 0.650 0.400 6 6 0.62 1.1 7.0 0.01–3.9a
39.2 50.9 37.4 35.0 43.0 10 7 45 41 41 38–93a
4.59 7.35 8.45 6.93 8.00 2 2 6.5 4 4 5
Variable, values measured for each specimen.
if the mean S–N curve based on analytical calculations equals the mean experimental S–N curve. Previous studies have shown that this method also reduces the standard error of estimation (stan-
In Fig. 6 initial semi-elliptical cracks with depths xi = 0.2 mm or xi = 0.05 mm were assumed. In comparison with the scatter observed in Fig. 4, the scatter in Fig. 6 is reduced by 20.0% for a 0.2 mm assumed initial crack and for a 0.05 mm assumed initial crack the respective reduction is 26.9%. From Fig. 6 it can be noted that if the initial crack size of xi = 0.05 mm is assumed, the mean Dr*–N curve based on the experimental results is practically coincident with analytical curve computed using Cmean = 1.7 1013. In order to achieve coincident curves with an assumed continuous crack, a much smaller assumed initial crack depth would be needed. From the statistical information in Table 2, it is clearly seen that xi = 0.05 mm provides the best fit for the data if a semi-elliptical crack is assumed. In Figs. 7 and 8, the experimental and predicted strengths for each of the 152 data points are compared based on nominal stress ranges in cases of xi = 0.2 and 0.05 mm, respectively. The righthand figure in each case shows the comparison based on the
Fig. 5. Equivalent structural stress range versus N in continuous toe crack case, when xi = 0.2 and 0.05 mm.
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Fig. 6. Equivalent structural stress range versus N in semi-elliptical crack case, when xi = 0.2 and 0.05 mm.
Table 2 Standard deviation in log(1/C), Eq. (6) xi (mm)
Continuous initial crack
Elliptical initial crack
0.025 0.05 0.075 0.1 0.2
0.2226 0.2217 0.2290 0.2324 0.2544
0.2514 0.2236 0.2242 0.2260 0.2446
predicted characteristic fatigue strengths, i.e., using Cchar = 5.21 1013, while the left-hand figure is based on the predicted mean strengths, Cmean = 1.7 1013. 4.3. The effect of local geometry As was seen in Figs. 2 and 3, for high quality welds that have a relatively large q and small xi, the effect of b on fatigue strength is
small as compared to the effect of q. The effect of throat thickness, a, is also small [3]. Others have reported a mild effect of a [27,28]. If the LEFM based predicted fatigue strengths for the test specimens at 2 106 cycles (m = 3) are drawn as a function of q/T, the effects of b and a appear as ‘‘scatter” as seen in Fig. 9a. In this figure xi = 0.05 mm was assumed for all specimens. All fatigue strength values lie on virtually on a single line for all variations of b and a. The increased scatter at low q/T indicates that these geometric features are expected to have an influence of fatigue life for small q/T. The experimental results, presented as fatigue strengths at 2 106 cycles (m = 3) are shown in Fig. 9b as a function of the reported q/T. The scatter in this figure is greater than that observed in Fig. 9a. The reasons for the scatter are, at least partly, the same as for the LEFM based calculations. However, since these points represent actual experimental data, other factors like initial crack depth variation between specimens, actual crack shape, small crack growth behaviour, welding residual stresses and secondary
Fig. 7. Correlation between predicted and experimental fatigue strengths, if semi-elliptical toe crack with xi = 0.2 mm is assumed.
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Fig. 8. Correlation between predicted and experimental fatigue strengths, if semi-elliptical toe crack with xi = 0.05 mm is assumed.
Fig. 9. (a) Predicted fatigue strengths, Dr, at 2 106 cycles as a function of q/T ratio with assumed semi-elliptical toe crack xi = 0.05 mm and (b) experimental fatigue strengths at 2 106 cycles, m = 3.
bending may occur. The degree of penetration may also vary in the test specimens. The LEFM model assumed no penetration. In spite of these experimental uncertainties, the experimental mean curve Drmean = 156.3 (q/T)0.12 at 2 106 cycles is very close to the predicted mean curves Drmean = 159.9 (q/T)0.125 at 2 106 cycles. Also the experimental characteristic curve Drchar = 107.3 (q/T)0.12 at 2 106 cycles nearly coincides to the predicted characteristic curve. In summary, the LEFM assessments have led to a simplified relationship which can be used for high quality fillet welded cruciform joints when q/T P 0.02 and the initial crack depth, xi < 0.05 mm. q0:125 Drmean ¼ 159:9 T
and
q0:125 Drchar ¼ 110:1 T
ð9Þ
These equations are nearly identical to those found by statistical analysis of 152 experimental results from six different studies of
non-load-carrying fillet welded cruciform joints where physical characteristics of the weld geometry were measured and reported and (q/T) P 0.02. q0:12 Drmean ¼ 156:3 T
and
q0:12 Drchar ¼ 107:3 T
ð10Þ
The exponents in Eqs. (9) and (10) are lower than exponents observed in previous studies of the effect of (q/T) on stress concentration factors for welded joints with various geometries [29–31]. These previous studies, however, were concerned with the elastic stress concentration factor, Kt, rather than the fatigue stress concentration factor, Kf, which is conceptually closer to Eqs. (9) and (10). The value Kt is related to the peak stress at the surface of a notch while Eq. (9) relates to the stress and stress gradient just below the surface. The good agreement between analytical and experimental observed relations indicates that the important features of the process have been captured.
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4.4. Relation between the Paris law and equivalent structural stress Based on the left-hand portion of Eq. (6) and with m = 3, the Paris law coefficient Cmean = 1.7 1013 leads to a mean value of the equivalent structural stress range, Dr*, equal to 143.3 MPa mm1/6 at Nf = 2 106 cycles. Note that this value is independent of the crack shape, initial crack depth or joint type because it is based solely on the crack growth rate coefficient. Using the right-hand portion of Eq. (6), an assumed semi-elliptical toe crack with xi = 0.05 mm gives a mean value of Dr* = 141.4 MPa mm1/6 for the published experimental data. This practically coincides to the LEFM based value of Dr* = 143.3 MPa mm1/6. The scatter in Fig. 9b is large, but the characteristic Dr*–N curve of the experimental data is in good agreement with the characteristic Dr*–N curve obtained from Eq. (6), if Cchar = 5.21 1013 recommended by IIW [8] is used. On the basis of the experimental fatigue lives of welded cruciform joints seen in Fig. 6b, Cchar = 1/(1.97 1012) = 5.08 1013 is computed. This value nearly coincides with Cchar recommended by IIW. If the LUT-results [5] are ignored and an initial semi-elliptical toe crack with depth of 0.05 mm is assumed, the computed mean equivalent structural stress range, Dr*, for the experimental data is still near the value 143.3 MPa mm1/6 [2–4]. In this case, however, the predicted characteristic Dr*–N line corresponds to a crack growth coefficient Cchar = 3.0 1013. This is the value proposed by the previous IIW recommendations [32]. In other words, the addition of the LUT data slightly increases the observed scatter in the calculations. It is interesting to note that, for the cases single- or double-edge cracked plates in tension, Dr . Dr* when xi = 0.05 mm and Dr is only slightly dependent on plate width. The resulting fatigue strength is FAT 99 if Cchar = 5.21 1013 is used. This FAT-value is virtually identical to the fatigue strength, FAT 100, of manually thermally cut plate edges recommended by IIW which has been determined by statistical evaluation of a large experimental data base [6]. Therefore, the simple cases of single- or double-edge cracked plates in tension with xi = 0.05 mm further verify the usefulness of the proposed Dr–N curve.
5. Conclusions The influence of local geometric parameters on the fatigue strength of non-load-carrying cruciform fillet welded joint under tensile loading has been studied using linear elastic fracture mechanics calculations and based on previously reported experimental fatigue data. The primary goal has been to use both experimental data and analytical methods to develop an equation relating the geometric parameters to the fatigue strength which can be used is routine design assessment. On the basis of theoretical calculations and comparisons between predictions and experimental results, the following conclusions can be made: (1) Local geometrical variations of the weld and weld throat size have only a small effect on the fatigue strength, if the depth of an initial toe crack is greater than 0.2 mm. As the depth of the initial toe crack increases, the local geometrical effects disappear. (2) The effect of weld angle on the fatigue strength is small when the toe radius is large. For high quality welds, the weld toe radii should be large and the initial crack depth should be very small. According to this study the fatigue strength of joints with large toe radii increases approximately 20– 40% as the initial crack depth decreases from 0.2 mm to 0.05 mm.
(3) If the stress term is presented using the equivalent structural stress range, Dr*, and Cmean = 1.7 1013 is used in Eq. (6), the best fit between predicted and experimental mean fatigue strengths is achieved when an initial semi-elliptical toe crack with depth of 0.05 mm is assumed. (4) If the experimental data is presented using equivalent structural stress range, Dr*, the characteristic Dr*–N curve corresponds to the characteristic Paris law coefficient, Cchar = 1/ (1.97 1012) = 5.08 1013. This is very close to the value recommended by IIW. (5) If the predicted and experimental fatigue strengths at 2 106 cycles (m = 3) are drawn as a function of q/T, the corresponding fitted curves, Eq. (9) and (10) are almost identical, when an initial semi-elliptical toe crack with depth of 0.05 mm is assumed. The results are based on 152 experimental data points. Predicted: q0:125 Drmean ¼ 159:9 T q when P 0:02 T
and
q0:125 Drchar ¼ 110:1 T ð9aÞ
Experimental: q0:12 Drmean ¼ 156:3 T q when P 0:02 T
and
q0:12 Drchar ¼ 107:3 T ð10aÞ
Acknowledgements This study was a part of the weld quality project ‘‘LAATU” which was carried out in the Laboratory of Fatigue and Strength at Lappeenranta University of Technology. The support of Metso Paper Inc., Andritz Oy, KCI Konecranes Oyj, John Deere Forestry Oy, Ruukki, VR, Wärtsilä, Auramo, Ponsse, Bronto Skylift Oy, Stalatube Oy and the National Technology Agency of Finland, are greatly appreciated. Prof. Luca Susmel and the co-editors are thanked for the invitation to contribute to this special publication. References [1] Maddox SJ. Fatigue strength of welded structures. Cambridge: Abington; 1991. [2] Nykänen T, Li X, Björk T, Marquis G. A parametric fracture mechanics study of welded joints with toe cracks and lack of penetration. Eng Fract Mech 2005;72:1580–609. [3] Nykänen T, Marquis G, Björk T. Fatigue analysis of non-load-carrying fillet welded cruciform joints. Eng Fract Mech 2007;74(3):399–415. [4] Nykänen T, Marquis G, Björk T. Effect of local geometrical variations on the fatigue strength of fillet welded joints. In: Proceedings of the IX finnish mechanics days, Lappeenranta University of Technology, Finland; 2006. p. 359–77. [5] Nykänen T, Marquis G, Björk T. Effect of weld geometry on the fatigue strength of fillet welded cruciform joints.In: Marquis G, Samuelsson J, Agerskov H, Haagensen PJ, editors. Proceedings of the international symposium on integrated design and manufacturing of welded structures, March 13–14, 2007. Sweden: Eskilstuna; March 2007. p. 23. ISBN: 978-952-214-363-1, ISSN: 1459-2924. [6] Lazzarin P, Tovo R. A notch intensity factor approach to the stress analysis of welds. Fatigue Fract Eng Mater Struct 1998;21:1089–103. [7] Atzori B, Meneghetti G, Susmel L. Estimation of the fatigue strength of light alloy welds by an equivalent notch stress analysis. Int J Fatigue 2002;24(5): 591–9. [8] Hobbacher A, Recommendations for fatigue design of welded joints and components. International Institute of Welding, XIII-2151-07/XV-1254-07, Paris; 2007. [9] EC3 (2002c). prEN 1993-1-8. Eurocode 3: design of steel structures. Part 1–8, design of joints (draft 26 February 2002). [10] Verreman Y, Limodin N. Fatigue notch factor and short crack propagation. Eng Fract Mech 2008;75(6):1320–35. [11] Maddox SJ. Int J Fract 1975;11:221–43. [12] Brown WF, Srawley JE. Plane strain crack toughness testing of high strength metallic materials. West Conshohocken, PA: ASTM STP 410, ASTM; 1966.
T. Nykänen et al. / International Journal of Fatigue 31 (2009) 79–87 [13] Newman JC, Raju IS. Stress-intensity factor equations for cracks in threedimensional finite bodies. Fracture mechanics. Springer; 1983. [14] Paris PC, Erdogan F. A critical analysis of crack propagation laws. J Basic Eng 1963;85:528–34. [15] VTT Symposium 100. Fatigue design of structures. Technical Research Centre of Finland (VTT), Finland; 1989 (in Finnish). [16] Dong P, Hong JK, et al. Life predictions using mesh-insensitive structural stress method. Fatigue design and evaluation committee of the SAE, spring 2003 meeting, April 15–16, 2003. Hosted by Caterpillar in Peoria, Illinois. http:// www.fatigue.org/Minutes/Spring-2003/contents.html. [17] Gurney TR. Fatigue of welded structures. Cambridge: Cambridge University Press; 1979. [18] Pang HLJ. A review of stress intensity factors for semi-elliptical surface crack in a plate and fillet welded joint. The Welding Institute, Cambridge, England: Abington Publishing; 1990. [19] Engesvik KM, Moan T. Probabilistic analysis of the uncertainty in the fatigue capacity of welded joints. Eng Fract Mech 1983;18(4):743–62. [20] NIMS 1979. Data sheets on fatigue properties of non-load-carrying cruciform welded joints of SM50B rolled steel for welded structure. Effect of specimen size. http://tsuge.nims.go.jp/. [21] NIMS 1980. Data sheets on fatigue properties for non-load-carrying cruciform welded joints of SM50B rolled steel for welded structure. Effect of welding procedure. http://tsuge.nims.go.jp/. [22] Branco CM, Maddox SJ, Infante V, Gomes EC. Fatigue performance of tungsten inert gas (TIG) and plasma welds in thin sections. Int J Fatigue 1999;21: 587–601.
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[23] Lindqvist J. Fatigue strengths thickness dependence in welded constructions. Master thesis. Borlänge, Sweden; 2002. http://hem.passagen.se/johanlindq/ Exjobb.pdf. [24] Kuhlmann U et al. Erhöhung der Ermüdungsfestigkeit von geschweißten höherfesten Baustählen durch Anwendung von Nachbehandlungsverfaren. Stahlbau, Stahlbau, 2005;74: H. 5, S. 358–65. [25] Couweleers F, Skotheim Ø, Tveiten BW. Presented at 8th international symposium on measurement and quality control in production, October 2004. Erlangen, Germany. [26] Nieminen T. Non-destructive measurement of weld surface geometries. MS thesis. Lappeenranta University of Technology, Lappeenranta, Finland; 2006 (in Finnish). [27] Labesse F, Recho N. Geometrical stress level at the weld toe and associated local effects. Weld World 1999;43(1):23–32. [28] Poutiainen I, Marquis G. A fatigue assessment method based on weld stress. Int J Fatigue 2006;28(9):1037–46. [29] Radaj D, Zhang. Multiparameter design optimisation in respect of stress concentrations. Engineering optimisation in design processes. Berlin: Springer; 1991. p. 181–9. [30] Niu X, Glinka G. The weld profile effect on the stress intensity factors in weldments. Int J Fract 1987;35:3–20. [31] Yung JY, Lawrence FV. Analytical and graphical aids for the fatigue design of weldments. Fatigue Fract Eng Mat Struct 1985;8(3):223–41. [32] Hobbacher A. Recommendations for fatigue design of welded joints and components. Cambridge: Abington Publishing; 1996.