Modelling the fatigue crack growth in friction stir welded joint of 2024-T351 Al alloy

Modelling the fatigue crack growth in friction stir welded joint of 2024-T351Al alloyA.F.Golestaneh *,Aidy Ali,M.ZadehDepartment of Mechanical and Manufacturing Engineering,University Putra Malaysia,43400UPM Serdang,Selangor,Malaysiaa r t i c l e i n f o Article history:Received 31October 2008Accepted 7January 2009Available online 11January 2009Keywords:Failure analysis (H)Fatigue (E)Welding (D)a b s t r a c tIn this work the fatigue crack propagation within the friction stir welded (FSW)joint of 2024-T351Al alloy is studied as well as fatigue lifetime of the joint using Walker and Nicholls models.The FSW joint is characterised in terms of the residual stress (using the hole drilling technique),material,and cyclic properties.The material surface is polished in order to avoid any surface irregularities.The crack initia-tion is detected applying scanning electron microscopy (SEM),however plastic replication technique is used to monitor the crack propagation.The concepts of crack closure,residual stress and stress relaxation are incorporated into both models.Finally the results are validated and compared together regarding to the experiments.Ó2009Elsevier Ltd.All rights reserved.1.IntroductionFriction stir welding (FSW)is a type of solid state welding,in-vented in 1991by The Welding Institute (TWI)in Cambridge UK [1,2].This type of welding involves in joining structures with no fu-sion and filler substance.A threaded or non-threaded pin which is installed on a cylindrical tool,translates along the plane joint line (PJL)of two butted plates,rotating fast as shown in Fig.1.FSW joint macrostructure consists of five different zones called:(1)nugget zone (NZ),(2)flow arm zone (FAZ),(3)thermomechan-ically affected zone (TMAZ),(4)heat affected zone and (5)parent plate zone (PZ).Fig.2illustrates the various zones along the cross section of a joint.According to the previous studies,fatigue crack propagation through the FSW joints is intensely affected by (1)microstructure [2–6],(2)hardness [2–5,7],and (3)residual stress [1,5,7–9]where these characteristics depend on the joined material types and the welding process.Any changes in the parameters of the welding process,such as tool geometry,feeding speed,and tool material,cause different properties of the welded zones [10–15].The hard-ness is not uniform along the thickness of FSW joint and it changes through the thickness especially within the nugget zone.In fact material microstructure varies obviously from top surface to the bottom within the NZ which influences the hardness characteristic through the thickness [3,7,16–18].Hardness variation along the zones is not usually negligible.The series of 2xxx and 7xxx Al alloy show maximum hardness at the HAZ and the minimum value at the TMAZ [7,18–20].Previous research on the distribution of resid-ual stress along the FSW zones presents that residual stress is notuniform and varies from one zone to another as well as along the specimen thickness [1,7,8,21,22].Fatigue crack behavior of a T-joint under mixed-model loading was successfully simulated by Xiang et al.[23]based on Paris mod-el.They considered several various models in order to incorporate the mixed-mode condition into the Paris model and define the effective stress intensity factor.Yongshou et al.[24]has applied Paris model to the crack propagation along polyethylene methac-rylate and investigated the effect of temperature on the crack growth rate.The effect of various stress ranges on the fatigue crack growth rate within a nickel alloy was studied by Zheng et al.[25]based on Walker model for two different conditions:(1)constant applied load range (D P )and (2)constant stress intensity factor (SIF).In other work Al-Rubaie et al.[26]applied two types of fati-gue growth models to predict the fatigue of 7475-T7351Al alloy under constant amplitude and stress range of R =0.5.The results showed better prediction using Priddle model compared with Col-lipriest.However modified Forman model presented the best agreement with experiments.Forman–Newman–de Koning model in the work space of FRANC3D was used by Barlow et al.[27]in or-der to simulate the crack propagation along the attachment of mil-itary aircraft engine blade in three dimensions.A mixed-mode fracture condition was considered due to complicated geometry of blade attachment and loading condition.Previous research on fatigue crack growth has focused on crack behavior within one material,with homogeneous properties.How-ever in this study the fatigue crack behavior within the FSW joint of 2024-T351Al alloy was investigated through different welding zones using two types of crack growth models:(1)Walker and (2)Nicholls models.Fatigue lifetime of the FSW joint was deter-mined based on both models and compared with experiments for validation.0261-3069/$-see front matter Ó2009Elsevier Ltd.All rights reserved.doi:10.1016/j.matdes.2009.01.006*Corresponding author.Tel.:+60122749592;fax:+60386567122.E-mail address:gs16938@.my (A.F.Golestaneh).Materials and Design 30(2009)2928–2937Contents lists available at ScienceDirectMaterials and Designj o u r n a l h o m e p a g e :w w w.e l s e vier.c om/loc ate/matdes2.Experiment2.1.Macrostructure and specimenThe experimental tests were performed on the FSW plates with the size of 80Â60Â13mm,provided by Airbus UK Ltd.The plates were welded along the long edge in longitudinal direction and mechanically polished to a 1/4l m for optical observation pur-poses.Finally it was lightly etched in Keller’s reagent in accordance with ASTM E340-00in order to avoid any surface irregularities,which hides the small surface cracks from detection.The specimen was subjected to the four-point bending test using an Instron dig-itally controlled test machine of 100KN capacity as shown in Fig.3.Loading was under constant amplitude with the frequency of 20Hz and load ratio of R =0.1.The fatigue endurance tests were carried out on the specimens in accordance with ASTM D6272(1998).Fig.4represents the extension of different FSW zones away from PJL and through the thickness on a cross section of a as a symmetrical circular area located at the center of the weld,extended to 5–6mm away from PJL,when FAZ,between the NZ and the welded surface spread to 9mm.The size of TMAZ was wide up to 4mm,on the top welding surface however it narrowedNomenclature a half of the internal crack length a c critical crack lengtha H crack length at the HAZ–PZ boundary a i initial crack lengtha Tcrack length at the TMAZ–HAZ boundary da dNcrack growth rateC coefficient of Paris modelC H coefficient of Paris model at HAZ C o coefficient of Walker modelC oH coefficient of Walker model at HAZ C oP coefficient of Walker model at PZ C oT coefficient of Walker model at TMAZ C P coefficient of Paris model at PZ C T coefficient of Paris model at TMAZCT compact tension specimenE modulus of elasticity (Young modulus)FAZ flow arm zoneFSW friction stir weldingH strain hardening coefficient HAZ heat affected zone HCF high cycle fatigue K c fracture toughnessK c ,H fracture toughness of HAZ K c ,P fracture toughness of PZ K c ,T fracture toughness of TMAZ LCF low cycle fatigueLEFM linear elastic fracture mechanics m exponent of Paris model m 1exponent of Walker modelm 1H exponent of Walker model at HAZ m 1Pexponent of Walker model at PZm 1T exponent of Walker model at TMAZ m H exponent of Paris model at HAZ m P exponent of Paris model at PZ m Texponent of Paris model at TMAZ Max r rex maximum stress after relaxation Min r rex minimum stress after relaxation n strain hardening exponent N f fatigue lifeN p number of propagation cycles NZ nugget zone PZ parent zone Rstress ratioTMAZ thermomechanically affected zone D K stress intensity factor rangeD K effective stress intensity factor range D r stress rangeD r effeffective stress range c Walker constantc H Walker constant at HAZ c P Walker constant at PZ c T Walker constant at TMAZ r maxmaximum applied stressr max+res maximum stress after incorporating residual stress r minminimum applied stressr min+res minimum stress after incorporating residual stress r op crack-opening stress r res residual stress r Y yield strengthr Y,H yield strength of HAZ r Y,P yield strength of PZ r Y,Tyield strength of TMAZFig.1.Schematic illustration of FSW butt joint.Fig.2.Various zones along the cross section of FSW joint.A.F.Golestaneh et al./Materials and Design 30(2009)2928–29372929and vanished through out the thickness of10.5mm from the plate surface.HAZ widened through the thickness from the5mm on the top surface to the14mm at the bottom.The coordinate of the mac-rostructural boundaries was mapped by using optical PolyVarMet microscopy as shown in Fig.4.2.2.Hardness and residual stressHardness measurement was carried out according to the stan-dard test method for Vickers hardness test ASTM E92-82(1989). Hardness was measured on top and bottom of the specimen and at the different distances from the PJL with various microstructural types.Fig.5a shows six different positions to measure the hardness where the profiles1and2were located in the NZ,profile3was in the FAZ,TMAZ and HAZ,profiles4and5were in HAZ and profile6 was in the PZ.In order to investigate the hardness variation through the specimen depth,microhardness test was performed by a digitally controlled hardness test machine applying1.0kg force for15s.Fig.5b illustrates the measured hardness variation along the FSW zones at top and bottom surfaces.Residual stress was measured using hole drilling technique,in accordance to the ASTM E837-99(2000).A1.6mm nominal diam-eter holes were drilled at several locations in welding zones,on both sides of the specimen(see Fig.6a).Three equiangular strain rosettes(CEA-06-062UL-120)were positioned at the drilled holes to measure the principle strains.Finally the principle residual stresses and consequently the longitudinal and latitudinal residual stresses were calculated using the obtained strains.Fig.6b shows the residual stress distribution along the FSW zones at the top and bottom surfaces of the specimen.2.3.Crack initiation and propagationScanning electron microscopy(SEM)analysis was used on the fracture surface of the failed specimens from different stress ranges in order to analyze the defect level,initiation site and to mark any possible crack coalescence and failure mechanism in FSW speci-mens.The results showed the high influence of applied loading on the crack initiation site and size,where a higher applied stress will increase the length of the initiated crack and change the crack site further along the PJL.Quantitative microanalysis of initiation areas on the surface was carried out using the Energy Dispersive X-ray analysis(EDX)method.Fig.7shows the crack initiation sites observed by SEM for high cycle fatigue(HCF)of161MPa maxi-mum applied stress and low cycle fatigue(LCF)of300MPa.The positions of the initiation sites,for both161MPa applied stress 300MPa,have been plotted on the hardness–distance diagram in Fig.5b.As it is observed there is a good consistency between crack initiation sites and hardness distribution in the FSW joint for both loadings where the crack initiations were observed at the positions with low hardness characteristic.Fig.6b represents the correlation between residual stress distribution and the position of the fatigue initiation sites observed by SEM in Fig.7.The residual stress distri-bution and initiation sites are consistent where the initiations oc-cur at the points with high residual stress(points A,B and E in Fig.6b).However the residual stress distribution does not show a strong correlation with the initiation sites where the defects exist (points C and D in Fig.6b).In the present work the crack propaga-tion was monitored using surface replication technique as repre-sented in Fig.8.3.Specimen geometry and materials propertiesIn four-point bending test the moment is uniformly distributed between two top spans(see Fig.3)where bending stress distribu-tion is a linear gradient through the thickness with the maximum magnitude on the surface.Therefore the maximum crack growth rate occurs on the surface.In the current modelling a rectangular plate with a size of60Â20mm was considered to model the sur-face of the specimen between two spans.Fig.9shows the FSW zones modelled along the geometry in accordance with the size of zones measured in experiment(Fig.4).4.LoadingAccording to the previous studies[2,5,6,27]on intense influence of residual stress on crack propagation,here different values of residual stress was considered for each welding zone regarding to Fig.6b.Note that residual stress through the PZ is negligible due to this region does not experience any mechanical and heattreatment.Fig.3.FSW specimen under bending fatiguetest.Fig.4.The transverse cross section in an FSW2024-T351Al Alloy joint mapping the boundaries of the macro structural zones. 2930 A.F.Golestaneh et al./Materials and Design30(2009)2928–2937Elber [28,29]showed,the existence of residual stress within the plastic wake along the crack faces keeps the crack faces close for the significant portion of the cycles.Based on the strong effect of crack closure on the stress intensity factor range [30–32],here the effective stress range (D r eff )was calculated,accounting for the residual stress and crack closure:D r eff ¼r max þr res Àr opifr min þr res r op ;ð1ÞotherwiseD r eff ¼ðr max Àr min Þ;ð2Þwhere r max is the maximum applied stress,r min is the minimum ap-plied stress,r res denotes residual stress,and r op represents opening stress value.It is worth noting that whenever the applied stress ex-ceeds the material yield strength,some amount of residual stress is released as the result of plastic deformation.For the loading condi-tion of 270MPa maximum stress and R =0.1,the maximum and minimum stresses after incorporating the residual stress (r max+res ,r min+res )were:r max þres ¼r max þr res ¼270þ96¼366MPa ;r min þres ¼r max R þr res ¼27þ96¼123MPa :ð3ÞDue to the maximum stress exceeded the yield strength of TMAZ (272MPa),the residual stress relaxation was incorporated as follows:366¼Max r rex þðMax r rex Þn )366¼Max r rex 68;000þðMax r rex 800Þ0:1266)Max r rex ¼318MPa ;ð4Þwhere E is the modulus of elasticity,H and n are the strain harden-ing coefficient and exponent presented in Table 1respectively,Max r rex is the maximum stress after incorporating the residual stress relaxation.Therefore the new value of minimum stress can be calculated as Min r rex ¼r min þres Àð366À318Þ¼75MPa.Accord-ing to Eq.(1)and r op ¼110MPa,the effective stress range is D r eff ¼Max r rex Àr op ¼208MPa.5.Crack initiationThe initial crack detection in Fig.7determined a crack initiation site at the TMAZ for HCF.However the initiation site was observed at the end of TMAZ,adjacent to the HAZ for LCF.Therefore in the current work crack growth was modelled for initial crack within TMAZ with the lowest hardness and highest residual stress.The smallest initial crack size identified by the replication work,for the stress condition of 270MPa maximum stress,was about 0.112mm where this value escalated to 0.62mm for the 300MPa maximum stress.Therefore the initial crack with the length of 0.2mm was considered for HCF (loading conditions be-low 300MPa maximum stress)to predict the fatigue life.The length of initial crack increased to 1mm for LCF (loadings beyond 300MPa maximumstress).Fig.5.(a)The hardness measurement at six positions and (b)the hardness variation along the FSW zones of 2024-T351Al Alloy joint.A.F.Golestaneh et al./Materials and Design 30(2009)2928–293729316.Crack growth models 6.1.Walker modelAlthough Walker [33]established his model based on Paris equation [2,16,23],this model was developed so that the coeffi-cient and exponent of the equation do not depend on load ratio and are only influenced by material characteristics.Walker modelexpresses a linear relationship between the crack growth rate (da )and effective stress intensity factor range (D K )in a logarithmic scale.This model predicts the growth rate during the stable prop-agation through the region II as follows:dadN¼C o ðD K Þm 1;ð5Þwhere C o is the Walker coefficient,m 1denotes the Walker exponent and D K is defined by stress intensity factor range (D K ),load ratioand Walker constant (c )as:D ¼D Kð1ÀR Þ1Àc.c is a constant in the range of 0.4–0.9.Therefore Walker model can be rearranged as:da dN ¼C oð1ÀR Þm 1ð1Àc ÞðD K Þm 1;ð6Þwhich is the same with Paris model if C oð1ÀR Þm 1ð1Àc Þis replaced with Paris coefficient (C ).The number of cycles (N p )for a crack propagation from an initial length of a i to the arbitrary length of a can be determined by inte-grating the Eq.(6)with respect to the crack size as presented in Eq.(7).It is worth noting that the fatigue life N f is estimated by substi-tuting the critical crack length a c for the upper limit of the integral in Eq.(7)ZN pdN ¼ð1ÀR Þm 1ð1Àc ÞC oZaa ida½D K ða Þ m 1:ð7ÞHowever for the case of FSW joint consisting of various zones,Eq.(7)was presented as some sub-integrals in order to cover the crack propagation through each zone.In the present work with an initial crack detected within the TMAZ,fatigue life can be calcu-lated by Eq.(8)Fig.6.(a)The residual stress measurement at several positions and (b)the residual stress variation along the FSW zones of 2024-T351Al Alloy joint.2932 A.F.Golestaneh et al./Materials and Design 30(2009)2928–2937ZN fdN ¼ð1ÀR Þm 1T ð1Àc T ÞC oTZa Ta ida ½D K ða Þ m 1T þð1ÀR Þm 1H ð1Àc H ÞC oH ÂZa Ha Tda ½D K ða Þ m 1H þð1ÀR Þm 1P ð1Àc P ÞC oP Za c a H da ½D K ða Þm 1P ;ð8Þwhere subscripts T,H and P represent the values of C o ,m 1and c for TMAZ,HAZ and PZ,respectively.a T and a H denote the crack lengths at the end of TMAZ (TMAZ–HAZ boundary)and at the end of HAZ (HAZ–PZ boundary).6.2.Nicholls modelNicholls law presents another model for stable crack propaga-tion,which defines that the propagation rate depends on D K andmaterial properties as below:da dN ¼14E Y K cD K 4;ð9Þwhere r Y is material yield strength and K c denotes the fracture toughness presented in Table 1.Integration of Nicholls modelalongFig.7.SEM fractograph images of crack initiation in a FSW joint of 2024-T351Al alloy for (a)161MPa maximum applied stress and (b)300MPa.A.F.Golestaneh et al./Materials and Design 30(2009)2928–29372933FSW zones yields the number of cycles during the crack propaga-tion.Fatigue life can be calculated by Nicholls model as follows:ZN pdN ¼4ErY ;T K 2c ;TZa Ta idaD K 4ða Þþr Y ;H K 2c ;HZa Ha TdaD K 4ða Þ"þrY ;P K 2c ;PZa ca HdaD K ða Þ#:ð10Þ7.Adaptation of the Walker and Nicholls modelsIn order to adapt the Walker and Nicholls models the mecha-nism of the fatigue crack propagation within the FSW joint was analyzed.The sizes of the initial cracks detected by replication work were higher than 0.1mm for HCF and higher than 0.5mm for LCF,therefore in the current work the initial cracks were con-sidered as the long cracks compared to the short cracks in stage I with the size order of 20l m.In other words in these tests the cracks grew from defects in stage II where the propagation could be modelled using Walker and Nicholls equations.Note that although the applied equations in the present modelling do not cover the fast propagation phe-nomenon through the stage III,the obtained fatigue lifetimes pro-vided good accuracies.In fact crack growth rate is high along the stage III where the crack propagation does not affect the predicted fatiguelife.Fig.8.Replica images of the FSW of 2024-T351Al alloy for (a)270MPa applied stress and (b)300MPa.Fig.9.The specimen geometry subjected to the distributing loading.Table 1Material properties of FSW zones in 2024-T351Al Alloy.FSW regimesNZ TMAZ HAZ PZ ExperimentalYield stress (MPa)350272448370Modulus of elasticity (GPa)68686868Hardening coefficient (H)–800719770Hardening exponent (n )–0.12660.05540.0860Fracture toughness (MPa ffiffiffiffiffim p )544961322934 A.F.Golestaneh et al./Materials and Design 30(2009)2928–2937The Walker and Nicholls equations are empirical models which are based on experimental data.The parameters in Nicholls model (r Y ,K c ,and E )were measured directly through the experiments on material characteristics as presented in Table.In order to deter-mine the crack behavior by Walker model,the parameters of this equation (C o ,m 1,and c )were calculated fitting a curve through the test data.7.1.Determining m 1The Walker exponent can be considered as the average of the Paris exponent (m )for several load ratios as well as the same value with Paris exponent.In the present modelling the Walker expo-nents for FSW zones were determined the same with Paris expo-nents as presented in Table 2.7.2.Determining C o ,and cConsidering the m ¼m 1and taking the logarithms of Eq.(6)yield:log ðda =dN ÞÀm log ðD K Þ¼log C o Àm ð1Àc Þlog ð1ÀR Þ:ð11ÞSince the left side of Eq.(11)is equal to the Paris coefficient it can be rearranged as log C ¼log C o Àm ð1Àc Þlog ð1ÀR Þ.Therefore C o ,and c can be determined by regressing three or more numbers of C and (1ÀR )while they are plotted in the logarithmic scale.In fact C o is the Paris exponent for R =0and c can be extracted easily from the slope of the plotted line as shown in Fig.10.Table 2represents Walker coefficients and exponents for differ-ent FSW zones where Paris constants have been mentioned for comparison purpose.8.Results and discussionFig.11shows the fatigue crack propagation within the different zones of FSW joint predicted by Walker and Nicholls models in addition to the experimental results.As it is observed the crack propagation process accelerates along the welding zones and the slope of the curve decreases.The crack behavior is intensely af-fected by the variation of hardness and residual stress along the zones.Increase in hardness from the TMAZ (118Hv1)to the high-est value of 167(Hv1)at the next zone (HAZ)supports higher crack growth rate (decrease in the slope of the curve)from TMAZ to HAZ.However due to the decrease in hardness after HAZ,the hardness characteristic contrasts with the observed increase in the crack propagation rate along PZ.The increase in crack growth rate within the PZ compared with the HAZ is attributed to the lower residual stress (negative residual stress)within the HAZ.During crack prop-agation phenomenon the crack length increases which causes higher crack growth rate according to Eqs.(6),(9),and (11):D K /D r ffiffiffiffiffiffip a p ;ð12Þwhere D r is stress range.Therefore,hardness variation and the crack growth phenomenon both have the positive impact on the in-crease in crack growth rate,within the HAZ compared with the TMAZ.Although hardness has a negative effect on the increase ofcrack growth rate along PZ,residual stress and crack growth phe-nomenon support higher growth rate through PZ compared with the HAZ.It is interesting that Walker predictions show more agree-ment with the experiment compared to the Nicholls results,how-ever both of the models calculate the crack growth rate less than the experiment.The number of cycles at the end of each FSW zone was pre-sented for various loading conditions,based on Walker and Nicho-lls models,in Table 3.Final numbers of cycles before fatigue failure (fatigue lifetime),extracted from Table 3,were plotted in the form of S–N curves in Fig.12for Walker and Nicholls models.The exper-imental lifetimes obtained from fatigue crack tests were illustrated in the same figure for validation purpose.Fig.12represents higher agreement of Walker model with experiments compared with Nicholls model especially for the high cycle fatigue.In fact the pre-diction of fatigue crack behavior in Walker model is under theinfluence of coefficient C oð1ÀR Þm 1ð1Àc Þand exponent ðm 1Þ.These fac-tors are both affected by material characteristics like microstruc-Table 2Walker and Paris constants for FSW zones of 2024-T351Al alloy.FSW zones Paris C ðCycle ÞÀ1Walker C o ðCycle ÞÀ1Paris–Walker m ¼m 1Walker cNZ 2.8338Â10À122.53Â10À123.800.72TMAZ 5:5837Â10À124.86Â10À12 2.760.52HAZ 1:1778Â10À12 1.03Â10À12 2.790.53PZ2:8500Â10À122.49Â10À122.940.56Fig.10.Schematic representation of Walker model in logarithmicscale.Fig.11.Fatigue crack propagation within FSW zones under 270MPa applied stress.A.F.Golestaneh et al./Materials and Design 30(2009)2928–29372935ture,hardness and residual stress and vary from one welding zone to another.On the other hand Nicholls model is only a function ofone coefficient 14E r Y K 2cwhere the exponent of D K is identical for allthe zones.Therefore Walker equation shows more reliable model for the case of crack propagation in FSW joints than Nicholls equa-tion.However by increasing the applied loading,Nicholls model represented higher agreement with those two other models and experiments,where for the LCF conditions all three models yielded the same results close to experiments.9.Conclusions1.Fatigue crack propagation through FSW joint consisting of four different zones with various characteristics was modelled using Walker and Nicholls fatigue models incorporating the effects of residual stress,stress relaxation,and crack closure.The results showed good agreement with experiments.However Walker model presented more accuracy on crack growth prediction compared with the Nicholls model.2.Fatigue lifetimes of the FSW joint of 2024-T351Al alloy were predicted based on two models and presented in the form of a S–N curve which showed a good consistent with test results.3.Although both of the models presented acceptable predictions,Walker equation yielded higher accuracy compared to the Nich-olls equation,especially for the HCF.However Nicholls model showed higher agreement for higher values of applied loadings in LCF conditions.AcknowledgementThe authors would like to appreciate University Putra Malay-sia (UPM)for awarding fellowships to two of the authors (A.F.Golestaneh and M.Zadeh Mohammadi)and for supporting this research.References[1]Fratinia L,Zuccarellob B.An analysis of through-thickness residual stresses inaluminium FSW butt joints.Int J Mach Tool Manufac 2006;46:611–9.[2]Scialpi A,de Filippis LAC,Cavaliere P.Influence of shoulder geometry onmicrostructure and mechanical properties of friction stir welded 6082aluminium alloy.Mater Design 2007;28:1124–9.[3]Ali A,Brown MW,Rodopoulos CA,Gardiner S.Characterization of 2024-T351friction stir welding joints.J Fail Anal Prev 2006;6:41–53.[4]Cavaliere P,Nobilea R,Panellaa FW,Squillaceb A.Mechanical andmicrostructural behaviour of 2024-7075aluminium alloy sheets joined by friction stir welding.Int J Mach Tool Manufac 2006;46:588–94.[5]Ceschini L,Boromei I,Minak G,Morri A,Tarterini F.Effect of friction stirwelding on microstructure,tensile and fatigue properties of the AA7005/10vol.%Al2O3p 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A,Tarterini F.Microstructure,tensile andfatigue properties of AA6061/20vol.%Al2O3p friction stir welded posites:Part A 2007;38:1200–10.[18]Jata KV,Sankaran KK,Ruschau JJ.Friction stir welding effects onmicrostructure and fatigue of aluminium alloy 7050-T7451.MMTA 2000;31:2181–92.[19]Booth D,Sinclair I.Fatigue of friction stir welded 2024-T351aluminium alloy.Mater Sci Forum 2002:1671–6.Table 3Number of cycles at the end of each FSW zone for various stress conditions predicted by Walker and Nicholls models.Max stress (MPa)At TMAZ–HAZ boundary (Cycles)At HAZ–PZ boundary (Cycles)Last propagation step (Cycles)WalkerNicholls Walker Nicholls Walker Nicholls 2701750,00188,000365,000388,000370,000388,0002741550,00175,000300,000315,000304,000316,0002851190,00155,000249,000269,000253,000271,00029592,000140,000212,000227,000216,000228,00030580,000110,000186,000205,000189,000207,00031067,00085,000161,000167,000162,500168,50033057,00073,000116,500129,500124,000131,00035346,00056,00094,000111,00096,000112,00037537,50038,00086,00088,00087,50088,50040031,50033,50066,50069,50068,50071,00044427,00027,50055,00055,50056,00061,00046024,00026,50052,00052,00053,00054,100Fig.12.Fatigue life predictions of FSW joint in 2024-T351Al alloy by Walker and Nicholls models.2936 A.F.Golestaneh et al./Materials and Design 30(2009)2928–2937。