Numerical and experimental investigation of fitting

Aerospace Science and Technology 78 (2018) 461–470

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Aerospace Science and Technology www.elsevier.com/locate/aescte

Numerical and experimental investigation of fitting tolerance effects on damage and failure of CFRP/Ti double-lap single-bolt joints Yuejie Cao a , Zengqiang Cao a,∗ , Yangjie Zuo a , Lubin Huo a , Jianping Qiu b , Duquan Zuo a a b

School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an 710072, China Xi’an Aircraft Industry (Group) Company Ltd, AVIC, Xi’an 710089, China

a r t i c l e

i n f o

Article history: Received 19 January 2018 Received in revised form 4 April 2018 Accepted 25 April 2018 Available online 26 April 2018 Keywords: Composite Bolted joint Clearance Interference Damage

a b s t r a c t CFRP/Ti bolted joints are increasingly used in aircraft structures. Optimizing the joint design is vital for overall composite structure designs. Therefore, a progressive damage model was developed for investigating the effects of clearance and interference sizes on the damage and failure of CFRP/Ti doublelap, single-bolt joints under quasi-static loads, in which the improved three dimensional Hashin failure criterion and Tan degradation rules were used through an ABAQUS user-define-field (USDFLD) subroutine. The corresponding quasi-static tensile tests and fatigue tests were also conducted. Joints strength were evaluated and failure mechanism was discussed. Numerical results showed that the matrix compression failure dominated the joint failure mode. Joint ultimate strength decreased gradually with the increase of clearance sizes, while joint bearing strength and stiffness exhibited an increase with interference sizes at first and then decreased rapidly due to the initial installation damage. Moreover, the maximum strength was achieved at the interference size of 0.5%. Those results were in well agreement with corresponding experimental results. In addition, interference sizes were also revealed a correlation with the fatigue life of the joints. The study presented here will be useful for optimization of composite structure designs. © 2018 Elsevier Masson SAS. All rights reserved.

1. Introduction Carbon fiber reinforced polymer (CFRP) composites are increasingly applied in modern aviation industry, which have advantages of high specific strength, specific stiffness, fatigue design, corrosion resistance [1–4]. For example, the fuselages of both Boeing 787 and Airbus A350XWB, which are two characteristic examples of the latest generation of large commercial aircrafts, are manufactured with the amount of composites more than 50% in weight. Although the composite structures of aircraft have been developed toward the integration of design and manufacture, the joining technology is still unavoidable in composite structure designs of modern aircraft due to the limitations of geometrically complex structures and their sizes [5]. For load transfer and repair requirements, bolted joints are still the dominant joining methods in primary structural parts of composite [6]. Despite of the advantages of bolted joining, bolted joints represent the potential weak points of composite structures due to localized stress concentration, where the damage initiation and failure are prone to occur under external loading. A number of recent studies have been conducted to improve the composite joint

*

Corresponding author. E-mail address: [email protected] (Z. Cao).

https://doi.org/10.1016/j.ast.2018.04.042 1270-9638/© 2018 Elsevier Masson SAS. All rights reserved.

designs in aircraft structures. Typically, BOJCAS (Bolted Joints in Composite Aircraft Structures) is to develop advanced numerical design methods for composite bolted joints [7], in which the clearance fit and net fit joints were studied. With the development of modern aircraft manufacturing technology, many researchers have investigated the effects of interference fit on the mechanical strength of composite bolted joints. Kiral [8] studied the clearance and interference-fit on failure of pin-loaded composite joints, and found that both clearance fit and interference fit did not change the failure mode. However, failure loads were developed for all configurations when interference-fit was used. McCarthy [9] conducted a detailed numerical simulation and experimental investigation on multi-bolt composite joints with variable bolt–hole clearances, and results showed that clearance can also significantly reduce the load carrying capacity when the initial failure occurred. Raju et al. [10] found that an interference-fit bolted joint had approximately 10% higher load sharing than that of a neat-fit joint by finite element analysis and experiment. Zhang et al. [11] investigated the effect of interference fit on load capacity of composite bolted joint, and results showed that the load capacity of joint structure increased at first and then decreased with the increase of interference sizes within a certain range. Kelly et al. [12] studied the effects of bolt–hole clearance on bearing strength of composite laminates, the hole deformation was observed to be slightly

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Y. Cao et al. / Aerospace Science and Technology 78 (2018) 461–470

larger for the clearance-fit composite laminates compared to the neat-fit under a given load condition. Liu et al. [13] reported that proper bolt-hole fit conditions and preloads could delay the fiber failures around the bolt holes and improve the bearing capacity of the joints eventually. Lawlor et al. [14] carried out experiments to study the effects of clearance fit in double-lap, multi-bolt composite joints, and concluded that clearance fit had a significant influence on load distribution, initial load and fatigue life, while it had no influence on the ultimate static strength. Chen et al. [15] studied the effect of interference fit condition and tightening torque on composite bolted joints, and found that the combined effect of bolt-hole interference fit condition and tightening torque had an influence on the strength of the joints and their mechanism. The effect of interference fit on the fatigue life of double lap joints was evaluated by detailed experiments and finite element simulation by Chakherlou et al. [16]. The experimental results suggested that the interference fit joints had a longer fatigue life under low amplitude cyclic load. Pradhan et al. [17] found that the localized precompression stresses were introduced during bolt interference-fit installation process, which decreased the magnitude of the tensile stress under quasi-static loading. Song et al. [18] developed a stress distribution model for interference-fit area around composite laminates, and results showed that the maximum values of stress components and stiffness of composite material increased with the interference size linearly before damage initiation because of the linear elasticity of pin and laminates. Zuo et al. [19] also reported that the dynamic behaviors of CFRP/Ti pinned joints, which exhibited obvious sensitivity to interference sizes. However, the previous researches only focused on the influence of clearance fit or interference fit, the effects of fitting tolerances from clearance fit to interference fit on the joints are not analyzed systematically. Meanwhile, the fitting tolerance effects on the damage and failure of CFRP/Ti bolted joints, which are more and more widely used by aircraft structures, are still not well understood. Thus, in order to optimize composite structure designs, it is necessary to systematically investigate the fitting tolerance influences on CFRP/Ti bolted joints. In this paper, a progressive damage model based on the improved three dimensional Hashin failure criterion and Tan degradation rules was developed for investigating the effects of clearance and interference sizes on the damage and failure of CFRP/Ti double-lap, single-bolt joints under quasi-static loads. The corresponding experimental tests were conducted to valid the simulation results. Moreover, the effects of interference sizes on fatigue life of the joints were also investigated by fatigue tests. The bearing loads and tensile strengths of the joints were evaluated, furthermore, the damage propagation and failure mechanism of the joints were discussed. Results presented included load-displacement responses and failure mechanism discussions. 2. Progressive failure model In order to simulate the damage and failure process of composite materials, the Hashin failure criteria and degradation rules were used here. In this model, the improved Hashin Criterion was defined as: Fiber tensile failure (σ11 > 0):

σ11

2

+

XT

σ12 S 12

2

+

σ13 S 13

2 ≥1

(1)

Fiber compression failure (σ11 < 0):

σ11 XC

2 ≥1

Matrix tensile failure (σ22 + σ33 > 0):

(2)

Table 1 Material properties of degradation rules. Properties degradation rules

Failure mode

= D t1 E 11 = D c1 E 11 = D t2 E 22 , G d12 = D t4 G 12 , G d23 = D t4 G 23 = D t1 E 11 , E d22 = D t2 E 22 , G d12 = D t4 G 12 , G d23 = D t4 G 23 E d11 = D c1 E 11 , E d22 = D t2 E 22 , G d12 = D t4 G 12 , G d23 = D t4 G 23 E d22 = D c2 E 22 , G d12 = D c4 G 12 , G d23 = D c4 G 23 E d11 = D t1 E 11 , E d22 = D c2 E 22 , G d12 = D c4 G 12 , G d23 = D c4 G 23 E d11 = D c1 E 11 , E d22 = D c2 E 22 , G d12 = D c4 G 12 , G d23 = D c4 G 23 E d11 E d11 E d22 E d11

FV1

FV2

FV3

FV4

1 0 0 1

0 1 0 0

0 0 1 1

0 0 0 0

0

1

1

0

0 1

0 0

0 0

1 1

0

1

0

1

Note: E i j and G i j are Young’s modulus and shear modulus before degradation, respectively. E dij and G dij are Young’s modulus and shear modulus after degradation, respectively. i , j = 1, 2, 3.

σ22 + σ33

2 +

YT

1

2 23

σ − σ22 σ33 +

2 S 23

σ12 S 12

≥1

2

+

σ13

2

S 13 (3)

Matrix compression failure (σ22 + σ33 < 0):

σ22 + σ33

YC

YC

+

2S 23

2

(σ22 + σ33 )2 −1 + 2

σ − σ22 σ33 σ12 2 23

2 S 23

S 12

2

+

4S 23

σ13

2

S 13

≥1

(4)

Fiber–matrix shear failure (σ11 > 0):

σ11

2

+

XC

σ12

2

+

S 12

σ13

2 ≥1

S 13

(5)

Delamination in tension (σ33 > 0):

σ33

2

+

ZT

σ13

2

+

S 13

σ23

2 ≥1

S 23

(6)

Delamination in compression (σ33 < 0):

σ33 ZC

2

+

σ13 S 13

2

+

σ23 S 23

2 ≥1

(7)

The details of laminate failure criteria and degradation rules are shown in Table 1. Delamination and shear failure damage modes were not considered in this model. The FV1, FV2, FV3 and FV4 represented fiber tensile failure, fiber compression failure, matrix tensile failure and matrix compression failure, respectively. Camanho’s material degradation rule [20] was given in Table 1, in which the degradation parameters were: D t1 = 0.07, D c1 = 0.14, D c2 = D c4 = 0.4, D t2 = D t4 = 0.2. In order to implement failure analysis and material stiffness degradation in loading process, a USDFLD user-defined subroutine failure criterion was written using Fortran 95, and the stiffness degradation criterion was implemented by the filed variables which were according to the failure criterion of each damage types. By introducing four field variables FV1, FV2, FV3 and FV4, which represent four types of damage, the USDFLD controlled the degradation of material by changing the field variable from 0 to 1 when a certain type of damage occurred on the element. At the start of each increment, the USDFLD used GETVRM (Get Variables of Material Point) to access the quantities of material point for every integration point in the model.


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Fig. 2. Specimen geometry of a double-lap composite bolted joint (mm).

Table 2 Mechanical properties of T800 carbon/epoxy composites laminate.

Fig. 1. Flow chart of progressive damage analysis process.

In the course of calculation, when the stress of the element did not reach the requirements of the criterion, the solution-dependent state variable SDVs < 1. The field variable FV = 0 and the material attributes were still calculated according to the defined attributes. At each load increment, the subroutine called stresses from the previous increment and then evaluated failure modes. Once the failure criteria was reached, the solution-dependent state variable SDVs ≥ 1 reaching the criterion requirements of unit failure, and field variables FV = 1. Then the material stiffness of failed element was degraded according to the degradation rule in Table 1. When material properties were degraded at a point, the load re-distributed to other points, which could then fail themselves. Therefore, when the material properties changed, they must been iterated at the same loading level to determine if other material points failed. The user-define-field (USDFLD) flowchart is shown within the diagram of Fig. 1. At the initial state of the analysis, all field variables were equal to their original values. Then the external load was applied progressively, and an iterative method was used for simulation calculation at each load increment until that an equilibrium state of the analysis converged. If the failure criteria corresponding to Eqs. (1)–(4) were not reached, the load increased and the program kept on calculating. Once the failure occurred, the stiffness of the failed plies were degraded according to the given degradation criteria, and the stiffness after degradation was used for the next load increment. When the excessive element distortion or designed load had been reached, the program was end. 3. Modeling 3.1. Specimen details Considering that the single lap structure is prone to cause secondary bending and reduce the structure strength, the double lap joint is widely accepted to represent the joints in aircraft structures [8,21]. Therefore, the CFRP/Ti double-lap, single-bolt joint

E 11 (GPa)

E 22 (GPa)

E 33 (GPa)

G 12 (GPa)

G 13 (GPa)

G 23 (GPa)

180

8.73

8.73

4.49

4.49

3.28

ν12

ν13

ν23

X T (MPa)

X C (MPa)

Y T (MPa)

0.33

0.33

0.48

2668

1444

91.8

Y C (MPa)

Z T (MPa)

Z C (MPa)

S 12 (MPa)

S 13 (MPa)

S 23 (MPa)

291

91.8

291

131

131

131

Note: E i j is the Young’s modulus; G i j is the shear modulus; νi j is the Poisson ratio; X T /C is the tension or compressive strength on the direction 1; Y T /C is the tension or compressive strength on the direction 2; Z T /C is the tension and compressive strength on the direction 3; S i j is the shear strength. i , j = 1, 2, 3.

was selected to be investigated in this paper, and the geometry of the joint was shown in Fig. 2. Multidirectional composite laminates are widely used in aircraft structures to meet strength and rigidity requirements under transverse and shear loadings. The composite laminate used in all specimens were fabricated by unidirectional T800 carbon/epoxy composites with symmetric lay-ups [+45/ − 45/0/ + 45/90/ − 45/ + 45/90/ − 45]s , which was provided by Commercial Aircraft Corporation of China Ltd (COMAC) in Shanghai and applied to C919. The nominal thickness of each ply was 0.188 mm, which results in the laminate thickness of t1 = 3.384 mm. The metal splice plate was titanium alloy with the thickness of t2 = 3.9 mm. In order to accurately simulate the failure process under quasi-static load, the joint was designed to promote bearing failure, which were associated with fiber and matrix tensile and compression failures. The length of the composite laminate was 110 mm. All of the plates were designed with the same width of 30 mm and the end distance of 20 mm. The protruding Hi-lock bolt fasteners had a shank diameter of 4.8 mm and the shank length of 11.1 mm. The fastener systems used were aerospace grade titanium alloy protruding fasteners (HST10AG6-7) with 7075-T6 aluminum alloy HI-LITE collars (HST79CY6). The bolt clamping pressure was applied by torquing off the collars with 5 Nm bolt torque. The main mechanical properties of the composite and metals were shown in Table 2 and Table 3, respectively. The fitting tolerance I was determined by the bolt diameter D 1 and the hole diameter D 0 of the composite plate, which was defined as:

I=

D1 − D0 D0

× 100%

(8)

Here, the negative value of I represented clearance fit, while the positive value of I represented interference fit.

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Table 3 Mechanical properties of metallic materials. Material TC4 Plate HI-Lock Bolt

Tensile strength (MPa)

Elasticity modulus (GPa)

Poisson ratio

σS (MPa)

Yield strength

896 931

105 112

0.34 0.31

827 862

3.2. FE simulation A 3D finite element models was established for accurate stress analyses of the specimens by the commercial software ABAQUS 6.12/standard. Only half of the geometry was used according to the symmetry of the joint, as shown in Fig. 3. The laminates were divided into 18 layers in thickness direction and each ply was a single layer of elements. The C3D8R solid elements were used to simulate the failure process of protruding head composite joints. The TC4 plate was meshed with 8 layers of elements in the thickness direction, and in the CFRP plate each ply was represented by using one layer of elements. The nodes at the end of the TC4 plate were fixed in X , Y and Z directions, and uniform displacement was applied at the end nodes of the CFRP plate along the X direction. Two contact pairs were established in the model. One was located between the composite laminate and the TC4 metal plate, and the other was located between the composite and bolt. A surface-to-surface discretization was employed for the contacts

between bolts and plates, and a node-to-surface discretization was used for the contact between the plates to prevent element interpenetration at the edges of the parts. The contact between the Hi-Lite bolt and the inner surface of the hole was then simulated using a surface to surface contact type. The contact property was applied to the plate–plate and hole–bolt contacts. The composite laminate was the master surface for the plate-to-plate contact, and the bolt was chosen the slave surface for the hole-to-bolt contact. The contacts were solved using the penalty method with hard contact, friction, small sliding and finite sliding. Penalty contact was included between the titanium alloy Hi-lock bolt and the composite laminate along the bearing surface with a coefficient of friction of 0.1, and the plate-to-plate contact was 0.2. 4. Results and discussion 4.1. Influence of fitting tolerances 4.1.1. Clearance fit The load-displacement curves of the clearance fit joints are shown in Fig. 4. It was suggested that the load-displacement curves of clearance fit joints exhibited four main stages [20]: the load increased linearly at first due to the joint load being reacted solely by static friction forces acting at the shear plane; then, a sliding occurred corresponding to that the large bolt–hole clearance was taken up and the bolt shank began to contact the laminates; when contact was established between the bolt and the

Fig. 3. Finite element model of the CFRP/Ti joint.

Fig. 4. Load-displacement curves of clearance fit joints: (a) simulation results, (b) typical model.


Fig. 5. Load-displacement curves of interference fit joint.

laminates, the bolt started to transmit load and the load increased linearly again; finally, with the load increasing to 12000–13000 N, the initial damage occurred causing joint stiffness degradation and a nonlinear damage region was observed. Here, the typical forcedisplacement curve of the clearance fit joints was concluded in Fig. 4(b). Furthermore, the mechanical properties were obviously sensitive to clearance sizes. The stiffness of the joints decreased gradually with the increase of clearance sizes, moreover, the bearing strength also exhibited a decrease with the increase of clearance sizes, for example a 9.5% decrease in bearing strength occurred at the clearance size of 3% compared with that of net fit. Those results indicated that increasing clearance size leaded to an increase in bolt rotation and a decrease in bolt-hole contact area resulting in a higher level of local stress and then causing an obvious decrease in joint stiffness and bearing strength, which was also reported by literature [22].

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placement corresponding to the initial damage was also almost the same. After initial damage occurred, the stiffness of interference fit joints degraded obviously. With the increase of interference sizes, the joint stiffness increased gradually. However, the joint failure strength increased with the interference size at first, and then the decreased. Here, the maximum value of failure strength was obtained at the interference size of 0.5%. Under the condition of interference fit, the peak radial stress was lower than that under the condition of clearance fit. The lower peak radial stress was the result of two conditions: one was that a larger contact area decreased the load density of bolt hole, and another reason was that localized pre-compression reduced the magnitude of the resulting tensile stresses under loading. The applied load on laminates was split into two parts: releasing the plate pre-deformation and squeezing the bolt. The stress brought by applied load was therefore less than clearance fit, which was beneficial to the joint structures [23]. The curves of joint bearing strength and failure load corresponding to fitting tolerances are shown in Fig. 6. The curves of joint bearing strength and failure load were quite similar, both of which can be divided into four main stages. In stage I, the strengths were lower than that of other stages and increased significantly with the increase of fitting tolerances. In stage II, the strengths reached a saturation, in which the strengths were not sensitive to fitting tolerance. When fitting tolerance increased to larger than 0.0%, the strengths of the joints increased with the increasing of fitting tolerances and reached maximum values at the interference size of 0.5%, corresponding to stage III. In the last stage (stage IV), with the increasing of fitting tolerance, the strengths tended to decline. In general, the increased contact area in interference fit joints could reduce the bearing stresses and increase the bearing strength of the joints. Clearance fit should be avoided in the joints because increased clearance will lead to reduction in contact area between bolt shanks and holes, which caused higher stress concentration under identical loading condition. 4.2. Damage propagation and failure mechanism

4.1.2. Interference fit The load-displacement responses of interference fit joints are shown in Fig. 5. The load-displacement curves exhibited a linear elastic behavior in the beginning until the damage occurred causing stiffness degradation of the joints, which were quite different from that of clearance fit joints. The stiffness of the joints obviously increased with interference sizes. The stiffness of interference fit joints was close at the linear elastic stage, and the dis-

In order to understand the failure mechanism of the joints, the typical failure process of composite laminate in the net fit joint was shown in Fig. 7. The fiber compression failure (FV2) was observed to be the first damage mode of the laminate, while the matrix tensile failure (FV3) of 0◦ ply was the final damage mode. The fiber tensile failure (FV1) initiated in the topmost surface (+45◦ ply) during the early stage of loading and then spread downwards

Fig. 6. Failure load and bearing strength curves corresponding to the fitting tolerance.

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Fig. 7. Progressive failure process of the laminate in the net fit joint.

Fig. 8. Damage distribution around the hole under the load of 17.8 KN with different fit sizes.

to the 90◦ ply through the thickness direction. Matrix compression failure (FV4) was the most obvious damage mode and mainly distributed in the upper and lower surface of the laminate in the direction of ±45◦ . The damage of FV2 was mainly concentrated in −45◦ layer and distributed along the tensile direction, while the damage of FV3 was vertical distribution. The displacement of bolted joint at final failure state was about 1.2 mm and FV4 was the main failure mode of the laminate. To investigate the effects of fitting tolerances on the damage mechanism of the joints, the distribution of the damage under the load of 17.8 KN at different fits conditions (I = −2.0%, 0, 0.5%, 1.5%) were shown in Fig. 8. The failure modes included fiber tensile failure, matrix tensile failure, fiber and matrix compression failure. The regions of matrix compression failure were enlarged with the increasing of interference sizes, and a large number of matrix compression failures existed, comparing with other failure types, due to that the matrix strength was much lower than fiber strength. Therefore, matrix compression failure became the main failure mode under quasi-static tensile load. Matrix compression failure region was around the hole and exhibited mainly on the bearing side. As could be seen from the results, the fiber com-

pression failure was obviously occurred in 0◦ ply on the left side of hole and the tensile failure of fiber was mainly concentrated ±45◦ . Compared with other fits conditions, the minimal damage was observed at the interference size of 0.5%. 5. Experimental test 5.1. Quasi-static tensile test 5.1.1. Test details Four sets of fit size were selected for testing so as to verify the accuracy of the simulation results. The quasi-static tensile experiments were conducted in Test Resources 300 series universal test machine, as showed in Fig. 9. Quasi-static tensile tests on protruding head composite bolted joints was according to ASTM (American Society for Testing and Materials) standard D5961/D5961M-13 [24], the specimen was loaded with 1 mm/min until final failure occurred in a bearing failure mode. Delamination is one of the most typical damage mode in the process of composite drilling. In order to prevented drilling delamination in the specimens, a composite laminate was placed under the composite laminates of the specimens before drilling, and then CNC (Computer Numerical


467

Fig. 9. Quasi-static tensile test of specimens.

Control) machining centers was used for drilling by using the Y330 carbide drill, the cutting speed of 34 m/min, and the feed rate of 0.03 mm/rev, and the Ti→CFRP→Ti drilling sequence was also selected [25–27]. Finally the reaming speed of 500 r/min was used for reaming holes. 5.1.2. Results and discussion The load-displacement curves were gained by quasi-static tensile tests, as shown in Fig. 10. In the initial loading stage, due to the same pre-tightening force, the curves under different joining conditions were approximately coincident. Compared with the net fit, clearance fit significantly reduced joint stiffness in the linear elastic loading stage, and the stiffness of the joints were gradually increased with the increase of interference sizes, which can verify the simulation results in Section 4. The typical failure mode of the joints is showed in Fig. 11. The failure of the joint was dominated by the composite laminate, while no obvious failure occurred at the Ti plate and bolt.

Fig. 10. Load-displacement responses of specimens in tests.

For composite laminate, the main damage occurred at the bottom including delamination and splitting, which was probably associated with the drilling process. However, the top surface around the fastener hole was primarily dominated by matrix and fiber compression damage. In the bearing failure area of top surface, a crushed area was observed clearly on the bearing side of the hole, and the unrecoverable elongation deformation of the hole occurred. The size of the join area was almost as the same size as that of the nut in Fig. 11, but the shape of the area was not a perfect circular. This could be due to the surface of the composite laminate not being perfectly flat and non-uniform pre-tightening force distribution around the bolted hole [28]. A comparison of experimental and numerical failure loads was listed in Table 4. It could be seen that only small variation existed within the groups, and the numerical results were in well agreement with the average values of experimental results.

Fig. 11. Typical failure mode of the joint: (a) top surface of composite; (b) bottom surface of composite; (c) Ti plate and bolt.

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Table 4 Comparison of experimental and numerical results. Fitting tolerance (%)

Numerical value

Experimental value

Load (N)

Strength (MPa)

Load (N)

Strength (MPa)

Elative error (%)

−2 0 0.5 0.8

18732.02 18884.8 19771.72 19218.66

1153.2 1162.6 1213.5 1183.2

17953 17982 18974 18306

1105.3 1107.1 1164.6 1127

4.3% 5.0% 4.2% 5.0%

Fig. 13. Fatigue life with different fitting tolerances. Fig. 12. Fatigue test of CFRP/Ti double-lap, single-bolt joint.

5.2. Fatigue test 5.2.1. Test details Interference fit technology is a useful method for the life extension of the joints. In this experiment, MTS 810 electro-hydraulic servo-controlled fatigue testing machine was used to apply tensiletensile alternating load to the bolted joints, the experimental device is shown in Fig. 12. The fatigue life of joints was measured by applying alternating load cycles when the joint failed. During the fatigue test, the displacement of the specimen after the 220–230 cycles is accurate, when the displacement of the specimen is increased by 0.25 mm, it is considered that the specimen is destroyed and the test is terminated. Normally, the fatigue limit of most metal materials is 40–50% of the static strength, while the fatigue limit of the composite material can reach more than 80% of the static strength [29]. According to this conclusion, the fatigue load was set as high as 85% of the static strength, and stress ratio, R = σmin /σmax , equaled 0.1. The article stated that in the cyclic loading process, when the permanent deformation of the hole reached 5% of the aperture value or the cycle number reached to 106 , the join hole was considered to have failed. Due to the poor heat dissipation performance of the composite material, the test piece is easy to generate heat during the test. According to the past experience and the test verification, the test frequency was set as 6 Hz. Taking the fatigue tensile loading of the bolted joint structure as 85%F on the basis of the static loading tensile strength of the bolted structure F = 17.8 KN, four groups of specimens were tested under the same load condition [30]. The sizes of the specimens were the same with those in the static loading experiments. 5.2.2. Results and fatigue enhancement mechanism Similar with the failure of the joints in tensile tests, the failure of the joints was also dominated by the composite in fatigue tests, and the Ti plates and bolts exhibited a strong resistance for

Fig. 14. Comparison of stress amplitude under alternating load.

fatigue loading and the failure didn’t occurred at them. Fatigue test results are shown in Fig. 13. Clearance fit was observed to slightly reduce the fatigue life of the joints compared to net fit. With the interference size of 0.2%, the fatigue life of joints has been considerably improved. Furthermore, the life of bolted joints is greatly improved under the conditions of 0.5% interference fit. The average life span of 0.5% interference fit with respect to the clearance fit, net fit, and 0.2% interference fit increased by 212.9%, 180.7%, 96.1% respectively. The fatigue enhancement mechanism of interference fit can be explained in two ways. One is that interference fit can effectively reduce the local stress amplitude of the bolt hole under cyclical loading. Fig. 14 shows the comparison of the actual maximum tangential stress change between the net fit and interference fit when the external alternating load varies from 0 to P , in which σ1 is the stress amplitude of the net fit, and σ2 is the interference fit with the stress amplitude. It can be indicated that the stress amplitude of interference fit is significantly lower than that of net fit, which delays the initiation of cracks and reduces the crack propagation rate. This means that interference fit can effectively reduce the local stress amplitude of the bolt hole, thereby significantly improving the fatigue life [16]. Another is that interference


469

creased significantly with the increase of fitting tolerances; then in stage II, the strengths reached a saturation and were not sensitive to the increase of fitting tolerances; subsequently, the strengths of the joints increased with the increasing of fitting tolerance again and reached maximum values at the interference size of 0.5% in stage III; finally, the strengths began to decline with the increase of fitting tolerances. 4) Interference fit can effectively increase fatigue life of the joints by reducing the local stress amplitude and stress concentration under fatigue loading. The average fatigue life of the joints at the interference size of 0.5% was 2.13 times as much as that of the joints at the clearance size of −2.0%. Conflict of interest statement Fig. 15. Stress analysis of open-hole plate under different join condition.

fit can reduce the stress concentration of the joints. As shown in Fig. 15, A and B respectively show the stress state of the clearance fit under the condition of no external load and external load; figure C and D respectively indicate the stress state of the interference fit under the condition of no external load and external load. Under the condition of clearance fit, when the structure is subjected to the action of applied loading F , the stress concentration phenomenon will occur at the hole edge. In this condition, the maximum stress σmax appears at the hole edge. Under interference fit join condition, the strain ε F of the structure under the applied load is smaller than the springback εs of the material deformation caused by the interference fit, the stress concentration does not occur. The stress distribution of the hole edge is changed by the combination of the initial stress caused by the interference fit and the mechanical joint, and when the stress ratio of the hole edge is decreased, the bearing capacity and fatigue life can be naturally increased [31]. 6. Conclusions To investigate the effects of clearance and interference sizes on the damage and failure of CFRP/Ti double-lap, single-bolt composite joints, a progressive damage model with the ABAQUS subroutine user-define-field (USDFLD) was established based on three dimensional Hashin failure criterion and Tan degradation rules. The corresponding experimental tests were also conducted to verify the simulation results. The damage model does not require extensive and costly experimental test data for calibration of the damage parameters, which can be considered as an improvement. The damage mechanism of the joints was presented and the optical interference size was also given. This is vital for the optimization of composite structure designs, and can be seen as the contribution of this paper. The following conclusions were obtained: 1) The simulation results demonstrated the ability of the model to investigate the damage and failure of CFRP/Ti single-bolt, double-lap joint under quasi-static tensile loading, which were verified by the corresponding experimental tests with the error of less than 5%. 2) The damage and failure of the joints were dominated by the damage and failure of CFRP. The matrix compression failure was observed to be the main failure mode in the joints under quasi-static tensile load, moreover, the fiber compression failure was mainly occurred in 0◦ ply. Fitting tolerances had an obvious influence on the damage of the joints, and the 0.5% interference fit condition exhibited the minimal damage under the load of 17.8 KN. 3) The strengths of the joints were sensitive to fitting tolerances, and exhibited four main stages: in stage I, the strengths in-

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