Strain-amplitude and Strain-rate Dependent Craze Damage of Poly(methyl methacrylate)

Transcription

1 Liu Xiu, Luo Wenbo, and Yin Boyuan Strain-amplitude and Strain-rate Dependent Craze Damage of Poly(methyl methacrylate) Liu Xiu, Luo Wenbo*, and Yin Boyuan College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan , China Received: 29 April 2014, Accepted: 15 May 2014 Summary Dynamic mechanical analysis tests and quasi-static tensile tests were conducted on polymethyl methacrylate (PMMA). Craze damage images on PMMA samples surface were acquired by using an optical microscope. Evolution of the crazing damage was investigated. The results suggest that crazing is loading rate and strainamplitude dependent. In dynamic mechanical tests, the craze damage becomes more and more serious with the increase in strain amplitude, resulting in the Payne effect. Under quasi-static loading, there is a critical strain over which the surface crazes become visible; the greater the loading rate, the greater the critical strain. Moreover, stretching at different rates leads to difference to the morphology of crazes. The surface crazes stressed at lower loading rate are longer and more fully developed than those at higher loading rates, which results in a faster decline in static elastic modulus. Keywords: Damage; Craze; Strain rate; Strain-amplitude; PMMA 1. Introduction Polymethylmethacrylate (PMMA) is widely used in many engineering fields such as mechanical engineering, automobile engineering and aerospace engineering due to its nice transparency and excellent mechanical properties. When it is subjected to a load, there will be damage or defects caused in the material. From damage to fracture, crazing is a particular phenomenon in glassy polymer, accompanying with the whole process 1. Crazing involves craze initiation, craze growth and craze breakdown. Once formed, crazes will grow both by lengthening and by widening or thickening 2,3. When stress is sufficiently high, a craze is able to transform into a growing crack through the progressive break down of craze fibrils, ultimately, leading to failure of the material 2. Thus, crazing is often regarded as a precursor of the brittle fracture of glassy polymers, Smithers Information Ltd., 2014 which plays a crucial role in linking up microscopic mechanism with macroscopic failure. Therefore, it is of theoretical significance and important application value to gain in-depth knowledge on crazing mechanism and craze evolution. To date, many researches on craze behavior have been done. In these studies, some scholars focus on the craze microstructure 4-8. For example, Hui 5 investigated craze failure near the tip of a crack embedded inside a craze and presented a micromechanics model based on the presence of crosstie fibrils in the craze micro-structure. Basu 7 modeled the growth and eventual failure of a craze fibril in a glassy polymer. Some others concentrated on the craze initiation and crazing mechanism 1,9-13. For the past few years, Luo et al. have also devoted to craze damage of polymers. * * Corresponding author. College of Civil Engineering and Mechanics, Xiangtan University, China. Tel: ; address: luowenbo@xtu.edu.cn (W. Luo) They derived the control equation for craze zone growth by taking the craze zone at crack tip as a nonlinear damage zone 8. In addition, they developed an efficient micro-optical method to investigate the creep crazing damage evolution by using a type of gradually varied cross-section sample and presented a time-stress crazing evolution model 2,14. The model indicates that craze initiation is a time and stress dependent phenomenon and the craze initiation time decreases with increase in applied stress. In this work, dynamic mechanical analysis tests and quasi-static loading and unloading tensile tests were performed on PMMA samples to investigate damage and its strainamplitude dependence. Craze initiation and craze sizes under tensile tests with different strain rates were also discussed. Moreover, dynamic mechanical properties of PMMA were explained by the crazing damage evolution. Polymers & Polymer Composites, Vol. 22, No. 8,

2 Strain-amplitude and Strain-rate Dependent Craze Damage of Poly(methyl methacrylate) 2. Experimental The sample material was a commercial grade of PMMA, with a dimension of mm 3 in a shape of rectangle. The samples were divided into two groups. One group was used for dynamic mechanical tests and the other for quasi-static tensile tests. 2.1 Dynamic Mechanical Tests When a viscoelastic material is subjected to a sinusoidal excitation: e (t) =ε 0 + sin(ωt) (1) with a dynamic strain amplitude D, an angular frequency w and a prestrain ε 0, the corresponding stress response is out of phase with strain excitation and can be expressed by: s(t) = σ 0 + E* sin(ωt +d )= σ 0 + [E sin(ωt) + E cos(ωt)] (2) in which d is the hysteresis phase angle, E = E * cosd, E = E* sind, tand = E /E are the storage modulus, the loss modulus and the loss factor (loss tangent), respectively. Isothermal dynamic strain amplitude sweep tests were carried out with a Gabo Eplexor 500N working in the tensile mode at 40 C. The samples were sinusoidally stretched under a prestrain of 2%, and the superimposed strain amplitudes varied from 0.1% to 0.21%, 0.44%, 0.53%, 0.60%, 0.76%, at a frequency of 1 Hz. In order to investigate the craze damage evolution in such strain amplitude sweep tests, the sample surface was observed under an optical microscope with 20 times magnification. conducted in such a way that: 1) to apply a tension load at a constant strain rate up to a maximum strain of 0.5%; 2) unload at the same rate; 3) acquire sample surface image with an optical microscope; 4) reload to the next maximum strain which is higher than the previous maximum strain by an increment of 0.5%, then, unload and perform image acquisition again. Such loading-unloading-image acquisition sequence was repeated until to the final fracture of the sample, as depicted in Figure Results and discussions Figure 2 shows the variation of dynamic mechanical properties with strain amplitude from DMA tests. It can be seen that there exists a critical dynamic strain amplitude D c, below which the storage modulus E, the loss modulus E and the loss factor tand are almost independent on the strain amplitude. Such critical value for the tested material is approximate to 0.1%. However, when the strain amplitude goes greater than the critical value of 0.1%, the E declines monotonically, while both E and tand increase with the strain amplitude. This dynamic mechanical behavior is similar to the Payne effect which refers to the dependence of dynamic moduli on strain amplitude and reveals a typical nonlinear viscoelastic behavior of rubber materials. The Payne effect is well-known for filled rubbers and, physically, can often be attributed to deformation-induced changes in material s microstructure, i.e. to breakage and reforming of weak physical bonds between the filler aggregates 15. In this study, the test Figure 1. Schematic diagram of cyclic loading-unloading tensile test Figure 2. Variation of the storage modulus E, loss modulus E and loss factor tan d of PMMA at a frequency of 1 Hz 2.2 Quasi-static Tensile Tests Cyclic loading-unloading tensile tests were performed at various speeds on PMMA samples using Instron 5943 material testing machine at room temperature. The strain rates were 10-4 s -1, s -1 and 10-3 s -1, respectively. A special loading sequence was 738 Polymers & Polymer Composites, Vol. 22, No. 8, 2014

3 Liu Xiu, Luo Wenbo, and Yin Boyuan behavior suggests that there are craze damage occurring in the material. Figure 3 presents the images of craze damage on the samples surface corresponding to the decrease in storage modulus. It is obvious that craze damage becomes more and more serious with the increase in strain amplitude, which indicates that crazing is strain amplitude dependent. Crazing is a time, temperature and stress dependent damage behavior in polymers. Thus, crazing should be rate dependent, too. Below, we investigate the craze damage evolution in tensile tests with various strain rates. Figure 4, Figure 5 and Figure 6 show the variation of surface morphology of PMMA with the experienced maximum strain when the sample stretched in cyclic loading-unloading tensile test at a constant strain rate of 10-4 s -1, s -1 and 10-3 s -1, respectively. From these three figures, it can be seen that the strain for visible crazes on the sample surface is dependent on the loading rate; such critical strains are about 3%, 3.5% and 5%, corresponding to the strain rate of 10-4 s -1, s -1 and 10-3 s -1. That is to say, the greater the loading rate, the greater the critical strain. This behavior is attributed to the fact that the occurrence of the visible crazes needs time elapsed, and smaller loading rate can provide more time for craze initiation, which agrees with the time-stress crazing evolution model in our previous study 14. For each test at a constant loading rate, the surface crazes become more and more remarkable with the experienced strain. Furthermore, of even greater interest is that the morphology and size of surface crazes varies with the loading rate. In the tensile test at a loading rate of 10-4 s -1, the surface crazes are longer and more fully developed than those at loading rates of s -1 and 10-3 s -1. All these behaviors demonstrate that crazing is strain and strain rate dependent. Figure 3. Craze damage on the sample s surface and the corresponding storage modulus in DMA tests Figure 4. Evolution of surface morphology of PMMA under tensile test at a constant strain rate of 10-4 s -1, showing craze damage at magnification 20 Figure 5. Evolution of surface morphology of PMMA under tensile test at a constant strain rate of 3x10-4 s -1, showing craze damage at magnification 20 As we know, the craze consists of voids and highly oriented fibrils. They Polymers & Polymer Composites, Vol. 22, No. 8,

4 Strain-amplitude and Strain-rate Dependent Craze Damage of Poly(methyl methacrylate) Figure 6. Evolution of surface morphology of PMMA under tensile test at a constant strain rate of 10-3 s -1, showing craze damage at magnification 20 Figure 7. Variation of elastic modulus with experienced maximum strain in cyclic loading-unloading tensile tests under different strain rates connect each other to form a network structure. The craze can usually contain voids with volume fraction of 50~80 percent and voids may cause decrease of elastic modulus. Figure 7 shows the variation of elastic modulus with the maximum strain in cyclic loading-unloading tensile tests. The results suggest that smaller loading rates cause faster descent in elastic modulus due to more craze occurring in the material. 3. Conclusions In this study, the evolution of crazing damage was experimentally investigated in a transparent PMMA sheet under dynamic and quasi-static loading. In DMA tests, the craze damage becomes more and more serious with the increase in strain amplitude, resulting in the Payne effect. Under quasi-static loading, there is a critical strain beyond which the surface crazes become visible. Such critical strain is rate dependent, the greater the loading rate, the greater the critical strain. Moreover, the surface crazes stressed at lower loading rate are longer and more fully developed than those at higher loading rates resulting in a faster descend in static elastic modulus. Acknowledgements This work was supported by the NSFC (No ), Hunan Provincial Science and Technology Program (No.2014TT2031) and Scientific Research Fund of Hunan Provincial Education Department (No.13A098). References 1. De Focatiis D.S. and Buckley C.P., Determination of craze initiation stress in very small polymer specimens. Polymer Testing, 27(2) (2008) Luo W. and Liu W., Incubation time to crazing in stressed poly(methyl methacrylate). Polymer Testing, 26(3) (2007) Sha Y., Hui C.Y., and Kramer E.J.. Simulation of craze failure in a glassy polymer: rate dependent drawing and rate dependent failure models. Journal of Materials Science. 34(15) (1999) Xu D., Hui C.Y., Kramer E.J., et al., A micromechanical model of crack growth along polymer interfaces. Mechanics of Materials, 11(3) (1991) Hui C.Y., Ruina A., Creton C., et al., Micromechanics of crack growth into a craze in a polymer glass. Macromolecules, 25(15) (1992) Lauterwasser B.D. and Kramer E.J., Microscopic mechanisms and mechanics of craze growth and fracture. Philosophical Magazine A., 39(4) (1979) Basu S., Mahajan D.K., and van der Giessen E., Micromechanics of the growth of a craze fibril in glassy polymers. Polymer, 46(18) (2005) Luo W., Yang T., and Wang X., Time-dependent craze zone growth at a crack tip in polymer solids. Polymer, 45(10) (2004) Argon A.S., Craze initiation in glassy polymers-revisited. Polymer, 52(10) (2011) Wu G., Zhu X., Gao Z., et al., Experimental study on crazing initiation and damage in PMMA under creep. Journal of Aeronautical Materials, 32(3) (2012) van Melick H.G.H, Bressers O.F.J.T, den Toonder J.M.J, et al., A microindentation method for probing the craze-initiation stress in glassy polymers, Polymer, 44(8) (2003) Wang T.T., Matsuo M., and Kwei T.K., Criteria of craze initiation in glassy polymers. Journal of Applied Physics, 42(11) (2003) Polymers & Polymer Composites, Vol. 22, No. 8, 2014

5 Liu Xiu, Luo Wenbo, and Yin Boyuan 13. Kitagawa M., Craze initiation of glassy polymers under the action of crazing agent. Journal of Polymer Science: Polymer Physics Edition, 14(11) (1976) Luo W., Wang C., Zhao R., et al., Creep behavior of poly(methyl methacrylate) with growing damage. Materials Science and Engineering: A, (2008) Luo W., Hu X., Wang C., et al., Frequency-and strain-amplitudedependent dynamical mechanical properties and hysteresis loss of CB-filled vulcanized natural rubber. International Journal of Mechanical Sciences, 52(2) (2010) Polymers & Polymer Composites, Vol. 22, No. 8,

6 Strain-amplitude and Strain-rate Dependent Craze Damage of Poly(methyl methacrylate) 742 Polymers & Polymer Composites, Vol. 22, No. 8, 2014