The aim of this paper is to investigate the effects of weld toe grinding and weld profiling on the fatigue strength of welded joints and the main influencing factors. Thus, experimental test results of welds improved by different grinding techniques are reviewed. In total, 445 small- and full-scale fatigue test results of various weld types and steel grades with yield strengths up to 1100 MPa are analysed. The obtained improvements of two FAT classes correspond well with current guidelines; however, a new S–N curve slope of m = 4 is recommended—in line with proposals for other weld geometry improvement techniques. Keywords: post-weld treatment; fatigue strength improvement; weld toe grinding; high-strength steel; burr grinding 1 Introduction Welding is a widely used method to join steel plates. Due to the solidification of weld material, sharp notches at weld toes are created that decrease the fatigue strength compared to the parent material. The main reason is that local stress concentration and tensile residual stress occur at weld toes, which are the main driving factors for fatigue cracks. Thus, attempts to improve the fatigue strength of welded joints are either based on weld geometry improvement or on altering of the residual stress state at the weld toes [1], see Fig. 1 for an overview of available of post-weld improvement techniques. Weld geometry techniques reduce the stress concentrations by smoothing the weld toe transition and removing possible welding defects, while residual stress methods alter tensile welding residual stresses or introduce compressive stresses. In recent years, methods that alter residual stress states at weld toes have been addressed in many research projects and in the industry [2-4]; however, weld geometry improvement techniques are still widely applied and within the focus of R&D activities as well [5-9]. Recently, a statistical assessments of high frequency impact treatment (HFMI) and tungsten inert gas (TIG) dressing were performed by Yıldırım and Marquis [10], and Yıldırım [9] in order to improve the fatigue assessment © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ of post-weld treated welded joints. Although grinding is one of the oldest and most applied post-weld improvement techniques in many industries, no such assessment exists for weld toe ground and weld profiled joints. Thus, the aim of this paper is to investigate the effect of both techniques on the fatigue strength and the main influencing factors (weld details, steel strength, stress ratio etc.) in more detail. For this purpose, we collected 445 fatigue test results from different 33 publications—including butt-welded joints, longitudinal welds, doubling plates, load-carrying transverse, non-load carrying transverse welded steel joints, as well as I-section with cope holes, and longitudinal gusset plates. Moreover, fatigue test data of weld toe ground specimens with various yield strength and stress ratio are analyzed and evaluated. This study focuses exclusively on steel welded joints, since data on ground aluminum joints is limited; however, since Ye and Moan [11] obtained a fatigue strength improvement for aluminum joints similar to existing recommendations for steel, a transferability of the outcome of this study is probable. At first, a general description of weld geometry improvement techniques and in particular weld toe grinding is given in Section 2. Section 3 serves to explain the assessment procedure for the obtained data on fatigue strength improvement by means of weld toe grinding and weld profiling. Subsequently, the results are presented and discussed in Section 4 and 5, respectively, and compared with current design guidelines in Section 6. Fig. 1. Overview of post-weld improvement techniques based on Marquis and Barsoum [3] 2 State-of-the-art 2.1 Weld geometry improvement techniques and influencing factors Among all post-weld improvement techniques, grinding is a widely applied technique to alter local stress concentrations at weld toes and to remove possible welding defects in order to increase the fatigue strength of welded joints; however, it is also frequently applied as a repair method after crack detection. Most of the existing Special weldingtechniquesMachiningRemeltingWeld geometryimprovement ThermalOverloadingPeeningResidual stressstateGrinding flushWeld toe grindingDisc grindingBurr grindingWaterjet erodingWeld profiling © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ literature focuses on weld toe grinding by means of burr grinding; however, studies from Clegg et al. [12], Mecséri and Kövesdi [13], Booth [14], and Knight [15] have shown the benefits of disc grinding and weld profiling as an alternative to burr grinding. The difference between weld toe grinding and weld profiling is that for the latter, the full weld is ground (not only the weld toe). Apart from that, the equipment and procedure is basically the same, see Fig. 2. Fig. 2. Basic principle of weld toe grinding and weld profiling, including grinding depth recommendations by Haagensen and Maddox [1] (a) and equipment typically applied for grinding (b) There are many parameters that may influence the effectiveness of grinding and that should be considered within the assessment of post-weld improved welded joints, see Kirkhope et al. [16, 17] for an extensive summary. Unsurprisingly, the radius after grinding has a major influence on the fatigue strength improvement, see Uchida et al. [18]. Furthermore, the plate thickness is expected to affects the fatigue strength improvement after grinding, see Mecséri and Kövesdi [13] and Hanzawa et al. [19]. In both studies, a higher fatigue strength after grinding was measured for the thicker steel plates; however, the number of performed tests is too small to draw conclusions from these comparisons. Grinding is often applied for maritime structures. Thus, Booth [14], Matsumoto [20], and Baptista et al. [21] studied the effectiveness of burr grinding on the fatigue strength under the influence of corrosive media. Finally, Knight [15] and Braun et al. [22] performed tests with different steel types to explore the influence of parent material strength on the effectiveness of weld toe grinding and weld profiling. Similar to other post-weld treatment methods, a positive effect of parent material strength on fatigue strength was observed. 2.2 Equipment for weld toe grinding and weld profiling The aim of grinding welds is to remove crack-like defects at the weld toe, from where fatigue cracks originate, and to increase the weld toe radii by smoothening the transition between the base plate and the weld face, which reduces the stress concentration at the weld toe and thereby improves fatigue strength, see Fig. 3. Disc grinder(b)Burr grinder Depth of grinding should be at least 0.5 mm, but 2 mm or 7% of plate thickness at max.Weld toe grindingWeld profiling(a) © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Fig. 3. Micrographs of welded joint in as-welded (a) and burr ground (b) state (as-welded micrograph taken from Braun et al. [23]); scale in millimeters For burr grinding, it is possible to use high speed pneumatic, hydraulic, or electric grinders with hemispherical tool bits, often made of tungsten carbide. Moreover, the size of the tool should scale with the plate thickness t, and the resulting diameter should be no less than 0.25t [1]. Alternatively, bonded or coated abrasives may be used for disc grinding and CNC tools for weld profiling. 2.3 Effect of weld toe grinding and weld profiling on fatigue strength of joints First of all, it is worth mentioning that the quality of grinding depends on the skills of the operator. Thus, design codes and the International Institute of Welding (IIW) recommendations [1, 24] account for poor workmanship and possibly low fatigue strength improvement after grinding. Consequently, the improvement of weld toe grinding and weld profiling is limited to fatigue design classes with a reference fatigue strength (FAT class) of FAT 90 or lower in accordance with the IIW recommendations [1]. Higher classes include already improved details and un-welded structural details. Thus, fatigue strength is not exclusively defined by weld toe failure. It is worth mentioning that improvement is limited to cases were fatigue cracking is expected to originate from weld toes. In some cases, grinding may lead to cracks initiating at weld roots. Thus, a separate assessment is required for welds with incomplete penetration [1]. An increase factor of 1.3 on stress range (corresponding to 2.2 on life, based on a S–N curve slope m = 3) is granted tor weld details, with FAT 90 or lower classes. The highest class that can be reached is the closest class below the FAT value obtained by multiplying the as-welded FAT value by 1.3, which roughly corresponds to an increase of two FAT classes. For steel welds, the highest class that can be claimed for ground welds is FAT 112, which corresponds to an increase of two FAT class relative to the highest detail class FAT 90. Towards the low cycle region, all S–N curves are limited by the design S–N curve for the parent material FAT 160 with a slope of m = 5 for steel. [1] Interestingly, in DNVGL-RP-005 [25] and BS 7806 [26] an improvement in fatigue strength by grinding is granted by changing the !–# curve slope to m = 3.5, but otherwise the same improvement factor (1.3) is used. This results in a smaller change in fatigue strength towards the low cycle fatigue regime but a larger increase for #>2×10!. © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ 3 Background on statistical assessment of fatigue data on ground welds and comparison with the as-welded state Statistical methods are widely used to evaluate the experimental test data in order to characterize fatigue strength and to predict the performance of engineering structures. For different applications—such as bridges, offshore structures, and ships—the most efficient and reliable post-weld improvement method should be selected considering feasibility and fabrication costs. Post-weld improvement methods are often chosen based on comparisons of S–N curves derived from tests with small-scale fatigue test specimens; however, in order to ensure generality of conclusions, large data sets are required. In order to avoid biased conclusions based on small data sets, statistical analysis of test data collected from various literature sources is a well-accepted approach to improve design recommendations, see [9, 10]. 3.1 Data obtained from literature study In this study, fatigue test results obtained from 33 studies concerning fatigue strength improvement by weld toe grinding and weld profiling are analyzed. The fatigue data sets include the treatment by means of disc and burr grinding as well as weld profiling. In total, 445 fatigue test results from 69 data sets were evaluated. Except for a few studies using transverse load-carrying welds, the majority of fatigue test data was obtained under axial loading. Moreover, most tests were performed under constant amplitude loading—except for Tai and Miki [27], who transformed the variable amplitude loading test results into equivalent constant amplitude stress ranges. The yield strength of the parent material ranges from 235 to 1100 MPa, and thickness varies between 5 to 40 mm. In a study by Kliman et al. [28], butt joints between circular solid section (steel rods) with diameter of 16mm were used. In some studies, grinding leads to fracture originating from the weld roots after grinding; however, only specimens with fracture originating from ground weld toes are taken into account in the statistical assessment of this study. 3.2 Statistical assessment of obtained fatigue test results The statistical assessment follows the recommended IIW practice [24, 29]. This procedure is found to be more reliable than other assessment procedures [30], especially for tests with small sample size and data sets without varying load level or small variance of stress ranges during the tests. After excluding run-outs, the two parameters of the S–N curve—slope m and intercept log C—as well as a 95% prediction bound (resulting in a survival probability of Ps = 97.5%) can be calculated by the following procedure. Here, the notation of the IIW recommendations is applied to calculate S–N curves in the form: (1) For as-welded steel joints, a fixed slope exponent m = 3 is recommended if the number of sample size is small (i.e. number of specimens n < 10), or if the data are not sufficiently spread to determine m exactly [24]. In this study, a slope m = 3 will be used for as-welded data, and a best-fit slope m will be calculated from the data of ground specimens in order to analyze the most suitable slope m to be recommended for welded joints improved by grinding. Since the IIW recommendations are based on the assumption of a fixed slope exponent m = 3, the best fit slope and standard deviation of the slope are calculated according to recommendations by the German Welding log#=log-−/log∆1 © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Association for the assessment of fatigue test data [31]. From linear regression of the logarithm of the fatigue life 2=log# and the applied stress range 3=log∆1, the slope exponent / is obtained by: (2) Test results for a number of cycles to failure larger than the knee point typically assumed for small-scale specimens (#"=2×10!) are not included in the calculation due to the lack of data to sufficiently determine the actual knee point of each data set. A maximum likelihood approach might be applied for a statistical assessment of the knee point; however, this requires a small standard deviation of test results and data that spans a large range of cycles to failure, see Baumgartner et al. [32] for an extensive discussion. All of the data sets assessed in this study were too small to fulfil these two requirements. Thus, the typically assumed knee point for small-scale specimens was applied in this study. Based on the estimate of the slope m, the intercept corresponding to stress range of ∆1 = 1 MPa, 5#=log-# can be estimated with: (3) The mean value of log-=5$ is then obtained from: (4) and the standard deviation of the intercept 6789(log-) of log- with: (5) Finally, the standard deviation of the slope exponent 6789(/) is obtained with: (6) For design purposes, the characteristic value xk (corresponding to 97.5% survival probability) is determined from Eq. (7): (7) where parameter k is obtained by using Eq. (8): (8) Thus, the 95% confidence bands for the mean S–N curve can be computed by inserting Eq. (7) in Eq. (1): (9) 5#=log2−/log3 6789(/)=6789(log-)<∑3%−(∑3)%> 6789(log-)=?∑(5$−5#)%n−1 / = ∑32 − ∑3·∑2>∑3% − (∑3)%> log-=5$=B5#> 5&=5$−C∙6789(log-) C=1.645I1+1√>L log#=(5$±C∙6789(log-))−/∙log∆1 © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ For further details, see Hobbacher and Lefebrve et al. [24, 29]. Using the aforementioned assessment procedure, test results of data obtained from Huther et al. [33] are presented in Fig. 4 to illustrate the chosen assessment procedure. Fig. 4. Fatigue data of Huther et al. [33]-5 assessed by the IIW statistical assessment practice but applying a free slope exponent m 3.3 Mean fatigue strength of as-welded joints Instead of using Eq. (1), fatigue strength of as-welded joints is often simply stated by the reference fatigue strength (FAT class) corresponding to stress range by 97.5% survival probability at #"=2×10! cycles of failure ∆σ97.5%; however, in order to calculate the mean increase in fatigue strength after grinding the stress ranges for 50% survival probability at #"=2×10! cycles of failure ∆σ50% are used in this study. This is due to the higher reliability of correctly estimating the mean fatigue strength of small data sets. According to Fricke [34], ∆σ50% for as-welded specimens can be calculated assuming a standard deviation 6789(log-)=0.0687, which corresponds to a standard deviation of 6789(-)=0.206 for a slope m = 3. Thus, the mean fatigue strength is calculated from (10) Table 1 gives an overview of the mean and FAT classes according to the IIW recommendations [24] prior and after grinding for all specimen geometries considered in this study. Table 1. Weld details with FAT classes for as-welded steel joints, corresponding mean fatigue strength, and FAT classes after grinding according to the IIW [24] Type of welds Description FAT class for as-welded Assumed mean fatigue strength (survival probability FAT class after grinding 104105106107Cycles to failure Nf50100200500Nominal stress range nom [MPa] Mean curve95% ConfidencebandS355 steel run-outR = 0.5Huther et al. (2005) Methodm ± stdv(m)Burr grinding 3.38 ± 0.33 162.8 MPa 141.9 MPaΔσR,50%ΔσR,97.5% ∆1'(%=∆1*+.'%×1.366 © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ recommended by the IIW [24] of 50%) based on Eq. (10) according to the IIW [24] Transverse butt welds 90 123 112 Longitudinal fillet welded gusset of length L < 150 mm L < 300 mm 71 63 97 86 90 80 Doubling plates 50 mm < L ≤ 150 mm 71 97 90 Transverse load-carrying welds 71 97 90 Transverse non-load-carrying welds 80 110 100 Longitudinal butt weld, fillet weld or intermittent weld (I-section) with cope holes 50 68 63 Longitudinal gusset plates with L < 150 mm 50 68 63 © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ 4 Effect of weld toe grinding and weld profiling on fatigue strength of joints 4.1 Calculation of S-N curve slope exponent Recent studies have found a change of slope exponent after applying different post-weld improvement techniques to welded joints (see [9, 10]). Thus, in a first assessment step, the best-fit slope and standard deviation of each data set obtained from literature are calculated based on the aforementioned procedure. The results for butt joints, longitudinal attachments, doubling plates, transverse load-carrying welds, and transverse non-load-carrying welds are shown in Fig. 5 for different numbers of test specimens n. The slopes for I-section with cope hole and longitudinal gusset plate test specimens cannot be calculated due to a lack of fatigue data and tests performed for the same stress range. For comparison, Fig. 5 represents the S–N slope m = 3 (currently recommended for welded joints treated by burr grinding and similar processes) and the median value of all slopes with horizonal lines. A possible explanation for the large range of obtained values of best-fit-slopes could be a small variation in applied stress range in the fatigue tests and the generally small number of less than 10 test specimens in most studies. Due to the aforementioned reasons, it was not possible to determine a best-fit slope for some of the data sets. In order to assess whether the number of specimens per study had an influence on the obtained slope exponent, Pearson correlation coefficients r and probability value p are computed. The probability value p is a measure for the statistical significance of the obtained correlation coefficient. Applying a typical significance threshold of 5%, a p-value below 0.05 means that the obtained result is statistically significant and the null hypothesis (there is no correlation or relationship) has to be rejected. It is important to note that the sample sizes of this study—as for most fatigue studies—are rather small. Thus, these two values should be treated with caution. In order to avoid a biased decision on which sample size is sufficient to calculate r and p, they have been computed for each comparison in Fig. 5. © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Fig. 5. Calculation of median slope exponent m for ground welded joints based on number of specimens and weld detail As expected, the standard deviation of the slope exponent 6789(log-) generally decreases with increasing specimen number; however, there is no evidence of a correlation between specimen number per study and the slope exponent. Furthermore, as depicted in Fig. 5, m = 3 is below the best-fit slope of the majority of data sets and the median slope for most joint types—with the only exception of transverse load-carrying joints. (a) Butt joints (b) Longitudinal attachments (c) Doubling plates (d) Transverse load-carrying welds (e) Transverse non-load-carrying welds0 2 4 6 8 10 12 14 16Numbers of specimens in data series n05101520Slope mr = 0.66 p = 0.34S350 R=0 (Clegg et al., 2013)S350 R=0 (Clegg et al., 2013)Grade A R=-1 (Kim et al., 2006)YS=430MPa R=0.1(Lotsberg et al., 2014)m=3Median of m=5.760 2 4 6 8 10 12 14 16Numbers of specimens in data series n05101520Slope mr = -0.74 p = 0.09S355J2C+C R=-1 (Kliman et al., 2014S355 R=0.5 (Huther et al., 2005)S355 R=0.5 (Huther et al., 2005)DOMEX 600 R=0 (Costa et al., 2010)HT50A R=0 (Hanzawa et al., 1977)HT50B R=0 (Hanzawa et al., 1977)m=3Median of m=6.83 0 2 4 6 8 10 12 14 16Numbers of specimens in data series n05101520Slope mr = 0.84 p = 0.07(Booth, 1978)(Booth, 1978)YS=764MPa R=0 (Matsumoto, 1999) YS=272MPa R=0 (Matsumoto, 1999)A515 R=0 (Dickerson and Branco, 1994)m=3Median of m=2.95 0 5 10 15 20 25Numbers of specimens in data series n05101520Slope mr = -0.02 p = 0.92S700 R=0.1 (Pedersen et al., 2009 )A36 R=0 (Mendez et al., 2017)A36 R=0 (Mendez et al., 2017)Low carbon micro alloyed R=0.1(Haagensen, 1993)S420 R=0 (Miki et al., 1999)S355 R=0.5 A (Huther et al., 2001)S355 R=0.5 B (Huther et al., 2001)S355 R=0.5 C (Huther et al., 2001)S355 R=0.5 D (Huther et al., 2001)DH36 R=0.1 (Polezhayeva et al., 2009)DH36 R=0.1 (Gao et al., 2015)S355 R=0.1 (Zhang and Maddox, 2009)Grade A R=0.1 (Rutherford et al., 2006)S700 R=0.2 (Lieurade et al., 2005)S275 R=0 (Hansen et al., 2007)304L R=0.1 (Baptista et al., 2007)S31803 R=0.1 (Baptista et al., 2007)S31803 R=0.1 (Baptista et al., 2007)Grade 43A R=-1 (Booth, 1981)Grade 43A R=0.5 (Booth, 1981)Grade 43A R=0 (Knight, 1976)Grade 43A R=0 (Knight, 1976)Grade 43A R=0 (Knight, 1976)Supereiso70 R=0 (Knight, 1976)Supereiso70 R=0 (Knight, 1976)Supereiso70 R=0 (Knight, 1976)BS15 R=-1 (Gurney, 1968)S355 R=0 (Braun et al., 2020)F51 R=0 (Braun et al., 2020)S690 R=0 (Braun et al., 2020)S900 R=0 (Braun et al., 2018)SUS316L R=0.1 (Iwata et al., 2006)m=3Median of m=3.900 2 4 6 8 10 12 14 16Numbers of specimens in data series n05101520Slope mr = -0.11 p = 0.71S500 R=-1 (Tai and Miki, 2012)S690QL R=0.1 (Weich, 2008)Grade A R=-1 (Kim et al., 2006)BS15 R=-1 (Gurney, 1968)BS968 R=0(Gurney, 1968)S690,S960,S1100 R=0.2 (Puthli et al. 2006)S690,S960,S1100 R=0.2 (Puthli et al. 2006)SM490YA R=0 (Uchida et al., 2016)SM490YA R=0 (Uchida et al., 2016)SM490YA R=0 (Uchida et al., 2016)SM490YA R=0 (Uchida et al., 2016)SM490YA R=0 (Uchida et al., 2016)SM490YA R=0 (Uchida et al., 2016)m=3Median of m=4.03 © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ An unweighted median slope of m = 4.13 is calculated based on the best-fit slopes of all data sets (not separated according to weld detail). The benefit of the median over the mean is that it is less sensitive to being skewed by extreme results (outliers), e.g. very large or small calculated slopes due to small sample sizes. Thus, no weighting according to sample size is required. The so-obtained median slope agrees well with the expectation of shallower S–N curve slopes for mild notches as compared to sharp notches at weld toes. Moreover, results of studies on fatigue assessment of ground fillet welded joints by Ahola et al. [5] and weld geometry improvement by means of TIG-dressing by Yıldırım [9] found similar slopes. Moreover, the obtained slope is higher than the recommendation by DNVGL-RP-005 [25] and BS 7806 [26] of m = 3.5, but below slope exponents obtained for residual stress state altering techniques [3]. 4.2 Influencing factors on slope exponent for ground welded joints Based on the large amount of available fatigue data for transverse non-load-carrying welds, Fig. 6 shows the results for S–N slope estimates grouped by parent material yield strength. No correlation between median slope m and yield strength is observed within the three assessed yield strength ranges (if data for S900 from Braun et al. [35] is considered an outlier due to the apparently underestimated slope exponent m of this data set); however, a slight increase of the median slope is obtained if the three median slopes are compared. Clearly, more tests are needed to analyze the effect of yield strength on the slope of S–N curves. © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Fig. 6. Calculation of median slope exponent m for transverse non-load-carrying welds improved by weld toe grinding and weld profiling based on parent material yield strength 1YS It is often assumed that small-scale test specimens behave differently than full-scale structures or, in general, larger test specimens. Thus, the effect of plate thickness t on the slope exponent was analyzed next. As can be seen from Fig. 7, no correlation between plate thickness and slope was obtained for the transverse non-load-carrying welded joints. (b) 460< σYS < 690 MPa (c) 690 < σYS < 980 MPa (a) 235 < σYS < 460 MPa 690 725 760 795 830 865 900 940 980Parent material yield strength YS [MPa]05101520Slope mr = -0.95 p = 0.05S700 R=0.1 n=11 (Pedersen et al., 2009)S700 R=0.2 n=8 (Lieurade et al., 2005)S690 R=0 n=21 (Braun et al., 2020)S900 R=0 n=11 (Braun et al., 2018)m=3Median of m=4.26 460 500 540 580 620 660 690Parent material yield strength YS [MPa]05101520Slope mr = -0.14 p = 0.79S31803 R=0.1 n=8 (Baptista et al., 2007)S31803 R=0.1 n=8 (Baptista et al., 2007)Supereiso70 R=0 n=3 (Knight, 1976)Supereiso70 R=0 n=3 (Knight, 1976)Supereiso70 R=0 n=3 (Knight, 1976)F51 R=0 n=17 (Braun et al., 2020)m=3Median of m=4.07235 275 315 355 395 435 460Parent material yield strength YS [MPa]05101520Slope mr = -0.11 p = 0.62A36 R=0 n=4 (Mendez et al., 2017)A36 R=0 n=4 (Mendez et al., 2017)Grade A R=-1 n=10 (Kim et al., 2006)Low carbon micro alloyed R=0.1 n=6 (Haagensen, 1993)YS=420 R=0 n=5 (Miki et al., 1999)S355 R=0.5 A n=3 (Huther et al., 2001)S355 R=0.5 B n=12 (Huther et al., 2001)S355 R=0.5 C n=11 (Huther et al., 2001)S235 R=0.5 D n=8 (Huther et al., 2001)DH36 R=0.1 n=5 (Polezhayeva et al., 2009)DH36 R=0.1 n=10 (Gao et al., 2015 )S355 R=0.1 n=2 (Zhang and Maddox ,2009)Grade A R=0.1 n=7 (Rutherford et al., 2006)S275 R=0 n=5 (Hansen et al., 2007)304L R=0.1 n=3 (Baptista et al., 2007)Grade 43A R=-1 n=5 (Booth, 1981)Grade 43A R=0.5 n=4 (Booth, 1981)Grade 43A R=0 n=5 (Knight, 1976)Grade 43A R=0 n=6 (Knight, 1976)Grade 43A R=0 n=9 (Knight, 1976)BS15 R=-1 n=4 (Gurney, 1968)S355 R=0 n=15 (Braun et al., 2020)SUS316L R=0.1 n=7 (Iwata et al., 2006)m=3Median of m=3.45 © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Fig. 7. Assessment of specimen thickness effect on slope exponent m of transverse non-load-carrying welded joints improved by weld toe grinding and weld profiling Finally, the effect of the grinding techniques is assessed by comparing the distributions of slope exponents obtained for each method. Compared to the number of studies on burr grinding, there is not much data on disc grinding and weld profiling. The results are therefore presented as boxplots, showing the median values and scatter of slope exponents in Fig. 8. Interestingly, the highest median slope exponent (/Q) is obtained for the test series treated by disc grinding, and the lowest for the joints treated by weld profiling. Comparing the surface roughness for these methods, the opposite results would have been predicted; however, the number of test series and the scatter of the estimated slope exponents is too large to draw reliable conclusions from this comparison. Again, more tests are required to analyze the effect of grinding methods on the slope exponent. Fig. 8. Comparison of grinding method effect on obtained slope exponent m. The median values are above the boxplots (/Q), which were created with a default setting, i.e. the maximum whiskers length equals 1.5 times interquartile range. In order to allow for an easy comparison between different weld geometry improvement methods and the as-welded state, all subsequent comparisons of fatigue strength improvement are given for a fixed slope exponent of m = 4 (rounded median slope) and m = 3, apart from the assessment results obtained for a free slope exponent. 0 5 10 15 20 25 30 35 40 45Plate thickness t [mm]05101520Slope mr = 0.05 p = 0.78S700 R=0.1 (Pedersen et al., 2009 )A36 R=0 (Mendez et al., 2017)A36 R=0 (Mendez et al., 2017)Low carbon micro alloyed R=0.1 (Haagensen, 1993)S420 R=0 (Miki et al., 1999)S355 R=0.5 A (Huther et al., 2001)S355 R=0.5 B (Huther et al., 2001)S355 R=0.5 C (Huther et al., 2001)S355 R=0.5 D (Huther et al., 2001)DH36 R=0.1 (Polezhayeva et al., 2009)DH36 R=0.1 (Gao et al., 2015)S355 R=0.1 (Zhang and Maddox, 2009)Grade A R=0.1 (Rutherford et al., 2006)S700 R=0.2 (Lieurade et al., 2005)S275 R=0 (Hansen et al., 2007)304L R=0.1 (Baptista et al., 2007)S31803 R=0.1 (Baptista et al., 2007)S31803 R=0.1 (Baptista et al., 2007)Grade 43A R=-1 (Booth, 1981)Grade 43A R=0.5 (Booth, 1981)Grade 43A R=0 (Knight, 1976)Grade 43A R=0 (Knight, 1976)Grade 43A R=0 (Knight, 1976)Supereiso70 R=0 (Knight, 1976)Supereiso70 R=0 (Knight, 1976)Supereiso70 R=0 (Knight, 1976)BS15 R=-1 (Gurney, 1968)S355 R=0 (Braun et al., 2020)F51 R=0 (Braun et al., 2020)S690 R=0 (Braun et al., 2020)S900 R=0 (Braun et al., 2018)SUS316L R=0.1 (Iwata et al., 2006)m=3Median of m=3.90 05101520Slope mm = 4.0 m = 4.6 m = 3.8 Burr Disc Weldgrinding grinding profiling~~~ © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ 5 Comparison of endurable stresses between as-welded and ground specimens The results for all analyzed welding details improved by grinding are summarized in Tables 3 to 9. Results are given for the three mentioned slope exponents m1 (index 1 indicating # < 10+). As stated before, it was not possible to obtain results for a free slope exponent for all data sets. These data sets are commented in the tables. Moreover, in some studies, the yield stress of the specimens was not reported. Thus, the values corresponding to the minimum value according to the steel type are used to specify the yield stress. If the steel type was not stated in the studies, fields are marked with ‘-’ in Tables 3 to 9. For most data sets, the mean fatigue strength ∆σ50% after grinding assessed by a best-fit slope results in a positive fatigue strength improvement compared with mean fatigue strength for as-welded joints; however, in some cases the assessment yields a decrease in fatigue strength. The assessment with a fixed slope m1 = 4 leads to a higher fatigue strength increase compared to fixed slope m1 = 3 as one would expect. 5.1 Applied grinding technique and relevant process variations In the Tables 3 to 9, the specimens from