Influence of Residual Stress on Fatigue Weak Areas and Simulation

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Article Inﬂuence of Residual Stress on Fatigue Weak Areas and Simulation Analysis on Fatigue Properties Based on Continuous Performance of FSW Joints

Guoqin Sun 1,*, Xinhai Wei 1, Jiangpei Niu 2, Deguang Shang 1 and Shujun Chen 1

1 College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100124, China; [email protected] (X.W.); [email protected] (D.S.); [email protected] (S.C.) 2 Production R&D center, CRRC Tangshan Co. Ltd., No.3 Changqian Rd, Tangshan 064000, China; [email protected] * Correspondence: [email protected]; Tel.: +86-010-6739-6888

Received: 1 February 2019; Accepted: 26 February 2019; Published: 2 March 2019

Abstract: The fatigue weak area of aluminum alloy for a friction stir-welded joint is investigated based on the hardness proﬁle, the residual stress measurement and the simulation analysis of fatigue property. The maximum residual stresses appeared at the heat-affected zone of the joint in the fatigue damage process, which was consistent with the fracture location of the fatigue specimen. The fatigue joint model of continuous performance is established ignoring the original negative residual stress; considering that it will be relaxed soon when the joint is under tension-tension cyclic loading. The fatigue parameters of joint model is based on the static mechanical properties of the joint that obtained from the micro-tensile tests and four-point correlation method. The predicted results for the fatigue weak locations and fatigue lives based on the continuous performance joint model are closer to the fatigue experimental results by comparison with the simulation results of the partitioned performance joint model.

Keywords: friction stir welding; residual stress; weak area; ﬁnite element simulation; life prediction

1. Introduction Friction stir welding (FSW) of aluminum alloy has been widely used in the automotive, aerospace and ship industries. The anti-fatigue design is worthy of attention for the load-carrying FSW components. The influencing factors on the failure location of the joints are needed to be focused on. The hardness distribution of the friction stir-welded joints is related to the materials and welding process. It is considered that it has a relation to the fatigue fracture position of alloy joints [1–6]. But some studies showed that fatigue cracks were independent from hardness distributions in the weld seams and the fatigue cracks initiated at the inhomogeneous microstructure [7]. Fatigue fracture of the large plate happened at the lowest hardness location in the heat affect zone (HAZ) [8]. But the tensile strength of the FSW joint has a linear relationship with the weld nugget hardness [9]. The fatigue properties of aluminum alloy FSW joints are also affected by the residual stress [2–4]. The residual stresses of aluminum alloy welded joints are dependent on the welding parameters and their distribution has a typical “M” profile [10–13]. The locations of the maximum residual tensile stress are different for different alloy joints. The compressive residual stress delays the crack growth and increases the fatigue life of the welded joint and the tensile residual stress accelerates the propagation of the crack [14–17]. Fratini et al. [4] found that the residual stress had an influence on the crack propagation of base metal area and had no obvious effect on the welding area. The effect of residual stress on the joint would weaken with the increase of fatigue cycle or the crack length [18,19].

Metals 2019, 9, 284; doi:10.3390/met9030284 www.mdpi.com/journal/metals Metals 2019, 9, 284 2 of 13

Metals 2018, 8, x FOR PEER REVIEW 2 of 14 Finite element numerical simulation has been applied on the evaluation of mechanical properties forit is FSW non-negligible joints. In addition, [20]. Rao the and residual Simar [21,22] stress canestablished be preloaded the finite into element the joint model model of as the a prestress FSW joint if itthrough is non-negligible the partition [20 ].method Rao and to Simarobtain [ 21the,22 tensile] established properties. the finite The friction element stir model welding of the joints FSW were joint throughdivided into the partitiondifferent methodregions to to simulate obtain the the tensile mechanical properties. properties The frictionof the weak stir weldingregions [23,24]. joints were dividedThe into simulation different regionsmethod to with simulate the thepartitioned mechanical performance properties of thejoint weak model regions has [ 23the,24 ].stress concentrationThe simulation at the methodregional with boundary the partitioned positions performance because of the joint discontinuity model has the of material stress concentration properties. atThe the continuous regional boundary performance positions joint because model does of the not discontinuity have the effect of material of the properties.area partition The and continuous obtains performancemore accurate joint stress–strain model does data. not haveTherefore, the effect the of fatigue the area finite partition element and obtainsmodel moreof continuous accurate stress–strainperformance data.for the Therefore, FSW joint the fatigueis established finite element to simulate model ofthe continuous weak areas performance and the stress–strain for the FSW jointresponse. is established The life prediction to simulate is proceeded the weak areas based and on the the simulation stress–strain results response. and a Thecomparison life prediction between is proceededthe continuous based performance on the simulation joint model results and and the a partitioned comparison performance between the joint continuous model is performance carried out. jointAlso, model the relationship and the partitioned between the performance fatigue weak joint areas model of is2219-T6 carried aluminum out. Also, alloy the relationship friction stir-welded between thejoints fatigue and mechanical weak areas ofproperties 2219-T6 aluminumis analyzed alloy with friction experimental. stir-welded joints and mechanical properties is analyzed with experimental. 2. Experimental 2. Experimental 2.1. Materials and Specimens 2.1. Materials and Specimens The test specimens is cut from 2219-T6 aluminum alloy FSW butt plate of 800 mm × 300 mm × The test specimens is cut from 2219-T6 aluminum alloy FSW butt plate of 800 mm × 300 mm × 6 mm size. The chemical compositions and mechanical properties of base metal are given in Tables 6 mm size. The chemical compositions and mechanical properties of base metal are given in Tables1 1 and 2. The alloy plates were welded perpendicular to the rolling direction with a rotation speed of and2. The alloy plates were welded perpendicular to the rolling direction with a rotation speed of 800 rpm and an advancing speed of 180 mm/min. The FSW tool consists of a shoulder with a diameter 800 rpm and an advancing speed of 180 mm/min. The FSW tool consists of a shoulder with a diameter of 18 mm and a tool pin of 5.7 mm in length and 6 mm in diameter. The tool axis is tilted by 2° with of 18 mm and a tool pin of 5.7 mm in length and 6 mm in diameter. The tool axis is tilted by 2◦ with respect to the vertical axis of the plate surface. The welding was finished in the China Academy of respect to the vertical axis of the plate surface. The welding was finished in the China Academy of Launch Vehicle Technology. The fatigue samples were wire cut from the plate, which its axial Launch Vehicle Technology. The fatigue samples were wire cut from the plate, which its axial direction direction was perpendicular to the weld line. The surfaces and sides of the specimens were ground was perpendicular to the weld line. The surfaces and sides of the specimens were ground with silicon with silicon carbide sandpaper from 150 to 2000 grit and the surfaces were polished with diamond carbide sandpaper from 150 to 2000 grit and the surfaces were polished with diamond polishing pastes polishing pastes from 4000 to 10,000 grit. The thickness of the fatigue specimen is 6 mm and the from 4000 to 10,000 grit. The thickness of the fatigue specimen is 6 mm and the dimensions is shown dimensions is shown in Figure 1. in Figure1. Table 1. Chemical composition of 2219 aluminum alloy. Table 1. Chemical composition of 2219 aluminum alloy. Chemical Composition (wt%) Chemical Composition (wt%) Cu Mn Fe Zn Si Zr Ti V Al Cu6.48 Mn 0.32 Fe0.23 0.04 Zn 0.49 Si 0.2 Zr 0.06 Ti0.08 Vbalance Al 6.48 0.32 0.23 0.04 0.49 0.2 0.06 0.08 balance Table 2. Mechanical properties of 2219-T6 aluminum alloy. Table 2. Mechanical properties of 2219-T6 aluminum alloy. Elasticity Modulus Ultimate Strength Yield Strength Material Material Elasticity Modulus（ (GPa)GPa） Ultimate Strengthσu (MPa)σu (MPa) Yieldσp0.2 Strength (MPa)σ p0.2 (MPa) 2219-T62219-T6 7272 416 416 315 315

Figure 1. Shape and size of fatigue specimen.

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2.2. Metallographic Morphology The cross-sectionalcross-sectional metallographic morphology of the specimen was observed with the opticaloptical microscope (Shanghai optical instrument factory, Shanghai,Shanghai, China) after the specimenspecimen waswas etchedetched withwith keller’s reagent consisting consisting of of 2.5 2.5 mL mL HNO HNO3,3 ,1.5 1.5 mL mL HCL, HCL, 1 1mL mL HF HF and and 95 95 mL mL H2 HO2 forO for about about 15 15s. According s. According to the to metallographic the metallographic morphology morphology of the of welded the welded joint in joint Figure in Figure 2 and2 theand sizes the sizesof the ofgrain, the the grain, welded the weldedjoint is divided joint is into divided different into regions: different the regions: weld nugget the weld zone nugget (WNZ), zone the thermo- (WNZ), themechanically thermo-mechanically affected zone affected (TMAZ), zone the (TMAZ), HAZ and the the HAZ base and material the base (BM). material The (BM).HAZ Theis further HAZ isdivided further into divided high-hardness into high-hardness heat affect heat zone affect (HHAZ) zone (HHAZ)and low-hardness and low-hardness heat affect heat zone affect (LHAZ) zone (LHAZ)based on based the hardness on the hardnessdistribution distribution and the phase and thesizes. phase The sizes.phase Thein the phase HHAZ in thehas HHAZthe similar has size the similaras that in size the as BM, that while in the the BM, hardness while the in HHAZ hardness is inlower HHAZ than is that lower of BM. than In that addition, of BM. according In addition, to accordingthe rotation to thedirection rotation of directionthe weld ofing the tool, welding the joint tool, is thedivided joint isinto divided the advancing into the advancing side (AS) side and (AS) the andretreating the retreating side (RS). side The (RS). dimensions The dimensions of the ofdifferent the different zones zonesthat marked that marked in the in hardness the hardness profiles proﬁles can canbe obtained be obtained by combining by combining the themetallographic metallographic morphology, morphology, phase phase size size and and the thehardness hardness profile. proﬁle.

FigureFigure 2. 2.Metallograph Metallograph of of the the aluminum aluminum alloy alloy FSW FSW joints: joints: ( A(a)) WNZ,WNZ, ((Bb)) TMAZ,TMAZ, ((Cc)) HAZ, HAZ, ( (dD)) BM. BM. 2.3. Hardness Measurements 2.3. Hardness Measurements The microhardness distributions were measured on the upper and the lower surfaces of the The microhardness distributions were measured on the upper and the lower surfaces of the welded joint with a load of 1.95 N for 15 s with a SCTMC DHV-1000Z Vickers hardness tester (Shangcai welded joint with a load of 1.95 N for 15 s with a SCTMC DHV-1000Z Vickers hardness tester tester machine Co, Ltd, Shanghai, China). The measurement spacing between each two adjacent points (Shangcai tester machine Co, Ltd, Shanghai, China). The measurement spacing between each two was 0.5 mm. adjacent points was 0.5 mm. 2.4. Fatigue Experiments 2.4. Fatigue Experiments All fatigue tests were carried out using MTS858 hydraulic servo system (MTS Systems Corporation, All fatigue tests were carried out using MTS858 hydraulic servo system (MTS Systems Minneapolis, MN, USA) under the axial stress range from 216 to 261 MPa with a stress ratio of 0.1 Corporation, Minneapolis, MN, USA) under the axial stress range from 216 to 261 MPa with a stress and a frequency of 10 Hz until the specimens fractured. The fatigue loading parameters and total ratio of 0.1 and a frequency of 10 Hz until the specimens fractured. The fatigue loading parameters fatigue lives are available from Ref. [25]. The curve of cyclic stress range versus fatigue lives for the and total fatigue lives are available from Ref. [25]. The curve of cyclic stress range versus fatigue lives FSW specimens is shown in Figure3. for the FSW specimens is shown in Figure 3. 2.5. Residual Stress Measurements280 R=0.1 The residual stresses of the original and the fatigue-damaged specimens were measured by

D8 Discover X-ray diffraction 260 meter (Bruker Corporation, Karlsruhe, Germany). The specimen was electrochemically polished to remove the effect of mechanical polishing before the residual stress measurement. The original/MPa residual stress distributionslgΔσ=2.86488-0.1068lgN of the upper (1/m=9.4) and the lower surfaces for the Δσ joint were measured before240 fatigue test. Then, the cyclic stress range of 216 MPa with a stress ratio of 0.1 was loaded on the joint and the fatigue test was stopped when the fatigue life was 30,000 cycles. Then, the surface residual stresses of the fatigue-damaged specimen were measured again to analyze

the effect of the residual stress range Stress 220 distribution in the fatigue process on fatigue damage.

200 0.0 2.0x104 4.0x104 6.0x104 8.0x104 1.0x105 Number of cycle to failure/N f

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2.2. Metallographic Morphology The cross-sectional metallographic morphology of the specimen was observed with the optical microscope (Shanghai optical instrument factory, Shanghai, China) after the specimen was etched with keller’s reagent consisting of 2.5 mL HNO3, 1.5 mL HCL, 1 mL HF and 95 mL H2O for about 15 s. According to the metallographic morphology of the welded joint in Figure 2 and the sizes of the grain, the welded joint is divided into different regions: the weld nugget zone (WNZ), the thermo- mechanically affected zone (TMAZ), the HAZ and the base material (BM). The HAZ is further divided into high-hardness heat affect zone (HHAZ) and low-hardness heat affect zone (LHAZ) based on the hardness distribution and the phase sizes. The phase in the HHAZ has the similar size as that in the BM, while the hardness in HHAZ is lower than that of BM. In addition, according to the rotation direction of the welding tool, the joint is divided into the advancing side (AS) and the retreating side (RS). The dimensions of the different zones that marked in the hardness profiles can be obtained by combining the metallographic morphology, phase size and the hardness profile.

Figure 2. Metallograph of the aluminum alloy FSW joints: (a) WNZ, (b) TMAZ, (c) HAZ, (d) BM.

2.3. Hardness Measurements The microhardness distributions were measured on the upper and the lower surfaces of the welded joint with a load of 1.95 N for 15 s with a SCTMC DHV-1000Z Vickers hardness tester (Shangcai tester machine Co, Ltd, Shanghai, China). The measurement spacing between each two adjacent points was 0.5 mm.

2.4. Fatigue Experiments All fatigue tests were carried out using MTS858 hydraulic servo system (MTS Systems Corporation, Minneapolis, MN, USA) under the axial stress range from 216 to 261 MPa with a stress ratio of 0.1 and a frequency of 10 Hz until the specimens fractured. The fatigue loading parameters andMetals total2019 fatigue, 9, 284 lives are available from Ref. [25]. The curve of cyclic stress range versus fatigue 4lives of 13 for the FSW specimens is shown in Figure 3. 280 R=0.1 Metals 2018, 8, x FOR PEER REVIEW 4 of 14 260 Figure 3. S-N curve of FSW specimens. /MPa lgΔσ=2.86488-0.1068lgN (1/m=9.4) Δσ 2.5. Residual Stress Measurements240 The residual stresses of the original and the fatigue-damaged specimens were measured by D8 Discover X-ray diffraction meter (Bruker Corporation, Karlsruhe, Germany). The specimen was

Stress range range Stress 220 electrochemically polished to remove the effect of mechanical polishing before the residual stress measurement. The original residual stress distributions of the upper and the lower surfaces for the joint were measured before200 fatigue test. Then, the cyclic stress range of 216 MPa with a stress ratio of 4 4 4 4 5 0.1 was loaded on the joint and0.0 the2.0x10 fatigue 4.0x10test was 6.0x10stopped8.0x10 when the1.0x10 fatigue life was 30,000 cycles. Then, the surface residual stresses of theNumber fatigue-damaged of cycle to failure/Nspecimen were measured again to analyze f the effect of the residual stress distribution in the fatigue process on fatigue damage. Figure 3. S-N curve of FSW specimens. 3.3. ExperimentalExperimental ResultsResults

3.1.3.1. HardnessHardness DistributionDistribution TheThe upperupper andand thethe lowerlower surfacessurfaces hardness proﬁlesprofiles of the welded joint are shown in Figure 44.. TheThe hardness distributions distributions of of the the joint joint upper upper and and lower lower surfaces surfaces present present the approximate the approximate “W” shape. “W” shape.The hardness The hardness in the welded in the weldedregion is region obviously is obviously lower than lower the thanbase thematerial. base material. The minimum The minimum hardness hardnessvalues of values the upper of the and upper the and lower the lowersurfaces surfaces are both are both in the in the LHAZ LHAZ according according to to the the hardnesshardness distributiondistribution ofof thethe joints,joints, whichwhich isis notnot inin coincidencecoincidence withwith thethe failurefailure positionposition ofof HHAZHHAZ forfor mostmost fatiguefatigue specimens.specimens. HardnessHardness has has a a relation relation with with the the material material strength strength but but the the fatigue fatigue weak weak area area of the of jointthe joint is not is necessarilynot necessarily corresponding corresponding to the to location the loca oftion minimum of minimum hardness hardness [7]. It [7]. has It a has relation a relation with thewith variation the variation of the hardnessof the hardness gradient, gradient, which correspondswhich corresponds to the variation to the variation of the mechanical of the mechanical property andproperty heterogeneous and heterogeneous microstructure. microstructure.

(a) (b)

FigureFigure 4.4. Hardness distributionsdistributions ofof ((aa)) upperupper andand ((bb)) lowerlower surfacessurfaces inin thethe joint.joint.

3.2.3.2. FatigueFatigue ExperimentalExperimental ResultsResults TheThe failurefailure locationslocations inin thethe jointsjoints werewere observedobserved withwith thethe opticaloptical microscopemicroscope afterafter thethe specimensspecimens fractured.fractured. First,First, thethe locationslocations ofof thethe fatiguefatigue crackcrack sourcessources areare neededneeded toto bebe found and observed. Then, thethe sidessides or or the the surfaces surfaces of theof the sample sample near near the locationthe location of fatigue of fatigue crack sourcescrack sources are etched are withetched Keller’s with reagent.Keller’s Thereagent. failure The locations failure canlocations be afﬁrmed can be through affirmed the through metallographic the metallographic morphologies morphologies of the samples. of the samples. The statistics of failure locations for 11 specimens are listed as follow: 10 specimens fractured in HHAZ, 1 specimen broke in WNZ.

3.3. Residual Stress Distribution The residual stress distributions are shown in Figures 5 and 6. The transverse residual stresses are the stresses perpendicular to the weld and the longitudinal residual stresses are the stresses

Metals 2018, 8, x FOR PEER REVIEW 5 of 14

parallel to the weld direction. The center of the WNZ was taken as the zero coordinate and the test points were selected on both sides along the axial direction of the specimen. The measured residual stresses before fatigue test are called as the original residual stresses of the specimen in this paper. The residual stresses of the fatigue-damaged specimens were measured after the fatigue cycle reached 30,000 cycles under the cyclic stress range of 216 MPa with a stress ratio of 0.1. Figure 5 shows the variation of the transverse and longitudinal residual stress distribution Metals 2018, 8, x FOR PEER REVIEW 5 of 14 curvesMetals 2019 in, the9, 284 upper surface of the welded joint. It can be seen that the maximums of the transverse5 of 13 and longitudinal residual stresses in the original welded joint appear in the WNZ and the values are parallelbasically to negative the weld or direction. near zero. The The center original of thenegative WNZ residual was taken stresses as the in zero the weldedcoordinate joint and is beneficial the test pointstoThe the statistics werefatigue selected of life. failure However, on locations both si thedes for originalalong 11 specimens the compress axial are direction listedresidual as of follow: stressthe specimen. will 10 specimens be relaxed The measured fractured and the inresidual positive HHAZ, stressesstress1 specimen willbefore brokeappear fatigue in soon WNZ. test onceare called the tension-tension as the original residualstress is stresses loaded. of The the specimenpositive transverse in this paper. and Thelongitudinal residual residualstresses stressesof the fatigue-damagedarose in the fatigue sp processecimens and were the measuredmaximum residualafter the stress fatigue appeared cycle 3.3. Residual Stress Distribution reachedat the LHAZ 30,000 during cycles theunder cyclic the loading. cyclic stress range of 216 MPa with a stress ratio of 0.1. Figure 5 shows the variation of the transverse and longitudinal residual stress distribution The120 residual stress distributions are shown in Figures5 and6. The transverse residual stresses are Original specimen 120 curves in the upper surface of the welded joint. It can be seen that the maximums Original of specimen the transverse the stresses perpendicular to Fatigue the weld damaged and specimen the longitudinal residual stresses are the stresses parallel MPa 90 / 90 Fatigue damaged specimen andto thelongitudinal weld direction. residual The stresses center in of the the original WNZ waswelded taken joint as appear the zero in coordinate the WNZ and and the the values test points are 60 basicallywere selected negative on bothor near sides zero. along The theoriginal axial negative direction residual of the60 specimen. stresses in The the measured welded joint residual is beneficial stresses tobefore the fatigue30 fatigue life. test However, are called asthe the original original compress residual stressesresidual30 of stress the specimen will be relaxed in this paper. and the The positive residual

HHAZ stressstresses will0 of theappear fatigue-damaged soon once the specimens tension-tensionHHAZ were measured stress0 afteris loaded. the fatigue The cyclepositive reached transverse 30,000 cyclesand longitudinal residual stresses arose in the fatigue process and the maximum residual stress appeared under-30 the cyclic stress range of 216 MPa with a stress ratio-30 of 0.1. at the LHAZ during the cyclic loading. HHAZ HHAZ -60 LHAZ LHAZ -60 LHAZ 120 residualTransverse stress LHAZ Original specimen 120Longitudinal residual stress/MPa -90 -90 Original specimen RS AS TM FatigueNZ damagedTM specimenRS AS TM NZ TM MPa 90 / 90 Fatigue damaged specimen -15 -10 -5 0 5 10 15 -15 -10 -5 0 5 10 15 60 Distance from the weld center/mm 60 Dsitance from the weld center/mm 30 30

HHAZ 0 HHAZ 0 (a) (b) -30 -30 Figure 5. (a) Transverse and (b) longitudinal residual stress distributionsHHAZ of upper surface in the HHAZjoint. -60 LHAZ LHAZ -60 LHAZ Transverse residualTransverse stress LHAZ Longitudinal residual stress/MPa -90 -90 RS Figure 6AS showsTM the variationNZ TM of theRS transverse and longitudinalAS TM residualNZ stressTM distribution curves in -15the lower -10 surface -5 of 0 the 5welded 10 joint. 15 The residual-15 stresses -10 is negative -5 0 in the 5 original 10 15joint. The maximumDistance stresses from appeared the weld nearcenter/mm the boundary of NZ andDsitance TMAZ fromin the the fatigue weld center process/mm and the values were far lower than the residual stresses in the upper surface. The residual stress of the upper surface in the joint that produced in the fatigue process should have more effect on the fatigue (a) (b) damage. FigureFigure 5. 5. (a()a Transverse) Transverse and and (b (b) longitudinal) longitudinal residual residual stress stress distributions distributions of of upper upper surface surface in in the the joint. joint.

Original specimen Original specimen Figure80 6 shows the variation of the transverse and80 longitudinal residual stress distribution Fatigue damaged specimen Fatigue damaged specimen MPa MPa / curves in the lower surface of the welded joint. The residual/ stresses is negative in the original joint. The maximum40 stresses appeared near the boundary of NZ40 and TMAZ in the fatigue process and the values were0 far lower than the residual stresses in the upper0 surface. The residual stress of the upper surface in the joint that produced in the fatigue process should have more effect on the fatigue -40 damage.-40

-80 -80 LHAZ LHAZ HHAZ HHAZ Transverse Transverse residual stress Longitudinal residual stress TM TM HHAZ TM OriginalTM specimen HHAZ -120 Original specimen -12080 AS LHAZ LHAZ 80 AS RS FatigueNZ damaged specimenRS FatigueNZ damaged specimen MPa MPa / -15 -10 -5 0 5 10 15 / -10 -5 0 5 10 40 40 Dsitance from the weld center/mm Distance from the weld center/mm 0 (a) 0 (b)

-40Figure 6. ((aa)) Transverse Transverse and ( b) longitudinal longitudinal residual stress -40 distributions of lower surface in the joint.

-80 -80 Figure5 shows the variation of the transverse and longitudinal residualLHAZ stressLHAZ distribution curves 4. Fatigue Numerical Simulation HHAZ HHAZ Transverse Transverse residual stress HHAZ TM TM HHAZ Longitudinal residual stress TM TM in the-120 upper surfaceLHAZ of the welded joint. It can be seen-120 thatAS the maximums of the transverseRS and AS NZ LHAZ RS NZ longitudinal residual stresses in the original welded joint appear in the WNZ and the values are -15 -10 -5 0 5 10 15 -10 -5 0 5 10 Dsitance from the weld center/mm basically negativeDistance or from near the zero. weld The center/mm original negative residual stresses in the welded joint is beneﬁcial to the fatigue life. However, the original compress residual stress will be relaxed and the positive stress (a) (b) will appear soon once the tension-tension stress is loaded. The positive transverse and longitudinal residualFigure stresses 6. (a) Transverse arose in theandfatigue (b) longitudinal process residual and the stress maximum distributions residual of lower stress surface appeared in the at joint. the LHAZ during the cyclic loading. 4. Fatigue Numerical Simulation

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Figure6 shows the variation of the transverse and longitudinal residual stress distribution curves in the lower surface of the welded joint. The residual stresses is negative in the original joint. The maximum stresses appeared near the boundary of NZ and TMAZ in the fatigue process and the values were far lower than the residual stresses in the upper surface. The residual stress of the upper surface in the joint that produced in the fatigue process should have more effect on the fatigue damage. Metals 2018, 8, x FOR PEER REVIEW 6 of 14 4. Fatigue Numerical Simulation 4.1. Fatigue Parameters of the Welded Joint 4.1. Fatigue Parameters of the Welded Joint The fatigue finite element numerical analysis is further proceeded in order to obtain the stress– strain Theresponses fatigue and ﬁnite evaluate element the weak numerical area of analysisthe joint with is further the simulation proceeded method. in order Since to the obtain original the residualstress–strain stress responseswas negative and and evaluate would the be weakrelaxed area once of the the tension-tens joint with theion simulation stress was method.loaded. It Sincedid notthe considered original residual to be added stress on was the negative joint as and a pres wouldtress bein relaxedthe numerical once the analysis tension-tension under the stress tension- was tensionloaded. cyclic It did loading. not considered to be added on the joint as a prestress in the numerical analysis under theThe tension-tension fatigue parameters cyclic loading. are different in different zones since the materials of different zones in the jointThe have fatigue different parameters microstructures are different and in mechanic different zonesal properties. since the They materials can be of used different in some zones fatigue in the lifejoint prediction have different models microstructures to calculate fatigue and mechanical lives or as properties. the intermediate They can variables be used into somecalculate fatigue other life cyclicprediction strength models parameters. to calculate The fatiguefatigue livesparameters or as the of intermediate different positions variables in the to calculate welded otherjoint were cyclic obtainedstrength by parameters. four-point Thecorrelation fatigue parametersmethod proposed of different by Manson positions [26]. in the welded joint were obtained by four-pointThe four-point correlation correlation method method proposed is based by Manson on the [26 elastic]. and plastic strain-life lines. The respectiveThe four-pointtwo points correlation on elastic methodand plastic is based lines onare the definite. elastic On and the plastic elastic strain-life line, a point lines. is The at respective1/4 cycle two points on elastic and plastic lines are deﬁnite. On the elastic line, a point is at 1/4 cycle with a with a strain range of 2.5 𝜎/E, where σf is the fracture strength, E is the elastic modulus. The other pointstrain is rangeat 105 ofcycles 2.5 σ withf/E, wherea strainσ frangeis the of fracture 0.9 σu/ strength,E, where Eσuis is the the elastic ultimate modulus. tensile Thestrength. other On point the is 5 plasticat 10 line,cycles a withpoint a locates strain rangeat 10 ofcycles 0.9 σ uwith/E, wherea strainσu rangeis the of ultimate 1/4D3/4 tensile, where strength. D is the On logarithmic the plastic 3/4 .∆∗ line, a point locates at 10 cycles with a strain range4 of 1/4D , where D is the logarithmic ∗ ductility of ductility of the material. Another point is at 10 cycles with a strain range− of∗ , Δ𝜀 indicates the material. Another point is at 104 cycles with a strain range of 0.0132 ∆εe , ∆ε∗.indicates the value of the value of elastic strain range at 104 cycles on the elastic line, as shown1.91 in Figuree 7. elastic strain range at 104 cycles on the elastic line, as shown in Figure7.

Figure 7. Four-point correlation method by Manson. Figure 7. Four-point correlation method by Manson. The static mechanical properties of different positions in the joint were obtained from the micro-tensileThe static mechanical tests. Microspecimens properties of from different different posi regionstions inwere the joint cut parallelwere obtained to the weldfrom directionthe micro- of tensilewelded tests. joints. Microspecimens The static mechanical from different properties regions of were each cut zone parallel were measuredto the weld by direction using Instron of welded 5948 joints.Microtester The static (Instron mechanical Corporation, properties Norwood, of each MA, zone USA). were Themeasured calculated by using fatigue Instron parameters 5948 Microtester of different (Instronpositions Corporation, in the welded Norwood, joint are MA listed, USA). in Table The3 .calculated fatigue parameters of different positions in the welded joint are listed in Table 3.

Table 3. Fatigue parameters of the welded joint.

Cutting Cites Fatigue Fatigue Fatigue Fatigue Cyclic Cyclic Strain Elastic of the Micro Strength Strength Ductility Ductility Strength Hardening Modulus Specimens Coefficient Exponent Exponent Coefficient Coefficient exponent E (GPa) X (mm) σ’f (MPa) b c ε’f K’(MPa) n’ −11 64 364 −0.078 −0.33 0.041 781 0.24 −7 53 275 −0.079 −0.31 0.037 635 0.25 −5 58 324 −0.077 −0.37 0.062 578 0.21 0 59 334 −0.078 −0.37 0.059 610 0.21 6 61 313 −0.076 −0.35 0.055 581 0.21

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Table 3. Fatigue parameters of the welded joint.

Cutting Cites of Elastic Fatigue Strength Fatigue Fatigue Cyclic Strength Cyclic Strain 0 Fatigue Strength the Micro Modulus Coefficient σ f Ductility Ductility Coefficient Hardening Exponent b 0 0 0 Specimens X (mm) E (GPa) (MPa) Exponent c Coefficient ε f K (MPa) Exponent n −11 64 364 −0.078 −0.33 0.041 781 0.24 −7 53 275 −0.079 −0.31 0.037 635 0.25 −5 58 324 −0.077 −0.37 0.062 578 0.21 0 59 334 −0.078 −0.37 0.059 610 0.21 6 61 313 −0.076 −0.35 0.055 581 0.21 8 62 263 −0.058 −0.33 0.043 458 0.18 11 63 328 −0.076 −0.34 0.047 656 0.23

4.2. Continuous Performance Joint Model The continuous performance joint model is established by inputting different elastic moduli and fatigue stress–strain data at different areas of the joint with ABAQUS software. The WNZ center of the joint is the zero coordinate of the X axis in the model. The different coordinates correspond to the different locations of the joint along the axial loading direction. The elastic moduli of different positions with the coordinate X that listed in Table3 were obtained from the micro tension tests. The elastic moduli of the other positions in the joint can be obtained by interpolation according to the data in Table3. The mechanical properties of the joint also vary with change of the coordinate. The materials in different zones of the joint have different stress–strain responses. The cyclic stress–strain at different locations of the joint were obtained using Ramberg–Osgood equation and applied to the ﬁnite element simulation. The Ramberg–Osgood equation is shown below.

1 σ σ 0 ε = a + a n (1) a E K0 0 0 where εa is the strain amplitude, σa is the stress amplitude, K is cyclic strength coefﬁcient, n is the cyclic strain hardening exponent. They can be obtained from the following equations.

σ0 K0 = f (2) 0 n0 εf

n0 = b/c (3)

The cyclic yield strength was measured by the stress value of 0.2% plastic strain in the cyclic stress–strain curve. The nonlinear kinematic hardening model of the material attribute was adopted for the joint material. User subroutine USDFLD in the ABAQUS software can be used to describe material properties. The material properties is defined as a function of field variables and the variables can be solved with USDFLD subroutine. The variation of elastic modulus, yield stress and plastic strain with the coordinate X were computed with the interpolation method using the known data of the specific coordinate through the subroutine. The joint model is constrained at one end and loaded the cyclic stress range of 216 MPa with a stress ratio of 0.1 at another end of the joint in the X-axial direction. The loaded cyclic stress is schematically drawn in Figure8. The hexahedron mesh with eight nodes element type of C3D8R is selected to solve the structure. The size of each element is approximately 1.3 mm × 0.8 mm × 1.2 mm. 3600 elements and 4758 nodes are obtained to simulate the FSW joints, as shown in Figure9. The model does not include the clamping part and the cyclic stress as a surface load is directly applied to the section of the right end. Metals 2018, 8, x FOR PEER REVIEW 8 of 14

Metals 2018, 8, x FOR PEER REVIEW 8 of 14 Metals 2019, 9, 284 8 of 13

Metals 2018, 8, x FOR PEER REVIEWσ/MPa 8 of 14

σ/MPa σ/MPa

0 t/s

Figure 8. Schematic of loaded cyclic stress on the joint. 0 t/s 0 t/s Figure 8. Schematic of loaded cyclic stress on the joint. FigureFigure 8. SchematicSchematic of of loaded loaded cyclic cyclic stress stress on the joint.

Figure 9. Meshed joint.

4.3. Partitioned Performance Joint Model Figure 9. Meshed joint. Figure 9. Meshed joint. 4.3. PartitionedTo compare Performance the effectiveness Joint Model of Figurethe continuous 9. Meshed joint.performance joint model for the fatigue 4.3. Partitioned Performance Joint Model performanceTo compare simulation the effectiveness of the FSW joints, of the the continuous partitioned performance performance jointjoint model was for established the fatigue 4.3. Partitioned Performance Joint Model accordingperformanceTo compare to the simulation metallurgical the effectiveness of the morphologies, FSW joints,of the the hardnesscontinuous partitioned profile performance performance of the joints joint joint and model the material wasfor establishedthe attributes fatigue inaccordingperformance differentTo compare to regions thesimulation metallurgical the of the effectiveness of joint the morphologies, [25].FSW Thejoints, of thejoint the continuous hardnessis partitioned composed proﬁle performance performanceof ofthe the WNZ, joints joint jointTMAZ, and modelmodel the HHAZ, material forwas theLHAZestablished attributes fatigue and BM,performanceinaccording different as shown to regions thesimulation in metallurgical Figure of the of joint10. the The [morphologies,25FSW ].fatigue The joints, joint parameters the is hardness composedpartitioned of profile different of performance the of WNZ, the positions joints TMAZ, joint and of model HHAZ, thethe material FSW was LHAZ jointsestablished attributes and were BM, calculatedaccordingasin showndifferent intoaccording regions Figurethe metallurgical 10 of to. Thethethe joint fatiguefour-point morphologies, [25]. parameters The correlation joint hardness ofis composed different methods. profile positions Theof of the stress–strainthe WNZ, ofjoints the TMAZ, FSWand data the joints HHAZ, materialin different were LHAZ calculatedattributes zones and ofinaccordingBM, thedifferent as joint shown to wereregions the in four-pointobtained Figure of the 10.jointwith correlation The [Ramberg–Osgood25 fatigue]. The methods. joi parametersnt is composed The equation. stress–strainof different of The the materialWNZ, datapositions in TMAZ, differentproperty of the HHAZ, zonesFSWdoes LHAZjointsnot of the have were jointand a changeBM,werecalculated as obtained within shown according eachwith in Figure region. Ramberg–Osgood to the 10. four-point The fatigue equation.correlation parameters The methods. material of different The property stress–strain positions does not of data thehave in FSW adifferent change joints within zones were calculatedeachof the region. joint according were obtained to the withfour -Ramberg–Osgoodpoint correlation methods. equation. The The stress material–strain property data in does different not havezones a ofchange the joint within were each obtained region. with Ramberg–Osgood equation. The material property does not have a change within each region.

Figure 10. Partitioned performance joint model of the FSW joint. Figure 10. Partitioned performance joint model of the FSW joint. 5. Simulation Results 5.5.1. Simulation Stress Distribution Results Figure 10. Partitioned performance joint model of the FSW joint. Figure 10. Partitioned performance joint model of the FSW joint. 5.1. StressVon MisesDistribution stress distributions of continuous and partitioned performance joints are shown in Figure5. Simulation 11a,b. The Results stress distribution of the partitioned performance joint shows a signiﬁcant mutation 5.at Simulation theVon junction Mises Results of stress different distributions regions, especially of continuous at the junctionand partitioned of TMAZ performance and HAZ. The joints simulation are shown results in Figureof5.1. continuous Stress 11a,b. Distribution The performance stress distribution joints show of the the partitioned changes of performance stress and strain joint areshows smoother. a significant mutation 5.1. Stress Distribution at theVon junction Mises of stress different distributions regions, ofespecially continuous at the an djunction partitioned of TMAZ performance and HAZ. joints The are simulation shown in resultsFigureVon of11a,b. continuousMises The stress stress performance distr distributionibutions joints of thecontinuous show partitioned the changesand performance partitioned of stress joint performanceand showsstrain area significantjoints smoother. are shown mutation in Figureat the 11a,junctionb. The of stress different distribution regions, of especially the partitioned at the performance junction of TMAZjoint shows and aHAZ. significant The simulation mutation atresults the junction of continuous of different performance regions, joints especially show theat the changes junction of stress of TMAZ and strain and HAZ. are smoother. The simulation results of continuous performance joints show the changes of stress and strain are smoother.

Metals 2018, 8, x FOR PEER REVIEW 9 of 14

Metals 2019, 9, 284 9 of 13 Metals 2018, 8, x FOR PEER REVIEW 9 of 14

(a)

(a) (b)

Figure 11. Von Mises stress contour plots of (a) continuous joint model and (b) partitioned joint model.

To observe the fatigue performance of the joint, the cyclic stress range of 216 MPa with the stress ratio of 0.1 was loaded on the joint. The maximum von Mises equivalent stress appeared in the upper surface of the joint in the partitioned performance joint model. The stress distribution trend of the

upper and the lower surfaces in the continuous pe(brformance) joint model is the same. The von Mises stress data of upper surface centerline were extracted from the simulation results of the continuous Figure 11. Von Mises stress contour plots of (a) continuous joint model and (b) partitioned joint and Figurethe partitioned 11. Von Mises performance stress contour joint plots models. of (a) continuous The maximum joint model von andMises (b) partitionedstresses both joint appear model.ed in model. the HHAZTo observe for the the two fatigue models, performance as shown of in the Figure joint, 12. the cyclic stress range of 216 MPa with the stress The sudden change of stress in the partitioned performance joint model is obvious at the junction ratio ofTo 0.1 observe was loaded the fatigue on the performance joint. The maximum of the joint, von th Misese cyclic equivalent stress range stress of 216 appeared MPa with in the the upper stress of adjacent regions in the joint. The distribution of von Mises equivalent stress obtained from the surfaceratio of of0.1 the was joint loaded in the on partitionedthe joint. The performance maximum von joint Mises model. equivalent The stress stress distribution appeared trendin the ofupper the continuous performance joint model is relatively continuous for the joint, which is closer to the uppersurface and of the lowerjoint in surfaces the partitioned in the continuous performance performance joint model. joint The model stress is thedistribution same. The trend von Misesof the practical condition. The maximum stress appeared at the boundary of LHAZ and HHAZ for the stressupper data and ofthe upper lower surface surfaces centerline in the continuous were extracted performance from the joint simulation model is results the same. of the The continuous von Mises partitioned performance joint model and it occurred at HHAZ near the LHAZ for the continuous andstress the data partitioned of upper performance surface centerline joint models. were extracte The maximumd from the von simulation Mises stresses results both of appeared the continuous in the performance joint model. The location of the maximum stress has a little difference for the two HHAZand the for partitioned the two models, performance as shown joint in models. Figure 12 The. maximum von Mises stresses both appeared in models. the HHAZ for the two models, as shown in Figure 12. 320 The sudden change of stress in the partitioned performance joint model is obvious at the junction Partitioned model of adjacent regions in the joint. The distribution of von Mises equivalent stress obtained from the Continuous model continuous performance 280joint model is relatively continuous for the joint, which is closer to the practical condition. The maximum stress appeared at the boundary of LHAZ and HHAZ for the partitioned performance 240joint model and it occurred at HHAZ near the LHAZ for the continuous performance joint model. The location of the maximum stress has a little difference for the two models. 200 320 160 LHAZ PartitionedLHAZ model Von Mises stress/MPa Continuous model 280 TMAZ 120 TMAZ BM HHAZ WNZ HHAZ BM 240 -40-30-20-100 10203040 Distance from the weld center/mm 200 Figure 12. Von Mises stresses distributions of upper surface in the joint model. Figure 12. Von Mises stresses distributions of upper surface in the joint model. LHAZ The sudden change of160 stress in the partitioned performanceLHAZ joint model is obvious at the junction Von Mises stress/MPa of adjacentThe stress regions components in the joint. of continuous The distribution and partit of vonioned Mises joint equivalent models were stress analyzed. obtained There from is the no TMAZ TMAZ continuousstress in the performance Z direction. joint The120 modelshear isstresses relatively are continuousso small that for their the joint,effects which on the is closerfatigue to performance the practical BM HHAZ WNZ HHAZ BM condition. The maximum stress-40-30-20-100 appeared at the boundary 10203040 of LHAZ and HHAZ for the partitioned performance joint model and it occurredDistance at HHAZfrom the near weld the center/mm LHAZ for the continuous performance joint model. The location of the maximum stress has a little difference for the two models. The stress components of continuous and partitioned joint models were analyzed. There is no Figure 12. Von Mises stresses distributions of upper surface in the joint model. stress in the Z direction. The shear stresses are so small that their effects on the fatigue performance of the welded joint are ignored. It can be considered that the stresses in the X and the Y directions The stress components of continuous and partitioned joint models were analyzed. There is no stress in the Z direction. The shear stresses are so small that their effects on the fatigue performance

Metals 2018, 8, x FOR PEER REVIEW 10 of 14 Metals 2019, 9, 284 10 of 13 of the welded joint are ignored. It can be considered that the stresses in the X and the Y directions determine the total stress distribution of the FSW joints. The stresses in the X and the Y directions of determineupper surface the total in the stress models distribution were extracted of the FSW for analysis joints. The as an stresses example, in the as Xshown and thein Figure Y directions 13. The ofstresses upper surfacein the X in direction the models are larger were extractedin the two for models analysis since as anthe example,tension-tension as shown stress in is Figure loaded 13 .in Thethe stresses X direction. in the XThe direction stress fluctuation are larger in appeared the two modelsin the X since and the the tension-tension Y directions of stress the partitioned is loaded inperformance the X direction. joint The model. stress The ﬂuctuation stress distribution appeared of in the the continuous X and the Yperformance directions of joint the model partitioned has no performanceobvious sudden joint change. model. The stress distribution of the continuous performance joint model has no obvious sudden change.

360 Partitioned model, X axis direction Continuous model, X axis direction 300 Partitioned model, Y axis direction Continuous model, Y axis direction 240

180

LHAZ 120 LHAZ Stress/MPa

60 TMAZ TMAZ HHAZ WNZ HHAZ 0 BM BM

-40-30-20-100 10203040 Distance from the weld center/mm

Figure 13. Stress distributions in the X and Y directions in upper surface of the joint model. Figure 13. Stress distributions in the X and Y directions in upper surface of the joint model. 5.2. Strain Distribution 5.2.The Strain weak Distribution area of joint fatigue performance can be determined by the stress and strain response of differentThe weak zones area in theof joint joint fatigue from theperformance simulation can results be determined of the fatigue by the property. stress and The strain maximum response principalof different strains zones at thein the centerline joint from of upper the simulati surface,on which results extracted of the fatigu frome theproperty. continuous The maximum and the partitionedprincipal performancestrains at the joint centerline models of under upper the surfac cyclice, stress which range extracted of 216 MPafrom with the acontinuous stress ratio and of 0.1, the arepartitioned presented inperformance Figure 14. Due joint to models the abrupt under change the cyclic of material stress properties, range of 216 the MPa partitioned with a performance stress ratio of joint0.1, model are presented caused a correspondingin Figure 14. stressDue to concentration the abrupt atchange the junction of material of different properties, regions the and partitioned resulted inperformance larger maximum joint principal model caused strains a than corresponding that of the continuous stress concentration performance at jointthe junction model. Theof different larger theregions loaded and cyclic resulted stress in in larger the model, maximum the moreprincipal obvious strains the than abrupt that changeof the continuous of strain distribution. performance Thejoint maximum model. The principal larger strainthe loaded is inthe cyclic LHAZ stress near in the model, TMAZ the for themore partitioned obvious the performance abrupt change joint of modelstrain and distribution. it appears The inthe maximum HHAZ closeprincipal to the strain LHAZ is in for the the LHAZ continuous near the performance TMAZ for the joint partitioned model, whichperformance is approximatelyMetals joint2018, 8, xmodel FOR consistent PEER andREVIEW it with appears the fatigue in the failure HHAZ position. close to The the simulated LHAZ fatiguefor the11 of weak14continuous area withperformance the continuous joint performancemodel, which joint is approximately model is more consistent close to the with fatigue the experimentalfatigue failure results. position. The

simulated fatigue weak area with0.03 the continuous performance joint model is more close to the fatigue experimental results. Partitioned model Continuous model By comparison with the partitioned performance joint model, the continuous performance joint

model has a higher accuracy 0.02on predicting the fatigue weak areas of the FSW joint according to the stress and strain distributions. It eliminates the large stress concentration caused by the abrupt change of material properties in the adjacentLHAZ area andLHAZ more accurately simulates the fatigue

performance of the joint. 0.01 Maximum principal strain BM TMAZ TMAZ BM HHAZ WNZ HHAZ 0.00 -40-30-20-100 10203040 Distance from the weld center/mm

Figure 14. Maximum principal strain distributions of upper surface in the joint model. Figure 14. Maximum principal strain distributions of upper surface in the joint model. By comparison with the partitioned performance joint model, the continuous performance joint 6. Fatigue Life Prediction model has a higher accuracy on predicting the fatigue weak areas of the FSW joint according to the The joint models established in this paper not only evaluate the fatigue weak areas and obtain the stress and strain values of the joint, but they also predict the fatigue lives of the joints. In this section, the stress and strain values of the weak areas obtained from the continuous and the partitioned performance joint models are used to predict the fatigue lives of the FSW joints. The validity of the continuous performance joint model is further verified by comparison with the experimental results. Crack initiation lives were estimated with Smith–Watson–Topper (SWT) method, which considered the effect of average stress [27]. The maximum principal stresses and corresponding maximum principal strain ranges of the weak area of the joint were extracted from the simulation results of the joint models. Fatigue parameters of weak areas are used to predict the fatigue crack initiation lives of joints. The SWT formula is shown below.

' 2 Δε σ + σ = f (2N)2b +σ ' ε ' (2N)b c (4) max 2 E f f

where σmax is the maximum principal stress, Δε is the maximum principal strain range, N is the fatigue life. The experimental results in Ref. [28] showed that the size of fatigue crack initiation was defined as 1 mm and the crack initiation lives for the HAZ and the WNZ of aluminum alloy welded joints were 40.21% and 60.67% of the total fatigue lives, respectively. The research in Ref. [29] showed that the crack initiation lives accounted for 40–50% of total fatigue lives. Therefore, the crack initiation life is selected as 50% of the total fatigue life in this paper. The life prediction results of FSW joints are shown in Figure 15. The predicted errors of the fatigue lives based on the continuous and the partitioned performance joint models are basically within the factor of two by comparison with the experimental results. The fatigue life prediction results with the simulation data obtained from the continuous performance joint model are closer to the experimental lives because the continuous performance joint model has not the stress and strain concentrations caused by the area partition. It is shown that the continuous performance joint model is suitable for life prediction of the FSW joints.

Metals 2019, 9, 284 11 of 13 stress and strain distributions. It eliminates the large stress concentration caused by the abrupt change of material properties in the adjacent area and more accurately simulates the fatigue performance of the joint.

6. Fatigue Life Prediction The joint models established in this paper not only evaluate the fatigue weak areas and obtain the stress and strain values of the joint, but they also predict the fatigue lives of the joints. In this section, the stress and strain values of the weak areas obtained from the continuous and the partitioned performance joint models are used to predict the fatigue lives of the FSW joints. The validity of the continuous performance joint model is further veriﬁed by comparison with the experimental results. Crack initiation lives were estimated with Smith–Watson–Topper (SWT) method, which considered the effect of average stress [27]. The maximum principal stresses and corresponding maximum principal strain ranges of the weak area of the joint were extracted from the simulation results of the joint models. Fatigue parameters of weak areas are used to predict the fatigue crack initiation lives of joints. The SWT formula is shown below.

02 ∆ε σ + σ = f (2N)2b + σ0ε0 (2N)b c (4) max 2 E f f where σmax is the maximum principal stress, ∆ε is the maximum principal strain range, N is the fatigue life. The experimental results in Ref. [28] showed that the size of fatigue crack initiation was deﬁned as 1 mm and the crack initiation lives for the HAZ and the WNZ of aluminum alloy welded joints were 40.21% and 60.67% of the total fatigue lives, respectively. The research in Ref. [29] showed that the crack initiation lives accounted for 40–50% of total fatigue lives. Therefore, the crack initiation life is selected as 50% of the total fatigue life in this paper. The life prediction results of FSW joints are shown in Figure 15. The predicted errors of the fatigue lives based on the continuous and the partitioned performance joint models are basically within the factor of two by comparison with the experimental results. The fatigue life prediction results with the simulation data obtained from the continuous performance joint model are closer to the experimental lives because the continuous performance joint model has not the stress and strain concentrations caused by the area partition. It is shown that the continuous performance joint model is suitable for life predictionMetals 2018 of the, 8, x FOR FSW PEER joints. REVIEW 12 of 14

106

105 Predicted life/N Partitioned model Continuous model

104 104 105 106 Experimental life/N

Figure 15. FigureLife prediction15. Life prediction of joint of joint based based on on continuous continuous and and partitioned partitioned performance performance joint models. joint models.

7. Conclusions7. Conclusions (1) The original(1) The original transverse transverse and and longitudinal longitudinal resi residualdual stresses stresses in the in welded the welded joint before joint fatigue before fatigue are negativeare andnegative the and maximum the maximum tensile tensile residual residual stressstress occurs occurs in the in theHAZ HAZ during during the tens theion–tension tension–tension cyclic loading process. cyclic loading(2) process. The fatigue parameters of different areas are obtained with four-point correlation method and the static mechanical property parameters of micro-tensile specimen at different locations of the joint. The continuous performance joint model is established by inputting different elastic moduli and fatigue stress–strain data at different locations of the FSW joint with user subroutine USDFLD. The stress components in the X and the Y directions determine the stress distribution of the FSW joints. The continuous performance joint model eliminates the stress and strain concentration caused by the area partition and more accurately simulates the fatigue performance of the joint by comparison with the partitioned performance joint model. The simulated fatigue weak area with the continuous performance joint model is more close to the fatigue experimental results. (3) The fatigue life prediction of the FSW joints is proceeded with SWT method based on the simulation results of the continuous and the partitioned performance joint models. The results show that the predicted lives with the continuous performance joint model are closer to the experimental results and the life prediction error is within the factor of two.

Author Contributions: Guoqin Sun designed and performed the experiments; Guoqin Sun, Jiangpei Niu and Xinhai Wei analyzed the experimental data and simulated the joint model; Deguang Shang and Shujun Chen gave some advices for the research; Guoqin Sun and Xinhai Wei wrote the paper.

Funding: This research was founded by the National Natural Science Foundation of China (Grant No. 11672010, 51535001 and 51575012).

Conflicts of Interest: The authors declare no conflicst of interest.

Abbreviations

FSW Friction stir welding

WNZ Weld nugget zone

TMAZ Thermo-mechanically affected zone

Metals 2019, 9, 284 12 of 13

(2) The fatigue parameters of different areas are obtained with four-point correlation method and the static mechanical property parameters of micro-tensile specimen at different locations of the joint. The continuous performance joint model is established by inputting different elastic moduli and fatigue stress–strain data at different locations of the FSW joint with user subroutine USDFLD. The stress components in the X and the Y directions determine the stress distribution of the FSW joints. The continuous performance joint model eliminates the stress and strain concentration caused by the area partition and more accurately simulates the fatigue performance of the joint by comparison with the partitioned performance joint model. The simulated fatigue weak area with the continuous performance joint model is more close to the fatigue experimental results. (3) The fatigue life prediction of the FSW joints is proceeded with SWT method based on the simulation results of the continuous and the partitioned performance joint models. The results show that the predicted lives with the continuous performance joint model are closer to the experimental results and the life prediction error is within the factor of two.

Author Contributions: G.S. designed and performed the experiments; G.S., J.N. and X.W. analyzed the experimental data and simulated the joint model; D.S. and S.C. gave some advices for the research; G.S. and X.W. wrote the paper. Funding: This research was founded by the National Natural Science Foundation of China (Grant No. 11672010, 51535001 and 51575012). Conﬂicts of Interest: The authors declare no conﬂicst of interest.

Abbreviations

FSW Friction stir welding WNZ Weld nugget zone TMAZ Thermo-mechanically affected zone HAZ Heat affect zone BM Base material HHAZ High-hardness heat affect zone LHAZ Low-hardness heat affect zone AS Advancing side RS Retreating side SWT Smith-Watson-Topper

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