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Numerical assessment of fatigue design curve of welded T-joint improved by high-frequency mechanical impact (HFMI) treatment
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Numerical assessment of fatigue design curve of welded T-joint improved by high-frequency mechanical impact (HFMI) treatment Caiyan Deng a,b, Yaru Niu a,b, Baoming Gong a,b,∗, Yong Liu a,b, Dongpo Wang a,b a b
Department of Materials Science and Engineering, Tianjin University, Tianjin 300354, China Tianjin Key Laboratory of Advanced Joining Technology, Tianjin 300354, China
a r t i c l e
i n f o
Article history: Received 17 March 2017 Revised 3 May 2017 Accepted 28 June 2017 Available online xxx Keywords: Structural hot spot stress approach High frequency mechanical impact Fatigue design Thickness effect Material strength
a b s t r a c t In the paper, the fatigue performances of as-welded T-joint and T-joint improved by high frequency mechanical impact (HFMI) were numerically investigated using structural hot spot stress approaches: linear surface extrapolation (LSE) and through thickness at the weld toe (TTWT). The effects of main plate thickness and material strength for HFMI-treated joints were investigated. The results showed that the TTWT method was more effective to study the effect of thickness on T-joints improved by HFMI treatment than LSE method. For as-welded T-joints, the thickness correction exponent n = 0.04 was obtained when the attachment plate thickness was set as constant. For HFMI-treated T-joints, a reverse thickness effect was observed with negative thickness correction exponents, and the thickness correction exponents increased with material strength. In addition, the adoption of S–N slope varying with yield strength was proven to be more proper for HFMI improvement assessment. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction Welded structures subjected to cyclic loading are sensitive to fatigue damage, and fatigue crack tends to initiate from weld toe because of the local stress concentration and welding residual tensile stress. Recently, high-frequency mechanical impact (HFMI) treatment has been widely used as a post-weld treatment, which utilizes powerful energy to drive the needle to impact the object material at a high frequency. Therefore, the effectiveness of HFMI treatment is attributed to the smoothing of local stress concentration, refinement of microstructure and generation of local compressive residual stress at the weld toe [1–12]. Some works [13– 15] demonstrate that the improvement degree of HFMI treatment is better than commonly applied methods recommended by [16]. Previous studies [17–21] indicate that the fatigue performances of HFMI-treated welded joints are quite different from the aswelded ones. According to IIW [22], the slope value of S-N curves for welded joints of steel and aluminum is designated as m = 3, independent of material strength and stress range. However, the related works demonstrate that the slope value of S-N curve for post-weld treated joints is gentler than that of as-welded joints [17–19], and the degree of improvement varies with material
∗ Corresponding author at:. Tianjin Key Laboratory of Advanced Joining Technology, Department of Materials Science and Engineering, Tianjin University, Tianjin 300354, China. E-mail address: [email protected] (B. Gong).
strength [20]. The guidelines proposed by IIW [22] roughly adjusted the strength levels of specific joints. Recently, Yildirim and Marquis [18] provided an overview of 228 published data on fatigue performance of HFMI-treated joints and a new fatigue design recommendation was suggested that by choosing fy = 355 MPa as a reference, approximately 12.5% increase in fatigue strength for every 200 MPa increase in yield strength with an assumed S-N slope m = 5 for HFMI-treated welded joints. Wang et al. [19] also studied the effect of HFMI treatment on fatigue performances of welded joints, and reported that the slope values of S-N curves of HFMItreated joints may vary from 6.3 to 23 and m = 10 was thus proposed for fatigue design of UPT welded joints. Moreover, the thickness effect on HFMI-treated joints is not trivial. According to IIW [22], the effect of plate thickness on fatigue strength should be taken into consideration in cases fatigue crack initiates from weld toe. The thickness reduction factor f(t) for as-welded joints is given as follows:
f (t ) =
tre f te f f
n
(1)
where tref = 25 mm, n is the thickness correction exponent dependent on the effective thickness teff and the joint category. Numerous experiments of HFMI treatment, fatigue tests and residual stress measurements are both time-consuming and expensive, it is hard to obtain full measurement of stress field. Therefore, dynamic explicit finite element method (FEM) has been widely used to simulate the process of HFMI treatment [23–27]. Yang et
http://dx.doi.org/10.1016/j.advengsoft.2017.06.017 0965-9978/© 2017 Elsevier Ltd. All rights reserved.
Please cite this article as: C. Deng et al., Numerical assessment of fatigue design curve of welded T-joint improved by high-frequency mechanical impact (HFMI) treatment, Advances in Engineering Software (2017), http://dx.doi.org/10.1016/j.advengsoft.2017.06.017
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al [23]. investigated the fatigue performance of AISI304 stainless steel treated by ultrasonic impact treatment. The finite element model was established using Johnson-Cook material model to get the residual stress. Kuilin and Yoichi [26] numerically studied the effect of ultrasonic impact treatment on welded joints. A good agreement was observed between the predicted and measured results. The numerical simulation method has been proved to be an effective method, and the validity of numerical simulation method has been demonstrated [27]. Although noticeable progress on fatigue assessment of welded joints improved by post-weld treatment methods has been achieved, systematic investigation for different material strengths and thickness effects is still under development. In this paper, the numerical simulation method was adopted to study the fatigue performance of HFMI-treated fillet T-joint using structural hot spot stress approaches, i.e., linear surface extrapolation (LSE) and through thickness at the weld toe (TTWT). Four kinds of main plate thicknesses: 8 mm, 16 mm, 25 mm and 35 mm, were chosen to take the effect of main plate thickness into consideration. In addition, materials with different steel grades (20 steel, AISI 1006, 45 steel and AISI 2205) were employed due to the sensitivity of fatigue performance to material strength for HFMI-treated joints. At first, the process of HFMI treatment was simulated; Secondly, external load was applied to the HFMI-treated welded joints and the final stress fields were used to evaluate the structural hot spot stress. The aim of this work is to evaluate the thickness effect for HFMI-treated joints with different yield strengths using structural hot spot stress approaches.
Table 1 Constitutive model parameters. Material
A (MPa)
B (MPa)
C
p
q
20 steel AISI 1006 45 steel AISI 2205
258 350 507 622
329 275 320 785.25
0.0323 0.022 0.064 0.035
1.05 1.0 1.06 0.1515
0.235 0.36 0.28 0.5046
2.2. Johnson–Cook constitutive model In this article, steels with different yield strengths (20 steel, AISI 1006, 45 steel, AISI 2205) are included to take into account the effect of material strength. According to the high speed and nonlinear characteristics of HFMI treatment, the strain rate must be taken into consideration. Johnson-Cook constitutive model which considers the strain rate and work hardening is selected.
ε˙ σ = (A + Bε ) 1 + C ln ε˙ 0 q
T − Tr p 1−( ) Tm − Tr
(2)
where σ means the von Mises stress, and A, B and C represent the initial yield strength, the strain hardening coefficient and strain rate sensitivity, respectively. The parameters p and q mean the thermal softening effect and the strain hardening role. The corresponding Johnson-Cook parameters are given in Table 1 [29–32]. The other material parameters used in simulation are set to be the same: Young’s modulus 210 GPa, material density 7900 kg/m3 and Poisson’s ratio 0.3. 2.3. Structural hot spot stress approaches
2. Numerical modeling 2.1. Finite element model of HFMI treatment The three-dimensional FEA model of HFMI-treated T-joint, axial section of the T-joint and needles along the weld direction are shown in Fig. 1. Half of T-joint is taken into consideration by virtue of the symmetry. A portion of T-joint is employed with the width of 5 mm and the length of 50 mm. The main plate thicknesses t used in this paper are 8 mm, 16 mm, 25 mm and 35 mm, the attachment plate thickness is set as a constant 8 mm. The leg lengths of the joints are set as 6.4 mm and the radius of the weld toe is assumed to be 1.5 mm. All dimensions apart from the main plate thickness are essentially the same. Both the distances between the first needle and the target model and the interval of the adjacent needles along the impact direction and the weld direction are set as 0.2 mm. It is an optimal compromise between the computing time and the sufficient overlap of the impacts. A high-speed video camera was used by Deng et al. [28] to determine the impact velocity during HFMI process. Accordingly, the impact velocity is set as 3.34 m/s with a coulomb friction coefficient of 0.3. The paths to extract the residual stress are plotted in Fig. 1(b). To discretize the target model, three-dimensional 8-node hexahedral solid elements with reduced integration and hourglass control (C3D8R) are employed. To improve the accuracy of simulation and reduce the consumption of time, local refined mesh is employed. The mesh near the contact surface of weld toe is refined with the minimum element size of 50 μm × 50 μm × 15 μm and a biased mesh is adopted in the thickness direction. The impact needle is set as shell with a diameter of 3 mm and it is meshed using the linear quadrilateral elements (S4R). In the dynamic simulation of HFMI process, the needles are assumed as rigid bodies and the rotational degrees of freedom of the needles are restricted to ensure the stability of the impact process.
Structural hot spot stress approach avoids the defects associated with the nominal stress approach, and is computationally less demanding than fracture mechanics methods. Structural hot spot stress takes into consideration the dimensions and stress concentrating effects of the detail at the anticipated crack initiation site while excluding the local non-linear stress peak caused by the notch at the weld toe. Recently, there is growing interest in the structural hot spot stress for welded joint assessment [33–35]. According to Niemi et al. [36,37], linear surface extrapolation (LSE) determines the structural hot spot stress based on the reference points located in front of the weld toe and extrapolation:
σhs = 1.670.4t − 0.671.0t
(3)
where t represents the thickness of main plate, 0.4t and 1.0t distances from the weld toe are used as shown in Fig. 2(a) [22]. In the through thickness at the weld toe (TTWT) procedure, the structural hot spot stress is calculated in terms of cross-section stress in the weld toe as shown in Fig. 2(b) [22]. The stress distribution is non-linear including membrane force (σ m ), bending force (σ b ) and nonlinear stress peak (σ lnp ), a linear stress field can be obtained by ignoring the nonlinear stress peak. The hot spot stress can be computed by Eqs. (4)–(6) [33,38].
σm = σm ·
1 t
t 0
σx (y ) · dy
t2 t2 + σb · = 2 6
(4) t
0
σx (y ) · y · dy
σhs = σm + σb
(5) (6)
3. Residual stress distributions after external loading In the Section, the residual stress distributions after external loading for HFMI-treated T-joint are determined numerically to assess the fatigue performance by structural hot spot stress approaches.
Please cite this article as: C. Deng et al., Numerical assessment of fatigue design curve of welded T-joint improved by high-frequency mechanical impact (HFMI) treatment, Advances in Engineering Software (2017), http://dx.doi.org/10.1016/j.advengsoft.2017.06.017
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Fig. 1. (a) Three-dimensional FEA model of HFMI-treated T-joint; (b) Axial section of the T-joint; (c) Needles along the weld direction.
Fig. 2. Structural hot spot stress approaches: (a) linear surface extrapolation (LSE); (b) through thickness at the weld toe (TTWT).
3.1. Stress distributions on the surface The stress distributions on the surface of the weld toe of HFMItreated T-joints after external loading are plotted in Fig. 3. For each material, only one applied load is plotted as the shapes of the residual stress curves are similar under different applied loads. The applied nominal stresses after HFMI treatment are 150 MPa, 20 0 MPa, 30 0 MPa and 350 MPa, respectively. It is found that the stresses at 0.4t and 1.0t are almost the same for specimens with different main plate thicknesses except the specimen with equal attachment thickness and main plate thickness. As a result, the structural hot spot stresses are almost independent of plate thickness, so it is considered that the linear surface extrapolation (LSE) method is not appropriate to study the effect of main plate thickness. 3.2. Stress distributions along the thickness The residual stress distributions along the thickness after HFMI treatment are plotted in Fig.4. The numerical results have been
well validated in terms of the residual stress distribution, according to Weich [39,40], residual stress measurements with neutron, synchrotron radiation and with the hole drilling method prove that compressive residual stresses are produced up to a depth of 1.5 to 2 mm, with maximum values at a depth of approximately 0.4 to 0.5 mm, and longitudinal to the welding direction, the maximum compressive residual stresses reach the yield strength. The residual stress distributions after HFMI treatment are in good aggreement with experimental results. The residual stress distributions along the thickness after external loading are depicted in Figs. 5–9. For as-welded joints at the applied nominal stress of 100 MPa, the thickness effect is noticeable, the maximum stress increases with plate thickness. For HFMI-treated joints, the effect of material strength and plate thickness are distinct. The introduced compressive residual stresses increase with material strength. In addition, the maximum compressive stress locates relatively closer to the weld toe as the increase of plate thickness and material strength. For 20 steel and AISI 1006 steel, the maximum compressive stress increases with plate thickness under different applied loads. On the contrary, the maximum
Please cite this article as: C. Deng et al., Numerical assessment of fatigue design curve of welded T-joint improved by high-frequency mechanical impact (HFMI) treatment, Advances in Engineering Software (2017), http://dx.doi.org/10.1016/j.advengsoft.2017.06.017
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Fig. 3. Residual stress distributions on the surface: (a) 20 steel; (b) AISI 1006; (c) 45 steel; (d) AISI 2205.
Fig. 4. Residual stress distributions after HFMI treatment: (a) AISI 1006; (b) AISI 2205.
Table 2 Effective structural SCF values determined by TTWT method for as-welded T-joints. Plate thickness/mm
8
16
25
35
Effective structural SCF values
1.23
1.28
1.29
1.30
4. Evaluation of plate thickness effect by structural hot spot stress approach 4.1. Plate thickness correction exponent for as-welded joints
Fig. 5. Residual stress distributions after external loading of as-welded T-joints.
compressive stress tends to decrease with plate thickness for 45 steel and AISI 2205.
The effective structural SCF values determined by TTWT method for as-welded T-joints with different plate thicknesses are given in Table 2. It is found that the SCF values increase with plate thickness. According to the IIW [22], the plate thickness correction exponent in the structural hot spot stress approach for as-welded joints can be evaluated as:
F ATassess =
σhs,re f · F ATre f σhs,assess
(7)
Please cite this article as: C. Deng et al., Numerical assessment of fatigue design curve of welded T-joint improved by high-frequency mechanical impact (HFMI) treatment, Advances in Engineering Software (2017), http://dx.doi.org/10.1016/j.advengsoft.2017.06.017
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Fig. 6. Residual stress distributions after external loading of HFMI treated 20 steel: (a) 150 MPa; (b) 180MP.
Fig. 7. Residual stress distributions after external loading of HFMI treated AISI 1006: (a) 200 MPa; (b) 250 MPa.
Fig. 8. Residual stress distributions after external loading of HFMI treated 45 steel: (a) 300 MPa; (b) 350 MPa.
Fig. 9. Residual stress distributions after external loading of HFMI treated AISI 2205: (a) 350 MPa; (b) 480 MPa.
Please cite this article as: C. Deng et al., Numerical assessment of fatigue design curve of welded T-joint improved by high-frequency mechanical impact (HFMI) treatment, Advances in Engineering Software (2017), http://dx.doi.org/10.1016/j.advengsoft.2017.06.017
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C. Deng et al. / Advances in Engineering Software 000 (2017) 1–9 Table 3 Slopes of S-N curves determined by TTWT method for HFMI-treated T-joints. Plate thickness/mm
8
16
25
35
20 steel AISI 1006 45 steel AISI 2205
3.84 4.34 6.02 8.40
5.00 5.38 6.76 11.15
5.64 5.95 7.94 11.16
6.24 6.29 8.13 11.23
Table 4 Plate thickness correction exponents for HFMI-treated T-joints.
Fig. 10. Thickness effect for as-welded T-joints in the hot spot stress approach.
S = Sre f ·
tre f te f f
n (8)
where the reference plate thickness is tref = 25 mm. The thickness effect for as-welded T-joints by TTWT method is shown in Fig. 10, a thickness correction exponent of n = 0.04 is obtained. Some experiments [41,42] indicate that the thickness correction exponents for as-welded joints obtained by nominal stress method are between n = 0.05 and 0.1. Therefore, the determined plate thickness correction exponent n in the present work is in good agreement with the experimental data. 4.2. Plate thickness effect for HFMI-treated T-joints 4.2.1. Effective structural hot spot stress concentration factor (SCF) For HFMI-treated T-joints, the SCF values determined by TTWT method for different materials with plate thickness variation are shown in Fig. 11. It can be found that the SCF values of HFMItreated T-joints are lower than that of as-welded joints. Moreover, the SCF values of HFMI-treated T-joints significantly depend on material strength and plate thickness. It is observed in Fig. 11 that the SCF values decrease noticeably with material strength for specimens with the same plate thickness. Furthermore, the SCF value tends to decrease as plate thickness increases at the lower load level. However, the thickness-dependence becomes weaker as the external load increases. 4.2.2. Slope of S-N curves for HFMI-treated T-joints For as-welded joints, the fatigue life can be predicted as follows [22]:
C = σm · N
(9)
Accordingly, for HFMI-treated joints, the fatigue life of HFMItreated joints can be evaluated as:
C=
σhs ·
SC FHF MI SC FAW
m
·N
(10)
where SCFHFMI is the effective structural SCF value of HFMI-treated joint, and SCFAW represents the effective structural SCF value of as-welded joint. Accordingly, the corresponding S-N curves determined by TTWT method for HFMI-treated T-joints with different plate thicknesses are presented in Fig. 12. The slopes of four kinds of steels with different plate thicknesses are listed in Table 3. It is demonstrated that the slope value of S-N curve for HFMI-treated joint determined by TTWT method is larger than that of as-welded joint. Moreover, the slope values of HFMI-treated joints determined
Material
20 steel
AISI 1006
45 steel
AISI 2205
Thickness correction exponent
−0.23
−0.21
−0.17
−0.12
by TTWT method increase with material strength and plate thickness. 4.2.3. Thickness correction exponents for HFMI-treated T-joints As discussed previously, the fatigue performances of HFMItreated T-joints are dependent on plate thickness and material strength. The FAT values of HFMI-treated T-joints with different material strengths can be evaluated as:
F ATHF MI = 106 · fy
m−3 1/m
(11)
where m means the slope of S-N curve of HFMI-treated joint, fy represents material strength. The FAT values determined by TTWT method for different steels with different plate thicknesses are plotted in Fig. 13. Moreover, the FAT values for as-welded joints are also included. It is clearly indicated that the FAT values determined by TTWT method increase with material strength and plate thickness when the attachment plate thickness is set as a constant. The plate thickness correction exponents n for HFMI-treated Tjoints are reported in Table 4, where the thickness correction exponents increase with material strength. However, a reverse thickness effect is observed for HFMI-treated T-joints with negative thickness correction exponents using structural hot spot stress approach (TTWT). It can be found that the results of FEA deviate from the experiment. According to Yildirim et al. [43] the thickness effect depends mainly on three factors: statistical, technological and geometric factors. According to Weibull statistical theory, the size effect is caused by the increase probability of the presence of defects in thicker plates to some extent, which is not captured in the present FE models. Defects play an important role on the reduction of fatigue strength. Studies by Fidelis [44] show that below a thickness of 4 mm, fatigue strength actually decreases as the plate becomes thinner, this observation in thin-walled joints can be attributed to the greater negative impact of weld toe defects. According to Marquis [45], the experimental fatigue strength is reduced due to the defects for high strength steel. In addition, the reverse thickness effect may due to that the fictitious radius of ρ = 1.5 mm was initially developed for as-welded joints in the finite element model. Since the stress concentration factor is a function of (t/ρ )1/2 , a larger ρ results a slower increase in the stress concentration for increasing thickness. 5. Proposed FAT values for HFMI-treated T-joints Since a reverse thickness effect is observed for the four kinds of steels, the specimens with a plate thickness of 8 mm are used to evaluate the FAT values varying with material strength. The SCF values for different materials determined by TTWT method are plotted in Fig. 14. The predicted S-N curves for different materials are presented in Fig. 15. It can be found the slope values of HFMI treated joints are higher than as-welded joints and increase with
Please cite this article as: C. Deng et al., Numerical assessment of fatigue design curve of welded T-joint improved by high-frequency mechanical impact (HFMI) treatment, Advances in Engineering Software (2017), http://dx.doi.org/10.1016/j.advengsoft.2017.06.017
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Fig. 11. Effective structural SCF values determined by TTWT method for HFMI-treated joints: (a) 20 steel; (b) AISI 1006; (c) 45 steel; (d) AISI 2205.
Fig. 12. S-N curves for HFMI-treated T-joints determined by TTWT method: (a) 20 steel; (b) AISI 1006; (c) 45 steel; (d) AISI 2205.
Please cite this article as: C. Deng et al., Numerical assessment of fatigue design curve of welded T-joint improved by high-frequency mechanical impact (HFMI) treatment, Advances in Engineering Software (2017), http://dx.doi.org/10.1016/j.advengsoft.2017.06.017
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Fig. 13. The FAT values for different steels with different plate thicknesses. Fig. 16. Slope m values of S-N curves varying with material strength for HFMItreated T-joints.
Fig. 14. Effective stress concentration factors for different materials calculated by TTWT method. Fig. 17. Predicted FAT values varying with material strength for HFMI-treated Tjoints.
also plotted. Comparing with the experimental data in the literature [17–19], the result m = 5 is over-conservative for low strength steel, whereas that by m = 10 tends to be over-optimistic without enough safety margin. When the material strength is higher, the fatigue strength obtained by numerical simulation is a little higher than experimental results, according to Marquis [45], this may be caused by the defects induced by HFMI treatment for high strength steel. 6. Conclusion
Fig. 15. S-N curves for HFMI treated joints determined by TTWT method.
steel grade. The relationship between the slope values and steel grades is plotted in Fig. 16. The linear fitting equation is given as below:
m = 0.012 fy + 0.28
(12)
Accordingly, the predicted FAT values varying with material strength for HFMI-treated T-joints are given in Fig. 17. Meanwhile, the FAT values predicted on the basis of fixed m = 10 and m = 5 recommended by Wang et al. [19] and Yildirim et al. [17] are
In the study, four kinds of materials with different yield strengths and four kinds of specimens with different main plate thicknesses are investigated numerically. The thickness effect on the fatigue behaviors of as-welded and HFMI treated T-joints is studied using two kinds of structural hot spot stress approaches: linear surface extrapolation (LSE) and through thickness at the weld toe (TTWT). In summary, the following conclusions can be drawn: a) due to the modified local stress distribution around weld toe after HFMI treatment, the structural hot spot stress approach based on through thickness at the weld toe (TTWT) method seem to be more effective and accurate to study the effect of thickness for HFMI treated T-joints than linear surface extrapolation (LSE) method; b) For HFMI treated T-joints, the thickness correction exponents increase with material strength, whilst a reverse thickness
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effect is observed; c) The comparison between experimental data and numerical results indicates that the slopes of S-N curves for HFMI treated joints depend on material strength, and the adoption of S–N slope varying with yield strength is proven to be more proper for HFMI improvement assessment. Acknowledgements The research is financially supported by National Natural Science Foundation of China (NSFC) (Grant No. 51305295 and 51375331) and Doctoral Fund of Ministry of Education of China (Grant No. 20130 032120 0 06). References [1] Leitner M, Simunek D, Shah SF, et al. Numerical fatigue assessment of welded and HFMI-treated joints by notch stress/strain and fracture mechanical approaches. Adv Eng Softw 2016. [2] Wang D, Zhang H, Gong B, et al. Residual stress effects on fatigue behaviour of welded T-joint: A finite fracture mechanics approach. Mater Des 2016;91:211–17. [3] Foehrenbach J, Hardenacke V, Farajian M. High frequency mechanical impact treatment (HFMI) for the fatigue improvement: numerical and experimental investigations to describe the condition in the surface layer. Weld World 2016:1–7. [4] Yildirim HC, Marquis GB. A round robin study of high-frequency mechanical impact (HFMI)-treated welded joints subjected to variable amplitude loading. Weld World. 2013;57(3):437–47. [5] Leitner M, Stoschka M, Eichlseder W. Fatigue enhancement of thin-walled, high-strength steel joints by high-frequency mechanical impact treatment. Weld World 2014;58(1):29–39. [6] Zhang H, Wang D, Xia L, et al. Effects of ultrasonic impact treatment on pre– fatigue loaded high-strength steel welded joints. Int J Fatigue 2015;80:278–87. [7] Liu Y, Zhao X, Wang D. Determination of the plastic properties of materials treated by ultrasonic surface rolling process through instrumented indentation. Mat Sci Eng A. 2014:21–31 60 0.60 0. [8] Yin D, Wang D, Jing H, et al. The effects of ultrasonic peening treatment on the ultra-long life fatigue behavior of welded joints. Mater Des. 2010;31(7):3299–307. [9] Weich I, Ummenhofer T, Nitschke-Pagel T, et al. Fatigue behaviour of welded high-strength steels after high frequency mechanical post-weld treatments. Weld World 2009;53(11-12):R322–32. [10] Cheng X, Fisher JW, Prask HJ, et al. Residual stress modification by post-weld treatment and its beneficial effect on fatigue strength of welded structures. Int J Fatigue 2003;25(9):1259–69. [11] Huo LX, Wang DP, Zhang YF, et al. Investigation on improving fatigue properties of welded joints by ultrasonic peening method. Key Eng Mat 20 0 0;183-187:1315–20 187. [12] Feng Y, Hu S, Wang D, et al. Influence of surface topography and needle size on surface quality of steel plates treated by ultrasonic peening. Vacuum 2016;132:22–30. [13] Pedersen MMM, Mouritsen MOØ, Hansen MMR, et al. Comparison of post-weld treatment of high-strength steel welded joints in medium cycle fatigue. Weld World 2013;54(7):R208–17. [14] Dekhtyar AI, Mordyuk BN, Savvakin DG, et al. Enhanced fatigue behavior of powder metallurgy Ti–6Al–4 V alloy by applying ultrasonic impact treatment. Mat Sci Eng A 2015;641:348–59. [15] Huo L, Wang D, Zhang Y. Investigation of the fatigue behavior of the welded joints treated by TIG dressing and ultrasonic peening under variable-amplitude load. Int J Fatigue 2005;27(1):95–101. [16] Haagensen PJ, Maddox SJ. IIW recommendations on methods of improving the fatigue lives of welded joints. Cambridge/Paris: Woodhead Publishing Ltd./ International Institute of Welding; 2013. [17] Yildirim HC, Marquis GB. Overview of fatigue data for high frequency mechanical impact treated welded joints. Weld World 2012;56(7):82–96. [18] Yildirim HC, Marquis GB. Fatigue strength improvement factors for high strength steel welded joints treated by high frequency mechanical impact. Int J Fatigue 2012;44:168–76.
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[19] Wang T, Wang D, Huo L, et al. Discussion on fatigue design of welded joints enhanced by ultrasonic peening treatment (UPT). Int J Fatigue 2009;31(4):644–50. [20] Marquis GB, Mikkola E, Yildirim HC, et al. Fatigue strength improvement of steel structures by high-frequency mechanical impact: proposed fatigue assessment guidelines. Weld World 2013;57(6):803–22. [21] Zhao X, Wang D, Huo L. Analysis of the S – N curves of welded joints enhanced by ultrasonic peening treatment. Mater Des 2011;32(1):88–96. [22] Hobbacher A. IIW Recommendations for fatigue design of welded joints and components. IIW Doc. XIII-2460-13. 2013. [23] Yang X, Ling X, Zhou J. Optimization of the fatigue resistance of AISI304 stainless steel by ultrasonic impact treatment. Int J Fatigue 2014;61(2):28–38. [24] Guo C, Wang Z, Wang D, et al. Numerical analysis of the residual stress in ultrasonic impact treatment process with single-impact and two-impact models. Appl Surf Sci 2015;347:596–601. [25] Chaise T, Li J, Nélias D, et al. Modelling of multiple impacts for the prediction of distortions and residual stresses induced by ultrasonic shot peening (USP). J Mater Process Tech 2012;212(10):2080–90. [26] Yuan K, Sumi Y. Simulation of residual stress and fatigue strength of welded joints under the effects of ultrasonic impact treatment (UIT). Int J Fatigue 2016;92:321–32. [27] Mylonas GI, Labeas G. Numerical modelling of shot peening process and corresponding products: Residual stress, surface roughness and cold work prediction. Surf Coat Tech. 2011;205(19):4480–94. [28] Deng C, Liu Y, Gong B, et al. Numerical implementation for fatigue assessment of butt joint improved by high frequency mechanical impact treatment: A structural hot spot stress approach. Int J Fatigue 2016;92:211–19. [29] Fan Z, Gao D, Qin Z, et al. Experimental study of 20# steel under tensile impact. Gas Turbine Expt Res. 2006;19(4):35–7. [30] Johnson GR, Cook WH. Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng Fract Mech. 1985;21(1):31–48. [31] Chen G, Chen Z, Tao J, et al. Investigation and validation on plastic constitutive parameters of 45 steel. Explosion Shock Wave 2005;25(5):451–6. [32] Sanjurjo P, Rodríguez C, Peñuelas I, et al. Influence of the target material constitutive model on the numerical simulation of a shot peening process. Surf Coat Tech 2014;258:822–31. [33] Poutiainen I, Tanskanen P, Marquis G. Finite element methods for structural hot spot stress determination–a comparison of procedures. Int J Fatigue 2004;26(11):1147–57. [34] Maddox SJ. Hot spot stress design curves for fatigue assessment of welded structures. Int J Offshore Polar 2002;12(2):134–41. [35] Yildirim HC, Marquis GB, Barsoum Z. Fatigue assessment of high frequency mechanical impact (HFMI)-improved fillet welds by local approaches. Int J Fatigue 2013;52(1):57–67. [36] Niemi E, Fricke W, Maddox SJ. Fatigue Analysis of Welded Components: Designer’s Guide to the Structural Hot-Spot Stress Approach. Woodhead Publishing; 2006. [37] Niemi E, Tanskanen P. Hot spot stress determination for welded edge gussets. Weld World 20 0 0;44(5):31–7. [38] Radaj D, Sonsino CM, Fricke W. Recent developments in local concepts of fatigue assessment of welded joints. Int J Fatigue 2009;31(1):2–11. [39] Weich I. Edge layer condition and fatigue strength of welds improved by mechanical post-weld treatment. 2011, 55.1-2: 3–12. [40] Weich I, Ummenhofer T, Nitschke-Pagel T, et al. Fatigue behaviour of welded high-strength steels after high frequency mechanical post-weld treatments. Weld World 2009;53(11-12):R322–32. [41] Yamamoto N, Mouri M, Okada T, et al. Analytical and experimental study on the thickness effect to fatigue strength. Classnk Tech B 2013;31:33–44. [42] Yagi J, Machida S, Tomita Y, et al. Thickness effect criterion for fatigue evaluation of welded steel structures. J. Offshore Mech Arct. 1993;115(1):58–65. [43] Hakimi PS, Yildirim HC, Emrani MA. The thickness effect of welded details improved by high-frequency mechanical impact treatment. Int J Fatigue 2017;99(1):111–24. [44] Fidelis RM, Zhao XL, Manfred A Hirt, et al. Size effect of welded thin walled tubular joints. Int J Struct Stab Dy 2007;7(01):101–27. [45] Marquis G. Failure modes and fatigue strength of improved HSS welds. Eng Fract Mech 2010;77(11):2051–62.
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Numerical assessment of fatigue design curve of welded T-joint improved by high-frequency mechanical impact (HFMI) treatment Caiyan Deng a,b, Yaru Niu a,b, Baoming Gong a,b,∗, Yong Liu a,b, Dongpo Wang a,b a b
Department of Materials Science and Engineering, Tianjin University, Tianjin 300354, China Tianjin Key Laboratory of Advanced Joining Technology, Tianjin 300354, China
a r t i c l e
i n f o
Article history: Received 17 March 2017 Revised 3 May 2017 Accepted 28 June 2017 Available online xxx Keywords: Structural hot spot stress approach High frequency mechanical impact Fatigue design Thickness effect Material strength
a b s t r a c t In the paper, the fatigue performances of as-welded T-joint and T-joint improved by high frequency mechanical impact (HFMI) were numerically investigated using structural hot spot stress approaches: linear surface extrapolation (LSE) and through thickness at the weld toe (TTWT). The effects of main plate thickness and material strength for HFMI-treated joints were investigated. The results showed that the TTWT method was more effective to study the effect of thickness on T-joints improved by HFMI treatment than LSE method. For as-welded T-joints, the thickness correction exponent n = 0.04 was obtained when the attachment plate thickness was set as constant. For HFMI-treated T-joints, a reverse thickness effect was observed with negative thickness correction exponents, and the thickness correction exponents increased with material strength. In addition, the adoption of S–N slope varying with yield strength was proven to be more proper for HFMI improvement assessment. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction Welded structures subjected to cyclic loading are sensitive to fatigue damage, and fatigue crack tends to initiate from weld toe because of the local stress concentration and welding residual tensile stress. Recently, high-frequency mechanical impact (HFMI) treatment has been widely used as a post-weld treatment, which utilizes powerful energy to drive the needle to impact the object material at a high frequency. Therefore, the effectiveness of HFMI treatment is attributed to the smoothing of local stress concentration, refinement of microstructure and generation of local compressive residual stress at the weld toe [1–12]. Some works [13– 15] demonstrate that the improvement degree of HFMI treatment is better than commonly applied methods recommended by [16]. Previous studies [17–21] indicate that the fatigue performances of HFMI-treated welded joints are quite different from the aswelded ones. According to IIW [22], the slope value of S-N curves for welded joints of steel and aluminum is designated as m = 3, independent of material strength and stress range. However, the related works demonstrate that the slope value of S-N curve for post-weld treated joints is gentler than that of as-welded joints [17–19], and the degree of improvement varies with material
∗ Corresponding author at:. Tianjin Key Laboratory of Advanced Joining Technology, Department of Materials Science and Engineering, Tianjin University, Tianjin 300354, China. E-mail address: [email protected] (B. Gong).
strength [20]. The guidelines proposed by IIW [22] roughly adjusted the strength levels of specific joints. Recently, Yildirim and Marquis [18] provided an overview of 228 published data on fatigue performance of HFMI-treated joints and a new fatigue design recommendation was suggested that by choosing fy = 355 MPa as a reference, approximately 12.5% increase in fatigue strength for every 200 MPa increase in yield strength with an assumed S-N slope m = 5 for HFMI-treated welded joints. Wang et al. [19] also studied the effect of HFMI treatment on fatigue performances of welded joints, and reported that the slope values of S-N curves of HFMItreated joints may vary from 6.3 to 23 and m = 10 was thus proposed for fatigue design of UPT welded joints. Moreover, the thickness effect on HFMI-treated joints is not trivial. According to IIW [22], the effect of plate thickness on fatigue strength should be taken into consideration in cases fatigue crack initiates from weld toe. The thickness reduction factor f(t) for as-welded joints is given as follows:
f (t ) =
tre f te f f
n
(1)
where tref = 25 mm, n is the thickness correction exponent dependent on the effective thickness teff and the joint category. Numerous experiments of HFMI treatment, fatigue tests and residual stress measurements are both time-consuming and expensive, it is hard to obtain full measurement of stress field. Therefore, dynamic explicit finite element method (FEM) has been widely used to simulate the process of HFMI treatment [23–27]. Yang et
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Please cite this article as: C. Deng et al., Numerical assessment of fatigue design curve of welded T-joint improved by high-frequency mechanical impact (HFMI) treatment, Advances in Engineering Software (2017), http://dx.doi.org/10.1016/j.advengsoft.2017.06.017
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al [23]. investigated the fatigue performance of AISI304 stainless steel treated by ultrasonic impact treatment. The finite element model was established using Johnson-Cook material model to get the residual stress. Kuilin and Yoichi [26] numerically studied the effect of ultrasonic impact treatment on welded joints. A good agreement was observed between the predicted and measured results. The numerical simulation method has been proved to be an effective method, and the validity of numerical simulation method has been demonstrated [27]. Although noticeable progress on fatigue assessment of welded joints improved by post-weld treatment methods has been achieved, systematic investigation for different material strengths and thickness effects is still under development. In this paper, the numerical simulation method was adopted to study the fatigue performance of HFMI-treated fillet T-joint using structural hot spot stress approaches, i.e., linear surface extrapolation (LSE) and through thickness at the weld toe (TTWT). Four kinds of main plate thicknesses: 8 mm, 16 mm, 25 mm and 35 mm, were chosen to take the effect of main plate thickness into consideration. In addition, materials with different steel grades (20 steel, AISI 1006, 45 steel and AISI 2205) were employed due to the sensitivity of fatigue performance to material strength for HFMI-treated joints. At first, the process of HFMI treatment was simulated; Secondly, external load was applied to the HFMI-treated welded joints and the final stress fields were used to evaluate the structural hot spot stress. The aim of this work is to evaluate the thickness effect for HFMI-treated joints with different yield strengths using structural hot spot stress approaches.
Table 1 Constitutive model parameters. Material
A (MPa)
B (MPa)
C
p
q
20 steel AISI 1006 45 steel AISI 2205
258 350 507 622
329 275 320 785.25
0.0323 0.022 0.064 0.035
1.05 1.0 1.06 0.1515
0.235 0.36 0.28 0.5046
2.2. Johnson–Cook constitutive model In this article, steels with different yield strengths (20 steel, AISI 1006, 45 steel, AISI 2205) are included to take into account the effect of material strength. According to the high speed and nonlinear characteristics of HFMI treatment, the strain rate must be taken into consideration. Johnson-Cook constitutive model which considers the strain rate and work hardening is selected.
ε˙ σ = (A + Bε ) 1 + C ln ε˙ 0 q
T − Tr p 1−( ) Tm − Tr
(2)
where σ means the von Mises stress, and A, B and C represent the initial yield strength, the strain hardening coefficient and strain rate sensitivity, respectively. The parameters p and q mean the thermal softening effect and the strain hardening role. The corresponding Johnson-Cook parameters are given in Table 1 [29–32]. The other material parameters used in simulation are set to be the same: Young’s modulus 210 GPa, material density 7900 kg/m3 and Poisson’s ratio 0.3. 2.3. Structural hot spot stress approaches
2. Numerical modeling 2.1. Finite element model of HFMI treatment The three-dimensional FEA model of HFMI-treated T-joint, axial section of the T-joint and needles along the weld direction are shown in Fig. 1. Half of T-joint is taken into consideration by virtue of the symmetry. A portion of T-joint is employed with the width of 5 mm and the length of 50 mm. The main plate thicknesses t used in this paper are 8 mm, 16 mm, 25 mm and 35 mm, the attachment plate thickness is set as a constant 8 mm. The leg lengths of the joints are set as 6.4 mm and the radius of the weld toe is assumed to be 1.5 mm. All dimensions apart from the main plate thickness are essentially the same. Both the distances between the first needle and the target model and the interval of the adjacent needles along the impact direction and the weld direction are set as 0.2 mm. It is an optimal compromise between the computing time and the sufficient overlap of the impacts. A high-speed video camera was used by Deng et al. [28] to determine the impact velocity during HFMI process. Accordingly, the impact velocity is set as 3.34 m/s with a coulomb friction coefficient of 0.3. The paths to extract the residual stress are plotted in Fig. 1(b). To discretize the target model, three-dimensional 8-node hexahedral solid elements with reduced integration and hourglass control (C3D8R) are employed. To improve the accuracy of simulation and reduce the consumption of time, local refined mesh is employed. The mesh near the contact surface of weld toe is refined with the minimum element size of 50 μm × 50 μm × 15 μm and a biased mesh is adopted in the thickness direction. The impact needle is set as shell with a diameter of 3 mm and it is meshed using the linear quadrilateral elements (S4R). In the dynamic simulation of HFMI process, the needles are assumed as rigid bodies and the rotational degrees of freedom of the needles are restricted to ensure the stability of the impact process.
Structural hot spot stress approach avoids the defects associated with the nominal stress approach, and is computationally less demanding than fracture mechanics methods. Structural hot spot stress takes into consideration the dimensions and stress concentrating effects of the detail at the anticipated crack initiation site while excluding the local non-linear stress peak caused by the notch at the weld toe. Recently, there is growing interest in the structural hot spot stress for welded joint assessment [33–35]. According to Niemi et al. [36,37], linear surface extrapolation (LSE) determines the structural hot spot stress based on the reference points located in front of the weld toe and extrapolation:
σhs = 1.670.4t − 0.671.0t
(3)
where t represents the thickness of main plate, 0.4t and 1.0t distances from the weld toe are used as shown in Fig. 2(a) [22]. In the through thickness at the weld toe (TTWT) procedure, the structural hot spot stress is calculated in terms of cross-section stress in the weld toe as shown in Fig. 2(b) [22]. The stress distribution is non-linear including membrane force (σ m ), bending force (σ b ) and nonlinear stress peak (σ lnp ), a linear stress field can be obtained by ignoring the nonlinear stress peak. The hot spot stress can be computed by Eqs. (4)–(6) [33,38].
σm = σm ·
1 t
t 0
σx (y ) · dy
t2 t2 + σb · = 2 6
(4) t
0
σx (y ) · y · dy
σhs = σm + σb
(5) (6)
3. Residual stress distributions after external loading In the Section, the residual stress distributions after external loading for HFMI-treated T-joint are determined numerically to assess the fatigue performance by structural hot spot stress approaches.
Please cite this article as: C. Deng et al., Numerical assessment of fatigue design curve of welded T-joint improved by high-frequency mechanical impact (HFMI) treatment, Advances in Engineering Software (2017), http://dx.doi.org/10.1016/j.advengsoft.2017.06.017
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Fig. 1. (a) Three-dimensional FEA model of HFMI-treated T-joint; (b) Axial section of the T-joint; (c) Needles along the weld direction.
Fig. 2. Structural hot spot stress approaches: (a) linear surface extrapolation (LSE); (b) through thickness at the weld toe (TTWT).
3.1. Stress distributions on the surface The stress distributions on the surface of the weld toe of HFMItreated T-joints after external loading are plotted in Fig. 3. For each material, only one applied load is plotted as the shapes of the residual stress curves are similar under different applied loads. The applied nominal stresses after HFMI treatment are 150 MPa, 20 0 MPa, 30 0 MPa and 350 MPa, respectively. It is found that the stresses at 0.4t and 1.0t are almost the same for specimens with different main plate thicknesses except the specimen with equal attachment thickness and main plate thickness. As a result, the structural hot spot stresses are almost independent of plate thickness, so it is considered that the linear surface extrapolation (LSE) method is not appropriate to study the effect of main plate thickness. 3.2. Stress distributions along the thickness The residual stress distributions along the thickness after HFMI treatment are plotted in Fig.4. The numerical results have been
well validated in terms of the residual stress distribution, according to Weich [39,40], residual stress measurements with neutron, synchrotron radiation and with the hole drilling method prove that compressive residual stresses are produced up to a depth of 1.5 to 2 mm, with maximum values at a depth of approximately 0.4 to 0.5 mm, and longitudinal to the welding direction, the maximum compressive residual stresses reach the yield strength. The residual stress distributions after HFMI treatment are in good aggreement with experimental results. The residual stress distributions along the thickness after external loading are depicted in Figs. 5–9. For as-welded joints at the applied nominal stress of 100 MPa, the thickness effect is noticeable, the maximum stress increases with plate thickness. For HFMI-treated joints, the effect of material strength and plate thickness are distinct. The introduced compressive residual stresses increase with material strength. In addition, the maximum compressive stress locates relatively closer to the weld toe as the increase of plate thickness and material strength. For 20 steel and AISI 1006 steel, the maximum compressive stress increases with plate thickness under different applied loads. On the contrary, the maximum
Please cite this article as: C. Deng et al., Numerical assessment of fatigue design curve of welded T-joint improved by high-frequency mechanical impact (HFMI) treatment, Advances in Engineering Software (2017), http://dx.doi.org/10.1016/j.advengsoft.2017.06.017
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Fig. 3. Residual stress distributions on the surface: (a) 20 steel; (b) AISI 1006; (c) 45 steel; (d) AISI 2205.
Fig. 4. Residual stress distributions after HFMI treatment: (a) AISI 1006; (b) AISI 2205.
Table 2 Effective structural SCF values determined by TTWT method for as-welded T-joints. Plate thickness/mm
8
16
25
35
Effective structural SCF values
1.23
1.28
1.29
1.30
4. Evaluation of plate thickness effect by structural hot spot stress approach 4.1. Plate thickness correction exponent for as-welded joints
Fig. 5. Residual stress distributions after external loading of as-welded T-joints.
compressive stress tends to decrease with plate thickness for 45 steel and AISI 2205.
The effective structural SCF values determined by TTWT method for as-welded T-joints with different plate thicknesses are given in Table 2. It is found that the SCF values increase with plate thickness. According to the IIW [22], the plate thickness correction exponent in the structural hot spot stress approach for as-welded joints can be evaluated as:
F ATassess =
σhs,re f · F ATre f σhs,assess
(7)
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Fig. 6. Residual stress distributions after external loading of HFMI treated 20 steel: (a) 150 MPa; (b) 180MP.
Fig. 7. Residual stress distributions after external loading of HFMI treated AISI 1006: (a) 200 MPa; (b) 250 MPa.
Fig. 8. Residual stress distributions after external loading of HFMI treated 45 steel: (a) 300 MPa; (b) 350 MPa.
Fig. 9. Residual stress distributions after external loading of HFMI treated AISI 2205: (a) 350 MPa; (b) 480 MPa.
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C. Deng et al. / Advances in Engineering Software 000 (2017) 1–9 Table 3 Slopes of S-N curves determined by TTWT method for HFMI-treated T-joints. Plate thickness/mm
8
16
25
35
20 steel AISI 1006 45 steel AISI 2205
3.84 4.34 6.02 8.40
5.00 5.38 6.76 11.15
5.64 5.95 7.94 11.16
6.24 6.29 8.13 11.23
Table 4 Plate thickness correction exponents for HFMI-treated T-joints.
Fig. 10. Thickness effect for as-welded T-joints in the hot spot stress approach.
S = Sre f ·
tre f te f f
n (8)
where the reference plate thickness is tref = 25 mm. The thickness effect for as-welded T-joints by TTWT method is shown in Fig. 10, a thickness correction exponent of n = 0.04 is obtained. Some experiments [41,42] indicate that the thickness correction exponents for as-welded joints obtained by nominal stress method are between n = 0.05 and 0.1. Therefore, the determined plate thickness correction exponent n in the present work is in good agreement with the experimental data. 4.2. Plate thickness effect for HFMI-treated T-joints 4.2.1. Effective structural hot spot stress concentration factor (SCF) For HFMI-treated T-joints, the SCF values determined by TTWT method for different materials with plate thickness variation are shown in Fig. 11. It can be found that the SCF values of HFMItreated T-joints are lower than that of as-welded joints. Moreover, the SCF values of HFMI-treated T-joints significantly depend on material strength and plate thickness. It is observed in Fig. 11 that the SCF values decrease noticeably with material strength for specimens with the same plate thickness. Furthermore, the SCF value tends to decrease as plate thickness increases at the lower load level. However, the thickness-dependence becomes weaker as the external load increases. 4.2.2. Slope of S-N curves for HFMI-treated T-joints For as-welded joints, the fatigue life can be predicted as follows [22]:
C = σm · N
(9)
Accordingly, for HFMI-treated joints, the fatigue life of HFMItreated joints can be evaluated as:
C=
σhs ·
SC FHF MI SC FAW
m
·N
(10)
where SCFHFMI is the effective structural SCF value of HFMI-treated joint, and SCFAW represents the effective structural SCF value of as-welded joint. Accordingly, the corresponding S-N curves determined by TTWT method for HFMI-treated T-joints with different plate thicknesses are presented in Fig. 12. The slopes of four kinds of steels with different plate thicknesses are listed in Table 3. It is demonstrated that the slope value of S-N curve for HFMI-treated joint determined by TTWT method is larger than that of as-welded joint. Moreover, the slope values of HFMI-treated joints determined
Material
20 steel
AISI 1006
45 steel
AISI 2205
Thickness correction exponent
−0.23
−0.21
−0.17
−0.12
by TTWT method increase with material strength and plate thickness. 4.2.3. Thickness correction exponents for HFMI-treated T-joints As discussed previously, the fatigue performances of HFMItreated T-joints are dependent on plate thickness and material strength. The FAT values of HFMI-treated T-joints with different material strengths can be evaluated as:
F ATHF MI = 106 · fy
m−3 1/m
(11)
where m means the slope of S-N curve of HFMI-treated joint, fy represents material strength. The FAT values determined by TTWT method for different steels with different plate thicknesses are plotted in Fig. 13. Moreover, the FAT values for as-welded joints are also included. It is clearly indicated that the FAT values determined by TTWT method increase with material strength and plate thickness when the attachment plate thickness is set as a constant. The plate thickness correction exponents n for HFMI-treated Tjoints are reported in Table 4, where the thickness correction exponents increase with material strength. However, a reverse thickness effect is observed for HFMI-treated T-joints with negative thickness correction exponents using structural hot spot stress approach (TTWT). It can be found that the results of FEA deviate from the experiment. According to Yildirim et al. [43] the thickness effect depends mainly on three factors: statistical, technological and geometric factors. According to Weibull statistical theory, the size effect is caused by the increase probability of the presence of defects in thicker plates to some extent, which is not captured in the present FE models. Defects play an important role on the reduction of fatigue strength. Studies by Fidelis [44] show that below a thickness of 4 mm, fatigue strength actually decreases as the plate becomes thinner, this observation in thin-walled joints can be attributed to the greater negative impact of weld toe defects. According to Marquis [45], the experimental fatigue strength is reduced due to the defects for high strength steel. In addition, the reverse thickness effect may due to that the fictitious radius of ρ = 1.5 mm was initially developed for as-welded joints in the finite element model. Since the stress concentration factor is a function of (t/ρ )1/2 , a larger ρ results a slower increase in the stress concentration for increasing thickness. 5. Proposed FAT values for HFMI-treated T-joints Since a reverse thickness effect is observed for the four kinds of steels, the specimens with a plate thickness of 8 mm are used to evaluate the FAT values varying with material strength. The SCF values for different materials determined by TTWT method are plotted in Fig. 14. The predicted S-N curves for different materials are presented in Fig. 15. It can be found the slope values of HFMI treated joints are higher than as-welded joints and increase with
Please cite this article as: C. Deng et al., Numerical assessment of fatigue design curve of welded T-joint improved by high-frequency mechanical impact (HFMI) treatment, Advances in Engineering Software (2017), http://dx.doi.org/10.1016/j.advengsoft.2017.06.017
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Fig. 11. Effective structural SCF values determined by TTWT method for HFMI-treated joints: (a) 20 steel; (b) AISI 1006; (c) 45 steel; (d) AISI 2205.
Fig. 12. S-N curves for HFMI-treated T-joints determined by TTWT method: (a) 20 steel; (b) AISI 1006; (c) 45 steel; (d) AISI 2205.
Please cite this article as: C. Deng et al., Numerical assessment of fatigue design curve of welded T-joint improved by high-frequency mechanical impact (HFMI) treatment, Advances in Engineering Software (2017), http://dx.doi.org/10.1016/j.advengsoft.2017.06.017
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Fig. 13. The FAT values for different steels with different plate thicknesses. Fig. 16. Slope m values of S-N curves varying with material strength for HFMItreated T-joints.
Fig. 14. Effective stress concentration factors for different materials calculated by TTWT method. Fig. 17. Predicted FAT values varying with material strength for HFMI-treated Tjoints.
also plotted. Comparing with the experimental data in the literature [17–19], the result m = 5 is over-conservative for low strength steel, whereas that by m = 10 tends to be over-optimistic without enough safety margin. When the material strength is higher, the fatigue strength obtained by numerical simulation is a little higher than experimental results, according to Marquis [45], this may be caused by the defects induced by HFMI treatment for high strength steel. 6. Conclusion
Fig. 15. S-N curves for HFMI treated joints determined by TTWT method.
steel grade. The relationship between the slope values and steel grades is plotted in Fig. 16. The linear fitting equation is given as below:
m = 0.012 fy + 0.28
(12)
Accordingly, the predicted FAT values varying with material strength for HFMI-treated T-joints are given in Fig. 17. Meanwhile, the FAT values predicted on the basis of fixed m = 10 and m = 5 recommended by Wang et al. [19] and Yildirim et al. [17] are
In the study, four kinds of materials with different yield strengths and four kinds of specimens with different main plate thicknesses are investigated numerically. The thickness effect on the fatigue behaviors of as-welded and HFMI treated T-joints is studied using two kinds of structural hot spot stress approaches: linear surface extrapolation (LSE) and through thickness at the weld toe (TTWT). In summary, the following conclusions can be drawn: a) due to the modified local stress distribution around weld toe after HFMI treatment, the structural hot spot stress approach based on through thickness at the weld toe (TTWT) method seem to be more effective and accurate to study the effect of thickness for HFMI treated T-joints than linear surface extrapolation (LSE) method; b) For HFMI treated T-joints, the thickness correction exponents increase with material strength, whilst a reverse thickness
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effect is observed; c) The comparison between experimental data and numerical results indicates that the slopes of S-N curves for HFMI treated joints depend on material strength, and the adoption of S–N slope varying with yield strength is proven to be more proper for HFMI improvement assessment. Acknowledgements The research is financially supported by National Natural Science Foundation of China (NSFC) (Grant No. 51305295 and 51375331) and Doctoral Fund of Ministry of Education of China (Grant No. 20130 032120 0 06). References [1] Leitner M, Simunek D, Shah SF, et al. Numerical fatigue assessment of welded and HFMI-treated joints by notch stress/strain and fracture mechanical approaches. Adv Eng Softw 2016. [2] Wang D, Zhang H, Gong B, et al. Residual stress effects on fatigue behaviour of welded T-joint: A finite fracture mechanics approach. Mater Des 2016;91:211–17. [3] Foehrenbach J, Hardenacke V, Farajian M. High frequency mechanical impact treatment (HFMI) for the fatigue improvement: numerical and experimental investigations to describe the condition in the surface layer. Weld World 2016:1–7. [4] Yildirim HC, Marquis GB. A round robin study of high-frequency mechanical impact (HFMI)-treated welded joints subjected to variable amplitude loading. Weld World. 2013;57(3):437–47. [5] Leitner M, Stoschka M, Eichlseder W. Fatigue enhancement of thin-walled, high-strength steel joints by high-frequency mechanical impact treatment. Weld World 2014;58(1):29–39. [6] Zhang H, Wang D, Xia L, et al. Effects of ultrasonic impact treatment on pre– fatigue loaded high-strength steel welded joints. Int J Fatigue 2015;80:278–87. [7] Liu Y, Zhao X, Wang D. Determination of the plastic properties of materials treated by ultrasonic surface rolling process through instrumented indentation. Mat Sci Eng A. 2014:21–31 60 0.60 0. [8] Yin D, Wang D, Jing H, et al. The effects of ultrasonic peening treatment on the ultra-long life fatigue behavior of welded joints. Mater Des. 2010;31(7):3299–307. [9] Weich I, Ummenhofer T, Nitschke-Pagel T, et al. Fatigue behaviour of welded high-strength steels after high frequency mechanical post-weld treatments. Weld World 2009;53(11-12):R322–32. [10] Cheng X, Fisher JW, Prask HJ, et al. Residual stress modification by post-weld treatment and its beneficial effect on fatigue strength of welded structures. Int J Fatigue 2003;25(9):1259–69. [11] Huo LX, Wang DP, Zhang YF, et al. Investigation on improving fatigue properties of welded joints by ultrasonic peening method. Key Eng Mat 20 0 0;183-187:1315–20 187. [12] Feng Y, Hu S, Wang D, et al. Influence of surface topography and needle size on surface quality of steel plates treated by ultrasonic peening. Vacuum 2016;132:22–30. [13] Pedersen MMM, Mouritsen MOØ, Hansen MMR, et al. Comparison of post-weld treatment of high-strength steel welded joints in medium cycle fatigue. Weld World 2013;54(7):R208–17. [14] Dekhtyar AI, Mordyuk BN, Savvakin DG, et al. Enhanced fatigue behavior of powder metallurgy Ti–6Al–4 V alloy by applying ultrasonic impact treatment. Mat Sci Eng A 2015;641:348–59. [15] Huo L, Wang D, Zhang Y. Investigation of the fatigue behavior of the welded joints treated by TIG dressing and ultrasonic peening under variable-amplitude load. Int J Fatigue 2005;27(1):95–101. [16] Haagensen PJ, Maddox SJ. IIW recommendations on methods of improving the fatigue lives of welded joints. Cambridge/Paris: Woodhead Publishing Ltd./ International Institute of Welding; 2013. [17] Yildirim HC, Marquis GB. Overview of fatigue data for high frequency mechanical impact treated welded joints. Weld World 2012;56(7):82–96. [18] Yildirim HC, Marquis GB. Fatigue strength improvement factors for high strength steel welded joints treated by high frequency mechanical impact. Int J Fatigue 2012;44:168–76.
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Please cite this article as: C. Deng et al., Numerical assessment of fatigue design curve of welded T-joint improved by high-frequency mechanical impact (HFMI) treatment, Advances in Engineering Software (2017), http://dx.doi.org/10.1016/j.advengsoft.2017.06.017