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Impact damage tolerance of laminated composite helicopter blades
Composite Structures 62 (2003) 367–371 www.elsevier.com/locate/compstruct
Impact damage tolerance of laminated composite helicopter blades E.V. Morozov b
a,*
, S.A. Sylantiev b, E.G. Evseev
b
a School of Mechanical Engineering, University of Natal, Durban 4041, South Africa Department of Mechanics and Optimization of Processes and Structures, MATI––Russian State University of Technology, 3 Orshanskaya St, Moscow 125351, Russia
Abstract The paper is concerned with the study of the damage resistance of laminated composite helicopter blades subjected to impact loading. Dynamic stress intensity factors are determined for composite laminate and separate layers using combined theoretical and experimental approach. The effect of the projectile size on the damage tolerance of composite blade is investigated and tolerable sizes of the defects are estimated. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Damage tolerance; Composite helicopter rotor blades; Impact loading
1. Introduction Structural components made from laminated polymer matrix composites are susceptible to the various defects caused by impact loading. In many applications, the through-thickness cracks or perforations induced by the projectile impact loading (bullets, stones, fragments, etc.) should be treated as the most hazardous kind of damage initiators that could lead to the catastrophic development of the fracture processes and consequent structural failure. In such cases, prediction of the tolerable defect size plays a significant role in the damagetolerant design for laminated composite structures. The damage-tolerant design methodology based on the combined analytical and experimental techniques applied to the laminated composite helicopter rotor blades is discussed in this paper. The blades under consideration are of sandwich construction including thin-walled composite load-bearing spar. The wall of the spar is made from a hybrid glass-carbon/epoxy-phenol composite laminate consisting of 16 layers (/ ¼ 0°) and 4 layers (/ ¼ 45°) reinforced with glass fabric T-25(VM), and 13 layers reinforced with carbon fiber tape LU-3 (/ ¼ 0°). The structure of the laminate is symmetrical with the total thickness of 6.95 mm. Mechanical properties of the unidirectional composites under tension, *
Corresponding author. Fax: +27-31-260-3217. E-mail addresses: [email protected] (E.V. Morozov), evg_seev@ public.mtu.ru (E.G. Evseev). 0263-8223/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2003.09.034
shear, and compression were determined experimentally by testing specially fabricated specimens. The experimental values of elastic constants, i.e., two moduli of elasticity in the principal directions, E1 and E2 , Poisson’s ratio m21 , and shear modulus, G12 for each material are presented in Table 1. Each characteristic of the unidirectional composites presented in Table 1 is the average of the results obtained from the testing of 10–15 specimens.
2. Dynamic stress intensity factors for laminates In order to characterize damage tolerance of composite components under impact loading the dynamic stress intensity factors should be determined. Consider notched composite laminated specimen subjected to the impact bending loading as shown in Fig. 1. Assume that the notch geometry can be approximated with the ellipse curve. Then the curvature radius, q of the crack tip is presented as q¼
2 d 1 2 a
ð1Þ
where a is the height of the notch (see Fig. 1), and d is the crack opening displacement. In this case, stress intensity factor KI is related to the stress concentration factor Kt for the considered notch geometry as follows
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E.V. Morozov et al. / Composite Structures 62 (2003) 367–371
Table 1 Mechanical properties of unidirectional composites Material
E1 , MPa
E2 , MPa
G12 , MPa
m21
T-25(VM) LU-3
50,000 150,000
16,000 8600
5200 5400
0.235 0.26
z
P
h
h
2
x a L/2
Taking into account, that the nominal bending stress r ¼ 3PL=2th2 , where t is the width of the specimen, and Kt ¼ ra =r, the equation for the stress concentration factor, Kt can be obtained in the form rA 2 a þ 2d ðb1 þ b2 Þ ¼ ða þ dÞ þ k Kt ¼ ð7Þ h 2 r From Eqs. (1) and (4) we get
t
L
a¼ Fig. 1. Dynamic bending of the notched laminated composite specimen.
pffiffiffiffiffiffi KI ¼ 12Kt r pq
ð2Þ
where r is the nominal stress. On the other hand stress intensity factor is defined as pffiffiffi KI ¼ r a Y ða=hÞ ð3Þ Hence, the curvature radius of the crack tip could be found excluding KI from Eqs. (2) and (3) in the form q¼
4aY 2 ða=hÞ Kt2 p
ð4Þ
For the loading case under consideration (see Fig. 1) stress acting at the tip of the crack could be calculated using the following equation [1] PL a þ 2d ra ¼ ða þ dÞ þ k ðb1 þ b2 Þ ð5Þ 4I 2 where I is the moment of inertia of the specimen crosssection, d is the distance from the neutral plane, k ¼ 2a=d, b1 and b2 are the imaginary parts of the roots of the characteristic equation written for the laminated composite as follows 4
2
ax l þ ð2bx þ cxy Þl þ by ¼ 0
d Kt pffiffiffi p 4Y ða=hÞ
ð8Þ
Substituting a from Eq. (8) into Eq. (3) and replacing Kt according to Eq. (7), finally the following equation for KI can be obtained sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ffiffiffi dY ða=hÞ p a þ 2d 4 ðb1 þ b2 Þ p ða þ dÞ þ k KI ¼ r pffiffiffiffiffi 2 2h ð9Þ In order to calculate dynamic stress intensity factor, the experimentally determined value of the crack opening displacement d ¼ dD should be substituted into Eq. (9). Parameter dD is determined using results of the dynamic test conducted on the instrumented with sensors impact testing machine that provides an opportunity to measure a deflection, wD at the point of application of the load during the impact test. For known wD the crack opening displacement d ¼ dD can be found from the geometry considerations (see Fig. 2). From the similarity of the triangles in Fig. 2 we have P
θ wD
ð6Þ
where ax ¼
B22 ; D
bx ¼
B11 1 ; ay ¼ bx ; cxy ¼ ; B44 D n X hðkÞ ðkÞ ðkÞ Bij ¼ Aij hðkÞ ¼ h ; h k¼1
B12 ; D
D ¼ B11 B22 B212 ;
by ¼
Here, n is the number of layers, hðkÞ is the thickness of ðkÞ the kth layer, and stiffness coefficients Aij are calculated for the kth layer in terms of the elastic properties of the unidirectional composite and the angle of the layer orientation [2].
θ r (h - a )
a
δa δ L
Fig. 2. Crack opening geometry.
E.V. Morozov et al. / Composite Structures 62 (2003) 367–371
d a þ rðh aÞ ¼ da rðh aÞ
ð10Þ
where da is the crack opening displacement at the tip of the notch, r is the rotation factor, which is equal to 0.3 for a=h ¼ 0:25 . . . 0:55 [3]. On the other hand the crack tip opening displacement da ¼ 2rðh aÞ tan h and tan h ¼ wD =ðL=2Þ (see Fig. 2). Taking these relations into account, the Eq. (10) yields dD ¼
4wD ½a þ rðh aÞ L
ð11Þ
The deflection, wD at any instant can be found from the experimental load–displacement, P versus wD , diagram obtained form the impact test. Then the corresponding value of the crack opening displacement d ¼ dD can be calculated using Eq. (11) and after that the stress intensity factor, KID can be found from Eq. (9). In case of tensile loading of the composite flat specimen with central crack, the stress concentration factor is calculated as follows [1] Kt ¼ 1 þ
2l ðb þ b2 Þ d 1
ð12Þ
where l is the half crack length. Repeating similar derivations as for the bending case the following equation can be obtained for the stress intensity factor under tension pffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð13Þ KID ¼ 12PD 4 p Y ðl=hÞ dD þ 2lðb1 þ b2 Þ where r ¼ PD =F , and F is the cross-sectional area of the specimen.
3. Impact damage tolerance of helicopter rotor blade Consider the laminated helicopter rotor blade made from composite materials as discussed in Introduction and subjected to impacts of the spherical steel projectiles with diameters of 4, 10, 20 and 40 mm. The corresponding impact load can be calculated as follows 3=5 5mV0 P ¼ k 2=5 ð14Þ 4 where V0 is the velocity of the projectile at the first contact with the blade wall, m is the projectile mass, k is the material properties parameter, which is determined by the following equation [4] 4 R1=2 k¼ ð15Þ 3 l1 þ l2 where R is the radius of projectile, and ðiÞ 2 li ¼ ½1 ðm21 Þ =Ei . Assume that the projectile hits the blade with the velocity of 5 m/s. The values of the critical
369
stress intensity factors for the materials under study were determined experimentally for the same velocity of impact loading using impact testing machine. The resulting perforation occurs at the cross-section of the blade situated at the distance of 0:6L, where L is the length of the blade. The width of the blade at this crosssection is equal to 220 mm, and the working stress is 110 MPa. The acting impact stress is calculated as r ¼ ð0:489P þ 110Þ MPa, where P is determined by Eq. (14). Dynamic stress intensity factors have been calculated for each composite layer and the laminate as a whole using Eq. (13) for various crack sizes and diameters of the projectiles. Results of the analysis are presented in Table 2 and in Figs. 3–5. Critical values of the stress intensity factors for the laminate were calculated in terms of the critical values of stress intensity factors for layers and the layers thicknesses [5]
KIC ¼
n 1X ðkÞ K hðkÞ h k¼1 IC
ð16Þ
The critical values of stress intensity factors for the glass fiber reinforced composite layers and carbon fiber reinforced composite layer were determined experimentally, using aforementioned approach [6]. For glass fiber reD inforced (/ ¼ 0°) material, T-25(VM) KIC ¼ 3430 N/ 3=2 mm , for the same composite reinforced under / ¼ 45°, (T-25(VM)45) the critical value of the stress D intensity factor was KIC ¼ 2070 N/mm3=2 , and for the unidirectional composite reinforced with carbon fiber D tape (LU-3) KIC ¼ 1990 N/mm3=2 . For the composite laminate composed from these layers as described earlier D critical stress intensity factor, KIC ¼ 2830 N/mm3=2 was calculated using Eq. (16). Corresponding critical crack sizes were found from the diagrams shown in Figs. 3–5 and presented in Table 3. As can be seen some critical (maximum allowable) defect sizes found for the glass fiber reinforced layers (T-25(VM)0° for 2 mm projectile and T-25(VM)45° for 2 and 5 mm projectiles) exceed the width of the blade at the cross-section under study, which is equal to 220 mm. This means that the damage caused by the impacts of these projectiles at the initial velocity of 5 m/s does not lead to the fracture of the composite layers under consideration. At the same time, the layers reinforced with carbon fiber tape (LU-3) fail as a result of the fracture initiated by the defects with the lengths of 43.2 and 25.4 mm for 2 and 5 mm radii of the projectiles respectively. The projectiles with the radii exceeding 5 mm initiate fracture of the layer starting from the 10 mm length of the crack. Critical sizes of the defects for the 2, 5 and 10 mm projectiles for the whole laminate are presented in the last row of Table 3. Analyses performed for the
370
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Table 2 Dynamic stress intensity factors for the layers and laminate l, mm
10
20
30
60
80
100
R ¼ 2 mm T-25ðVMÞ
KID
, N/mm3=2
LU-3 , N/mm3=2 KID T-25ðVMÞ45
KID
, N/mm3=2 3=2
KID , N/mm
448
634
969
1350
1930
2870
1340
1910
2920
4070
5840
8640
178
249
380
531
760
1130
662
937
1430
2000
2860
4230
R ¼ 5 mm T-25ðVMÞ
KID
, N/mm3=2
LU-3 , N/mm3=2 KID T-25ðVMÞ45 , N/mm3=2 KID
KID , N/mm3=2
610
862
1320
1840
2630
3900
1830
2600
3980
5540
7940
11,750
240
339
517
772
1030
1540
900
1280
1940
2720
3890
5760
R ¼ 10 mm T-25ðVMÞ
, N/mm3=2
1190
1690
2580
3600
5160
7650
LU-3 , N/mm3=2 KID T-25ðVMÞ45 , N/mm3=2 KID
3580
5097
7790
10,850
15,550
23,000
470
664
1010
1420
2030
3000
KID , N/mm3=2
1760
2500
3810
5330
7620
11,280
3530
5000
7640
10,680
–
–
–
KID
R ¼ 20 mm T-25ðVMÞ
KID
, N/mm3=2
LU-3 , N/mm3=2 KID T-25ðVMÞ45 , N/mm3=2 KID
10,600
KID , N/mm3=2
KI N / mm
–
–
1390
1970
3000
5220
7390
11,300
4190
– – 5990
–
8900
–
–
3/2
R = 5 mm
R = 10 mm
4000
R = 2 mm
K Ic = 3430
R = 10 mm
3000
K Ic = 2070
R = 5 mm
2000
R = 2 mm
1000 lc = 57.1
lc = 81.1
lc = 94.2
lc = 112
lc = 117
lc = 130
0
0
10
20
30
40
50
60
70
80
90
100
110
120
130
Fig. 3. Dependencies of the dynamic stress intensity factor on the size of the defect for glass-reinforced composite T-25(VM); ( (––) / ¼ 45°.
projectiles with the radius of 20 mm show that the fracture initiation of the blade cross-section in all the
l mm ) / ¼ 0°,
layers (and consequently in the whole laminate) occurs for all the defect sizes starting from 10 mm and higher.
E.V. Morozov et al. / Composite Structures 62 (2003) 367–371
371
3/2
KI N / mm
R = 10 mm
3000
2500
R = 5 mm
R = 2 mm
R = 5 mm R = 2 mm
K Ic = 2830 2500
2000 K Ic= 1990
2000
1500
1500 1000
1000
500
500 lc = 12.7
lc = 26.2
lc = 21.6
0
l mm 0
10
20
30
lc = 65.1
lc = 81.9
0
l mm 0
40
10
20
30
40
50
60
70
80
90
100
Fig. 5. Dependencies of the dynamic stress intensity factor on the size of the defect for composite laminate.
Fig. 4. Dependencies of the dynamic stress intensity factor on the size of the defect for carbon-reinforced composite (LU-3).
Table 3 Critical sizes of the defects (lcr , mm) caused by the projectile impacts Material Glass fiber reinforced layer T-25(VM)0°, lcr , mm Glass fiber reinforced layer T-25(VM)45°, lcr , mm Carbon fiber reinforced layer (LU-3), lcr , mm Laminate, lcr , mm
4. Conclusions Impact damage tolerance of composite helicopter rotor blade was analyzed using combined theoretical and experimental approaches. It was shown that the methodology adopted for the study could produce results applicable to the analysis and damage tolerant design of composite structural components subjected to impact loading by projectiles. Dynamic stress intensity factors were calculated for composite layers and the laminate as functions of the size of the defects caused by the projectile impacts. Comparison of the experimentally determined critical values of the stress intensity factors with the computational results yielded maximum allowable sizes of the defects depending on the size of the projectiles. Acknowledgements Authors gratefully acknowledge the support of a National Research Foundation (South Africa) grant
Radius of the projectile, R, mm 2
5
10
224 260 43.2 163.8
188.4 234 25.4 130.2
114.2 162.2 – 52.4
(NRF GUN 2050592/2053318) (EM) and a Russian Fund for Fundamental Research grant no 00-01-00423 (EE, SS) to enable this research to be undertaken.
References [1] Savin GN. Stress distribution in the holes vicinity. Kiev: Naukova Dumka; 1968. [2] Vasiliev VV, Morozov EV. Mechanics and analysis of composite materials. Elsevier; 2001. [3] Fudji T, Dzako M. Fracture mechanics of composite materials. Moscow: Mir; 1982. [4] Broutman LJ, Krock RH, editors. Composite materials. Fracture and fatigue, vol. 5. 1978. [5] Morozov EV, Silantiev SA, Evseev EG, Lessmann HG. Nonlinear fracture analysis of hybrid polymer composite materials and structures. Compos Struct 2000;48:135–8. [6] Morozov EV, Silantiev SA, Evseev EG. Dynamic fracture of notched composite laminates. In: Proceedings of the 12th International Conference on Composite Materials (ICCM-12), Paris, France, July 1999, CD-ROM.
Impact damage tolerance of laminated composite helicopter blades E.V. Morozov b
a,*
, S.A. Sylantiev b, E.G. Evseev
b
a School of Mechanical Engineering, University of Natal, Durban 4041, South Africa Department of Mechanics and Optimization of Processes and Structures, MATI––Russian State University of Technology, 3 Orshanskaya St, Moscow 125351, Russia
Abstract The paper is concerned with the study of the damage resistance of laminated composite helicopter blades subjected to impact loading. Dynamic stress intensity factors are determined for composite laminate and separate layers using combined theoretical and experimental approach. The effect of the projectile size on the damage tolerance of composite blade is investigated and tolerable sizes of the defects are estimated. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Damage tolerance; Composite helicopter rotor blades; Impact loading
1. Introduction Structural components made from laminated polymer matrix composites are susceptible to the various defects caused by impact loading. In many applications, the through-thickness cracks or perforations induced by the projectile impact loading (bullets, stones, fragments, etc.) should be treated as the most hazardous kind of damage initiators that could lead to the catastrophic development of the fracture processes and consequent structural failure. In such cases, prediction of the tolerable defect size plays a significant role in the damagetolerant design for laminated composite structures. The damage-tolerant design methodology based on the combined analytical and experimental techniques applied to the laminated composite helicopter rotor blades is discussed in this paper. The blades under consideration are of sandwich construction including thin-walled composite load-bearing spar. The wall of the spar is made from a hybrid glass-carbon/epoxy-phenol composite laminate consisting of 16 layers (/ ¼ 0°) and 4 layers (/ ¼ 45°) reinforced with glass fabric T-25(VM), and 13 layers reinforced with carbon fiber tape LU-3 (/ ¼ 0°). The structure of the laminate is symmetrical with the total thickness of 6.95 mm. Mechanical properties of the unidirectional composites under tension, *
Corresponding author. Fax: +27-31-260-3217. E-mail addresses: [email protected] (E.V. Morozov), evg_seev@ public.mtu.ru (E.G. Evseev). 0263-8223/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2003.09.034
shear, and compression were determined experimentally by testing specially fabricated specimens. The experimental values of elastic constants, i.e., two moduli of elasticity in the principal directions, E1 and E2 , Poisson’s ratio m21 , and shear modulus, G12 for each material are presented in Table 1. Each characteristic of the unidirectional composites presented in Table 1 is the average of the results obtained from the testing of 10–15 specimens.
2. Dynamic stress intensity factors for laminates In order to characterize damage tolerance of composite components under impact loading the dynamic stress intensity factors should be determined. Consider notched composite laminated specimen subjected to the impact bending loading as shown in Fig. 1. Assume that the notch geometry can be approximated with the ellipse curve. Then the curvature radius, q of the crack tip is presented as q¼
2 d 1 2 a
ð1Þ
where a is the height of the notch (see Fig. 1), and d is the crack opening displacement. In this case, stress intensity factor KI is related to the stress concentration factor Kt for the considered notch geometry as follows
368
E.V. Morozov et al. / Composite Structures 62 (2003) 367–371
Table 1 Mechanical properties of unidirectional composites Material
E1 , MPa
E2 , MPa
G12 , MPa
m21
T-25(VM) LU-3
50,000 150,000
16,000 8600
5200 5400
0.235 0.26
z
P
h
h
2
x a L/2
Taking into account, that the nominal bending stress r ¼ 3PL=2th2 , where t is the width of the specimen, and Kt ¼ ra =r, the equation for the stress concentration factor, Kt can be obtained in the form rA 2 a þ 2d ðb1 þ b2 Þ ¼ ða þ dÞ þ k Kt ¼ ð7Þ h 2 r From Eqs. (1) and (4) we get
t
L
a¼ Fig. 1. Dynamic bending of the notched laminated composite specimen.
pffiffiffiffiffiffi KI ¼ 12Kt r pq
ð2Þ
where r is the nominal stress. On the other hand stress intensity factor is defined as pffiffiffi KI ¼ r a Y ða=hÞ ð3Þ Hence, the curvature radius of the crack tip could be found excluding KI from Eqs. (2) and (3) in the form q¼
4aY 2 ða=hÞ Kt2 p
ð4Þ
For the loading case under consideration (see Fig. 1) stress acting at the tip of the crack could be calculated using the following equation [1] PL a þ 2d ra ¼ ða þ dÞ þ k ðb1 þ b2 Þ ð5Þ 4I 2 where I is the moment of inertia of the specimen crosssection, d is the distance from the neutral plane, k ¼ 2a=d, b1 and b2 are the imaginary parts of the roots of the characteristic equation written for the laminated composite as follows 4
2
ax l þ ð2bx þ cxy Þl þ by ¼ 0
d Kt pffiffiffi p 4Y ða=hÞ
ð8Þ
Substituting a from Eq. (8) into Eq. (3) and replacing Kt according to Eq. (7), finally the following equation for KI can be obtained sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ffiffiffi dY ða=hÞ p a þ 2d 4 ðb1 þ b2 Þ p ða þ dÞ þ k KI ¼ r pffiffiffiffiffi 2 2h ð9Þ In order to calculate dynamic stress intensity factor, the experimentally determined value of the crack opening displacement d ¼ dD should be substituted into Eq. (9). Parameter dD is determined using results of the dynamic test conducted on the instrumented with sensors impact testing machine that provides an opportunity to measure a deflection, wD at the point of application of the load during the impact test. For known wD the crack opening displacement d ¼ dD can be found from the geometry considerations (see Fig. 2). From the similarity of the triangles in Fig. 2 we have P
θ wD
ð6Þ
where ax ¼
B22 ; D
bx ¼
B11 1 ; ay ¼ bx ; cxy ¼ ; B44 D n X hðkÞ ðkÞ ðkÞ Bij ¼ Aij hðkÞ ¼ h ; h k¼1
B12 ; D
D ¼ B11 B22 B212 ;
by ¼
Here, n is the number of layers, hðkÞ is the thickness of ðkÞ the kth layer, and stiffness coefficients Aij are calculated for the kth layer in terms of the elastic properties of the unidirectional composite and the angle of the layer orientation [2].
θ r (h - a )
a
δa δ L
Fig. 2. Crack opening geometry.
E.V. Morozov et al. / Composite Structures 62 (2003) 367–371
d a þ rðh aÞ ¼ da rðh aÞ
ð10Þ
where da is the crack opening displacement at the tip of the notch, r is the rotation factor, which is equal to 0.3 for a=h ¼ 0:25 . . . 0:55 [3]. On the other hand the crack tip opening displacement da ¼ 2rðh aÞ tan h and tan h ¼ wD =ðL=2Þ (see Fig. 2). Taking these relations into account, the Eq. (10) yields dD ¼
4wD ½a þ rðh aÞ L
ð11Þ
The deflection, wD at any instant can be found from the experimental load–displacement, P versus wD , diagram obtained form the impact test. Then the corresponding value of the crack opening displacement d ¼ dD can be calculated using Eq. (11) and after that the stress intensity factor, KID can be found from Eq. (9). In case of tensile loading of the composite flat specimen with central crack, the stress concentration factor is calculated as follows [1] Kt ¼ 1 þ
2l ðb þ b2 Þ d 1
ð12Þ
where l is the half crack length. Repeating similar derivations as for the bending case the following equation can be obtained for the stress intensity factor under tension pffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð13Þ KID ¼ 12PD 4 p Y ðl=hÞ dD þ 2lðb1 þ b2 Þ where r ¼ PD =F , and F is the cross-sectional area of the specimen.
3. Impact damage tolerance of helicopter rotor blade Consider the laminated helicopter rotor blade made from composite materials as discussed in Introduction and subjected to impacts of the spherical steel projectiles with diameters of 4, 10, 20 and 40 mm. The corresponding impact load can be calculated as follows 3=5 5mV0 P ¼ k 2=5 ð14Þ 4 where V0 is the velocity of the projectile at the first contact with the blade wall, m is the projectile mass, k is the material properties parameter, which is determined by the following equation [4] 4 R1=2 k¼ ð15Þ 3 l1 þ l2 where R is the radius of projectile, and ðiÞ 2 li ¼ ½1 ðm21 Þ =Ei . Assume that the projectile hits the blade with the velocity of 5 m/s. The values of the critical
369
stress intensity factors for the materials under study were determined experimentally for the same velocity of impact loading using impact testing machine. The resulting perforation occurs at the cross-section of the blade situated at the distance of 0:6L, where L is the length of the blade. The width of the blade at this crosssection is equal to 220 mm, and the working stress is 110 MPa. The acting impact stress is calculated as r ¼ ð0:489P þ 110Þ MPa, where P is determined by Eq. (14). Dynamic stress intensity factors have been calculated for each composite layer and the laminate as a whole using Eq. (13) for various crack sizes and diameters of the projectiles. Results of the analysis are presented in Table 2 and in Figs. 3–5. Critical values of the stress intensity factors for the laminate were calculated in terms of the critical values of stress intensity factors for layers and the layers thicknesses [5]
KIC ¼
n 1X ðkÞ K hðkÞ h k¼1 IC
ð16Þ
The critical values of stress intensity factors for the glass fiber reinforced composite layers and carbon fiber reinforced composite layer were determined experimentally, using aforementioned approach [6]. For glass fiber reD inforced (/ ¼ 0°) material, T-25(VM) KIC ¼ 3430 N/ 3=2 mm , for the same composite reinforced under / ¼ 45°, (T-25(VM)45) the critical value of the stress D intensity factor was KIC ¼ 2070 N/mm3=2 , and for the unidirectional composite reinforced with carbon fiber D tape (LU-3) KIC ¼ 1990 N/mm3=2 . For the composite laminate composed from these layers as described earlier D critical stress intensity factor, KIC ¼ 2830 N/mm3=2 was calculated using Eq. (16). Corresponding critical crack sizes were found from the diagrams shown in Figs. 3–5 and presented in Table 3. As can be seen some critical (maximum allowable) defect sizes found for the glass fiber reinforced layers (T-25(VM)0° for 2 mm projectile and T-25(VM)45° for 2 and 5 mm projectiles) exceed the width of the blade at the cross-section under study, which is equal to 220 mm. This means that the damage caused by the impacts of these projectiles at the initial velocity of 5 m/s does not lead to the fracture of the composite layers under consideration. At the same time, the layers reinforced with carbon fiber tape (LU-3) fail as a result of the fracture initiated by the defects with the lengths of 43.2 and 25.4 mm for 2 and 5 mm radii of the projectiles respectively. The projectiles with the radii exceeding 5 mm initiate fracture of the layer starting from the 10 mm length of the crack. Critical sizes of the defects for the 2, 5 and 10 mm projectiles for the whole laminate are presented in the last row of Table 3. Analyses performed for the
370
E.V. Morozov et al. / Composite Structures 62 (2003) 367–371
Table 2 Dynamic stress intensity factors for the layers and laminate l, mm
10
20
30
60
80
100
R ¼ 2 mm T-25ðVMÞ
KID
, N/mm3=2
LU-3 , N/mm3=2 KID T-25ðVMÞ45
KID
, N/mm3=2 3=2
KID , N/mm
448
634
969
1350
1930
2870
1340
1910
2920
4070
5840
8640
178
249
380
531
760
1130
662
937
1430
2000
2860
4230
R ¼ 5 mm T-25ðVMÞ
KID
, N/mm3=2
LU-3 , N/mm3=2 KID T-25ðVMÞ45 , N/mm3=2 KID
KID , N/mm3=2
610
862
1320
1840
2630
3900
1830
2600
3980
5540
7940
11,750
240
339
517
772
1030
1540
900
1280
1940
2720
3890
5760
R ¼ 10 mm T-25ðVMÞ
, N/mm3=2
1190
1690
2580
3600
5160
7650
LU-3 , N/mm3=2 KID T-25ðVMÞ45 , N/mm3=2 KID
3580
5097
7790
10,850
15,550
23,000
470
664
1010
1420
2030
3000
KID , N/mm3=2
1760
2500
3810
5330
7620
11,280
3530
5000
7640
10,680
–
–
–
KID
R ¼ 20 mm T-25ðVMÞ
KID
, N/mm3=2
LU-3 , N/mm3=2 KID T-25ðVMÞ45 , N/mm3=2 KID
10,600
KID , N/mm3=2
KI N / mm
–
–
1390
1970
3000
5220
7390
11,300
4190
– – 5990
–
8900
–
–
3/2
R = 5 mm
R = 10 mm
4000
R = 2 mm
K Ic = 3430
R = 10 mm
3000
K Ic = 2070
R = 5 mm
2000
R = 2 mm
1000 lc = 57.1
lc = 81.1
lc = 94.2
lc = 112
lc = 117
lc = 130
0
0
10
20
30
40
50
60
70
80
90
100
110
120
130
Fig. 3. Dependencies of the dynamic stress intensity factor on the size of the defect for glass-reinforced composite T-25(VM); ( (––) / ¼ 45°.
projectiles with the radius of 20 mm show that the fracture initiation of the blade cross-section in all the
l mm ) / ¼ 0°,
layers (and consequently in the whole laminate) occurs for all the defect sizes starting from 10 mm and higher.
E.V. Morozov et al. / Composite Structures 62 (2003) 367–371
371
3/2
KI N / mm
R = 10 mm
3000
2500
R = 5 mm
R = 2 mm
R = 5 mm R = 2 mm
K Ic = 2830 2500
2000 K Ic= 1990
2000
1500
1500 1000
1000
500
500 lc = 12.7
lc = 26.2
lc = 21.6
0
l mm 0
10
20
30
lc = 65.1
lc = 81.9
0
l mm 0
40
10
20
30
40
50
60
70
80
90
100
Fig. 5. Dependencies of the dynamic stress intensity factor on the size of the defect for composite laminate.
Fig. 4. Dependencies of the dynamic stress intensity factor on the size of the defect for carbon-reinforced composite (LU-3).
Table 3 Critical sizes of the defects (lcr , mm) caused by the projectile impacts Material Glass fiber reinforced layer T-25(VM)0°, lcr , mm Glass fiber reinforced layer T-25(VM)45°, lcr , mm Carbon fiber reinforced layer (LU-3), lcr , mm Laminate, lcr , mm
4. Conclusions Impact damage tolerance of composite helicopter rotor blade was analyzed using combined theoretical and experimental approaches. It was shown that the methodology adopted for the study could produce results applicable to the analysis and damage tolerant design of composite structural components subjected to impact loading by projectiles. Dynamic stress intensity factors were calculated for composite layers and the laminate as functions of the size of the defects caused by the projectile impacts. Comparison of the experimentally determined critical values of the stress intensity factors with the computational results yielded maximum allowable sizes of the defects depending on the size of the projectiles. Acknowledgements Authors gratefully acknowledge the support of a National Research Foundation (South Africa) grant
Radius of the projectile, R, mm 2
5
10
224 260 43.2 163.8
188.4 234 25.4 130.2
114.2 162.2 – 52.4
(NRF GUN 2050592/2053318) (EM) and a Russian Fund for Fundamental Research grant no 00-01-00423 (EE, SS) to enable this research to be undertaken.
References [1] Savin GN. Stress distribution in the holes vicinity. Kiev: Naukova Dumka; 1968. [2] Vasiliev VV, Morozov EV. Mechanics and analysis of composite materials. Elsevier; 2001. [3] Fudji T, Dzako M. Fracture mechanics of composite materials. Moscow: Mir; 1982. [4] Broutman LJ, Krock RH, editors. Composite materials. Fracture and fatigue, vol. 5. 1978. [5] Morozov EV, Silantiev SA, Evseev EG, Lessmann HG. Nonlinear fracture analysis of hybrid polymer composite materials and structures. Compos Struct 2000;48:135–8. [6] Morozov EV, Silantiev SA, Evseev EG. Dynamic fracture of notched composite laminates. In: Proceedings of the 12th International Conference on Composite Materials (ICCM-12), Paris, France, July 1999, CD-ROM.