- Email: [email protected]
Fatigue strength assessment of misaligned laser beam welded T-joints by effective stress method
International Journal of Pressure Vessels and Piping 173 (2019) 68–78
Contents lists available at ScienceDirect
International Journal of Pressure Vessels and Piping journal homepage: www.elsevier.com/locate/ijpvp
Fatigue strength assessment of misaligned laser beam welded T-joints by effective stress method
T
P.I. Oliveiraa,∗, A. Loureiroa, J.M. Costaa, J. Ferreiraa, L. Borregoa,b a b
CEMMPRE, Mechanical Engineering Department, University of Coimbra, Rua Luís Reis Santos, 3030-788, Coimbra, Portugal Mechanical Engineering Department, Coimbra Polytechnic, ISEC, Rua Pedro Nunes, 3030-199, Coimbra, Portugal
ARTICLE INFO
ABSTRACT
Keywords: Effective stress Fatigue strength Laser beam welding Angular misalignment Aluminium thin plates
This paper investigates the effect of the joint misalignment and the weld geometry on the fatigue strength of successive double-sided laser beam welded AA2024 and AA7075 T-joints using AA4047 filler wire. A finite element model was set up considering the misalignment and the weld geometry to obtain the notch stress. The effective notch stress was calculated by the fictitious radius concept and a microstructural length of 0.15 mm was estimated. Master design curves are proposed for different weld toe radii and microstructural length. The experimental results were better characterized by both a reference weld toe radius of 0 mm and a microstructural length of 0.15 mm. Furthermore, the geometric imperfections caused by variations on the weld toe generate fractures initiated by crack multinucleation.
1. Introduction The interest in reducing the weight of airplane structures and in reducing both cost and time of aircraft manufacturing are the main reasons why the aviation industry investigates laser beam welding (LBW) as a joining technology to replace the riveted joints in stiffened panels [1]. However, the welding process leads to undesirable outcomes such as residual stresses and distortions. These problems are very common in welded joints of aluminium alloys due to their high thermal expansion coefficient. In general, residual stress and distortion are inversely related. Furthermore, residual stress and distortion are strongly affected by restraint degree during the welding process. Thus, the welded joints with higher restraint degree have lower distortion but higher residual stress and vice-versa. The laser welded T-joints studied by Zain-ul-abdein et al. [2], for instance, presented very small transverse residual stress because only the clip restricted the out-of-plane displacements in its experimental set up. Despite this, the angular distortion is the largest welding deformation in laser welded joints made of thin sheets of aluminium alloys [3]. For laser welded T-joints made of 2.5 mm thick sheets of AA6056-T4, the compressive longitudinal residual stress in the heat-affected zone induced a significant deformation of the skin sheet in the vicinity of the fusion zone. This residual plastic strain was caused by both softening of the fusion zone material and positioning of the stringer [2]. Beyond the welding distortions and residual stresses, other factors such as variation in weld geometry along
∗
the weld seam, weld defects, and the high gradients of microstructure and hardness in the vicinity of the notch may significantly affect the fatigue assessment of welded joints [4]. In this research, only the influence of the joint and weld geometry will be addressed. The crack initiation occurring at the weld toe in simultaneous double-sided laser welded T-joints [5] and in single-sided laser welded T-joints was studied by Ventzke et al. [6]. However, the effect of the weld toe on the fatigue strength was neglected concerning the laser welded butt-joints studied by Eibl et al. [7] due to their modest weld toe curvature. In addition, the same authors mention that a single-sided laser welded T-joint and a butt-joint had the same fatigue strength when their weld toe curvatures were similar [7]. Another factor that may affect the local stress at the weld toe of welded T-joints is the angular misalignment caused by the welding process. According to Burk and Lawrence [8], the partial straightening of a misaligned specimen under axial load induces bending even when the angular distortion is small. Therefore, the bending stress cannot be ignored when bending and axial loads are combined, unless the fatigue assessment is carried out by applying a design S–N curve (FAT class) and the misalignment is lower than the one which is already included in that FAT class [9]. Besides this, geometric imperfections increase the scatter of the fatigue data mainly in the welded joints of thin sheets. Liinalampi et al. [10] measured the weld geometry on a microscale to apply realistic radii in the fatigue assessment of laser-hybrid butt joints. However,
Corresponding author. E-mail address: [email protected] (P.I. Oliveira).
https://doi.org/10.1016/j.ijpvp.2019.05.001 Received 14 September 2018; Received in revised form 17 April 2019; Accepted 1 May 2019 Available online 02 May 2019 0308-0161/ © 2019 Elsevier Ltd. All rights reserved.
International Journal of Pressure Vessels and Piping 173 (2019) 68–78
P.I. Oliveira, et al.
The microstructural length is a material parameter and related to material strength, as observed by Liinalampi et al. [10]. Therefore, the microstructural length is different for the base material (BM), heat-affected zone (HAZ) and fusion zone (FZ), depending in which of these zones the crack initiation occurs [13]. Zhang et al. [14] presented a = 0.21 mm for aluminium welds. This value was calculated value of considering a complete fatigue data. These data were fitted by least squares method using a power law function. The effective stress ranges were calculated using the Neuber's solution for a given value of . The variation of in the computing of e resulted in regressions with different coefficient of determination (R2). Thus, the value of that resulted in a regression with the maximum value of R2 was chosen as the microstructural length for aluminium welds. Liinalampi et al. [10] observed, for laser-hybrid welded butt-joints made with 3 mm thick steel sheets, a large axial misalignment caused by the high stress gradient. However, the influence of a stress gradient was almost com= 0.40 mm , pletely neglected in the effective stress calculation using the value commonly used for steels. Additionally, they verified that = 0.05 mm was more sensitive to the stress gradient caused by the joint misalignment. This was evidenced by the lowest value of the S–N = 0.05 mm when S–N scatter was examined scatter that occurred for as a function of . The multiaxial factor depends on the loading mode (1, 2, 3 or mixed), the strength criterion (normal stress or von Mises) and the multiaxiality condition (plane stress or plane strain) [15]. According to Berto et al. [16], the value of s converges to a plateau value for . On the other hand, the value of s may be different from the plateau value for < . However, the same authors considered that the plateau values of s are satisfactory for engineering applications in structural strength assessments of V-notch specimens ( = 0 ) considering different values of both microstructural length and notch opening angle. Beyond that, the notch opening angle has a significant influence on s, since its plateau value for normal stress criterion considering Fillipi's equations [17], for instance, varies from 2.0 to 6.38 when the notch opening angle is varied from 0° to 150° [16]. Taking into account that the weld toe radius might be uneven along the weld seam and that the angular misalignment cannot be neglected to evaluate the local stress at the weld toe, the aim of this research is to investigate which geometric factors affect the fatigue strength of successive double-sided laser beam welded T-joints made of AA2024 as the skin, AA7075 as the clip and using AA4047 as the filler wire.
Fig. 1. Neuber's stress averaging approach to calculate effective notch stress at a welded joint and fictitious notch radius.
realistic radii are difficult to measure [4]. Therefore, in general, the effect of variations in geometry are addressed by the effective notch stress approach [10]. For the fatigue assessment of laser beam welded thin-sheet joints (t 3 mm ) at the weld root notches, the most successful notch stress approach has been the one that applies a reference radius of 0.05 mm [11]. In this case, the notch stress can be applied directly on the fatigue assessment without considering any support effects. However, the notch stresses obtained at the weld toe with this reference radius are not realistic therefore its use is restricted to root notch assessments [4]. On the other hand, Neuber's stress average approach [12] has been proposed to assess the effective stress ( e ) at the notch by taking into account the effect of the stress field gradient in the notch ligament [4]. The effective stress is calculated by equation (1), where is the microstructural length and x (y ) is the stress distribution along the normal path to the sheet surface, as illustrated in Fig. 1. e
=
1
2. Materials and experimental methods 2.1. Base materials and filler wire
x (y ) dy
(1)
0
Dissimilar T-joints made of 2 mm thick plates of AA2024-T3 as the skin and AA7075-T6 as the clip were welded using AA4047 filler wire with 1 mm diameter. The size of the plates was 500 mm × 160 mm and 500 mm × 40 mm, respectively, for the skin and the clip, and they were cut perpendicular to the plate rolling direction. Table 1 presents the chemical composition of the base materials and the filler metal used and Table 2 shows the mechanical properties of the base materials obtained experimentally according to ASTM E 8 Standard. In order to obtain the mechanical properties, the tensile tests were performed with a tensile tester INSTRON model 4206 using an upper crosshead speed of 2.0 mm/min.
To simplify the procedure to obtain e , the concept of fictitious notch round was introduced by Neuber [12]. According to this concept, the effective stress is determined directly by means of an artificial enlargement of the notch radius, so that the fictitious-notch stress be equal to the effective stress of the real structure. The fictitious notch radius ( f ) is computed by equation (2), where is the actual notch radius and s is the factor that consider the effects of multiaxial stress on failure. The fictitious notch radius is illustrated in Fig. 1. f
=
+s
(2)
Table 1 Chemical composition of base materials and filler wire (% wt.) [18]. Alloy
Si
Fe
Cu
Mn
Mg
Cr
Zn
Ti
Al
AA2024 AA7075 AA4047
max 0.50 max 0.40 11.00 13.00
max 0.50 max 0.50 max 0.6
3.80 4.90 1.20 2.00 max 0.30
0.30 0.90 max 0.30 max 0.15
1.20 1.80 2.10 2.90 max 0.10
– 0.18 0.28 –
max 0.25 5.10 6.10 max 0.20
max 0.15 max 0.20 max 0.15
Bal. Bal. Bal.
69
International Journal of Pressure Vessels and Piping 173 (2019) 68–78
P.I. Oliveira, et al.
Table 2 Mechanical properties of the base materials. Ultimate Stress, AA2024-T3 AA7075-T6
UTS
(MPa)
Yield stress,
479 592
YS
(MPa)
359 529
Young's modulus, E (GPa)
Strain at σUTS (%)
78.6 74.4
13.6 9.1
Fig. 2. Schematic diagram of T-joint welding. Table 3 Welding parameters used in the series studied. Weld series
α (°)
s (mm/s)
F (m/min)
P (kW)
δ (mm)
1 2 3 4
10 10 15 15
40 40 40 35
4.3 4.3 4.3 3.8
3.4 2.9 3.4 3.0
0.0 0.3 0.0 0.0
P - laser beam power, s - welding speed, F - feed rate of filler wire, α - incident beam angle and δ - incident beam position.
2.2. Experimental set-up and welding conditions The base material plates were burnished with a steel brush and cleaned with acetone in order to remove the oxides and contaminated layers from the surfaces of the work pieces before carrying out the welding. Then, the successive double-sided laser beam welded T-joints were carried out according to the scheme shown in Fig. 2. Fig. 2a presents the incident beam position (δ) and the incident beam angle (α), the angle α is 5° lower than the angle between the skin surface and the supply plane. According to Fig. 2b, both shielding gas and filler wire were supplied in the same plane, the gas nozzle is set behind the laser beam and the filler wire in the leading direction, forming angles of 25° with the welding direction.
Fig. 4. –Geometry of fatigue test specimens.
A continuous wave disk laser TruDisk 16002 with 12 kW maximum power was used to generate a laser beam with 1.030 μm wavelength. Furthermore, a focusing optic BEO D70 with 200 mm focal length was applied and the focal point was established on the clip surface. The laser spot diameter was 600 μm, the same diameter as the optical fibre. Further, argon was used as the shielding gas with a flow rate of 10 l/ min.
Fig. 3. Schematic diagram of misaligned specimen. 70
International Journal of Pressure Vessels and Piping 173 (2019) 68–78
P.I. Oliveira, et al.
The weld series studied in this work were produced mainly by varying the laser beam power (P) and incident beam angle (α), though other parameters such as the welding speed (s), the feed rate of filler wire (F), and the incident beam position (δ) were changed too, according to Table 3. These weld series were chosen because they presented low amount of porosity according to previous investigations [19].
Table 4 –Number of fatigue tests and their load levels. Load (N)
Number of tests
6000 5500 5250 5000 4500 4250 4000 4125 3750
3 5 3 3 9 4 1 7 4
2.3. Geometrical features of the misaligned specimens The geometric features of the misaligned specimens depicted in Fig. 3 are angular distortion (θ), distance between weld toes (d) and
Fig. 5. Gripping of the model: a) initial position and b) final position.
Fig. 6. Finite element mesh.
Fig. 7. σxx stress field (weld series 4; p = 8000 N).
71
International Journal of Pressure Vessels and Piping 173 (2019) 68–78
P.I. Oliveira, et al.
2.4. Fatigue testing Fatigue testing was conducted according to ASTM E 466 Standard. The fatigue tests were carried out in load control at a frequency of 25 Hz, applying sinusoidal tensile loadings with constant amplitude and stress ratio (R) equal to 0.02 using a machine INSTRON model 1341 with an 8800 series servo-hydraulic control system from INSTRON. The specimens were manufactured according to Fig. 4. The number of fatigue tests carried out and their loads are presented in Table 4. After the fatigue testing, the fracture surfaces of the specimens were characterized using a scanning electron microscope Zeiss Merlin-61-50. 3. Finite element analysis The local stress approach was used to assess the influence of the combined bending and axial loading on the fatigue life of the misaligned T-joints, since axial loading induces bending in them. Thus, the notch stresses were obtained with help of finite element models. The misaligned specimens were analysed by the finite element method using the software Marc-Mentat. As illustrated in Fig. 5a, the model was fixed on the left side to an extension of 30 mm in order to simulate the gripping step, that is, in order to avoid any type of rotation and displacement of the left extremity. The right side of the model, initially free, was gripped, as depicted in Fig. 5b, and then a longitudinal loading of up to a maximum load of 8 kN was applied on the right side of the model. The load was uniformly distributed on the 26 nodes of the right extremity of the model. During the loading phase, it was considered that there was no friction between the model and the grippers so that only the displacement in the loading direction was allowed. The loading was divided into 900 increments, 100 were related to gripping and 800 related to the axial load application. The finite element procedure that simulate the gripping step was like the experimental procedure. However, the load applying procedure was not the same used in experimental procedure, since the gripper did not displace together with the right extremity of the model neither there was friction between them. The finite element mesh, shown in Fig. 6, is composed of two-dimensional linear elements with 4 nodes and full integration, consisting of 16,400 elements and 17,106 nodes. The mesh is finer at the weld toe zone, where the greatest stresses are expected. The model presents 3 zones with different materials, the: molten zone, 2024 aluminium alloy
Fig. 8. Relation between notch stress and structural stress. Table 5 Dimensions of the joint. Weld Series
θ (°)
d (mm)
r (mm)
1 2 3 4
1.15 1.45 1.30 1.45
7,17 6,25 7,03 6,36
128.56 83.68 111.03 86.46
concordance radius (r). Furthermore, detail A of the figure indicates that the weld seam has an average angle of 120° and detail B shows the definition of the weld toe radius (ρ). The average angular distortions were measured using a digital goniometer model Schut GR180. The distance between the weld toes was measured from cross section as shown in Fig. 3, using a stereo microscope provided with digital micrometres in two perpendicular directions. Furthermore, a Mitutoyo projector was used to measure the X–Y coordinates of three points on the weld seam profile of the fatigue specimens to obtain the weld toe radius by means of the software Geogebra. Samples of up to 23 radii values were obtained for all the weld series and statistically treated.
Fig. 9. Examples of macrographs of the weld beads.
72
International Journal of Pressure Vessels and Piping 173 (2019) 68–78
P.I. Oliveira, et al.
Table 6 Statistical results of the weld toe radius (ρ) data. Weld Series
Data number
Mean (mm)
Mean standard deviation (mm)
1 2 3 4
22 23 21 22
2.06 2.44 2.28 2.13
0.51 0.61 0.83 0.35
and 7075 aluminium alloy. All materials were assumed as homogeneous, isotropic and linear elastic during the simulation. The Young's moduli used in finite element model were those presented in Table 2 for 2024 and 7075 aluminium alloys and the value of E adopted for the molten zone was 70 GPa, value found in the literature for aluminium alloys [18]. The Poisson's ratio used in finite element analysis was 0.33 for all zones, in agreement with the literature [18]. According to Fig. 7, the maximum notch stress occurred at the weld toe, assuming the value of 609.9 MPa when the model of weld series 4 was under a nominal stress of 320 MPa. An elastic analysis was carried out in this study because the FITNET – European Fitness for Service Network [20] stresses that the fatigue assessment using notch stresses can be done since the notch stress range is lower than 2 YS . Thus, the notch stress can be approximated as purely elastic when the plastic deformation is not appreciable. According to IIW recommendations [9], the stress at the weld toe ( wt ) for misaligned joints is composed by membrane stress ( memb ), bending stress ( bend ) and non-linear stress peak ( nl ). Considering the through-thickness stress distribution depicted in Fig. 1, the values of memb and bend can be obtained from finite element results, respectively, by equations (3) and (4), where t is the plate thickness. Then, the structural stress (Ss ) is calculated by equation (5). Thus, the stress concentration factor (Kt ) is computed according to equation (6) for a stress cycle with a stress ratio equal to zero. In this theoretical definition of Kt , both notch stress and structural stress consider the bending stress induced by the gripping, as well as the membrane stress and the secondary bending stress induced by axial loading. memb
bend
Ss = Kt =
1 t
=
=
6 t2
memb
t x (y )
dy
(3)
0
t
( x (y )
memb )
0
+
t2 2
y dy
bend
wt
Ss
(4) (5) Fig. 10. Stresses for K t calculation: a) bending stress, b) notch stress and c) membrane stress.
(6)
According to Fig. 8, the notch stress at the weld toe varies linearly with the structural stress, and Kt is the slope of a straight line that represents the relation between them. This straight line was obtained by linear regression of the data of both notch stress and throughthickness stress distribution generated during the loading phase of the finite element model for each loading increment. In addition, the normal stress criterion was adopted to generate these data.
toe radius data obtained from the fatigue specimens. According to these data, weld series 4 presented the lowest radii scatter and weld series 3 the largest one. The data on the weld toe radius presented a random variation along the weld seams. Therefore, considering that the fatigue life is a weakest link problem, a smallest radius is always more representative of the experimental results.
4. Experimental results and discussion 4.1. Geometry of the joints
4.2. Stress concentration factor
The geometrical features of the misaligned specimens are presented in Table 5, according to Fig. 3. Thus, the variation in the angular distortion among the weld series is significant. Weld series 1 presented the lowest angular distortion while weld series 2 and 4 showed the highest ones. The distance between the weld toes was obtained from the macrographs such as those presented in Fig. 9. Table 6 presents the results of the statistical treatment of the weld
The stress concentration factor was calculated according to equation (6). Therefore, before the calculation of Kt was necessary to obtain the local stress at the weld toe from the finite element models, as well as to calculate both the membrane stress and the bending stress induced by both the gripping and the axial loading from finite element data by equations (3) and (4) respectively. The variations of wt , memb and bend with nominal stress are shown in Fig. 8, taking the load increments of 73
International Journal of Pressure Vessels and Piping 173 (2019) 68–78
P.I. Oliveira, et al.
material is assumed linear elastic. Furthermore, Fig. 10a shows that the bend increases with angular distortion and that the curves of bend for weld series with the same θ are overlapped. The curves of memb of all weld series also are overlapped, as shown Fig. 10c. Thus, the values of memb and bend can be obtained, respectively, by equations (7) and (8), where n is the nominal stress. The coefficients ai (for i = 0, 1, 2 and 3) of equation (7) and bj (for j = 0 and 1) of equation (8) are presented in Table 7 for each weld series. The correlation coefficients (R2) of equations (7) and (8) were, respectively, 99,997% and 100% for all weld series.
Table 7 Coefficients of equations (7) and (8) for each weld series. Weld Series
a3
a2
a1
a0
b1
b0
1 2 3 4
0.000003 0.000004 0.000004 0.000004
−0.001981 −0.002679 −0.002263 −0.002654
0.779266 0.973324 0.867794 0.976271
36.404651 45.751669 41.503778 45.856614
1.0005 1.0004 1.0013 0.9998
−0.1153 −0.1379 −0.0571 −0.1810
memb bend
= a3
= b1
n n
3
+ a2
n
2
+ a1
n
+ a 0.
(7) (8)
+ b0
Thus, the values obtained for local stress at the weld toe vary linearly with the values of structural stress, as shown in Fig. 11. From this figure, the values of Kt for the weld series were obtained by linear regression. The relation between the stress concentration factor and the weld toe radius, considering eight radii that varied from 1.38 to 2.44 mm, is presented in Fig. 12. Thus, the relationship obtained for the variation of Kt with ρ was: (9)
0.121
Kt = 1.2606
with a correlation coefficient of 95.32%. Fig. 11. Relation between
wt
4.3. Fatigue testing
and.Ss
Master design curves were obtained for nominal, structural and effective notch stresses. The characteristic curves for a survival probability of 97.7% were obtained in agreement with IIW recommendations [9]. The design curves were presented with R = 0 in order to eliminate the effect of uneven mean stress caused by non-linear variation of both wt and bend with nominal stress. Thus, the equivalent stress cycles were calculated by the Smith-Watson-Topper [21] equation: ar
=
max
×
a
=
max
1
R 2
(10)
where ar is the stress amplitude range of the reverse cycle, max is the maximum stress and a is the stress amplitude. The effective notch stresses were computed by means of equation: e
Fig. 12. Relation between K t and ρ
= 1.2606
f
0.121
Ss
(11)
where f is the fictitious radius and Ss is the structural stress. The value of f was obtained by equation (2), adopting the value of multiaxiality factor obtained by Filippi et al. [17] for normal stress criterion and opening angle equal to 120° (s = 3.67 ), the same conditions under investigation in this work. As there is no verified value of microstructural length for aluminium welds so far [14], an estimation of this value was carried out basing in the complete fatigue data. The estimation of ρ* consisted in the calculation of the effective notch stress ( e ) for the fatigue data, applying equation (11) for a given value of . Then, a power law function was fitted by least squares method to the calculated e data and to the experimental data of fatigue life. The variation of from 0.05 to 0.5 mm resulted in regressions with different correlation coefficients (R2). Thus, the value of estimated by this method was the one that reached the maximum correlation coefficient. The values of ρ used during the eswere defined, considering the worst-case scenario for timation of weld series 1, 2 and 3, since their fracture surfaces presented multinucleation, as will be seen in the next section. In this work, the worstcase scenario is that in which the fictitious radius assumes the smallest value for a given . Therefore, the value of ρ for the weld series 1, 2 and 3 ( 1, 2 and 3 respectively) was 1 = 2 = 3 = 0 mm . On the other hand, value of ρ for the weld series 4 ( 4 ) was 4 > 0 mm , since multinucleation was not observed in weld series 4. Thus, the value of 4
Fig. 13. Relation between R2 and.
the finite element model into account. Thus, the local stress at the weld toe and the bending stress did not vary linearly with the nominal stress, as can be seen in Fig. 10a and 10b respectively. On the other hand, the membrane stress varies linearly, see Fig. 10c, as expected since the 74
International Journal of Pressure Vessels and Piping 173 (2019) 68–78
P.I. Oliveira, et al.
Fig. 14. Master S–N curves for: a) nominal stress, b) structural stress c) effective notch stress obtained for case 1, d) effective notch stress obtained for case 2, e) effective notch stress obtained for case 3.
correlation coefficients are plotted as a function of microstructural length considering 1 = 2 = 3 = 0 mm and 4 = 0.70 mm . This figure shows that the maximum value of R2 occurs for = 0.15 mm . Thus, the estimated value of microstructural length ( = 0.15 mm ) and the one proposed by Zhang et al. [14] for aluminium welds ( = 0.21 mm ) were used to compute the effective notch stresses in this investigation. The former value of was used because led to the best correlation of the experimental data. The latter one was applied since the crack initiation occurred in the filler material for all weld series under investigation, as will be discussed in the next section. The master S–N curves were created considering the nominal
Table 8 Cases for effective stress calculation. Case 1 2 3
(mm) 0.15 0.21 0.15
1
0 0 0
(mm)
2
0 0 0
(mm)
3
0 0 0
(mm)
4
(mm)
0 0 0.70
was defined from the statistical treatment presented in Table 6. The adopted value ( 4 = 0.70 mm ) had the same probability of the radius of the weld series with the lowest probability of being zero. In Fig. 13, the 75
International Journal of Pressure Vessels and Piping 173 (2019) 68–78
P.I. Oliveira, et al.
Fig. 15. 95% confidence bands and comparison between median S–N curves for: a) effective notch stress (case 1) and b) nominal stress.
(Fig. 14a), structural (Fig. 14b) and effective notch (Fig. 14c-e) stresses. The effective notch stresses were calculated by means of equation (11), considering the cases summarised in Table 8. Cases 1 and 2 considered the worst-case scenario for all weld series. In case 3, the worst-case scenario was assumed for weld series 1, 2 and 3 because of the multinucleation at their fracture surfaces, as already mentioned. On the other hand, a value of 4 > 0 mm was chosen in order to minimize the data scatter, considering that multinucleation was not observed in weld series 4. The scatter of the S–N curves for nominal (Fig. 14a) and structural (Fig. 14b) presented almost the same value. This indicates that the angular misalignment, considered in the curve for structural stress, did not affect the scatter data. Beyond that, the S–N curves for the effective notch stresses obtained considering cases 1 and 2 (Fig. 14c-d) presented the same scatter of the structural stress (T = 1.29). Thus, the data scatter did not change when the same value of was adopted for all weld series. Furthermore, the S–N curve for the effective notch stresses
obtained considering case 3 (Fig. 14e) presented the lowest scatter (T = 1.20) . This means that the weld toe radius of weld series 4 significantly affected the data scatter. Finally, all master S–N curves presented in Fig. 14 present a low value of scatter since all have T < 1.40 [7]. Furthermore, the lowest S–N curve slope was obtained for the nominal stress (m = 4.7 ). The slope of the curve for the structural stress is equal to the ones for the effective notch stresses obtained considering cases 1 and 2 (m = 5.1). Beyond that, the highest S–N curve slope was obtained with case 3 (m = 6.2 ). According to these results, the angular misalignment affected the slope, since the S–N curve slope for structural stress, that considered the misalignment, was higher than the one for nominal stress. Beyond that, the increase in 4 increased the value of the slope, comparing Fig. 14c and 14e. Additionally, the value of fatigue resistance of the characteristic curve (Ps = 97.7%) for the life of 2 × 106 is higher in case 1 than in case 2. This occurred because the value of was different in each case. 76
International Journal of Pressure Vessels and Piping 173 (2019) 68–78
P.I. Oliveira, et al.
= 0.15 mm led to values of e slightly higher than the ones for Thus, = 0.21 mm . Fig. 15 presents the 95% confidence bands for the median S–N curves according to ASTM E 739 Standard, using all the data from the four welded series under study. The S–N curves from other authors are also superimposed for comparison. Fig. 15a presents the S–N curve for the effective notch stress calculated considering case 1. Superimposed on this figure is the median S–N curve presented by Eibl et al. [7] for thin-sheets of laser beam welded aluminium alloys. According to the figure, the median S–N curves can be consider equivalents, for the data interval analysed in this research, because the curve of Eibl et al. [7] was plotted integrally inside of the confidence bands. This indicates that the experimental results are better characterized by case1. On the other hand, Fig. 15b presents the median S–N curve for the nominal stress of the joints in study and the S–N curve presented by Prisco et al. [5] for a laser welded T-joint made with AA6156 as the skin and with AA2139 as the clip. The fatigue strength of the joints studied was higher than that presented by Prisco et al. [5]. In addition, they cannot be considered equivalent because the median S–N curve was not plotted thoroughly inside of the confidence bands. Finally, a comparison was carried out between the fatigue life of the laser welded T-joints under investigation and the lifetime obtained by Yasniy et al. [22] for 6 mm thick plates of AA2024-T3 with cold expanded hole, a process that improves the fatigue life by creating a compressive residual stress in the holes of structural elements such as those used in riveted structures. Considering a nominal stress of 147 MPa and a stress ratio of 0.02, the total lifetime for the laser welded T-joint, for the plate with a hole with 8 mm diameter and for the plate with cold expanded hole (with 8 mm diameter and cold expansion degree of 2.37%) are, respectively, 209,511 cycles, 94,047 cycles and 189,791 cycles. Thus, it is possible to note that the laser welded joint had the highest total lifetime. The fatigue life of the welded joint had 115,464 more cycles than the plate with hole and 19,720 more cycles than the plate with cold expanded hole. 4.4. Fracture morphology SEM fractographies showed that the specimens of weld series 1, 2 and 3 present fractures with multinucleations, as illustrated in Fig. 16a
Fig. 16. Fracture surface of a) weld series 1 and b) weld series 4.
Fig. 17. Cracks progress up through the weld material and in the transition from the weld metal to the heat-affected material. a) Fracture surface of a specimen of series 3; b) magnification of the transition from the weld metal to the heat-affected material. 77
International Journal of Pressure Vessels and Piping 173 (2019) 68–78
P.I. Oliveira, et al.
with a specimen from series 1. On the other hand, the specimens of weld series 4 did not present multinucleation in their fracture surface, as shown in Fig. 16b as a typical example. The absence of multinucleation in weld series 4 can be explained by the lowest mean standard deviation of the weld toe radius presented in Table 6. While the higher values of scatter of the weld toe radius for the others weld series in Table 6 seem to contribute to the increase in multinucleation. That is, higher values of mean standard deviation for weld toe radii are related to geometric imperfections that affect the fatigue strength. Therefore, the use of the worst-case scenario is justified. In addition, the crack initiation occurred in the filler material for all the weld series. Fig. 17 shows pores at the fracture surface which indicates that the cracks progress through the added material. Additionally, the detail shows the transition from the fusion zone to the heat-affected base material.
[2]
[3] [4] [5]
[6] [7]
5. Conclusions
[8] [9] [10]
The following conclusions can be drawn based on the results presented in this study: (1) The reference weld toe radius has effect on both the data scatter and the slope of the S–N curves; (2) The angular misalignment affects the slope of the S–N curves; (3) The median S–N curve obtained with a reference weld toe radius of 0 mm and with a microstructural length of 0.15 mm is equivalent to the S–N curve of laser welded joints, studied by Eibl et al. [7]; (4) The fatigue life of the laser welded T-joint is greater than the lifetime of some plates with cold expanded hole, investigated by Yasniy et al. [22]; and (5) The geometric imperfections caused by the variation of the weld toe radius generates multinucleation in some weld series.
[11] [12] [13]
[14] [15] [16]
Acknowledgments This research is sponsored by FEDER funds through the programme COMPETE – Programa Operacional Factores de Competitividade – and by national funds through FCT – Fundação para a Ciência e a Tecnologia –, under the project UID/EMS/00285/2013. The first author, Pedro I. P. Oliveira, is supported by the Brazilian National Council for Scientific and Technological Development (CNPq).
[17] [18] [19]
Appendix A. Supplementary data
[20] [21]
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.ijpvp.2019.05.001.
[22]
References [1] D. Dittrich, J. Standfuss, J. Liebscher, B. Brenner, E. Beyer, Laser beam welding of
78
hard to weld Al alloys for a regional aircraft fuselage design- First results, Phys. Procedia 12 (2011) 113–122, https://doi.org/10.1016/j.phpro.2011.03.015. M. Zain-ul-abdein, D. Nélias, D. Deloison, Experimental Investigation and Finite Element Simulation of Laser Beam Welding Induced Residual Stresses and Distortions in Thin Sheets of AA 6056-T4 vol. 527, (2010), pp. 3025–3039, https:// doi.org/10.1016/j.msea.2010.01.054. Z.Y. Huang, Z. Luo, Z.M. Liu, Y. Li, Y.C. Cai, Y. Zhang, Deformation behaviour of thin aluminium alloy plates during laser welding, 37 (2017) 291–309. J. Baumgartner, Review and considerations on the fatigue assessment of welded joints using reference radii, Int. J. Fatigue 101 (2017) 459–468, https://doi.org/10. 1016/j.ijfatigue.2017.01.013. A. Prisco, F. Acerra, A. Squillace, G. Giorleo, C. Pirozzi, U. Prisco, et al., LBW of similar and dissimilar skin-stringer joints. Part I: process optimization and mechanical characterization, Adv. Mater. Res. 38 (2008) 306–319 https://doi.org/10. 4028/www.scientific.net/AMR.38.306. V. Ventzke, S. Riekehr, M. Horstmann, P. Haack, N. Kashaev, One-sided Nd:YAG laser beam welding for the manufacture of T-joints made of aluminium alloys for aicraft construction, Weld. Cut. 13 (2014) 245–249. M. Eibl, C.M. Sonsino, H. e Kaufmann, G. Zhang, Fatigue assessment of laser welded thin sheet aluminium, Int. J. Fatigue 25 (2003) 719–731, https://doi.org/10.1016/ S0142-1123(03)00053-7. J.D. Burk, F.V. Lawrence, Influence of bending stresses on fatigue crack propagation life in butt joint welds, Weld. Res. Suppl. 2 (1977) 61–66. A. Hobbacher, Recommendations for fatigue design, Update 39 (2004) 33–46. S. Liinalampi, H. Remes, P. Lehto, I. Lillemäe, J. Romanoff, D. Porter, Fatigue strength analysis of laser-hybrid welds in thin plate considering weld geometry in microscale, Int. J. Fatigue 87 (2016) 143–152, https://doi.org/10.1016/j.ijfatigue. 2016.01.019. D. Radaj, C.M. Sonsino, W. Fricke, Recent developments in local concepts of fatigue assessment of welded joints, Int. J. Fatigue 31 (2009) 2–11, https://doi.org/10. 1016/j.ijfatigue.2008.05.019. H. Neuber, Theoretical calculation of strength at stress concentration, Czech. J. Phys. B 19 (1969) 400–400 https://doi.org/10.1007/BF01712885. C. Morgenstern, C.M. Sonsino, A. Hobbacher, F. Sorbo, Fatigue design of aluminium welded joints by the local stress concept with the fictitious notch radius of rf=1 mm, Int. J. Fatigue 28 (2006) 881–890, https://doi.org/10.1016/j.ijfatigue.2005. 10.006. G. Zhang, C.M. Sonsino, R. Sundermeier, Method of effective stress for fatigue: Part II - applications to V-notches and seam welds, Int. J. Fatigue 37 (2012) 24–40, https://doi.org/10.1016/j.ijfatigue.2011.09.016. D. Radaj, P. Lazzarin, F. Berto, Generalised Neuber concept of fictitious notch rounding, Int. J. Fatigue 51 (2013) 105–115, https://doi.org/10.1016/j.ijfatigue. 2013.01.005. F. Berto, P. Lazzarin, D. Radaj, Fictitious notch rounding concept applied to sharp V-notches: evaluation of the microstructural support factor for different failure hypotheses. Part II: microstructural support analysis, Eng. Fract. Mech. 76 (2009) 1151–1175, https://doi.org/10.1016/j.engfracmech.2008.01.015. S. Filippi, P. Lazzarin, R. Tovo, Developments of some explicit formulas useful to describe elastic stress fields ahead of notches in plates, Int. J. Solids Struct. 39 (2002) 4543–4565, https://doi.org/10.1016/S0020-7683(02)00342-6. ASM Handbook, Properties and Selection: Nonferrous Alloys and Special-Purpose Materials vol. 2, (2005). P.I. Oliveira, J.M. Costa, A. Loureiro, Effect of laser beam welding parameters on morphology and strength of dissimilar AA2024/AA7075 T-joints, J. Manuf. Process. 35 (2018), https://doi.org/10.1016/j.jmapro.2018.08.003. M. Koçak, S. Webster, J.J. Janosch, R.A. Ainsworth, R. Koers, FITNET: Fitness-ForService, GKSS Research Centre Geesthacht, 2008. J.D.M. Costa, J.S. Jesus, A. Loureiro, J.A.M. Ferreira, L.P. Borrego, Fatigue life improvement of mig welded aluminium T-joints by friction stir processing, Int. J. Fatigue 61 (2014) 244–254, https://doi.org/10.1016/j.ijfatigue.2013.11.004. P. Yasniy, S. Glado, V. Iasnii, Lifetime of aircraft alloy plates with cold expanded holes, Int. J. Fatigue 104 (2017) 112–119, https://doi.org/10.1016/j.ijfatigue. 2017.07.012.
Contents lists available at ScienceDirect
International Journal of Pressure Vessels and Piping journal homepage: www.elsevier.com/locate/ijpvp
Fatigue strength assessment of misaligned laser beam welded T-joints by effective stress method
T
P.I. Oliveiraa,∗, A. Loureiroa, J.M. Costaa, J. Ferreiraa, L. Borregoa,b a b
CEMMPRE, Mechanical Engineering Department, University of Coimbra, Rua Luís Reis Santos, 3030-788, Coimbra, Portugal Mechanical Engineering Department, Coimbra Polytechnic, ISEC, Rua Pedro Nunes, 3030-199, Coimbra, Portugal
ARTICLE INFO
ABSTRACT
Keywords: Effective stress Fatigue strength Laser beam welding Angular misalignment Aluminium thin plates
This paper investigates the effect of the joint misalignment and the weld geometry on the fatigue strength of successive double-sided laser beam welded AA2024 and AA7075 T-joints using AA4047 filler wire. A finite element model was set up considering the misalignment and the weld geometry to obtain the notch stress. The effective notch stress was calculated by the fictitious radius concept and a microstructural length of 0.15 mm was estimated. Master design curves are proposed for different weld toe radii and microstructural length. The experimental results were better characterized by both a reference weld toe radius of 0 mm and a microstructural length of 0.15 mm. Furthermore, the geometric imperfections caused by variations on the weld toe generate fractures initiated by crack multinucleation.
1. Introduction The interest in reducing the weight of airplane structures and in reducing both cost and time of aircraft manufacturing are the main reasons why the aviation industry investigates laser beam welding (LBW) as a joining technology to replace the riveted joints in stiffened panels [1]. However, the welding process leads to undesirable outcomes such as residual stresses and distortions. These problems are very common in welded joints of aluminium alloys due to their high thermal expansion coefficient. In general, residual stress and distortion are inversely related. Furthermore, residual stress and distortion are strongly affected by restraint degree during the welding process. Thus, the welded joints with higher restraint degree have lower distortion but higher residual stress and vice-versa. The laser welded T-joints studied by Zain-ul-abdein et al. [2], for instance, presented very small transverse residual stress because only the clip restricted the out-of-plane displacements in its experimental set up. Despite this, the angular distortion is the largest welding deformation in laser welded joints made of thin sheets of aluminium alloys [3]. For laser welded T-joints made of 2.5 mm thick sheets of AA6056-T4, the compressive longitudinal residual stress in the heat-affected zone induced a significant deformation of the skin sheet in the vicinity of the fusion zone. This residual plastic strain was caused by both softening of the fusion zone material and positioning of the stringer [2]. Beyond the welding distortions and residual stresses, other factors such as variation in weld geometry along
∗
the weld seam, weld defects, and the high gradients of microstructure and hardness in the vicinity of the notch may significantly affect the fatigue assessment of welded joints [4]. In this research, only the influence of the joint and weld geometry will be addressed. The crack initiation occurring at the weld toe in simultaneous double-sided laser welded T-joints [5] and in single-sided laser welded T-joints was studied by Ventzke et al. [6]. However, the effect of the weld toe on the fatigue strength was neglected concerning the laser welded butt-joints studied by Eibl et al. [7] due to their modest weld toe curvature. In addition, the same authors mention that a single-sided laser welded T-joint and a butt-joint had the same fatigue strength when their weld toe curvatures were similar [7]. Another factor that may affect the local stress at the weld toe of welded T-joints is the angular misalignment caused by the welding process. According to Burk and Lawrence [8], the partial straightening of a misaligned specimen under axial load induces bending even when the angular distortion is small. Therefore, the bending stress cannot be ignored when bending and axial loads are combined, unless the fatigue assessment is carried out by applying a design S–N curve (FAT class) and the misalignment is lower than the one which is already included in that FAT class [9]. Besides this, geometric imperfections increase the scatter of the fatigue data mainly in the welded joints of thin sheets. Liinalampi et al. [10] measured the weld geometry on a microscale to apply realistic radii in the fatigue assessment of laser-hybrid butt joints. However,
Corresponding author. E-mail address: [email protected] (P.I. Oliveira).
https://doi.org/10.1016/j.ijpvp.2019.05.001 Received 14 September 2018; Received in revised form 17 April 2019; Accepted 1 May 2019 Available online 02 May 2019 0308-0161/ © 2019 Elsevier Ltd. All rights reserved.
International Journal of Pressure Vessels and Piping 173 (2019) 68–78
P.I. Oliveira, et al.
The microstructural length is a material parameter and related to material strength, as observed by Liinalampi et al. [10]. Therefore, the microstructural length is different for the base material (BM), heat-affected zone (HAZ) and fusion zone (FZ), depending in which of these zones the crack initiation occurs [13]. Zhang et al. [14] presented a = 0.21 mm for aluminium welds. This value was calculated value of considering a complete fatigue data. These data were fitted by least squares method using a power law function. The effective stress ranges were calculated using the Neuber's solution for a given value of . The variation of in the computing of e resulted in regressions with different coefficient of determination (R2). Thus, the value of that resulted in a regression with the maximum value of R2 was chosen as the microstructural length for aluminium welds. Liinalampi et al. [10] observed, for laser-hybrid welded butt-joints made with 3 mm thick steel sheets, a large axial misalignment caused by the high stress gradient. However, the influence of a stress gradient was almost com= 0.40 mm , pletely neglected in the effective stress calculation using the value commonly used for steels. Additionally, they verified that = 0.05 mm was more sensitive to the stress gradient caused by the joint misalignment. This was evidenced by the lowest value of the S–N = 0.05 mm when S–N scatter was examined scatter that occurred for as a function of . The multiaxial factor depends on the loading mode (1, 2, 3 or mixed), the strength criterion (normal stress or von Mises) and the multiaxiality condition (plane stress or plane strain) [15]. According to Berto et al. [16], the value of s converges to a plateau value for . On the other hand, the value of s may be different from the plateau value for < . However, the same authors considered that the plateau values of s are satisfactory for engineering applications in structural strength assessments of V-notch specimens ( = 0 ) considering different values of both microstructural length and notch opening angle. Beyond that, the notch opening angle has a significant influence on s, since its plateau value for normal stress criterion considering Fillipi's equations [17], for instance, varies from 2.0 to 6.38 when the notch opening angle is varied from 0° to 150° [16]. Taking into account that the weld toe radius might be uneven along the weld seam and that the angular misalignment cannot be neglected to evaluate the local stress at the weld toe, the aim of this research is to investigate which geometric factors affect the fatigue strength of successive double-sided laser beam welded T-joints made of AA2024 as the skin, AA7075 as the clip and using AA4047 as the filler wire.
Fig. 1. Neuber's stress averaging approach to calculate effective notch stress at a welded joint and fictitious notch radius.
realistic radii are difficult to measure [4]. Therefore, in general, the effect of variations in geometry are addressed by the effective notch stress approach [10]. For the fatigue assessment of laser beam welded thin-sheet joints (t 3 mm ) at the weld root notches, the most successful notch stress approach has been the one that applies a reference radius of 0.05 mm [11]. In this case, the notch stress can be applied directly on the fatigue assessment without considering any support effects. However, the notch stresses obtained at the weld toe with this reference radius are not realistic therefore its use is restricted to root notch assessments [4]. On the other hand, Neuber's stress average approach [12] has been proposed to assess the effective stress ( e ) at the notch by taking into account the effect of the stress field gradient in the notch ligament [4]. The effective stress is calculated by equation (1), where is the microstructural length and x (y ) is the stress distribution along the normal path to the sheet surface, as illustrated in Fig. 1. e
=
1
2. Materials and experimental methods 2.1. Base materials and filler wire
x (y ) dy
(1)
0
Dissimilar T-joints made of 2 mm thick plates of AA2024-T3 as the skin and AA7075-T6 as the clip were welded using AA4047 filler wire with 1 mm diameter. The size of the plates was 500 mm × 160 mm and 500 mm × 40 mm, respectively, for the skin and the clip, and they were cut perpendicular to the plate rolling direction. Table 1 presents the chemical composition of the base materials and the filler metal used and Table 2 shows the mechanical properties of the base materials obtained experimentally according to ASTM E 8 Standard. In order to obtain the mechanical properties, the tensile tests were performed with a tensile tester INSTRON model 4206 using an upper crosshead speed of 2.0 mm/min.
To simplify the procedure to obtain e , the concept of fictitious notch round was introduced by Neuber [12]. According to this concept, the effective stress is determined directly by means of an artificial enlargement of the notch radius, so that the fictitious-notch stress be equal to the effective stress of the real structure. The fictitious notch radius ( f ) is computed by equation (2), where is the actual notch radius and s is the factor that consider the effects of multiaxial stress on failure. The fictitious notch radius is illustrated in Fig. 1. f
=
+s
(2)
Table 1 Chemical composition of base materials and filler wire (% wt.) [18]. Alloy
Si
Fe
Cu
Mn
Mg
Cr
Zn
Ti
Al
AA2024 AA7075 AA4047
max 0.50 max 0.40 11.00 13.00
max 0.50 max 0.50 max 0.6
3.80 4.90 1.20 2.00 max 0.30
0.30 0.90 max 0.30 max 0.15
1.20 1.80 2.10 2.90 max 0.10
– 0.18 0.28 –
max 0.25 5.10 6.10 max 0.20
max 0.15 max 0.20 max 0.15
Bal. Bal. Bal.
69
International Journal of Pressure Vessels and Piping 173 (2019) 68–78
P.I. Oliveira, et al.
Table 2 Mechanical properties of the base materials. Ultimate Stress, AA2024-T3 AA7075-T6
UTS
(MPa)
Yield stress,
479 592
YS
(MPa)
359 529
Young's modulus, E (GPa)
Strain at σUTS (%)
78.6 74.4
13.6 9.1
Fig. 2. Schematic diagram of T-joint welding. Table 3 Welding parameters used in the series studied. Weld series
α (°)
s (mm/s)
F (m/min)
P (kW)
δ (mm)
1 2 3 4
10 10 15 15
40 40 40 35
4.3 4.3 4.3 3.8
3.4 2.9 3.4 3.0
0.0 0.3 0.0 0.0
P - laser beam power, s - welding speed, F - feed rate of filler wire, α - incident beam angle and δ - incident beam position.
2.2. Experimental set-up and welding conditions The base material plates were burnished with a steel brush and cleaned with acetone in order to remove the oxides and contaminated layers from the surfaces of the work pieces before carrying out the welding. Then, the successive double-sided laser beam welded T-joints were carried out according to the scheme shown in Fig. 2. Fig. 2a presents the incident beam position (δ) and the incident beam angle (α), the angle α is 5° lower than the angle between the skin surface and the supply plane. According to Fig. 2b, both shielding gas and filler wire were supplied in the same plane, the gas nozzle is set behind the laser beam and the filler wire in the leading direction, forming angles of 25° with the welding direction.
Fig. 4. –Geometry of fatigue test specimens.
A continuous wave disk laser TruDisk 16002 with 12 kW maximum power was used to generate a laser beam with 1.030 μm wavelength. Furthermore, a focusing optic BEO D70 with 200 mm focal length was applied and the focal point was established on the clip surface. The laser spot diameter was 600 μm, the same diameter as the optical fibre. Further, argon was used as the shielding gas with a flow rate of 10 l/ min.
Fig. 3. Schematic diagram of misaligned specimen. 70
International Journal of Pressure Vessels and Piping 173 (2019) 68–78
P.I. Oliveira, et al.
The weld series studied in this work were produced mainly by varying the laser beam power (P) and incident beam angle (α), though other parameters such as the welding speed (s), the feed rate of filler wire (F), and the incident beam position (δ) were changed too, according to Table 3. These weld series were chosen because they presented low amount of porosity according to previous investigations [19].
Table 4 –Number of fatigue tests and their load levels. Load (N)
Number of tests
6000 5500 5250 5000 4500 4250 4000 4125 3750
3 5 3 3 9 4 1 7 4
2.3. Geometrical features of the misaligned specimens The geometric features of the misaligned specimens depicted in Fig. 3 are angular distortion (θ), distance between weld toes (d) and
Fig. 5. Gripping of the model: a) initial position and b) final position.
Fig. 6. Finite element mesh.
Fig. 7. σxx stress field (weld series 4; p = 8000 N).
71
International Journal of Pressure Vessels and Piping 173 (2019) 68–78
P.I. Oliveira, et al.
2.4. Fatigue testing Fatigue testing was conducted according to ASTM E 466 Standard. The fatigue tests were carried out in load control at a frequency of 25 Hz, applying sinusoidal tensile loadings with constant amplitude and stress ratio (R) equal to 0.02 using a machine INSTRON model 1341 with an 8800 series servo-hydraulic control system from INSTRON. The specimens were manufactured according to Fig. 4. The number of fatigue tests carried out and their loads are presented in Table 4. After the fatigue testing, the fracture surfaces of the specimens were characterized using a scanning electron microscope Zeiss Merlin-61-50. 3. Finite element analysis The local stress approach was used to assess the influence of the combined bending and axial loading on the fatigue life of the misaligned T-joints, since axial loading induces bending in them. Thus, the notch stresses were obtained with help of finite element models. The misaligned specimens were analysed by the finite element method using the software Marc-Mentat. As illustrated in Fig. 5a, the model was fixed on the left side to an extension of 30 mm in order to simulate the gripping step, that is, in order to avoid any type of rotation and displacement of the left extremity. The right side of the model, initially free, was gripped, as depicted in Fig. 5b, and then a longitudinal loading of up to a maximum load of 8 kN was applied on the right side of the model. The load was uniformly distributed on the 26 nodes of the right extremity of the model. During the loading phase, it was considered that there was no friction between the model and the grippers so that only the displacement in the loading direction was allowed. The loading was divided into 900 increments, 100 were related to gripping and 800 related to the axial load application. The finite element procedure that simulate the gripping step was like the experimental procedure. However, the load applying procedure was not the same used in experimental procedure, since the gripper did not displace together with the right extremity of the model neither there was friction between them. The finite element mesh, shown in Fig. 6, is composed of two-dimensional linear elements with 4 nodes and full integration, consisting of 16,400 elements and 17,106 nodes. The mesh is finer at the weld toe zone, where the greatest stresses are expected. The model presents 3 zones with different materials, the: molten zone, 2024 aluminium alloy
Fig. 8. Relation between notch stress and structural stress. Table 5 Dimensions of the joint. Weld Series
θ (°)
d (mm)
r (mm)
1 2 3 4
1.15 1.45 1.30 1.45
7,17 6,25 7,03 6,36
128.56 83.68 111.03 86.46
concordance radius (r). Furthermore, detail A of the figure indicates that the weld seam has an average angle of 120° and detail B shows the definition of the weld toe radius (ρ). The average angular distortions were measured using a digital goniometer model Schut GR180. The distance between the weld toes was measured from cross section as shown in Fig. 3, using a stereo microscope provided with digital micrometres in two perpendicular directions. Furthermore, a Mitutoyo projector was used to measure the X–Y coordinates of three points on the weld seam profile of the fatigue specimens to obtain the weld toe radius by means of the software Geogebra. Samples of up to 23 radii values were obtained for all the weld series and statistically treated.
Fig. 9. Examples of macrographs of the weld beads.
72
International Journal of Pressure Vessels and Piping 173 (2019) 68–78
P.I. Oliveira, et al.
Table 6 Statistical results of the weld toe radius (ρ) data. Weld Series
Data number
Mean (mm)
Mean standard deviation (mm)
1 2 3 4
22 23 21 22
2.06 2.44 2.28 2.13
0.51 0.61 0.83 0.35
and 7075 aluminium alloy. All materials were assumed as homogeneous, isotropic and linear elastic during the simulation. The Young's moduli used in finite element model were those presented in Table 2 for 2024 and 7075 aluminium alloys and the value of E adopted for the molten zone was 70 GPa, value found in the literature for aluminium alloys [18]. The Poisson's ratio used in finite element analysis was 0.33 for all zones, in agreement with the literature [18]. According to Fig. 7, the maximum notch stress occurred at the weld toe, assuming the value of 609.9 MPa when the model of weld series 4 was under a nominal stress of 320 MPa. An elastic analysis was carried out in this study because the FITNET – European Fitness for Service Network [20] stresses that the fatigue assessment using notch stresses can be done since the notch stress range is lower than 2 YS . Thus, the notch stress can be approximated as purely elastic when the plastic deformation is not appreciable. According to IIW recommendations [9], the stress at the weld toe ( wt ) for misaligned joints is composed by membrane stress ( memb ), bending stress ( bend ) and non-linear stress peak ( nl ). Considering the through-thickness stress distribution depicted in Fig. 1, the values of memb and bend can be obtained from finite element results, respectively, by equations (3) and (4), where t is the plate thickness. Then, the structural stress (Ss ) is calculated by equation (5). Thus, the stress concentration factor (Kt ) is computed according to equation (6) for a stress cycle with a stress ratio equal to zero. In this theoretical definition of Kt , both notch stress and structural stress consider the bending stress induced by the gripping, as well as the membrane stress and the secondary bending stress induced by axial loading. memb
bend
Ss = Kt =
1 t
=
=
6 t2
memb
t x (y )
dy
(3)
0
t
( x (y )
memb )
0
+
t2 2
y dy
bend
wt
Ss
(4) (5) Fig. 10. Stresses for K t calculation: a) bending stress, b) notch stress and c) membrane stress.
(6)
According to Fig. 8, the notch stress at the weld toe varies linearly with the structural stress, and Kt is the slope of a straight line that represents the relation between them. This straight line was obtained by linear regression of the data of both notch stress and throughthickness stress distribution generated during the loading phase of the finite element model for each loading increment. In addition, the normal stress criterion was adopted to generate these data.
toe radius data obtained from the fatigue specimens. According to these data, weld series 4 presented the lowest radii scatter and weld series 3 the largest one. The data on the weld toe radius presented a random variation along the weld seams. Therefore, considering that the fatigue life is a weakest link problem, a smallest radius is always more representative of the experimental results.
4. Experimental results and discussion 4.1. Geometry of the joints
4.2. Stress concentration factor
The geometrical features of the misaligned specimens are presented in Table 5, according to Fig. 3. Thus, the variation in the angular distortion among the weld series is significant. Weld series 1 presented the lowest angular distortion while weld series 2 and 4 showed the highest ones. The distance between the weld toes was obtained from the macrographs such as those presented in Fig. 9. Table 6 presents the results of the statistical treatment of the weld
The stress concentration factor was calculated according to equation (6). Therefore, before the calculation of Kt was necessary to obtain the local stress at the weld toe from the finite element models, as well as to calculate both the membrane stress and the bending stress induced by both the gripping and the axial loading from finite element data by equations (3) and (4) respectively. The variations of wt , memb and bend with nominal stress are shown in Fig. 8, taking the load increments of 73
International Journal of Pressure Vessels and Piping 173 (2019) 68–78
P.I. Oliveira, et al.
material is assumed linear elastic. Furthermore, Fig. 10a shows that the bend increases with angular distortion and that the curves of bend for weld series with the same θ are overlapped. The curves of memb of all weld series also are overlapped, as shown Fig. 10c. Thus, the values of memb and bend can be obtained, respectively, by equations (7) and (8), where n is the nominal stress. The coefficients ai (for i = 0, 1, 2 and 3) of equation (7) and bj (for j = 0 and 1) of equation (8) are presented in Table 7 for each weld series. The correlation coefficients (R2) of equations (7) and (8) were, respectively, 99,997% and 100% for all weld series.
Table 7 Coefficients of equations (7) and (8) for each weld series. Weld Series
a3
a2
a1
a0
b1
b0
1 2 3 4
0.000003 0.000004 0.000004 0.000004
−0.001981 −0.002679 −0.002263 −0.002654
0.779266 0.973324 0.867794 0.976271
36.404651 45.751669 41.503778 45.856614
1.0005 1.0004 1.0013 0.9998
−0.1153 −0.1379 −0.0571 −0.1810
memb bend
= a3
= b1
n n
3
+ a2
n
2
+ a1
n
+ a 0.
(7) (8)
+ b0
Thus, the values obtained for local stress at the weld toe vary linearly with the values of structural stress, as shown in Fig. 11. From this figure, the values of Kt for the weld series were obtained by linear regression. The relation between the stress concentration factor and the weld toe radius, considering eight radii that varied from 1.38 to 2.44 mm, is presented in Fig. 12. Thus, the relationship obtained for the variation of Kt with ρ was: (9)
0.121
Kt = 1.2606
with a correlation coefficient of 95.32%. Fig. 11. Relation between
wt
4.3. Fatigue testing
and.Ss
Master design curves were obtained for nominal, structural and effective notch stresses. The characteristic curves for a survival probability of 97.7% were obtained in agreement with IIW recommendations [9]. The design curves were presented with R = 0 in order to eliminate the effect of uneven mean stress caused by non-linear variation of both wt and bend with nominal stress. Thus, the equivalent stress cycles were calculated by the Smith-Watson-Topper [21] equation: ar
=
max
×
a
=
max
1
R 2
(10)
where ar is the stress amplitude range of the reverse cycle, max is the maximum stress and a is the stress amplitude. The effective notch stresses were computed by means of equation: e
Fig. 12. Relation between K t and ρ
= 1.2606
f
0.121
Ss
(11)
where f is the fictitious radius and Ss is the structural stress. The value of f was obtained by equation (2), adopting the value of multiaxiality factor obtained by Filippi et al. [17] for normal stress criterion and opening angle equal to 120° (s = 3.67 ), the same conditions under investigation in this work. As there is no verified value of microstructural length for aluminium welds so far [14], an estimation of this value was carried out basing in the complete fatigue data. The estimation of ρ* consisted in the calculation of the effective notch stress ( e ) for the fatigue data, applying equation (11) for a given value of . Then, a power law function was fitted by least squares method to the calculated e data and to the experimental data of fatigue life. The variation of from 0.05 to 0.5 mm resulted in regressions with different correlation coefficients (R2). Thus, the value of estimated by this method was the one that reached the maximum correlation coefficient. The values of ρ used during the eswere defined, considering the worst-case scenario for timation of weld series 1, 2 and 3, since their fracture surfaces presented multinucleation, as will be seen in the next section. In this work, the worstcase scenario is that in which the fictitious radius assumes the smallest value for a given . Therefore, the value of ρ for the weld series 1, 2 and 3 ( 1, 2 and 3 respectively) was 1 = 2 = 3 = 0 mm . On the other hand, value of ρ for the weld series 4 ( 4 ) was 4 > 0 mm , since multinucleation was not observed in weld series 4. Thus, the value of 4
Fig. 13. Relation between R2 and.
the finite element model into account. Thus, the local stress at the weld toe and the bending stress did not vary linearly with the nominal stress, as can be seen in Fig. 10a and 10b respectively. On the other hand, the membrane stress varies linearly, see Fig. 10c, as expected since the 74
International Journal of Pressure Vessels and Piping 173 (2019) 68–78
P.I. Oliveira, et al.
Fig. 14. Master S–N curves for: a) nominal stress, b) structural stress c) effective notch stress obtained for case 1, d) effective notch stress obtained for case 2, e) effective notch stress obtained for case 3.
correlation coefficients are plotted as a function of microstructural length considering 1 = 2 = 3 = 0 mm and 4 = 0.70 mm . This figure shows that the maximum value of R2 occurs for = 0.15 mm . Thus, the estimated value of microstructural length ( = 0.15 mm ) and the one proposed by Zhang et al. [14] for aluminium welds ( = 0.21 mm ) were used to compute the effective notch stresses in this investigation. The former value of was used because led to the best correlation of the experimental data. The latter one was applied since the crack initiation occurred in the filler material for all weld series under investigation, as will be discussed in the next section. The master S–N curves were created considering the nominal
Table 8 Cases for effective stress calculation. Case 1 2 3
(mm) 0.15 0.21 0.15
1
0 0 0
(mm)
2
0 0 0
(mm)
3
0 0 0
(mm)
4
(mm)
0 0 0.70
was defined from the statistical treatment presented in Table 6. The adopted value ( 4 = 0.70 mm ) had the same probability of the radius of the weld series with the lowest probability of being zero. In Fig. 13, the 75
International Journal of Pressure Vessels and Piping 173 (2019) 68–78
P.I. Oliveira, et al.
Fig. 15. 95% confidence bands and comparison between median S–N curves for: a) effective notch stress (case 1) and b) nominal stress.
(Fig. 14a), structural (Fig. 14b) and effective notch (Fig. 14c-e) stresses. The effective notch stresses were calculated by means of equation (11), considering the cases summarised in Table 8. Cases 1 and 2 considered the worst-case scenario for all weld series. In case 3, the worst-case scenario was assumed for weld series 1, 2 and 3 because of the multinucleation at their fracture surfaces, as already mentioned. On the other hand, a value of 4 > 0 mm was chosen in order to minimize the data scatter, considering that multinucleation was not observed in weld series 4. The scatter of the S–N curves for nominal (Fig. 14a) and structural (Fig. 14b) presented almost the same value. This indicates that the angular misalignment, considered in the curve for structural stress, did not affect the scatter data. Beyond that, the S–N curves for the effective notch stresses obtained considering cases 1 and 2 (Fig. 14c-d) presented the same scatter of the structural stress (T = 1.29). Thus, the data scatter did not change when the same value of was adopted for all weld series. Furthermore, the S–N curve for the effective notch stresses
obtained considering case 3 (Fig. 14e) presented the lowest scatter (T = 1.20) . This means that the weld toe radius of weld series 4 significantly affected the data scatter. Finally, all master S–N curves presented in Fig. 14 present a low value of scatter since all have T < 1.40 [7]. Furthermore, the lowest S–N curve slope was obtained for the nominal stress (m = 4.7 ). The slope of the curve for the structural stress is equal to the ones for the effective notch stresses obtained considering cases 1 and 2 (m = 5.1). Beyond that, the highest S–N curve slope was obtained with case 3 (m = 6.2 ). According to these results, the angular misalignment affected the slope, since the S–N curve slope for structural stress, that considered the misalignment, was higher than the one for nominal stress. Beyond that, the increase in 4 increased the value of the slope, comparing Fig. 14c and 14e. Additionally, the value of fatigue resistance of the characteristic curve (Ps = 97.7%) for the life of 2 × 106 is higher in case 1 than in case 2. This occurred because the value of was different in each case. 76
International Journal of Pressure Vessels and Piping 173 (2019) 68–78
P.I. Oliveira, et al.
= 0.15 mm led to values of e slightly higher than the ones for Thus, = 0.21 mm . Fig. 15 presents the 95% confidence bands for the median S–N curves according to ASTM E 739 Standard, using all the data from the four welded series under study. The S–N curves from other authors are also superimposed for comparison. Fig. 15a presents the S–N curve for the effective notch stress calculated considering case 1. Superimposed on this figure is the median S–N curve presented by Eibl et al. [7] for thin-sheets of laser beam welded aluminium alloys. According to the figure, the median S–N curves can be consider equivalents, for the data interval analysed in this research, because the curve of Eibl et al. [7] was plotted integrally inside of the confidence bands. This indicates that the experimental results are better characterized by case1. On the other hand, Fig. 15b presents the median S–N curve for the nominal stress of the joints in study and the S–N curve presented by Prisco et al. [5] for a laser welded T-joint made with AA6156 as the skin and with AA2139 as the clip. The fatigue strength of the joints studied was higher than that presented by Prisco et al. [5]. In addition, they cannot be considered equivalent because the median S–N curve was not plotted thoroughly inside of the confidence bands. Finally, a comparison was carried out between the fatigue life of the laser welded T-joints under investigation and the lifetime obtained by Yasniy et al. [22] for 6 mm thick plates of AA2024-T3 with cold expanded hole, a process that improves the fatigue life by creating a compressive residual stress in the holes of structural elements such as those used in riveted structures. Considering a nominal stress of 147 MPa and a stress ratio of 0.02, the total lifetime for the laser welded T-joint, for the plate with a hole with 8 mm diameter and for the plate with cold expanded hole (with 8 mm diameter and cold expansion degree of 2.37%) are, respectively, 209,511 cycles, 94,047 cycles and 189,791 cycles. Thus, it is possible to note that the laser welded joint had the highest total lifetime. The fatigue life of the welded joint had 115,464 more cycles than the plate with hole and 19,720 more cycles than the plate with cold expanded hole. 4.4. Fracture morphology SEM fractographies showed that the specimens of weld series 1, 2 and 3 present fractures with multinucleations, as illustrated in Fig. 16a
Fig. 16. Fracture surface of a) weld series 1 and b) weld series 4.
Fig. 17. Cracks progress up through the weld material and in the transition from the weld metal to the heat-affected material. a) Fracture surface of a specimen of series 3; b) magnification of the transition from the weld metal to the heat-affected material. 77
International Journal of Pressure Vessels and Piping 173 (2019) 68–78
P.I. Oliveira, et al.
with a specimen from series 1. On the other hand, the specimens of weld series 4 did not present multinucleation in their fracture surface, as shown in Fig. 16b as a typical example. The absence of multinucleation in weld series 4 can be explained by the lowest mean standard deviation of the weld toe radius presented in Table 6. While the higher values of scatter of the weld toe radius for the others weld series in Table 6 seem to contribute to the increase in multinucleation. That is, higher values of mean standard deviation for weld toe radii are related to geometric imperfections that affect the fatigue strength. Therefore, the use of the worst-case scenario is justified. In addition, the crack initiation occurred in the filler material for all the weld series. Fig. 17 shows pores at the fracture surface which indicates that the cracks progress through the added material. Additionally, the detail shows the transition from the fusion zone to the heat-affected base material.
[2]
[3] [4] [5]
[6] [7]
5. Conclusions
[8] [9] [10]
The following conclusions can be drawn based on the results presented in this study: (1) The reference weld toe radius has effect on both the data scatter and the slope of the S–N curves; (2) The angular misalignment affects the slope of the S–N curves; (3) The median S–N curve obtained with a reference weld toe radius of 0 mm and with a microstructural length of 0.15 mm is equivalent to the S–N curve of laser welded joints, studied by Eibl et al. [7]; (4) The fatigue life of the laser welded T-joint is greater than the lifetime of some plates with cold expanded hole, investigated by Yasniy et al. [22]; and (5) The geometric imperfections caused by the variation of the weld toe radius generates multinucleation in some weld series.
[11] [12] [13]
[14] [15] [16]
Acknowledgments This research is sponsored by FEDER funds through the programme COMPETE – Programa Operacional Factores de Competitividade – and by national funds through FCT – Fundação para a Ciência e a Tecnologia –, under the project UID/EMS/00285/2013. The first author, Pedro I. P. Oliveira, is supported by the Brazilian National Council for Scientific and Technological Development (CNPq).
[17] [18] [19]
Appendix A. Supplementary data
[20] [21]
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.ijpvp.2019.05.001.
[22]
References [1] D. Dittrich, J. Standfuss, J. Liebscher, B. Brenner, E. Beyer, Laser beam welding of
78
hard to weld Al alloys for a regional aircraft fuselage design- First results, Phys. Procedia 12 (2011) 113–122, https://doi.org/10.1016/j.phpro.2011.03.015. M. Zain-ul-abdein, D. Nélias, D. Deloison, Experimental Investigation and Finite Element Simulation of Laser Beam Welding Induced Residual Stresses and Distortions in Thin Sheets of AA 6056-T4 vol. 527, (2010), pp. 3025–3039, https:// doi.org/10.1016/j.msea.2010.01.054. Z.Y. Huang, Z. Luo, Z.M. Liu, Y. Li, Y.C. Cai, Y. Zhang, Deformation behaviour of thin aluminium alloy plates during laser welding, 37 (2017) 291–309. J. Baumgartner, Review and considerations on the fatigue assessment of welded joints using reference radii, Int. J. Fatigue 101 (2017) 459–468, https://doi.org/10. 1016/j.ijfatigue.2017.01.013. A. Prisco, F. Acerra, A. Squillace, G. Giorleo, C. Pirozzi, U. Prisco, et al., LBW of similar and dissimilar skin-stringer joints. Part I: process optimization and mechanical characterization, Adv. Mater. Res. 38 (2008) 306–319 https://doi.org/10. 4028/www.scientific.net/AMR.38.306. V. Ventzke, S. Riekehr, M. Horstmann, P. Haack, N. Kashaev, One-sided Nd:YAG laser beam welding for the manufacture of T-joints made of aluminium alloys for aicraft construction, Weld. Cut. 13 (2014) 245–249. M. Eibl, C.M. Sonsino, H. e Kaufmann, G. Zhang, Fatigue assessment of laser welded thin sheet aluminium, Int. J. Fatigue 25 (2003) 719–731, https://doi.org/10.1016/ S0142-1123(03)00053-7. J.D. Burk, F.V. Lawrence, Influence of bending stresses on fatigue crack propagation life in butt joint welds, Weld. Res. Suppl. 2 (1977) 61–66. A. Hobbacher, Recommendations for fatigue design, Update 39 (2004) 33–46. S. Liinalampi, H. Remes, P. Lehto, I. Lillemäe, J. Romanoff, D. Porter, Fatigue strength analysis of laser-hybrid welds in thin plate considering weld geometry in microscale, Int. J. Fatigue 87 (2016) 143–152, https://doi.org/10.1016/j.ijfatigue. 2016.01.019. D. Radaj, C.M. Sonsino, W. Fricke, Recent developments in local concepts of fatigue assessment of welded joints, Int. J. Fatigue 31 (2009) 2–11, https://doi.org/10. 1016/j.ijfatigue.2008.05.019. H. Neuber, Theoretical calculation of strength at stress concentration, Czech. J. Phys. B 19 (1969) 400–400 https://doi.org/10.1007/BF01712885. C. Morgenstern, C.M. Sonsino, A. Hobbacher, F. Sorbo, Fatigue design of aluminium welded joints by the local stress concept with the fictitious notch radius of rf=1 mm, Int. J. Fatigue 28 (2006) 881–890, https://doi.org/10.1016/j.ijfatigue.2005. 10.006. G. Zhang, C.M. Sonsino, R. Sundermeier, Method of effective stress for fatigue: Part II - applications to V-notches and seam welds, Int. J. Fatigue 37 (2012) 24–40, https://doi.org/10.1016/j.ijfatigue.2011.09.016. D. Radaj, P. Lazzarin, F. Berto, Generalised Neuber concept of fictitious notch rounding, Int. J. Fatigue 51 (2013) 105–115, https://doi.org/10.1016/j.ijfatigue. 2013.01.005. F. Berto, P. Lazzarin, D. Radaj, Fictitious notch rounding concept applied to sharp V-notches: evaluation of the microstructural support factor for different failure hypotheses. Part II: microstructural support analysis, Eng. Fract. Mech. 76 (2009) 1151–1175, https://doi.org/10.1016/j.engfracmech.2008.01.015. S. Filippi, P. Lazzarin, R. Tovo, Developments of some explicit formulas useful to describe elastic stress fields ahead of notches in plates, Int. J. Solids Struct. 39 (2002) 4543–4565, https://doi.org/10.1016/S0020-7683(02)00342-6. ASM Handbook, Properties and Selection: Nonferrous Alloys and Special-Purpose Materials vol. 2, (2005). P.I. Oliveira, J.M. Costa, A. Loureiro, Effect of laser beam welding parameters on morphology and strength of dissimilar AA2024/AA7075 T-joints, J. Manuf. Process. 35 (2018), https://doi.org/10.1016/j.jmapro.2018.08.003. M. Koçak, S. Webster, J.J. Janosch, R.A. Ainsworth, R. Koers, FITNET: Fitness-ForService, GKSS Research Centre Geesthacht, 2008. J.D.M. Costa, J.S. Jesus, A. Loureiro, J.A.M. Ferreira, L.P. Borrego, Fatigue life improvement of mig welded aluminium T-joints by friction stir processing, Int. J. Fatigue 61 (2014) 244–254, https://doi.org/10.1016/j.ijfatigue.2013.11.004. P. Yasniy, S. Glado, V. Iasnii, Lifetime of aircraft alloy plates with cold expanded holes, Int. J. Fatigue 104 (2017) 112–119, https://doi.org/10.1016/j.ijfatigue. 2017.07.012.