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Controllability of cryogenic Mode I delamination behavior in woven fabric composites using piezoelectric actuators
Engineering Fracture Mechanics 102 (2013) 171–179
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Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech
Controllability of cryogenic Mode I delamination behavior in woven fabric composites using piezoelectric actuators Yasuhide Shindo ⇑, Shunji Watanabe, Tomo Takeda, Masaya Miura, Fumio Narita Department of Materials Processing, Graduate School of Engineering, Tohoku University, Aoba-yama 6-6-02, Sendai 980-8579, Japan
a r t i c l e
i n f o
Article history: Received 5 July 2012 Received in revised form 11 January 2013 Accepted 25 January 2013
Keywords: Polymer matrix composites Piezoelectric materials Finite element analysis Fracture mechanics Delamination
a b s t r a c t This paper investigates experimentally and numerically the delamination behavior in woven glass fiber reinforced polymer (GFRP) composite laminates with surface-bonded piezoelectric ceramic actuators under Mode I loading at cryogenic temperatures. The piezoelectric actuators were used to control the delamination behavior in a composite double cantilever beam (DCB) specimen, and tests were performed at liquid nitrogen temperature (77 K). The finite element analysis of the DCB specimen with piezoelectric actuators was also carried out using temperature-dependent material properties of both the woven GFRP laminates and the piezoelectric ceramics, and the numerical predictions were compared with the experimental data. The dependence of the Mode I delamination behavior on the applied electric fields and the temperature was examined based on the experimental and numerical results, and the feasibility of piezoelectric control of cryogenic delamination behavior in composite laminates was demonstrated. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Composite materials have found widespread engineering applications including cryogenic systems because of their superior physical and mechanical properties. In particular, woven glass fiber reinforced polymer (GFRP) composite laminates are used as electrical and thermal insulation, and structural support in superconducting magnets. In laminated composites, delamination represents one of the most critical damage modes [1]. The delamination damage causes a considerable reduction in the stiffness and strength of structural composite laminates and limits their application. To secure the integrity of composite structures, it is important to control the delamination response in composite laminates at cryogenic temperatures. Piezoelectric materials have been widely used in a number of applications as actuators and sensors due to the intrinsic coupling effect between electrical and mechanical fields, and extensive studies have been performed on the electromechanical characteristics of piezoelectric material systems [2–4]. In the past decades, the concept of using a distributed piezoelectric actuator and sensor network to form a self-controlling and self-monitoring smart system in advanced engineering structures has attracted considerable attention in the research and industrial communities [5,6]. Piezoelectric actuators can also be used to suppress the onset and propagation of damage in structures during service [7]. There have been some theoretical studies on damage (crack) control in beam structures under mechanical loads using piezoelectric actuators (patches) [8,9]. Recently, Shindo et al. [10] have demonstrated experimentally and numerically the feasibility of piezoelectric control of delamination response in woven GFRP composite laminates under Mode I loading. These studies have been focused on piezoelectric damage control performance at only room temperature. Since material properties generally depend on temperature, the control capability may be affected by operating temperatures. In order to apply the piezoelectric damage control to real-life structures, the temperature dependence of controllability must be fully investigated. ⇑ Corresponding author. Tel./fax: +81 22 795 7341. E-mail address: [email protected] (Y. Shindo). 0013-7944/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.engfracmech.2013.01.013
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Nomenclature a delamination length B1 specimen width B2 actuator width c distance between the centers of the end block and the actuator in the specimen longitudinal direction d31, d33, d15 piezoelectric constants of the PZT ceramic D1, D2, D3 components of electric displacement vector E0 applied electric field E1, E2, E3 components of electric field intensity vector EC1 ; EC2 ; EC3 Young’s moduli of the woven composite GC12 ; GC23 ; GC31 shear moduli of the woven composite Mode I energy release rate GI 2H1 specimen thickness actuator thickness H2 L1 specimen length L2 actuator length P applied load s11, s12, s13, s22, s23, s33, s44, s55, s66 elastic compliance constants of the woven composite sE11 ; sE12 ; sE13 ; sE33 ; sE44 elastic compliance constants of the PZT ceramic measured in constant electric field S side length of the end blocks U⁄ prescribed displacement V0 voltage e11, e22, e33, e23, e31, e12 components of strain tensor T11 ; T33 dielectric constants of the PZT ceramic measured at constant stress
mC12 ; mC23 ; mC31 Poisson’s ratios of the woven composite r11, r22, r33, r23, r31, r12 components of stress tensor /
U
electric potential temperature
Superscript C woven composite
The purpose of this paper is to experimentally and numerically study the controllability of the cryogenic Mode I delamination behavior in woven GFRP composite laminates using piezoelectric ceramic actuators. Experiments were conducted on a double cantilever beam (DCB) specimen with surface-bonded actuators at liquid nitrogen temperature (77 K). Also, the finite element analysis was performed considering temperature-dependent material properties of both the woven GFRP laminates and the piezoelectric ceramics, and a comparison was made between the finite element predictions and the test results. Based on the experimental and numerical results, the dependence of the Mode I delamination response on the applied electric fields and the temperature was discussed. 2. Experimental procedure A DCB specimen with piezoelectric actuators was employed for experiments. The geometry and dimensions of the specimen are shown in Fig. 1. The DCB specimen was made of a panel of commercial woven composite laminates (Toyo Lite Co., Ltd., Japan), which are National Electrical Manufacturers Association (NEMA) grade G-11 woven GFRP laminates, and the nominal thickness of the panel 2H1 was 3.85 mm. The woven laminates were composed of a 20-layer plain weave E-glass fabric and a bisphenol-A epoxy resin matrix. The overall fiber volume fraction was about 39%. The plain weave is produced by interlacing warp fiber bundles and fill fiber bundles, and the specimen was cut with the length parallel to the warp direction. The dimensions of the specimen were 70 mm in length (L1) and 20 mm in width (B1). A nonadhesive insert was placed at the midplane. A polymer film was used as an insert material and its thickness was no greater than 13 lm, as suggested by the ASTM standard D 5528 [11]. To produce a delamination with length a, the specimen was precracked. Aluminum end blocks of side length S = 10 mm were adhesively bonded to the specimen to enable load application. In addition, soft lead zirconate titanate (PZT) ceramics C-91 (Fuji Ceramics Corporation, Japan) were used as the piezoelectric actuators for controlling the delamination behavior in the DCB specimen. The actuator thickness (H2) was 1.5 mm; the length (L2) was 10 mm; and the width (B2) was 20 mm (=B1), and c is the distance between the centers of the end block and the actuator in the specimen longitudinal direction. The poling direction of the actuators was along their longitudinal direction, and the electrodes 1 and 2 were adhered to the two opposite surfaces of the actuators. In the experiments, the piezoelectric actuators were attached using an adhesive, such that the center of the actuators coincided with the delamination front, i.e., c = a.
Y. Shindo et al. / Engineering Fracture Mechanics 102 (2013) 171–179
173
Fig. 1. Geometry and dimensions of DCB specimen with piezoelectric actuators.
The DCB specimen was tested under constant load P at 77 K. Testing at 77 K was accomplished by submerging the test fixture and the DCB specimen with piezoelectric actuators in liquid nitrogen throughout the duration of testing. A voltage V0 was applied to the electrodes 1, and the electrodes 2 were connected to ground. The load point displacement was measured by the testing machine’s displacement. 3. Finite element analysis 3.1. Constitutive relations The woven composite laminates were treated as one homogeneous orthotropic elastic material. For the woven laminates in the Cartesian coordinate system O-x1x2x3, we let the axes x1, x2 and x3 be coincident with the warp, fill and thickness directions, respectively. The constitutive relations for the woven laminates are
e11 3 2 s11 6 e22 7 6 s12 7 6 6 6 e 7 6s 6 33 7 6 13 7¼6 6 6 2e23 7 6 0 7 6 6 4 2e31 5 4 0 2e12 0 2
s12 s22 s23 0 0 0
s13 s23 s33 0 0 0
0 0 0 s44 0 0
0 0 0 0 s55 0
32 0 r11 3 7 6 0 76 r22 7 7 7 6 0 7 76 r33 7 76 7; 0 76 r23 7 76 7 0 54 r31 5 r12 s66
ð1Þ
where e11, e22, e33, e23, e31, e12 are the components of strain tensor, r11, r22, r33, r23, r31, r12 are the components of stress tensor, and s11, s12, . . . , s66 are the elastic compliance constants. The used piezoelectric ceramic is PZT, which exhibits symmetry of a hexagonal crystal of class 6 mm with respect to the axes x1, x2 and x3. The constitutive relations for the PZT ceramics with x3 as the poling direction are
3
2
2 sE11 sE12 sE13 0 e11 3 0 0 r11 3 2 0 0 d31 3 7 6 6 6 e 7 6 sE sE sE 76 0 0 r22 7 0 d31 7 72 3 7 6 0 6 22 7 6 12 11 13 0 76 7 E1 7 6 E 7 6 6 6 7 E E 6 e33 7 6 s13 s13 s33 0 6 r33 7 6 0 0 0 0 d33 76 7 7 74 E2 5; 7¼6 7þ6 6 6 7 7 7 6 6 2e 7 6 0 76 0 0 0 sE44 0 6 23 7 6 6 r23 7 6 0 d15 0 7 7 7 E3 7 6 7 6 6 6 7 E 4 2e31 5 4 0 0 0 0 s44 0 0 5 54 r31 5 4 d15 0 0 0 0 0 0 2 sE11 sE12 2e12 r12 0 0 0 2
r11 3 7 32 3 36 6 r22 7 2 T E1 0 6 11 0 0 7 7 6 76 7 7 r33 7 6 T þ E2 5; 0 56 0 0 4 5 4 11 6r 7 6 23 7 E3 0 6 0 0 T33 7 4 r31 5 r12
ð2Þ
2
2
D1
3
2
0 6 7 6 4 D2 5 ¼ 4 0 D3 d31
0
0
0
d15
0
0
d15
0
d31
d33
0
0
ð3Þ
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where E1, E2, E3 are the components of electric field intensity vector, D1, D2, D3 are the components of electric displacement vector, sE11 ; sE12 ; sE13 ; sE33 ; sE44 are the elastic compliance constants measured in constant electric field, d31, d33, d15 are the piezoelectric constants, and T11 ; T33 are the dielectric constants measured at constant stress. The relations between the electric potential / and the electric field components E1, E2, E3 are given by
E1 ¼ /;1 ;
E2 ¼ /;2 ;
E3 ¼ /;3 ;
ð4Þ
where a comma represents the partial differentiation with respect to the coordinates. 3.2. Material properties The micromechanics model of Hahn and Pandey [12] was used to calculate the orthotropic elastic properties, i.e., Young’s moduli EC1 ; EC2 ; EC3 , shear moduli GC12 ; GC23 ; GC31 and Poisson’s ratios mC12 ; mC23 ; mC31 , of G-11 woven GFRP laminates. The superscript C denotes the woven composite. The Poisson’s ratio mC12 reflects shrinkage (expansion) in the x2-direction, due to tensile (compressive) stress in the x1-direction. The model includes parameters to characterize the fabric architecture and constituent material (fiber and matrix) properties. The geometrical parameters of G-11 woven laminates were measured on the microscopy images of the laminate cross-sections. The elastic properties of the fiber (E-glass fiber) and matrix (bisphenol-A epoxy resin) were obtained from the exponential functions of temperature U [13] based on the experimental data. The predicted elastic moduli EC1 ; EC2 ; EC3 ; GC12 ; GC23 ; GC31 ; mC12 ; mC23 ; mC31 of G-11 woven laminates are shown in Fig. 2 as a function of temperature U. The available experimental data at room temperature (295 K) [10] and 77 K [14] are also plotted, showing reasonable agreement between the predicted and experimental data. In terms of the engineering constants, the elastic compliance constants s11, s12, . . . , s66 are defined as
s11 ¼ 1=EC1 ; s22 ¼ 1=EC2 ; s44 ¼
1=GC23 ;
9 s12 ¼ mC12 =EC1 ; s13 ¼ mC31 =EC3 ; > = s23 ¼ mC23 =EC2 ; s33 ¼ 1=EC3 ; s55 ¼
1=GC31 ;
s66 ¼
ð5Þ
> ;
1=GC12 :
Table 1 lists the supplier’s data for the elastic compliance constants sE11 ; sE12 ; sE13 ; sE33 ; sE44 of soft PZT ceramics C-91 at room temperature (RT). In order to evaluate the temperature dependence of the elastic compliance constant sE33 of C-91, the compression tests were conducted under constant electric field at room temperature and 77 K. The measured elastic compliance
9 C C G12 , G23 , G31 (GPa)
25
C
E1C, E2C, E3C (GPa)
30
20 15 10 5 50
C
E1
C
E2
C
E3
Prediction Experimental data
100
150
200
250
8 7 6 5
C
4 50
300
C
C
G12 G23 G31 Prediction
100
150
200
250
300
Φ (Κ)
Φ (Κ)
(b)
(a) 0.30
ν12C, ν23C, ν31C
0.25 0.20 0.15 0.10 0.05 50
ν12C ν23C ν31C Prediction Experimental data
100
150
200
250
300
Φ (Κ)
(c) Fig. 2. Temperature dependence of (a) Young’s moduli, (b) shear moduli and (c) Poisson’s ratios of G-11 woven GFRP laminates.
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Y. Shindo et al. / Engineering Fracture Mechanics 102 (2013) 171–179 Table 1 Elastic compliance constants of soft PZT ceramics C-91.
Supplier’s data Experimental data
RT RT 77 K
sE11 (1012 m2/N)
sE12
sE13
sE33
sE44
17.1 – –
6.3 – –
7.3 – –
18.6 16.3 8.6
41.4 – –
constants sE33 are also shown in the table, and there is a reasonable agreement between the measured and supplier’s data at room temperature. Also, the elastic compliance constant sE33 at 77 K from our experiments is about 0.5 times sE33 at room temperature. In this study, the elastic compliance constant sE33 was assumed to have a linear relationship with temperature U between room temperature and 77 K [15]. Furthermore, the other elastic compliance constants sE11 ; sE12 ; sE13 ; sE44 were presumed to have the same temperature dependence. According to the study of Shindo et al. [16], the temperature-dependent piezoelectric constants d31, d33, d15 of C-91 were evaluated theoretically. A thermodynamic model was employed to predict a monoclinic phase. A shift in the morphotropic phase boundary (MPB) between the tetragonal and rhombohedral/monoclinic phases with decreasing temperature was determined, and the temperature-dependent piezoelectric constants were obtained by considering the decrease in the piezoelectric constants due to the shift in the MPB. The temperature-dependent piezoelectric constants d31(U), d33(U), d15(U) can be given as
8 4 > < ð1:7 10 U þ 0:95Þhd31 ð295Þ; d33 ð295Þ; d15 ð295Þi; ð192 6 U 6 295Þ; hd31 ðUÞ; d33 ðUÞ; d15 ðUÞi ¼ ð1:0 105 U2 þ 2:4 103 U þ 0:15Þhd31 ð295Þ; d33 ð295Þ; d15 ð295Þi; > : ð0 < U 6 192Þ:
ð6Þ
The supplier’s data for the piezoelectric constants at room temperature d31(295), d33(295), d15(295) are listed in Table 2. The calculated temperature-dependent piezoelectric constants are reasonably accurate to describe the piezoelectric response of soft PZT at temperatures below room temperature. Additionally, the dielectric constants T11 ; T33 of C-91 were assumed to be independent of temperature. The following dielectric constants at room temperature from the supplier’s product data sheet were used in the analysis: T11 ¼ 395 1010 C=Vm and T33 ¼ 490 1010 C=Vm. 3.3. Computational model The DCB specimen with piezoelectric ceramic actuators was modeled using ANSYS finite element code. Fig. 3 shows the boundary conditions. The Cartesian coordinate system O-xyz is used with x-, y- and z-axes in the warp, fill and thickness directions of the woven laminate specimen, respectively. The poling direction of the actuators is parallel to the x-axis. Owing
Table 2 Piezoelectric constants of soft PZT ceramics C-91 at room temperature. d31 (1012 m/V)
d33
d15
340
645
836
Fig. 3. Boundary conditions for finite element model of the DCB specimen with piezoelectric ceramic actuator.
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to symmetry, only a quarter of the specimen was modeled. The end block and the actuator were assumed to be perfectly adhered to the surface of the DCB specimen, and adhesive layers were not considered. The specimen was loaded by prescribed displacement U⁄ in the z-direction at the center of the end block (x = S/2, 0 6 y 6 B1/2, z = H1 + S/2). The total nodal force at the center of the end block was doubled (on account of the plane of symmetry), and the calculated load corresponds to the experimental load P. The electrical boundary conditions can be written as
/ðS=2 þ c L2 =2; y; zÞ ¼ V 0 ; 0 6 y 6 B1 =2; H1 6 z 6 H1 þ H2 ; 0 6 y 6 B1 =2; H1 6 z 6 H1 þ H2 : /ðS=2 þ c þ L2 =2; y; zÞ ¼ 0;
ð7Þ
Eight-noded three-dimensional structural solid elements were utilized to mesh the DCB specimen and the end block, and eight-noded coupled-field solid elements were employed for the actuator. A mesh sensitivity study was performed to ensure a mesh independent solution. The virtual crack closure technique (VCCT) was used to determine the Mode I energy release rate [17].
4. Results and discussion Table 3 presents the load point displacements of the DCB specimen with the delamination length a = 19.8 mm under the applied loads P = 20, 30, 40 N and the applied electric fields E0 = V0/L2 = 0, 0.2, 0.5 MV/m at 77 K from the experiments and the finite element analysis. In the analysis, the distance between the centers of the end block and the actuator was considered to equal the delamination length, i.e., c = a = 19.8 mm, to conform to the experimental configuration. The increase in the applied electric field leads to the decrease in the load point displacement. Considering the fact that precise measurements of the small load point displacements are difficult under low applied loads, agreement between the experimental and numerical results is reasonably good. Fig. 4 shows the distributions of the Mode I energy release rate GI across the width of the DCB specimen for c = a = 19.8 mm under P = 30 N and E0 = 0, 0.2, 0.5 MV/m at 77 K. The Mode I energy release rate in the center part of the specimen is approximately constant and decreases with increasing the applied electric field. Also, the energy release rate near the specimen free edge (2y/B1 = 1) increases by applying the electric field. This is likely attributed to the bending across the width of the beam induced by the shrinkage of the actuator in the beam width (y-) direction under the electric field. The
Table 3 Load point displacements for the case that the center of the actuators coincides with the delamination front (c = a = 19.8 mm) at 77 K. P (N)
E0 (MV/m)
Load point displacement (mm) Experimental
Finite element analysis
20
0 0.2 0.5
0.128 0.124 0.120
0.157 0.151 0.143
30
0 0.2 0.5
0.209 0.205 0.201
0.235 0.230 0.222
40
0 0.2 0.5
0.292 0.290 0.286
0.313 0.308 0.300
10
Φ = 77 K c = a = 19.8 mm P = 30 N
GI (J/m2)
8 6 4 2
0
E0 = 0 MV/m = 0.2 MV/m = 0.5 MV/m 0.2
0.4
0.6
0.8
1
2y/B1 Fig. 4. Distributions of the Mode I energy release rate GI across the width of the DCB specimen at 77 K.
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applied positive electric field causes extension of the actuator in the longitudinal (x-) direction and, due to Poisson’s effects, contraction in the width (y-) and thickness (z-) directions. Fig. 5 presents the Mode I energy release rate GI at the center of the specimen (2y/B1 = 0) as a function of the applied electric field E0 for c = a = 19.8 mm under P = 30 N at 295 K and 77 K. The reduction in the energy release rate due to the increase in the applied electric field at 77 K is smaller than that at 295 K, which is caused by the decrease in the piezoelectric constants of the piezoelectric ceramics with decreasing temperature. The Mode I energy release rate GI at 2y/B1 = 0 is shown in Fig. 6 as a function of temperature U (77 K 6 U 6 295 K) for c = a = 19.8 mm under P = 30 N and E0 = 0, 0.2, 0.5 MV/m. The decrease in temperature results in the uniform decrease in the energy release rate under E0 = 0 MV/m. This arises from the temperature dependence of the elastic properties of the woven GFRP laminates and the piezoelectric ceramics. The energy release rate under E0 = 0.2, 0.5 MV/m also decreases uniformly by the decrease in temperature from 295 to 192 K. At this range of temperature, the reduction in the energy release rate due to the applied electric field is fairly constant. This comes from the fact that the piezoelectric constants of the piezoelectric ceramics are nearly constant between 295 and 192 K. Moreover, the reduction in the energy release rate resulting from the applied electric field becomes small when the temperature decreases from 192 to 77 K, because the piezoelectric constants of the piezoelectric ceramics decrease substantially with decreasing temperature from 192 to 77 K. Fig. 7 presents the Mode I energy release rate GI at 2y/B1 = 0 as a function of the distance between the center of the actuators and the delamination front in the longitudinal (x-) direction, i.e., actuator-delamination distance, c a (4 mm 6 c a 6 6 mm) for a = 19.8 mm under P = 30 N and E0 = 0, 0.5 MV/m at 77 K. The energy release rate decreases with applying the electric field even if the center of the actuators does not coincide with the delamination front. Also, the actuator location shows significant influence on the energy release rate, and the reduction rate of the energy release rate with the electric field is high when the center of the actuators is near the delamination front. For example, the reduction rates for the distances c a of 0 mm and 6 mm are 39.7% and 9.8%, respectively. The same trends are seen in the room temperature case [10].
14
c = a = 19.8 mm P = 30 N
GI (J/m2)
12
2y/B1 = 0
10
8
6
295 K 77 K 4 0
0.1
0.2
0.3
0.4
0.5
E0 (MV/m) Fig. 5. Mode I energy release rate GI as a function of applied electric field E0 at 295 K and 77 K.
15 12
c = a = 19.8 mm P = 30 N
GI (J/m2)
2y/B1 = 0 9 6 3 0 50
E0 = 0 MV/m = 0.2 MV/m = 0.5 MV/m 100
150
200
250
300
Φ (Κ) Fig. 6. Temperature dependence of the Mode I energy release rate GI.
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50
Φ = 77 K a = 19.8 mm P = 30 N
40
GI (J/m2)
2y/B1 = 0 30
E0 = 0 MV/m = 0.5 MV/m 20
10
0 −4
−2
0
2
4
6
c − a (mm) Fig. 7. Mode I energy release rate GI as a function of actuator-delamination distance c a at 77 K.
5. Conclusions In this paper, the controllability of the cryogenic Mode I delamination behavior in woven GFRP composite laminates using piezoelectric ceramic actuators was studied experimentally and numerically. Based on the results, the following conclusions can be drawn: 1. The load point displacements of the composite DCB specimen at cryogenic temperatures from the experiments and the finite element analysis can be reduced by the applied electric field of the surface-bonded actuators. 2. The Mode I energy release rate of the composite DCB specimen at cryogenic temperatures decreases as the applied electric field of the actuators increases, which indicates that the piezoelectric control of delamination response in composite materials under mechanical loading can be applicable to a cryogenic environment. 3. Since the material properties of the woven GFRP laminates and the piezoelectric ceramics vary with temperature, the effectiveness of the piezoelectric control strongly depends on temperature. This suggests that the temperature dependence of the control performance has to be taken into account when designing cryogenic structures containing piezoelectric ceramics as actuators. 4. The piezoelectric damage control performance is affected by the distance between the actuators and the delamination.
Acknowledgement This work was supported by Grant-in-Aid for JSPS Fellows (224782). References [1] Tay TE. Characterization and analysis of delamination fracture in composites: an overview of developments from 1990 to 2001. ASME Appl Mech Rev 2003;56(1):1–32. [2] Shindo Y, Yoshida M, Narita F, Horiguchi K. Electroelastic field concentrations ahead of electrodes in multilayer piezoelectric actuators: experiment and finite element simulation. J Mech Phys Solids 2004;52:1109–24. [3] Narita F, Shindo Y, Mikami M. Analytical and experimental study of nonlinear bending response and domain wall motion in piezoelectric laminated actuators under ac electric fields. Acta Mater 2005;53:4523–9. [4] Shindo Y, Narita F, Sato K, Takeda T. Nonlinear electromechanical fields and localized polarization switching of piezoelectric macrofiber composites. J Mech Mater Struct 2011;6(7–8):1089–102. [5] Crawley EF, de Luis J. Use of piezoelectric actuators as elements of intelligent structures. AIAA J 1987;25(10):1373–85. [6] Brunner AJ, Birchmeier M, Melnykowycz MM, Barbezat M. Piezoelectric fiber composites as sensor elements for structural health monitoring and adaptive material systems. J Intell Mater Syst Struct 2009;20:1045–55. [7] Rogers CA. Intelligent material systems – the dawn of a new materials age. J Intell Mater Syst Struct 1993;4:4–12. [8] Duan WH, Quek ST, Wang Q. Finite element analysis of the piezoelectric-based repair of a delaminated beam. Smart Mater Struct 2008;17:015017. [9] Liu TJ-C. Crack repair performance of piezoelectric actuator estimated by slope continuity and fracture mechanics. Engng Fract Mech 2008;75:2566–74. [10] Shindo Y, Miura M, Takeda T, Narita F, Watanabe S. Piezoelectric control of delamination response in woven fabric composites under mode I loading. Acta Mech, in press. [11] ASTM D 5528-01. Standard test method for mode I interlaminar fracture toughness of unidirectional fiber-reinforced polymer matrix composites. [12] Hahn HT, Pandey R. A micromechanics model for thermoelastic properties of plain weave fabric composites. ASME J Engng Mater Technol 1994;116:517–23.
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[13] Takeda T, Shindo Y, Narita F, Sanada K. Stress intensity factors for woven glass/epoxy laminates with cracks at cryogenic temperatures. Mech Adv Mater Struct 2004;11:109–32. [14] Miura M, Shindo Y, Takeda T, Narita F. Effect of damage on the interlaminar shear properties of hybrid composite laminates at cryogenic temperatures. Compos Struct 2010;93:124–31. [15] Sabat RG, Mukherjee BK, Ren W, Yang G. Temperature dependence of the complete material coefficients matrix of soft and hard doped piezoelectric lead zirconate titanate ceramics. J Appl Phys 2007;101:064111. [16] Shindo Y, Narita F, Sasakura T. Cryogenic electromechanical behavior of multilayer piezo-actuators for fuel injector applications. J Appl Phys 2011;110:084510. [17] Rybicki EF, Kanninen MF. A finite element calculation of stress intensity factors by a modified crack closure integral. Engng Fract Mech 1977;9:931–8.
Contents lists available at SciVerse ScienceDirect
Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech
Controllability of cryogenic Mode I delamination behavior in woven fabric composites using piezoelectric actuators Yasuhide Shindo ⇑, Shunji Watanabe, Tomo Takeda, Masaya Miura, Fumio Narita Department of Materials Processing, Graduate School of Engineering, Tohoku University, Aoba-yama 6-6-02, Sendai 980-8579, Japan
a r t i c l e
i n f o
Article history: Received 5 July 2012 Received in revised form 11 January 2013 Accepted 25 January 2013
Keywords: Polymer matrix composites Piezoelectric materials Finite element analysis Fracture mechanics Delamination
a b s t r a c t This paper investigates experimentally and numerically the delamination behavior in woven glass fiber reinforced polymer (GFRP) composite laminates with surface-bonded piezoelectric ceramic actuators under Mode I loading at cryogenic temperatures. The piezoelectric actuators were used to control the delamination behavior in a composite double cantilever beam (DCB) specimen, and tests were performed at liquid nitrogen temperature (77 K). The finite element analysis of the DCB specimen with piezoelectric actuators was also carried out using temperature-dependent material properties of both the woven GFRP laminates and the piezoelectric ceramics, and the numerical predictions were compared with the experimental data. The dependence of the Mode I delamination behavior on the applied electric fields and the temperature was examined based on the experimental and numerical results, and the feasibility of piezoelectric control of cryogenic delamination behavior in composite laminates was demonstrated. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Composite materials have found widespread engineering applications including cryogenic systems because of their superior physical and mechanical properties. In particular, woven glass fiber reinforced polymer (GFRP) composite laminates are used as electrical and thermal insulation, and structural support in superconducting magnets. In laminated composites, delamination represents one of the most critical damage modes [1]. The delamination damage causes a considerable reduction in the stiffness and strength of structural composite laminates and limits their application. To secure the integrity of composite structures, it is important to control the delamination response in composite laminates at cryogenic temperatures. Piezoelectric materials have been widely used in a number of applications as actuators and sensors due to the intrinsic coupling effect between electrical and mechanical fields, and extensive studies have been performed on the electromechanical characteristics of piezoelectric material systems [2–4]. In the past decades, the concept of using a distributed piezoelectric actuator and sensor network to form a self-controlling and self-monitoring smart system in advanced engineering structures has attracted considerable attention in the research and industrial communities [5,6]. Piezoelectric actuators can also be used to suppress the onset and propagation of damage in structures during service [7]. There have been some theoretical studies on damage (crack) control in beam structures under mechanical loads using piezoelectric actuators (patches) [8,9]. Recently, Shindo et al. [10] have demonstrated experimentally and numerically the feasibility of piezoelectric control of delamination response in woven GFRP composite laminates under Mode I loading. These studies have been focused on piezoelectric damage control performance at only room temperature. Since material properties generally depend on temperature, the control capability may be affected by operating temperatures. In order to apply the piezoelectric damage control to real-life structures, the temperature dependence of controllability must be fully investigated. ⇑ Corresponding author. Tel./fax: +81 22 795 7341. E-mail address: [email protected] (Y. Shindo). 0013-7944/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.engfracmech.2013.01.013
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Nomenclature a delamination length B1 specimen width B2 actuator width c distance between the centers of the end block and the actuator in the specimen longitudinal direction d31, d33, d15 piezoelectric constants of the PZT ceramic D1, D2, D3 components of electric displacement vector E0 applied electric field E1, E2, E3 components of electric field intensity vector EC1 ; EC2 ; EC3 Young’s moduli of the woven composite GC12 ; GC23 ; GC31 shear moduli of the woven composite Mode I energy release rate GI 2H1 specimen thickness actuator thickness H2 L1 specimen length L2 actuator length P applied load s11, s12, s13, s22, s23, s33, s44, s55, s66 elastic compliance constants of the woven composite sE11 ; sE12 ; sE13 ; sE33 ; sE44 elastic compliance constants of the PZT ceramic measured in constant electric field S side length of the end blocks U⁄ prescribed displacement V0 voltage e11, e22, e33, e23, e31, e12 components of strain tensor T11 ; T33 dielectric constants of the PZT ceramic measured at constant stress
mC12 ; mC23 ; mC31 Poisson’s ratios of the woven composite r11, r22, r33, r23, r31, r12 components of stress tensor /
U
electric potential temperature
Superscript C woven composite
The purpose of this paper is to experimentally and numerically study the controllability of the cryogenic Mode I delamination behavior in woven GFRP composite laminates using piezoelectric ceramic actuators. Experiments were conducted on a double cantilever beam (DCB) specimen with surface-bonded actuators at liquid nitrogen temperature (77 K). Also, the finite element analysis was performed considering temperature-dependent material properties of both the woven GFRP laminates and the piezoelectric ceramics, and a comparison was made between the finite element predictions and the test results. Based on the experimental and numerical results, the dependence of the Mode I delamination response on the applied electric fields and the temperature was discussed. 2. Experimental procedure A DCB specimen with piezoelectric actuators was employed for experiments. The geometry and dimensions of the specimen are shown in Fig. 1. The DCB specimen was made of a panel of commercial woven composite laminates (Toyo Lite Co., Ltd., Japan), which are National Electrical Manufacturers Association (NEMA) grade G-11 woven GFRP laminates, and the nominal thickness of the panel 2H1 was 3.85 mm. The woven laminates were composed of a 20-layer plain weave E-glass fabric and a bisphenol-A epoxy resin matrix. The overall fiber volume fraction was about 39%. The plain weave is produced by interlacing warp fiber bundles and fill fiber bundles, and the specimen was cut with the length parallel to the warp direction. The dimensions of the specimen were 70 mm in length (L1) and 20 mm in width (B1). A nonadhesive insert was placed at the midplane. A polymer film was used as an insert material and its thickness was no greater than 13 lm, as suggested by the ASTM standard D 5528 [11]. To produce a delamination with length a, the specimen was precracked. Aluminum end blocks of side length S = 10 mm were adhesively bonded to the specimen to enable load application. In addition, soft lead zirconate titanate (PZT) ceramics C-91 (Fuji Ceramics Corporation, Japan) were used as the piezoelectric actuators for controlling the delamination behavior in the DCB specimen. The actuator thickness (H2) was 1.5 mm; the length (L2) was 10 mm; and the width (B2) was 20 mm (=B1), and c is the distance between the centers of the end block and the actuator in the specimen longitudinal direction. The poling direction of the actuators was along their longitudinal direction, and the electrodes 1 and 2 were adhered to the two opposite surfaces of the actuators. In the experiments, the piezoelectric actuators were attached using an adhesive, such that the center of the actuators coincided with the delamination front, i.e., c = a.
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Fig. 1. Geometry and dimensions of DCB specimen with piezoelectric actuators.
The DCB specimen was tested under constant load P at 77 K. Testing at 77 K was accomplished by submerging the test fixture and the DCB specimen with piezoelectric actuators in liquid nitrogen throughout the duration of testing. A voltage V0 was applied to the electrodes 1, and the electrodes 2 were connected to ground. The load point displacement was measured by the testing machine’s displacement. 3. Finite element analysis 3.1. Constitutive relations The woven composite laminates were treated as one homogeneous orthotropic elastic material. For the woven laminates in the Cartesian coordinate system O-x1x2x3, we let the axes x1, x2 and x3 be coincident with the warp, fill and thickness directions, respectively. The constitutive relations for the woven laminates are
e11 3 2 s11 6 e22 7 6 s12 7 6 6 6 e 7 6s 6 33 7 6 13 7¼6 6 6 2e23 7 6 0 7 6 6 4 2e31 5 4 0 2e12 0 2
s12 s22 s23 0 0 0
s13 s23 s33 0 0 0
0 0 0 s44 0 0
0 0 0 0 s55 0
32 0 r11 3 7 6 0 76 r22 7 7 7 6 0 7 76 r33 7 76 7; 0 76 r23 7 76 7 0 54 r31 5 r12 s66
ð1Þ
where e11, e22, e33, e23, e31, e12 are the components of strain tensor, r11, r22, r33, r23, r31, r12 are the components of stress tensor, and s11, s12, . . . , s66 are the elastic compliance constants. The used piezoelectric ceramic is PZT, which exhibits symmetry of a hexagonal crystal of class 6 mm with respect to the axes x1, x2 and x3. The constitutive relations for the PZT ceramics with x3 as the poling direction are
3
2
2 sE11 sE12 sE13 0 e11 3 0 0 r11 3 2 0 0 d31 3 7 6 6 6 e 7 6 sE sE sE 76 0 0 r22 7 0 d31 7 72 3 7 6 0 6 22 7 6 12 11 13 0 76 7 E1 7 6 E 7 6 6 6 7 E E 6 e33 7 6 s13 s13 s33 0 6 r33 7 6 0 0 0 0 d33 76 7 7 74 E2 5; 7¼6 7þ6 6 6 7 7 7 6 6 2e 7 6 0 76 0 0 0 sE44 0 6 23 7 6 6 r23 7 6 0 d15 0 7 7 7 E3 7 6 7 6 6 6 7 E 4 2e31 5 4 0 0 0 0 s44 0 0 5 54 r31 5 4 d15 0 0 0 0 0 0 2 sE11 sE12 2e12 r12 0 0 0 2
r11 3 7 32 3 36 6 r22 7 2 T E1 0 6 11 0 0 7 7 6 76 7 7 r33 7 6 T þ E2 5; 0 56 0 0 4 5 4 11 6r 7 6 23 7 E3 0 6 0 0 T33 7 4 r31 5 r12
ð2Þ
2
2
D1
3
2
0 6 7 6 4 D2 5 ¼ 4 0 D3 d31
0
0
0
d15
0
0
d15
0
d31
d33
0
0
ð3Þ
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where E1, E2, E3 are the components of electric field intensity vector, D1, D2, D3 are the components of electric displacement vector, sE11 ; sE12 ; sE13 ; sE33 ; sE44 are the elastic compliance constants measured in constant electric field, d31, d33, d15 are the piezoelectric constants, and T11 ; T33 are the dielectric constants measured at constant stress. The relations between the electric potential / and the electric field components E1, E2, E3 are given by
E1 ¼ /;1 ;
E2 ¼ /;2 ;
E3 ¼ /;3 ;
ð4Þ
where a comma represents the partial differentiation with respect to the coordinates. 3.2. Material properties The micromechanics model of Hahn and Pandey [12] was used to calculate the orthotropic elastic properties, i.e., Young’s moduli EC1 ; EC2 ; EC3 , shear moduli GC12 ; GC23 ; GC31 and Poisson’s ratios mC12 ; mC23 ; mC31 , of G-11 woven GFRP laminates. The superscript C denotes the woven composite. The Poisson’s ratio mC12 reflects shrinkage (expansion) in the x2-direction, due to tensile (compressive) stress in the x1-direction. The model includes parameters to characterize the fabric architecture and constituent material (fiber and matrix) properties. The geometrical parameters of G-11 woven laminates were measured on the microscopy images of the laminate cross-sections. The elastic properties of the fiber (E-glass fiber) and matrix (bisphenol-A epoxy resin) were obtained from the exponential functions of temperature U [13] based on the experimental data. The predicted elastic moduli EC1 ; EC2 ; EC3 ; GC12 ; GC23 ; GC31 ; mC12 ; mC23 ; mC31 of G-11 woven laminates are shown in Fig. 2 as a function of temperature U. The available experimental data at room temperature (295 K) [10] and 77 K [14] are also plotted, showing reasonable agreement between the predicted and experimental data. In terms of the engineering constants, the elastic compliance constants s11, s12, . . . , s66 are defined as
s11 ¼ 1=EC1 ; s22 ¼ 1=EC2 ; s44 ¼
1=GC23 ;
9 s12 ¼ mC12 =EC1 ; s13 ¼ mC31 =EC3 ; > = s23 ¼ mC23 =EC2 ; s33 ¼ 1=EC3 ; s55 ¼
1=GC31 ;
s66 ¼
ð5Þ
> ;
1=GC12 :
Table 1 lists the supplier’s data for the elastic compliance constants sE11 ; sE12 ; sE13 ; sE33 ; sE44 of soft PZT ceramics C-91 at room temperature (RT). In order to evaluate the temperature dependence of the elastic compliance constant sE33 of C-91, the compression tests were conducted under constant electric field at room temperature and 77 K. The measured elastic compliance
9 C C G12 , G23 , G31 (GPa)
25
C
E1C, E2C, E3C (GPa)
30
20 15 10 5 50
C
E1
C
E2
C
E3
Prediction Experimental data
100
150
200
250
8 7 6 5
C
4 50
300
C
C
G12 G23 G31 Prediction
100
150
200
250
300
Φ (Κ)
Φ (Κ)
(b)
(a) 0.30
ν12C, ν23C, ν31C
0.25 0.20 0.15 0.10 0.05 50
ν12C ν23C ν31C Prediction Experimental data
100
150
200
250
300
Φ (Κ)
(c) Fig. 2. Temperature dependence of (a) Young’s moduli, (b) shear moduli and (c) Poisson’s ratios of G-11 woven GFRP laminates.
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Y. Shindo et al. / Engineering Fracture Mechanics 102 (2013) 171–179 Table 1 Elastic compliance constants of soft PZT ceramics C-91.
Supplier’s data Experimental data
RT RT 77 K
sE11 (1012 m2/N)
sE12
sE13
sE33
sE44
17.1 – –
6.3 – –
7.3 – –
18.6 16.3 8.6
41.4 – –
constants sE33 are also shown in the table, and there is a reasonable agreement between the measured and supplier’s data at room temperature. Also, the elastic compliance constant sE33 at 77 K from our experiments is about 0.5 times sE33 at room temperature. In this study, the elastic compliance constant sE33 was assumed to have a linear relationship with temperature U between room temperature and 77 K [15]. Furthermore, the other elastic compliance constants sE11 ; sE12 ; sE13 ; sE44 were presumed to have the same temperature dependence. According to the study of Shindo et al. [16], the temperature-dependent piezoelectric constants d31, d33, d15 of C-91 were evaluated theoretically. A thermodynamic model was employed to predict a monoclinic phase. A shift in the morphotropic phase boundary (MPB) between the tetragonal and rhombohedral/monoclinic phases with decreasing temperature was determined, and the temperature-dependent piezoelectric constants were obtained by considering the decrease in the piezoelectric constants due to the shift in the MPB. The temperature-dependent piezoelectric constants d31(U), d33(U), d15(U) can be given as
8 4 > < ð1:7 10 U þ 0:95Þhd31 ð295Þ; d33 ð295Þ; d15 ð295Þi; ð192 6 U 6 295Þ; hd31 ðUÞ; d33 ðUÞ; d15 ðUÞi ¼ ð1:0 105 U2 þ 2:4 103 U þ 0:15Þhd31 ð295Þ; d33 ð295Þ; d15 ð295Þi; > : ð0 < U 6 192Þ:
ð6Þ
The supplier’s data for the piezoelectric constants at room temperature d31(295), d33(295), d15(295) are listed in Table 2. The calculated temperature-dependent piezoelectric constants are reasonably accurate to describe the piezoelectric response of soft PZT at temperatures below room temperature. Additionally, the dielectric constants T11 ; T33 of C-91 were assumed to be independent of temperature. The following dielectric constants at room temperature from the supplier’s product data sheet were used in the analysis: T11 ¼ 395 1010 C=Vm and T33 ¼ 490 1010 C=Vm. 3.3. Computational model The DCB specimen with piezoelectric ceramic actuators was modeled using ANSYS finite element code. Fig. 3 shows the boundary conditions. The Cartesian coordinate system O-xyz is used with x-, y- and z-axes in the warp, fill and thickness directions of the woven laminate specimen, respectively. The poling direction of the actuators is parallel to the x-axis. Owing
Table 2 Piezoelectric constants of soft PZT ceramics C-91 at room temperature. d31 (1012 m/V)
d33
d15
340
645
836
Fig. 3. Boundary conditions for finite element model of the DCB specimen with piezoelectric ceramic actuator.
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to symmetry, only a quarter of the specimen was modeled. The end block and the actuator were assumed to be perfectly adhered to the surface of the DCB specimen, and adhesive layers were not considered. The specimen was loaded by prescribed displacement U⁄ in the z-direction at the center of the end block (x = S/2, 0 6 y 6 B1/2, z = H1 + S/2). The total nodal force at the center of the end block was doubled (on account of the plane of symmetry), and the calculated load corresponds to the experimental load P. The electrical boundary conditions can be written as
/ðS=2 þ c L2 =2; y; zÞ ¼ V 0 ; 0 6 y 6 B1 =2; H1 6 z 6 H1 þ H2 ; 0 6 y 6 B1 =2; H1 6 z 6 H1 þ H2 : /ðS=2 þ c þ L2 =2; y; zÞ ¼ 0;
ð7Þ
Eight-noded three-dimensional structural solid elements were utilized to mesh the DCB specimen and the end block, and eight-noded coupled-field solid elements were employed for the actuator. A mesh sensitivity study was performed to ensure a mesh independent solution. The virtual crack closure technique (VCCT) was used to determine the Mode I energy release rate [17].
4. Results and discussion Table 3 presents the load point displacements of the DCB specimen with the delamination length a = 19.8 mm under the applied loads P = 20, 30, 40 N and the applied electric fields E0 = V0/L2 = 0, 0.2, 0.5 MV/m at 77 K from the experiments and the finite element analysis. In the analysis, the distance between the centers of the end block and the actuator was considered to equal the delamination length, i.e., c = a = 19.8 mm, to conform to the experimental configuration. The increase in the applied electric field leads to the decrease in the load point displacement. Considering the fact that precise measurements of the small load point displacements are difficult under low applied loads, agreement between the experimental and numerical results is reasonably good. Fig. 4 shows the distributions of the Mode I energy release rate GI across the width of the DCB specimen for c = a = 19.8 mm under P = 30 N and E0 = 0, 0.2, 0.5 MV/m at 77 K. The Mode I energy release rate in the center part of the specimen is approximately constant and decreases with increasing the applied electric field. Also, the energy release rate near the specimen free edge (2y/B1 = 1) increases by applying the electric field. This is likely attributed to the bending across the width of the beam induced by the shrinkage of the actuator in the beam width (y-) direction under the electric field. The
Table 3 Load point displacements for the case that the center of the actuators coincides with the delamination front (c = a = 19.8 mm) at 77 K. P (N)
E0 (MV/m)
Load point displacement (mm) Experimental
Finite element analysis
20
0 0.2 0.5
0.128 0.124 0.120
0.157 0.151 0.143
30
0 0.2 0.5
0.209 0.205 0.201
0.235 0.230 0.222
40
0 0.2 0.5
0.292 0.290 0.286
0.313 0.308 0.300
10
Φ = 77 K c = a = 19.8 mm P = 30 N
GI (J/m2)
8 6 4 2
0
E0 = 0 MV/m = 0.2 MV/m = 0.5 MV/m 0.2
0.4
0.6
0.8
1
2y/B1 Fig. 4. Distributions of the Mode I energy release rate GI across the width of the DCB specimen at 77 K.
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applied positive electric field causes extension of the actuator in the longitudinal (x-) direction and, due to Poisson’s effects, contraction in the width (y-) and thickness (z-) directions. Fig. 5 presents the Mode I energy release rate GI at the center of the specimen (2y/B1 = 0) as a function of the applied electric field E0 for c = a = 19.8 mm under P = 30 N at 295 K and 77 K. The reduction in the energy release rate due to the increase in the applied electric field at 77 K is smaller than that at 295 K, which is caused by the decrease in the piezoelectric constants of the piezoelectric ceramics with decreasing temperature. The Mode I energy release rate GI at 2y/B1 = 0 is shown in Fig. 6 as a function of temperature U (77 K 6 U 6 295 K) for c = a = 19.8 mm under P = 30 N and E0 = 0, 0.2, 0.5 MV/m. The decrease in temperature results in the uniform decrease in the energy release rate under E0 = 0 MV/m. This arises from the temperature dependence of the elastic properties of the woven GFRP laminates and the piezoelectric ceramics. The energy release rate under E0 = 0.2, 0.5 MV/m also decreases uniformly by the decrease in temperature from 295 to 192 K. At this range of temperature, the reduction in the energy release rate due to the applied electric field is fairly constant. This comes from the fact that the piezoelectric constants of the piezoelectric ceramics are nearly constant between 295 and 192 K. Moreover, the reduction in the energy release rate resulting from the applied electric field becomes small when the temperature decreases from 192 to 77 K, because the piezoelectric constants of the piezoelectric ceramics decrease substantially with decreasing temperature from 192 to 77 K. Fig. 7 presents the Mode I energy release rate GI at 2y/B1 = 0 as a function of the distance between the center of the actuators and the delamination front in the longitudinal (x-) direction, i.e., actuator-delamination distance, c a (4 mm 6 c a 6 6 mm) for a = 19.8 mm under P = 30 N and E0 = 0, 0.5 MV/m at 77 K. The energy release rate decreases with applying the electric field even if the center of the actuators does not coincide with the delamination front. Also, the actuator location shows significant influence on the energy release rate, and the reduction rate of the energy release rate with the electric field is high when the center of the actuators is near the delamination front. For example, the reduction rates for the distances c a of 0 mm and 6 mm are 39.7% and 9.8%, respectively. The same trends are seen in the room temperature case [10].
14
c = a = 19.8 mm P = 30 N
GI (J/m2)
12
2y/B1 = 0
10
8
6
295 K 77 K 4 0
0.1
0.2
0.3
0.4
0.5
E0 (MV/m) Fig. 5. Mode I energy release rate GI as a function of applied electric field E0 at 295 K and 77 K.
15 12
c = a = 19.8 mm P = 30 N
GI (J/m2)
2y/B1 = 0 9 6 3 0 50
E0 = 0 MV/m = 0.2 MV/m = 0.5 MV/m 100
150
200
250
300
Φ (Κ) Fig. 6. Temperature dependence of the Mode I energy release rate GI.
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50
Φ = 77 K a = 19.8 mm P = 30 N
40
GI (J/m2)
2y/B1 = 0 30
E0 = 0 MV/m = 0.5 MV/m 20
10
0 −4
−2
0
2
4
6
c − a (mm) Fig. 7. Mode I energy release rate GI as a function of actuator-delamination distance c a at 77 K.
5. Conclusions In this paper, the controllability of the cryogenic Mode I delamination behavior in woven GFRP composite laminates using piezoelectric ceramic actuators was studied experimentally and numerically. Based on the results, the following conclusions can be drawn: 1. The load point displacements of the composite DCB specimen at cryogenic temperatures from the experiments and the finite element analysis can be reduced by the applied electric field of the surface-bonded actuators. 2. The Mode I energy release rate of the composite DCB specimen at cryogenic temperatures decreases as the applied electric field of the actuators increases, which indicates that the piezoelectric control of delamination response in composite materials under mechanical loading can be applicable to a cryogenic environment. 3. Since the material properties of the woven GFRP laminates and the piezoelectric ceramics vary with temperature, the effectiveness of the piezoelectric control strongly depends on temperature. This suggests that the temperature dependence of the control performance has to be taken into account when designing cryogenic structures containing piezoelectric ceramics as actuators. 4. The piezoelectric damage control performance is affected by the distance between the actuators and the delamination.
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