Numerical Simulation Investigation on Split Sleeve Cold Expansion of Ti-Al Stacked Structure

GAO Yue,LU Shihong,FU Jingyi

(College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China)

Abstract: Split sleeve cold expansion (SSCX) can effectively enhance fatigue life of holes by improving the field of residual stress.Numerical simulations were conducted to investigate the parameter influence mechanism and obtain higher compressive residual stress (CRS).Expansion method,degree of cold expansion(DCE),friction coefficient between laminations and depth-diameter ratio were analyzed.For Ti-Al stacked joint holes,two expansion methods are proposed,namely aluminum alloy first followed titanium alloy (Al first)and titanium alloy first followed aluminum alloy (Ti first).The results show that expansion method and DCE have significant effects on the field of circumferential residual stress,and the friction has a negligible influence.A higher value of CRS and a wider layer of plastic deformation are induced with Ti first.Optimal DCE of Ti-Al stacked structure is 5.2%-5.6%.As the depth-diameter ratio is in the range of 0.5-1.25,a positive linear correlation between the maximum compressive residual stress (CRSmax) and depth-diameter ratio is shown.

Key words: Ti-Al stacked structure;SSCX;residual stress;expansion method;DCE

1 Introduction

Fatigue fracture is the main failure form of aircraft structures,and 50%-90% of the fatigue failure is caused by the destruction of joint holes[1].Therefore,the hole strengthening is of great significance for improving the service life of aircraft.Split sleeve cold expansion (SSCX) has advantages of no weight gain,no structure change,simple operation and excellent strengthening effect,which is widely used in the joint hole strengthening processing.SSCX is stretching a tapered mandrel slightly less than the hole diameter through the hole with a split sleeve to produce compressive residual stress (CRS),which can reduce the tensile stress under cyclic loading,thereby achieving enhancement of fatigue life[2].

Fatigue life of the joint hole structure after SSCX is mainly determined by the field of CRS around the hole.During the past decades,many studies reported that CRS of holes after cold expansion is affected by many factors,such as degree of cold expansion(DCE,which is defined as Eq.(1)),friction and expansion method.The distribution of residual stress field after cold expansion of 2024-T351 and 7050-T7451 have been obtained by finite element simulation[3].The effect of DCE on Al7475-T7351 was analyzed and the propagation life improvement factor was found to be more than 4 with DCE of 5.58%[4].Achard Vet al[5]developed simulations where the expansion was carried out twice in the same direction and in two opposite directions.Faghih Set al[6]found that when the optimal DCE is 5%,CRS at the exit of AZ31B sheet is the maximum,and the microstructure was analyzed at the same time.Cheol Ket al[7]used finite element method to analyze the influence of the expansion mode for adjacent holes and found that simultaneous expansion is much better than continuous expansion.Liu Y Set al[8]carried out cold expansion simulations on rectangular plate and cylindrical plate respectively,analyzed the influences of process parameters,and found that the crack first appeared at the entrance face.A new expansion method with more uniform and symmetrical residual stress distribution were proposed,and a generalized mathematical model of residual stress distribution were obtained[9].Liu Jet al[10]found that the distribution of residual stress around the hole is not uniform along thickness direction,and cracks always appear first near the entrance face,which verified that the residual stress at the entrance is small.The CRS of two adjacent holes after cold expansion and its effect on the fatigue life were studied by numerical simulations and experiments in Ref.[11].Hou Set al[12]carried out hole expansion experiments and fatigue tests on corroding samples with fastening holes of 7B04-T6,and found that fatigue life is increased by 3 times when DCE is 5.7%.Ayatollahi M Ret al[13]studied the influence of edge distance on the distribution of residual stress around the hole,and found that for edge distance ratio＜3,it has a considerable effect on residual stress.

whereDCEis degree of cold expansion,Dmis the diameter of the mandrel,Dis the initial diameter of the hole,andtsis the thickness of the split sleeve.

Researches of SSCX technology mostly confined to a single material.The stacked structure of titanium and aluminum alloys has advantages of two materials,such as high specific strength,specific stiffness,good fatigue resistance,and meet the demand of lightweight at the same time.Ti-Al stacked structure is widely used in aircraft structures,such as wings,skins and body partitions.Many researches on Ti-Al stacked hole making technology have been carried out,a comparative experiment of low-frequency vibration hole making was implemented to analyze the differences in chip morphology and processing quality[14].A series of experiments were carried out to study the drilling process of Ti-Al stacked structure[15,16].However,the strengthening process of Ti-Al stacked structure is rarely studied.In this paper,3D parametric models have been established through developing the finite element simulation software.The result shows accurate compared with the known data.The influences of expansion method,DCE,friction and depthdiameter ratio on the distribution of residual stress field after SSCX have been analyzed.

2 Numerical simulation

2.1 Material

TC4 titanium alloy and 2024-T351 aluminum alloy,commonly used in aircraft stacked structure,are employed for numerical simulations.The material of the split sleeve is AISI301,an austenitic stainless steel.The mechanical properties of materials are shown in Table 1.The nonlinear material behavior with isotropic hardening plasticity rule and Von Mises criterion were used for materials in finite element models.

Table 1 Mechanical properties of materials

2.2 Finite element model

Based on Dynamics/Explicit algorithm,3D finite element models were established to simulate the SSCX process of stacked and single structures respectively.The dimension of specimens in simulations is 40 mm×40 mm×4 mm,which is showed in Fig.1(a)(t=4 mm),and the diameter of central holes is 8 mm.The stacked structure with equal thickness (t) is only considered.The mandrel is assumed an analytical rigid body,and the other parts are deformable.C3D8R,three dimensional eight-node hex linear reduced integral elements,was adopted for meshing the plates and the split sleeve.To ensure the calculation accuracy,mesh near the hole edge was refined.The finite element model,paths and directions of SSCX are shown in Fig.1.

Fig.1 Finite element model

Contact analysis is a typical boundary non-linear analysis.Surface-to-surface contact algorithm was used at the contact surfaces between the hole and the split sleeve and between the stacked surfaces.No friction is assumed between the mandrel and the sleeve,due to the presence of lubrication.Friction coefficient between the sleeve and the hole is 0.2.Friction coefficient between laminations and DCE were studied.Considering actual situation of SSCX,the plates are fixed,thus all the freedom of the upper and lower sides of the plates were limited and the axial displacement of the split sleeve was restricted.The numerical simulation consists of two steps: the first is to establish the contact stably,and the second is to simulate the SSCX process by applying an axial displacement.

The finite element software provides the graphical user interface (GUI) to facilitate the secondary development for users.The original interface was extended to achieve parametric modeling,thereby improving the efficiency of numerical simulation analysis.

2.3 Model validation

Comparison with existed test results in literature is performed to validate the finite element model.Residual stress of single TC4 alloy plate after SSCX presented by the model is in agreement with published experimental and simulation data in Ref.[17],as shown in Fig.2(a).The model developed can obtain residual stress with an acceptable level.Fig.2(b) is the contour of residual stress field.Residual stress at the entrance face is significantly lower than the middle face and the exit face,which is consistent with the conclusion in Ref.[18].Fatigue life mainly depends on the value of CRS.Therefore,the distribution of residual stress field at the entrance face is only considered in the following discussion.

Fig.2 Results of numerical simulations

Fig.3 Residual stress under different expansion methods of 2024-T351

3 Results and discussion

3.1 Expansion method

For Ti-Al stacked structure,the expansion method can be divided into three types: aluminum alloy first followed titanium alloy (Al first),titanium alloy first followed aluminum alloy (Ti first),and expanded separately then assembled.The third method has a problem of difficulty in assembly caused by the deformation after expansion,thus only two methods are considered.The SSCX process of Ti-Al stacked structure with 5.6% DCE was simulated in two ways,and comparison was made with single layer under SSCX.The results of 2024-T351 and TC4 under different SSCX simulations carried out are presented in Figs.3 and 4 respectively.In circumferential direction (S11),CRSmaxof 2024-T351 is -497.5 MPa under expansion method of Ti first,which is 5.6% higher than Al first,and CRSmaxof TC4 is -1 053 MPa under expansion method of Ti first,which is 2.2% higher than Al first.In radial direction (S22),CRSmaxof 2024-T351(TC4) under Ti first is 0.5%(5.9%) higher than another method.From Figs.3(a)-(c),circumferential residual stress of 2024-T351 with Ti first has similar distributions and the maximum value with single layer of Al alloy (single Al),and the plate with Al first has lower CRS.Radial residual stresses of stacked structure are higher than single layer(Figs.3(d)-(f)).The similar circumferential residual stress distribution of TC4 can be seen in Fig.4,and expansion method of Ti first introduce higher CRS of TC4.The second expanded plate has a more uniform stress distribution than the first one along Path-1,which is due to the change of actual DCE caused by the axial flow of materials.

Fig.4 Residual stress under different expansion methods of TC4

Fig.5 Residual stress under different expansion methods

Expansion method has a significant influence on circumferential residual stress distribution near the hole edge from Figs.5(a) and 5(c).Residual stress is compressive at the hole edge,which first increases,then presents tensile stress and finally approaches to zero.For the 2024-T351 plate,the value of CRS is the highest under expansion method of Ti first,and the width of residual stress layer is 4.52 mm,larger than Al first and single layer.The TC4 plate has higher CRS and wider residual stress layer of 3.89 mm under Al first.The material of the hole edge flows axially with the movement of the mandrel,the actual DCE at the exit face is larger,and thus the absolute value of residual stress at the exit is greater than the entrance.The second plate has a relatively high value and uniform distribution of residual stress field after SSCX.According to Figs.5(b) and 5(d),the trend of radial residual stress distribution within 10 mm close to the hole is similar.The residual stress around the surface is tensile stress,and then presents compressive stress.The difference is generated at the position other than 10 mm from the hole.

The equivalent plastic strain (PEEQ) of samples strengthened by SSCX is shown in Fig.6.PEEQ of plates at the exit is larger than the entrance,and the width of the plastic strain layer at the exit is larger than entrance.The value of plastic strain is greater under Al first,but the zone of plastic deformation is larger under Ti first.The plastic deformation layer of 2024-T351 is wider than that of TC4.The elastic modulus and strength of Al alloy are small,and it is easy to yield and form a plastic deformation layer.When the same DCE is employed,TC4 is more difficult to produce plastic deformation,so the width of the plastic deformation layer is smaller.In summary,in the SSCX process of Ti-Al stacked structure,expansion method of Ti first should be selected whenever possible.Presumably,in the SSCX process of stacked structure with different materials,the expansion starts from the side with high material strength,which can ensure the value of residual stress on the plate where low strength is larger and the distribution is more uniform.

Fig.6 PEEQ under different expansion methods

3.2 DCE

DCE is an important parameter during the process of SSCX.Residual stress produced is poorer if DCE is smaller.An initial crack may exist at the edge of the hole with a large DCE,and the material accumulation is serious at the exit face,which will weaken the strengthen effect and reduce the fatigue life[19].Determining the optimal DCE is important to improve the fatigue strengthen effect.With expansion method of Ti first,friction coefficient of 0.2,andtof 4 mm,the simulation results along Path-2 of different DCEs are shown in Fig.7.A stress mutation layer can be seen on 2024-T351 in Fig.7(a),located at about 3.94 mm.Residual stress changes from compression to tension.CRSmaxincreases first and then decreases with the increase of DCE and the position of CRSmaxis transferring to the hole edge.When DCE increases to 5.6%,CRSmaxof Ti-Al stacked structure reaches the maximum,which is -466 and -873 MPa,respectively.As DCE continues to increase,CRSmaxis reduced instead.When DCE increases from 3.6% to 6.0%,the width of CRS layer increases from 3.94 to 4.52 mm for 2024-T351 and from 2.84 to 3.56 mm for TC4.The CRS layer of 2024-T351 is wider than TC4,which is due to the fact that the yield strength and hardness of Al alloy is lower.The tensile residual stress away from the hole also increases accordingly,because smaller force can cause larger plastic deformation for the yield material.An optimal DCE range is existed,which should be controlled from 5.2% to 5.6% when Ti-Al stacked structure is expanded.Under this condition,the value of CRS and the width of the residual stress layer are relatively large,which is beneficial to fatigue life of holes.

Fig.7 Circumferential residual stress with different DCEs

3.3 Friction coefficient between laminations

According to Ref.[20],friction coefficient between the sleeve and the mandrel has little influence on the residual stress.However,the effect of friction coefficient between laminations is unclear.The simulation of SSCX was performed with different friction coefficients.The results are shown in Fig.8.The distribution trends of circumferential residual stress under different friction coefficients are basically the same,and only the values of 2024-T351 at the hole edge are slightly different.Friction coefficient between laminations also has little effect on residual stress.

Fig.8 Circumferential residual stress with different friction coefficients

3.4 Depth-diameter ratio

Depth-diameter ratio (t/D) refers to the ratio of the depth to the diameter of the hole,and the depth of the hole is equal to the thickness of the plate.A large number of literatures have studied the process parameters,but the influence of depth-diameter ratio on residual stress has not been systematically studied.The effect of different depth-diameter ratios was studied by changing the thickness of plates.The case of single Al alloy plate is considered.

Fig.9(a) reveals the relationship between the field of residual stress and the ratio.The values of residual stress increase first,then decrease along Path-2,and finally approach to zero.Fig.9(b) shows the influence of ratios on CRSmaxwhenDis 8 mm.CRSmaxincreases with the increase of the depth when the ratio is less than 0.5,then reaches the maximum at the ratio of 0.5.In the range of 0.5-1.25,CRSmaxpresents an approximately positive linear correlation with the ratio.And more than 1.25,CRSmaxis similar to achieve stability.With the increase of the depth,the distribution gradient of residual stress along Path-1 is more obvious.The difference of residual stress between the entrance and the exit is larger,because the increase of the depth leads to more materials flowing and accumulating at the exit.Fig.9(c) shows the distribution of CRSmaxwith the ratio of 0.5-1.Three curves are almost parallel,with the correlation coefficient about 0.65σs.Fitting formulas for different initial hole diameters are obtained as Eq.(2).In engineering practice,optimal value of depthdiameter ratio is 0.5,which means the depth is close to the radius of the hole.

Fig.9 Influence of depth-diameter ratios on single plate

where CRSmaxis the maximum of circumferential residual stress,Dis the initial diameter of the hole,tis the depth of the hole.

4 Conclusions

In order to improve the efficiency and accuracy of the simulation,the SSCX process parametric modeling GUI program of Ti-Al stacked structure was developed.The results have been compared with the known data to verify the accuracy of the simulation.Then influences of SSCX process have been studied.Finally,the optimization results of the process parameters of Ti-Al stacked structure are obtained.The conclusions are as follows:

a) In the process of SSCX strengthening on Ti-Al stacked structure,the appropriate expansion method is more conducive to producing a higher value and more uniform field of CRS.The strengthening effect obtained by expansion method of Ti first is better,and CRSmaxof 2024-T351 and TC4 are increased 5.6% and 2.2% respectively than Al first.Based on the above results,when the stacked structure of different materials is expanded,the plate with high material strength should be selected to start the expansion.

b) For Ti-Al stacked structure,the value and width of residual stress increase first and then decrease with the increase of DCE.An optimal range of DCE is existed,which is 5.2%-5.6%.Friction coefficient has little influence on the residual stress.

c) CRSmaxis the highest when depth-diameter ratio is 0.5.CRSmaxis approximately positive linearly correlated with the ratio in the range of 0.5-1.25,and the correlation coefficient is about 0.65σs.Therefore,the depth-diameter ratio should be close to 0.5 as far as possible in the actual production.

Conflict of interest

All authors declare that there are no competing interests.