A modified failure envelope method for failure prediction of multi-bolt composite joints

Composites Science and Technology 83 (2013) 54–63

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Composites Science and Technology journal homepage: www.elsevier.com/locate/compscitech

A modified failure envelope method for failure prediction of multi-bolt composite joints Fengrui Liu a, Libin Zhao b,⇑, Saqib Mehmood b, Jianyu Zhang a, Binjun Fei a a b

Institute of Solid Mechanics, Beihang University, Beijing 100191, PR China School of Astronautics, Beihang University, Beijing 100191, PR China

a r t i c l e

i n f o

Article history: Received 10 September 2012 Received in revised form 17 April 2013 Accepted 20 April 2013 Available online 3 May 2013 Keywords: A. Structural composites B. Strength C. Stress concentrations E. Welding/joining

a b s t r a c t This paper presents a modified failure envelope to predict final failure mode and strength of multi-bolt composite joints based on the conventional failure envelope method, which was presented by Hart-Smith from abundant strength tests of open hole laminates, double-lap single and multi-bolt joints with quasiisotropic or near-quasi-isotropic lay-ups. In contrast to the bearing ‘‘cutoff’’ of conventional failure envelope method, the modified one takes into account the effect of bypass load on the bearing failure and a new polyline consisted of two oblique lines is proposed. It is able to be established by an additional compressive strength test of laminates and semi-analytical or numerical analysis of fastener-hole laminates and open-hole laminates, combined with the point stress criterion. A flowchart of integration structure failure analysis process with the modified failure envelope method is provided. Series of tests were carried out to provide basic parameters and finite element analysis was conducted for the modified failure envelope. The method proposed was applied to two-bolt and four-bolt carbon-to-carbon double-lap joints with near-quasi-isotropic lay-ups. The predictions of the method proposed and the conventional one were compared with the tests data. The results indicate that the method proposed can obtain effective prediction of failure modes, and more accurate ultimate failure loads in double-lap composite bolted joints. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Fiber reinforced composite materials have attracted increasing and particular interest ranging from aviation and space to automotive and shipbuilding owing to their comparatively high strengthto-weight ratio and stiffness-to-weight ratio. They have been important components in aircraft changing from secondary to primary structures, and are edging out conventional metal materials. Since composite joints are crucial load carrying elements, their stress analysis and design is a key technique for large-scale use of composites on aircraft. Therefore, the design of composite joints, as a difficult and emphasized problem, attracts substantive attention in a series of light, low-cost and efficient composite integration projects [1–6]. Composite joints can be of two types: adhesive bonding and mechanical fastening. Adhesive bonding is an effective method of joints design, which has many advantages, such as high specific stiffness and continuity. But it exhibits disadvantages of unable dismantled and undetectable, which limit its application range. Due to the dramatically reduced reliability resulted from its unde⇑ Corresponding author. Tel./fax: +86 (0)10 8233 9228. E-mail address: [email protected] (L. Zhao). 0266-3538/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compscitech.2013.04.018

tectability, adhesive bonding is barely applied to primary structures. Mechanical fastening techniques using bolts are still widely used as a high load-capable, detectible, repairable and replaceable method to assemble the composite parts that belong to primary structures. As a result of the composites anisotropy and brittleness behaviors and prominent stress concentration phenomena along the fastener hole, mechanical joints are general weak parts in structures. The majority of mechanical joints are multi-bolt joints. A typical failure analysis procedure for the joints in integration structure contains four main parts as follows: (1) The integration structure is analyzed to determine the load circumstance of joints and critical joints. The typical methods are the empirical method and finite element method (FEM) [5,7]. (2) Multi-bolt joints analysis is acted to determine the load distribution and critical hole. The common methods include stiffness method [8], finite element method [9,10], spring-based method [11,12] and complex variable approach [13]. (3) Stress distribution around critical hole under bypass load and bearing load is determined by local detail finite element analysis or analytics solution [14]. Generally, the tensile stress corresponding to the bypass load is obtained by means of open-hole laminates subjected to net-section load, while the bearing stress is provided by fastener-hole laminates under bearing

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F. Liu et al. / Composites Science and Technology 83 (2013) 54–63

load. (4) Strength of critical hole is evaluated with appropriate failure criterion [15–17] by progressive damage method [18–21], characteristic length method [22–27] or failure envelope method [28], etc. The conventional failure envelope method is proposed by HartSmith [28], and has been developed by Crews and Naik [29], Camanho [22,30], Srinivasa [31], et al. It could drastically reduce the time and the cost of tests and has significant value to practical applications. This method assumes that there is a linear interaction relationship between failure strength and elastic isotropic stress concentration factor of hole plate with the same dimensions, which had been found in mass of strength tests of open hole laminates, double-lap single bolt joints and multi-bolt joints with quasi-isotropic or near-quasi-isotropic lay-ups, under tensile load. Follow from the experimental outcomes the failure envelope was proposed by Hart-Smith [28] to predict tensile and bearing failure of double-lap multi-bolt joints with quasi-isotropic or near-quasiisotropic lay-ups. The core of the method, i.e. failure envelope, is collected in ASTM standard [32]. It shows that tensile failure is the result of a combination of bearing and bypass load. However, the bypass load does not affect bearing failure, i.e., with invariant bearing failure load, the change of stress distribution around the critical hole is ignored when an additional bypass load is applied. Thus errors will be caused by losing sight of bypass load influence on bearing failure strength. To overcome such drawbacks, in this paper, the impact of bypass load on bearing failure strength is studied by some quantitative analysis of stress. Bearing strength predicting oblique line is proposed to replace horizontal line. A total of 30 specimens were tested to provide basic parameters and verify the feasibility of the modified method. An additional nonlinear finite element analysis is conducted by ANSYSÒ [33] to determine the modified failure envelope. Better agreement is found between the results of the modified method and the test, than that of the conventional method.

2. Conventional failure envelope

Bearing stress at point A is corresponding to the bearing failure strength of fastener-hole laminates rbru . rbru ¼ F bru =Dt, where D denotes hole diameter, t denotes thickness of the specimens. Net-section stress at point E is related to net-section tensile failure strength of open-hole laminates rnetu . rnetu ¼ F tu =ðW  DÞt, where, W denotes width of specimen. Equation of straight line CE is [28]:

K bc rbr þ K tc rnet ¼ ½rt 

ð1Þ

where rbr denotes bearing stress at the fastener hole of laminates, due to the bearing load F br , and rbr ¼ F br =Dt. rnet represents netsection tensile stress at the open hole of laminates, due to the bypass load F by , and rnet ¼ F by =ðW  DÞt. The tensile failure, as a result of combination of the bypass load and bearing load [28], occurs when load status of critical hole reaches line CE. Thus the slope of straight line CE gCE is obtained from Eq. (1):

gCE ¼ 

K tc K bc

ð2Þ

where K tc = ½rt =rnetu . According to [28], K tc and K bc could be expressed as follows:

K tc ¼ 1 þ C re ðK te  1Þ; K bc ¼

1 þ C re ½K be ðW=D  1Þ  1 W=D  1

where K te and K be are elastic isotropic stress concentration factors with respect to net-section tension and bearing stress, respectively, which can be found in Refs. [34,35]. C re is composite stress concentration relief factor, which is only related to material property, e.g., stacking sequence and material properties of the unidirectional layer but independent of dimensions. It establishes the relationship between the composite stress concentration factors and elastic isotropic stress concentration factor [28]. Thus, if C re is provided, the composite stress concentration factors are available by calculating the isotropic stress concentration factor of a hole plate with the same dimensions as the composite hole laminates. Equation of straight line AC can be written according to the bearing ‘‘cut off’’:

rbr ¼ rbru In the conventional failure envelope presented by Hart-Smith [28], the laminates tensile ultimate strength ½rt , tensile failure load of open-hole laminates F tu and bearing failure load of fastener-hole laminates F bru , should be predetermined from tests. Then two composite stress concentration factors at failure, K tc and K bc , which are correlative with net-section tension stress and bearing stress respectively, can be calculated. Conventional failure envelope which is based on parameters F tu ; F bru , K tc and K bc is shown in Fig. 1.

ð3Þ

ð4Þ

The bearing failure occurs when the load status of critical hole reaches line AC. It is worth noting that that line AC is horizontal, which means that the bypass load is ignored in bearing failure evaluation [28]. A load ratio, which is defined as bearing load divided by bypass load, is introduced to describe the load status of critical hole:

R¼

F br F by

ð5Þ

Eq. (5) can be illustrated in Fig. 1 by a corresponding stress ratio, i.e. the slope from the origin to arbitrary point on the failure envelope.

A

B

C

gO ¼

D

E O

Net-section stress / MPa Fig. 1. Conventional failure envelope.

rbr F br =D ðW  DÞ R ¼ ¼ D rnet F by =ðW  DÞ

ð6Þ

Load ratio/stress ratio represents the essential concept of load status, because there is a one-to-one relationship between arbitrary load status and the point on failure envelope for a joint. The gOA related to point A is infinite, corresponding to the bearing load status of fastener-hole laminates. And gOE with respect to point E is zero, concerning the net-section tensile load status of open-hole laminates. Other points in the failure envelope represent a combination of bearing load and bypass load. In addition, load ratio/stress ratio provides important information about failure modes of critical hole. A critical load ratio RC or stress ratio gOC is a division for the tensile failure and bearing failure mode.

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3. Modified failure envelope To deeply expatiate on the feasibility of the horizontal line AC, point stress criterion [25], which is extensively applied in strength prediction of bolted joints [36,37], was used here. This criterion assumes that failure occurs when the stress over some distance away from the discontinuity is equal to or greater than the strength of unnotched laminates. The point on which stress is equal to the compressive ultimate strength of the unnotched laminates is called compressive characteristic point. At load status corresponding to point A, the compressive characteristic point P can be determined. P (shown in Fig. 2a) is located at the intersection of the two curves, which are symmetrical axes of fastener-hole laminates and equal stress curve. The points on the equal stress curve have same compressive stress, which is equal to ½rc , the compressive strength of unnotched laminates. Keep the bearing load constant and increase the bypass load, which is corresponding to the load case F, as shown in Fig. 2b. Then the compressive stress around the fastener hole decreases as appearance of tensile stress due to the bypass load. Equal stress curve will move toward to fastener hole and away from point P, that means the compressive stress at point P is less than ½rc  and bearing failure does not occur according to the point stress criterion. If loads increase to load status point G with invariant load ratio, equal stress curve would pass P again and bearing failure occurs as shown in Fig. 2c. Thus, the horizontal line AC in Fig. 1 should be developed by an oblique line, as shown in Fig. 3. As described above, load status F is safe. Prolong the length OF to point G, which has the same load ratio with load status F, the bearing failure occurs. Thus the oblique line AG and its prolongation represent the physical bearing failure. Prolong lines AG and CE, an intersection point H is obtained. The formula of the slope of oblique line AH gAH will be deduced next. Because an arbitrary load status acted on the critical hole could be divided into a bearing load component and a bypass load component. At the same time, the stress analysis away from the hole can be an approximate linear problem when the joint contact nonlinearity exists alone. Consequently, the compressive and tensile stress at point P, have the following proportional relationships with the bearing load component and bypass load component, respectively.

rcP / F br ; rtP / F by

ð7Þ

Fig. 3. Modified failure envelope.

According to the point stress criterion, for load status corresponding to point A, the compressive stress at point P, which is resulted from bearing failure load F bru , is equal to the ultimate compressive strength ½rc  of composite laminates.

rcPA ¼ abr rbru ¼ ½rc 

ð9Þ

where the added subscript A represents load status A. The compressive scale factor is determined by abr ¼ ½rc =rbru . For load status H, which is a combination of bearing load and bypass load, superposed compressive stress at P could be obtained as follows

rPH ¼ rcPH  rtPH ¼ abr rbrH  aby rbyH

ð10Þ

Similarly, failure occurs when the stress at point P arrives ½rc . At the same time, from Fig. 3 it can be seen that rbrH ¼ rbru þ Drbr . Then formula (10) can be written as

abr ðrbru þ Drbr Þ  aby rbyH ¼ ½rc 

ð11Þ

Substituting formula (9) into Eq. (11):

abr Drbr  aby rbyH ¼ 0

ð12Þ

Thus, the slope of line AH gAH can be only determined by the nondimensional compressive and tensile scale factors:

gAH ¼

Drbr

rbyH

¼

aby abr

ð13Þ

Take into account rbr ¼ F br =Dt; rnet ¼ F by =ðW  DÞt, and introduce non-dimensional compressive scale factor abr and tensile scale factor aby . Then Eq. (7) could be rewritten as:

A modified failure envelope denoted by polyline AHE, as shown in Fig. 3, is defined by the position A, E and the slopes of line AH and CE. The stress ratio at point H or the slope of line OH could be obtained

rcP ¼ abr rbr ; rtP ¼ aby rnet

gOH ¼

ð8Þ

ð14Þ

Then, the corresponding load ratio at load status H is

equal stress curve

RH ¼ P

rbru ðK tc abr  aby K bc þ abr K bc Þ  aby ½rt  abr ð½rt   K bc rbru Þ

P

P

D g ðW  DÞ OH

ð15Þ

Furthermore, the failure mode could be evaluated by the load ratio/ stress ratio:

Tensile failure : 0 6 R < RH

or 0 6 gO < gOH

Tensile and bearing failure : R ¼ RH

or gO ¼ gOH

Bearing failure : RH < R < 1 or gOH < gO < 1

(a) Load status A (b) Load status F (c) Load status G Fig. 2. Schematic diagram of stress status.

In contrast to the conventional failure envelope, the modified one determines the bearing failure strength according to line AH and judges a tensile failure mode for load status on line CH rather than bearing failure. Thus it can be seen that the modified failure envelope forecasts different bearing strength and failure modes from the conventional one.

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Integration structure Load of multibolt joints

Tensile Properties of laminates

Net-section tensile strength

Kte

Bearing load and bypass load of critical hole Strength of critical hole

Bearing strength

UD elastic properties

Specimen information

Kbe

Cre Ftu

Ktc

Stress analysis Kbc

Strength of integration structure

Compressive properties of laminates

ηAH

Fbru

Modified failure envelope

Fig. 4. Failure analysis procedure of integration structure with modified failure envelope.

(a) Tension test specimen

(b) Compression test specimen

(c) Tension test specimen with open hole (d) Double-lap bolted joint for bearing strength Fig. 5. Configuration of specimens.

The analysis procedure to predict ultimate failure of integration structure with modified failure envelope is schematically showed in Fig. 4. The material parameters determined by standard test methods are showed in dot line frame in the upper right corner. Five parameters which determine modified failure envelope are showed in dot line frame in the lower right corner. Parameters K te ; K be can be found in common stress concentration factor handbook. Based on the basic parameters of conventional failure envelope, an additional compressive strength test of unnotched laminates and stress analysis procedure in dash line frame is proposed to determine the modified failure envelope. 4. Validation The accuracy of the proposed methodology is assessed by comparing the predictions with experimental data. A test plan for the generation of materials parameters to determinate failure

envelope and experimental data to compare with the numerical predictions determined by conventional and modified methods were made. 4.1. Failure envelope 4.1.1. Specimen preparation and test Specimens were made of CYCOM X850-35-12KIM+-190 carbon/ epoxy laminates with near-quasi-isotropic stacking sequence [45/ 0/45/0/90/0/45/0/45/0]s. The lamina thickness is 0.185 mm. The material properties are provided by material producer: E1 = 195 GPa, E2 = 8.58 GPa, G12 = 4.57 GPa, m12 = 0.33. Five materials parameters to fix failure envelope need to be achieved by tests as shown in Fig. 4. Four group of tests, tensile properties of laminates, compressive properties of laminates, open-hole tensile strength of laminates, bearing strength of fastener-hole laminates, were as per ASTM specification ASTM D

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Table 1 Dimensions of the specimens (Unit: mm). Dimension

Tension

Compression

Open hole tension

Bearing

a c t b s d e

250 56 3.7 25 – – –

145 65 3.7 25 – – –

300 40 3.7 30 15 4.76 –

150 70 3.7 30 15 4.76 15

25

No.1 No.2 No.3 No.4 No.5

M

Load / kN

20

15

N

10

5

0 0

1

2

3

4

5

6

Displacement / mm Fig. 6. Load–displacement curves for bearing failure.

inspection technique. Only specimens without defect were selected for the test, size of which were measured and recorded. An INSTRON-8803 hydraulic pressure servo material testing machine with the range of 250 kN was used for the test. The load was applied under the stroke control at a rate of 1 mm/min. During the loading process, load–displacement curves were directly recorded from the machine. Other test variations were as per ASTM specification. Five load–displacement curves for bearing strength tests are shown in Fig. 6. An oblique line MN is supposed, on the left of which load–displacement curves increased greatly, and on the right of which load–displacement curves fluctuated creeping up. Accordingly it can be surmised that on the left of line MN load starts from free, displacements are linear with loads. The elasticity deformation is produced only and bearing failure does not occur possibly or seldom occur. On the right of line MN substantially unchanged load and significantly increased displacement appear in the extending procedure of bearing damage. Fluctuations means bearing damage load is unsteady, and difference trends among five curves imply no regularity, so an obvious definition of bearing strength is quite difficult to obtain. Engineering definition is load of a certain degree bearing damage, such 2% or 4% deformations of hole diameter, but all of the deformations measurement methods are indirect, including ASTM specification [32]. Since the loads altered little on the right of line MN and the maximal load is easy to be measured and can present the bearing load capacity [42], bearing strength is defined by the maximal load. Fig. 7 shows a graphic representation of bearing failure hole after test, through-the-thickness shear cracks region [43] and outer ply delamination with mark a, b and c respectively. It can be inferred that through-the-thickness shear cracks and inter/outer ply delamination were caused by bearing failure and led to ultimate failure. The laminate tensile ultimate strength, the laminate compressive ultimate strength, open-hole tensile strength of laminates and the bearing failure strength are given in Table 2. 4.1.2. Conventional failure envelope Table 3 shows parameters for conventional failure envelope, which are calculated as to the analysis procedure in conventional failure envelope method. The load ratio or stress ratio, which is a symbol to distinguish failure mode, is also listed in Table 3.

Fig. 7. Bearing failure pattern of laminate with hole.

3039/D 3039M-00 [38], D 3410/D 3410M-03 [39], ASTM D 5766/D 5766M-02a [40] and ASTM D 5961/D 5961M-01 [41] respectively. Each group contains five specimens. Configuration of specimens is shown in Fig. 5. The dimensional values of the specimens are listed in Table 1. In Table 1d is hole-diameter of joints whose center is expressed with ‘+’ in Fig. 5d. The bolts used here are aerospace grade fasteners of a protruding head configuration HST12-6-7. All laminates were fabricated from unidirectional prepregs and cured in an autoclave over 200 °C in vacuum, the work volume of which is 0.5 m  0.5 m  0.5 m. Laminates and tab were stuck with EC2216 adhesive after eliminating filth. Manufactured composite panels were cut to size and drilled with high-precision machine tools. Before testing, all specimens were examined for internal damage due to manufacturing and machining by nondestructive

4.1.3. Modified failure envelope The compressive characteristic point and the stress distribution of open-hole laminates under net-section tensile load are necessary for the modified failure envelope. An orthogonal anisotropic stress analysis was conducted firstly to calculate the compressive characteristic length. In-plane elastic properties of orthogonal anisotropic laminates, which are related to stacking sequence and material properties of the unidirectional layer, were calculated with classical laminates theory as follows: EL1 ¼ 112:34 GPa, EL2 ¼ 43:17 GPa, mL12 ¼ 0:45, GL12 ¼ 22:63 GPa . A finite element model of the laminate containing an open hole and pin was modeled by the SOLID185 element, which is used for 3-D modeling of solid structures. It is defined by eight nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions in ANSYSÒ [33]. It also provides the contact element for the interface between the laminate and the pin. Nonlinear contact analysis was performed for the pin case to consider the change of the contact surface during deformation. For better results the mesh of finite elements near the hole was carefully divided into radial pattern as shown in Fig. 8. The constraint of displacements was imposed on Section C and a bearing load was applied on the Section A. A contact nonlinear analysis was carried out for this pin case model to determine the compress characteristic length. While an open hole laminates model by

F. Liu et al. / Composites Science and Technology 83 (2013) 54–63

59

Table 2 Failure loads of specimens. Type

Mean failure load (kN)

Coefficient of variation, Cv (%)

Mean failure strength (MPa)

Tension Compression Open-hole tension Bearing

141.56 66.52 90.90 20.59

9.51 8.18 3.15 5.58

1530 719 973 1169

Where C v ¼ sn1 = x.

on point P of 48 MPa, as shown in Fig. 9b. Thus, using Eq. (13), the slope of the oblique line AH could be obtained:

Table 3 Parameters for conventional failure envelope. Bearing failure strength (MPa)

Net-section tensile failure strength (MPa)

Ktc

Cre

Kbc

RC =gOC

1169

973

1.57

0.34

0.54

0.39/ 2.07

deleting the pin was used to calculate the stress distribution under net-section load. For this case the displacement of Section B was constrained and a net-section tensile load was acted on Section A. And a linear finite element analysis was executed since the pin was deleted. Compressive stress contour is shown in Fig. 9a with bearing load F bru , from which the characteristic length is 1.54 mm, determined by ½rc . Then the location of point P is determined. Moreover, the finite element model was subjected to an arbitrary netsection loads, 200 MPa is set here, which resulted in tensile stress

gAH ¼ ð48=200Þ=½719=1169 ¼ 0:39: Then the modified failure envelope A–H–E could be determined only by the slope of line AH, point A, E and the slope of line CE, as shown in Fig. 10. The stress ratio and the load ratio at point H is 2.70 and 0.51 using Eqs. (14) and (15), respectively. Conventional failure envelope A–C–E is simultaneously given with dash line in Fig. 10. From Fig. 10, it can be seen that the modified method forecasts a higher bearing strength than the conventional method dose when the load ratio is greater than RH , for which case the differences between the conventional and modified method increases as load ratio decreases. Moreover, it predicts a tensile failure mode and tensile strength which is obviously different from the conventional one does when the load ratio is less than RH and greater than RC . The validity of the modified method will be discussed in the following subsection.

Fig. 8. Finite element model.

(a) Compressive characteristic point P

(b) Stress with rbitrary tensile load 200MPa

Fig. 9. Compressive characteristic point P and stress contours.

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1400

A

1200

Bearing stress / MPa

determined and the corresponding coefficient is marked by a superscript ‘‘’’. Further the load/stress ratio of critical hole can be calculated. Two rays with slope of 5.76 and 2.60 corresponding to two-bolt joints and four-bolt joints, respectively, are plotted passing the origin of the coordinate as shown in Fig. 12. The former intersects conventional and modified failure envelope at W and X respectively. Due to the slope is greater than gOH , bearing failure mode is predicted for both methods. The ordinates of point W and X are corresponding to the bearing failure loads of critical hole given by conventional and modified method respectively. For the latter one, two intersection points Y and Z are obtained. A bearing failure mode is predicted by the conventional method but a tensile failure mode is forecasted by the new one. The ordinate of point Y and the abscissa of point Z represent the bearing failure strength and tensile strength predicted by the conventional and modified method, respectively.

H C

1000 800 600 400 200

E

0

O0

200

400

600

800

1000

Net-section stress / MPa Fig. 10. Conventional and modified failure envelope.

4.2. Numerical predictions and experiments of multi-bolt joints 4.2.1. Specimens and failure prediction Two-bolt and four-bolt carbon-to-carbon double-lap joints with the same composite materials and near-quasi-isotropic lay-ups as the specimens discussed in Section 4.1 were tested to validate the modified method. Configurations and dimensions of specimens are shown in Fig. 11. Values of specimens’ dimensions are as follows: a = 203 mm for Fig. 11a, and a = 255 mm for Fig. 11b, c = 65 mm, t = 3.7 mm, b = 30 mm, s = 15 mm, d = 4.76 mm, e = 15 mm, p = 20 mm. The manufacturing process for joints is as described forenamed. Because of the relatively brittle behavior of composites, there is little stress relief around fastener holes due to plastic deformation. Thus multiple bolts may share the load unequally. There are different methods for determining load distribution in bolted joints. Although recently the finite element analysis could provide comparatively accurate solution of load distribution, it requires long computing time. Thus, a simpler stiffness method [8], which is well suited for industrial usage, is used here. Load distributions for two joints are listed in Table 4, from which the critical hole is

t

a

c

t a

t

c

1 45°

t a

t

c

s

p

1

90°

b

45°

s

0°

e

a

c

t

s

2

90°

b

4.2.2. Experimental verification An INSTRON-8803 hydraulic pressure servo material testing machine with the range of 250 kN was used to test the static strength of bolted joints. The load was applied on the specimen at a rate of 1 mm/min until the collapse failure arrives. Bearing failure mode could be observed from all of the five doublelap two-bolt joints. However, net-section tensile failure mode was expressed by all of five double-lap four-bolt joints. Typical failure patterns for these two group specimens are shown in Fig. 13, from which a more severe bearing area could be observed near the first fastener hole for two-bolt joints, and through-the-thickness shear cracks region and outer ply delamination on bearing side of both holes were apparent. Laminate tensile failure across the first fastener hole, which resulted in the final collapse, occurred with very slender bearing failure of the other holes for four-bolt joints. The failure loads and corresponding strength are listed in Table 5. Based on the conventional failure envelope method [28] and the modified one, the failure strength and mode of critical hole of the multi-bolt joint could be obtained. Furthermore, the failure load of multi-bolt joint could be calculated by utilizing predicted failure strength, load acting area and load distributions coefficient (which

2

3

4

p p p

s

0°

e

e

(a) Double-lap two-bolt joint

e

(b) Double-lap four-bolt joint

Fig. 11. Configuration and geometry of specimens.

Table 4 Load distributions for two double-lap multi-bolt joints. Specimen Two-bolt joint Four-bolt joint a

The critical hole.

Fastener 1 a

0.52 0.33a

Fastener 2

Fastener 3

Fastener 4

Load/stress ratio

0.48 0.23

– 0.21

– 0.23

1.09/5.76 0.49/2.60

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1400 1254

Z X W

Bearing stress / MPa

1200

Y

1000 1169 800 600 400 200 519 0 0

200

400

600

800

1000

Net-section stress / MPa Fig. 12. Failure loads and failure mode.

is listed in Table 4) of critical hole. The failure loads and failure modes of multi-bolt joints and failure strength of critical holes determined by conventional and modified method are compared

(a) Typical bearing failure mode

with experimental data, as listed in Table 6. The upper script ‘‘b’’ denotes bearing failure mode, ‘‘t’’ denotes tensile failure mode and ‘‘w’’ denotes the prediction with a wrong failure mode. From Table 6, it can be seen that same bearing failure modes were detected for the two-bolt joint and four-bolt joint with the conventional method. Due to the ‘‘cut off’’ in the conventional method, same failure strengths (1169 MPa) of critical hole were predicted for two joints, which could be observed directly from points W and Y in Fig. 12. However, using the modified method, a bearing failure mode with the strength 1254 MPa and a tensile failure mode with the strength 519 MPa were detected for the two-bolt joint and four-bolt joint, respectively. Furthermore, for the two-bolt joints, the conventional and modified method give the same failure modes and different failure loads with the error 6.95% for conventional method, and 0.19% for modified method, respectively. The results in the table confirm that the modified method shows a better agreement with the test results than the conventional method does. For the four-bolt joints, the corresponding load ratio of the critical hole is greater than RC and less than RH, thus a tensile failure mode is predicted in accordance with the test phenomenon. The prediction error is only 1.91%. However, conventional method gives a completely different

(b) Typical net-section tensile failure mode

Fig. 13. Failure patterns for two multi-bolt joints.

Table 5 Tested failure loads and modes of multi-bolt joints. Double-lap two-bolt joints

Double-lap four-bolt joints

Failure load (kN) No. No. No. No. No.

1 2 3 4 5

41.36 43.28 42.52 43.60 41.72

Mean failure load (kN)

Failure load (kN)

42.50 Coefficient of variation (%) 2.27 Failure mode Bearing

No. No. No. No. No.

1 2 3 4 5

Mean failure load (kN) 70.10 72.83 71.68 71.00 68.84

70.89 Coefficient of variation (%) 2.14 Failure mode Tensile

Table 6 Failure loads and failure mode of joints. Joints

Twobolt Fourbolt

Tested mean failure load (kN)

Conventional method [28]

Modified method

Failure strength of critical hole (MPa)

Failure load of joint (kN)

Error (%)

Failure strength of critical hole (MPa)

Failure load of joint (kN)

Error (%)

42.50⁄b

1169⁄b

39.55⁄b

6.95

1254⁄b

42.42⁄b

0.19

70.89⁄t

1169⁄b

62.56⁄b

11.75⁄w

519⁄t

72.24⁄t

1.91

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failure mode and further leads to a useless strength result. This is particularly dangerous to engineer because a bearing failure which occurs slowly over time is the safest failure modes expected by designers. Joint designed to occur bearing failure according to the conventional failure envelope will fail in tensile failure, which brings safety trouble. 5. Conclusions

[3]

[4]

[5] [6]

A modified failure envelope consisting of two oblique lines corresponding to tensile envelope and bearing envelope respectively, is proposed to predict failure mode and strength for multi-bolt composite joints. Theory deduction and implement method of improved bearing envelope accounting for the influence of bypass load are presented. Design charts for the modified failure envelope method and its further application in failure predictions of integrated structure are illustrated. A modified failure envelope for CYCOM X850-35-12KIM+-190 graphite/epoxy double-lap composite laminates with near-quasi-isotropic stacking sequence [45/0/ 45/0/90/0/45/0/45/0]s and specific dimensions is plotted. It could be concluded that: (1) in cases where load ratio is greater than the critical one of the modified failure envelope, same bearing failure mode could be predicted by the proposed and conventional methods. Moreover, the proposed method is observed to predict higher bearing strength up to almost 18.5% in comparison with the conventional method. (2) For cases where load ratio is equal to the critical one of the modified failure envelope, a simultaneous tensile and bearing failure mode could be prognosticated by the proposed method and the corresponding tensile failure strength and bearing failure strength could be afforded. (3) For cases where load ratio is less than the critical load ratio of the modified failure envelope but more than that of the conventional one, tensile failure mode and corresponding tensile failure strength will be forecasted by the proposed method. However, bearing failure mode and bearing failure strength is likely to be predicted by the conventional one. (4) When the load ratio is less than the critical one corresponding to conventional failure envelope, same tensile failure mode and tensile failure strength can be obtained by the proposed method and the conventional one. Failure prediction of two-bolted and four-bolted carbon-to-carbon double-lap joints by the modified and conventional failure envelope method was compared with the experimental results. The load ratios of these two problems were observed to be in accordance with the first case and the third case described above, respectively. The results indicate that the proposed method can be used to make effective predictions of failure modes, and more accurate ultimate failure loads for double-lap multi-bolted composite joints. A particular risk to structural integrity has also been observed if a joint is designed to collapse with the safest bearing failure mode by means of the conventional method, however risk of failure under tensile mode, and is expected to be reduced by the proposed method.

[7] [8] [9]

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[19]

[20]

[21] [22]

[23] [24] [25] [26] [27] [28] [29] [30]

Acknowledgements

[31]

The research work is supported by the National High Technology Research and Development Program of China (2012AA040209) and the National Science Foundation of China (10902004).

[32]

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