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Evaluation of residual strength of notched fiber metal laminates
Materials Science and Engineering A 457 (2007) 338–349
Evaluation of residual strength of notched fiber metal laminates Guocai Wu ∗ , Yi Tan 1 , Jenn-Ming Yang Department of Materials Science and Engineering, University of California, Los Angeles, CA 90095, United States Received 5 January 2006; received in revised form 8 December 2006; accepted 11 December 2006
Abstract Fiber metal laminates (FML) are a family of hybrid materials consisting of alternating layers of thin metal sheets and fiber-reinforced epoxy prepregs. In contrast to aluminum alloys, the presence of notches in FML causes significant strength reductions. The objective of this study was to evaluate the residual strength of fiber-reinforced metal laminates with a circular open hole. Mechanical testing was performed to determine the unnotched tensile properties and notched strength of bi-directionally reinforced fiber metal laminates. The influence of specimen dimension and notch size on residual strength and notch sensitivity of fiber metal laminates was investigated. A modified point stress criterion was introduced to predict the residual strength of fiber metal laminates with open hole. An excellent agreement between experimental results and model prediction was obtained. The residual strength predicted from this modified model also correlated very well with the experimental data in the literature for various other types of fiber metal laminates. A computer simulation based on finite element method was performed to study stress concentration and stress concentration around notch. Failure modes, damage initiation and progression of notched fiber metal laminates are also characterized and discussed. © 2007 Elsevier B.V. All rights reserved. Keywords: Residual strength; Fiber metal laminates; Modified point stress criterion; Damage mechanism; Finite element simulation
1. Introduction Fiber-reinforced metal laminates (FML) are hybrid composites consisting of alternating thin layers of metal sheets and fiber-reinforced epoxy prepreg. The most commonly used metal for FML is aluminum, and the fibers can be Kevlar or glass. The FML with glass fibers (tradename GLARE), and Kevlar fibers (tradename ARALL) have been evaluated for many potential applications in aircraft structures [1–4]. More recently, GLARE has been selected for the upper fuselage skin structure of Airbus A380. The combination of metals and composites results in a new family of hybrid laminates with an ability to impede and arrest crack growth caused by cyclic loading, with excellent impact and damage tolerance characteristics and a low density. Most of investigations so far mainly focus on the behavior of fatigue crack propagation [5–7]. However, the residual/blunt notch strength is an important design parameter in engineering application, i.e. the residual strength of a material in the presence of holes, saw-cuts and cracks. In an aircraft, geomet∗ Corresponding author. Present address: Cummins Inc., Columbus, IN 47201, United States. E-mail address: [email protected] (G. Wu). 1 Present address: Dalian University of Technology, Dalian 116024, China.
0921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.12.135
rical notches cannot be avoided by the designers. The ideal unnotched structure is disturbed by many hatches, windows, doors and by thousands of rivet holes [8,9]. All these discontinuities will cause a disturbance of stress flow in the material and cause a stress concentration in the vicinity of the notch. Like most of fiber-reinforced composite materials, it has been found [5,8–10] that GLARE or ARALL laminates are highly notch sensitive in comparison with pure aluminum alloys, whether they are blunt notches or sharp cracks. Although some investigation has already been performed on the notch properties of ARALL by Vermeeren [10], Vogelesang and Gunnink [11], Teply et al. [12], Macheret et al. [13], Bucci et al. [14], Jin and Mai [15] or carbon fiber-reinforced aluminum laminates by Afaghi-Khatibi et al. [16], and some models have been developed for evaluating fracture behavior of fiber metal laminates, very limited work was done with the GLARE laminates, especially for newly developed GLARE laminates with cross-plied prepreg such as GLARE 4 and GLARE 5. Therefore, it is necessary to identify basic mechanical behavior and failure mechanisms, and to develop analytical methods for predicting the notch properties of GLARE laminates in order to lead it to expanded practical use. This paper presents an experimental and theoretical study to investigate the residual strength of fiber metal laminates
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with a center open hole. The laminates were loaded in longitudinal direction, and the influence of specimen dimensions and notch sizes on the notch sensitivity of GLARE laminates will be assessed. A brief review of analytical modeling of notched laminates is given first, and the validity of some practical models will be examined in the present study to establish a practical design methodology and attain understanding of the fundamentals of the notch behavior of fiber metal laminates. A modified point stress criterion is introduced to predict the notched strength of GLARE, and applicability of the present model to other types of fiber metal laminates is evaluated. The results are also compared with the predictions from other previous models including the point stress criterion (PSC) [17,18], and effective crack growth model (EGCM) [16,19]. A preliminary finite element simulation is performed. Failure modes, damage initiation and progression of notched fiber metal laminates are investigated by optical microscopy, scanning electron microscopy and X-ray radiography, and chemical deply technique. 2. Evaluation of residual strength of notched fiber metal laminates 2.1. A brief review of existing analytical models The residual strength prediction of notched fiber metal laminates is a difficult problem because of the complexity of the actual damage process before fracture, which involves matrix microcracking, fiber splitting or breakage, delamination and plastic zone development in the aluminum layer. An effective and common way to evaluate the residual strength of fiberreinforced metal laminates is to extend the current residual strength models developed for notched polymer–matrix fiber composite laminates. Awerbuch and Madhukar [20] provided a comprehensive review of current fracture modes of the notch strength of polymer composite laminates. Generally speaking, the existing notched strength model for fiber composite laminates can be categorized into three groups. The first category is the model based on stress-failure which was initially proposed by Whitney and Nuismer [17,18], and then further extended and modified by Karlak [21], Pipes et al. [22], and Tan [23]. All these models introduced a characteristic length to evaluate the notched strength of composite laminates. The second category is the model based on fracture mechanics, such as WEK model [24], the Mar–Lin criterion [25], the damage zone model (DZM) [26] and the damage zone criterion (DZC) [27]. DZM or DZC model states that damage zone is approximated by a crack with cohesive stresses acting on its surfaces, and damage in the material is taken into account by reducing the cohesive stresses with increased crack opening, which in turn corresponds to increased separation of materials. Similarly, an effective crack growth model was developed by Afaghi-Khatibi et al. [16] using an iterative technique to predict the residual strength of composite laminates containing a hole or sharp notches. The third group is the progressive damage model [28]. Such a model was developed to predict the extent of damage and damage progression in notched composite laminates. Because the evaluation of the pro-
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gressive damage model was based on the finite element method, it is less attractive than other closed form criteria. Application of some of these models to fiber-reinforced metal laminates was investigated by Teply et al. and Macheret et al. [12,13], Afaghi-Khatibi et al. [16], Van Rjin [29], and Lawcock et al. [30]. Van Rjin [29] reviewed the applicability of the above-mentioned residual strength models of polymer composite laminates to fiber-reinforced metal laminates. Based on the basic concept of fracture mechanics, a R-curve approach [31] was proposed to evaluate the residual strength of ARALL or GLARE. An effective crack growth model was developed by Afaghi-Khatibi et al. [16] to evaluate the strength of CARLL (carbon fiber-reinforced aluminum laminates) and ARALL with different notch sizes. In this model, damage is assumed to be initiated when the local normal stress ahead of notch tip reaches the tensile strength of composite layers and the yield strength of metal layers, respectively. 2.2. Evaluation of residual strength of notched fiber metal laminates in the present study Although there are few models to evaluate the residual strength of notched composite laminates, the point stress failure criterion is introduced into the present study because it is simple to apply and it is widely used in practical engineering application. Details of PSC model are not intended to repeat here, but relevant expressions and brief description is necessary. For an orthotropic plate with a circular hole under normal loads, PSC model states that when the normal stress σ y , at some distance d0 from the hole edge, reaches the failure strength of an unnotched plate, failure will occur in the notched plate. That is: σy (x, 0) = σ0
at x = r + d0
(1)
where r is the radius of the circular hole and d0 is the characteristic length. For an infinite orthotropic plate subjected to a uniform stress, σy∞ , applied parallel to the y-axis at infinity, the normal stress distribution, σ y along the x-axis ahead of the hole can be expressed as [32]: ∞ r 2 r 4 σy 2+ +3 σy (x, 0) = 2 x x r 6 r 8 , x>r (2) −(KT∞ − 3) 5 −7 x x where KT∞ is the stress concentration factor of the subject material for an infinite orthotropic plate with a circular hole:
Exx E xx ∞
KT = 1 + 2 (3) − νxy + Eyy Gxy where Exx , Eyy and Gxy are the axial, transverse and shear moduli, respectively, and νxy is the major Poisson’s ratio for the laminate. Substituting Eq. (2) into the Eq. (1), we obtain the PSC expression for normalized notched strength: 2 σN∞ = σ0 (2 + ε2 + 3ε4 − (KT∞ − 3)(5ε6 − 7ε8 )
(4)
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Table 1 Tensile test results for unnotched GLARE 4-3/2 laminate Specimen #
Thickness (in.)
Width (in.)
Fracture load (lb)
Fracture strength (MPa)
Fracture strain (%)
Modulus (GPa)
Poission’s ratio
G4-L-01 G4-L-02 G4-L-03a G4-L-04 G4-L-05 Average
0.072 0.072 0.072 0.072 0.0715 0.0719
1.032 0.986 1.009 0.973 0.988 0.998
8.565 8.270 8.255 8.002 8.351 8.288
794.75 803.18 783.45 787.54 815.06 796.80
4.04 4.19 3.84 4.01 4.23 4.06
50.5 50.6 51.5 50.8 51.0 50.9
/ / 0.259 0.271 0.267 0.266
a
Fracture site is near to the grip tab.
where σ 0 is the unnotched tensile strength of the laminate, σN∞ the notched strength of an infinite width plate and ε = r/(r + d0 ). The above described point stress criterion enables the prediction of the notched strength of composite laminates containing circular open hole. It is formulated assuming that the plates are of infinite width, so the infinite width notched strength, σN∞ , is predicted. However, experimental data are obtained on specimens with a finite width. For proper comparison between experimental results and predictions, the test data have to be normalized by using a finite width correction (FWC) factor. For an orthotropic plate with a circular hole, the finite width correction factor is expressed as [33]: KT∞ KT
=
3(1 − 2r/W) 1 2r + M 3 2 W 2 + (1 − 2r/W) 2 2r M × 1− W
6
(KT∞ − 3)
Fig. 1. Geometry and dimensions of specimens and location of strain gage A and B.
That is: −1
d0 = m
2r W
n (9)
where m is notch sensitivity factor and n is exponential parameter. Substituting Eq. (9) into Eq. (4), a modified point stress criterion is obtained: (5)
where 1 − 8[(3(1 − 2r/W))/(2 + (1 − 2r/W)3 ) − 1] − 1 2 M = 2(2r/W)2 (6) where KT /KT∞ is the FWC factor, and KT and KT∞ are stress concentration factor at the notch edge for a finite width plate and an infinite plate, respectively. In the above traditional point stress criterion, it is assumed that the characteristic dimension is a material parameter and independent of the notch size [17,18]. When the characteristic length is independent of open hole radius, accurate notched strength prediction can be achieved. However, some of previous experimental results with various materials and stacking sequence have shown that the characteristic length is not a constant and dependent on the specimen geometry [21,22]. The experimental result, which is given below, of GLARE 4-3/2 laminate with a circular open hole in the present study further confirm that the characteristic length in the traditional PSC is varied with the hole sizes and widths. So the classical point stress criterion needs to be modified to evaluate the residual strength of notched GLARE more accurately. A detailed analysis of the dependence of characteristic length d0 on the specimen geometry in this study shows that it follows an exponential relationship, which is consistent with the previous study by Kim and Kim [34] for predicting the notched strength of glass/epoxy composites.
σN∞ 2 = σ0 (2 + ε2 + 3ε4 − (KT∞ − 3)(5ε6 − 7ε8 )
(10)
where ε=
1
(11)
1 + 2n rn−1 W −n m−1
3. Experimental procedures 3.1. Materials and specimen preparation Fiber metal laminates used in the present experimental investigation are GLARE 4 with 3/2 lay-up provided by Aviation Equipment Structures, Inc. (Costa Mesa, CA). GLARE 4-3/2 consists of three layers of 2024-T3 aluminum alloy sheets and two layers of 67/33 glass prepreg with 67% of fibers in 0◦ direcTable 2 Notched strength test results for GLARE 4-3/2 laminate W (mm)
2r (mm)
2r/W
σ N (MPa)
σN∞ (MPa)
σN∞ /σ0
d0 (mm)
25.63 25.55 25.96 51.26 50.83 50.60 76.10 76.02 76.15
3.07 6.29 12.67 6.23 12.62 25.81 9.5 20.32 38.68
0.1198 0.2462 0.4881 0.1215 0.2483 0.5101 0.1248 0.2673 0.5079
480.68 390.14 266.11 439.75 363.34 249.3 421.95 345.71 244.33
488.22 418.46 364.83 446.79 390.05 353.75 429.11 375.78 345.63
0.6127 0.5252 0.4579 0.5608 0.4895 0.444 0.5386 0.4716 0.4338
0.6096 0.8230 1.0541 0.9652 1.3081 1.9228 1.3111 1.8694 2.6391
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tion and 33% fiber in 90◦ direction. All the tensile specimens were cut from 300 mm × 300 mm GLARE panels. The specimens used in this study were 300 mm in length and the width was chosen to be 25.4, 50.8 and 76.2 mm, respectively. For each width, three different hole sizes were chosen but the ratio of hole size to width is kept to be constant as 0.125, 0.25, 0.5, respectively. The actual average thickness of each layers for the as-received GLARE laminates were measured using optical micrographs. The average thickness of GLARE 4-3/2 was 0.304 mm for aluminum alloy sheets and 0.458 mm for prepreg layers. Therefore, the actual average thickness of GLAR4-3/2 laminate in the present study is 1.828 mm. The circular holes were prepared through the center of the specimen using carbide-tipped drill bits or diamond-tipped drill bits. A circular hole is machined by initially drilling a starter hole of small diameter, and then carefully enlarging it to its final dimensions by incremental drilling. In order to avoid delamination at the hole edge and to obtain a clean and smooth hole during drilling, a flat wooden plate was placed and clamped below the specimen. The notched region was hand polished using sand paper. The specimens containing holes were inspected with an X-ray technique to detect delamination caused by drilling. The laminates and holes are proved to have a good quality. After drilling, aluminum alloy end tabs were attached on both ends of specimens using aluminum putty adhesive. 3.2. Test procedures All the notched specimens were loaded along the longitudinal direction (parallel to 0◦ fiber direction). Static tensile tests were performed using a 22 kips servo-hydraulic Instron test frame with a cross-head speed of 1 mm/min at room temperature. Specimens were clamped by the hydraulic grip fitted on the testing machine. For each specimen configuration, three replicates were tested. As part of the notch sensitivity study, unnotched coupons were also tested to determine the unnotched tensile strength and in-plane laminate mechanical properties in accordance with ASTM D-3039. A summary of the mechanical properties of unnotched GLARE 4-3/2 is presented in Table 1. Strain gages were implemented for monitoring the strain. One strain gage was mounted on the front center line of specimen midway between the notch and gripping region to measure far-field strain. The other strain gage is placed at the hole edge along the center line of holes to measure the strain concentration at the hole edge as shown in Fig. 1. Omega 900 series data acquisition modules and LABTECH Notebook were used to record strains and applied loads. Post-fracture specimens were examined by optical and scanning electron microscopy to characterize the fracture mode. Zinc iodide-enhanced X-ray radiography was used to monitor delamination around the peripheral of the hole. Additional specimens were loaded to approximately 95% of the failure load to determine the damage growth pattern. The damage characteristics were determined from X-ray images and microscopic examination after chemical removal of the outer aluminum layers. The gross strength σ N is defined as the notched tensile strength and it is calculated using the ultimate fracture load
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Fig. 2. Effect of hole size and specimen width on the residual strength of GLARE 4 laminate.
divided by the specimen width and thickness. For each notched specimen, the normalized residual strength, σN∞ /σ0 is evaluated, where the infinite width gross strength, σN∞ , is calculated by multiplying the finite width gross strength σ N by a finite width correction factor, and σ 0 is the unnotched strength determined from tensile tests.
Fig. 3. Relationship between characteristic length and 2r/W for GLARE 4 laminate.
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Table 3 A comparison between experimental and predicted notched strength for GLARE 4-3/2 laminate W (in.)
25.63 25.55 25.96 51.26 50.83 50.6 76.1 76.02 76.15
2r/W
3.07 6.29 12.67 6.23 12.62 25.81 9.5 20.32 38.68
2r (in.)
0.1198 0.2462 0.4881 0.1215 0.2483 0.5101 0.1248 0.2673 0.5079
Test σ N (MPa)
480.68 390.14 266.11 439.75 363.34 249.3 421.95 345.71 244.33
Modified PSC
PSC
σ N (MPa)
Relative error (%)
σ N (MPa)
Relative error (%)
481.02 391.05 266.65 437.79 366.42 248.41 420.82 347.49 243.74
0.07 0.23 0.20 −0.45 0.85 −0.36 −0.27 0.52 −0.24
534.46 393.64 249.29 502.51 371.29 230.29 485.24 349.71 227.13
11.19 0.90 −6.32 14.27 2.189 −7.63 15.00 1.16 −7.04
4. Experimental results and model verification 4.1. Evaluation of residual strength of notched GLARE 4 laminates The notched strength of GLARE 4-3/2 with different hole sizes and widths are summarized in Table 2. The normalized strength is shown for both finite width and infinite width after employing width correction factor (Eq. (5)). It clearly shows that the specimens containing a small hole have a higher notched strength, and notch sensitivity increases with the size of hole. For the specimen containing the smallest hole size to width ratio (0.125), the strength of notched GLARE 4 decreases approxi-
mately 40%. Fig. 2 presents the effect of specimen width and hole size on the normalized notched strength. The results show that the notched strength decreases with increasing 2r/W ratio regardless of the specimen width. Also for a given 2r/W ratio, the notched strength was found to increase with decreasing specimen width. The differences in notched strength with different specimen width can be explained through the variation of the size of the plastic zone in the aluminum layers and the degree of localized delamination. For notched GLARE laminates, there is a highly stressed area at the notch root, and the plastic zone in the aluminum layer is small for specimen with a small width at a constant 2r/W ratio. This results in significant shear stresses between the aluminum and fiber layers that are likely to create
Fig. 4. A comparison between experimental and predicted results for GLARE 4 laminate. (a) W = 25.4 mm; (b) W = 50.8 mm; (c) W = 76.2 mm.
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Fig. 5. A comparison between experimental and predicted results for ARALL and GLARE-2 laminates. (a) ARALL-1; (b) ARALL-1X; (c) ARALL-2; (d) GLARE-2.
earlier local delamination for small specimen. The presence of delamination would postpone fiber failure and cause the stress redistribution, thus increases the notched strength of GLARE laminates [10]. For each specimen, the characteristic length (d0 ) is determined from the PSC Eq. (4). The calculated characteristic length value from experimental results is shown in Table 2. Evidently, the characteristic length is neither a constant, nor independent of the notch size. The characteristic length d0 was found to increase with the increase in hole diameter (2r), and the specimen width (W) for the same hole size. After a detailed analysis of the dependence of characteristic length on the geometry of the specimen (2r and W), it was found that the characteristic length d0 increases exponentially with increasing of notch diameter and specimen width ratio (2r/W) as expressed by Eq. (9). Fig. 3 shows the exponential relationship between the characteristic length d0 and the ratio of circular notch diameter and plate width (2r/W) obtained from tensile test of GLARE 4-3/2. The value of parameter m and n in Eq. (9), which is associated with the variation of characteristic length, is also shown in Fig. 3. It can be seen that the notch sensitivity coefficient (m) was relatively small for wider specimen and notch
sensitivity tends to decrease with the increase of specimen width. The comparison of the experimental results and the predicted value of σN∞ /σ0 using both the PSC and the present model are presented in Table 3. It clearly indicates that the notched strength predicted from the modified PSC agrees closer to the experimental results than those predicted from classical PSC. Therefore, the modified PSC is useful and accurate for predicting the notched tensile strength of GLARE 4-3/2 laminates. The predicted effect of hole sizes on the normalized notched strength and experimental results are shown in Fig. 4. This plot shows that the PSC overpredicts the residual strength of the laminate with small notches and underpredicts the residual strength of the laminate with large notches. Table 4 Mechanical properties of ARALL and GLARE 2 laminates [10,35]
ARALL-1 ARALL-1X ARALL-2 GLARE-2
Eyy (GPa)
Exx (GPa)
νyx
Gyx (GPa)
σ 0 (MPa)
68.95 70.33 68.53 63.43
49.3 53.09 51.64 46.4
0.310 0.340 0.340 0.318
18.13 19.65 18.55 16.41
779.79 827.36 684.92 1101.5
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Fig. 7. X-ray images of the damage area in GLARE-4 laminate. (a) W = 25.4 mm; (b) W = 50.8 mm.
4.2. Evaluation of modified PSC criterion applicability of other fiber metal laminates The applicability of using the present modified PSC model to predict the notched strength of other types of fiber metal laminates with different configurations is examined carefully. Four groups of experimental data of notched ARALL-1, ARALL-2, ARALL-1X [35] and GLARE-2 laminates [10] from open literature were adopted in the evaluation. All specimens were a five ply “3/2” fiber metal laminates. The mechanical properties of these laminates are listed in Table 4. This prediction is compared with both experimental results and predictions from other previous models including PSC [17,18] and effective crack growth model by Afaghi-Khatibi et al. [16,19]. The effect of hole size on notched strength of ARALL-1 laminate in the longitudinal direction is shown in Fig. 5(a). The specimen width is W = 50.8 mm and the hole diameter varies from 3.18 to 12.7 mm. It was found that the characteristic length d0 also exhibits an exponential relationship with the ratio of hole size and specimen width (2r/W) as shown in Fig. 6(a). An excellent agreement is obtained between the experimental results and the prediction based on the present model. The notched strength versus notch size of ARALL-2 and ARALL-1X is illustrated in Fig. 5(b and c), respectively. It can be seen again that the present modified PSC model is more
Fig. 6. Relationship between characteristic length and 2r/W for ARALL and GLARE-2 laminates. (a) ARALL; (b) GLARE-2.
Fig. 8. Delamination pattern after chemical removal of aluminum layers. (a) W = 25.4 mm; (b) W = 50.8 mm.
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accurate for predicting the notched strength of ARALL laminates. Comparing the value of notch sensitivity factor (m) for these three ARALL laminates, it is found ARALL-2 is the most notch sensitive and ARALL-1 is the least notch sensitive. This is consistent with the previous investigation by Hidde and Herakovich [35]. Figs. 5(d) and 6(b) show the applicability of the present model into GLARE-2 laminates. Similar characteristics are observed for GLARE-2 laminates loaded in the longitudinal direction. Therefore, the modified PSC is capable of predicting the notched strength of fiber metal laminates with a circular hole. 5. Damage mechanism and characteristics of notched fiber metal laminates The fracture surfaces of notched specimens were macroscopically and microscopically examined. Delamination, fiber breakage and splitting are major mechanisms of fracture in
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notched GLARE 4 laminates. Fig. 7 shows the X-ray images of the typical damage zone in the post-failure notched specimen with 25.4 and 50.8 mm. A distinctive triangular (linear) delamination shape was observed for all notched specimens with different hole sizes and specimen widths. The dark area also indicates the fiber breakage and splitting. The same delamination shape was found by Teply et al. [12] for Aramid-fiber aluminum laminates (ARALL) with a central crack and Lawcock et al. [19–36] for untreated carbon-fiber aluminum laminates (CRALL) with a circular hole. Earlier study [10] also showed that ARALL laminates with a circular hole do not show any signs of delamination but delamination is present for GLARE 2 laminates with a hole. The presence of delamination causes the stress redistribution and was found to increase the notched strength of laminates. Chemical removal of the aluminum layer confirms the delamination pattern from X-ray tests as shown in Fig. 8. It was found the delamination zone size is consistent with
Fig. 9. X-ray images of damage progression pattern in the specimen with 50.8 mm width and 12.7 mm hole. (a) Initiation; (b) further loading; (c) fracture.
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the region of fiber breakage and splitting. So the X-ray radiography can be used to assess the damage state such as delamination size and shape in the laminates. There is no stable crack growth observed for aluminum layers prior to unstable fracture. This is attributed to be caused by the presence of delamination and high ductility of aluminum layers. The presence of delamination allows greater plastic deformation in the aluminum layers that reduce the stress intensity at the crack tip, so the plastic deformation rather than crack growth occurred in the aluminum layers [19]. The damage is expected to initiate in the prepreg layers because the ultimate strain of glass fibers is significantly smaller than that of aluminum. The prepreg layers control the residual strength of notched fiber metal laminates. With the increasing of the load, the yielding occurred first in the aluminum layer. When the load reaches a value almost close to critical fracture load, there were audible signs of fiber breakage and delamination growth near the edge of hole in the prepreg layers. Subsequently, it was followed by a rapid unstable crack growth across the whole specimen width leading to catastrophically failure. Fig. 9 shows X-ray images of damage progression of GLARE 4 laminates during fracture. It is obvious that the damage initiated at the hole edge and grew in size with the increasing load up to the final fracture. For some specimens, strains were measured in the loading direction at locations marked by A and B in Fig. 1. Strain gage A was placed remote to the hole and gripping, and the strain gages at B were located at the hole boundary. The measurement result indicated that all stress–strain curves recorded corresponding to gage A showed a bilinear behavior similar to that in unnotched laminates under tensile loading up to fracture load. However, the stress–strain behavior for strain gage at B close to the hole is quite different from that in gage A as shown in Fig. 10. Except a lower slope of stress–strain that is caused by the stress concentration of notch, a platform of stress–strain curve was observed around 95% critical failure load until the final fracture. This is associated with the occurrence of damage initiation such as fiber breakage, splitting and delamination at hole edge. 6. Finite element analysis of notched fiber metal laminates 6.1. Finite element mesh In this numerical study, the ANSYS SHELL91 element is employed. SHELL 91 is a nonlinear layered structural shell element. This element has six degrees of freedom at each node: translations in the nodal x, y, and z directions and rotations about the nodal x, y, and z-axes. The element is defined by eight nodes, layer thicknesses, layer material direction angles, and orthotropic material properties. A relatively fine mesh was used adjacent to the notch where splitting and delamination were expected. With element refinements around the notch region, mapping mesh technique is used for the entire domain. Due to symmetry, only one fourth of the plate was molded. The symmetrical boundary conditions are applied at the two sides of symmetry. Along the line X = 0, the nodes are constrained to
Fig. 10. Different load–strain relationship at different locations for notched GLARE 4 laminate. (a) Strain gage A; (b) strain gage B.
displacements in Y direction only. The nodes along line X = 0 are constrained to displacement in the X direction only. The glass fiber/epoxy layers were modeled with homogenized linear elastic orthotropic materials, and the Von Mises yield criterion was used to describe the elasto-plastic behavior of aluminum layers. Fig. 11 shows the FEM mesh for GLARE 4-3/2 laminate with a width of 50.8 mm and a hole of 12.7 mm. 6.2. Stress analysis and notch sensitivity analysis Fig. 12 illustrates the distribution of Von Mises equivalent stress in different layers in GLARE 4-3/2 laminate with a width of 50.8 mm and a central hole of 12.7 mm. It is evident that there is a big difference in the stress contour plots of different layers in GLARE 4 laminate. As shown in Fig. 12(a and b), there is a very high stress concentration near the notch edge in the fiber/epoxy layers, so the damage will initiate at the edge of the hole in fiber/epoxy layers. However, the stress is widely distributed over a wide range of aluminum layers as shown in Fig. 12(c) com-
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Fig. 11. (a) Finite element mesh of notched GLARE 4-3/2 laminate; (b) zoom in of the notch region mesh showing the layer element.
pared to that stress concentration in the fiber/epoxy layers is more localized in a small region at the hole edge. Stress concentration in aluminum layers is reduced because aluminum exhibits a significant plasticity, so the plastic zone ahead of notch tip can level off the stress concentration. It is consistent with our experimental observation that the plastic deformation rather than crack growth occurred in the aluminum layers before fracture described above. Fig. 13 shows the axial stress distribution along the y-axis direction for various r/W ratios. The stress exhibits a substantial stress concentration at the hole edge and drops below the far-field stress. The stress concentration factor increases as r/W increases. The stress ration near to plate straight edge drops below a unit. Greater the r/W ratio is, the lower drops. The stress concentration for the smaller hole is much more localized than for that for the larger hole. This leads to a higher strength for the smaller hole as shown in Fig. 2 due to the greater opportunity to redistribute stress and smaller volume of highly stressed materials for the smaller hole. A further study on incorporating the progressive damage model into finite element simulation is necessary to predict the effect of damage on property retention and residual strength and of notched fiber meal laminates. 7. Summary The residual strength behavior and notch sensitivity of fiber metal laminates with a central hole have been investigated.
It was shown that the residual strength of glass fiber metal laminates with central open hole increases with decreasing specimen width and decreasing hole diameter, and notch sensitivity increases with the size of hole. The presence of a hole in GLARE laminates gives a strength reduction about 40%. The characteristic length d0 in PSC was found to follow an exponential expression with the ratio of hole size and specimen width. A modified PSC was introduced to predict the residual strength. An excellent agreement was obtained between experimental results and model predictions. The applicability of the modified PSC to previous investigations on other types of fiber metal laminates validated that this model is capable to evaluate the notched strength of fiber metal laminates. Delamination, fiber breakage and splitting are major mechanisms of fracture in GLARE laminates with a center hole. A distinctive triangular (linear) delamination shape was observed for all notched specimens. Only plastic deformation and no stable crack growth in the aluminum layers prior to unstable fracture were found. The stress analysis on the notched GLARE laminates based on FEM computer simulation verified the analytical and experimental results of notched strength. The present study broadens the applicable range of the stress fracture criteria and provides a simple and useful tool to predict the residual strength of notched fiber metal laminates for engineering application. More experimental tests are needed to confirm the validity of this modified model for fiber metal laminates with various notch shapes.
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Fig. 12. Von Mises stress profile in different layers in GLARE 4-3/2 laminate. (a) 0◦ fiber layer; (b) 90◦ fiber layer; (c) aluminum layer.
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Fig. 13. The effect of notch size on axial stress distribution along y-axis (W = 50.8 mm).
Acknowledgements This work was partially supported by the Federal Aviation Administration (FAA) through the Center of Excellence on Composites and Advanced Materials. Curt Davies is the program manager. References [1] C.A.J.R. Vermeeren, Appl. Compos. Mater. 189 (2003) 189–205. [2] A. Vlot, L.B. Vogelesang, T.J. de Vries, Aircraft Eng. Aerospace Technol. 71 (6) (1999) 558–570. [3] A. Afaghi-Khatibi, L. Ye, Y.W. Mai, Compr. Compos. Mater. 249 (2000) 249–290. [4] G. Wu, J.-m. Yang, JOM (January) (2005) 72–79. [5] R.C. Alderliesten, M. Hagenbeek, J.J. Homan, P.A. Hooijmeijer, T.J. de Vries, C.A.J.R. Vermeeren, Appl. Compos. Mater. 10 (2003) 223–242. [6] J.R. Yeh, Int. J. Solids Struct. 32 (14) (1995) 2063–2075. [7] Y.J. Guo, X.R. Wu, Fatigue Fract. Eng. Mater. Struct. 21 (1998) 1133–1145. [8] R.V. Roojen, J. Sinke, T.J. De Veris, S.V.D. Zwaag, Appl. Compos. Mater. 11 (2) (2004) 63–76.
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Evaluation of residual strength of notched fiber metal laminates Guocai Wu ∗ , Yi Tan 1 , Jenn-Ming Yang Department of Materials Science and Engineering, University of California, Los Angeles, CA 90095, United States Received 5 January 2006; received in revised form 8 December 2006; accepted 11 December 2006
Abstract Fiber metal laminates (FML) are a family of hybrid materials consisting of alternating layers of thin metal sheets and fiber-reinforced epoxy prepregs. In contrast to aluminum alloys, the presence of notches in FML causes significant strength reductions. The objective of this study was to evaluate the residual strength of fiber-reinforced metal laminates with a circular open hole. Mechanical testing was performed to determine the unnotched tensile properties and notched strength of bi-directionally reinforced fiber metal laminates. The influence of specimen dimension and notch size on residual strength and notch sensitivity of fiber metal laminates was investigated. A modified point stress criterion was introduced to predict the residual strength of fiber metal laminates with open hole. An excellent agreement between experimental results and model prediction was obtained. The residual strength predicted from this modified model also correlated very well with the experimental data in the literature for various other types of fiber metal laminates. A computer simulation based on finite element method was performed to study stress concentration and stress concentration around notch. Failure modes, damage initiation and progression of notched fiber metal laminates are also characterized and discussed. © 2007 Elsevier B.V. All rights reserved. Keywords: Residual strength; Fiber metal laminates; Modified point stress criterion; Damage mechanism; Finite element simulation
1. Introduction Fiber-reinforced metal laminates (FML) are hybrid composites consisting of alternating thin layers of metal sheets and fiber-reinforced epoxy prepreg. The most commonly used metal for FML is aluminum, and the fibers can be Kevlar or glass. The FML with glass fibers (tradename GLARE), and Kevlar fibers (tradename ARALL) have been evaluated for many potential applications in aircraft structures [1–4]. More recently, GLARE has been selected for the upper fuselage skin structure of Airbus A380. The combination of metals and composites results in a new family of hybrid laminates with an ability to impede and arrest crack growth caused by cyclic loading, with excellent impact and damage tolerance characteristics and a low density. Most of investigations so far mainly focus on the behavior of fatigue crack propagation [5–7]. However, the residual/blunt notch strength is an important design parameter in engineering application, i.e. the residual strength of a material in the presence of holes, saw-cuts and cracks. In an aircraft, geomet∗ Corresponding author. Present address: Cummins Inc., Columbus, IN 47201, United States. E-mail address: [email protected] (G. Wu). 1 Present address: Dalian University of Technology, Dalian 116024, China.
0921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.12.135
rical notches cannot be avoided by the designers. The ideal unnotched structure is disturbed by many hatches, windows, doors and by thousands of rivet holes [8,9]. All these discontinuities will cause a disturbance of stress flow in the material and cause a stress concentration in the vicinity of the notch. Like most of fiber-reinforced composite materials, it has been found [5,8–10] that GLARE or ARALL laminates are highly notch sensitive in comparison with pure aluminum alloys, whether they are blunt notches or sharp cracks. Although some investigation has already been performed on the notch properties of ARALL by Vermeeren [10], Vogelesang and Gunnink [11], Teply et al. [12], Macheret et al. [13], Bucci et al. [14], Jin and Mai [15] or carbon fiber-reinforced aluminum laminates by Afaghi-Khatibi et al. [16], and some models have been developed for evaluating fracture behavior of fiber metal laminates, very limited work was done with the GLARE laminates, especially for newly developed GLARE laminates with cross-plied prepreg such as GLARE 4 and GLARE 5. Therefore, it is necessary to identify basic mechanical behavior and failure mechanisms, and to develop analytical methods for predicting the notch properties of GLARE laminates in order to lead it to expanded practical use. This paper presents an experimental and theoretical study to investigate the residual strength of fiber metal laminates
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with a center open hole. The laminates were loaded in longitudinal direction, and the influence of specimen dimensions and notch sizes on the notch sensitivity of GLARE laminates will be assessed. A brief review of analytical modeling of notched laminates is given first, and the validity of some practical models will be examined in the present study to establish a practical design methodology and attain understanding of the fundamentals of the notch behavior of fiber metal laminates. A modified point stress criterion is introduced to predict the notched strength of GLARE, and applicability of the present model to other types of fiber metal laminates is evaluated. The results are also compared with the predictions from other previous models including the point stress criterion (PSC) [17,18], and effective crack growth model (EGCM) [16,19]. A preliminary finite element simulation is performed. Failure modes, damage initiation and progression of notched fiber metal laminates are investigated by optical microscopy, scanning electron microscopy and X-ray radiography, and chemical deply technique. 2. Evaluation of residual strength of notched fiber metal laminates 2.1. A brief review of existing analytical models The residual strength prediction of notched fiber metal laminates is a difficult problem because of the complexity of the actual damage process before fracture, which involves matrix microcracking, fiber splitting or breakage, delamination and plastic zone development in the aluminum layer. An effective and common way to evaluate the residual strength of fiberreinforced metal laminates is to extend the current residual strength models developed for notched polymer–matrix fiber composite laminates. Awerbuch and Madhukar [20] provided a comprehensive review of current fracture modes of the notch strength of polymer composite laminates. Generally speaking, the existing notched strength model for fiber composite laminates can be categorized into three groups. The first category is the model based on stress-failure which was initially proposed by Whitney and Nuismer [17,18], and then further extended and modified by Karlak [21], Pipes et al. [22], and Tan [23]. All these models introduced a characteristic length to evaluate the notched strength of composite laminates. The second category is the model based on fracture mechanics, such as WEK model [24], the Mar–Lin criterion [25], the damage zone model (DZM) [26] and the damage zone criterion (DZC) [27]. DZM or DZC model states that damage zone is approximated by a crack with cohesive stresses acting on its surfaces, and damage in the material is taken into account by reducing the cohesive stresses with increased crack opening, which in turn corresponds to increased separation of materials. Similarly, an effective crack growth model was developed by Afaghi-Khatibi et al. [16] using an iterative technique to predict the residual strength of composite laminates containing a hole or sharp notches. The third group is the progressive damage model [28]. Such a model was developed to predict the extent of damage and damage progression in notched composite laminates. Because the evaluation of the pro-
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gressive damage model was based on the finite element method, it is less attractive than other closed form criteria. Application of some of these models to fiber-reinforced metal laminates was investigated by Teply et al. and Macheret et al. [12,13], Afaghi-Khatibi et al. [16], Van Rjin [29], and Lawcock et al. [30]. Van Rjin [29] reviewed the applicability of the above-mentioned residual strength models of polymer composite laminates to fiber-reinforced metal laminates. Based on the basic concept of fracture mechanics, a R-curve approach [31] was proposed to evaluate the residual strength of ARALL or GLARE. An effective crack growth model was developed by Afaghi-Khatibi et al. [16] to evaluate the strength of CARLL (carbon fiber-reinforced aluminum laminates) and ARALL with different notch sizes. In this model, damage is assumed to be initiated when the local normal stress ahead of notch tip reaches the tensile strength of composite layers and the yield strength of metal layers, respectively. 2.2. Evaluation of residual strength of notched fiber metal laminates in the present study Although there are few models to evaluate the residual strength of notched composite laminates, the point stress failure criterion is introduced into the present study because it is simple to apply and it is widely used in practical engineering application. Details of PSC model are not intended to repeat here, but relevant expressions and brief description is necessary. For an orthotropic plate with a circular hole under normal loads, PSC model states that when the normal stress σ y , at some distance d0 from the hole edge, reaches the failure strength of an unnotched plate, failure will occur in the notched plate. That is: σy (x, 0) = σ0
at x = r + d0
(1)
where r is the radius of the circular hole and d0 is the characteristic length. For an infinite orthotropic plate subjected to a uniform stress, σy∞ , applied parallel to the y-axis at infinity, the normal stress distribution, σ y along the x-axis ahead of the hole can be expressed as [32]: ∞ r 2 r 4 σy 2+ +3 σy (x, 0) = 2 x x r 6 r 8 , x>r (2) −(KT∞ − 3) 5 −7 x x where KT∞ is the stress concentration factor of the subject material for an infinite orthotropic plate with a circular hole:
Exx E xx ∞
KT = 1 + 2 (3) − νxy + Eyy Gxy where Exx , Eyy and Gxy are the axial, transverse and shear moduli, respectively, and νxy is the major Poisson’s ratio for the laminate. Substituting Eq. (2) into the Eq. (1), we obtain the PSC expression for normalized notched strength: 2 σN∞ = σ0 (2 + ε2 + 3ε4 − (KT∞ − 3)(5ε6 − 7ε8 )
(4)
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Table 1 Tensile test results for unnotched GLARE 4-3/2 laminate Specimen #
Thickness (in.)
Width (in.)
Fracture load (lb)
Fracture strength (MPa)
Fracture strain (%)
Modulus (GPa)
Poission’s ratio
G4-L-01 G4-L-02 G4-L-03a G4-L-04 G4-L-05 Average
0.072 0.072 0.072 0.072 0.0715 0.0719
1.032 0.986 1.009 0.973 0.988 0.998
8.565 8.270 8.255 8.002 8.351 8.288
794.75 803.18 783.45 787.54 815.06 796.80
4.04 4.19 3.84 4.01 4.23 4.06
50.5 50.6 51.5 50.8 51.0 50.9
/ / 0.259 0.271 0.267 0.266
a
Fracture site is near to the grip tab.
where σ 0 is the unnotched tensile strength of the laminate, σN∞ the notched strength of an infinite width plate and ε = r/(r + d0 ). The above described point stress criterion enables the prediction of the notched strength of composite laminates containing circular open hole. It is formulated assuming that the plates are of infinite width, so the infinite width notched strength, σN∞ , is predicted. However, experimental data are obtained on specimens with a finite width. For proper comparison between experimental results and predictions, the test data have to be normalized by using a finite width correction (FWC) factor. For an orthotropic plate with a circular hole, the finite width correction factor is expressed as [33]: KT∞ KT
=
3(1 − 2r/W) 1 2r + M 3 2 W 2 + (1 − 2r/W) 2 2r M × 1− W
6
(KT∞ − 3)
Fig. 1. Geometry and dimensions of specimens and location of strain gage A and B.
That is: −1
d0 = m
2r W
n (9)
where m is notch sensitivity factor and n is exponential parameter. Substituting Eq. (9) into Eq. (4), a modified point stress criterion is obtained: (5)
where 1 − 8[(3(1 − 2r/W))/(2 + (1 − 2r/W)3 ) − 1] − 1 2 M = 2(2r/W)2 (6) where KT /KT∞ is the FWC factor, and KT and KT∞ are stress concentration factor at the notch edge for a finite width plate and an infinite plate, respectively. In the above traditional point stress criterion, it is assumed that the characteristic dimension is a material parameter and independent of the notch size [17,18]. When the characteristic length is independent of open hole radius, accurate notched strength prediction can be achieved. However, some of previous experimental results with various materials and stacking sequence have shown that the characteristic length is not a constant and dependent on the specimen geometry [21,22]. The experimental result, which is given below, of GLARE 4-3/2 laminate with a circular open hole in the present study further confirm that the characteristic length in the traditional PSC is varied with the hole sizes and widths. So the classical point stress criterion needs to be modified to evaluate the residual strength of notched GLARE more accurately. A detailed analysis of the dependence of characteristic length d0 on the specimen geometry in this study shows that it follows an exponential relationship, which is consistent with the previous study by Kim and Kim [34] for predicting the notched strength of glass/epoxy composites.
σN∞ 2 = σ0 (2 + ε2 + 3ε4 − (KT∞ − 3)(5ε6 − 7ε8 )
(10)
where ε=
1
(11)
1 + 2n rn−1 W −n m−1
3. Experimental procedures 3.1. Materials and specimen preparation Fiber metal laminates used in the present experimental investigation are GLARE 4 with 3/2 lay-up provided by Aviation Equipment Structures, Inc. (Costa Mesa, CA). GLARE 4-3/2 consists of three layers of 2024-T3 aluminum alloy sheets and two layers of 67/33 glass prepreg with 67% of fibers in 0◦ direcTable 2 Notched strength test results for GLARE 4-3/2 laminate W (mm)
2r (mm)
2r/W
σ N (MPa)
σN∞ (MPa)
σN∞ /σ0
d0 (mm)
25.63 25.55 25.96 51.26 50.83 50.60 76.10 76.02 76.15
3.07 6.29 12.67 6.23 12.62 25.81 9.5 20.32 38.68
0.1198 0.2462 0.4881 0.1215 0.2483 0.5101 0.1248 0.2673 0.5079
480.68 390.14 266.11 439.75 363.34 249.3 421.95 345.71 244.33
488.22 418.46 364.83 446.79 390.05 353.75 429.11 375.78 345.63
0.6127 0.5252 0.4579 0.5608 0.4895 0.444 0.5386 0.4716 0.4338
0.6096 0.8230 1.0541 0.9652 1.3081 1.9228 1.3111 1.8694 2.6391
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tion and 33% fiber in 90◦ direction. All the tensile specimens were cut from 300 mm × 300 mm GLARE panels. The specimens used in this study were 300 mm in length and the width was chosen to be 25.4, 50.8 and 76.2 mm, respectively. For each width, three different hole sizes were chosen but the ratio of hole size to width is kept to be constant as 0.125, 0.25, 0.5, respectively. The actual average thickness of each layers for the as-received GLARE laminates were measured using optical micrographs. The average thickness of GLARE 4-3/2 was 0.304 mm for aluminum alloy sheets and 0.458 mm for prepreg layers. Therefore, the actual average thickness of GLAR4-3/2 laminate in the present study is 1.828 mm. The circular holes were prepared through the center of the specimen using carbide-tipped drill bits or diamond-tipped drill bits. A circular hole is machined by initially drilling a starter hole of small diameter, and then carefully enlarging it to its final dimensions by incremental drilling. In order to avoid delamination at the hole edge and to obtain a clean and smooth hole during drilling, a flat wooden plate was placed and clamped below the specimen. The notched region was hand polished using sand paper. The specimens containing holes were inspected with an X-ray technique to detect delamination caused by drilling. The laminates and holes are proved to have a good quality. After drilling, aluminum alloy end tabs were attached on both ends of specimens using aluminum putty adhesive. 3.2. Test procedures All the notched specimens were loaded along the longitudinal direction (parallel to 0◦ fiber direction). Static tensile tests were performed using a 22 kips servo-hydraulic Instron test frame with a cross-head speed of 1 mm/min at room temperature. Specimens were clamped by the hydraulic grip fitted on the testing machine. For each specimen configuration, three replicates were tested. As part of the notch sensitivity study, unnotched coupons were also tested to determine the unnotched tensile strength and in-plane laminate mechanical properties in accordance with ASTM D-3039. A summary of the mechanical properties of unnotched GLARE 4-3/2 is presented in Table 1. Strain gages were implemented for monitoring the strain. One strain gage was mounted on the front center line of specimen midway between the notch and gripping region to measure far-field strain. The other strain gage is placed at the hole edge along the center line of holes to measure the strain concentration at the hole edge as shown in Fig. 1. Omega 900 series data acquisition modules and LABTECH Notebook were used to record strains and applied loads. Post-fracture specimens were examined by optical and scanning electron microscopy to characterize the fracture mode. Zinc iodide-enhanced X-ray radiography was used to monitor delamination around the peripheral of the hole. Additional specimens were loaded to approximately 95% of the failure load to determine the damage growth pattern. The damage characteristics were determined from X-ray images and microscopic examination after chemical removal of the outer aluminum layers. The gross strength σ N is defined as the notched tensile strength and it is calculated using the ultimate fracture load
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Fig. 2. Effect of hole size and specimen width on the residual strength of GLARE 4 laminate.
divided by the specimen width and thickness. For each notched specimen, the normalized residual strength, σN∞ /σ0 is evaluated, where the infinite width gross strength, σN∞ , is calculated by multiplying the finite width gross strength σ N by a finite width correction factor, and σ 0 is the unnotched strength determined from tensile tests.
Fig. 3. Relationship between characteristic length and 2r/W for GLARE 4 laminate.
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Table 3 A comparison between experimental and predicted notched strength for GLARE 4-3/2 laminate W (in.)
25.63 25.55 25.96 51.26 50.83 50.6 76.1 76.02 76.15
2r/W
3.07 6.29 12.67 6.23 12.62 25.81 9.5 20.32 38.68
2r (in.)
0.1198 0.2462 0.4881 0.1215 0.2483 0.5101 0.1248 0.2673 0.5079
Test σ N (MPa)
480.68 390.14 266.11 439.75 363.34 249.3 421.95 345.71 244.33
Modified PSC
PSC
σ N (MPa)
Relative error (%)
σ N (MPa)
Relative error (%)
481.02 391.05 266.65 437.79 366.42 248.41 420.82 347.49 243.74
0.07 0.23 0.20 −0.45 0.85 −0.36 −0.27 0.52 −0.24
534.46 393.64 249.29 502.51 371.29 230.29 485.24 349.71 227.13
11.19 0.90 −6.32 14.27 2.189 −7.63 15.00 1.16 −7.04
4. Experimental results and model verification 4.1. Evaluation of residual strength of notched GLARE 4 laminates The notched strength of GLARE 4-3/2 with different hole sizes and widths are summarized in Table 2. The normalized strength is shown for both finite width and infinite width after employing width correction factor (Eq. (5)). It clearly shows that the specimens containing a small hole have a higher notched strength, and notch sensitivity increases with the size of hole. For the specimen containing the smallest hole size to width ratio (0.125), the strength of notched GLARE 4 decreases approxi-
mately 40%. Fig. 2 presents the effect of specimen width and hole size on the normalized notched strength. The results show that the notched strength decreases with increasing 2r/W ratio regardless of the specimen width. Also for a given 2r/W ratio, the notched strength was found to increase with decreasing specimen width. The differences in notched strength with different specimen width can be explained through the variation of the size of the plastic zone in the aluminum layers and the degree of localized delamination. For notched GLARE laminates, there is a highly stressed area at the notch root, and the plastic zone in the aluminum layer is small for specimen with a small width at a constant 2r/W ratio. This results in significant shear stresses between the aluminum and fiber layers that are likely to create
Fig. 4. A comparison between experimental and predicted results for GLARE 4 laminate. (a) W = 25.4 mm; (b) W = 50.8 mm; (c) W = 76.2 mm.
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Fig. 5. A comparison between experimental and predicted results for ARALL and GLARE-2 laminates. (a) ARALL-1; (b) ARALL-1X; (c) ARALL-2; (d) GLARE-2.
earlier local delamination for small specimen. The presence of delamination would postpone fiber failure and cause the stress redistribution, thus increases the notched strength of GLARE laminates [10]. For each specimen, the characteristic length (d0 ) is determined from the PSC Eq. (4). The calculated characteristic length value from experimental results is shown in Table 2. Evidently, the characteristic length is neither a constant, nor independent of the notch size. The characteristic length d0 was found to increase with the increase in hole diameter (2r), and the specimen width (W) for the same hole size. After a detailed analysis of the dependence of characteristic length on the geometry of the specimen (2r and W), it was found that the characteristic length d0 increases exponentially with increasing of notch diameter and specimen width ratio (2r/W) as expressed by Eq. (9). Fig. 3 shows the exponential relationship between the characteristic length d0 and the ratio of circular notch diameter and plate width (2r/W) obtained from tensile test of GLARE 4-3/2. The value of parameter m and n in Eq. (9), which is associated with the variation of characteristic length, is also shown in Fig. 3. It can be seen that the notch sensitivity coefficient (m) was relatively small for wider specimen and notch
sensitivity tends to decrease with the increase of specimen width. The comparison of the experimental results and the predicted value of σN∞ /σ0 using both the PSC and the present model are presented in Table 3. It clearly indicates that the notched strength predicted from the modified PSC agrees closer to the experimental results than those predicted from classical PSC. Therefore, the modified PSC is useful and accurate for predicting the notched tensile strength of GLARE 4-3/2 laminates. The predicted effect of hole sizes on the normalized notched strength and experimental results are shown in Fig. 4. This plot shows that the PSC overpredicts the residual strength of the laminate with small notches and underpredicts the residual strength of the laminate with large notches. Table 4 Mechanical properties of ARALL and GLARE 2 laminates [10,35]
ARALL-1 ARALL-1X ARALL-2 GLARE-2
Eyy (GPa)
Exx (GPa)
νyx
Gyx (GPa)
σ 0 (MPa)
68.95 70.33 68.53 63.43
49.3 53.09 51.64 46.4
0.310 0.340 0.340 0.318
18.13 19.65 18.55 16.41
779.79 827.36 684.92 1101.5
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Fig. 7. X-ray images of the damage area in GLARE-4 laminate. (a) W = 25.4 mm; (b) W = 50.8 mm.
4.2. Evaluation of modified PSC criterion applicability of other fiber metal laminates The applicability of using the present modified PSC model to predict the notched strength of other types of fiber metal laminates with different configurations is examined carefully. Four groups of experimental data of notched ARALL-1, ARALL-2, ARALL-1X [35] and GLARE-2 laminates [10] from open literature were adopted in the evaluation. All specimens were a five ply “3/2” fiber metal laminates. The mechanical properties of these laminates are listed in Table 4. This prediction is compared with both experimental results and predictions from other previous models including PSC [17,18] and effective crack growth model by Afaghi-Khatibi et al. [16,19]. The effect of hole size on notched strength of ARALL-1 laminate in the longitudinal direction is shown in Fig. 5(a). The specimen width is W = 50.8 mm and the hole diameter varies from 3.18 to 12.7 mm. It was found that the characteristic length d0 also exhibits an exponential relationship with the ratio of hole size and specimen width (2r/W) as shown in Fig. 6(a). An excellent agreement is obtained between the experimental results and the prediction based on the present model. The notched strength versus notch size of ARALL-2 and ARALL-1X is illustrated in Fig. 5(b and c), respectively. It can be seen again that the present modified PSC model is more
Fig. 6. Relationship between characteristic length and 2r/W for ARALL and GLARE-2 laminates. (a) ARALL; (b) GLARE-2.
Fig. 8. Delamination pattern after chemical removal of aluminum layers. (a) W = 25.4 mm; (b) W = 50.8 mm.
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accurate for predicting the notched strength of ARALL laminates. Comparing the value of notch sensitivity factor (m) for these three ARALL laminates, it is found ARALL-2 is the most notch sensitive and ARALL-1 is the least notch sensitive. This is consistent with the previous investigation by Hidde and Herakovich [35]. Figs. 5(d) and 6(b) show the applicability of the present model into GLARE-2 laminates. Similar characteristics are observed for GLARE-2 laminates loaded in the longitudinal direction. Therefore, the modified PSC is capable of predicting the notched strength of fiber metal laminates with a circular hole. 5. Damage mechanism and characteristics of notched fiber metal laminates The fracture surfaces of notched specimens were macroscopically and microscopically examined. Delamination, fiber breakage and splitting are major mechanisms of fracture in
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notched GLARE 4 laminates. Fig. 7 shows the X-ray images of the typical damage zone in the post-failure notched specimen with 25.4 and 50.8 mm. A distinctive triangular (linear) delamination shape was observed for all notched specimens with different hole sizes and specimen widths. The dark area also indicates the fiber breakage and splitting. The same delamination shape was found by Teply et al. [12] for Aramid-fiber aluminum laminates (ARALL) with a central crack and Lawcock et al. [19–36] for untreated carbon-fiber aluminum laminates (CRALL) with a circular hole. Earlier study [10] also showed that ARALL laminates with a circular hole do not show any signs of delamination but delamination is present for GLARE 2 laminates with a hole. The presence of delamination causes the stress redistribution and was found to increase the notched strength of laminates. Chemical removal of the aluminum layer confirms the delamination pattern from X-ray tests as shown in Fig. 8. It was found the delamination zone size is consistent with
Fig. 9. X-ray images of damage progression pattern in the specimen with 50.8 mm width and 12.7 mm hole. (a) Initiation; (b) further loading; (c) fracture.
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the region of fiber breakage and splitting. So the X-ray radiography can be used to assess the damage state such as delamination size and shape in the laminates. There is no stable crack growth observed for aluminum layers prior to unstable fracture. This is attributed to be caused by the presence of delamination and high ductility of aluminum layers. The presence of delamination allows greater plastic deformation in the aluminum layers that reduce the stress intensity at the crack tip, so the plastic deformation rather than crack growth occurred in the aluminum layers [19]. The damage is expected to initiate in the prepreg layers because the ultimate strain of glass fibers is significantly smaller than that of aluminum. The prepreg layers control the residual strength of notched fiber metal laminates. With the increasing of the load, the yielding occurred first in the aluminum layer. When the load reaches a value almost close to critical fracture load, there were audible signs of fiber breakage and delamination growth near the edge of hole in the prepreg layers. Subsequently, it was followed by a rapid unstable crack growth across the whole specimen width leading to catastrophically failure. Fig. 9 shows X-ray images of damage progression of GLARE 4 laminates during fracture. It is obvious that the damage initiated at the hole edge and grew in size with the increasing load up to the final fracture. For some specimens, strains were measured in the loading direction at locations marked by A and B in Fig. 1. Strain gage A was placed remote to the hole and gripping, and the strain gages at B were located at the hole boundary. The measurement result indicated that all stress–strain curves recorded corresponding to gage A showed a bilinear behavior similar to that in unnotched laminates under tensile loading up to fracture load. However, the stress–strain behavior for strain gage at B close to the hole is quite different from that in gage A as shown in Fig. 10. Except a lower slope of stress–strain that is caused by the stress concentration of notch, a platform of stress–strain curve was observed around 95% critical failure load until the final fracture. This is associated with the occurrence of damage initiation such as fiber breakage, splitting and delamination at hole edge. 6. Finite element analysis of notched fiber metal laminates 6.1. Finite element mesh In this numerical study, the ANSYS SHELL91 element is employed. SHELL 91 is a nonlinear layered structural shell element. This element has six degrees of freedom at each node: translations in the nodal x, y, and z directions and rotations about the nodal x, y, and z-axes. The element is defined by eight nodes, layer thicknesses, layer material direction angles, and orthotropic material properties. A relatively fine mesh was used adjacent to the notch where splitting and delamination were expected. With element refinements around the notch region, mapping mesh technique is used for the entire domain. Due to symmetry, only one fourth of the plate was molded. The symmetrical boundary conditions are applied at the two sides of symmetry. Along the line X = 0, the nodes are constrained to
Fig. 10. Different load–strain relationship at different locations for notched GLARE 4 laminate. (a) Strain gage A; (b) strain gage B.
displacements in Y direction only. The nodes along line X = 0 are constrained to displacement in the X direction only. The glass fiber/epoxy layers were modeled with homogenized linear elastic orthotropic materials, and the Von Mises yield criterion was used to describe the elasto-plastic behavior of aluminum layers. Fig. 11 shows the FEM mesh for GLARE 4-3/2 laminate with a width of 50.8 mm and a hole of 12.7 mm. 6.2. Stress analysis and notch sensitivity analysis Fig. 12 illustrates the distribution of Von Mises equivalent stress in different layers in GLARE 4-3/2 laminate with a width of 50.8 mm and a central hole of 12.7 mm. It is evident that there is a big difference in the stress contour plots of different layers in GLARE 4 laminate. As shown in Fig. 12(a and b), there is a very high stress concentration near the notch edge in the fiber/epoxy layers, so the damage will initiate at the edge of the hole in fiber/epoxy layers. However, the stress is widely distributed over a wide range of aluminum layers as shown in Fig. 12(c) com-
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Fig. 11. (a) Finite element mesh of notched GLARE 4-3/2 laminate; (b) zoom in of the notch region mesh showing the layer element.
pared to that stress concentration in the fiber/epoxy layers is more localized in a small region at the hole edge. Stress concentration in aluminum layers is reduced because aluminum exhibits a significant plasticity, so the plastic zone ahead of notch tip can level off the stress concentration. It is consistent with our experimental observation that the plastic deformation rather than crack growth occurred in the aluminum layers before fracture described above. Fig. 13 shows the axial stress distribution along the y-axis direction for various r/W ratios. The stress exhibits a substantial stress concentration at the hole edge and drops below the far-field stress. The stress concentration factor increases as r/W increases. The stress ration near to plate straight edge drops below a unit. Greater the r/W ratio is, the lower drops. The stress concentration for the smaller hole is much more localized than for that for the larger hole. This leads to a higher strength for the smaller hole as shown in Fig. 2 due to the greater opportunity to redistribute stress and smaller volume of highly stressed materials for the smaller hole. A further study on incorporating the progressive damage model into finite element simulation is necessary to predict the effect of damage on property retention and residual strength and of notched fiber meal laminates. 7. Summary The residual strength behavior and notch sensitivity of fiber metal laminates with a central hole have been investigated.
It was shown that the residual strength of glass fiber metal laminates with central open hole increases with decreasing specimen width and decreasing hole diameter, and notch sensitivity increases with the size of hole. The presence of a hole in GLARE laminates gives a strength reduction about 40%. The characteristic length d0 in PSC was found to follow an exponential expression with the ratio of hole size and specimen width. A modified PSC was introduced to predict the residual strength. An excellent agreement was obtained between experimental results and model predictions. The applicability of the modified PSC to previous investigations on other types of fiber metal laminates validated that this model is capable to evaluate the notched strength of fiber metal laminates. Delamination, fiber breakage and splitting are major mechanisms of fracture in GLARE laminates with a center hole. A distinctive triangular (linear) delamination shape was observed for all notched specimens. Only plastic deformation and no stable crack growth in the aluminum layers prior to unstable fracture were found. The stress analysis on the notched GLARE laminates based on FEM computer simulation verified the analytical and experimental results of notched strength. The present study broadens the applicable range of the stress fracture criteria and provides a simple and useful tool to predict the residual strength of notched fiber metal laminates for engineering application. More experimental tests are needed to confirm the validity of this modified model for fiber metal laminates with various notch shapes.
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Fig. 12. Von Mises stress profile in different layers in GLARE 4-3/2 laminate. (a) 0◦ fiber layer; (b) 90◦ fiber layer; (c) aluminum layer.
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Fig. 13. The effect of notch size on axial stress distribution along y-axis (W = 50.8 mm).
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