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Experimental and numerical failure analysis of pinned-joints in composite materials
Composite Structures 89 (2009) 459–466
Contents lists available at ScienceDirect
Composite Structures journal homepage: www.elsevier.com/locate/compstruct
Experimental and numerical failure analysis of pinned-joints in composite materials b,1 _ Alaattin Aktasß a,*, Hüseyin Imrek , Yusuf Cunediog˘lu c,2 a b c
Usßak University, Faculty of Engineering, Department of Mechanical Engineering, Usßak, Turkey Selçuk University, Faculty of Engineering, Department of Mechanical Engineering, Konya, Turkey Nig˘de University, Faculty of Engineering, Department of Mechanical Engineering, Nig˘de, Turkey
a r t i c l e
i n f o
Article history: Available online 1 November 2008 Keywords: Parallel pinned-joint Failure load Glass-epoxy Yamada-Sun criterion
a b s t r a c t In this paper, failure load and failure mode of glass-epoxy composite plates with single and double parallel pinned-joints have analysed experimentally and numerically. Two variables were investigated during analyses; the distance from the free edge of plate to the diameter of the first hole (E/D) ratio (2, 3, 4, 5), and the width of the specimen to the diameter of the holes (W/D) ratios (2, 3, 4, 5). Experiments were carried out according to the ASTM D953-D [ASTM D 953-D, Standard test method for bearing strength of plastics, ASTM designation. p. 342–6.]. The numerical study was performed by means of ANSYS finite element analysis program. Yamada-Sun failure criterion was used for failure analyses. Mechanical properties of the composite material were obtained according to ASTM standards. The results showed that the pin hole farthest from the free edge is subjected to the highest stress. A good agreement was obtained between experimental results and numerical predictions. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Fibre reinforced composite materials have been gaining wide application in aircraft submarine and spacecraft constructions. These applications require joining composites either to composites or to metals. Most commonly, joints are formed using mechanical fasteners. Therefore, suitable revealing methods for the failure strength would help in selecting the appropriate joint size in a given application. Joints present potential problem regions to the designers due to stress concentrations, and therefore, the strength of such a structure is dependent on the strength of its joints. This aspect of pinned-joints has attracted attention from many composite researchers. Among them, Aktas and Dirikolu [2] have studied the effect of stacking sequence of carbon-epoxy composite laminates, with [0°/45°/45°/90°]S, and [90°/45°/45°/0°]S configuration, on pinned-joint. They found, for both configurations, that the bearing strength reaches their maximum value at W/D = 4 and E/D = 4 geometric configuration. Karakuzu et al. [3] have investigated failure mode, failure load and bearing strength in a laminated woven glass-vinylester composite plate with two parallel circular holes which are subjected to traction forces by two parallel rigid pins. They have been observed the behavior of pin loaded
* Corresponding author. Tel.: +90 276 2634195/215; fax: +90 276 2634196. E-mail addresses: [email protected] (A. Aktasß), [email protected] _ (H. Imrek), [email protected] (Y. Cunediog˘lu). 1 Tel.: +90 332 2233457; fax: +90 332 2410041. 2 Tel.: +90 388 2252303; fax: +90 388 2250112. 0263-8223/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2008.09.009
composite plates with various dimensions experimentally and numerically. They have used LUSAS FEM program. This program does not give the good results for composite material because this program was developed for civil engineering applications. Sheng et al. [4] have experimentally studied the pinned-joint for various stacking sequences of a T80011/3900-2 carbon-epoxy composite laminate and determined the maximum bearing strength and the failure mode. Okutan et al. [5] have studied the bearing strength of pin loaded Kevlar-epoxy laminates experimentally. Shokrieh and Lessard [6] have developed a three-dimensional nonlinear finite element code to analyze the effects of material nonlinearity and edge effects on the state of stress and failure prediction near the stress concentrations of a pin-loaded graphite-epoxy laminated composite plate. Dano et al. [7] have discussed influence of failure criteria and the inclusion of geometric and shear non-linearity. Ahn et al. [8] have performed a nonlinear finite element analysis to considerate the contact and friction between the pin and the laminate for unidirectional and woven composite laminated joints of an aircraft control rod. Pierron et al. [9] have studied the behavior of woven glass fiber epoxy pin joints both numerically and experimentally, with particular attention given to the sensitivity of the model to different parameters such as clearance, friction, and material nonlinearity. In this study, the effects of E/D and W/D ratios on failure mode and failure load are investigated in the laminated woven glass fiber composite plate with single and double parallel circular holes. The behavior of pin loaded composite plates has been observed experimentally and numerically with various dimensions. The numerical study was performed by assistance of ANSYS commercial software.
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Yamada-Sun failure criteria are used to obtain failure load and mode of the laminated plates. 2. Problem description
S: Shear-out plane
In this study, two types of pin joint plates are analyzed. One has single and the other has two parallel holes as shown in Fig. 1a and b, respectively. The specimen with single hole of diameter D is located along the centerline of the plate (Fig. 1a). The center of the hole is located a distance E from one end. A uniform tensile load P is then applied to the plate, and this load is resisted by a rigid pin. The load is parallel to the plate and is symmetric with respect to the centerline. The specimens are of two parallel holes, which are located a distance E from one free edge and W/2 from the other. The distance between the two parallel holes is taken 24 mm so that the failure mode gives the bearing mode. Since this mode gives the highest strength in pinned-joint uses. Then uniform tensile load P is then applied to the plate with the procedure of the single hole case. In general, there are three basic pinned-joint failure modes related to composites: These are net tension, shear-out, and bearing. Combination of these, i.e., mixed modes, may also appear as shown in Fig. 2. Net tension occurs catastrophically and presents the least strength. Designers are required to obtain the optimum E/D and W/ D ratios to get the bearing mode, which shows the highest strength in pinned-joint uses. The behavior of the joint could be influenced by four groups of parameters [10]. Material parameters: Fibre types and form, resin type, fibre orientation, laminate stacking sequence, etc. Geometry parameters: Specimen width, W, or ratio of width to hole diameter, W/D, edge distance, E, or ratio of the edge distance to hole diameter E/D, specimen thickness, t, etc. Fastener parameters: Fastener type, clamping area, hole size. Design parameters: Loading type, loading direction, failure criteria. Clearly, there are many variables involved in practical joints; therefore, complete characterization of joints is highly dependent on the hole geometry of the connection, including the edge distance, and the width.
P W
D
Dimensions in mm 100
E
a) Single hole
) D
P 24
b) Serial
D
Dimensions in mm 100
E
)
W/2
N: Net tension plane B: Bearing plane
N
N-S: Mixed planes
S N
B S
Fig. 2. Three basic failure planes for pinned-joints.
3. Specimen preparation and testing procedure Woven prepreg glass-epoxy composite blanks with thickness of 3.14 mm, EP GC 203, were obtained from Izoreel Co. Turkey. 3.1. Specimen preparation Woven glass-epoxy composite blanks are cut into rectangle shapes with a water-cooled diamond-tipped rotary wheel for two types of testing. All cut edges were finished using a fine silicon carbide paper to remove any edge defects. The holes, typical in size of fasteners used in many airframe assemblies, were drilled using by a modified high-speed steel drilling tool with three sharp contact points to prevent fuzzy edges [2]. In this way, a 6.5 mm diameter holes is obtained on the specimens (Fig. 1). Specimens for each type were produced in the following manner: While keeping the E/D ratio as 4, the W/D ratio is varied as 2, 3, 4, and 5; and maintaining W/D as 4, E/D is changed as 2, 3, 4, and 5. Three specimens are prepared for each configuration. To find the values of the longitudinal modulus, E1, the Poisson’s ratio, v12, and the longitudinal tensile strength, Xt, a flat piece of woven plate, the principal axis of which coincides with the loading direction, was taken, and two strain gauges perpendicular to each other were stuck on. One of them was on principal and the other was on transverse direction. The specimen was loaded step by step to rupture by means of a 50 kN loading capacity testing machine at a speed of 1.5 mm/ min, and for all steps e1 and e2 were measured by an indicator. The same procedure has been performed for the determination of transverse modulus, E2, and the transverse tensile strength, Yt. To define the respective longitudinal and transverse compressive strengths, Xc and Yc, a flat piece of woven plate, the principal axis of which coincides with the loading direction was taken, and it was subjected to compressive loading up to failure. To obtain the shear modulus, G12; a plate whose principal axis was on 45° was taken. Then, a strain gauge was stuck along the loading direction. The specimen was loaded step by step up to rupture, and G12 was calculated by measurement of ex, which is the strain in the tensile direction [10]. To obtain the rail-shear strength, S, a series of specimens were tested. These tests were performed by placing the shear fixture into the testing machine and by applying compressive load. The rail-shear strength is obtained by dividing the
b) Double parallel holes t
Fig. 1. The geometry of the single and double pinned-joints.
P
Table 1 Mechanical properties of the glass-epoxy composite plate. E1 = E2 (GPa)
G12 (GPa)
m12
Xt = Yt (MPa)
Xc = Yc (MPa)
S (MPa)
Fiber (%)
Rot (mm)
Roc (mm)
20
7.54
0.18
320
550
55
60
1.11
0.83
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ultimate failure load of the laminate by the sheared cross section. The mechanical properties of the composite laminate determined in this manner are given in Table 1. 3.2. Testing procedures The tests were conducted with reference to ASTM D953-D [1] at room temperature of 20 °C. One for single hole and two for parallel holes through-hardening steels, 42CrMo4, hardened (by heating at 850 °C for 2 h and then quenched in oil at room temperature) and polished pins were later inserted in the holes without clearance. Then, experiments were performed by means of custom fixtures on the 50 kN loading capacity universal machine with a speed of 1.5 mm/min.
The dimensions of the thickness, t was chosen as 3 mm and E, W were 26 mm so that the failure mode gives the bearing mode. Since this mode gives the highest strength in pinned-joint uses. The failure load (Pfailure) was measured by the bearing failure test. The point stress criterion was applied to the results of the bearing failure test and the ‘‘characteristic length for compression” was obtained as shown in Fig. 3c. In this criterion, failure occurs when the compressive stress in the load direction equaled bearing strength (rb) at some distance from the arc edge. In this study, the compressive stress distribution at Pfailure was calculated by using finite element method (FEM) and Roc was obtained from those results and given in Table 1. 5. Numerical study
4. Characteristic lengths
5.1. Failure criterion
4.1. Characteristic length for tension (Rot)
In order to determine the failure loads and the failure modes, a failure criterion must be applied. In this investigation, the YamadaSun failure criterion is used. This criterion is quadratic theory. Involving the shear stress s12 and the longitudinal stress r1 along the fibers, and the following criterion for laminate failure is proposed.
In this study, the characteristic length for tension was determined by applying the point stress criterion to the tensile specimen with a hole. This criterion has been suggested by Whitney and Nuismer [11]. Fig. 3a shows the description of the point stress criterion. In this criterion, failure has been said to occur when the tensile stress (ry) in the load direction is equal to unnotched laminate strength (r0) at some distance (Rot) from the edge of the hole. Rot has been called characteristic length for tension and find in the procedure reference [10] and given in Table 1.
4.2. Characteristic length for compression (Roc)
Tensile Stress (σy)
In order to find the characteristic length for compression (Roc), bearing failure test was used. Fig. 3b shows the schematic diagram of the bearing failure test. The specimen containing a machined half circle, 6.5 mm diameter, is at the center. The bearing failure test was applied by the hardened steel jig, 6.5 mm diameter. The bearing failure test was conducted at cross head speed 1.5 mm/min.
r 2 1
X
þ
s 2 12
S
¼ e2
e 1 Failure e 1 no failure
ð1Þ
where r1 is the longitudinal stress along the fibers; X is longitudinal tensile strength of ply; s12 is shear stress along the fibers; S is the rail-shear strength. The failure criterion (Eq. (1)) only predicts whether the pin joint failed or not. It does not predict the failure mode. To obtain the failure mode the characteristic curve must be drawn. This curve is specified by Eq. (2).
Rc ðhÞ ¼ D=2 þ ROT þ ðROC ROT Þ cos h
ð2Þ
Fig. 4 shows the description of the characteristic curve. Failure occurs when e is equal to unity at any point on the characteristic curve. The calculation procedure described above also provides
Compressive Stress (σy) R0C Bearing strength (σb)
Tensile Strength (σ0)
R Distance from hole edge
Rot
(a)
(C) P
S ecimen
(b) Fig. 3. Description of point stress criterion.
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(c) The stresses (rx, ry and sxy) are calculated using the finite element method. (d) If e equals or exceeds unity in any ply along the characteristic curve, the joint is decided to have failed.
y Characteristic Curve
θfail
The procedure outlined above is used to numerically predict whether or not failure occurs under a given load, P. The calculated stresses are linearly proportional to the applied load (see Fig. 6). A relationship is employed to determine the maximum load (Pmax), which can be imposed on the joint. For a given load P, values of e are calculated on the characteristic curve as discussed above. The highest value of e (e0) is determined, and the maximum load is calculated by the expression:
ROC
x
D ROt
Pmax ¼ Fig. 4. Description of the characteristic curve for double parallel holes.
: Bearing failure
30 < hf < 60
: Shear-out failure
75 < hf < 90
: Net tension failure
ð4Þ
In order to find the failure mode the criterion of Eq. (3) used. The procedure outlined above is shown as a chart in Fig. 8.
the location (angle hfail showing in Fig. 4) at which e is equal to unity on the characteristic curve. A knowledge of hfail provides an estimate of the failure mode of failure, as follows [12],
0 < hf < 15
P e0
ð3Þ
At intermediate values of hfail, failure may be caused by combination of these modes. 5.2. Finite element analysis AnsysTM finite element package has been used in the numerical analyses. Whether or not a joint fails under a given condition is determined by the finite element analysis as follows: (a) The geometry of the problem is modeled for single and double holes using SHELL91 elements with the characteristic curve. The composite plates were modeled as a half model because of the symmetry of loading, geometry and material with respect to x-axis the displacements of the symmetry surface are zero in y direction (Fig. 4). A typical FEM mesh and its boundary condition for double parallel joints are given in Fig. 5. (b) To simulate the rigid pin, radial displacement constraints were used on the right hand sides of the hole. The load was applied to the nodes of the laminate positioned left hand side of the model (Fig. 5).
6. Results and discussions The failure loads and failure modes of composite specimens with single and double parallel holes which are subjected to reaction force by two rigid pins are investigated experimentally and numerically. In order to obtain the optimum geometry for two cases, the ratio of the edge distance to the pin diameter (E/D), and the ratio of the specimen width to the pin diameter (W/D) have systematically been varied during analyses. Custom made fixtures on a testing machine and AnsysTM finite element package has, respectively been used for pinned-joint experiments and numerical solutions. Three tests were conducted for each type of specimen and average bearing load values were calculated. 6.1. Bearing load The bearing loads with respect to E/D (W/D = 4 is constant) for single and double pinned-joints are shown in Fig. 7. In this figure, the double failure loads divided by 2 so that the failure loads of the single and double pins can be compared. When E/D is equal to 2 and 4, the failure loads takes its minimum and maximum value, respectively for two cases and both experimentally and numerically. The results from both analyses show the same trends. An interesting result is that the failure loads of parallel pins are less than single one. It is clear that there is a good agreement between numerical and experimental results. The bearing loads with respect to W/D (E/D = 4 is constant) for single and double pinned-joints are shown in Fig. 8. In this figure,
Fig. 5. A typical FEM mesh and its boundary condition in double parallel joints.
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A. Aktasß et al. / Composite Structures 89 (2009) 459–466
Bearing Failure test
FEM Stress Analysis
Tensile test with A hole Point Stress Criterion
Point Stress Criterion
Stress Distribution in each ply Characteristic Length for tension Rot
Characteristic Length for compressive R oc
Yamada-Sun Criterion + Characteristic Curve
y Characteristic Curve
ROC
x D
ROt
Prediction of joint failure load &failure mode Fig. 6. Flow chart for failure load and failure mode procedure.
4500
4000
Pb [N]
3500
3000 Parallel Exp. 2500
Single Exp. Single FEM Parallel FEM
2000
1500 1
2
3
4
5
6
E/D Fig. 7. The effect of E/D ratio on failure load for single and double pinned-joints.
the failure loads of double holes also divided by 2 for comparison. When W/D is equal to 2 and 4, the failure loads takes its minimum and maximum value, respectively for two cases and both experimentally and numerically. The result of this figure is nearly the same with Fig. 7. In two figures the maximum failure loads are reached at E/D = 4 and W/D = 4, and greater than these points.
6.2. Failure mode In case double holes in parallel; Fig. 9 shows some photographs and FEM results of the double holes failed specimens with different failure modes. In these figures, failure modes are bearing mode, which shows the highest strength for E/D P 4 and W/D P 4, net tension, which shows least strength for W/D/2 (E/D = 4), and mixed
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4500 4000 3500
Pb [N]
3000 2500 Parallel Exp.
2000
Single Exp. Single FEM
1500
Parallel FEM 1000 500 1
2
3
4
5
W/D Fig. 8. The effect of W/D ratio on failure load for single and double pinned-joints.
Fig. 9. FEM and experimental results of failed specimens for double pinned-joints.
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465
Fig. 10. FEM and experimental results of failed specimens for single pinned-joints.
mode in Fig. 9a–c, respectively. The other configuration of E/D and W/D give bearing mode. In case single hole; Fig. 10 show some FEM and experimental results of single hole failed specimens with different failure modes. When W/D = 2, E/D = 4 and E/D = 2, W/D = 4 failure modes give net tension and mixed-mode, respectively. Expect from these geometrical configurations, failure mode gives bearing mode. It can be seen from the Figs. 9 and 10 that failure modes obtained from the experimental and numerical results are very close.
Failure modes give net tension and mixed-mode when W/D = 2 (E/D = 4) and E/D = 2 (W/D = 4) but other geometrical configurations give bearing mode. In the case of a double hole Minimum bearing load is obtained W/D = 2 (E/D is constant) and E/D = 2 (W/D is constant). Maximum bearing load is obtained at E/D P 4 and W/D P 4. Failure modes give shear-out and net tension at E/D = 2 (W/ D = 4) and W/D = 2 (E/D = 4), respectively.
7. Conclusions References In present paper, failure strength and failure mode of glassepoxy composite plates with single and double parallel pinnedjoints has analysed experimentally and numerically. Two variables were investigated during analyses; the distance from the free edge of plate to the diameter of the first hole (E/D) ratio (2, 3, 4, 5), and the width of the specimen to the diameter of the holes (W/D) ratios (2, 3, 4, 5). Experiments were carried out according to the ASTM D953-D [1]. The numerical study was performed by means of ANSYS finite element analysis program. The following results are found from the numerical and experimental results: In the case of a single hole Minimum failure load is obtained W/D = 2 (E/D is constant) and E/D = 2 (W/D is constant). Maximum failure load is obtained when E/D and W/D is equal to 4, and greater than these points.
[1] ASTM D 953-D, Standard test method for bearing strength of plastics, ASTM designation. p. 342–6. [2] Aktas A, Dirikolu MH. The effect of stacking sequence of carbon epoxy composite laminates on pinned-joint. Composite Structures 2003;62:107–11. [3] Karakuzu R, Taylak N, Icten B, Aktas M. Effects of geometric parameters on failure behavior in laminated composite plates with two parallel pin-loaded holes. Composite Structures 2008;85:1–9. [4] Sheng H, Hung C, Chang FK. Bearing failure of bolted composite joints. Part I: experimental characterization. Journal of Composite Material 1996;30:1285–313. [5] Okutan B, Aslan Z, Karakuzu R. A study of the effects of various geometric parameters on the failure strength of pin-loaded woven glass-fibre reinforced epoxy laminate. Composite Science and Technology 2001:1491–7. [6] Shokrieh MM, Lessard LB. Effects of material nonlinearity on the threedimensional stress state of pin-loaded composite laminates. Journal of Composite Material 1996;30(7):839–61. [7] Dano ML, Gendron G, Piccard A. Stress and failure analysis of mechanically fastened joints in composite laminates. Composite Structures 2000;50:287–96. [8] Ahn HS, Kweon JH, Choi JH. Failure of unidirectional-woven composite laminated pin-loaded joints. Journal of Reinforce Plastic Composites 2005;24(7):735–52.
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[9] Pierron F, Cerisier F, Grediac M. A numerical and experimental study of woven composite pin-joints. Journal of Composite Materials 2000;34(12): 1028–54. [10] Aktas A, Dirikolu MH. An experimental and numerical investigation of strength characteristics of carbon-epoxy pinned-joint plates. Composites Science and Technology 2004;64:1605–11.
[11] Whitney JM, Nuismer RJ. Stress fracture criteria for laminated composites containing stress concentrations. Journal of Composite Materials 1974;8:253–65. [12] Aktas A, Karakuzu R. Failure analysis of two-dimensional carbon epoxy composite plate pinned joint. Mechanics Composites Materials and Structures 1999;6:347–61.
Contents lists available at ScienceDirect
Composite Structures journal homepage: www.elsevier.com/locate/compstruct
Experimental and numerical failure analysis of pinned-joints in composite materials b,1 _ Alaattin Aktasß a,*, Hüseyin Imrek , Yusuf Cunediog˘lu c,2 a b c
Usßak University, Faculty of Engineering, Department of Mechanical Engineering, Usßak, Turkey Selçuk University, Faculty of Engineering, Department of Mechanical Engineering, Konya, Turkey Nig˘de University, Faculty of Engineering, Department of Mechanical Engineering, Nig˘de, Turkey
a r t i c l e
i n f o
Article history: Available online 1 November 2008 Keywords: Parallel pinned-joint Failure load Glass-epoxy Yamada-Sun criterion
a b s t r a c t In this paper, failure load and failure mode of glass-epoxy composite plates with single and double parallel pinned-joints have analysed experimentally and numerically. Two variables were investigated during analyses; the distance from the free edge of plate to the diameter of the first hole (E/D) ratio (2, 3, 4, 5), and the width of the specimen to the diameter of the holes (W/D) ratios (2, 3, 4, 5). Experiments were carried out according to the ASTM D953-D [ASTM D 953-D, Standard test method for bearing strength of plastics, ASTM designation. p. 342–6.]. The numerical study was performed by means of ANSYS finite element analysis program. Yamada-Sun failure criterion was used for failure analyses. Mechanical properties of the composite material were obtained according to ASTM standards. The results showed that the pin hole farthest from the free edge is subjected to the highest stress. A good agreement was obtained between experimental results and numerical predictions. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Fibre reinforced composite materials have been gaining wide application in aircraft submarine and spacecraft constructions. These applications require joining composites either to composites or to metals. Most commonly, joints are formed using mechanical fasteners. Therefore, suitable revealing methods for the failure strength would help in selecting the appropriate joint size in a given application. Joints present potential problem regions to the designers due to stress concentrations, and therefore, the strength of such a structure is dependent on the strength of its joints. This aspect of pinned-joints has attracted attention from many composite researchers. Among them, Aktas and Dirikolu [2] have studied the effect of stacking sequence of carbon-epoxy composite laminates, with [0°/45°/45°/90°]S, and [90°/45°/45°/0°]S configuration, on pinned-joint. They found, for both configurations, that the bearing strength reaches their maximum value at W/D = 4 and E/D = 4 geometric configuration. Karakuzu et al. [3] have investigated failure mode, failure load and bearing strength in a laminated woven glass-vinylester composite plate with two parallel circular holes which are subjected to traction forces by two parallel rigid pins. They have been observed the behavior of pin loaded
* Corresponding author. Tel.: +90 276 2634195/215; fax: +90 276 2634196. E-mail addresses: [email protected] (A. Aktasß), [email protected] _ (H. Imrek), [email protected] (Y. Cunediog˘lu). 1 Tel.: +90 332 2233457; fax: +90 332 2410041. 2 Tel.: +90 388 2252303; fax: +90 388 2250112. 0263-8223/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2008.09.009
composite plates with various dimensions experimentally and numerically. They have used LUSAS FEM program. This program does not give the good results for composite material because this program was developed for civil engineering applications. Sheng et al. [4] have experimentally studied the pinned-joint for various stacking sequences of a T80011/3900-2 carbon-epoxy composite laminate and determined the maximum bearing strength and the failure mode. Okutan et al. [5] have studied the bearing strength of pin loaded Kevlar-epoxy laminates experimentally. Shokrieh and Lessard [6] have developed a three-dimensional nonlinear finite element code to analyze the effects of material nonlinearity and edge effects on the state of stress and failure prediction near the stress concentrations of a pin-loaded graphite-epoxy laminated composite plate. Dano et al. [7] have discussed influence of failure criteria and the inclusion of geometric and shear non-linearity. Ahn et al. [8] have performed a nonlinear finite element analysis to considerate the contact and friction between the pin and the laminate for unidirectional and woven composite laminated joints of an aircraft control rod. Pierron et al. [9] have studied the behavior of woven glass fiber epoxy pin joints both numerically and experimentally, with particular attention given to the sensitivity of the model to different parameters such as clearance, friction, and material nonlinearity. In this study, the effects of E/D and W/D ratios on failure mode and failure load are investigated in the laminated woven glass fiber composite plate with single and double parallel circular holes. The behavior of pin loaded composite plates has been observed experimentally and numerically with various dimensions. The numerical study was performed by assistance of ANSYS commercial software.
460
A. Aktasß et al. / Composite Structures 89 (2009) 459–466
Yamada-Sun failure criteria are used to obtain failure load and mode of the laminated plates. 2. Problem description
S: Shear-out plane
In this study, two types of pin joint plates are analyzed. One has single and the other has two parallel holes as shown in Fig. 1a and b, respectively. The specimen with single hole of diameter D is located along the centerline of the plate (Fig. 1a). The center of the hole is located a distance E from one end. A uniform tensile load P is then applied to the plate, and this load is resisted by a rigid pin. The load is parallel to the plate and is symmetric with respect to the centerline. The specimens are of two parallel holes, which are located a distance E from one free edge and W/2 from the other. The distance between the two parallel holes is taken 24 mm so that the failure mode gives the bearing mode. Since this mode gives the highest strength in pinned-joint uses. Then uniform tensile load P is then applied to the plate with the procedure of the single hole case. In general, there are three basic pinned-joint failure modes related to composites: These are net tension, shear-out, and bearing. Combination of these, i.e., mixed modes, may also appear as shown in Fig. 2. Net tension occurs catastrophically and presents the least strength. Designers are required to obtain the optimum E/D and W/ D ratios to get the bearing mode, which shows the highest strength in pinned-joint uses. The behavior of the joint could be influenced by four groups of parameters [10]. Material parameters: Fibre types and form, resin type, fibre orientation, laminate stacking sequence, etc. Geometry parameters: Specimen width, W, or ratio of width to hole diameter, W/D, edge distance, E, or ratio of the edge distance to hole diameter E/D, specimen thickness, t, etc. Fastener parameters: Fastener type, clamping area, hole size. Design parameters: Loading type, loading direction, failure criteria. Clearly, there are many variables involved in practical joints; therefore, complete characterization of joints is highly dependent on the hole geometry of the connection, including the edge distance, and the width.
P W
D
Dimensions in mm 100
E
a) Single hole
) D
P 24
b) Serial
D
Dimensions in mm 100
E
)
W/2
N: Net tension plane B: Bearing plane
N
N-S: Mixed planes
S N
B S
Fig. 2. Three basic failure planes for pinned-joints.
3. Specimen preparation and testing procedure Woven prepreg glass-epoxy composite blanks with thickness of 3.14 mm, EP GC 203, were obtained from Izoreel Co. Turkey. 3.1. Specimen preparation Woven glass-epoxy composite blanks are cut into rectangle shapes with a water-cooled diamond-tipped rotary wheel for two types of testing. All cut edges were finished using a fine silicon carbide paper to remove any edge defects. The holes, typical in size of fasteners used in many airframe assemblies, were drilled using by a modified high-speed steel drilling tool with three sharp contact points to prevent fuzzy edges [2]. In this way, a 6.5 mm diameter holes is obtained on the specimens (Fig. 1). Specimens for each type were produced in the following manner: While keeping the E/D ratio as 4, the W/D ratio is varied as 2, 3, 4, and 5; and maintaining W/D as 4, E/D is changed as 2, 3, 4, and 5. Three specimens are prepared for each configuration. To find the values of the longitudinal modulus, E1, the Poisson’s ratio, v12, and the longitudinal tensile strength, Xt, a flat piece of woven plate, the principal axis of which coincides with the loading direction, was taken, and two strain gauges perpendicular to each other were stuck on. One of them was on principal and the other was on transverse direction. The specimen was loaded step by step to rupture by means of a 50 kN loading capacity testing machine at a speed of 1.5 mm/ min, and for all steps e1 and e2 were measured by an indicator. The same procedure has been performed for the determination of transverse modulus, E2, and the transverse tensile strength, Yt. To define the respective longitudinal and transverse compressive strengths, Xc and Yc, a flat piece of woven plate, the principal axis of which coincides with the loading direction was taken, and it was subjected to compressive loading up to failure. To obtain the shear modulus, G12; a plate whose principal axis was on 45° was taken. Then, a strain gauge was stuck along the loading direction. The specimen was loaded step by step up to rupture, and G12 was calculated by measurement of ex, which is the strain in the tensile direction [10]. To obtain the rail-shear strength, S, a series of specimens were tested. These tests were performed by placing the shear fixture into the testing machine and by applying compressive load. The rail-shear strength is obtained by dividing the
b) Double parallel holes t
Fig. 1. The geometry of the single and double pinned-joints.
P
Table 1 Mechanical properties of the glass-epoxy composite plate. E1 = E2 (GPa)
G12 (GPa)
m12
Xt = Yt (MPa)
Xc = Yc (MPa)
S (MPa)
Fiber (%)
Rot (mm)
Roc (mm)
20
7.54
0.18
320
550
55
60
1.11
0.83
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ultimate failure load of the laminate by the sheared cross section. The mechanical properties of the composite laminate determined in this manner are given in Table 1. 3.2. Testing procedures The tests were conducted with reference to ASTM D953-D [1] at room temperature of 20 °C. One for single hole and two for parallel holes through-hardening steels, 42CrMo4, hardened (by heating at 850 °C for 2 h and then quenched in oil at room temperature) and polished pins were later inserted in the holes without clearance. Then, experiments were performed by means of custom fixtures on the 50 kN loading capacity universal machine with a speed of 1.5 mm/min.
The dimensions of the thickness, t was chosen as 3 mm and E, W were 26 mm so that the failure mode gives the bearing mode. Since this mode gives the highest strength in pinned-joint uses. The failure load (Pfailure) was measured by the bearing failure test. The point stress criterion was applied to the results of the bearing failure test and the ‘‘characteristic length for compression” was obtained as shown in Fig. 3c. In this criterion, failure occurs when the compressive stress in the load direction equaled bearing strength (rb) at some distance from the arc edge. In this study, the compressive stress distribution at Pfailure was calculated by using finite element method (FEM) and Roc was obtained from those results and given in Table 1. 5. Numerical study
4. Characteristic lengths
5.1. Failure criterion
4.1. Characteristic length for tension (Rot)
In order to determine the failure loads and the failure modes, a failure criterion must be applied. In this investigation, the YamadaSun failure criterion is used. This criterion is quadratic theory. Involving the shear stress s12 and the longitudinal stress r1 along the fibers, and the following criterion for laminate failure is proposed.
In this study, the characteristic length for tension was determined by applying the point stress criterion to the tensile specimen with a hole. This criterion has been suggested by Whitney and Nuismer [11]. Fig. 3a shows the description of the point stress criterion. In this criterion, failure has been said to occur when the tensile stress (ry) in the load direction is equal to unnotched laminate strength (r0) at some distance (Rot) from the edge of the hole. Rot has been called characteristic length for tension and find in the procedure reference [10] and given in Table 1.
4.2. Characteristic length for compression (Roc)
Tensile Stress (σy)
In order to find the characteristic length for compression (Roc), bearing failure test was used. Fig. 3b shows the schematic diagram of the bearing failure test. The specimen containing a machined half circle, 6.5 mm diameter, is at the center. The bearing failure test was applied by the hardened steel jig, 6.5 mm diameter. The bearing failure test was conducted at cross head speed 1.5 mm/min.
r 2 1
X
þ
s 2 12
S
¼ e2
e 1 Failure e 1 no failure
ð1Þ
where r1 is the longitudinal stress along the fibers; X is longitudinal tensile strength of ply; s12 is shear stress along the fibers; S is the rail-shear strength. The failure criterion (Eq. (1)) only predicts whether the pin joint failed or not. It does not predict the failure mode. To obtain the failure mode the characteristic curve must be drawn. This curve is specified by Eq. (2).
Rc ðhÞ ¼ D=2 þ ROT þ ðROC ROT Þ cos h
ð2Þ
Fig. 4 shows the description of the characteristic curve. Failure occurs when e is equal to unity at any point on the characteristic curve. The calculation procedure described above also provides
Compressive Stress (σy) R0C Bearing strength (σb)
Tensile Strength (σ0)
R Distance from hole edge
Rot
(a)
(C) P
S ecimen
(b) Fig. 3. Description of point stress criterion.
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(c) The stresses (rx, ry and sxy) are calculated using the finite element method. (d) If e equals or exceeds unity in any ply along the characteristic curve, the joint is decided to have failed.
y Characteristic Curve
θfail
The procedure outlined above is used to numerically predict whether or not failure occurs under a given load, P. The calculated stresses are linearly proportional to the applied load (see Fig. 6). A relationship is employed to determine the maximum load (Pmax), which can be imposed on the joint. For a given load P, values of e are calculated on the characteristic curve as discussed above. The highest value of e (e0) is determined, and the maximum load is calculated by the expression:
ROC
x
D ROt
Pmax ¼ Fig. 4. Description of the characteristic curve for double parallel holes.
: Bearing failure
30 < hf < 60
: Shear-out failure
75 < hf < 90
: Net tension failure
ð4Þ
In order to find the failure mode the criterion of Eq. (3) used. The procedure outlined above is shown as a chart in Fig. 8.
the location (angle hfail showing in Fig. 4) at which e is equal to unity on the characteristic curve. A knowledge of hfail provides an estimate of the failure mode of failure, as follows [12],
0 < hf < 15
P e0
ð3Þ
At intermediate values of hfail, failure may be caused by combination of these modes. 5.2. Finite element analysis AnsysTM finite element package has been used in the numerical analyses. Whether or not a joint fails under a given condition is determined by the finite element analysis as follows: (a) The geometry of the problem is modeled for single and double holes using SHELL91 elements with the characteristic curve. The composite plates were modeled as a half model because of the symmetry of loading, geometry and material with respect to x-axis the displacements of the symmetry surface are zero in y direction (Fig. 4). A typical FEM mesh and its boundary condition for double parallel joints are given in Fig. 5. (b) To simulate the rigid pin, radial displacement constraints were used on the right hand sides of the hole. The load was applied to the nodes of the laminate positioned left hand side of the model (Fig. 5).
6. Results and discussions The failure loads and failure modes of composite specimens with single and double parallel holes which are subjected to reaction force by two rigid pins are investigated experimentally and numerically. In order to obtain the optimum geometry for two cases, the ratio of the edge distance to the pin diameter (E/D), and the ratio of the specimen width to the pin diameter (W/D) have systematically been varied during analyses. Custom made fixtures on a testing machine and AnsysTM finite element package has, respectively been used for pinned-joint experiments and numerical solutions. Three tests were conducted for each type of specimen and average bearing load values were calculated. 6.1. Bearing load The bearing loads with respect to E/D (W/D = 4 is constant) for single and double pinned-joints are shown in Fig. 7. In this figure, the double failure loads divided by 2 so that the failure loads of the single and double pins can be compared. When E/D is equal to 2 and 4, the failure loads takes its minimum and maximum value, respectively for two cases and both experimentally and numerically. The results from both analyses show the same trends. An interesting result is that the failure loads of parallel pins are less than single one. It is clear that there is a good agreement between numerical and experimental results. The bearing loads with respect to W/D (E/D = 4 is constant) for single and double pinned-joints are shown in Fig. 8. In this figure,
Fig. 5. A typical FEM mesh and its boundary condition in double parallel joints.
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Bearing Failure test
FEM Stress Analysis
Tensile test with A hole Point Stress Criterion
Point Stress Criterion
Stress Distribution in each ply Characteristic Length for tension Rot
Characteristic Length for compressive R oc
Yamada-Sun Criterion + Characteristic Curve
y Characteristic Curve
ROC
x D
ROt
Prediction of joint failure load &failure mode Fig. 6. Flow chart for failure load and failure mode procedure.
4500
4000
Pb [N]
3500
3000 Parallel Exp. 2500
Single Exp. Single FEM Parallel FEM
2000
1500 1
2
3
4
5
6
E/D Fig. 7. The effect of E/D ratio on failure load for single and double pinned-joints.
the failure loads of double holes also divided by 2 for comparison. When W/D is equal to 2 and 4, the failure loads takes its minimum and maximum value, respectively for two cases and both experimentally and numerically. The result of this figure is nearly the same with Fig. 7. In two figures the maximum failure loads are reached at E/D = 4 and W/D = 4, and greater than these points.
6.2. Failure mode In case double holes in parallel; Fig. 9 shows some photographs and FEM results of the double holes failed specimens with different failure modes. In these figures, failure modes are bearing mode, which shows the highest strength for E/D P 4 and W/D P 4, net tension, which shows least strength for W/D/2 (E/D = 4), and mixed
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4500 4000 3500
Pb [N]
3000 2500 Parallel Exp.
2000
Single Exp. Single FEM
1500
Parallel FEM 1000 500 1
2
3
4
5
W/D Fig. 8. The effect of W/D ratio on failure load for single and double pinned-joints.
Fig. 9. FEM and experimental results of failed specimens for double pinned-joints.
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465
Fig. 10. FEM and experimental results of failed specimens for single pinned-joints.
mode in Fig. 9a–c, respectively. The other configuration of E/D and W/D give bearing mode. In case single hole; Fig. 10 show some FEM and experimental results of single hole failed specimens with different failure modes. When W/D = 2, E/D = 4 and E/D = 2, W/D = 4 failure modes give net tension and mixed-mode, respectively. Expect from these geometrical configurations, failure mode gives bearing mode. It can be seen from the Figs. 9 and 10 that failure modes obtained from the experimental and numerical results are very close.
Failure modes give net tension and mixed-mode when W/D = 2 (E/D = 4) and E/D = 2 (W/D = 4) but other geometrical configurations give bearing mode. In the case of a double hole Minimum bearing load is obtained W/D = 2 (E/D is constant) and E/D = 2 (W/D is constant). Maximum bearing load is obtained at E/D P 4 and W/D P 4. Failure modes give shear-out and net tension at E/D = 2 (W/ D = 4) and W/D = 2 (E/D = 4), respectively.
7. Conclusions References In present paper, failure strength and failure mode of glassepoxy composite plates with single and double parallel pinnedjoints has analysed experimentally and numerically. Two variables were investigated during analyses; the distance from the free edge of plate to the diameter of the first hole (E/D) ratio (2, 3, 4, 5), and the width of the specimen to the diameter of the holes (W/D) ratios (2, 3, 4, 5). Experiments were carried out according to the ASTM D953-D [1]. The numerical study was performed by means of ANSYS finite element analysis program. The following results are found from the numerical and experimental results: In the case of a single hole Minimum failure load is obtained W/D = 2 (E/D is constant) and E/D = 2 (W/D is constant). Maximum failure load is obtained when E/D and W/D is equal to 4, and greater than these points.
[1] ASTM D 953-D, Standard test method for bearing strength of plastics, ASTM designation. p. 342–6. [2] Aktas A, Dirikolu MH. The effect of stacking sequence of carbon epoxy composite laminates on pinned-joint. Composite Structures 2003;62:107–11. [3] Karakuzu R, Taylak N, Icten B, Aktas M. Effects of geometric parameters on failure behavior in laminated composite plates with two parallel pin-loaded holes. Composite Structures 2008;85:1–9. [4] Sheng H, Hung C, Chang FK. Bearing failure of bolted composite joints. Part I: experimental characterization. Journal of Composite Material 1996;30:1285–313. [5] Okutan B, Aslan Z, Karakuzu R. A study of the effects of various geometric parameters on the failure strength of pin-loaded woven glass-fibre reinforced epoxy laminate. Composite Science and Technology 2001:1491–7. [6] Shokrieh MM, Lessard LB. Effects of material nonlinearity on the threedimensional stress state of pin-loaded composite laminates. Journal of Composite Material 1996;30(7):839–61. [7] Dano ML, Gendron G, Piccard A. Stress and failure analysis of mechanically fastened joints in composite laminates. Composite Structures 2000;50:287–96. [8] Ahn HS, Kweon JH, Choi JH. Failure of unidirectional-woven composite laminated pin-loaded joints. Journal of Reinforce Plastic Composites 2005;24(7):735–52.
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[9] Pierron F, Cerisier F, Grediac M. A numerical and experimental study of woven composite pin-joints. Journal of Composite Materials 2000;34(12): 1028–54. [10] Aktas A, Dirikolu MH. An experimental and numerical investigation of strength characteristics of carbon-epoxy pinned-joint plates. Composites Science and Technology 2004;64:1605–11.
[11] Whitney JM, Nuismer RJ. Stress fracture criteria for laminated composites containing stress concentrations. Journal of Composite Materials 1974;8:253–65. [12] Aktas A, Karakuzu R. Failure analysis of two-dimensional carbon epoxy composite plate pinned joint. Mechanics Composites Materials and Structures 1999;6:347–61.