Combined and interactive effects of interference fit and preloads on composite joints

To appear in:

Accepted Manuscript

Liu Longquan, Zhang Junqi, Chen Kunkun, Wang Hai

PII: DOI:

Reference:

S1000-9361(14)00084-3 http://dx.doi.org/10.1016/j.cja.2014.04.014 CJA 287

Received Date: 6 June 2013

Revised Date: 6 August 2013

Accepted Date: 7 October 2013

Please cite this article as: L. Longquan, Z. Junqi, C. Kunkun, W. Hai, Combined and interactive effects of interference fit and preloads on composite joints, (2014), doi: http://dx.doi.org/10.1016/j.cja.2014.04.014

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Combined and interactive effects of interference fit and preloads on

composite joints

Liu Longquan*, Zhang Junqi, Chen Kunkun, Wang Hai

School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China

and the preloads of the fasteners on the load carrying

Received 6 June 2013; revised in revised form 20 August 2013; accepted 7 October 2013

Abstract

The combined and interactive effects of the bolt-hole fit conditions capacity of single-lap composite-to-titanium bolted joints have been investigated both experimentally and numerically. Quasi-static tests of the hybrid joints with different fit conditions are implemented, and a three dimensional finite element progressive failure analysis model is proposed to predict the influences of the bolt-hole fit conditions and fastener's preloads on the mechanical behaviors of the joints. Based on the experimental validated simulation method, a multi-factor, mixed levels orthogonal design table and the analysis of variance method are used to arrange the simulation conditions and to further study the interactive effects of preloads and fit conditions. Through the analysis of the results, for the researched double bolt, single-lap composite-titanium joints, it is found that: the effects of both the interference fit and the preloads change from positive into negative mode with the increase of the interference fit values or preload values; appropriate bolt-hole fit conditions and preloads can improve the bolt-hole contact conditions of the loaded joints, and then retard the fiber failures around the fastener holes, and increase the load carrying capacity of the joints eventually; the interactive effect of the bolt-hole interference fit conditions and preloads cannot be ignored and the parameters need to be considered together and synthetically as the joints are being optimized.

Keywords: Interactive effect; Composite; Bolted joints; Interference fit; Preloads

* Corresponding author. Tel.:+86 21 34205479. E-mail address: liulongquan76@sjtu.edu.cn

1. Introduction1

Composite materials are increasingly utilized in aviation structures due to their comparatively high specific strength and stiffness and the potentiality of reducing energy consumption.1'2 Although the application of composite materials increases the integrity of aircraft structures' many composite components still need be joined to other components through bonding, mechanical fastening or hybrid of them. Among these methods' bolted joint is the most favorite one because it is relatively more reliable to transfer higher loads, easier to assemble and disassemble, more tolerant to environmental damages, and helpful in preventing interlamination3-5. However, the enhanced stress concentration around the fastener hole often decreases the load carrying capacity of the composite structures6. Comparing with the metallic structures, joining technology in the composite laminate structures is a significant issue with 60-85 percent of failures occurring at the fastening joint7. In order to increase the load carrying capacity of the composite mechanical joints, a large quantity of parametric studies have already been performed, and it can be concluded that the joint strength is influenced not only by joint geometries, joint configurations, material parameters and loading condition, but also by the assembly factors such as the preloads of the bolts and the fit conditions between the fastener shank and the hole8, 9.

In the past, the fit conditions between the fasteners and plates are normally clearance fit, with 0.1 mm typical clearance in aircraft joints8. However, the formerly McDonnel Douglas Corp has stated that interference-fit joining can improve the fatigue life of carbon epoxy composites 7 10. Other researchers have also concluded that the interference-fit joining will not only influence the load sharing between the multiple fasteners 11, but also improve the static strength and fatigue strength of bolted joints 12-14. Whereas, excessive interference fit between the fastener shank and hole will produce interlaminar shearing stress and cause delamination around the hole boundary, and then decrease the joint strength 15 16. Therefore, an appropriate interference fit value is needed for specific composite joint structures.

Tightening torque will bring clamping force and lateral constraint to the area covered by the fastener head or nut, and the beneficial effect of clamping forces/preload on the bearing strength of composite has been studied extensively. Sen et al. 6, Khashaba et al. 8, Cooper et al.17 and Rosales-Iriarte et al. 18 all have performed experimental researches on the influences of the tightening torque on the mechanical

behaviors of composite joints. Fu-Kuo Chang et al.19 have numerically investigated the lateral constraining effect on bolted composite joints using ABAQUS software. In these studies, all of the researchers have found the bearing strength of bolted joint improves with the increase of tightening torque in a range for the specified joint configurations. However, it is well known that laminate composite structures have poor properties in the through-the-thickness (TTT) direction and are susceptible to damage and failure because the properties in the TTT direction is comparatively matrix-dominated. Thus, the composite components may fail in advance if the clamping force of the bolts is too big 6. NASA Marshall Space Flight Center has developed an in-house standard, MSFC-STD-486B, to specify tightening torque values of the threaded fastener joint, and it is recommended that the bolt preload should be less than 30 percent of the fastener yield strength for typical preloaded composite structural assemblies in tension 20. Thomas and Zhao 21 have tested the single plain composite plate made of graphite/epoxy with different thicknesses and bolt diameters and found that preload limits as specified by MSFC-STD-486B are acceptable. Nevertheless, the preload values above are directly related to the tension property of the fastener and consider neither the difference among the properties of different composite structural members in the TTT direction, nor the secondary bending effect in single-lap joints which will also introduce out-of-plane stress in the region surrounding the fastener hole. Therefore, the preload may also lead to both positive and negative effects. The positive effect is that, as the preload is increased, the friction forces between the joint members become higher and the lateral constraint introduced by the tightening torque will suppress the local delamination to be onset and progress to some extent, and then the load carrying capacity will grow. On the other hand, the negative mode effect is that too high out-of-plane stresses introduced by the preload can lead to a premature failure of the joint22, 23. Therefore, an appropriate preload value is needed for specific composite joint structures.

From all the above-mentioned descriptions and analyses, it can be seen that both the bolt-hole fit conditions and preloads of the fasteners affect the joint behaviors through changing the stress state surrounding the fastener hole, and the effects of both the fit condition and the preload have been investigated a lot separately in the past studies. Nevertheless, the optimized values of them have not been founded in these researches. Moreover, unlike laboratory studies, the practical joint strength is affected by lot of different parameters simultaneously. That is to say the effects of both the fit conditions and

preloads may impact each other, and the optimized preload of the composite joint with a certain bolt-hole fit condition may no longer the best for the similar joints with other fit conditions, and vice versa. However, the interaction of them has received little attention up to now. Consequently, the main objective of the present work is to investigate the combined and interactive effects of bolt-hole interference fit conditions and preloads of the fasteners on the load carrying capacities of the single-lap composite joints, and to optimize the parameter of the joints. Experimental test method, three-dimensional finite element method and analysis of variance (ANOVA) method will be synthetically applied in the following study.

2. Problem statements

Two typical composite-to-titanium, two-bolt, single-lap joints with the same configurations other than the bolt-hole fit conditions will be used in this study, and the geometry and dimensions of the joints are shown in Fig.1, in which the locations and dimensions tolerances conform to the general tolerance requirements for composite products HB 7741-2004. Both the composite plate and titanium plate are 210 mm long, with 60 mm griping length. The thicknesses of the composite plate and titanium plate are 3.8 mm and 2 mm respectively. The two plates are joined together by two HST10AP6 hi-lite fasteners, and the diameter of the fastener shank is 4.8 mm with tolerance being ±0.013 mm. The diameters of the fastener holes of the two different joints are 4.8+001 mm and 4.8r00104 mm, respectively. Thus, the fit conditions between the fastener shanks and holes of the two different kinds of joints can be seen neat fit and 1.5% interference fit, respectively.

Fig.1 Specimen geometry dimensions

The materials of the titanium plate and the two HST10AP6 hi-lite fasteners are both Ti6Al4V titanium alloy manufactured per AMS 4967. Its elastic modulus is 110000 GPa and Poisson ratio is 0.34. The material of the composite plate is a hybrid material manufactured from unidirectional tape lamina (CYCOM 977-2-35%-12KHTS-134-300 of Cytec Industries Inc.) and twill woven carbon fabric composite (CYCOM 977-2A-37%-3KHTA-5HS-280-1200 of Cytec Industries Inc.) with stacking sequence being [(±45)/0/±18/±36/+54/(0/90)/-54/±72/90]s. In the stacking sequence, the angle value, such as +54, represents the unidirectional tape lamina with its fiber direction shifting 54o from the 0o direction shown in Fig.1, and (angle value), such as (±45), represents the woven fabric with its warp direction shifting 45o from the 0o direction shown in Fig.1. The material system of the laminate coincides with the geometry coordinate system of the specimen, which means the 1, 2 and 3 directions of the

unidirectional tape lamina with 0 degree and the L, T and Z directions of the woven fabric with 0 degree are coincident with the x, y, and z directions of the coordinate system shown in Fig.1, respectively. The

1, 2 and 3 directions are the longitudinal, transverse and thickness directions of the unidirectional tape lamina, and L, T and Z directions are the warp, weft and thickness directions of the woven fabric lamina. The thicknesses of the unidirectional tape lamina and woven fabric are 0.131 mm and 0.295 mm, respectively, and the mechanical properties of the two different laminas are shown in Table 1 and Table

2, respectively. Since the thickness properties of the composite are very difficult to obtain, it is customarily assumed that the matrix properties apply in the thickness direction 24. Therefore it can be said E22=E33, G12=G13, and v12=v13 apply for the unidirectional lamina. In Table 1 and 2, the superscripts T and C denote tension and compression respectively.

Table 1 Mechanical properties of the unidirectional tape lamina

Elastic

property

En(GPa) £22(GPa) EaaCGPa) Gn(GPa) G^(GPa) G2a(GPa)

131.85

Strength property

S T S C

(MPa) (MPa)

°33 12

(MPa) (MPa)

a) (MPa) (M .5 45.3

Table 2 Mechanical properties of the woven fabric lamina

Elastic EL(GPa) ET(GPa) EZ(GPa) GTGPa) GrZ(GPa) GLZ(GPa) ult ulz utz

property f

Value 66.16 61.04 20.24 6.54 8.76 ^ 8.76 0.04 0.3 0.3

Strength property ST (MPa) SC (MPa) S t (MPa) StC (MPa) sT (MPa) SC (MPa) SLT ( MPa ) STZ ( MPa ) Slz (MPa )

Value 895.5 922.6 872.6 885.7 80.7 480.1 119 80.7 80.7

3. Finite element simulation

3.1. Three-dimensional finite element meshes

The three-dimensional numerical model of the specimens described in Fig.1 is constructed using the commercial finite element code, ABAQUS/standard 25, which is shown in Fig.2. Both the composite and titanium plates are modeled to be 150 mm long since the effective lengths of the plates are 150 mm. Because of the symmetry features of the structure, ply sequence, and boundary conditions with respect to XZ plane shown in Fig.1, and considering that the composite plate is comparatively thick, half of the joint is modeled to shorten the computing time, therefore, the two plates are both modeled as 15 mm wide. Furthermore, since the nut and fastener shank are engaged together, they are modeled as one part to decrease the contact surfaces which ensue the shorting of processing time.

To avoid the shear locking problem, to simulate the bending deformation introduced by the secondary

bending effect more accurately, and to decrease the computing time, the enhanced hourglass control and reduced integration linear eight-node brick elements, C3D8R, are used to model each ply of the laminate and the metallic parts of the model. The modeling method of one element for per ply provides a reasonable approximation of the through-thickness stresses.

Finite element

The mesh density and aspect ratio in the contact areas between the fastener shank and hole will affect the convergence of the simulation results, and the meshes in these areas are more refined than those in other areas. Ten elements are equally distributed in the area covered by each fastener head along the radial direction, and 20 are elements equally distributed on the half periphery of each fastener hole along circumferential direction. Thus, the aspect ratios of the elements surrounding the hole are 2.5, and there will be 40 elements around the whole periphery of the fastener hole, which is similar to the mesh convergence results of Rosales-Iriarte et al. 26 and Padhi et al.27.

3.2. Boundary conditions

The boundary conditions of the finite element model are shown in Fig.2 (a). The symmetry surfaces of the two joint plates and fasteners are constrained in translational direction Uy. The left end of titanium plate is held fixed in all three translational directions (Ux, Uy and Uz). The right end of the laminate plate is declared as a rigid body and has tie relationship with a reference node. Thus, the motion of the right side surface is governed by the motion of the reference node, which is held fixed in two translational directions(Uy and Uz) and three rotational directions (Rx, Ry and Rz), while a pull load is applied along Ux direction. The preload produced by the tightening torque was applied through Bolt load function in Abaqus CAE, and it is 4 kN for the whole intersection of the fastener shank and 2 kN for half of

the intersection of the fastener shank according to the preload test results of Huang and Wang 28.

3.3. Contact relationships

There are totally nine contact pairs in the two-bolt composite-to-titanium joint. Four of them are located between the fasteners shanks and holes (including two contact pairs for each fastener), four of them are between fastener heads/nuts and the outer surfaces of the two plates (including two contact pairs for each fastener), and one of them is between the faying surface of two plates (including one contact pair). The contact pairs around one of the fasteners are shown in Fig.2(b). Finite sliding formulation is used to model all the contact relationships. The bolt-hole fit conditions can be changed through setting the Interference fit values of the four contact pairs between the fastener shanks and holes. The frictional coefficient between titanium materials is set to be 0.4 29, and that between the titanium material and composite material is set to be 0.1 according to the results of Olmedo and Santiuste 30,31.

3.4. Failure criteria and degradation rules

The failure modes of the unidirectional tape lamina mainly include fiber tensile/compression failure, matrix tensile/compression failure, and delamination, and the failure modes of the trill woven composite mainly include warp tensile/compression failure, weft tensile/compression failure and delamination. Generally, progressive failure analysis consists of

two major steps 32. The first step is to choose appropriate failure criteria to justify which failure mode occurs prior to others. In terms of failure prediction, the maximum stress criterion, the maximum strain criterion, Hoffman criterion, Tsai-Wu criterion and Hashin criterion are widely employed in failure predictions for composite materials. Up to date, there have been several researchers who have combined and modified different criteria to form a single set of failure criteria to predict damage within a composite laminate.

Table 3 Failure criteria

F.Rosales-Iriarte et al. have comparatively evaluated the reliability of the different failure equations and degradation rules, and they have found that the best overall three-dimensional failure predictions obtained is the combination of Hashin criteria and Ye delamination criteria. Thus, Hashin and Ye failure criteria 33, 34 are adopted to predict the failure of the composite materials in this study. The failure criteria of unidirectional lamina and woven fabric were shown in Table 3 and 4.

of the unidirectional lamina

Failure mode

Failure criterion

Fiber tensile failure ( C n > 0)

Fiber compressive failure ( C n < 0 )

Matrix tensile failure ( C 22 + C 33 > 0 )

(Cf)2+C2)2+C3)2 > i

Si i Sio S

Matrix compressive failure

( C 22 + C33 < 0

Delamin;

(C22 + C33 C

( S 22

^11 S C

2 . C23 C22C33 , tC12\2 . (C13\2

.+ ÇHL)2 + (^i!)2 > 1

S12 S13

f SC v

V 23 y

(c22 + C33 ) +

C22 + C33 23

l- ( -C22C33 )+ C2)2 + C3)2 > 1

S12 S13

nation failure

V y V 11 y V y í \2 í \2 í \2

V S33 y

V S13 y

V S23 y

> 1, c33 > 0

> 1, c33 < 0

where, C - (i,j=1, 2, 3) are the scalar components of

the stress tensor, and Sj (i,j=1, 2, 3) are the material strengths(the 1, 2 and 3 directions are the longitudinal, transverse and thickness directions of

the unidirectional tape lamina, respectively); the superscripts T and C denote tension and compression respectively.

Table 4 Failure criteria of the woven fabric lamina

Failure mode

Failure criterion

Warp tensile failure ( C 11 > 0 )

Warp compressive failure ( C 11 < 0 )

Weft tensile failure ( C 22 > 0 )

(-1-)2 + R2)2 + R3)2 > 1

Sj S lt S

v SC ,

ÇHL)2 + (J^)

2 + C^2 > ]

Weft compressive failure (C 22 < 0 )

Delamination failure

22 T +C +

s T i v slz

v SC ,

V Slz )

> 1,t33 > 0 > 1,t33 < 0

where, the L, T and Z directions represent the warp, weft and thickness directions of the woven fabric lamina, respectively.

The second step is to choose a suitable material degradation rule for the reduction of the stiffness of the composite material after the occurrence of a certain type of failure. The commonly used degradation methods are the total discount method,

the limit discount method and the residual property method. The limit discount method of the unidirectional lamina in this research is referred to the degradation rules of Tan 35 and that of the woven fabric is referred to Zhao et al36. These two degradation methods are shown in Table 5 and 6 respectively.

Table 5 Degradation rules of the unidirectional tape lamina

Failure mode E11(GPa) E22(GPa) En(GPa) U12 U13 U23 G12(GPa) Gu(GPa) G23(GPa)

No failure 1 1 1 1 1 1 1 1 1

Fiber failure 0.2 1 1 0.2 0.2 1 0.2 0.2 1

Matrix failure 1 0.2 0.2 1 1 0.2 1 1 0.2

Delamination 1 1 0.1 1 0 0 1 0.1 0.1

Table 6 Degradation rules of the woven tape lamina

Failure mode E,(GPa) £r(GPa) Ez(GPa)

'23 Gir(GPa) Grz(GPa) GLz(GPa)

No failure 66.16 61.04 20.24 0.04 0.3 0.3 6.54 8.76 8.76 8.76

Fiber failure 13.232 61.04 20.24 0.008 0.06 0.3 1.308 1.752

Matrix failure 66.16 12.208 4.048 0.04 0.3 0.06 6.54 8.76 1.752

Delamination 66.16 61.04 2.024 0.04 0 0 6.54 0.876 0.876

For composite materials, the failure criteria are implemented using ABAQUS user subroutine USDFLD, and the degradation rules are implemented using the filed variables which are depended on the failure criterion of each damage mechanism. The user subroutine USDFLD within ABAQUS provides the user a method to write a program that updates the field variables at every integration point for each increment in the analysis, according to failure criteria values obtained during the solution. At the beginning of each increment, the user subroutine USDFLD, using the utility subroutine GETVRM, accesses the material point quantities for every integration point in the model. The stress and strains components are then used to compute the failure criterion values. If any of the values are greater or equal to 1, the related field variable for the integration point with the highest failure criterion value is set permanently to 1, indicating failure (it is important to note that degradation models implemented within ABAQUS degrade integration points rather than elements). And these solution-dependent filed variables are then used to define the material properties of the next iteration.

4. Model validation

To validate the three-dimensional finite element modeling method for the composite joint, simulation results are compared with the experimental results, and two characteristics, load-displacement curves and bearing strain-load curves, are utilized as the criteria.

Quasi-static tests of the specimens were conducted using a MTS Landmark electron-hydraulic servo-

controlled material testing machine as shown in Fig.3. The view on the left side of Fig.3 shows the test setup method, and the view on the right side is the detail view indicates the strain measuring method. The joint specimen was clamped by the two heads of the testing machine, and tensile load was exerted to the specimen through fixing the stationary head and moving up the moveable head. One YYJ-1040 electronic extensometer, whose gauge length is 50 mm and accuracy is 0.036%, was used to measure the bearing deformation of the fastener hole. The test setup method and the bearing measurement method are based on the composite bearing response and bearing/bypass interaction response test standards of American Society for Testing and Materials, ASTM D5961/D5961M-0837 and ASTM D7248/D7248M-0838. In order to avoid the bending effect, three BX120-3AA strain gauges, whose accuracy is 1%, were used to center aligned the specimens in accordance with the test standard of American Society for Testing and Materials, ASTM D3039-08 39. The quasi-static tensile tests were performed in displacement control mode with the constant speed being 1 mm/min, which kept proceeding until the joint can not take any further load. The circumstance temperature was kept being 23+/-5 degree Celsius, and the relative humidity was kept being 55+/-5% during test.

Since the load-displacement relationships of the test results with the same configuration are quite consistent, the test result of just one specimen for each geometry configuration is chosen to compare with the simulation results. The comparisons of the load-displacement curves between the test results and the simulation results are shown in Fig.4. Fig.4(a) illustrates the load-displacement curves of the joints with bolt-hole fit condition being neat fit, and Fig.4(b) illustrates the load-displacement curves of the joints with bolt-hole interference fit value being 1.5%. The load-displacement curves in both Fig.4(a) and Fig.4 (b) are linear before the displacements are about 1 mm, following that, the slopes of the curves keep declining, which means that the stiffness values of the joints are decreasing and certain kinds of failures have taken place. Finally, the loads reach their summits as the displacements are around 2.0 mm.

And the maximum load values of the joints whose

bolt-hole interference fit value is 1.5% are bigger than those of the joints with neat fit, however, the maximum displacement of the joints with 1.5% interference fit are smaller than that of the joints with neat fit. Fig.4 shows that the simulation results agree with the test results quite well. It can also be seen from Fig.4(a) that the mean value of the maximum test loads is 26158 N and the maximum load of the simulation result is 24914 N. The difference between the simulation results and the test results of the joints with neat fit is about 4.7%. From Fig.4(b), it can be seen that the mean value of the maximum test loads is 27918 N and the maximum load of the simulation result is 26844 N. The difference between the simulation results and the test results of the joints with 1.5% interference fit is about 4.0%. Therefore, the simulation results are quite close to the test results in regard to the load-displacement relationships.

- Simulation results

- Tust results

1.0 1.5 Displacement (mm) (a) Joints with neat fit

Fig.4 Load-displacement curves

According to ASTM D5961/D5961M-08 37, the bearing strains of the single-lap joints can be demonstrated as:

£br =-

where, the D indicates the diameter of the fastener hole and 5 indicates the deformation obtained by the extensometer.

The bearing strains of just three specimens of each batch of specimens are measured and the comparison

of the bearing strain-load curves between the test results and simulation results are shown in Fig.5. Fig.5 (a) shows the bearing strain-load curves of the joints with bolt-hole fit condition being neat fit, and Fig.5 (b) shows the bearing strain-load curves of the joints whose bolt-hole interference fit values are

1.5%. Similar to what is shown in Fig.4, the bearing strain-load relationships of the simulation results agree with that of the test results quite well. It is worth to mention that the bolted joints can normally be seen fail as the bearing strain reaches 4%.

Therefore, through the comparison with the test results on both the load-displacement curves and the bearing strain-load curves of the joints, the simulation results are found to be consistent and in agreement with the experimental test results, and these validate the modeling method of the composite-to-titanium single-lap joint proposed in this paper.

5. Parametric studies

For the intentional interference fitting, the fastener shank and the hole are not exactly matched, and the mismif is defined by a parameter A which relates the hole radius a and the fastener shank radius a1 40:

a = a (1+X)

To investigate the combined and interactive effects of different fit conditions and preloads, different finite element models are constructed to simulate the joints with different bolt-hole fit conditions ( X are 0%, 0.5%, 1%, 1.5%, 2%, 2.5%, 3%, and 3.5%, respectively) and fasteners' preloads (P are 0, 2, 4, 6 kN, respectively) .

Load(kN) (b) Joints with 1.5% interference fil

-load curves

5.1. The influence of bolt-hole fit conditions

The load carrying capacities of the joints with the same preload values (4 kN for the whole fastener) but different fastener-hole fit values ( X ) are shown in Fig.6, from which it can be seen that the bolt-hole fit condition will influence the load carrying capacity. The load carrying capacity of the joint increases with the increase of bolt-hole interference fit values as the interference fit values are smaller than 1.5%, and decreases with the increase of bolt-hole interference fit values as the interference fit values are bigger than 1.5%. As the interference fit value reaches 3.5%, the load carrying capacity of the joint is even lower than that of the similar joint with neat fit condition. Thus, the effect of the bolt-hole interference fit condition on the load carrying capacity of the joints will change from positive into negative mode with the increase of the interference fit values. For the specific joint configuration described in this study, the joint with 1.5% interference fit value has the highest load carrying capacity, and increases the strength of the joints by about 7.5% comparing with that of the joints with neat fit.

Fig. 6 Load carrying capacity of joints with different interference fit conditions

In order to understand the causes of the fit effects on the mechanical performances of the joints Three types of joints with different fastener-hole interference fit values ( A are 0%, 1.5%, and 3%, respectively) are studied in detail. Since the load carrying capacity of the laminate is mainly depended on the strength and failure conditions of the lamina in fiber direction (longitude direction), just the fiber failure state surrounding the fastener holes are analyzed. Fig.7 shows the fiber failure states of three different joints conditions (the preload is 2 kN and interference fit values are zero, 1.5% and 3.0%, respectively) before and after loading. In Fig.7, the FV1 represents the fiber failure index of the elements, and the there will have fiber failure as the FV1 of the element in the relevant location equals to 2. Fig.7 (a) illustrates the fiber failure condition the joint with neat fit under 0 kN tensile load, and Fig.7 (d) illustrates the fiber failure condition of joint with neat fit under 20 kN tensile load. Fig.7 (b) and Fig.7 (e) illustrate the fiber failure conditions of the joint with fastener-hole fit value being 1.5%. Fig.7 (c) and Fig.7

(f) illustrate the fiber failure conditions of the joint with fastener-hole fit value being 3%. Massive fiber failures occur around the hole r egion as the composite mechanical joints structure is under tensile load, and the failure area will spread with the increase of load. The structure cannot continue bearing load as the fiber failure comes to a certain degree.

From the comparisons among Fig.7 (a), Fig.7 (b) and Fig.7 (c), it can be seen that, before the joints are tensile loaded, the fiber failure area surrounding the fastener hole increase with the increase of the bolt-hole interference fit conditions. Whereas, from the comparisons among the Fig.7 (d), Fig.7 (e) and Fig.7 (f), it can be seen that, as the joints are tensile loaded to 20 kN, the fiber failure area of the joint with 1.5% interference fit is the smallest among the three different joints. This partially explains the reason that the joint with 1.5% interference fit has higher load carrying capacity than the joint with neat fit and the joint with 3% interference fit.

Fig.7 Fiber failure status of the joints with different interference fit conditions

Fig.8 illustrates the corresponding contact stress distributions surrounding the hole of the joints under the same condition as shown in the Fig.7. In Fig.8, the CPRESS represents the contact pressure, and its unit is MPa. From the comparisons among Fig.8 (a), Fig.8 (b) and Fig.8 (c), it can be seen that, before the joints are tensile loaded, there is no contact stress distributing around the fastener hole of the joints with neat fit, but there are a certain extent of contact stress distributing around the fastener hole of the joints with 1.5% and 3% interference fits, and the peak contact stress of the joints with 3% is 1795 MPa, which is the

highest among the peak contact stress of the three different joints. From the comparisons among the Fig.8 (d), Fig.8 (e) and Fig.8 (f), it can be seen that, after the joints are tensile loaded to 20 kN, the contact areas of the joints with 1.5% and 3% interference fit are bigger than that of the joint with neat fit, and the peak contact stress of the joint with 1.5% is about 2281 MPa, which is the lowest among the peak contact stress of the three different joints. This explains the reason that the fiber failure area of joint with 1.5% interference fit is the smallest among those of the three different joints.

Fig. 8 Contact stress distributions of the joints with different interference fit conditions

Synthetically considering the contact stress and fiber failure surround the fastener hole shown in Fig.7 and Fig.8, the conclusions can be drawn that: for the joints with neat fit, the contact stress distribution surrounding the hole is severely uneven after tensile loading, which causes large range of fiber damage at the bearing side and premature failure of the structure; for the joints with 3% interference fit, the contact stress distribution is relatively uniform before and after tensile loading. Exaggerated initial stress produced since the interference fit is too large, which will generate premature failure and reduce the carrying capability of the structure in turn; the 1.5% interference fit value suits the composite joint structures the best by producing some initial stress before loading and relatively uniform contact stress between bolt and plates after loading, which maximizes the strength of the joints. Therefore, the effect of the bolt-hole interference fit condition on the joint strength will change from positive into negative mode with the

increase of the interference fit values, and for the joints with 4 kN preload described in this section, the 1.5% interference fit can provide the maximum load carrying capacity.

5.2. The effect of preload

The load carrying capacities of the joints with fixed interference value of 1.5% but various preloads (P) are shown in Fig.9. It can be seen that the joints strength will increase and then decrease with the increase of the fastener's preloads, that is to say, the effect of preload will changed from positive into negative mode with the increase of preload values. For the specific joint configuration described in this study, the joint with the fasteners' preloads being 4 kN achieves the maximum load carrying capacity, and increases the strength of the joints by about 3.3% comparing with that of the joints without preload.

Fig.9 Load carrying capacity of joints with different preloads

The fiber damage failure conditions of the joints with three preload values (P are 0 kN, 4 kN and 6 kN, respectively) before and after loading are shown in Fig. 10. Fig. 10 (a) illustrates the fiber failure condition the joint with fasteners' preload being 0 kN and tensile load being 0 kN, and Fig.7 (d) illustrates the fiber failure condition of joint with fasteners' preload being 0 kN and tensile load being 20 kN. Fig.7 (b) and Fig.7 (e) illustrate the fiber failure conditions of the joint with fasteners' preload being 4 kN. Fig.7 (c) and Fig.7 (f) illustrate the fiber failure conditions of the joint with fasteners' preload being 6 kN.

From the comparisons among Fig.10 (a), Fig.10 (b) and Fig.10 (c), it can be seen that, before the tensile loads are applied to the joints, there are some extent of fibre failure surrounding the fastener hole for all joints with three different clamping forces, and the fibre failure area increase with the increase of the clamping forces. This is because the delamination area will increase with the increase of the clamping forces, and then, the stress will redistributed in the

surrounding area of the fastener hole, and finally, this will induce some more fiber failure. Whereas, from the comparisons among the Fig.10 (d), Fig.10 (e) and Fig.10 (f) it can be seen that, as the joints are loaded to 20 kN, the fibre failure area of the joint with 0 kN clamping force as shown in Fig.10 (d) will be larger than that of the joint with 4 kN clamping force as shown in Fig.10 (e), which indicates that certain clamping force may have some initial impact on fibre damage, but it can prevent the damage evolution at the loading process, which is beneficial to joints strength; the fibre failure area of the joint with 6 kN clamping force as shown in Fig.10 (f) is also larger than that of the joint with 4 kN clamping force as shown in Fig.10 (e), this is because 6 kN clamping force is overlarge for the composite structure, and the too large clamping force aggravates the spread of fibre damage instead of preventing it. Therefore, the joint with 4 kN clamping force has higher load capacity comparing with the joints with clamping forces being 0 kN and 6 kN.

Fig.10 Fiber failure status of the joints with different preloads

Figure 11 illustrates the corresponding contact stress distributions surrounding the hole of the joints under the same condition as shown in the Fig.10. From the comparisons among Fig.11 (a), Fig.11 (b) and Fig.11 (c), it can be seen that, before the joints are loaded, the contact stress distribution and values are almost the same for the three different joints, and the contact stresses of the joints with preloads are a little higher than the contact stresses of the joints without preloads. From the comparisons among the

Fig.11 (d), Fig.11 (e) and Fig.11 (f), it can be seen that, after the joints are loaded to 20 kN, the difference among the contact stresses of the joints with different preloads are larger, and the peak contact stress of joint with 4 kN preload is 2281 MPa, which is the lowest among the that of the three different kinds of joints. This explains the reason that the fiber failure area of joint with 4 kN preload is the smallest among those of the three different joints.

Fig. 11 Contact stress distributions of the joints with different preloads

Synthetically considering the contact stress and fiber failure surrounding the fastener hole shown in Fig.10 and Fig.11, the conclusions can be drawn that: the effect of the fasteners' preload on the joint strength changes from positive into negative mode with the increase of the preload values, and for the joints with 1.5% interference fit described in this section, the 4 kN preload can provide the maximum load carrying capacity.

5.3. Interactive effect analysis

interactive effect of the two factors (interference fit and preloads) on the load carrying capacity of the defined composite-to-titanium single-lap mechanical joint, and the nine-factor, mixed levels (one factor with 8 levels and the other 8 factors with 4 levels) orthogonal design L32 (8 x 48 ) 41 was used to arrange different simulation conditions. The arrangement of different factors and levels is shown in Table.7. The simulation results of the joints with different bolt-hole fit conditions and fastener's preloads are shown in in Table 8. The results are analyzed by the

ANOVA method 9.

The joint configurations with eight different bolt-hole fit values (0%,0.5%,1%,1.5%,2%,2.5%,3%, and 3.5%) and with four different fastener's preload values (0, 2, 4, 6 kN) are used to investigate the

Table 7 Factors and levels that affect load carrying capacity

, which are illustrated in Table

Level 1 2 3 4 5 6 7 8

Interference fit (%) A 0 0.5 1 1.5 2 2.5 3 3.5

Preload (kN) B 0 2 4 6 - - - -

Table 8 Simulation results of the maximum load

Condition No.

Maximum

7 8 9 load(N)

1 1 1 23830.2

2 2 2 24319.9

3 3 3 24914.6

4 4 4 24636.6

3 4 4 24413.4

4 3 3 24903.9

1 2 2 25884.3

2 1 1 25404.5

2 3 4 24703.7

1 4 3 25626.6

4 1 2 26534.7

3 2 1 26165.7

4 2 1 25937.8

3 1 2 26305.8

2 4 3 26772.9

1 3 4 25822.4

3 2 3 25909.3

4 1 4 25986.2

1 4 1 26124.8

2 3 2 25677.6

1 3 2 25807.4

2 4 1 25883.0

3 1 4 25503.9

4 2 3 25247.1

4 4 2 25452.7

3 3 1 25722.5

2 2 4 25256.1

1 1 3 24864.5

2 1 3 24961.1

1 2 4 25329.5

4 3 1 24817.2

3 4 2 24601.3

10 11 12

20 21 22

4 2 1 4

4 2 1 4 3

4 1 2 4 3 2 1

Table 9 ANOVA of the simulation results

Condition No. A B AxB

A(1) 24425.3 25127.0 25146.7

A(2) 25151.5 25509.7 25120.0

A(3) 25757.7 25726.1 25646.3

A (4) 26209.7 25302.5 25764.7

A(5) 25924.5

A(6) 25610.3

A(7) 25324.0

A(8) 24927.3

R 1784.4 599.1 644.7

r 4 8 8

4~r 2 2.8284 2.8284

d 0.34 0.45 0.45

R' 1213.4 762.5 820.6

In Table 8, factor 1 represents the bolt-hole fit condition, factor 2 represents the preloads of the fasteners, and factor 3 represents the interactive effect of bolt-hole fit condition and preload. The S(i) (i is the level number of each factor) represents the summarized results for the factors with the same level, for example, the S(7) of the first factor is the summarized results with the seventh interference fit level (3%), and the S(3) of second factor is the summarized results with the third preload level (4 kN), and the latter can be demonstrated as:

5 (3) = 24914.6 + 25884.3 + 26534.7 +

26772.9 + 26124.8 + 25503.9 + (3)

25256.3 + 25806.8 = 205798.3 And the M(i) (i is the level number of each factor) represent the average results for the factors with the same level, and the M(3) of second factor is the average results with the third preload level (4 kN), and it can be demonstrated as:

M(3) =5(3)78 =25782.4

The R represents the tolerance of the average results for the factors with different levels, and the R of the second factor (preload), for example, can be demonstrated as:

R=Max(M(0)-Min(M(0)=25782.4-25127.0=655.4

The r is the number of the test/calculation conditions with the same level for each factor, and there are 8 tests with the same level for the second factor in the whole test matrix shown in Table.8, thus the r for the second factor is 8. The d is the conversion coefficient which is dependent on r, and it values 0.34 as r is 4 and values 0.45 as r is 8. The R is the modified tolerance and it reflects the influence degree of each factor. The R' can be expressed as 44:

R' = yfr x R x d

From the ANOVA results it can be seen that R' values of fit condition, preload and their interactive effect are 1213.4, 762.5 and 820.6 respectively. The R' value of fit condition is the biggest, and the R' value of the interactive effect is a little bigger than that of preload. Therefore, the bolt-hole fit condition has the largest influence on the load carrying capacity comparing to the preload and the interactive effect,

and the interactive effect is larger than the effect of preload, thus, the interactive effect cannot be ignored.

As the bolt-hole fit condition is 2.5% interference fit, the joint with 2 kN preload has the highest load carrying capacity among the joints with different preload values. However, as the bolt-hole fit condition is 1% interference fit, the joint with 4kN preload has the highest load carrying capacity among the joints with different preload values. Similarly, as the preloads of the fasteners are 2 kN, the joint with 1.5% interference fit has the highest load carrying capacity among the joints with different interference fit conditions, and as the preload of the fasteners are 6 kN, the joints with 1% interference fit has the highest load carrying capacity among the joints with different interference fit conditions. This reflects the interactive effect of the bolt-hole fit condition and the preload, and both these two parameters need to consider synthetically and simultaneously when optimizing the bolted joint structures.

The load carrying capacity of the joint with 1.5% interference fit and 4 kN preload is 26772.9 N, and the load carrying capacity of the joint with neat fit and 0 kN preload is 23830.2 N. The former is about 12.3% bigger than the latter, and 12.3% is the combined effect of bolt-hole fit condition and fas tener ' s preload on the load carrying capacity of the composite joints. The individual effect of bolt-hole fit condition on the load carrying capacity of the composite joints is 7.5% per the analysis in section VI, and the individual effect of fastener's preload on the load carrying capacity of the composite joints is 3.3 % per the analysis in section VII. Therefore, the combined effect is bigger than the sum of the two individual effects (10.8%). This also illustrates the existence of the interactive effect of the bolt-hole fit condition and fastener's preload on the load carrying capacity of the joints.

From the average values of the different factors with different levels, it can be seen that the average value of factor 1(fit condition) peaks its value as the bolt-hole fit reaches 1.5%, and the average value of factor 2 (preload) peaks its value as the preload is 4 kN, therefore, the load carrying capacity should reach its maximum value as the bolt-holt interference fit is 1.5% and the preloads of the fasteners are 4 kN. The all-level results testify this point.

The orthogonal design incorporated ANOVA method can not only analyze the interactive effects and the influence degree of different factors, but also

will be especially effective and valuable for the optimization work over more than three factors. Such as, for the joints with eight different interference fit values(8 levels), four different preload values (4 levels), four different friction coefficient values (4 levels), and four different joint geometries (4 levels), it will need totally 512 (512=8x4x4x4) different calculate/test conditions to find the best result, whereas, using the orthogonal design table presented in this paper, it will just need 32 different calculate/test conditions to reveal the effects of different factors and their interactive effect, and then optimize the joints over various parameters. If the factors and/or levels are different with those described in this paper, other orthogonal design tables can be selected, which can refer to the relevant literatures, such as reference 41.

6. Conclusions

(1) Both the effects of bolt-hole interference fit value and the preloads on load carrying capacity change from positive mode into negative mode with the increase of their values, and their optimized values are applied to specified joints.

(2) There is interactive effect between the bol hole interference fit conditions and preloads The interference fit condition and preload influences the effects of each other's. The optimized interference fit value of a joint with a specified preload will not the optimized value for the joints with different preload values anymore, and vice versa.

(3) The assembly parameters, which include the fit conditions and the preloads, influence the mechanical behavior through changing the stress state at the surroundings of the fastener hole, and they need to be considered together during the process of optimizing composite bolted joints.

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Liu Longquan is a Ph.D. in the School of Aeronautics and Astronautics at Shanghai Jiao Tong University. His main research interests are aircraft design and mechanical of composite materials.

Zhang Junqi is a Master Degree Candidate in the School of Aeronautics and Astronautics at Shanghai Jiao Tong University. His main research interests are aircraft design and mechanical of composite materials.

Chen Kunkun received the Master Degree in the School of Aeronautics and Astronautics and is working for a Ph.D. degree in the School of Mechanical at Shanghai Jiao Tong University. His main research interests are aircraft design and Vehicle engineering.

Wang Hai is professor in School of Aeronautics and Astronautics at Shanghai Jiao Tong University. His main research interests are aircraft design and mechanical of composite materials.