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Prediction of post-impact residual strength and fatigue characteristics after impact of CFRP composite structures
Composites: Part B 61 (2014) 300–306
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Composites: Part B journal homepage: www.elsevier.com/locate/compositesb
Prediction of post-impact residual strength and fatigue characteristics after impact of CFRP composite structures Jae-Mean Koo a, Jung-Hun Choi b, Chang-Sung Seok a,⇑ a b
School of Mechanical Engineering, Sungkyunkwan University, 300 Cheoncheon-dong, Jangan-gu, Suwon, Gyeonggi-do 440-746, South Korea Research & Development Division, Hyundai Motor Co., Ltd., 772-1, Jangduk-dong, Hwaseong-si, Gyeonggi-do 445-706, South Korea
a r t i c l e
i n f o
Article history: Received 23 September 2013 Received in revised form 7 January 2014 Accepted 13 January 2014 Available online 24 January 2014 Keywords: A. Carbon fiber A. Prepreg B. Fatigue B. Residual/internal stress
a b s t r a c t The residual strength and fatigue life of CFRP (Carbon Fiber-Reinforced Plastic) composite structures with impact damage were predicted by using the characteristic length of the composite with the hole corresponding to the impact damage area. Since the specimen has a C-shaped structure that is different from the shape of a standard specimen, the shape factor was obtained from the concentration of the plate specimen and that of the structure using finite element analysis. The fatigue life of composite structures with impact damage can be predicted accurately by applying the prediction model, which takes into account the residual strength after impact, the shape factor which considers geometric characteristics, and the fatigue characteristics of virgin composites that have not been impacted to the model for strength degradation following impact. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Structures composed of fiber-reinforced composite materials have become quite popular due to their high strength-to-weight and stiffness-to-weight ratios. However, these materials are susceptible to damage caused by low-velocity impact load during manufacture and while in service. If an external object strikes a composite structure in the direction perpendicular to a surface, it can degrade both its static and fatigue load-bearing capacity [1–5]. If repeated fatigue loads are applied after such damage, the damage grows and eventually leads to complete structure failure. Therefore, in order to ensure a margin of safety and damage tolerance in composite structures, understanding the strength degradation of composites due to impact damage and fatigue load is required, as well as an understanding of these factors’ interactions. Therefore, many researchers have conducted studies to evaluate residual strength and fatigue characteristics of composite structures with impact damage [6–8]. However, because the failure mechanism of impact damage is complex, it is very difficult to evaluate the residual strength and fatigue life of composite structures damaged by impact [9–11]. Caprino [12,13] suggested a prediction model for the residual strength after impact:
rR Eth ¼ ro Ei
a
⇑ Corresponding author. Tel.: +82 31 290 7446; fax: +82 31 290 7482. E-mail address: [email protected] (C.-S. Seok). http://dx.doi.org/10.1016/j.compositesb.2014.01.024 1359-8368/Ó 2014 Elsevier Ltd. All rights reserved.
ð1Þ
where ro and rR indicate tensile strength and residual strength, respectively. Ei and Eth are the incident impact energy and threshold impact energy, respectively, and a is a constant. It has been reported that Eth and a are influenced by the shape and size of the impactor as well as the shape, size and boundary conditions of the specimen or structure. Koo et al. reported that for low-velocity impact, the influence of the mass of an impactor on the residual strength of the composite materials is small for the impact mass (3–7 kg) and impact energy (23 J) [28]. Cui et al. [14] investigated the tensile residual strength of composite laminates after lowvelocity impact by using numerical and experimental methods and reported that an increase in the impact energy increases the damaged area and decreases the residual strength. Davies et al. [15] reported that the residual strength is rapidly reduced with increasing damage area, and that the relationship between the residual compressive strength and impact energy finally approaches an asymptote. Chen et al. [16] reported that when the composites receive a load after impact damage, since the stress concentrates near the interface of the impact and damage areas, the stress concentration factor is an important indicator of the residual load-carrying capability. They recognized that the stiffness reduction within the damaged area causes a stress concentration near the interface of the intact and damaged areas under loading. They supposed that the worst case of stiffness reduction is a hole. Also, Koo et al. [17] proposed a prediction model for residual strength after impact, in which the damaged area is replaced with an equivalent hole notch when sufficient impact is received. The model is as follows:
J.-M. Koo et al. / Composites: Part B 61 (2014) 300–306
rR rHR Di Ei ¼ 1 1:45 ro DI Eth
2
0:01
ð2Þ
where rHR is the hole notch strength and DI and Di are the diameters of the impactor and the permanent impression, respectively. It was reported that since the results predicted by Eq. (2) agree well with the experimental results of CFRP composites, the residual strength after impact can be estimated by measuring the size of the permanent impression on the surface of the composite. Whitney and Nuismer [18,19] proposed the point-stress criterion (PSC) and average-stress criterion (ASC), which require evaluation of the characteristic length. Such a characteristic length is assumed to be a material property, independent of the hole size or geometry of the plate. However, Pipes et al. [20] proposed a modified PSC model that assumes an exponential relationship between the characteristic length and the size of the discontinuity rather than regarding the characteristic length as a material constant. Also, Kim and Kim [21] reported the effects of hole size and specimen width on the fracture behavior of woven glass and woven carbon fabric composites. Kim et al. [22] suggested a failure model for notch strength and characteristic length, considering the effects of hole size and specimen width. Broutman and Sahu [23] suggested a fatigue life prediction model under block loading as a function of residual strength, on the basis of experimental observations that the residual strength decreases as the number of fatigue loading cycle increases. When a series of m fatigue blocks of cycle number ni at a maximum stress ri are applied, the residual strength rm is given by:
m X ro ri n i i¼1
ro rm N i
¼1
ð3Þ
where Ni is the fatigue life when ri is applied. They assumed that failure occurs when the maximum cyclic stress exceeds the residual strength. Hahn and Kim [24] reported that fatigue failure of composites is not dictated by the initiation and growth of a dominant crack as in metallic materials, and assumed that the rate of residual strength reduction is inversely proportional to the residual strength. From this assumption and the static strength distribution, they derived the fatigue life distribution. Whitworth [25] proposed a model for relating the residual strength of graphite/epoxy laminates to the applied fatigue cycles and the maximum applied stress. Based on the model, the statistical distribution of the residual strength was derived. Kang and Kim [26] introduced the strength reduction concept, based on Broutman’s model under 2-stage loading, to describe the fatigue behavior of the impacted laminates. Also, Koo et al. [17] assumed that damages by impact and fatigue are due to two-step block loading and proposed a prediction model in which the prediction equation for the residual strength after impact is applied to the prediction equation for the fatigue life after impact. In this study, in order to predict the residual strength of the composite structures damaged by impact, the hole notched strength was analytically predicted by applying the characteristic length to the composite structures with the hole corresponding to an impact damage area. Next, after the shape factor was obtained from the concentration factor of a plate specimen and that of the structure with the hole corresponding to an impact damage area by finite element analysis, those factors were substituted into the prediction model for the residual strength after the impact of the CFRP composites [17], thereby computing the residual strength based on the geometric characteristics. Also, the prediction model for the residual strength after impact was applied to the prediction model for fatigue life based on the residual strength reduction concept, and the fatigue life was predicted and then verified against the results of an actual fatigue test of composite structures with impact damage.
301
2. Evaluation of residual strength of CFRP composite structures with impact damage 2.1. Residual strength test of CFRP composite structures with impact damage This residual strength test was performed with WSN3K material, which is a plain-woven carbon prepreg with a thickness of 0.27 mm, made by Hankuk Carbon Co., Ltd. in Korea. The laminated plate was molded for 60 min in an autoclave at a temperature of 140 °C and pressure of 5.88 MPa, and the 16-ply fabricated laminate was 3.6 mm thick. The structure specimen was made into a C shape as shown in Fig. 1, with dimensions W = 40 mm, H = 25 mm, L = 200 mm, and Hg = 20 mm. The chemical compositions of the prepreg are shown in Table 1 and the mechanical properties of specimens are shown in Table 2. The impact damage was applied to the center of the composite structures using a drop impact tester in which an impactor of 7 kg in mass drops with an initial velocity of 0 m/s, with a block inserted inside the body in order to implement the plane support conditions (Fig. 2). The incident impact energy (Ei) of 23.5 J was applied using impactors 15.8 mm and 25.4 mm in diameter. Also, to evaluate the residual strength after the impact of the C-shaped structure specimen, tensile tests were performed at room temperature at a speed of 3 mm/min using a universal testing machine with a capacity of 250 kN (Instron, Co.). The residual strength tests after impact using an impactor 15.8 mm in diameter were performed three times (Fig. 3). The measured residual strength values were 345–383 MPa, with mean value 364.3 MPa. Similar tests using an impactor 25.4 mm in diameter were performed twice. The residual strength values were 320– 373 MPa, with a mean value of 346.5 MPa. 2.2. Notch strength of a finite plate Whitney and Nuismer [18,19] assumed that failure occurs when the normal stress is equal to the fracture strength at a certain distance from the tip of a discontinuity in a material. Also, the PSC is expressed as follows from the normal stress distribution at the tip of the hole:
r1 2 R N ¼ ; g¼ 6 8 R þ d0 r0 2 þ g2 þ 3g4 ðK 1 T 3Þð5g 7g Þ
ð4Þ
where r1 N is the notch strength for an infinite plate, do is the characteristic length, R is the hole radius and K 1 T is the stress concentration factor of an infinite plate:
K1 T
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! u sffiffiffiffiffi u Ey Ey t ¼1þ 2 mxy þ Ex Gxy
Fig. 1. Appearance of C-shaped structure specimen.
ð5Þ
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Table 1 Chemical compositions of prepreg. Fabric wt. (g/m2)
Resin wt. (g/m2)
Resin content (%)
Total wt. (g/m2)
205
148
42 ± 2
353
M2 ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h i 3ð12R=WÞ 1 8 2þð12R=WÞ 3 1 1 2ð2R=WÞ2
ð7Þ
Kim and Kim [21] evaluated the notch strength as a function of the width of a composite specimen and the hole size and suggested a characteristic length as follows, considering the effects of hole size and specimen width.
Table 2 Mechanical properties of prepreg. Ex (GPa)
Ey (GPa)
gxy
Gxy (GPa)
55
55
0.13
4.75
d0 ¼
m 1 2R k W
ð8Þ
where k is a notch sensitivity coefficient related to 2R and W, and m is the characteristic length change ratio (0 < m < 1). After Kim, et al. [22] obtained the experimental relationship between the characteristic length and notched strength of CFRP composites by regression analysis, the relationship for an infinite plate was converted into the following equation for a finite plate:
rN 1 d0 1 2R ¼ ; d0 ¼ k W r0 Y 0:2R þ d0
m ð9Þ
They reported that the constant of Eq. (9), m, is the material constant and the value of k changes according to 2R/W [22]. In the present study, the characteristic length was obtained using Eq. (9). 2.3. Application of characteristic length to composite structures From the point-stress criterion (PSC), the applied stress can be defined as the residual strength when the normal stress is equal to the tensile strength at the characteristic length do. Therefore, in this study, using the commercial finite element analysis program, ANSYS, the applied stress was acquired from the case of the normal stress reaching the tensile strength at the point of the characteristic length do. In this analysis, shell 99 for layered applications of a structural shell model was used and 16 plies were stacked. Also, as shown in Fig. 4, a quad mapped mesh was applied in the vicinity of the hole using a mesh size of 0.19do, for which the maximum principal stress converges to a constant value. The model for FEA was composed of 5200 elements and 15,960 nodes. The elastic moduli Ex and Ey in the x and y directions and Poisson’s ratio mxy, and shear modulus Gxy in Table 2 were given as the material properties. According to Koo et al. [17,28], since the permanent impression made by an impactor nose diameter of 15.8 mm corresponds to the hole notch of Di = 6.4 mm, finite element analysis was performed for a standard plate specimen with a hole notch 6.4 mm in diameter, with a width of 25 mm and thickness of 3.6 mm. The characteristic length was computed by using Eq. (9). Kim et al. [22] reported that m is 0.35 and k is 0.883 when the width of the CFRP composite
Fig. 2. Setup for inflicting impact on a C-shaped structure specimen.
Fig. 3. Load–displacement curves for C-shaped structure specimen (impactor diameter = 15.8 mm) [34].
Here, Ex, Ey, Gxy and txy are the effective elastic moduli and Poisson’s ratio of the laminate. If rN represents the notch strength for a finite plate, the notch strength for an infinite plate r1 N can be expressed as YrN, where Y is the finite plate correction factor. From Tan’s study [27], the approximate finite width correction factor of composites with a circular hole can be obtained by using Eq. (6).
"
6 #1 1 2R 2R 1 M ðK T 3Þ 1 M Y¼ þ W 2 þ ð1 2R=WÞ3 2 W 3ð1 2R=WÞ
ð6Þ where W is the width of the specimen and M is expressed by the following equation:
Fig. 4. Finite element modeling near a circular hole in the specimen.
J.-M. Koo et al. / Composites: Part B 61 (2014) 300–306
specimen is 25 mm and the hole notch diameter is 6.4 mm. Applying the constant to Eq. (9), the characteristic length was do = 0.703 mm. Fig. 5 shows the maximum principal stress distribution at the applied load 31,325 N, that is, the remote stress of 358 MPa, when the maximum principal stress reaches the tensile strength (780 MPa) at the characteristic length do. By substituting the hole notch strength (358 MPa) computed using FEM into Eq. (2), the residual strength after impact of 369 MPa was obtained. Because the mean residual strength after impact of the damaged specimen by an impactor 15.8 mm in diameter is 364.4 MPa according to the results of Koo et al. [28] (Fig. 6), it can be seen that the prediction using Eq. (2) agrees well with the experimental result. The shape of the composite structure for finite element analysis is identical to that for the residual strength test of the structure (Fig. 1), but with the inclusion of a hole of 6.4 mm diameter in the center of the structure. The finite element analysis model was formulated by the same method as depicted in Fig. 4. Because the C-shaped structure specimen differs in shape from the plate specimen, the width of the structure was defined in this study as the width of a specimen with both wing parts unfolded; namely, 73 mm (Fig. 7). This is because stress acts across the cross-section. The characteristic length do = 0.830 mm was obtained from Eq. (9). When the maximum principal stress reaches the tensile strength (780 MPa) at the characteristic length do, the remote stress was obtained from the applied load. The result predicted for the residual strength of the CFRP composite structure after impact was 432 MPa when substituting the remote stress into Eq. (2). The mean residual strength of the structure in the actual test was 364.3 MPa; thus, the difference between the predicted result and the experimental result was about 68 MPa. This considerable difference is thought to be caused by the change in the characteristic length, and by the stress concentration effect of the damaged area due to a change in the structure’s geometry. Therefore, the shape factor was defined as the ratio of the stress concentration factor of the standard plate specimen to that of the composite structure:
F¼
K t;specimen K t;structure
303
Fig. 6. Residual strength versus impactor diameter [28].
ð10Þ
If this shape factor is applied to Eq. (2), Eq. (2) becomes
rR F rHR Di Ei ¼ 1 1:45 ro DI Eth
2
0:01
ð11Þ
Fig. 7. Definition of width to calculate the characteristic length of the C-shaped structure.
After stress analysis was performed for the standard plate specimen with width (W) = 73 mm, thickness (t) = 3.5 mm, and hole notched diameter = 6.4 mm, the shape factor of 0.879 was calculated from the stress concentration factors for the standard plate specimen with width = 73 mm and the C-shaped structure specimen in Fig. 1 as follows:
F¼
Fig. 5. Analysis results for a standard plate specimen [34].
K t;specimen 2:532 ¼ ¼ 0:879 K t;structure 2:882
ð12Þ
When this shape factor was substituted into Eq. (11), the residual strength was about 379 MPa. The predicted result can be seen to agree with the tested mean residual strength of the structure after impact (364.3 MPa), with a difference of about 14.7 MPa.
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For the case in which an impactor of diameter 25.4 mm was used, since the maximum diameter of the permanent impression appearing on the surface was 7.6 mm, finite element analysis was performed for the C-shaped structure with a hole notch diameter of 7.6 mm in the center of the structure. By using Eq. (9), the characteristic length do of about 0.860 mm was obtained. A remote stress applied to the structure was obtained when the maximum principal stress reached 780 MPa at the characteristic length do, and the predicted residual strength after impact of the composite structures was calculated to be 407 MPa by substituting this characteristic length into Eq. (2). Also, from the finite element analysis, after the stress concentration factors were calculated for the standard plate specimen of width W = 73 mm and hole notch diameter 2R = 7.6 mm, and for the C-shaped structure specimen, and by substituting those stress concentration factors into Eq. (10), the shape factor was calculated to be 0.872. By applying this shape factor to Eq. (11), the residual strength was calculated to be 356 MPa. This result differs by 9.5 MPa from the 346.5 MPa mean residual strength of the C-shaped structure specimen determined by tensile residual strength testing, but this difference is within the range of variation of the experimental results, 320–373 MPa. From these results, it can be seen that the residual strength of the CFRP composite structure after impact can be predicted by Eqs. (10) and (11) regardless of the impactor diameter.
3. Evaluation of fatigue characteristics after impact 3.1. Fatigue test after impact Standard plate specimens and C-shaped structure specimens for the fatigue test were made using identical manufacturing materials and methods used to make specimens for the residual strength test. The standard plate specimens were made according to the D3039 ASTM standard [29] (Fig. 8), while the C-shaped structure specimens used were identical in shape and dimensions to the depiction in Fig. 1. A constant load amplitude fatigue test with a stress ratio (R) of 0.1 was performed at room temperature (23 °C) using a universal testing machine with a capacity of 250 kN (Instron Co.). The wave form of the fatigue load was a sine wave, and its frequency was about 5 Hz. The results of fatigue tests for the standard plate specimens with no impact damage and with impact damage at an incident impact energy of 5 J are shown in Fig. 9. Impact damage was applied to composite specimens using a drop impact; an incident impact energy of 5 J resulted in a residual strength corresponding to approximately 70% of the tensile strength. The impactor diameter was 15.8 mm and the diameter of the permanent impression (Di) on the specimen surface created by an impactor diameter (D) of 15.8 mm was about 6.4 mm. Also, the maximum applied stress smax was determined to be 0.75–0.95 times the residual strength. The fatigue life of the composite materials can be seen to decrease due to the impact damage.
Fig. 9. Predicted and actual fatigue behavior of impacted specimens and structures.
Impact damage was applied to the center of the composite structures using a drop impact tester, with a block inserted inside the body to implement the plane support conditions. After an incident impact energy (Ei) of 10 J was given using an impactor 15.8 mm in diameter, fatigue tests were performed in conditions identical to those used in the tests on standard plate specimens. The maximum applied stress was determined to be 0.95–0.99 times the residual strength. The test results were similar to those shown in Fig. 9. 3.2. Prediction of fatigue life of impact damaged composite structures If the case of two-step block loading is applied to Eq. (3) as in the method of Broutman and Sahu [23], the result is as follows:
ro r1 n1 n2 þ ¼1 ro r2 N1 N2
ð13Þ
If the composite materials are under two-step block loading, the composite material undergoes n1 repeated cycles under the firststep block load of r1, and is then destroyed after undergoing n2 cycles under the second-step block load of r2. Broutman and Sahu [23] reported that the strength degradation due to the first block is (ro–r1)n1/N1. If it is assumed that the strength degradation after impact damage is equivalent to that by first-step block loading, the strength degradation by impact damage, ro–rR, can be expressed as
ro rR ¼ ðro r1 Þ
n1 N1
ð14Þ
Therefore, Eq. (13) can be expressed as
ro rR n2 þ ¼1 ro r2 N2
ð15Þ
In addition, because the fatigue damage after impact under constant-amplitude fatigue loading is equivalent to the damage by the second block loading, the maximum stress of the constant amplitude fatigue (rmax) is substituted for r2 [30–32], and the fatigue life of impacted composite materials (Ni) is substituted to n2. The fatigue life of non-impacted composite materials (Nf) is substituted for N2. The substitutions allow Eq. (15) to be rewritten as follows:
Nf Ni ro rR ¼ ro rmax Nf
Fig. 8. Specimen configuration.
ð16Þ
If Eq. (16) is expressed as the fatigue life after impact, the result becomes:
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Ni ¼ Nf
rR rmax ro rmax
ð17Þ
Hwang and Han [33] proposed the following equation as a fatigue life prediction model for composite materials without impact:
rmax q Nf ¼ p 1
ð18Þ
ro
where p and q are material constants obtained from the fatigue tests for composite materials without impact. From the fatigue test results for composite materials without impact, the values obtained for p and q are 1.305 1011 and 9.815, respectively. If the prediction equation of Hwang and Han for the fatigue life of composite materials without impact [33] is applied to Eq. (17), the equation becomes:
Ni ¼
rR rmax rmax p 1 ro rmax ro
q ð19Þ
If the residual strength prediction model of Eq. (2) is substituted into Eq. (19), the result is as follows: " # 2 Di Ei rHR rmax ro p Ni ¼ 1 þ 1:45 þ 0:01 D Eth ro ro rmax rmax q 1
ro
ð20Þ In the case of composite structures, since the shape factor (F) should be considered, Eq. (20) becomes as follows; " # 2 Di Ei F rHR rmax ro Ni ¼ 1 þ 1:45 þ 0:01 p D Eth ro ro rmax rmax q 1
ro
ð21Þ
In this study, to evaluate the influence of the residual strength on the fatigue life of the standard plate specimen, the result of Eq. (20) and the result of substituting Eq. (1) from the prediction model of Caprino [12,13] into Eq. (19) were compared to the fatigue test results. The fatigue prediction from Eq. (20) agreed well with the fatigue test results shown in Fig. 9. On the other hand, since the result from the fatigue prediction model applying Caprino’s model is located in the lower boundary area of the fatigue test results (see Fig. 10), the fatigue prediction model applying Caprino’s model produces slightly conservative results.
For the case in which an incident impact energy of 10 J was inflicted on a CFRP composite structure by an impactor 15.8 mm in diameter, the residual strength was predicted to be about 496 MPa using the characteristic length method described in Section 2.3. The prediction curve for fatigue life applying the predicted hole notched strength to Eq. (21) agrees well with the actual test results for this case (Fig. 8). This result indicates that the fatigue life of CFRP composite structures with impact damage can be predicted accurately by the combined application of the prediction model for the residual strength after impact, the shape factor considering the geometric characteristics, and the fatigue characteristics of virgin composites without impact to the model of strength degradation due to impact damage. 4. Conclusions In this study, residual strength and fatigue characteristics were predicted for the CFRP composite structures that received a damaging impact. The following results were obtained. (1) Using finite element analysis, the hole notched strength of a standard plate specimen, with the hole corresponding to an area of impact damage, was acquired from the point-stress criterion (PSC). The residual strength was calculated by substituting the hole notched strength of a standard plate specimen into the prediction model for the residual strength after impact. The predicted result agrees well with the experimental result. (2) To apply s method for predicting residual strength using the point-stress criterion (PSC) to a C-shaped structure, the shape factor obtained from the concentration factor of a K plate specimen and that of the structure, that is, F ¼ Kt;specimen t;structure was applied to the prediction model for the residual strength. The predicted result agreed well with the experimental result. (3) In this study, the following prediction model for fatigue life was proposed and the fatigue test results agreed well with the fatigue prediction results. Ni ¼
"
# 2 Di Ei F rHR rmax ro þ 0:01 p D Eth ro ro rmax q
1 þ 1:45
rmax 1
ro
(4) The fatigue life of CFRP composite structures with impact damage can be predicted accurately by the combined application of a prediction model that takes into account the residual strength after impact, the shape factor which considers geometric characteristics, and the fatigue characteristics of virgin composites that have not been impacted to the model of the strength degradation due to impact damage. Acknowledgments This work was supported by the National Research Foundation of Korea (NRF) (No. 2011-0020024 and 2012R1A1A2043624). References
Fig. 10. Predicted and actual fatigue behaviors for impacted specimens.
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Composites: Part B journal homepage: www.elsevier.com/locate/compositesb
Prediction of post-impact residual strength and fatigue characteristics after impact of CFRP composite structures Jae-Mean Koo a, Jung-Hun Choi b, Chang-Sung Seok a,⇑ a b
School of Mechanical Engineering, Sungkyunkwan University, 300 Cheoncheon-dong, Jangan-gu, Suwon, Gyeonggi-do 440-746, South Korea Research & Development Division, Hyundai Motor Co., Ltd., 772-1, Jangduk-dong, Hwaseong-si, Gyeonggi-do 445-706, South Korea
a r t i c l e
i n f o
Article history: Received 23 September 2013 Received in revised form 7 January 2014 Accepted 13 January 2014 Available online 24 January 2014 Keywords: A. Carbon fiber A. Prepreg B. Fatigue B. Residual/internal stress
a b s t r a c t The residual strength and fatigue life of CFRP (Carbon Fiber-Reinforced Plastic) composite structures with impact damage were predicted by using the characteristic length of the composite with the hole corresponding to the impact damage area. Since the specimen has a C-shaped structure that is different from the shape of a standard specimen, the shape factor was obtained from the concentration of the plate specimen and that of the structure using finite element analysis. The fatigue life of composite structures with impact damage can be predicted accurately by applying the prediction model, which takes into account the residual strength after impact, the shape factor which considers geometric characteristics, and the fatigue characteristics of virgin composites that have not been impacted to the model for strength degradation following impact. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Structures composed of fiber-reinforced composite materials have become quite popular due to their high strength-to-weight and stiffness-to-weight ratios. However, these materials are susceptible to damage caused by low-velocity impact load during manufacture and while in service. If an external object strikes a composite structure in the direction perpendicular to a surface, it can degrade both its static and fatigue load-bearing capacity [1–5]. If repeated fatigue loads are applied after such damage, the damage grows and eventually leads to complete structure failure. Therefore, in order to ensure a margin of safety and damage tolerance in composite structures, understanding the strength degradation of composites due to impact damage and fatigue load is required, as well as an understanding of these factors’ interactions. Therefore, many researchers have conducted studies to evaluate residual strength and fatigue characteristics of composite structures with impact damage [6–8]. However, because the failure mechanism of impact damage is complex, it is very difficult to evaluate the residual strength and fatigue life of composite structures damaged by impact [9–11]. Caprino [12,13] suggested a prediction model for the residual strength after impact:
rR Eth ¼ ro Ei
a
⇑ Corresponding author. Tel.: +82 31 290 7446; fax: +82 31 290 7482. E-mail address: [email protected] (C.-S. Seok). http://dx.doi.org/10.1016/j.compositesb.2014.01.024 1359-8368/Ó 2014 Elsevier Ltd. All rights reserved.
ð1Þ
where ro and rR indicate tensile strength and residual strength, respectively. Ei and Eth are the incident impact energy and threshold impact energy, respectively, and a is a constant. It has been reported that Eth and a are influenced by the shape and size of the impactor as well as the shape, size and boundary conditions of the specimen or structure. Koo et al. reported that for low-velocity impact, the influence of the mass of an impactor on the residual strength of the composite materials is small for the impact mass (3–7 kg) and impact energy (23 J) [28]. Cui et al. [14] investigated the tensile residual strength of composite laminates after lowvelocity impact by using numerical and experimental methods and reported that an increase in the impact energy increases the damaged area and decreases the residual strength. Davies et al. [15] reported that the residual strength is rapidly reduced with increasing damage area, and that the relationship between the residual compressive strength and impact energy finally approaches an asymptote. Chen et al. [16] reported that when the composites receive a load after impact damage, since the stress concentrates near the interface of the impact and damage areas, the stress concentration factor is an important indicator of the residual load-carrying capability. They recognized that the stiffness reduction within the damaged area causes a stress concentration near the interface of the intact and damaged areas under loading. They supposed that the worst case of stiffness reduction is a hole. Also, Koo et al. [17] proposed a prediction model for residual strength after impact, in which the damaged area is replaced with an equivalent hole notch when sufficient impact is received. The model is as follows:
J.-M. Koo et al. / Composites: Part B 61 (2014) 300–306
rR rHR Di Ei ¼ 1 1:45 ro DI Eth
2
0:01
ð2Þ
where rHR is the hole notch strength and DI and Di are the diameters of the impactor and the permanent impression, respectively. It was reported that since the results predicted by Eq. (2) agree well with the experimental results of CFRP composites, the residual strength after impact can be estimated by measuring the size of the permanent impression on the surface of the composite. Whitney and Nuismer [18,19] proposed the point-stress criterion (PSC) and average-stress criterion (ASC), which require evaluation of the characteristic length. Such a characteristic length is assumed to be a material property, independent of the hole size or geometry of the plate. However, Pipes et al. [20] proposed a modified PSC model that assumes an exponential relationship between the characteristic length and the size of the discontinuity rather than regarding the characteristic length as a material constant. Also, Kim and Kim [21] reported the effects of hole size and specimen width on the fracture behavior of woven glass and woven carbon fabric composites. Kim et al. [22] suggested a failure model for notch strength and characteristic length, considering the effects of hole size and specimen width. Broutman and Sahu [23] suggested a fatigue life prediction model under block loading as a function of residual strength, on the basis of experimental observations that the residual strength decreases as the number of fatigue loading cycle increases. When a series of m fatigue blocks of cycle number ni at a maximum stress ri are applied, the residual strength rm is given by:
m X ro ri n i i¼1
ro rm N i
¼1
ð3Þ
where Ni is the fatigue life when ri is applied. They assumed that failure occurs when the maximum cyclic stress exceeds the residual strength. Hahn and Kim [24] reported that fatigue failure of composites is not dictated by the initiation and growth of a dominant crack as in metallic materials, and assumed that the rate of residual strength reduction is inversely proportional to the residual strength. From this assumption and the static strength distribution, they derived the fatigue life distribution. Whitworth [25] proposed a model for relating the residual strength of graphite/epoxy laminates to the applied fatigue cycles and the maximum applied stress. Based on the model, the statistical distribution of the residual strength was derived. Kang and Kim [26] introduced the strength reduction concept, based on Broutman’s model under 2-stage loading, to describe the fatigue behavior of the impacted laminates. Also, Koo et al. [17] assumed that damages by impact and fatigue are due to two-step block loading and proposed a prediction model in which the prediction equation for the residual strength after impact is applied to the prediction equation for the fatigue life after impact. In this study, in order to predict the residual strength of the composite structures damaged by impact, the hole notched strength was analytically predicted by applying the characteristic length to the composite structures with the hole corresponding to an impact damage area. Next, after the shape factor was obtained from the concentration factor of a plate specimen and that of the structure with the hole corresponding to an impact damage area by finite element analysis, those factors were substituted into the prediction model for the residual strength after the impact of the CFRP composites [17], thereby computing the residual strength based on the geometric characteristics. Also, the prediction model for the residual strength after impact was applied to the prediction model for fatigue life based on the residual strength reduction concept, and the fatigue life was predicted and then verified against the results of an actual fatigue test of composite structures with impact damage.
301
2. Evaluation of residual strength of CFRP composite structures with impact damage 2.1. Residual strength test of CFRP composite structures with impact damage This residual strength test was performed with WSN3K material, which is a plain-woven carbon prepreg with a thickness of 0.27 mm, made by Hankuk Carbon Co., Ltd. in Korea. The laminated plate was molded for 60 min in an autoclave at a temperature of 140 °C and pressure of 5.88 MPa, and the 16-ply fabricated laminate was 3.6 mm thick. The structure specimen was made into a C shape as shown in Fig. 1, with dimensions W = 40 mm, H = 25 mm, L = 200 mm, and Hg = 20 mm. The chemical compositions of the prepreg are shown in Table 1 and the mechanical properties of specimens are shown in Table 2. The impact damage was applied to the center of the composite structures using a drop impact tester in which an impactor of 7 kg in mass drops with an initial velocity of 0 m/s, with a block inserted inside the body in order to implement the plane support conditions (Fig. 2). The incident impact energy (Ei) of 23.5 J was applied using impactors 15.8 mm and 25.4 mm in diameter. Also, to evaluate the residual strength after the impact of the C-shaped structure specimen, tensile tests were performed at room temperature at a speed of 3 mm/min using a universal testing machine with a capacity of 250 kN (Instron, Co.). The residual strength tests after impact using an impactor 15.8 mm in diameter were performed three times (Fig. 3). The measured residual strength values were 345–383 MPa, with mean value 364.3 MPa. Similar tests using an impactor 25.4 mm in diameter were performed twice. The residual strength values were 320– 373 MPa, with a mean value of 346.5 MPa. 2.2. Notch strength of a finite plate Whitney and Nuismer [18,19] assumed that failure occurs when the normal stress is equal to the fracture strength at a certain distance from the tip of a discontinuity in a material. Also, the PSC is expressed as follows from the normal stress distribution at the tip of the hole:
r1 2 R N ¼ ; g¼ 6 8 R þ d0 r0 2 þ g2 þ 3g4 ðK 1 T 3Þð5g 7g Þ
ð4Þ
where r1 N is the notch strength for an infinite plate, do is the characteristic length, R is the hole radius and K 1 T is the stress concentration factor of an infinite plate:
K1 T
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! u sffiffiffiffiffi u Ey Ey t ¼1þ 2 mxy þ Ex Gxy
Fig. 1. Appearance of C-shaped structure specimen.
ð5Þ
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Table 1 Chemical compositions of prepreg. Fabric wt. (g/m2)
Resin wt. (g/m2)
Resin content (%)
Total wt. (g/m2)
205
148
42 ± 2
353
M2 ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h i 3ð12R=WÞ 1 8 2þð12R=WÞ 3 1 1 2ð2R=WÞ2
ð7Þ
Kim and Kim [21] evaluated the notch strength as a function of the width of a composite specimen and the hole size and suggested a characteristic length as follows, considering the effects of hole size and specimen width.
Table 2 Mechanical properties of prepreg. Ex (GPa)
Ey (GPa)
gxy
Gxy (GPa)
55
55
0.13
4.75
d0 ¼
m 1 2R k W
ð8Þ
where k is a notch sensitivity coefficient related to 2R and W, and m is the characteristic length change ratio (0 < m < 1). After Kim, et al. [22] obtained the experimental relationship between the characteristic length and notched strength of CFRP composites by regression analysis, the relationship for an infinite plate was converted into the following equation for a finite plate:
rN 1 d0 1 2R ¼ ; d0 ¼ k W r0 Y 0:2R þ d0
m ð9Þ
They reported that the constant of Eq. (9), m, is the material constant and the value of k changes according to 2R/W [22]. In the present study, the characteristic length was obtained using Eq. (9). 2.3. Application of characteristic length to composite structures From the point-stress criterion (PSC), the applied stress can be defined as the residual strength when the normal stress is equal to the tensile strength at the characteristic length do. Therefore, in this study, using the commercial finite element analysis program, ANSYS, the applied stress was acquired from the case of the normal stress reaching the tensile strength at the point of the characteristic length do. In this analysis, shell 99 for layered applications of a structural shell model was used and 16 plies were stacked. Also, as shown in Fig. 4, a quad mapped mesh was applied in the vicinity of the hole using a mesh size of 0.19do, for which the maximum principal stress converges to a constant value. The model for FEA was composed of 5200 elements and 15,960 nodes. The elastic moduli Ex and Ey in the x and y directions and Poisson’s ratio mxy, and shear modulus Gxy in Table 2 were given as the material properties. According to Koo et al. [17,28], since the permanent impression made by an impactor nose diameter of 15.8 mm corresponds to the hole notch of Di = 6.4 mm, finite element analysis was performed for a standard plate specimen with a hole notch 6.4 mm in diameter, with a width of 25 mm and thickness of 3.6 mm. The characteristic length was computed by using Eq. (9). Kim et al. [22] reported that m is 0.35 and k is 0.883 when the width of the CFRP composite
Fig. 2. Setup for inflicting impact on a C-shaped structure specimen.
Fig. 3. Load–displacement curves for C-shaped structure specimen (impactor diameter = 15.8 mm) [34].
Here, Ex, Ey, Gxy and txy are the effective elastic moduli and Poisson’s ratio of the laminate. If rN represents the notch strength for a finite plate, the notch strength for an infinite plate r1 N can be expressed as YrN, where Y is the finite plate correction factor. From Tan’s study [27], the approximate finite width correction factor of composites with a circular hole can be obtained by using Eq. (6).
"
6 #1 1 2R 2R 1 M ðK T 3Þ 1 M Y¼ þ W 2 þ ð1 2R=WÞ3 2 W 3ð1 2R=WÞ
ð6Þ where W is the width of the specimen and M is expressed by the following equation:
Fig. 4. Finite element modeling near a circular hole in the specimen.
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specimen is 25 mm and the hole notch diameter is 6.4 mm. Applying the constant to Eq. (9), the characteristic length was do = 0.703 mm. Fig. 5 shows the maximum principal stress distribution at the applied load 31,325 N, that is, the remote stress of 358 MPa, when the maximum principal stress reaches the tensile strength (780 MPa) at the characteristic length do. By substituting the hole notch strength (358 MPa) computed using FEM into Eq. (2), the residual strength after impact of 369 MPa was obtained. Because the mean residual strength after impact of the damaged specimen by an impactor 15.8 mm in diameter is 364.4 MPa according to the results of Koo et al. [28] (Fig. 6), it can be seen that the prediction using Eq. (2) agrees well with the experimental result. The shape of the composite structure for finite element analysis is identical to that for the residual strength test of the structure (Fig. 1), but with the inclusion of a hole of 6.4 mm diameter in the center of the structure. The finite element analysis model was formulated by the same method as depicted in Fig. 4. Because the C-shaped structure specimen differs in shape from the plate specimen, the width of the structure was defined in this study as the width of a specimen with both wing parts unfolded; namely, 73 mm (Fig. 7). This is because stress acts across the cross-section. The characteristic length do = 0.830 mm was obtained from Eq. (9). When the maximum principal stress reaches the tensile strength (780 MPa) at the characteristic length do, the remote stress was obtained from the applied load. The result predicted for the residual strength of the CFRP composite structure after impact was 432 MPa when substituting the remote stress into Eq. (2). The mean residual strength of the structure in the actual test was 364.3 MPa; thus, the difference between the predicted result and the experimental result was about 68 MPa. This considerable difference is thought to be caused by the change in the characteristic length, and by the stress concentration effect of the damaged area due to a change in the structure’s geometry. Therefore, the shape factor was defined as the ratio of the stress concentration factor of the standard plate specimen to that of the composite structure:
F¼
K t;specimen K t;structure
303
Fig. 6. Residual strength versus impactor diameter [28].
ð10Þ
If this shape factor is applied to Eq. (2), Eq. (2) becomes
rR F rHR Di Ei ¼ 1 1:45 ro DI Eth
2
0:01
ð11Þ
Fig. 7. Definition of width to calculate the characteristic length of the C-shaped structure.
After stress analysis was performed for the standard plate specimen with width (W) = 73 mm, thickness (t) = 3.5 mm, and hole notched diameter = 6.4 mm, the shape factor of 0.879 was calculated from the stress concentration factors for the standard plate specimen with width = 73 mm and the C-shaped structure specimen in Fig. 1 as follows:
F¼
Fig. 5. Analysis results for a standard plate specimen [34].
K t;specimen 2:532 ¼ ¼ 0:879 K t;structure 2:882
ð12Þ
When this shape factor was substituted into Eq. (11), the residual strength was about 379 MPa. The predicted result can be seen to agree with the tested mean residual strength of the structure after impact (364.3 MPa), with a difference of about 14.7 MPa.
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For the case in which an impactor of diameter 25.4 mm was used, since the maximum diameter of the permanent impression appearing on the surface was 7.6 mm, finite element analysis was performed for the C-shaped structure with a hole notch diameter of 7.6 mm in the center of the structure. By using Eq. (9), the characteristic length do of about 0.860 mm was obtained. A remote stress applied to the structure was obtained when the maximum principal stress reached 780 MPa at the characteristic length do, and the predicted residual strength after impact of the composite structures was calculated to be 407 MPa by substituting this characteristic length into Eq. (2). Also, from the finite element analysis, after the stress concentration factors were calculated for the standard plate specimen of width W = 73 mm and hole notch diameter 2R = 7.6 mm, and for the C-shaped structure specimen, and by substituting those stress concentration factors into Eq. (10), the shape factor was calculated to be 0.872. By applying this shape factor to Eq. (11), the residual strength was calculated to be 356 MPa. This result differs by 9.5 MPa from the 346.5 MPa mean residual strength of the C-shaped structure specimen determined by tensile residual strength testing, but this difference is within the range of variation of the experimental results, 320–373 MPa. From these results, it can be seen that the residual strength of the CFRP composite structure after impact can be predicted by Eqs. (10) and (11) regardless of the impactor diameter.
3. Evaluation of fatigue characteristics after impact 3.1. Fatigue test after impact Standard plate specimens and C-shaped structure specimens for the fatigue test were made using identical manufacturing materials and methods used to make specimens for the residual strength test. The standard plate specimens were made according to the D3039 ASTM standard [29] (Fig. 8), while the C-shaped structure specimens used were identical in shape and dimensions to the depiction in Fig. 1. A constant load amplitude fatigue test with a stress ratio (R) of 0.1 was performed at room temperature (23 °C) using a universal testing machine with a capacity of 250 kN (Instron Co.). The wave form of the fatigue load was a sine wave, and its frequency was about 5 Hz. The results of fatigue tests for the standard plate specimens with no impact damage and with impact damage at an incident impact energy of 5 J are shown in Fig. 9. Impact damage was applied to composite specimens using a drop impact; an incident impact energy of 5 J resulted in a residual strength corresponding to approximately 70% of the tensile strength. The impactor diameter was 15.8 mm and the diameter of the permanent impression (Di) on the specimen surface created by an impactor diameter (D) of 15.8 mm was about 6.4 mm. Also, the maximum applied stress smax was determined to be 0.75–0.95 times the residual strength. The fatigue life of the composite materials can be seen to decrease due to the impact damage.
Fig. 9. Predicted and actual fatigue behavior of impacted specimens and structures.
Impact damage was applied to the center of the composite structures using a drop impact tester, with a block inserted inside the body to implement the plane support conditions. After an incident impact energy (Ei) of 10 J was given using an impactor 15.8 mm in diameter, fatigue tests were performed in conditions identical to those used in the tests on standard plate specimens. The maximum applied stress was determined to be 0.95–0.99 times the residual strength. The test results were similar to those shown in Fig. 9. 3.2. Prediction of fatigue life of impact damaged composite structures If the case of two-step block loading is applied to Eq. (3) as in the method of Broutman and Sahu [23], the result is as follows:
ro r1 n1 n2 þ ¼1 ro r2 N1 N2
ð13Þ
If the composite materials are under two-step block loading, the composite material undergoes n1 repeated cycles under the firststep block load of r1, and is then destroyed after undergoing n2 cycles under the second-step block load of r2. Broutman and Sahu [23] reported that the strength degradation due to the first block is (ro–r1)n1/N1. If it is assumed that the strength degradation after impact damage is equivalent to that by first-step block loading, the strength degradation by impact damage, ro–rR, can be expressed as
ro rR ¼ ðro r1 Þ
n1 N1
ð14Þ
Therefore, Eq. (13) can be expressed as
ro rR n2 þ ¼1 ro r2 N2
ð15Þ
In addition, because the fatigue damage after impact under constant-amplitude fatigue loading is equivalent to the damage by the second block loading, the maximum stress of the constant amplitude fatigue (rmax) is substituted for r2 [30–32], and the fatigue life of impacted composite materials (Ni) is substituted to n2. The fatigue life of non-impacted composite materials (Nf) is substituted for N2. The substitutions allow Eq. (15) to be rewritten as follows:
Nf Ni ro rR ¼ ro rmax Nf
Fig. 8. Specimen configuration.
ð16Þ
If Eq. (16) is expressed as the fatigue life after impact, the result becomes:
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Ni ¼ Nf
rR rmax ro rmax
ð17Þ
Hwang and Han [33] proposed the following equation as a fatigue life prediction model for composite materials without impact:
rmax q Nf ¼ p 1
ð18Þ
ro
where p and q are material constants obtained from the fatigue tests for composite materials without impact. From the fatigue test results for composite materials without impact, the values obtained for p and q are 1.305 1011 and 9.815, respectively. If the prediction equation of Hwang and Han for the fatigue life of composite materials without impact [33] is applied to Eq. (17), the equation becomes:
Ni ¼
rR rmax rmax p 1 ro rmax ro
q ð19Þ
If the residual strength prediction model of Eq. (2) is substituted into Eq. (19), the result is as follows: " # 2 Di Ei rHR rmax ro p Ni ¼ 1 þ 1:45 þ 0:01 D Eth ro ro rmax rmax q 1
ro
ð20Þ In the case of composite structures, since the shape factor (F) should be considered, Eq. (20) becomes as follows; " # 2 Di Ei F rHR rmax ro Ni ¼ 1 þ 1:45 þ 0:01 p D Eth ro ro rmax rmax q 1
ro
ð21Þ
In this study, to evaluate the influence of the residual strength on the fatigue life of the standard plate specimen, the result of Eq. (20) and the result of substituting Eq. (1) from the prediction model of Caprino [12,13] into Eq. (19) were compared to the fatigue test results. The fatigue prediction from Eq. (20) agreed well with the fatigue test results shown in Fig. 9. On the other hand, since the result from the fatigue prediction model applying Caprino’s model is located in the lower boundary area of the fatigue test results (see Fig. 10), the fatigue prediction model applying Caprino’s model produces slightly conservative results.
For the case in which an incident impact energy of 10 J was inflicted on a CFRP composite structure by an impactor 15.8 mm in diameter, the residual strength was predicted to be about 496 MPa using the characteristic length method described in Section 2.3. The prediction curve for fatigue life applying the predicted hole notched strength to Eq. (21) agrees well with the actual test results for this case (Fig. 8). This result indicates that the fatigue life of CFRP composite structures with impact damage can be predicted accurately by the combined application of the prediction model for the residual strength after impact, the shape factor considering the geometric characteristics, and the fatigue characteristics of virgin composites without impact to the model of strength degradation due to impact damage. 4. Conclusions In this study, residual strength and fatigue characteristics were predicted for the CFRP composite structures that received a damaging impact. The following results were obtained. (1) Using finite element analysis, the hole notched strength of a standard plate specimen, with the hole corresponding to an area of impact damage, was acquired from the point-stress criterion (PSC). The residual strength was calculated by substituting the hole notched strength of a standard plate specimen into the prediction model for the residual strength after impact. The predicted result agrees well with the experimental result. (2) To apply s method for predicting residual strength using the point-stress criterion (PSC) to a C-shaped structure, the shape factor obtained from the concentration factor of a K plate specimen and that of the structure, that is, F ¼ Kt;specimen t;structure was applied to the prediction model for the residual strength. The predicted result agreed well with the experimental result. (3) In this study, the following prediction model for fatigue life was proposed and the fatigue test results agreed well with the fatigue prediction results. Ni ¼
"
# 2 Di Ei F rHR rmax ro þ 0:01 p D Eth ro ro rmax q
1 þ 1:45
rmax 1
ro
(4) The fatigue life of CFRP composite structures with impact damage can be predicted accurately by the combined application of a prediction model that takes into account the residual strength after impact, the shape factor which considers geometric characteristics, and the fatigue characteristics of virgin composites that have not been impacted to the model of the strength degradation due to impact damage. Acknowledgments This work was supported by the National Research Foundation of Korea (NRF) (No. 2011-0020024 and 2012R1A1A2043624). References
Fig. 10. Predicted and actual fatigue behaviors for impacted specimens.
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