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On failure mechanisms of composite laminates with an open hole subjected to compressive load
COMPOSITES SCIENCE AND TECHNOLOGY Composites Science and Technology 66 (2006) 634–641 www.elsevier.com/locate/compscitech
On failure mechanisms of composite laminates with an open hole subjected to compressive load H. Suemasu a
a,*
, H. Takahashi b, T. Ishikawa
c
Department of Mechanical Engineering, Faculty of Science and Technology, Sophia University, 7-1, Kioicho, Chiyoda-ku, Tokyo 102-8554, Japan b Graduate School, Sophia University, 7-1 Kioicho, Chiyoda-ku, Tokyo 102-8554, Japan c Japan Aerospace Exploration Agency, 6-13-1 Ohsawa, Mitaka-shi, Tokyo 181-0015, Japan Received 10 November 2004; accepted 18 July 2005 Available online 7 October 2005
Abstract In the present study, the compressive failure mechanism of quasi-isotropic composite laminates with an open hole was experimentally and numerically studied to explain the mechanical meaning of the open hole compression (OHC) strength. In the experiment, we adopted a fixture for the OHC test method proposed by the National Aerospace Laboratory (NAL III). Two types of composite systems were tested to examine the dependence of failure behavior on the material properties such as interlaminar toughness. The damage which appeared first was fiber micro-buckling in the 0° layer. Some accumulation of damage, such as further fiber micro-buckling in the 0° layers and interlaminar delaminations in several interfaces, was observed before the final unstable fracture in the laminate with high interlaminar toughness, while sudden failure occurred in the laminate with low interlaminar toughness. In the numerical study, a full three-dimensional finite element analysis was conducted. At the transverse edge of the hole, not only stress singularity at the interface but also high stress concentration at the 0° layers was obtained. Singular stress at the interfaces decreased quickly to a level much below the interlaminar strength. To consider the effect of micro-buckling on the stress redistribution and further damage accumulation, a damage analysis was conducted by reducing the stiffness components of the corresponding elements to 1/10. When one element was damaged, the maximum stress next to the damaged element became higher than the maximum stress for the intact laminate. The maximum stress decreased with the increase in number of the damaged element in the transverse direction and became lower than that for intact laminate after some extension of the damage area. This result indicates that some unstable damage progress of limited size would be expected just at the first damage occurrence and a stable increase of damage would follow it with further compressive load increase until other damage systems occurred. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Composite laminate; Open hole compression; Finite element method; Fiber micro-buckling; Delamination
1. Introduction Composite laminates are used particularly for aerospace structures due to their high specific strength and stiffness. However, the toughness is not sufficient compared to the conventional metal materials such as aluminum alloys. When composite laminates are used as a structural material it is very important to evaluate the over-all performance of
*
Corresponding author. Tel.: +81 3 3238 3857; fax: +81 3 3238 3311. E-mail address: [email protected] (H. Suemasu).
0266-3538/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2005.07.042
the composite laminates with an appropriate method which considers the various damage tolerant properties as a structural material. The open hole compression (OHC) test [1] as well as the compression after impact test (CAI) [2,3] provides us useful design data for the compression strength of the composite laminates having cut-outs, defect, and so on. So, demand for the OHC test has been increasing since it is more economical and easier to perform compared to the CAI test which has been widely used to obtain the damage tolerant compressive strength of the composite materials. But the mechanical meaning of OHC strength is not clear yet. It is very important to understand the failure mecha-
H. Suemasu et al. / Composites Science and Technology 66 (2006) 634–641
nism of the OHC specimen to properly utilize the OHC strength data. This study also contributes to the understanding of the general problem of the failure from a portion of the stress concentration. The OHC strength is thought to be the strength of a composite material with some damage. The stress around a circular hole is very complex due to the effect of the inhomogeneous material properties as well as the stress concentration. The singularity of the interlaminar stress [4,5] whose power of singularity is very small compared to one half of a typical crack makes the problem difficult to estimate. The large stress near the hole surface due to the singularity may not cause the initial damage because of the stress relaxation mechanism at the interface, but it does play an important roll in the fatigue, which is another important problem to be solved. The compressive strength of the fiber reinforced composites in the fiber direction is usually weak compared to the tensile strength. The low strength is caused by the micro-buckling of the fiber which is embedded in the compliant matrix [6–10]. The strength of each ply is not a fixed value but depends on the stacking sequence, ply thickness, total thickness of the laminate and so on. Furthermore, the strength of the ply subjected to non-uniform stress may not be equal to the strength measured under uniform stress. Many studies about damage and failure from a circular hole in a composite laminate under compressive load have been carried out because of interest in the OHC test as well as the practical importance of this problem, such as failure at bolt holes [11–22]. However, there still remain various uncertainties about the failure mechanism. In the present paper, we study experimentally and numerically the failure mechanism of the quasi-isotropic laminates with a hole. In the experiment, the NAL III method was adopted owing to its efficiency. The damage accumulation history was observed during the test with a digital microscope. The magnitude of the damage was studied through the C-scan image and the micrographs of the damaged cross-sectional area. The results observed are discussed by referring the finite element results. A chart estimating the OHC strength is proposed.
635
Fig. 1. OHC test apparatus and fixture (NAL III method).
2. Experiment Figs. 1 and 2 show the test apparatus and the fixture which were prepared following the instructions for the OHC test procedure (NAL III) proposed by the National Aerospace Laboratory, (Japan) [1]. A fixture with the same size of gage area and open window as that of the SACMA 3R-94 test method enables us to use a smaller specimen and to get almost same results as the SACMA test method. The instruction and the test results of NAL III method are well explained in [1] by comparison with SACMA method. The quasi-isotropic laminates ([(45/0/–45/90)2]sym) shown in Fig. 3 were supported by the fixture to prevent from the buckling and then placed in a hydraulic test machine. Two types of materials T800H/3633 and TR30/#340 lami-
Fig. 2. Fixture for OHC test (NAL III method).
nate were tested. The T800H/3633 laminate has a comparatively tougher interface than the TR30/#340 laminate. The close-up picture of the hole surface of T800/3633 specimen is shown in Fig. 3(b), which had been manufactured for a round robin test for NAL III test method following the instruction for OHC test using recommended tool. The specimens made of TR30/#340 laminate prepared by our department engineers were carefully drilled and the hole surfaces were grinded to make the surface as smooth
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H. Suemasu et al. / Composites Science and Technology 66 (2006) 634–641
-2 5
Force (kN)
-2 0
-1 5
-1 0
-5
0 0
-0.2
-0.4 -0. 6 -0.8 Displacement (mm)
-1
-1.2
Fig. 4. Applied load against the displacement of the fixture.
Fig. 3. OHC test specimen for NAL III method: (a) overall view (b) close up picture of the hole surface of T800/#3633 specimen.
as possible. The transverse hole surface where the damage was expected to occur first due to the stress concentration was observed by using a digital microscope during the experiment. The top of the specimen was pushed through a flat fixture surface. The pushing bar was supported by horizontal bar through a ball-bearing in order to minimize the inclination of the pushing bar during experiment. The cross-head speed was set very slow less than 0.1 mm/min to allow as long time to identify the damage initiation. A relation between the applied load and the displacement of end fixture is plotted in Fig. 4. There is some reduction of the compressive stiffness around 17 kN and further reduction is found at about 19 kN. The damage accumulation process of the T800H/3633 specimen observed with the digital microscope is shown in Fig. 5. Damage due to fiber micro-buckling appeared first in the 0° layer at about 17.5kN (Fig. 5(b)), which correspond to the first reduction of the stiffness. The damage finally occurred in all 0° layers (Fig. 5(c)). The damaged portions grew by some amount (Fig. 5(d)). The magnified pictures of the damage showed that the small portion of the 0° layer buckled out from the hole surface. Then, a delaminated surface layer suddenly broke at 22.7 kN (Fig. 5(e)): this result was probably caused by the delamination buckling. This meant that the delamination had spread by some amount at this stage. The specimen finally failed at 23.2 kN (Fig. 5(f)). The specimen of TR30/#340 having a low interfacial toughness failed suddenly without visible damage. A photograph of
the radial cross-section and a C-scan image of T800H/ 3633 damaged specimen are shown in Fig. 6. The specimen was removed from the fixture before rupture. Transverse cracks found in all 0° layers at the hole surface are thought to originate from the compressive failure site. Significant delaminations emanating from the damages of the 0° layers are observed at the interfaces between the 0° and ±45° layers near the surface. The overview of the delaminations are observed around the damage site also in Fig. 6(b). The loads at the onset of damage and the final failure obtained are listed in Table 1 with the data of the other material systems shown in [1] in order to understand clearly the effect of the compressive strength of the unidirectional fiber composite and the interlaminar toughness on the failure of the laminates with an open hole. Laminate KA/#410 broke without visible damage and had very high OHC strength. Laminates IM600/QC133 and IM600/QC101 with toughened interfaces [1] showing the initiation of damage in 0° layers at a very low load level kept their load bearing capability up to about 23 kN. The low compressive load at damage initiation may be caused by low stiffness interface, which fosters the deformation of the 0° layers by the interfacial stress. The present two types of specimens, T800H/ 3633 and TR30/#340, showed intermediate results. We may say that the compressive strength of the 0° layer governed the final failure load for the laminates with low interface toughness compared to the compressive strength in the fiber direction and the delamination size might govern the strength of the laminates with toughened interfaces. 3. Finite element analysis and results The analytical model is illustrated in Fig. 7 with the coordinate system. The material properties are EL = 148 GPa, ET = 9.56 GPa, GLT = 4.55 GPa, GTT = 3.17 GPa,
H. Suemasu et al. / Composites Science and Technology 66 (2006) 634–641
637
Fig. 5. Damage progress during OHC test taken by a digital microscope. Specimen thickness is 3.2 mm and please see the size of the damage (T800H/3633 [(45/0/–45/90)2]s).
mLT = 0.3, and mTT = 0.49. Since the deformation of the quasi-isotropic laminate is symmetric with respect to midsurface of the laminate and the center line of the hole (z-axis), only one quarter of the plate is modeled. The boundary conditions on the mid-surface (z = 0, y = ±b/2 and x = l/2) are written, respectively, w ¼ sxz ¼ sxz ¼ 0
on z ¼ 0;
ry ¼ sxy ¼ syz ¼ 0 on y ¼ b=2; u ¼ u0 ; sxz ¼ sxy ¼ 0 on x ¼ l=2;
ð1Þ
The condition of symmetry about z-axis is realized by the following equations: uð0; y; zÞ þ uð0; y; zÞ ¼ 0; vð0; y; zÞ þ vð0; y; zÞ ¼ 0 wð0; y; zÞ wð0; y; zÞ ¼ 0.
on x ¼ 0;
ð2Þ
A commercially available finite element code (ABAQUS 6.3) [24] was used to conduct the numerical analysis. A three-dimensional 20 node brick element was used. A 0° layer and its neighboring portions were refined to get an accurate magnitude of the stress concentration, because damage was observed first in the 0° layers and inter-laminar stresses were also expected to be significant at the interfaces between the 0° layer and the neighboring layers. The finite element mesh is shown in Fig. 8. To impose the symmetric condition of Eq. (2) at the surface of x = 0 the displacements of the corresponding nodes were constrained through an Ôequation commandÕ provided by the ABAQUS code. The number of elements and nodes of the model was 21,112 and 91,257, respectively. Distributions of normal stress in the fiber direction rL when 1 MPa of average stress is applied at the end of the specimen are plotted in Fig. 9. Fig. 9(a) is the stress at
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H. Suemasu et al. / Composites Science and Technology 66 (2006) 634–641
Fig. 6. Damage state near the hole edge of the quasi-isotropic laminates of T800H/3633 material system [(45/0/–45/90)2]s) before final failure under the OHC test: (a) micrographs of damage at a radial cross-section; (b) C scan image of damage. Table 1 Comparison of the loads at initial damage and failure loads for various materials obtained by OHC test Material system
Initial damage (kN)
Failure load (kN)
Strength (MPa)
Standard deviation (MPa)
Compressive strength of UD composite (MPa)
KA/#410 [1] TR30/#340 T800H/#3633 IM600/#133 [23] IM600/#101 [23]
29.4 22.0 17.5 6 4
29.4 22.0 23.2 24.5 23.7
370.2 255.8 276.8 272.0 271.3
1.9 – – 7.4 5.0
– – – 1037 [23] –
The data with shadow rows are our experimental result. The other data were in [1,23] to refer.
the hole surface and cross-section in the radial direction. Though the stress distribution is not accurately expressed due to the smoothing technique of the visualization system of the post-processor, the effect of the inhomogeneity of the laminate on the stress distribution at the hole area can be well seen. The compressive stress is extremely large at the
transverse edges of the 0° layers as expected. The stress rL in the ±45° layers was even smaller at the hole surface than that at the inside portion, since the fiber stress had to be released at the surface. The released stress must be carried by the 0° layers and made the stress concentration of the 0° layers even higher.
H. Suemasu et al. / Composites Science and Technology 66 (2006) 634–641
639
Fig. 7. Analytical model of OHC test specimen (mm).
Fig. 10. Normal stress rx along the thickness direction at the hole surface (h = 90°).
Fig. 8. Finite element mesh.
The stress distributions rx at the section (h = 90°) in the thickness direction are plotted in Fig. 10. The normal stress rx is 11.62 times the applied average stress at the loading edge. The stress component rx in the 45° layer is small. The shear stress sxz at the section (h = 90°) in the thickness direction is plotted in Fig. 11. As reported by many researchers the stress sxz clearly shows existence of a singularity at the interface [3,4]. The stress singularity became
uncertain at the interfaces whose neighboring layers were not sufficiently divided. The shear stress sxz along the transverse direction at a interface between 0° and 45° layers are plotted in Fig. 12. The stress reduces very quickly to zero with the distance from the free edge. It is very difficult to assess the significance of the large stress in a very small area to the failure and some fracture mechanical consideration may be needed. In the experiment, small and finite size micro-buckled portion appeared in the 0° layers at the moment of the damage initiation when sudden failure did not occur. This damage is thought to play a roll of a natural initial damage. A series of FEM analysis was performed to explain the reason of this small and unstable growth of damage. Though it was imperfect to explain failure process, it may show a hint to understand the initial failure mechanisms. All the elastic moduli of the designated elements were dropped to 1/10 of those of the intact material to represent the zone of compressive failure. We call this less stiff element Ôdam-
90°
-45 °
0°
45 °
90 °
-45 °
0°
45 °
Stress τxz[MPa]
0.2
0
-0.2
-0.4 0 Fig. 9. Distribution of the normal stress rL in the fiber direction (maximum stress is 11.62 MPa): (a) hole surface and radial cross-section; (b) stress in the 0° layer.
0.2
0.4
0.6
0.8
1
Specimen Height [mm]
Fig. 11. Shear stress sxz along the thickness direction at the hole surface (h = 90° and 90°).
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H. Suemasu et al. / Composites Science and Technology 66 (2006) 634–641
-11.53 Compressive stress [MPa]
Interlaminar Stress τ xz [MPa]
0 -0.1
-0.2
-0.3
-12.35-12.31-12.24 -12.14
-11.88 -12.6 7-11.2 6
-10
-10.56
no damage damage 1 damage 2 damage 3 damage 4 damage 7 damage 8 damage 9 damage 12
-5
-0.4 3.175
6
9 12 15 Distance from the hole center[mm]
18
0
0
0.1
0.2 0.3 0.4 Radial direction [mm]
0.5
0.6
Fig. 12. Shear stress sxz along a interface between the 0° and 45° layers in the radial cross-section (h = 90°).
Fig. 14. Change of the stress distribution and maximum stress in the 0° layer with the increase of damage area.
aged elementÕ. We do not know what value of the reduction factor is most appropriate. 1/10 is not impractical and is a little larger than the value usually used in damage analyses. The replacement of the intact elements with the damaged elements causes the stress redistribution and some increases of stresses in the intact elements near the replaced damaged elements. As the stress increase in the surrounding portion would be related to the rate of the reduction of the load carrying capacity of the damaged area, the present modest reduction of the modulus would cause less stress increase. So, we may say that the unstable damage progress would occur in the real laminates when the unstable propagation was expected in the present analysis. In this analysis, the symmetry condition of the mid-plane was not used and one half of the laminate was analyzed to consider the case where the damage occurs in one of the 0° layers. The damage zone was increased one element by one element from the edge of the hole to transverse direction as shown in Fig. 13 and a stress analysis was conducted for every expansion of the damaged area. The stress distributions along the radial direction are plotted from the edge of the hole to the radial direction in Fig. 14 at every expansion of the damage zone. The line with solid circles is the stress distribution for the intact plate. The stress decayed from 11.53 to about 5.7 at the point 0.6 mm from the hole surface. (The maximum stress became 0.5% lower than the former result owing to the coarser discretization.) The
maximum compressive stress rx appeared at the point just next to the damaged element due to the redistribution of the stresses and the value (12.35) was higher than that (11.53) of undamaged model. This means that the damage caused by high stress at the edge brings about higher stress and will generate the further damage. If failure is assumed to start at the hole surface at this load level and the resulting state shows higher stress than the maximum compressive stress of 11.53, we may say further damage created by the stress. The next line with triangle is the stress distribution when only one element was replaced with a damaged element. When two elements are damaged, the maximum stress is smaller than that for one damaged element but is still larger than that with no damage element, that is, further damage growth would be expected. When more than six elements are damaged the maximum stress became smaller than that with no damage case, which means that the damage propagation should decelerates and stops. The order of the initial damage is expected to be around 0.3 mm from the present rough analysis. It is because the stresses are redistributed also in the neighboring ±45° layers, whose load carrying capability increases with the distance from the hole surface as was indicated in Fig. 9(a). We may say that there exists some unstable finite expansion and arrest after a small expansion of the damage unless other types of damage become unstable. This damage is thought to play an initial damage. In the present experiment, delaminations seemed to spread from the damage. 4. Discussion and summary
-45˚ 0˚ 45˚
damage1 0.1375
90˚z y
0.42
x unit : mm
0.05
damage2
Fig. 13. The assumption of damage area, where the elastic constants are reduced to 1/10 of the original element.
From the present experimental and numerical study, we have the following conclusions about OHC strength: 1. The specimens with tough interface show the first damage in 0° layer and fails after some further increase in the load, while the specimens with a brittle interface break suddenly without visible damage.
H. Suemasu et al. / Composites Science and Technology 66 (2006) 634–641
2. The stress concentration at the 0° layer is about 11.6 times larger than the average applied stress for the quasi-isotropic laminates. 3. The maximum stress in the 0° layers of the damaged laminate is larger than that of the intact laminate at first and decreases with the increase of damage. This indicates that a small unstable formation of the damage zone is expected to occur at the initiation stage and then the damage arrests unless the other damage unstably propagates following the initial damage. We propose a failure mechanism of the OHC test as shown in Fig. 15. The vertical axis is the applied load and the horizontal axis refers a magnitude or a significance of damage. The chained lines are the critical size of the damage depending on the toughness which decrease with the load according to the fracture mechanical theory. The compressive strength in the fiber direction tends to be weak when the interface is toughened. For the laminate with the tough interface, the 0° layer first fails due to fiber micro-buckling but the size of the damage zone in the 0° layer is not large enough to cause further growth of other types of damage such as delaminations. With the load increase the damage gradually spreads in the radial direction until the stress is large enough for the damage to be unstable. The delamination near the surface causes the buckling of the surface delaminated layer, which just precedes the final failure. In this case, the toughness of the interface plays an important role in controlling the OHC strength. If the interlaminar toughness is low and/or the compressive stress is high, the initial damage, which is large enough to bring about the further growth of other types of damage, causes total rapture of the laminate. This scenario explains very well the experimental results of OHC strength. If the mechanisms are reasonable, the OHC test results for the composite laminates with tough interfaces are adequate to measure its performance with consideration of the damage tolerance, whereas the OHC test results for the composite laminates with brittle interfaces show only the compressive strength in the direction of the fiber at the stress concentration area. Load
Damage size Critical Damage Size
high
Compressive Strength of 0° layer
Load of first
high
damage
Interlaminar toughness low
low
Damage Size Fig. 15. Failure mechanism and material properties.
641
References [1] Ishikawa T, Shikata N, Hamaguchi Y, Bion G. Behavior in open hole compression (OHC) tests and proposal of shorter specimen. In: Proceedings of ICCM-14. USA: Society of Manufacturing Engineers; 2003. CD-ROM. [2] Ishikawa T, Sugimoto S, Matsushima M, Hayashi Y. Some experimental findings in CAI tests of CF/PEEK and conventional CF/ epoxy flat plates. Compos Sci Technol 1995;55:349–62. [3] Lee SM. Compression-after-impact of composite with toughened matrices. SAMPE J 1986:64–8. [4] Iarve E, Pagano NJ. Singular full-field stresses in composite laminates with an open hole. Int J Solids Struct 2001;38:1–28. [5] Iarve E. Spline variational three dimensional stress analysis of laminated composite plates with open holes. Int J Solids Struct 1996;33(14):2095–118. [6] Lankford J. The compressive failure of polymeric composites under hydrostatic confinement. Compos Part A 1997;28A:409–18. [7] Berbinau P, Soutis C, Guzl IA. Compressive failure of 0° unidirectional carbon fiber-reinforced plastic (CFRP) laminates by fiber microbuckling. Compos Sci Technol 1999;59:1451–5. [8] Lessard LB, Chang F-K. Effect of load distribution on fiber buckling strength of unidirectional composites. J Compos Mater 1991;25:65–87. [9] Guynn EG, Bradley WL, Ochoa OO. A parametric study of variables that affect fiber microbuckling initiation in composite laminates: part 2 – experiments. J Compos Mater 1992;26(11):1594–616. [10] Rhodes MD, Mikulas MM, McGowan PE. Effects of orthotropy on the compression strength of graphite–epoxy panels with holes. AIAA J 1984;22(9):1283–92. [11] Andrews SD et al. The effect of fastener hole defects. J Compos Mater 1993;27(1):2–20. [12] Afaghi-Khatibi A, Ye L, Mai Y-W. An effective crack growth model for residual strength evaluation of composite laminates with circular holes. J Compos Mater 1996;30(2):142–63. [13] Nguyen BN. Three-dimensional modeling of damage in laminated composites containing a central hole. J Compos Mater 1997;31(17):1672–93. [14] Lee HH, Hyer MW. Postbuckling failure of composite plates with holes. AIAA J 1993;31(7):1293–8. [15] Ireman T, Eriksson I. Strength of composite laminates containing holes and subjected to complex loading conditions. J Compos Mater 1997;31(2):1214–48. [16] Chang K-Y, Liu S, Chang F-K. Damage tolerance of laminated composites containing an open hole and subjected to tensile loadings. J Compos Mater 1991;25:274–301. [17] Chang F-K, Lessard LB. Damage tolerance of laminated composites containing an open hole and subjected to compressive loadings. Part I – analysis. J Compos Mater 1991;25:2–43. [18] Lessard LB, Chang F-K. Damage tolerance of laminated composites containing an open hole and subjected to compressive loadings. Part II – experiment. J Compos Mater 1991;25:44–64. [19] Soutis C, Fleck NA, Smith PA. Failure prediction technique for compression loaded carbon fiber–epoxy laminate with open holes. J Compos Mater 1991;25:1476–98. [20] Soutis C, Fleck NA. Static compression failure of carbon fibre T800/ 924C composite plate with a single hole. J Compos Mater 1990;24:536–58. [21] Tang SC. Finite-width correction factors for anisotropic plate containing a central opening. J Compos Mater 1988;22:1080–97. [22] Zhang C, Hoa SV, Ganesan R. Edge effects in laminated composites with pin loaded holes. AIAA J 1998;36(10):1883–93. [23] Advanced Composites Database System: NAL-ACDB; Ver. 02-1, Advanced Composite Evaluation Technology Center in National Aerospace Laboratory of Japan. Available from: http://www.nalacdb.com. [24] ABAQUS/Standard userÕs manual, vols. I–III.
On failure mechanisms of composite laminates with an open hole subjected to compressive load H. Suemasu a
a,*
, H. Takahashi b, T. Ishikawa
c
Department of Mechanical Engineering, Faculty of Science and Technology, Sophia University, 7-1, Kioicho, Chiyoda-ku, Tokyo 102-8554, Japan b Graduate School, Sophia University, 7-1 Kioicho, Chiyoda-ku, Tokyo 102-8554, Japan c Japan Aerospace Exploration Agency, 6-13-1 Ohsawa, Mitaka-shi, Tokyo 181-0015, Japan Received 10 November 2004; accepted 18 July 2005 Available online 7 October 2005
Abstract In the present study, the compressive failure mechanism of quasi-isotropic composite laminates with an open hole was experimentally and numerically studied to explain the mechanical meaning of the open hole compression (OHC) strength. In the experiment, we adopted a fixture for the OHC test method proposed by the National Aerospace Laboratory (NAL III). Two types of composite systems were tested to examine the dependence of failure behavior on the material properties such as interlaminar toughness. The damage which appeared first was fiber micro-buckling in the 0° layer. Some accumulation of damage, such as further fiber micro-buckling in the 0° layers and interlaminar delaminations in several interfaces, was observed before the final unstable fracture in the laminate with high interlaminar toughness, while sudden failure occurred in the laminate with low interlaminar toughness. In the numerical study, a full three-dimensional finite element analysis was conducted. At the transverse edge of the hole, not only stress singularity at the interface but also high stress concentration at the 0° layers was obtained. Singular stress at the interfaces decreased quickly to a level much below the interlaminar strength. To consider the effect of micro-buckling on the stress redistribution and further damage accumulation, a damage analysis was conducted by reducing the stiffness components of the corresponding elements to 1/10. When one element was damaged, the maximum stress next to the damaged element became higher than the maximum stress for the intact laminate. The maximum stress decreased with the increase in number of the damaged element in the transverse direction and became lower than that for intact laminate after some extension of the damage area. This result indicates that some unstable damage progress of limited size would be expected just at the first damage occurrence and a stable increase of damage would follow it with further compressive load increase until other damage systems occurred. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Composite laminate; Open hole compression; Finite element method; Fiber micro-buckling; Delamination
1. Introduction Composite laminates are used particularly for aerospace structures due to their high specific strength and stiffness. However, the toughness is not sufficient compared to the conventional metal materials such as aluminum alloys. When composite laminates are used as a structural material it is very important to evaluate the over-all performance of
*
Corresponding author. Tel.: +81 3 3238 3857; fax: +81 3 3238 3311. E-mail address: [email protected] (H. Suemasu).
0266-3538/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2005.07.042
the composite laminates with an appropriate method which considers the various damage tolerant properties as a structural material. The open hole compression (OHC) test [1] as well as the compression after impact test (CAI) [2,3] provides us useful design data for the compression strength of the composite laminates having cut-outs, defect, and so on. So, demand for the OHC test has been increasing since it is more economical and easier to perform compared to the CAI test which has been widely used to obtain the damage tolerant compressive strength of the composite materials. But the mechanical meaning of OHC strength is not clear yet. It is very important to understand the failure mecha-
H. Suemasu et al. / Composites Science and Technology 66 (2006) 634–641
nism of the OHC specimen to properly utilize the OHC strength data. This study also contributes to the understanding of the general problem of the failure from a portion of the stress concentration. The OHC strength is thought to be the strength of a composite material with some damage. The stress around a circular hole is very complex due to the effect of the inhomogeneous material properties as well as the stress concentration. The singularity of the interlaminar stress [4,5] whose power of singularity is very small compared to one half of a typical crack makes the problem difficult to estimate. The large stress near the hole surface due to the singularity may not cause the initial damage because of the stress relaxation mechanism at the interface, but it does play an important roll in the fatigue, which is another important problem to be solved. The compressive strength of the fiber reinforced composites in the fiber direction is usually weak compared to the tensile strength. The low strength is caused by the micro-buckling of the fiber which is embedded in the compliant matrix [6–10]. The strength of each ply is not a fixed value but depends on the stacking sequence, ply thickness, total thickness of the laminate and so on. Furthermore, the strength of the ply subjected to non-uniform stress may not be equal to the strength measured under uniform stress. Many studies about damage and failure from a circular hole in a composite laminate under compressive load have been carried out because of interest in the OHC test as well as the practical importance of this problem, such as failure at bolt holes [11–22]. However, there still remain various uncertainties about the failure mechanism. In the present paper, we study experimentally and numerically the failure mechanism of the quasi-isotropic laminates with a hole. In the experiment, the NAL III method was adopted owing to its efficiency. The damage accumulation history was observed during the test with a digital microscope. The magnitude of the damage was studied through the C-scan image and the micrographs of the damaged cross-sectional area. The results observed are discussed by referring the finite element results. A chart estimating the OHC strength is proposed.
635
Fig. 1. OHC test apparatus and fixture (NAL III method).
2. Experiment Figs. 1 and 2 show the test apparatus and the fixture which were prepared following the instructions for the OHC test procedure (NAL III) proposed by the National Aerospace Laboratory, (Japan) [1]. A fixture with the same size of gage area and open window as that of the SACMA 3R-94 test method enables us to use a smaller specimen and to get almost same results as the SACMA test method. The instruction and the test results of NAL III method are well explained in [1] by comparison with SACMA method. The quasi-isotropic laminates ([(45/0/–45/90)2]sym) shown in Fig. 3 were supported by the fixture to prevent from the buckling and then placed in a hydraulic test machine. Two types of materials T800H/3633 and TR30/#340 lami-
Fig. 2. Fixture for OHC test (NAL III method).
nate were tested. The T800H/3633 laminate has a comparatively tougher interface than the TR30/#340 laminate. The close-up picture of the hole surface of T800/3633 specimen is shown in Fig. 3(b), which had been manufactured for a round robin test for NAL III test method following the instruction for OHC test using recommended tool. The specimens made of TR30/#340 laminate prepared by our department engineers were carefully drilled and the hole surfaces were grinded to make the surface as smooth
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-2 5
Force (kN)
-2 0
-1 5
-1 0
-5
0 0
-0.2
-0.4 -0. 6 -0.8 Displacement (mm)
-1
-1.2
Fig. 4. Applied load against the displacement of the fixture.
Fig. 3. OHC test specimen for NAL III method: (a) overall view (b) close up picture of the hole surface of T800/#3633 specimen.
as possible. The transverse hole surface where the damage was expected to occur first due to the stress concentration was observed by using a digital microscope during the experiment. The top of the specimen was pushed through a flat fixture surface. The pushing bar was supported by horizontal bar through a ball-bearing in order to minimize the inclination of the pushing bar during experiment. The cross-head speed was set very slow less than 0.1 mm/min to allow as long time to identify the damage initiation. A relation between the applied load and the displacement of end fixture is plotted in Fig. 4. There is some reduction of the compressive stiffness around 17 kN and further reduction is found at about 19 kN. The damage accumulation process of the T800H/3633 specimen observed with the digital microscope is shown in Fig. 5. Damage due to fiber micro-buckling appeared first in the 0° layer at about 17.5kN (Fig. 5(b)), which correspond to the first reduction of the stiffness. The damage finally occurred in all 0° layers (Fig. 5(c)). The damaged portions grew by some amount (Fig. 5(d)). The magnified pictures of the damage showed that the small portion of the 0° layer buckled out from the hole surface. Then, a delaminated surface layer suddenly broke at 22.7 kN (Fig. 5(e)): this result was probably caused by the delamination buckling. This meant that the delamination had spread by some amount at this stage. The specimen finally failed at 23.2 kN (Fig. 5(f)). The specimen of TR30/#340 having a low interfacial toughness failed suddenly without visible damage. A photograph of
the radial cross-section and a C-scan image of T800H/ 3633 damaged specimen are shown in Fig. 6. The specimen was removed from the fixture before rupture. Transverse cracks found in all 0° layers at the hole surface are thought to originate from the compressive failure site. Significant delaminations emanating from the damages of the 0° layers are observed at the interfaces between the 0° and ±45° layers near the surface. The overview of the delaminations are observed around the damage site also in Fig. 6(b). The loads at the onset of damage and the final failure obtained are listed in Table 1 with the data of the other material systems shown in [1] in order to understand clearly the effect of the compressive strength of the unidirectional fiber composite and the interlaminar toughness on the failure of the laminates with an open hole. Laminate KA/#410 broke without visible damage and had very high OHC strength. Laminates IM600/QC133 and IM600/QC101 with toughened interfaces [1] showing the initiation of damage in 0° layers at a very low load level kept their load bearing capability up to about 23 kN. The low compressive load at damage initiation may be caused by low stiffness interface, which fosters the deformation of the 0° layers by the interfacial stress. The present two types of specimens, T800H/ 3633 and TR30/#340, showed intermediate results. We may say that the compressive strength of the 0° layer governed the final failure load for the laminates with low interface toughness compared to the compressive strength in the fiber direction and the delamination size might govern the strength of the laminates with toughened interfaces. 3. Finite element analysis and results The analytical model is illustrated in Fig. 7 with the coordinate system. The material properties are EL = 148 GPa, ET = 9.56 GPa, GLT = 4.55 GPa, GTT = 3.17 GPa,
H. Suemasu et al. / Composites Science and Technology 66 (2006) 634–641
637
Fig. 5. Damage progress during OHC test taken by a digital microscope. Specimen thickness is 3.2 mm and please see the size of the damage (T800H/3633 [(45/0/–45/90)2]s).
mLT = 0.3, and mTT = 0.49. Since the deformation of the quasi-isotropic laminate is symmetric with respect to midsurface of the laminate and the center line of the hole (z-axis), only one quarter of the plate is modeled. The boundary conditions on the mid-surface (z = 0, y = ±b/2 and x = l/2) are written, respectively, w ¼ sxz ¼ sxz ¼ 0
on z ¼ 0;
ry ¼ sxy ¼ syz ¼ 0 on y ¼ b=2; u ¼ u0 ; sxz ¼ sxy ¼ 0 on x ¼ l=2;
ð1Þ
The condition of symmetry about z-axis is realized by the following equations: uð0; y; zÞ þ uð0; y; zÞ ¼ 0; vð0; y; zÞ þ vð0; y; zÞ ¼ 0 wð0; y; zÞ wð0; y; zÞ ¼ 0.
on x ¼ 0;
ð2Þ
A commercially available finite element code (ABAQUS 6.3) [24] was used to conduct the numerical analysis. A three-dimensional 20 node brick element was used. A 0° layer and its neighboring portions were refined to get an accurate magnitude of the stress concentration, because damage was observed first in the 0° layers and inter-laminar stresses were also expected to be significant at the interfaces between the 0° layer and the neighboring layers. The finite element mesh is shown in Fig. 8. To impose the symmetric condition of Eq. (2) at the surface of x = 0 the displacements of the corresponding nodes were constrained through an Ôequation commandÕ provided by the ABAQUS code. The number of elements and nodes of the model was 21,112 and 91,257, respectively. Distributions of normal stress in the fiber direction rL when 1 MPa of average stress is applied at the end of the specimen are plotted in Fig. 9. Fig. 9(a) is the stress at
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Fig. 6. Damage state near the hole edge of the quasi-isotropic laminates of T800H/3633 material system [(45/0/–45/90)2]s) before final failure under the OHC test: (a) micrographs of damage at a radial cross-section; (b) C scan image of damage. Table 1 Comparison of the loads at initial damage and failure loads for various materials obtained by OHC test Material system
Initial damage (kN)
Failure load (kN)
Strength (MPa)
Standard deviation (MPa)
Compressive strength of UD composite (MPa)
KA/#410 [1] TR30/#340 T800H/#3633 IM600/#133 [23] IM600/#101 [23]
29.4 22.0 17.5 6 4
29.4 22.0 23.2 24.5 23.7
370.2 255.8 276.8 272.0 271.3
1.9 – – 7.4 5.0
– – – 1037 [23] –
The data with shadow rows are our experimental result. The other data were in [1,23] to refer.
the hole surface and cross-section in the radial direction. Though the stress distribution is not accurately expressed due to the smoothing technique of the visualization system of the post-processor, the effect of the inhomogeneity of the laminate on the stress distribution at the hole area can be well seen. The compressive stress is extremely large at the
transverse edges of the 0° layers as expected. The stress rL in the ±45° layers was even smaller at the hole surface than that at the inside portion, since the fiber stress had to be released at the surface. The released stress must be carried by the 0° layers and made the stress concentration of the 0° layers even higher.
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639
Fig. 7. Analytical model of OHC test specimen (mm).
Fig. 10. Normal stress rx along the thickness direction at the hole surface (h = 90°).
Fig. 8. Finite element mesh.
The stress distributions rx at the section (h = 90°) in the thickness direction are plotted in Fig. 10. The normal stress rx is 11.62 times the applied average stress at the loading edge. The stress component rx in the 45° layer is small. The shear stress sxz at the section (h = 90°) in the thickness direction is plotted in Fig. 11. As reported by many researchers the stress sxz clearly shows existence of a singularity at the interface [3,4]. The stress singularity became
uncertain at the interfaces whose neighboring layers were not sufficiently divided. The shear stress sxz along the transverse direction at a interface between 0° and 45° layers are plotted in Fig. 12. The stress reduces very quickly to zero with the distance from the free edge. It is very difficult to assess the significance of the large stress in a very small area to the failure and some fracture mechanical consideration may be needed. In the experiment, small and finite size micro-buckled portion appeared in the 0° layers at the moment of the damage initiation when sudden failure did not occur. This damage is thought to play a roll of a natural initial damage. A series of FEM analysis was performed to explain the reason of this small and unstable growth of damage. Though it was imperfect to explain failure process, it may show a hint to understand the initial failure mechanisms. All the elastic moduli of the designated elements were dropped to 1/10 of those of the intact material to represent the zone of compressive failure. We call this less stiff element Ôdam-
90°
-45 °
0°
45 °
90 °
-45 °
0°
45 °
Stress τxz[MPa]
0.2
0
-0.2
-0.4 0 Fig. 9. Distribution of the normal stress rL in the fiber direction (maximum stress is 11.62 MPa): (a) hole surface and radial cross-section; (b) stress in the 0° layer.
0.2
0.4
0.6
0.8
1
Specimen Height [mm]
Fig. 11. Shear stress sxz along the thickness direction at the hole surface (h = 90° and 90°).
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-11.53 Compressive stress [MPa]
Interlaminar Stress τ xz [MPa]
0 -0.1
-0.2
-0.3
-12.35-12.31-12.24 -12.14
-11.88 -12.6 7-11.2 6
-10
-10.56
no damage damage 1 damage 2 damage 3 damage 4 damage 7 damage 8 damage 9 damage 12
-5
-0.4 3.175
6
9 12 15 Distance from the hole center[mm]
18
0
0
0.1
0.2 0.3 0.4 Radial direction [mm]
0.5
0.6
Fig. 12. Shear stress sxz along a interface between the 0° and 45° layers in the radial cross-section (h = 90°).
Fig. 14. Change of the stress distribution and maximum stress in the 0° layer with the increase of damage area.
aged elementÕ. We do not know what value of the reduction factor is most appropriate. 1/10 is not impractical and is a little larger than the value usually used in damage analyses. The replacement of the intact elements with the damaged elements causes the stress redistribution and some increases of stresses in the intact elements near the replaced damaged elements. As the stress increase in the surrounding portion would be related to the rate of the reduction of the load carrying capacity of the damaged area, the present modest reduction of the modulus would cause less stress increase. So, we may say that the unstable damage progress would occur in the real laminates when the unstable propagation was expected in the present analysis. In this analysis, the symmetry condition of the mid-plane was not used and one half of the laminate was analyzed to consider the case where the damage occurs in one of the 0° layers. The damage zone was increased one element by one element from the edge of the hole to transverse direction as shown in Fig. 13 and a stress analysis was conducted for every expansion of the damaged area. The stress distributions along the radial direction are plotted from the edge of the hole to the radial direction in Fig. 14 at every expansion of the damage zone. The line with solid circles is the stress distribution for the intact plate. The stress decayed from 11.53 to about 5.7 at the point 0.6 mm from the hole surface. (The maximum stress became 0.5% lower than the former result owing to the coarser discretization.) The
maximum compressive stress rx appeared at the point just next to the damaged element due to the redistribution of the stresses and the value (12.35) was higher than that (11.53) of undamaged model. This means that the damage caused by high stress at the edge brings about higher stress and will generate the further damage. If failure is assumed to start at the hole surface at this load level and the resulting state shows higher stress than the maximum compressive stress of 11.53, we may say further damage created by the stress. The next line with triangle is the stress distribution when only one element was replaced with a damaged element. When two elements are damaged, the maximum stress is smaller than that for one damaged element but is still larger than that with no damage element, that is, further damage growth would be expected. When more than six elements are damaged the maximum stress became smaller than that with no damage case, which means that the damage propagation should decelerates and stops. The order of the initial damage is expected to be around 0.3 mm from the present rough analysis. It is because the stresses are redistributed also in the neighboring ±45° layers, whose load carrying capability increases with the distance from the hole surface as was indicated in Fig. 9(a). We may say that there exists some unstable finite expansion and arrest after a small expansion of the damage unless other types of damage become unstable. This damage is thought to play an initial damage. In the present experiment, delaminations seemed to spread from the damage. 4. Discussion and summary
-45˚ 0˚ 45˚
damage1 0.1375
90˚z y
0.42
x unit : mm
0.05
damage2
Fig. 13. The assumption of damage area, where the elastic constants are reduced to 1/10 of the original element.
From the present experimental and numerical study, we have the following conclusions about OHC strength: 1. The specimens with tough interface show the first damage in 0° layer and fails after some further increase in the load, while the specimens with a brittle interface break suddenly without visible damage.
H. Suemasu et al. / Composites Science and Technology 66 (2006) 634–641
2. The stress concentration at the 0° layer is about 11.6 times larger than the average applied stress for the quasi-isotropic laminates. 3. The maximum stress in the 0° layers of the damaged laminate is larger than that of the intact laminate at first and decreases with the increase of damage. This indicates that a small unstable formation of the damage zone is expected to occur at the initiation stage and then the damage arrests unless the other damage unstably propagates following the initial damage. We propose a failure mechanism of the OHC test as shown in Fig. 15. The vertical axis is the applied load and the horizontal axis refers a magnitude or a significance of damage. The chained lines are the critical size of the damage depending on the toughness which decrease with the load according to the fracture mechanical theory. The compressive strength in the fiber direction tends to be weak when the interface is toughened. For the laminate with the tough interface, the 0° layer first fails due to fiber micro-buckling but the size of the damage zone in the 0° layer is not large enough to cause further growth of other types of damage such as delaminations. With the load increase the damage gradually spreads in the radial direction until the stress is large enough for the damage to be unstable. The delamination near the surface causes the buckling of the surface delaminated layer, which just precedes the final failure. In this case, the toughness of the interface plays an important role in controlling the OHC strength. If the interlaminar toughness is low and/or the compressive stress is high, the initial damage, which is large enough to bring about the further growth of other types of damage, causes total rapture of the laminate. This scenario explains very well the experimental results of OHC strength. If the mechanisms are reasonable, the OHC test results for the composite laminates with tough interfaces are adequate to measure its performance with consideration of the damage tolerance, whereas the OHC test results for the composite laminates with brittle interfaces show only the compressive strength in the direction of the fiber at the stress concentration area. Load
Damage size Critical Damage Size
high
Compressive Strength of 0° layer
Load of first
high
damage
Interlaminar toughness low
low
Damage Size Fig. 15. Failure mechanism and material properties.
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