CHIN. PHYS. LETT. Vol. 27, No. 6 (2010) 066201
Dynamic Tensile Behavior and Fracture Mechanism of Polymer Composites Embedded with Tetraneedle-Shaped ZnO Nanowhiskers * RONG Ji-Li(荣吉利)1** ,WANG Xi(王玺)1 , CAO Mao-Sheng(曹茂盛)2 , WANG Da-Wei(王大伟)2 , ZHOU Wei(周伟)2 , XU Tian-Fu(徐天富)1 1
2
School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081 School of Material Science and Engineering, Beijing Institute of Technology, Beijing 100081
(Received 4 February 2010) Dynamic tensile properties of glass-fiber polymer composites embedded with ZnO nanowhiskers are investigated by a split Hopkinson tensile bar. The stress-strain curves, ultimate strength, failure strain and elastic modulus are obtained and the failure mechanism of the composites is investigated by the macroscopic and microscopic observation of fractured specimens. The strain rate effect on the mechanical behavior is discussed and a constitutive model is derived by simulating the experimental data. The experimental results show that the materials have an obvious non-linear constitutive relation and strain rate strengthening effect. The composites with ZnO nanowhiskers under dynamic loading have various failure modes and better mechanical properties.
DOI: 10.1088/0256-307X/27/6/066201 mainly focused on the microwave absorption properties and dielectric response. However, few studies on the mechanical behavior of ZnO𝑤 reinforced composites have been reported. In our previous work, plain woven glass fiber reinforced plastic laminates embedded with ZnO𝑤 were prepared and the compressive strength of GFRP embedded with ZnO𝑤 was studied.[15,16] In this Letter, we concentrate on the dynamic tensile mechanical behavior of fiber reinforced composites embedded with ZnO𝑤 , the failure mechanism and strain rate effect of the composites are discussed. R3 (a) 10 3 20
2.9
20 50 Cylindrical steel fixture
Screw
(b)
Ø4 5
15 (c)
Ø12
Composites are increasingly replacing conventional metallic materials in aerospace, military, civil engineering, armored vehicles, marine and automobile industries, since the excellent properties of high ratio strength, high ratio modulus, anti-fatigue, antishock. Recently, the reinforcement of composites has been achieved by incorporating fibers, whiskers, particles and sheets. Due to being a single crystal with rare defects and high strength and modulus, whiskers can serve as new composite reinforcements and whisker-reinforced composites have become a very active area of research and have been extensively investigated.[1−4] As wide band-gap semiconductors, ZnO nanowhiskers (ZnO𝑤 ) have been synthesized and investigated widely on their specific electrical, optoelectronic and microwave absorption properties[5−7] and mechanical properties[8] for several decades. Lin et al.[9,10] have prepared PZT-based nanocomposites embedded with ZnO𝑤 by a normal sintering process. The results indicate that the mechanical properties of the PZT/ZnO𝑤 composites are improved significantly without decreasing the piezoelectric properties greatly. They also discussed the possible reinforcement mechanisms of the ZnO𝑤 on the mechanical responses of the composites. Hu et al.[11] investigated the mechanical properties, morphology and crystal structure of Nylon11/T-ZnO𝑤 . Zhao et al.[12] successfully synthesized cage-like nano-tetrapod ZnO and revealed that the linking legs of the tetrapod ZnO have a different growth process. Shi et al.[13,14] reported the excellent dielectric response and broadband of three-layer graded ZnO nanowhisker/polyester composites. Thus, the investigation of the ZnO𝑤 has
Ø6
PACS: 62. 20. Mm, 81. 05. Lg
1
3
Spcimen
25 2
Strain gauge 1 Striker 2 Strain gauges
2
4
Digital storage 3 Incident bar
5
Computer 4 Spcimen 5 Transmitter bar
Fig. 1. (a) Geometry of tensile specimen, (b) connection of specimen and fixture, (c) schematic diagram of the SHTB.
* Supported
by the National Natural Science Foundation under Grant Nos 10672020 and 50742007. whom correspondence should be addressed. Email:
[email protected] c 2010 Chinese Physical Society and IOP Publishing Ltd ○ ** To
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Three laminates with different mass percentages of ZnO𝑤 (0, 10 and 20%) were selected to investigate the strain rate effect. The tensile specimens with 26 plies for quasi-static and dynamic tests were the same size as shown in Fig. 1(a). The quasi-static tensile tests were conducted on a Instron Testing machine and the dynamic tensile tests were conducted on a split Hopkinson tensile bar.[17−20] Taking into account the dispersion of composite materials, the quasi-static tests were conducted with five specimens and the dynamic tests were conducted with three specimens for each sample. Accurate results were obtained by calculating the mean and selecting the typical samples. The SHTB is composed of a striker, incident bar, transmitter bar, digital storage and computer, and the specimen was sandwiched between the incident bar and transmitter bar by a special fixture which is connected to the incident bar and transmitter bar by screwing. Figure 1(b) shows the connection of the specimen and fixture. Figure 1(c) shows a schematic diagram of the SHTB. The analysis of the SHTB provides stress, strain rate and strain in the specimens as follows: 2𝐶0 𝐿𝑆
𝜀𝑆 (𝑡) =
𝜀˙𝑆 (𝑡) =
∫︁
Figure 2 shows the stress-strain curves of the specimens with different ZnO𝑤 contents at a strain rate of 0.001 s−1 under quasi-static loading. The stress-strain curves of all the specimens are nonlinear. In the initial stage of loading, the specimens without whiskers show linear elastic characteristics without damage. With the increase of loading, the accumulation of damage leads to a significant drop of modulus. When the stress reaches the limitation, brittle fracture happens. However, for the specimens with ZnO𝑤 , the stressstrain curves are mainly linear-elastic. With the increase of loading, the modulus decreases and the failure mode is still brittle fracture. Table 1 lists the ultimate strength, failure strain and elastic modulus of specimens under quasi-static loading. The tensile strength and elastic modulus of specimens with ZnO𝑤 are higher than that without ZnO𝑤 , while the fracture strain is lower. Table 1. The ultimate strength, failure strain and elastic modulus of specimens under quasi-static loading. Property Ultimate strength (MPa) Failure strain Elastic modulus (GPa)
𝑡
[𝜀𝐼 (𝜏 ) − 𝜀𝑇 (𝜏 )] 𝑑𝜏,
(1)
0
2𝐶0 [𝜀𝐼 (𝑡) − 𝜀𝑇 (𝑡)] , 𝐿𝑆
(2)
𝐸𝐴 𝜀𝑇 (𝑡), (3) 𝐴𝑆 √︀ where 𝐴, 𝐸 and 𝐶0 (𝐶0 = 𝐸/𝜌, 𝜌 is the mass density of the bar) are the cross-sectional area, Young’s modulus and wave speed of the bar, respectively. 𝐿𝑠 and 𝐴𝑠 are the length and cross-sectional area of the specimen, 𝜀𝐼 (𝑡) and 𝜀𝑇 (𝑡) are the axial strains of the incident pulse and transmitted pulse respectively, measured in the incident and transmitted bars versus time 𝑡.
0% 211.78 0.0186 23.14
10% 203.7 0.007 28.337
20% 271.09 0.0113 27.499
Table 2. The ultimate strength, failure strain and elastic modulus of specimens under dynamic loading. Property Ultimate strength (MPa) Failure strain Elastic modulus (GPa)
0% 1288 0.02694 47. 13
10% 1289 0.02313 61.40
20% 1530 0.03331 51.98
𝜎𝑆 (𝑡) =
1600
Stress (MPa)
1200
20%
0% 800
10%
400
20%
250
Stress (MPa)
200
0 0.00
0%
10%
0.01
0.02
0.03
0.04
Strain
Fig. 3. Stress-strain curves of dynamic tensile specimens. 150
100
50
0 0.000
0.005
Strain 0.010
0.015
0.020
Fig. 2. Stress-strain curves of quasi-static tensile specimens.
Figure 3 shows the stress-strain curves of the specimens with different ZnO𝑤 contents at a strain rate of 860 s−1 under dynamic loading. The stress-strain curves indicate the viscoelastic characteristic behavior. When the stress reaches the limitation, the carrying capacity gradually reduces and eventually brittle fracture occurs. Because of the good plasticity of laminate and the shear-lag effect of the matrix, specimens remain at carrying capacity even if some fibers
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are broken. Table 2 shows the ultimate strength, failure strain and elastic modulus of specimens under dynamic loading. The above experimental results show that the tensile strength, fracture strain and elastic modulus of all specimens increase with increasing strain rate, and the tensile strength and elastic modulus show the strain rate strengthening effect. For specimens at the same strain rate, specimens with ZnO𝑤 have better tensile properties than that without ZnO𝑤 . This is because the resin matrix will transfer stress to the tetraneedlelike ZnO𝑤 under the outer loading and the ZnO𝑤 can transfer stress effectively and avoid the stress concentration due to the unique three-dimensional structure. As the loading increases and damage accumulates, ZnO𝑤 can deflect cracks in the matrix, prevent crack propagation and limit the deformation of the matrix resin. When the fracture of ZnO𝑤 occurs, fracture energy is absorbed. Moreover, ZnO𝑤 can maintain short fibers to enhance the matrix after breaking. Therefore, the mechanical properties of composites are improved by adding the high strength and tetrapodshaped ZnO𝑤 .
mode was brittle break with fiber pull-out and shearing fracture along a 45∘ angle. Figures 4(c) and 4(d) show the failure mode of specimens under dynamic loading. The failure mode was brittle break with fiber pull-out and fracture. Figure 5 shows the SEM image of tensile specimens under dynamic loading. The specimens mainly break through the fiber bundles and then fibers break. The one-dimensional damage constitutive equation is built using the damage mechanics theory[21,22] as follows: 𝜎 = 𝐸𝜀(1 − 𝐷), (4) where 𝜎 and 𝜀 are the stress and strain of materials, respectively; 𝐸 is the initial elastic modulus of the material; 𝐷 is the damage variable. Taking into account the material brittle, using strain to represent the damage variable 𝐷, defined as 𝐷 = 𝑚𝜀𝑛 ,
(5)
where 𝑛 is the parameter; 𝑚 is the variable associated with strain rate. Therefore, the one-dimensional elastic brittle damage constitutive model is obtained, 𝜎 = E𝜀(1 − 𝑚𝜀𝑛 ).
(a)
(6)
(b)
(c)
Assuming that where 𝑚 is the function associated with the strain 𝜀, the one-dimensional elastic brittle damage constitutive model is obtained by the method of polynomial fitting:
(d)
𝜎1 = 𝐸1 (7.93014𝑒6𝜀5 − 748945.14608𝜀4 + 23399.4216𝜀3 − 290.78964𝜀2 + 2.26857𝜀 + 0.00241),
Fig. 4. Typical tensile failure of composites (a) brittle break with fiber pullout; (b) shear fracture along 45∘ angle; (c) fiber pull-out and break; (d) brittle break with fiber pull-out.
(7)
5
4
𝜎2 = 𝐸2 (5.81587𝐸6𝜀 − 549267.09981𝜀 + 17160.84617𝜀3 − 213.26152𝜀2 + 1.66374𝜀0.00177),
(a)
ZnOw
5
(8) 4
𝜎3 = 𝐸3 (2.82739𝑒6𝜀 − 340110.6229𝜀
(b)
+ 12959.54385𝜀3 − 172.9606𝜀2 + 1.28034𝜀0.00128), Fiber bundles 1 mm
25 mm (c)
(d) Fiber Fiber
Matrix
Matrix 100 mm
10 mm
Fig. 5. Characterization of the tensile failure: (a) SEM image of ZnO𝑤 , (b) SEM image of tensile fractography, (c) breakage of fiber bundles, (d) fiber break.
The failure morphologies were characterized by SEM. Figures 4(a) and 4(b) show the failure mode of specimens under quasi-static loading. The failure
(9)
where 𝜎1 , 𝜎2 , 𝜎3 , 𝐸1 , 𝐸2 and 𝐸3 are the stress and initial elastic modulus of the materials in which the mass ratio of ZnO𝑤 is 0%, 10% and 20%. The relevant index of the fitting curves is 0.99405, 0.99605 and 0.99382, respectively. In summary, the stress-strain curves of composites with different mass ratios of ZnO𝑤 under quasi-static and dynamic tensile loading are obtained. Nonlinear characteristics and strain-rate dependence under dynamic loading are observed. It is found that ZnO𝑤 could improve the mechanical properties of GFRP composite laminates significantly. The failure mechanism of composites is characterized by macro and micro-images. The damage constitutive and failure mechanism are discussed elementarily.
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