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Cold hole expansion effect on the fatigue crack growth in welds of a 6061-T6 aluminum alloy
Accepted Manuscript Title: Cold hole expansion effect on the fatigue crack growth in welds of a 6061-T6 aluminum alloy Author: K.C. Viveros R.R. Ambriz A. Amrouche A. Talha C. Garc´ıa D. Jaramillo PII: DOI: Reference:
S0924-0136(14)00221-0 http://dx.doi.org/doi:10.1016/j.jmatprotec.2014.05.030 PROTEC 14017
To appear in:
Journal of Materials Processing Technology
Received date: Revised date: Accepted date:
25-11-2013 29-5-2014 29-5-2014
Please cite this article as: Viveros, K.C., Ambriz, R.R., Amrouche, A., Talha, A., Garc´ia, C., Jaramillo, D.,Cold hole expansion effect on the fatigue crack growth in welds of a 6061-T6 aluminum alloy, Journal of Materials Processing Technology (2014), http://dx.doi.org/10.1016/j.jmatprotec.2014.05.030 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Cold hole expansion effect on the fatigue crack growth in welds of a 6061-T6 aluminum alloy
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K.C. Viverosa, *R.R. Ambriza, A. Amroucheb, A. Talhac, C.Garcíad, D. Jaramilloa
a
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Instituto Politécnico Nacional CIITEC-IPN, Cerrada de Cecati S/N Col. Sta. Catarina C.P
b
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02250, Azcapotzalco, DF, México.
Laboratoire de Génie Civil et géo-Environnement LGCgE, EA 4515, Faculté des Sciences
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Appliquées FSA Béthune, Université d’Artois, France. c
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Ecole des Hautes Etudes d’Ingénieur (HEI), 13 rue de Toul, 59046 Lille, France. Mechanical and Aerospace Engineering, Carleton University, 1125 Colonel By Drive,
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Ottawa, ON, Canada K1S 5B6
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* Corresponding author: Tel. +52 57 29 60 00; fax: +52 55 61 75 36; E-mail: [email protected]
Abstract
Compact test specimens were extracted from a 6061-T6 aluminum alloy welded plate with a thickness of 9 mmto analyze the cold hole expansion effect on fatigue crack growth tests conducted in mode I cyclic loading. At R = 0.1, a sharp crack in base metal, weld metal and heat affected zone was propagated from 17 to 24 mm. The fatigue crack growth at 24 mm (α = a/W= 0.3) was delayed by drilling a hole at the crack tip and applying a cold hole expansion of 4.1%. The residual stress fields due to cold hole expansion were determined
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with the finite element method.The fatigue crack growth testing was continued up to a crack length of 35 mm (α~ 0.43) at the same R, and crack opening displacementsof the post-expansion crack were also determined with the finite element method.The results were
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expressed in terms of crack length versus number of cycles, as well as, fatigue crack growth
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rate as a function ofapplied and effectivestress intensity factor range.Thecold hole
expansion contributed to delay the fatigue crack growthin base metal, and to a lesser extent
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inthe weld metaland heat affected zone.A crack closure effect was determined by means of load versus crack opening displacement curves of the post-expansion crack, which was,
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completely or partially closed, in welded zones with compressive residual stress fields.The
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fracture surfaces of each welded zone were analyzed to elucidate the crack nucleation zone and its relation with the residual stress field. In all cases the crack was initiated at the
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surface of the specimen where the residual stresses were positive.
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Keywords: 6061-T6; Welding; Coldhole expansion; Fatigue crack growth; Finite element simulation.
1.Introduction
The structures used in transportation industry are intended for large number of cycling loads during their service life. As a consequence, the fatigue crack growth rate in different zones of the welded joints (base metal (BM), weld metal (WM), and heat affected zone (HAZ))must be quantified to prevent mechanical failures and enhance structural design. In this sense,Ambriz et al. (2010) studied the fatigue crack growth under cyclic loading with a
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constant ratio (R=0.1) in welds of 6061-T6 aluminum alloy obtained by modified indirect electric arc (MIEA). The results were compared with those previously obtained by Moreira et al. (2008) by friction stir welding (FSW) in the same alloy. The authors found that
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fatigue crack growth in WMfor MIEA tends to be more severe than the nugget zone in
FSW, nevertheless, for the HAZ the crack growth rate was similar. Additionally, it was
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observed that BM exhibits better fatigue crack growth rateconditions than HAZ and WM or
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nugget zone.
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The cold hole expansion processisa mechanical method to induce compressive residual stresses around circular holes to improve the fatigue life of structural components of
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aluminum alloys(O'brien, 2000). Regularly, the expansion is performed by an oversized rigid tool, which is displaced at a constant speed across a hole to obtain elastic-plastic strain
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incompatibilities(Papanikos and Meguid, 1999). The cold hole expansion technique has
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been used to quantify its effect on the fatigue crack growth of aluminum alloy specimens. Amrouche et al. (2003) quantified the cold hole expansion effect ona 6005-T6 aluminum
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alloy using different expansion grades. They found that the number of cycles to failure were likely to increase when the degree of expansion was roughly 4.3 %.More recently, Ruzek et al. (2012) studied the indentation effect in cracked components of 2024-T3 aluminum alloy. The experimentation was carried out by different load ratios, crack lengths and impact energies. It was observed that the fatigue crack growth was delayeddue to the plastic strains and compressive residual stresses produced around the crack tip. The cold holeexpansion process has been analyzed with the finite element methodto determine the residual stresses around the hole. MahendraBabu et al. (2008)determined that cold expansion technique induced beneficial compressive stresses around circular holes to 3 Page 3 of 56
offset the applied tensile stress resulting in improved fatigue life. De Matos et al. (2005) determined the residual stresses produced by Split Sleeve Cold Expansion (FTI's)in 2024T351 aluminum alloy. It was identified that for cyclic loading, the crackswere likelyto
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nucleate on the surface where the residual stresses were positive. Pasta (2012) carried out a numerical simulation in aerospace structures of 6082-T6 aluminum alloy.The results were
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experimentally validated by means of displacement measurements, with the conclusion that
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the finite element method was a confident tool to determine residual stress fields introduced
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by cold hole expansion.
This paper reports the experimental results for fatigue crack growth tests in welds of 6061-
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T6 aluminum alloy(BM, WM and HAZ) before and after the cold hole expansion. The expansion was performed in a simple manner by passing a steel ball throughout a hole,
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located at the crack tip in compact tests specimens. This provided a practical method to
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produce plastic strain fields and compressive residual stresses.The finite element method was used to analyze the cold hole expansion, to determine the residual stress fields and the
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effect of residual stress fields in a post-expansion crack with different length sizes.
2. Methodology
2.1. Materials and welding
Plates of 6061-T6 aluminum alloy with dimensions of 100×300×9 mm were welded by means of the modified indirect electric arc (MIEA) welding technique. A basic description of the MIEA technique and joint geometry are shown in Figures 1a and 1b. Further details of the MIEA technique have been previously reported in the literatureby Ambriz et al.
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(2009). The joint preparation is shown in Figure 1b.Commercial ER4043 electrode with a diameter of 1.2 mm was used as filler metal. Chemical compositionsforplate and electrode
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areshown in Table I.
Figure 1. a) Schematic representation of the modified indirect electric arc (MIEA) technique and b) joint geometry details.
Table I. Chemical composition of 6061-T6 plates and ER4043 electrode used (wt. percent). Al
Si
Mg
Cu
Fe
Mn
Zn
Ti
6061-T6
97.63
0.561
0.986
0.310
0.289
0.052
0.024
0.018
ER4043
92.9
5.6
0.05
0.30
0.8
0.05
0.10
0.02
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The welding parameters were adjusted to obtain a spray metal transfer with argon shielding gas flow of 1.56 m3h-1, inverse polarity in a range of 200 to 210 A, visible stick out of 10 mm, voltage of 25.4 V, welding displacement of 3.6 mm s-1 and feeding speed of the filler
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metal of 180 mm s-1.
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2.2. Fatigue crack growth
Compact test specimens (CT) for BM, WMand HAZ were extracted from the welded
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plates, see Figure 2. Five samples were used for each region. Final dimension for the CT
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specimens according to ASTM E-647 is shown in Figure 3.
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Figure 2. Welded plate with schematic representation of the compact test (CT) specimens
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for base metal (BM), weld metal (WM) and heat affected zone (HAZ).
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Figure 3. Compact test (CT) specimen dimensions.
The notch in the CT specimens for WM and HAZ was aligned taking into account the instrumented indentation measurements previously obtained in Ambriz et al. (2011), as shown in Figure4.To eliminate stress concentrations, the specimens were grinded using different abrasive papers and then mirror polished with diamond paste of 3 μm.The fatigue crack growth tests were performed using an Instron 8516 servohydraulic fatigue testing machine. This machine was fitted with a stroke displacement of ± 75 mm and a load cell of 100 kN. The experimentation was done under ambient atmospheric air pressure and room temperature conditions. A sinusoidal constant load ratio of 0.1 with a frequency of 20 Hz was applied during the fatigue crack growth test and initial pre-cracking. The specimens 7 Page 7 of 56
were pre-cracked with a load range ΔP of 6.0 kN until reach an initial crack length of 17.0 mm. During the test, the crack was propagated to a length of 24 mm with ΔP of 5.0 kNfor
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each specimen.
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Figure 4. Localization of the CT specimens for WM and HAZ according to instrumented
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indentation measurements, Ambriz et al. (2011).
An accurate measurement of the crack length during cycling loading was providedby monitoring the crack propagation by a high resolution Kappa digital camera, connected to a monitor with a system resolution of 0.2 mm. The CT specimens were subjected to a reparation process at a crack length of 24 mm (a/W=0.3). The reparation processconsisted of drilling a hole of 6.1 mm in diameter at the crack tip, andpassing througha hard steel ball of 6.35 mm in diameter across the thickness of the CT specimen (cold hole expansion), as shown in Figure 5. This reparation process is 8 Page 8 of 56
a common practice in aluminum alloys used inland transport components to stop or
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delaythefatigue crackgrowth(Amrouche et al., 2003).
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Figure 5. Cold hole expansion process.
To determine and compare the differences between plain and expanded holesfor each material region, two of the five CT specimens were not subjected to the mechanical expansion. The remained three were subjected to a degree of cold hole expansion(DCE) of 4.1% according with equation 1. DCE % =
D−d × 100 (1) d
After the reparation process, the crack was propagateduntil final failurefor each CT specimenusing the same conditions dictated before. The results were presented in graphs of
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crack length a,as a function of number of cyclesN. Theapplied stress intensity factor range ΔKin each CT specimen was calculated by means of equation 2.
2 3 4 ⎡ a ⎛ a⎞ ⎛ a ⎞ ⎤ (2) ⎛ a ⎞ ⎢0.886 + 4.64 − 13 .32⎜ ⎟ + 14 .72⎜ ⎟ − 5.6⎜ ⎟ ⎥ W ⎝W ⎠ ⎝W ⎠ ⎝ W ⎠ ⎥⎦ ⎢⎣
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⎞ ⎟ ⎠ 3/ 2 ⎞ ⎟ ⎠
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a ⎛ ΔP ⎜ 2 + W ⎝ ΔK = a ⎛ BW 1 / 2 ⎜1 − ⎝ W
The fatigue crack growth rateda/dNas a function of ΔK for BM, WMand HAZ were
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represented in logarithmic graphs. The experimental data were adjusted according to the
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following expression:
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da = CΔK m (3) dN
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d
whereC and m are experimentally determinedconstants.
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2.3. Finite element simulation The residual stress fields generated by the reparation process of coldhole expansion on the
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CT specimenswere simulated with the finite element method (ANSYS software). Three
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finite element models were created for different regions on the welded plate(BM, WMand HAZ).Once the residual stress fields were determined, the simulation was extended
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tocompute the crack opening displacement (post-expansion) and the crack closure effect on
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the fatigue crack growth process.
The through-thickness variation of residual stress fields in the CT specimens due to cold
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hole expansion was considered by generating three-dimensional models, and explicitly modeling the oversized steel ballas a rigid body. The steel ball was incrementally displaced
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throughout the hole in the CT specimens.Afterwards,localcrack lengths of 1, 2, 3, 4 and 5
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mm (post-expansion) were introduced in the opposite edge of the hole to the pre-expansion
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reparation crack (a/W = 0.3). For each crack length, the CT specimen was incrementally loaded in tension from 0.55 kN to 5.5 kN (R = 0.1) which corresponded to the experimental fatigue crack growth test. The maximum tensile load was applied in ten increments. From the finite element results at each applied load increment to the CT specimen, the corresponding compliance curve was plotted to analyze the effect of the post-expansion residual stress fields on the crack closure effect. A crack opening load was determined for each crack length from the compliance curve according to the schematic representation shown in Figure 6, (Anderson, 2005).The computation of the crack opening load, indicated by the shift in the stiffness slope of the compliance curve, was used to compute an effective
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load range ΔPeff, used in conjunction with equation 2 to determine the effective stress intensity factor range ΔKeff. According to the ΔKeff, equation 3 couldbe re-written as follow:
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da = CΔK effm (4) dN
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Figure 6. a) Load-displacement behavior and b) schematic representation of the effective
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stress intensity factor range, (Anderson, 2005).
The contact conditions between thesteel ball and CT specimen were prescribed with augmented Lagrange and frictionless methods for normal and tangential behavior. To preventinterpenetration between upper and lower faces of the initial crack length of 24 mm (a/W=0.3),during the simulation of the cold hole expansion,was necessary to define contact conditions between the crack faces. A contact interaction between the faces of the postexpansion crack during the simulation of the fatigue cycle loading, was also used. The same contact properties defined for the steel ball and CT specimen were used for the crack faces.
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The boundary conditions of the CT specimen were prescribed to represent the experimental conditions (reparation and fatigue crack growth test), while preventing rigid body motions and over-constraint. In the case of the reparation conditions (Figure 7a), two surfaces over
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the exit face of the CT specimen were restricted to zero motion in the vertical displacement (Figure 7b). Furthermore, two corner nodes over the exit face were fixed as shown in
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Figure 7b. For the fatigue crack growth test conditions, all previous boundary conditions of
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the cold hole expansion simulation were deactivated. Instead, the CT specimen was restricted to zero motion (encastre condition) in all directions on the lower fastener hole,
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while the cycling load was applied on the upper fastener hole.
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The three-dimensional models were meshed with eight-node linear brick elements with full integration. The mesh around the hole was refined as shown in Figure 7b and 7c, and
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twelve elements were used throughout the thickness.
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The von Mises yield function and kinematic hardening rule were used to model the elastic-
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plastic behavior during the cold hole expansion.The materials properties are shown in Figure 8, andcorresponded to the experimental flow curves forBM, WMand HAZ.
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Figure 7. a) Cold hole expansion process in base metal (BM), b) top and side view of the
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CT specimen model with specified boundary conditions, and c) three dimension mesh.
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Figure 8. Tensile mechanical properties of BM, WM and HAZ of 6061-T6 aluminum alloy
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used for the finite element models.
3. Results and discussion
3.1. Fatigue crack nucleation
The mean results of crack length versus number of cycles for initial propagation, plain hole and hole expansion are shown in Figure 9. In all cases (BM, WMand HAZ) the crack length increasedexponentially as a function of the number of applied cycles.After the reparation process(initial propagation),the plain and expanded holes delayed the crack nucleation, by means of decreasing the crack sharpness and introducing compressive residual stress fieldsaround the circular hole. For WM(Figure 9b),the number of delayed cycles NDbetween plain and expanded holeswassimilar and less relevant than for BMand HAZ 15 Page 15 of 56
(Table II).This aspect could be attributed to the brittle microstructure of the WM, whose mechanical behavior might not favor a positive expansion effect to arrest crack nucleation. In contrast, the loss of hardening in the HAZ (decrease in yield strength),seemed to have a
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beneficial effect to arrest the crack (Figure 9c), i.e. an increment of the delayed number of cyclesfor the nucleation of the crack wasobserved. Though, it would be necessary to
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quantify the fatigue crack growth rate, because the expansion degree could induce higher
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stresses in the edge of the hole.
Figure 9. Crack length versus number of cycles, showing initial propagation as well as plain hole and cold hole expansion process for a) BM, b) WM and c) HAZ.
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Table II. Number of delayed cycles to nucleate a crack after plain hole and cold hole expansion process.
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Delayed cycles, ND Plain hole
Cold hole expansion
BM
~ 56 000
~ 112 000
WM
~ 87 000
~ 102 000
HAZ
~116 000
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Material region
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~ 170 000
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3.2. Fatigue crack growth
To elucidate the coldhole expansion effect in the different zones of the welded joint, the
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fatigue crack growth rate as a function of the stress intensity factor range was plotted in
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Figure 10.From Figure 10a for the BM,it was possible to note that cold hole expansion
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were likely to reduce the fatigue crack growth rate in comparison withplain hole and initial propagation. This means that a beneficial compressive residual stress field had been introduced during the expansion process.Despite having a decrease in the fatigue crack growth rate byintroducing a hole, the cold holeexpansion processdid not have the same effect in the WM and HAZ material (Figures 10b and 10c). Actually, the experimental values for the hole and cold hole expansion cases were similar between them.Therefore, both results were fitted to a single slope using equation 3, but experimental results for each case were preserved. This aspect could be attributed to the fact that for all materials the same degree of expansion was applied in spite of the different microstructure and mechanical properties between BM, WMand HAZ. In this sense, it could be deduced that 17 Page 17 of 56
the residual stress fields induced by the cold hole expansion were different among the three materials. Figure 10d presents the fatigue crack growth rate as a function of the effective stress intensity factor range ΔKeff. For the limited post-expansion crack lengths, it was
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apparent that the fatigue crack growth rate decreased after the cold hole expansion, which
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could be explained due to the elevated crack opening loads (0.5, 0.3 and 0.2 P/Pmax for BM,
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d
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WM and HAZ) because of the compressive residual stress fields.
Figure 10. Fatigue crack growth as a function of appliedstress intensity factor range for a) BM, b) WM, c) HAZ and d) fatigue crack growth as a function ofthe effective stress intensity factor range for post-expansion crackin BM, WM and HAZ.
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3.3. Finite element simulation The finite element results for BM, WMand HAZfor entrance and exit facesare presentedin Figure 11. Only the tangential component were shown, since it corresponded to the residual
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stress component aligned with the applied load range ΔP during the fatigue test. Because of
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the crack length of 24 mm, the residual stress fieldswere not uniform around the circular hole in each model. Indeed,the crack was not restricted to move during the cold hole
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expansion, so that a poor region of compressive residual stress fieldswas developed around
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the crack faces. BM(Figure 11a)shows the higher region of compressive residual stresseson the exit face at position of180° (clockwise from the crack);followed by a transition to a
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smaller zone of tensile residual stresses along the position at 180°moving away from the hole. The same trend applied for WM(Figure 11b), where the highest compressive residual
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stresses were presentedon the exit face and transitioned towards a tensile state moving
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away from the hole. Nevertheless, the minimum magnitude of residual stresses was
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different for BM and WM. For instance, the compressive and tensile residual stresseswere ~ -344 and ~+186 MPa for BM, and ~ -149 and ~+70 MPa for WM. HAZ(Figure 11c) shows the higher region of compressive residual stresseson the entrance face with positions at 90° and 270°(clockwise from the crack), however, these positions were meaningless for the fatigue crack growth phenomena. For the position at 180° (clockwise from the crack), the minimum compressive residual stress was ~ -128 MPa on the exit face and transitioned to a maximum tensile residual stress of ~ +73 MPa.
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ip t cr us an M d te Ac ce p Figure 11. Tangential residual stress distribution for a) BM, b) WM and c) HAZ. 20 Page 20 of 56
The cold hole expansion process caused an important variation of residual stresses within the thickness of the material, because of the gradual expansion-contraction by the steel ball
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in the surrounding of the hole. From this perspective, Figure 12shows the residual stress
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fields throughout the thickness for BM, WMand HAZ. Moreover, the residual stresses at
entrance face, center and exit face regionswere normalized with respect to yield strength of
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the material and plotted against the distance from the edge of the hole. As expected the
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higher residual stresses were presented in regions close to the hole in the opposite edge to the crack (a = 24mm). The residual stresses decreased along the width of the specimen,
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which corresponded to the expected fatigue crack growth plane. The residual stresses selfbalanced towards zero along the width of the specimen, but there was a transition area from
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a compressionto a tensionstatewhich wasnoticeableat the center of the specimen’s
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thickness. Furthermore, a small zoneof tensile residual stress waspresented closer to the edge of the holein the entrance face for BMand HAZ models, and exit face for WM model.
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From the normalized results, these zones of tensile residual stress were~0.4 for BM and WMmodels and ~0.3 for HAZ model. It is important to note that tensile regions of residual stresseshad a higher susceptibility to crack nucleation and growth. In fact the WMmodel showed the most extensive tensile region of residual stresses around the hole, while the opposite was true for the HAZmodel. The crack length versus number of cycles resultshadshown that after the cold hole expansion (Table II), the WMrequiredthe lower number of cycles and the HAZ the higher one to nucleate and to grow a crack.
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ip t cr us an M d te Ac ce p Figure 12. Residual stress field throughout the compact type specimen thickness for a) BM, b) WM and c) HAZ. 22 Page 22 of 56
On the other hand, the residual stress fields shown a stronger compressive nature at the surface of the hole for BM, followed by the HAZ and lastly WM, which explained the
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increase in fatigue life for BM(Figure 9).
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The fatigue life of the cold hole expansion components (Figure 9) could also be explained
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in terms of the crack closure effect induced bythe residual stress fields. As explained in the methodology section, the crack closure effect of the residual stress field was simulated for a
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post-reparation crack at lengths of 1, 2, 3, 4 and 5 mm (a/W = 0.43, 0.44, 0.46, 0.47 and 0.48). For these post-reparation crack lengths, the finite element results for thecrack
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opening displacement (COD) as a function of the normalized applied load (P/Pmax), known as the compliance curve are presented for the entrance and exit faces in Figure 13a
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and 13b for BM, 13c and 13d for WM, and 13e and 13f for HAZ. The numerical results
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were determined at a distance of 0.33 mm from the crack tip, which corresponded to the
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first node position behind the crack tip.
According to the minimum applied cycle load, the post-reparation crack was completely closed at length sizes of 3 mm (Figure 13a); 1, 2 and 3 mm (Figure 13b); 1, 2, 3 and 4 mm (Figure 13c); 2, 3, 4 and 5 mm (Figure 13d); 3 mm (Figure 13e); and 1, 2, 3 and 4 mm (Figure 13f). Indeed, the post-reparation crack lengths showed a non-linear behavior in the compliance curves, with the exception of 1, 2 and 3 mm (Figure 13b); and 3 mm (Figure 13d). These compliance curves with a linear behavior indicated that the crack was closed for the entire applied cycle load (see Figure 6).According to the maximum applied cycle load, the lower magnitudes of COD were observed for the post-reparation crack lengths on BM (Figure 13a and 13b), followed by the post-reparation crack length on WM (Figures 23 Page 23 of 56
13c and 13d). The higher magnitudes of COD were observed for the post-reparation crack length on HAZ (Figures 13e and 13f).
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In spite of the positive cycle stress ratio (R=0.1) applied during the fatigue test, the numerically determined compliance curves in Figure 13 demonstrated a crack closure effect
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induced by compressive residual stress fields. It is known that the crack closure effect
produces a reduction of the applied stress intensity factor range ΔKas indicated by Elber
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(1970). The applied cycle load required to open the post-reparation crack on the entrance
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face during loading of the CT specimens was of ~0.5, 0.3 and 0.2 P/Pmax for the BM, WM and HAZ, respectively. The computation of the crack opening load was just conducted for
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the entrance face as this was the position used during the fatigue crack growth experiments to measure the crack length. The complete or partial closure of the post-reparation crack,
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the magnitude of the COD and crack opening load were a consequence of the combined
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effect between the applied cycle load and the residual stress fields.An approximation of the
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da/dNas a function of the ΔKeff determined from the finite element simulation was already presented in Figure 10d for BM, WM and HAZ. From a quantitative perspective the finite element results should be interpreted with caution, because of the lack of experimental residual stress and COD measurements.Nevertheless, from a qualitative perspective the finite element results providedreliable andvaluable information to analyze the cold hole expansion effect in fatigue crack growthas revealed by the following fractography analysis.
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ip t cr us an M d te Ac ce p Figure 13. Finite element results of COD versus normalized load (P/Pmax) for entrance and exit faces of the CT specimen, a-b) BM, c-d) WM and e-f) HAZ.
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3.4. Fractography Figure 14,presents macroscopic views of the fracture surface for BM, WMand HAZ
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specimens with cold hole expansion process.The rectangles indicate the crack initiation zones for each specimen. These details at higher magnification are shown in Figure 15.For
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BMand HAZ, it was observed that the initiation of the crack corresponds to the entrance face of the specimen. Moreover, for WMit was located at the exit face. In all cases, the
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nucleation of the fatigue crack corresponded to zones on the specimen with tensile residual
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stresses as predicted by finite element results (Figure 11 and 12).The nucleationof the fatigue crack was presentedin the surface of the edge hole, where the residual stresses were
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likely in tension (Figure 12).For instance, the cold hole expansion process leaved residual stress fields in tension at the entrance face for BMand HAZ specimens, whereas for WM it
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waslocatedat the exit face. These tensile residual stress fields transitioned into compressive
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ones along the width of the specimen,reached a minimum value at approximately 2.0 and
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3.0 mm for BMand HAZ, respectively, and 3.0 mm for WM. These characteristics confirmed that material zones with tensile residual stress fields exhibited a higher susceptibility for crack nucleation and growth. In spite of the beneficial effect of the compressive residual stress fields, the results for WM and HAZ specimens suggested that either the cold hole expansion degree was unsuitable or local microstructural characteristics played a predominant role. In this sense it would be necessary to perform an additional research in order to elucidate the effect of the expansion degree in terms of microstructure, local mechanical properties and welding defects.
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Figure 14. General characteristics of the fracture surfaces for a) BM, b) WM and c) HAZ.
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Figure 15. Surface fracture details according to the rectangle shown in Figure 14.
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Conclusions
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• The degree of cold hole expansion of 4.1%,resulted in an effective reparation process to increase the fatigue life of a 6061-T6 aluminum alloy, butit was
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worthless for weld metal and heat affected zone specimens.
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• The finite element method was an effective tool to characterize the residual stress field as introduced by the cold hole expansion process.
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• The finite element results also revealed a crack closure effect for post-expansion
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cracks located in compressive residual stress fields. The crack closure effect induced elevated opening loads for the post-expansion crack, which resulted in
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lower fatigue crack growth rates.
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• Fracture surface and finite element analysis were in agreement and confirmed that
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tension zones of residual stresses showed a higher susceptibility to crack nucleation and growth.
Acknowledgments
This article was supported by the ConsejoNacional de Ciencia y Tecnología (CONACyT), project CB177834. SIP-IPN is also acknowledge.
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References Ambriz, R.R., Mesmacque, G., Ruiz, A., Amrouche, A., Lopez, V.H., Benseddiq, N., 2010.
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Fatigue crack growth under a constant amplitude loading of Al-6061-T6 welds
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obtained by the modified indirect electric arc technique. Science and Technology of Welding and Joining 15, 514-521.
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Ambriz, R.R., Barrera, G., García, R., López, V. H., 2009. A comparative study of the
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mechanical properties of 6061-T6 GMA welds obtained by the indirect electric arc (IEA) and the modified indirect electric arc (MIEA). Materials & Design 30, 2446-
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2453.
Ambriz, R.R., Chicot, D., Benseddiq, N., Mesmacque, G., de la Torre, S., 2011. Local
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mechanical properties of the 6061-T6 aluminum weld using micro-traction and
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instrumented indentation. European Journal of Mechanics A/Solids 30, 307-315.
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Amrouche, A., Mesmacque, G., García, S., Tahla, A., 2003. Cold expansion effect on the initiation and the propagation of the fatigue crack. International Journal of Fatigue 25, 949-954.
Anderson, T.L., 2005. Fracture Mechanics Fundamentals and Applications, third ed. CRC Taylor and Francis, Boca Raton, pp. 453-460.
Babu, N.C.M., Jagadish, T., Ramachandra, K., Sridhara, S.N., 2008. A simplified 3-D finite element simulation of cold expansion of a circular hole capture through thickness variation of residual stresses. Engineering Failure Analysis 15, 339-348.
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de Matos, P.F.P., Moreira, P.M.G.P., Camanho, P.P., de Castro, P.M.S.T., 2005. Numerical simulation of cold working of rivet holes. Finite Elements in Analysis and Design 41, 989-1007.
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Elber, W., 1970. Fatigue crack closure under cyclic tension. Engineering Fracture
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Mechanics 2, 37-44.
O'Brien, E.W., 2000. Beneficial residual stress from the cold expansion of large holes in
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thick light alloy plate. The Journal of Strain Analysis of Engineering for
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Engineering Design 35, 261-276.
Moreira, P.M.G.P., de Jesus, A.M.P.,Ribeiro, A.S., de Castro, P.M.S.T., 2008. Fatigue
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crack growth in friction stir welds of 6082-T6 and 6061-T6 aluminium alloys: A comparison. Theoretical and Applied Fracture Mechanics 50, 81-91.
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Papanikos, P., Meguid, S. A., 1999. Elasto-plastic finite-element analysis of the cold expansion of adjacent fastener holes. Journal of Materials Processing Technology
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92-93, 424-428.
Pasta, S., 2012. Residual stresses induced by cold expansion of adjacent and cut-out holes. Experimental Mechanics 53, 841-848.
Ruzek, R., Pavlas, J., Doubrava, R., 2012. Application of indentation as a retardation mechanism for fatigue crack growth. International Journal of Fatigue 37, 92-99.
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Figure captions
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Figure 1. a) Schematic representation of the modified indirect electric arc (MIEA) technique and b) joint geometry.
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Figure 2. Welded plate with schematic representation of the compact test (CT) specimens
Figure 3. Compact test (CT) specimen dimensions.
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for base metal (BM), heat affected zone (HAZ) and weld metal (WM).
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Figure 4. Localization of the CT specimens for WM and HAZ according to instrumented
Figure 5. Cold hole expansion process.
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indentation measurements,Ambriz et al. (2011).
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Figure 6. a) Load-displacement behavior and b) schematic representation of the effective
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stress intensity factor range, (Anderson, 2005).
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Figure 7. a) Cold hole expansion process in base metal (BM), b) top and side view of the CT specimen model with specified boundary conditions, and c) three dimension mesh. Figure 8. Tensile mechanical properties of BM, WM and HAZ of 6061-T6 aluminum alloy used for the finite element models. Figure 9. Crack length versus number of cycles, showing initial propagation as well as plain hole and cold hole expansion process for a) BM, b) WM and c) HAZ. Figure 10. Fatigue crack growth as a function of appliedstress intensity factor range for a) BM, b) WM, c) HAZ and d) fatigue crack growth as a function of the effective stress intensity factor range for post-expansion crack in BM, WM and HAZ. 32 Page 32 of 56
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Figure 11. Tangential residual stress distribution for a) BM, b) WM and c) HAZ. Figure 12. Residual stress field throughout the compact type specimen thickness for a) BM,
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b) WM and c) HAZ.
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Figure 13. Finite element results of COD versus normalized load (P/Pmax) for entrance and
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exit faces of the CT specimen, a-b) BM, c-d) WM and e-f) HAZ.
Figure 14. General characteristics of the fracture surfaces for a) BM, b) WM and c) HAZ.
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Figure 15. Surface fracture details according to the rectangle shown in Figure 14.
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Table captions
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Table I. Chemical composition of 6061-T6 plates and ER4043 electrode used (wt. percent). Table II. Number of delayed cycles to nucleate a crack after plain hole and cold hole
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expansion process.
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Highlights
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Experimental results for fatigue crack growth in welds of 6061-T6 aluminum alloy before and after cold hole expansion.
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The loss of hardening on the heat affected zone has a beneficial effect to arrest the crack
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nucleation.
Finite element simulation of the residual stress field generated by the cold hole expansion
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on different zones of the welded joint.
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determined by finite element simulation.
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Higher susceptibility to crack nucleation and growth in tension zones of residual stresses
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Tables
Table I. Chemical composition of 6061-T6 plates and ER4043 electrode used (wt. percent). Si
Mg
Cu
Fe
Mn
Zn
Ti
6061-T6
97.63
0.561
0.986
0.310
0.289
0.052
0.024
0.018
ER4043
92.9
5.6
0.05
0.30
0.8
0.05
0.10
0.02
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Al
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Table II. Number of delayed cycles to nucleate a crack after plain hole and cold hole expansion process. Delayed cycles, ND Plain hole
Cold hole expansion
BM
~ 56 000
~ 112 000
WM
~ 87 000
~ 102 000
HAZ
~116 000
~ 170 000
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S0924-0136(14)00221-0 http://dx.doi.org/doi:10.1016/j.jmatprotec.2014.05.030 PROTEC 14017
To appear in:
Journal of Materials Processing Technology
Received date: Revised date: Accepted date:
25-11-2013 29-5-2014 29-5-2014
Please cite this article as: Viveros, K.C., Ambriz, R.R., Amrouche, A., Talha, A., Garc´ia, C., Jaramillo, D.,Cold hole expansion effect on the fatigue crack growth in welds of a 6061-T6 aluminum alloy, Journal of Materials Processing Technology (2014), http://dx.doi.org/10.1016/j.jmatprotec.2014.05.030 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Cold hole expansion effect on the fatigue crack growth in welds of a 6061-T6 aluminum alloy
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K.C. Viverosa, *R.R. Ambriza, A. Amroucheb, A. Talhac, C.Garcíad, D. Jaramilloa
a
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Instituto Politécnico Nacional CIITEC-IPN, Cerrada de Cecati S/N Col. Sta. Catarina C.P
b
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02250, Azcapotzalco, DF, México.
Laboratoire de Génie Civil et géo-Environnement LGCgE, EA 4515, Faculté des Sciences
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Appliquées FSA Béthune, Université d’Artois, France. c
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Ecole des Hautes Etudes d’Ingénieur (HEI), 13 rue de Toul, 59046 Lille, France. Mechanical and Aerospace Engineering, Carleton University, 1125 Colonel By Drive,
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d
Ottawa, ON, Canada K1S 5B6
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* Corresponding author: Tel. +52 57 29 60 00; fax: +52 55 61 75 36; E-mail: [email protected]
Abstract
Compact test specimens were extracted from a 6061-T6 aluminum alloy welded plate with a thickness of 9 mmto analyze the cold hole expansion effect on fatigue crack growth tests conducted in mode I cyclic loading. At R = 0.1, a sharp crack in base metal, weld metal and heat affected zone was propagated from 17 to 24 mm. The fatigue crack growth at 24 mm (α = a/W= 0.3) was delayed by drilling a hole at the crack tip and applying a cold hole expansion of 4.1%. The residual stress fields due to cold hole expansion were determined
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with the finite element method.The fatigue crack growth testing was continued up to a crack length of 35 mm (α~ 0.43) at the same R, and crack opening displacementsof the post-expansion crack were also determined with the finite element method.The results were
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expressed in terms of crack length versus number of cycles, as well as, fatigue crack growth
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rate as a function ofapplied and effectivestress intensity factor range.Thecold hole
expansion contributed to delay the fatigue crack growthin base metal, and to a lesser extent
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inthe weld metaland heat affected zone.A crack closure effect was determined by means of load versus crack opening displacement curves of the post-expansion crack, which was,
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completely or partially closed, in welded zones with compressive residual stress fields.The
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fracture surfaces of each welded zone were analyzed to elucidate the crack nucleation zone and its relation with the residual stress field. In all cases the crack was initiated at the
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surface of the specimen where the residual stresses were positive.
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Keywords: 6061-T6; Welding; Coldhole expansion; Fatigue crack growth; Finite element simulation.
1.Introduction
The structures used in transportation industry are intended for large number of cycling loads during their service life. As a consequence, the fatigue crack growth rate in different zones of the welded joints (base metal (BM), weld metal (WM), and heat affected zone (HAZ))must be quantified to prevent mechanical failures and enhance structural design. In this sense,Ambriz et al. (2010) studied the fatigue crack growth under cyclic loading with a
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constant ratio (R=0.1) in welds of 6061-T6 aluminum alloy obtained by modified indirect electric arc (MIEA). The results were compared with those previously obtained by Moreira et al. (2008) by friction stir welding (FSW) in the same alloy. The authors found that
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fatigue crack growth in WMfor MIEA tends to be more severe than the nugget zone in
FSW, nevertheless, for the HAZ the crack growth rate was similar. Additionally, it was
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observed that BM exhibits better fatigue crack growth rateconditions than HAZ and WM or
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nugget zone.
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The cold hole expansion processisa mechanical method to induce compressive residual stresses around circular holes to improve the fatigue life of structural components of
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aluminum alloys(O'brien, 2000). Regularly, the expansion is performed by an oversized rigid tool, which is displaced at a constant speed across a hole to obtain elastic-plastic strain
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incompatibilities(Papanikos and Meguid, 1999). The cold hole expansion technique has
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been used to quantify its effect on the fatigue crack growth of aluminum alloy specimens. Amrouche et al. (2003) quantified the cold hole expansion effect ona 6005-T6 aluminum
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alloy using different expansion grades. They found that the number of cycles to failure were likely to increase when the degree of expansion was roughly 4.3 %.More recently, Ruzek et al. (2012) studied the indentation effect in cracked components of 2024-T3 aluminum alloy. The experimentation was carried out by different load ratios, crack lengths and impact energies. It was observed that the fatigue crack growth was delayeddue to the plastic strains and compressive residual stresses produced around the crack tip. The cold holeexpansion process has been analyzed with the finite element methodto determine the residual stresses around the hole. MahendraBabu et al. (2008)determined that cold expansion technique induced beneficial compressive stresses around circular holes to 3 Page 3 of 56
offset the applied tensile stress resulting in improved fatigue life. De Matos et al. (2005) determined the residual stresses produced by Split Sleeve Cold Expansion (FTI's)in 2024T351 aluminum alloy. It was identified that for cyclic loading, the crackswere likelyto
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nucleate on the surface where the residual stresses were positive. Pasta (2012) carried out a numerical simulation in aerospace structures of 6082-T6 aluminum alloy.The results were
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experimentally validated by means of displacement measurements, with the conclusion that
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the finite element method was a confident tool to determine residual stress fields introduced
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by cold hole expansion.
This paper reports the experimental results for fatigue crack growth tests in welds of 6061-
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T6 aluminum alloy(BM, WM and HAZ) before and after the cold hole expansion. The expansion was performed in a simple manner by passing a steel ball throughout a hole,
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located at the crack tip in compact tests specimens. This provided a practical method to
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produce plastic strain fields and compressive residual stresses.The finite element method was used to analyze the cold hole expansion, to determine the residual stress fields and the
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effect of residual stress fields in a post-expansion crack with different length sizes.
2. Methodology
2.1. Materials and welding
Plates of 6061-T6 aluminum alloy with dimensions of 100×300×9 mm were welded by means of the modified indirect electric arc (MIEA) welding technique. A basic description of the MIEA technique and joint geometry are shown in Figures 1a and 1b. Further details of the MIEA technique have been previously reported in the literatureby Ambriz et al.
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(2009). The joint preparation is shown in Figure 1b.Commercial ER4043 electrode with a diameter of 1.2 mm was used as filler metal. Chemical compositionsforplate and electrode
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areshown in Table I.
Figure 1. a) Schematic representation of the modified indirect electric arc (MIEA) technique and b) joint geometry details.
Table I. Chemical composition of 6061-T6 plates and ER4043 electrode used (wt. percent). Al
Si
Mg
Cu
Fe
Mn
Zn
Ti
6061-T6
97.63
0.561
0.986
0.310
0.289
0.052
0.024
0.018
ER4043
92.9
5.6
0.05
0.30
0.8
0.05
0.10
0.02
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The welding parameters were adjusted to obtain a spray metal transfer with argon shielding gas flow of 1.56 m3h-1, inverse polarity in a range of 200 to 210 A, visible stick out of 10 mm, voltage of 25.4 V, welding displacement of 3.6 mm s-1 and feeding speed of the filler
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metal of 180 mm s-1.
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2.2. Fatigue crack growth
Compact test specimens (CT) for BM, WMand HAZ were extracted from the welded
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plates, see Figure 2. Five samples were used for each region. Final dimension for the CT
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specimens according to ASTM E-647 is shown in Figure 3.
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Figure 2. Welded plate with schematic representation of the compact test (CT) specimens
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for base metal (BM), weld metal (WM) and heat affected zone (HAZ).
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Figure 3. Compact test (CT) specimen dimensions.
The notch in the CT specimens for WM and HAZ was aligned taking into account the instrumented indentation measurements previously obtained in Ambriz et al. (2011), as shown in Figure4.To eliminate stress concentrations, the specimens were grinded using different abrasive papers and then mirror polished with diamond paste of 3 μm.The fatigue crack growth tests were performed using an Instron 8516 servohydraulic fatigue testing machine. This machine was fitted with a stroke displacement of ± 75 mm and a load cell of 100 kN. The experimentation was done under ambient atmospheric air pressure and room temperature conditions. A sinusoidal constant load ratio of 0.1 with a frequency of 20 Hz was applied during the fatigue crack growth test and initial pre-cracking. The specimens 7 Page 7 of 56
were pre-cracked with a load range ΔP of 6.0 kN until reach an initial crack length of 17.0 mm. During the test, the crack was propagated to a length of 24 mm with ΔP of 5.0 kNfor
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each specimen.
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Figure 4. Localization of the CT specimens for WM and HAZ according to instrumented
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indentation measurements, Ambriz et al. (2011).
An accurate measurement of the crack length during cycling loading was providedby monitoring the crack propagation by a high resolution Kappa digital camera, connected to a monitor with a system resolution of 0.2 mm. The CT specimens were subjected to a reparation process at a crack length of 24 mm (a/W=0.3). The reparation processconsisted of drilling a hole of 6.1 mm in diameter at the crack tip, andpassing througha hard steel ball of 6.35 mm in diameter across the thickness of the CT specimen (cold hole expansion), as shown in Figure 5. This reparation process is 8 Page 8 of 56
a common practice in aluminum alloys used inland transport components to stop or
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delaythefatigue crackgrowth(Amrouche et al., 2003).
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Figure 5. Cold hole expansion process.
To determine and compare the differences between plain and expanded holesfor each material region, two of the five CT specimens were not subjected to the mechanical expansion. The remained three were subjected to a degree of cold hole expansion(DCE) of 4.1% according with equation 1. DCE % =
D−d × 100 (1) d
After the reparation process, the crack was propagateduntil final failurefor each CT specimenusing the same conditions dictated before. The results were presented in graphs of
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crack length a,as a function of number of cyclesN. Theapplied stress intensity factor range ΔKin each CT specimen was calculated by means of equation 2.
2 3 4 ⎡ a ⎛ a⎞ ⎛ a ⎞ ⎤ (2) ⎛ a ⎞ ⎢0.886 + 4.64 − 13 .32⎜ ⎟ + 14 .72⎜ ⎟ − 5.6⎜ ⎟ ⎥ W ⎝W ⎠ ⎝W ⎠ ⎝ W ⎠ ⎥⎦ ⎢⎣
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⎞ ⎟ ⎠ 3/ 2 ⎞ ⎟ ⎠
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a ⎛ ΔP ⎜ 2 + W ⎝ ΔK = a ⎛ BW 1 / 2 ⎜1 − ⎝ W
The fatigue crack growth rateda/dNas a function of ΔK for BM, WMand HAZ were
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represented in logarithmic graphs. The experimental data were adjusted according to the
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following expression:
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da = CΔK m (3) dN
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whereC and m are experimentally determinedconstants.
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2.3. Finite element simulation The residual stress fields generated by the reparation process of coldhole expansion on the
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CT specimenswere simulated with the finite element method (ANSYS software). Three
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finite element models were created for different regions on the welded plate(BM, WMand HAZ).Once the residual stress fields were determined, the simulation was extended
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tocompute the crack opening displacement (post-expansion) and the crack closure effect on
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the fatigue crack growth process.
The through-thickness variation of residual stress fields in the CT specimens due to cold
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hole expansion was considered by generating three-dimensional models, and explicitly modeling the oversized steel ballas a rigid body. The steel ball was incrementally displaced
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throughout the hole in the CT specimens.Afterwards,localcrack lengths of 1, 2, 3, 4 and 5
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mm (post-expansion) were introduced in the opposite edge of the hole to the pre-expansion
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reparation crack (a/W = 0.3). For each crack length, the CT specimen was incrementally loaded in tension from 0.55 kN to 5.5 kN (R = 0.1) which corresponded to the experimental fatigue crack growth test. The maximum tensile load was applied in ten increments. From the finite element results at each applied load increment to the CT specimen, the corresponding compliance curve was plotted to analyze the effect of the post-expansion residual stress fields on the crack closure effect. A crack opening load was determined for each crack length from the compliance curve according to the schematic representation shown in Figure 6, (Anderson, 2005).The computation of the crack opening load, indicated by the shift in the stiffness slope of the compliance curve, was used to compute an effective
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load range ΔPeff, used in conjunction with equation 2 to determine the effective stress intensity factor range ΔKeff. According to the ΔKeff, equation 3 couldbe re-written as follow:
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da = CΔK effm (4) dN
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Figure 6. a) Load-displacement behavior and b) schematic representation of the effective
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stress intensity factor range, (Anderson, 2005).
The contact conditions between thesteel ball and CT specimen were prescribed with augmented Lagrange and frictionless methods for normal and tangential behavior. To preventinterpenetration between upper and lower faces of the initial crack length of 24 mm (a/W=0.3),during the simulation of the cold hole expansion,was necessary to define contact conditions between the crack faces. A contact interaction between the faces of the postexpansion crack during the simulation of the fatigue cycle loading, was also used. The same contact properties defined for the steel ball and CT specimen were used for the crack faces.
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The boundary conditions of the CT specimen were prescribed to represent the experimental conditions (reparation and fatigue crack growth test), while preventing rigid body motions and over-constraint. In the case of the reparation conditions (Figure 7a), two surfaces over
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the exit face of the CT specimen were restricted to zero motion in the vertical displacement (Figure 7b). Furthermore, two corner nodes over the exit face were fixed as shown in
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Figure 7b. For the fatigue crack growth test conditions, all previous boundary conditions of
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the cold hole expansion simulation were deactivated. Instead, the CT specimen was restricted to zero motion (encastre condition) in all directions on the lower fastener hole,
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while the cycling load was applied on the upper fastener hole.
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The three-dimensional models were meshed with eight-node linear brick elements with full integration. The mesh around the hole was refined as shown in Figure 7b and 7c, and
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twelve elements were used throughout the thickness.
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The von Mises yield function and kinematic hardening rule were used to model the elastic-
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plastic behavior during the cold hole expansion.The materials properties are shown in Figure 8, andcorresponded to the experimental flow curves forBM, WMand HAZ.
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Figure 7. a) Cold hole expansion process in base metal (BM), b) top and side view of the
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CT specimen model with specified boundary conditions, and c) three dimension mesh.
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Figure 8. Tensile mechanical properties of BM, WM and HAZ of 6061-T6 aluminum alloy
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used for the finite element models.
3. Results and discussion
3.1. Fatigue crack nucleation
The mean results of crack length versus number of cycles for initial propagation, plain hole and hole expansion are shown in Figure 9. In all cases (BM, WMand HAZ) the crack length increasedexponentially as a function of the number of applied cycles.After the reparation process(initial propagation),the plain and expanded holes delayed the crack nucleation, by means of decreasing the crack sharpness and introducing compressive residual stress fieldsaround the circular hole. For WM(Figure 9b),the number of delayed cycles NDbetween plain and expanded holeswassimilar and less relevant than for BMand HAZ 15 Page 15 of 56
(Table II).This aspect could be attributed to the brittle microstructure of the WM, whose mechanical behavior might not favor a positive expansion effect to arrest crack nucleation. In contrast, the loss of hardening in the HAZ (decrease in yield strength),seemed to have a
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beneficial effect to arrest the crack (Figure 9c), i.e. an increment of the delayed number of cyclesfor the nucleation of the crack wasobserved. Though, it would be necessary to
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quantify the fatigue crack growth rate, because the expansion degree could induce higher
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stresses in the edge of the hole.
Figure 9. Crack length versus number of cycles, showing initial propagation as well as plain hole and cold hole expansion process for a) BM, b) WM and c) HAZ.
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Table II. Number of delayed cycles to nucleate a crack after plain hole and cold hole expansion process.
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Delayed cycles, ND Plain hole
Cold hole expansion
BM
~ 56 000
~ 112 000
WM
~ 87 000
~ 102 000
HAZ
~116 000
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Material region
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~ 170 000
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3.2. Fatigue crack growth
To elucidate the coldhole expansion effect in the different zones of the welded joint, the
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fatigue crack growth rate as a function of the stress intensity factor range was plotted in
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Figure 10.From Figure 10a for the BM,it was possible to note that cold hole expansion
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were likely to reduce the fatigue crack growth rate in comparison withplain hole and initial propagation. This means that a beneficial compressive residual stress field had been introduced during the expansion process.Despite having a decrease in the fatigue crack growth rate byintroducing a hole, the cold holeexpansion processdid not have the same effect in the WM and HAZ material (Figures 10b and 10c). Actually, the experimental values for the hole and cold hole expansion cases were similar between them.Therefore, both results were fitted to a single slope using equation 3, but experimental results for each case were preserved. This aspect could be attributed to the fact that for all materials the same degree of expansion was applied in spite of the different microstructure and mechanical properties between BM, WMand HAZ. In this sense, it could be deduced that 17 Page 17 of 56
the residual stress fields induced by the cold hole expansion were different among the three materials. Figure 10d presents the fatigue crack growth rate as a function of the effective stress intensity factor range ΔKeff. For the limited post-expansion crack lengths, it was
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apparent that the fatigue crack growth rate decreased after the cold hole expansion, which
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could be explained due to the elevated crack opening loads (0.5, 0.3 and 0.2 P/Pmax for BM,
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WM and HAZ) because of the compressive residual stress fields.
Figure 10. Fatigue crack growth as a function of appliedstress intensity factor range for a) BM, b) WM, c) HAZ and d) fatigue crack growth as a function ofthe effective stress intensity factor range for post-expansion crackin BM, WM and HAZ.
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3.3. Finite element simulation The finite element results for BM, WMand HAZfor entrance and exit facesare presentedin Figure 11. Only the tangential component were shown, since it corresponded to the residual
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stress component aligned with the applied load range ΔP during the fatigue test. Because of
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the crack length of 24 mm, the residual stress fieldswere not uniform around the circular hole in each model. Indeed,the crack was not restricted to move during the cold hole
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expansion, so that a poor region of compressive residual stress fieldswas developed around
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the crack faces. BM(Figure 11a)shows the higher region of compressive residual stresseson the exit face at position of180° (clockwise from the crack);followed by a transition to a
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smaller zone of tensile residual stresses along the position at 180°moving away from the hole. The same trend applied for WM(Figure 11b), where the highest compressive residual
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stresses were presentedon the exit face and transitioned towards a tensile state moving
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away from the hole. Nevertheless, the minimum magnitude of residual stresses was
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different for BM and WM. For instance, the compressive and tensile residual stresseswere ~ -344 and ~+186 MPa for BM, and ~ -149 and ~+70 MPa for WM. HAZ(Figure 11c) shows the higher region of compressive residual stresseson the entrance face with positions at 90° and 270°(clockwise from the crack), however, these positions were meaningless for the fatigue crack growth phenomena. For the position at 180° (clockwise from the crack), the minimum compressive residual stress was ~ -128 MPa on the exit face and transitioned to a maximum tensile residual stress of ~ +73 MPa.
19 Page 19 of 56
ip t cr us an M d te Ac ce p Figure 11. Tangential residual stress distribution for a) BM, b) WM and c) HAZ. 20 Page 20 of 56
The cold hole expansion process caused an important variation of residual stresses within the thickness of the material, because of the gradual expansion-contraction by the steel ball
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in the surrounding of the hole. From this perspective, Figure 12shows the residual stress
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fields throughout the thickness for BM, WMand HAZ. Moreover, the residual stresses at
entrance face, center and exit face regionswere normalized with respect to yield strength of
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the material and plotted against the distance from the edge of the hole. As expected the
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higher residual stresses were presented in regions close to the hole in the opposite edge to the crack (a = 24mm). The residual stresses decreased along the width of the specimen,
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which corresponded to the expected fatigue crack growth plane. The residual stresses selfbalanced towards zero along the width of the specimen, but there was a transition area from
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a compressionto a tensionstatewhich wasnoticeableat the center of the specimen’s
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thickness. Furthermore, a small zoneof tensile residual stress waspresented closer to the edge of the holein the entrance face for BMand HAZ models, and exit face for WM model.
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From the normalized results, these zones of tensile residual stress were~0.4 for BM and WMmodels and ~0.3 for HAZ model. It is important to note that tensile regions of residual stresseshad a higher susceptibility to crack nucleation and growth. In fact the WMmodel showed the most extensive tensile region of residual stresses around the hole, while the opposite was true for the HAZmodel. The crack length versus number of cycles resultshadshown that after the cold hole expansion (Table II), the WMrequiredthe lower number of cycles and the HAZ the higher one to nucleate and to grow a crack.
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ip t cr us an M d te Ac ce p Figure 12. Residual stress field throughout the compact type specimen thickness for a) BM, b) WM and c) HAZ. 22 Page 22 of 56
On the other hand, the residual stress fields shown a stronger compressive nature at the surface of the hole for BM, followed by the HAZ and lastly WM, which explained the
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increase in fatigue life for BM(Figure 9).
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The fatigue life of the cold hole expansion components (Figure 9) could also be explained
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in terms of the crack closure effect induced bythe residual stress fields. As explained in the methodology section, the crack closure effect of the residual stress field was simulated for a
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post-reparation crack at lengths of 1, 2, 3, 4 and 5 mm (a/W = 0.43, 0.44, 0.46, 0.47 and 0.48). For these post-reparation crack lengths, the finite element results for thecrack
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opening displacement (COD) as a function of the normalized applied load (P/Pmax), known as the compliance curve are presented for the entrance and exit faces in Figure 13a
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and 13b for BM, 13c and 13d for WM, and 13e and 13f for HAZ. The numerical results
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were determined at a distance of 0.33 mm from the crack tip, which corresponded to the
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first node position behind the crack tip.
According to the minimum applied cycle load, the post-reparation crack was completely closed at length sizes of 3 mm (Figure 13a); 1, 2 and 3 mm (Figure 13b); 1, 2, 3 and 4 mm (Figure 13c); 2, 3, 4 and 5 mm (Figure 13d); 3 mm (Figure 13e); and 1, 2, 3 and 4 mm (Figure 13f). Indeed, the post-reparation crack lengths showed a non-linear behavior in the compliance curves, with the exception of 1, 2 and 3 mm (Figure 13b); and 3 mm (Figure 13d). These compliance curves with a linear behavior indicated that the crack was closed for the entire applied cycle load (see Figure 6).According to the maximum applied cycle load, the lower magnitudes of COD were observed for the post-reparation crack lengths on BM (Figure 13a and 13b), followed by the post-reparation crack length on WM (Figures 23 Page 23 of 56
13c and 13d). The higher magnitudes of COD were observed for the post-reparation crack length on HAZ (Figures 13e and 13f).
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In spite of the positive cycle stress ratio (R=0.1) applied during the fatigue test, the numerically determined compliance curves in Figure 13 demonstrated a crack closure effect
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induced by compressive residual stress fields. It is known that the crack closure effect
produces a reduction of the applied stress intensity factor range ΔKas indicated by Elber
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(1970). The applied cycle load required to open the post-reparation crack on the entrance
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face during loading of the CT specimens was of ~0.5, 0.3 and 0.2 P/Pmax for the BM, WM and HAZ, respectively. The computation of the crack opening load was just conducted for
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the entrance face as this was the position used during the fatigue crack growth experiments to measure the crack length. The complete or partial closure of the post-reparation crack,
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the magnitude of the COD and crack opening load were a consequence of the combined
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effect between the applied cycle load and the residual stress fields.An approximation of the
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da/dNas a function of the ΔKeff determined from the finite element simulation was already presented in Figure 10d for BM, WM and HAZ. From a quantitative perspective the finite element results should be interpreted with caution, because of the lack of experimental residual stress and COD measurements.Nevertheless, from a qualitative perspective the finite element results providedreliable andvaluable information to analyze the cold hole expansion effect in fatigue crack growthas revealed by the following fractography analysis.
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ip t cr us an M d te Ac ce p Figure 13. Finite element results of COD versus normalized load (P/Pmax) for entrance and exit faces of the CT specimen, a-b) BM, c-d) WM and e-f) HAZ.
25 Page 25 of 56
3.4. Fractography Figure 14,presents macroscopic views of the fracture surface for BM, WMand HAZ
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specimens with cold hole expansion process.The rectangles indicate the crack initiation zones for each specimen. These details at higher magnification are shown in Figure 15.For
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BMand HAZ, it was observed that the initiation of the crack corresponds to the entrance face of the specimen. Moreover, for WMit was located at the exit face. In all cases, the
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nucleation of the fatigue crack corresponded to zones on the specimen with tensile residual
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stresses as predicted by finite element results (Figure 11 and 12).The nucleationof the fatigue crack was presentedin the surface of the edge hole, where the residual stresses were
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likely in tension (Figure 12).For instance, the cold hole expansion process leaved residual stress fields in tension at the entrance face for BMand HAZ specimens, whereas for WM it
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waslocatedat the exit face. These tensile residual stress fields transitioned into compressive
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ones along the width of the specimen,reached a minimum value at approximately 2.0 and
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3.0 mm for BMand HAZ, respectively, and 3.0 mm for WM. These characteristics confirmed that material zones with tensile residual stress fields exhibited a higher susceptibility for crack nucleation and growth. In spite of the beneficial effect of the compressive residual stress fields, the results for WM and HAZ specimens suggested that either the cold hole expansion degree was unsuitable or local microstructural characteristics played a predominant role. In this sense it would be necessary to perform an additional research in order to elucidate the effect of the expansion degree in terms of microstructure, local mechanical properties and welding defects.
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ip t cr us an M d
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Figure 14. General characteristics of the fracture surfaces for a) BM, b) WM and c) HAZ.
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Figure 15. Surface fracture details according to the rectangle shown in Figure 14.
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Conclusions
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• The degree of cold hole expansion of 4.1%,resulted in an effective reparation process to increase the fatigue life of a 6061-T6 aluminum alloy, butit was
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worthless for weld metal and heat affected zone specimens.
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• The finite element method was an effective tool to characterize the residual stress field as introduced by the cold hole expansion process.
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• The finite element results also revealed a crack closure effect for post-expansion
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cracks located in compressive residual stress fields. The crack closure effect induced elevated opening loads for the post-expansion crack, which resulted in
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lower fatigue crack growth rates.
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• Fracture surface and finite element analysis were in agreement and confirmed that
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tension zones of residual stresses showed a higher susceptibility to crack nucleation and growth.
Acknowledgments
This article was supported by the ConsejoNacional de Ciencia y Tecnología (CONACyT), project CB177834. SIP-IPN is also acknowledge.
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References Ambriz, R.R., Mesmacque, G., Ruiz, A., Amrouche, A., Lopez, V.H., Benseddiq, N., 2010.
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Fatigue crack growth under a constant amplitude loading of Al-6061-T6 welds
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obtained by the modified indirect electric arc technique. Science and Technology of Welding and Joining 15, 514-521.
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Ambriz, R.R., Barrera, G., García, R., López, V. H., 2009. A comparative study of the
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mechanical properties of 6061-T6 GMA welds obtained by the indirect electric arc (IEA) and the modified indirect electric arc (MIEA). Materials & Design 30, 2446-
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2453.
Ambriz, R.R., Chicot, D., Benseddiq, N., Mesmacque, G., de la Torre, S., 2011. Local
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mechanical properties of the 6061-T6 aluminum weld using micro-traction and
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instrumented indentation. European Journal of Mechanics A/Solids 30, 307-315.
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Amrouche, A., Mesmacque, G., García, S., Tahla, A., 2003. Cold expansion effect on the initiation and the propagation of the fatigue crack. International Journal of Fatigue 25, 949-954.
Anderson, T.L., 2005. Fracture Mechanics Fundamentals and Applications, third ed. CRC Taylor and Francis, Boca Raton, pp. 453-460.
Babu, N.C.M., Jagadish, T., Ramachandra, K., Sridhara, S.N., 2008. A simplified 3-D finite element simulation of cold expansion of a circular hole capture through thickness variation of residual stresses. Engineering Failure Analysis 15, 339-348.
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de Matos, P.F.P., Moreira, P.M.G.P., Camanho, P.P., de Castro, P.M.S.T., 2005. Numerical simulation of cold working of rivet holes. Finite Elements in Analysis and Design 41, 989-1007.
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Elber, W., 1970. Fatigue crack closure under cyclic tension. Engineering Fracture
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Mechanics 2, 37-44.
O'Brien, E.W., 2000. Beneficial residual stress from the cold expansion of large holes in
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thick light alloy plate. The Journal of Strain Analysis of Engineering for
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Engineering Design 35, 261-276.
Moreira, P.M.G.P., de Jesus, A.M.P.,Ribeiro, A.S., de Castro, P.M.S.T., 2008. Fatigue
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crack growth in friction stir welds of 6082-T6 and 6061-T6 aluminium alloys: A comparison. Theoretical and Applied Fracture Mechanics 50, 81-91.
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Papanikos, P., Meguid, S. A., 1999. Elasto-plastic finite-element analysis of the cold expansion of adjacent fastener holes. Journal of Materials Processing Technology
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92-93, 424-428.
Pasta, S., 2012. Residual stresses induced by cold expansion of adjacent and cut-out holes. Experimental Mechanics 53, 841-848.
Ruzek, R., Pavlas, J., Doubrava, R., 2012. Application of indentation as a retardation mechanism for fatigue crack growth. International Journal of Fatigue 37, 92-99.
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Figure captions
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Figure 1. a) Schematic representation of the modified indirect electric arc (MIEA) technique and b) joint geometry.
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Figure 2. Welded plate with schematic representation of the compact test (CT) specimens
Figure 3. Compact test (CT) specimen dimensions.
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for base metal (BM), heat affected zone (HAZ) and weld metal (WM).
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Figure 4. Localization of the CT specimens for WM and HAZ according to instrumented
Figure 5. Cold hole expansion process.
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indentation measurements,Ambriz et al. (2011).
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Figure 6. a) Load-displacement behavior and b) schematic representation of the effective
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stress intensity factor range, (Anderson, 2005).
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Figure 7. a) Cold hole expansion process in base metal (BM), b) top and side view of the CT specimen model with specified boundary conditions, and c) three dimension mesh. Figure 8. Tensile mechanical properties of BM, WM and HAZ of 6061-T6 aluminum alloy used for the finite element models. Figure 9. Crack length versus number of cycles, showing initial propagation as well as plain hole and cold hole expansion process for a) BM, b) WM and c) HAZ. Figure 10. Fatigue crack growth as a function of appliedstress intensity factor range for a) BM, b) WM, c) HAZ and d) fatigue crack growth as a function of the effective stress intensity factor range for post-expansion crack in BM, WM and HAZ. 32 Page 32 of 56
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Figure 11. Tangential residual stress distribution for a) BM, b) WM and c) HAZ. Figure 12. Residual stress field throughout the compact type specimen thickness for a) BM,
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b) WM and c) HAZ.
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Figure 13. Finite element results of COD versus normalized load (P/Pmax) for entrance and
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exit faces of the CT specimen, a-b) BM, c-d) WM and e-f) HAZ.
Figure 14. General characteristics of the fracture surfaces for a) BM, b) WM and c) HAZ.
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d
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Figure 15. Surface fracture details according to the rectangle shown in Figure 14.
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Table captions
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Table I. Chemical composition of 6061-T6 plates and ER4043 electrode used (wt. percent). Table II. Number of delayed cycles to nucleate a crack after plain hole and cold hole
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expansion process.
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Highlights
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Experimental results for fatigue crack growth in welds of 6061-T6 aluminum alloy before and after cold hole expansion.
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The loss of hardening on the heat affected zone has a beneficial effect to arrest the crack
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nucleation.
Finite element simulation of the residual stress field generated by the cold hole expansion
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on different zones of the welded joint.
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te
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determined by finite element simulation.
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Higher susceptibility to crack nucleation and growth in tension zones of residual stresses
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Tables
Table I. Chemical composition of 6061-T6 plates and ER4043 electrode used (wt. percent). Si
Mg
Cu
Fe
Mn
Zn
Ti
6061-T6
97.63
0.561
0.986
0.310
0.289
0.052
0.024
0.018
ER4043
92.9
5.6
0.05
0.30
0.8
0.05
0.10
0.02
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Al
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Table II. Number of delayed cycles to nucleate a crack after plain hole and cold hole expansion process. Delayed cycles, ND Plain hole
Cold hole expansion
BM
~ 56 000
~ 112 000
WM
~ 87 000
~ 102 000
HAZ
~116 000
~ 170 000
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