Shear strain rate

In order to properly describe the rate sensitivity of the out-of-plane shear strength, the associated shear strain rate on the failure plane should be evaluated. The shear strain rate can be converted from the axial strain rate through the coordinate transformation law as follows.

[ ]

In eqn (3.7), the prime coordinate is coincided with shear failure plane, while the un-prime system is defined based on the loading direction as shown in Figure 18. The α is the angle between the failure plane and the loading direction. From figure 18, it is easy to realize that the shear strain rate on the failure plane is indicated as γ& and the explicit form can be expressed as _{2 ′3} respectively. To calculate the shear strain rate, it is required to have the information about the two strain components. One way to achieve this goal is directly mounting two strain gages orthogonally on the specimen and then recording the two strain components respectively during the transverse compression test. However, there is an alternative way that only ε& ₂₂ component was measured, from which the other strain rates ε& can be ₃₃ derived using viscoplasticity theory. The following would demonstrate the procedure regarding the derivation of ε₃₃ and then the analytical result will be compared with the experimentally measured strain history at nominal stain

16

rates 10^-4/s and 10^-2/s in Figure 19 and 20.

The strain rate component ε& was decomposed into elastic and plastic ₃₃ parts. For the elastic part, it is calculated from the Poisson’s ratio effect of the elastic deformation in ε& . However, the plastic portion is described using ₂₂ the flow rule in conjunction with an appropriately selected plastic potential.

The 3-D plastic potential suitable for modeling plastic flow in anisotropic fiber composites has been proposed by Chen and Sun [18]. Using a micromechanics analysis, they showed that hydrostatic stresses could produce plastic deformations, but uniform dilatation does not result in any plastic flow.

If the composite is assumed to be transversely isotropic on the x –₂ x plane ₃ and also linear elastic in the fiber direction, then this 3-D plastic potential can be reduced as

where a₆₆ is a coefficient indicating the anisotropy in plasticity and σ_ij is the stress components in the material principal directions. Furthermore, if we assume the plane stress on the x₂–x₃ plane, the 3-D plastic potential given in eqn (3.9) were reduced to

( ) (

)

together with the plastic potential, the corresponding plastic strain rates were

17

For unidirectional composites subjected to only transverse loading,σ , ₂₂ the above formulations were reduced into

λ

It is noted that, from eqn (3.13), the plastic deformation in x direction ₃ is the same as that in the x₂ direction but containing negative sign. Thus, when ε& is measured, the ₂₂^p ε& could be obtained from eqn (3.13). In 33^p

compressive failure test, the total strain histories ε& were obtained from the ₂₂ strain gage signals mounted directly on the specimens. By subtracting the elastic part from the total strain rate, the plastic strain rate is given by

2 22 22

22 E

p ε σ

ε& = & − ^& (3.15)

The above equation could also be considered as the plastic strain rate in the x direction. It is important to note that the total strain rate and stress ₃ rate in eqn (3.15) are calculated by taking the time derivative of the stress and strain curves, respectively at the instance of out-of-plane shear failure. By including the elastic part, the total strain rate in the x direction can be ₃ derived as

18

p

E₂ ^{23 22}

33 σ22ν ε

ε_& =− ^& − _& (3.16)

where ν₂₃ is the Poisson’s ratio in the x and ₂ x plane. ₃

Thus by using eqns (3.8) and (3.16), the shear strain rate on the failure plane can be calculated with the experimentally measured uniaxial stress and strain histories.

3.3 Result and discussion

Base on Mohr-Coulomb type criterion, the out-of-plane shear strength could be expressed as a function of transverse compressive strength and failure plane orientation. In addition, through the forging derivation, the corresponding shear strain rate was calculated from axial strain rate. Table 3 showed the values of out-of-plane shear strength associated with its shear strain rate. From Table 3, the out-of-plane shear strengths versus the shear strain rate for CFA graphite/epoxy composites were plotted in Figure 21.

Apparently, the out-plane shear strength increases with the increment of the shear train rates. Again, a semi-logarithmic function in terms of the normalized shear strain rate was employed to describe the rate dependence of the out-plane shear strength. It is noted that in Figure 21 γ& is the _s quasi-static shear strain rate and assigned to be 1.56×10^-4/s in the analysis. In the same manner, the results for the S2/8552 glass/epoxy composites were summarized in Table 4 and the result were plotted in Figure 22. The rate dependent tendency of out-of–plane shear strength can be modeled with a semi-logarithmic function as shown in Figure 22.

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Chapter 4 Compressive failure of off-axis epoxy/clay fiber nanocomposites

In the precious chapters, it was indicated that the transverse compressive failure of fiber composites is mainly controlled by matrix properties and its adhesion to the surrounding fibers. The observation implies that the transverse compressive strength of composites can be improved if the corresponding matrix properties are enhanced. With the development of the nanotechnology, the fiber/epoxy composites modified with organoclay may become a possible potential material for achieving the goal. To understand the compressive strength of the off-axis fiber/epoxy nanocomposites and its corresponding failure mechanism, the samples will be prepared and tested in compression by using the same method presented previously.

4.1 Glass fiber/epoxy nanocomposite preparation

The epoxy resin used in this study is diglycidyl ether of bisphenol A (DGEBA, EPON828 with an epoxy equivalent weight of 187) supplied by Resolution Performance Products. The curing agent is a polyoxypropylenediamine (Jeffamine D-230 with a molecular weight of 230) provided by Huntsman Corp. The clay used for the synthesis of nanocomposites is organoclay (Nanomer I.30E), obtained from Nanocor Inc.

It is basically an octadecyl-ammonium ion surface modified montmorillonite

20

mineral designed to be easily dispersed into amine-cured epoxy resin and to form nanocomposites as well [19]. When preparing the epoxy-organoclay nanocomposite samples, the organoclay clay was dried in the vacuum oven for 6 hours at 90˚C in order to remove containing moisture, and then blended with EPON828 at 80˚C for 4 hours using a mechanical stirrer. The mixture was then sonicated using a sonicator (provided by Misonix, Sonicator^® 3000) with cooling system around the sample container until the compounds become transparent. The epoxy-organoclay mixture was degassed at room temperature in a vacuum oven for ten minutes and mixed with curing agent (32 wt% of EPON828). It is noted that when epoxy-organoclay mixture contains high organoclay loading, the viscosity would become higher and retard the degassing process. More degassing time is required to effectively eliminate the embedded bubbles. The mechanical stirrer was again utilized to blend the final mixture at room temperature for ten minutes.

Vacuum assisted hand lay-up procedures were adopted for preparing the fiber/epoxy nanocomposites. The final mixture of organoclay/epoxy together with curing agent prepared as described earlier was poured on one dry unidirectional glass fiber layer (provided by Vectorply^, E-LR 0908-14 unidirectional E-glass fiber). The resin was impregnated into the dry fiber by using hand roller. Then, another ply of dry fiber was stacked on it. The repeating process continued until the 18 layer glass fiber nanocomposites were fabricated. The fiber stack was sandwiched between two steel plates with

21

porous fabric separator on the surfaces and then sealed within a vacuum bag.

Subsequently, the whole laminates were cured in a hot press at 100˚C for 3 hours with additional 3 hours at 125˚C for post-curing under vacuum conditions. In the study, the nanocomposites containing 2.5%, 5% and 7.5%

loadings (by weight) of organoclay were prepared, respectively. It is noted that vacuum is essential for forming nanocomposites since it can facilitate the removal of the tiny bubbles trapped in the nanocomposites during the processing. However, when the nanocomposites contained high organoclay loading (7.5 wt %), it was a challenging task to efficiently remove the bubbles even if the vacuum system was applied.

4.2 Compression tests of glass fiber/epoxy nanocomposites

Off-axis block E-glass/epoxy nanocomposite specimens with dimension of 10.0×6.0×6.0 mm were employed for compression tests. The block specimens were cut from 18-ply unidirectional E-glass/epoxy nanocomposites using diamond wheel, and then lapped on a lapping machine with 14.5 µm abrasive slurry to have smooth and flat loading surfaces as presented previously in Chapter 2. Compressive loading were applied on the specimens by using the servo-hydraulic MTS machine presented previously in Chapter 2.

The nominal strain rate in this chapter was 1×10^-4/s, hence the stroke rate was set in 10^-3mm/s by MTS controller. During the tests, the applied load and

22

displacement histories were recorded using MTS software (Basic Testware).

The associated peak values in the loading curves were measured as the failure stress of the specimens.

Experimental results indicated that for the 30^o and 45^o specimens, in-plane shearing is the major failure mode. Figure 23 and 24 depicts the in-plane shearing failure mechanism for both 30 and 45 degree E-glass/epoxy nanocomposites and conventional E-glass/epoxy composites. However, for the 15^o specimen, the failure was dominated by fiber microbuckling. In addition, for off-axis specimens with off-axis angles greater than 45°, out of plane shear failure would take place. To evaluate the in-plane shear strength, the failure stress associated with in-plane shear failure was of interest. For off-axis specimens subjected to uniaxial loading, the in-plane shear stress σ₁₂ is always accompanied by the transverse normal stress σ₂₂. Through the coordinate transformation law, the axial compressive failure stress can be decomposed into transverse normal stress and shear stress in the principal material directions. Thus, the state of failure can be expressed in terms of the combination of σ₁₂ and σ₂₂ as shown in Figure 25. The results of Figure 25 can be regarded as the in-plane shear strength of the composite with the presence of transverse normal stresses. It is noted that the transverse normal stress has little effect on the failure shear stress and that the effect of transverse normal stress on the in-plane shear strength seems to be weakly proportional to

23

the compressive stress σ₂₂. Thus, the pure in-plane shear strength can be obtained by extending the straight lines to the vertical axis corresponding to σ22= 0.

For the measurement of transverse compressive strength, the unidirectional block E-glass/epoxy nanocomposite specimens were tested in transverse direction (10 mm direction). The corresponding failure specimens for E-glass/epoxy composites and E-glass/epoxy nanocomposites with 2.5%

and 5.0% concentration of organoclay were illustrated respectively in Figure 26. It is depicted that in these material systems, the failure of the specimens is dominated by out-of-plane shear failure occurring on the plane orientated around 36 degree with respect to the loading direction. Similar failure behaviors have also been observed in other polymeric composites [7].

4.3 Result and discussion

The pure in-plane shear strengths of E-glass/epoxy nanocomposites versus various organoclay concentrations were summarized in Table 5. It was shown that the E-glass/epoxy nanocomposites demonstrate higher failure stress than the conventional one without any organoclay included. Moreover, the in-plane shear strength increases with the increase of organoclay concentrations up to 5wt %, and thereafter, it become decreasing. The similar tendency was also observed in the transverse compressive strengths which were plotted versus the organoclay concentration in Figure 27. It is noted that,

24

in Figure 27, there are four specimens tested corresponding to each organoclay concentration. The average values of the transverse compressive strengths obtained from different specimens with the same organoclay loading were listed in Table 6. Again, it appears that for E-glass/epoxy nanocomposites, their failure stresses are relatively higher than those of the conventional one without any organoclay included. SEM observations on the failure surfaces of 30 ^o and 45 ^o conventional composites and E-glass/epoxy nanocomposites are shown in Figure 28 and 29. Smooth fiber surfaces and clear matrix grooves are found on the failure surfaces, which indicate that interfacial debonding (cohesive bonding failure) between fibers and the surrounding matrix is the dominant failure mechanism for both material systems. Moreover, the same failure mode was also found in the transverse compressive failure specimens as shown in Figure 30. Thus, for E-glass/epoxy nanocomposites, the corresponding improvement in both in-plane shear strength and transverse compressive strength could be a result of the enhanced interfacial bonding improved by the dispersed organoclay. However, for the nanocomposites with 7.5 % organoclay, the failure stress is on the decline. This reduction could be attributed to the cavities/defects generated possibly during the material processing since it is difficult to fully degas the compound with higher viscosity.

Chapter 5 Summary

Unidirectional composites were tested to failure at various strain rates.

Experimental results reveal that the transverse compressive strength increases with the increment of strain rate for both CFA graphite/epoxy and S2/8552 glass/epoxy composites. Furthermore, the transverse compressive strength could be expressed as a semi-logarithmic function in terms of the normalized strain rate.

The failure was found to initiate at around 25-35∘between the shear failure plane and the loading direction. SEM micrographics on failure surfaces indicate that for CFA graphite/epoxy, the fiber/matrix debonding is the dominant failure mode; however, matrix failure is the main failure mechanism in the S2/8552 glass/epoxy composites.

The fiber/matrix debonding can significantly reduce the transverse compressive of fiber composites. Moreover, for PPG A15037L graphite/epoxy composites, due to the improvement of the interfacial bonding, apparently the corresponding transverse is increased as compared to the CFA graphite/epoxy composites.

According to the Mohr-Coulomb type criterion together with the angle of shear failure plane, the out-of-plane shear strength was calculated. Base on viscoplasticity theory, the shear strain rate was evaluated. It was found that the out-of-plane shear strength was also significantly affected by a shear strain rate. Again, the out-of-plane shear strength was modeled using a semi-logarithmic function in terms of the normalized shear strain rate.

In addition, for E-glass/epoxy composites and nanocomposites, it was found that the corresponding in-plane shear strength and transverse compressive strength was enhanced which could be a result of the modified interfacial bonding improved by the dispersed organoclay.

Reference

[1] Rosen, B. W. 1965 “Mechanics of Composite Strengthening,” Fiber Composites Materials, Seminar at American Society of Metals, pp. 37-75.

[2] Sun, C. T. and Jun, A. W. 1994 “Compressive Strength of Unidirectional Fiber Composites with Matrix Non-linearity,” Composites Science and technology. Vol. 52, No. 4, pp.

577-587.

[3] Sun, C.T. and Tsai, J. 2004 “Dynamic Compressive Strengths of Polymeric Composites,”

International Journal of Solids and Structures, Vol. 41, No. 11, pp. 3211-3224.

[4] Budiansky, B. 1983, “Micromechanics,” Computer and Structures, Vol. 16, No. 1, pp.

3-12.

[5] Budiansky, B. and Fleck, N. A. 1993 “Compressive Failure of Fiber Composites,” Journal of the Mechanics and Physics of Solids, Vol. 41, No. 1, pp. 183-211.

[6] Collings, T. A. 1974 “Transverse compressive behaviour of unidirectional carbon fibre reinforced plastics,” Composites, Vol. 5, No. 3, pp. 108-116.

[7] Bazhenov, S. L. and Kozey, V. V. 1991 “Transversal compression fracture of unidirectional fibre-reinforced plastics,” Journal of Materials Science, Vol. 26, No. 10, pp. 2677-2684.

[8] Newaz, G. M. and Majumdar, B. S. 1993 “Failure modes in transverse metal-matrix composite lamina under compression,” Journal of Materials Science Letter, Vol. 12, No. 8, pp. 551-552.

[9] Lowe, A. 1996 “Transverse compressive testing of T300/914,” Journal of Materials Science, Vol. 31, No. 4, pp. 1005-1011.

[10] Hsiao, H. M., Daniel, I. M. and Cordes, R. D. 1998 “Dynamic Compressive Behavior of Thick Composite Materials,” Experimental Mechanics, Vol. 38, No. 3, pp. 172-180.

[11] Hsiao, H. M., Daniel, I. M. and Cordes, R. D. 1999 “Strain Rate Effects on the Transverse Compressive and Shear Behavior of Unidirectional Composites,” Journal of Composite Materials, Vol. 33, No. 17, pp. 1620-1642.

[12] Vural, M. and Ravichandran, G. 2004 “Transverse Failure in Thick S2-Glass/Epoxy Fiber-reinforced Composites,” Journal of Composite Materials, Vol. 38, No. 7, pp.

609-623.

[13] Guden, M. and Hall, I. W. 1998 “Quasi-static and dynamic compression behaviour of an FP^TM alumina-reinforced aluminium metal matrix composite,” Journal of Materials Science, Vol. 33, No. 13, pp. 3285-3291.

[14] Hall, I. W. and Guden, M. 2000 “High strain rate deformation behavior of a continuous fiber reinforced aluminum metal matrix composite,” Computers and Structures, Vol. 76, No. 1-3, pp. 139-144.

[15] Sih, G. C. and Skudra, A. M. 1985 Handbook of Composites, Vol. 3, Elsevier Science Publishing Company, Inc. New York.

[16] Ninan, L., Tsai, J. and Sun, C. T. 2001 “Use of split Hopkinson pressure bar for testing off-axis composites,” International Journal of Impact Engineering, Vol. 25, No. 3, pp.

291-313

[17] Graff, K. F. 1975 Wave motion in elastic solids, Ohio State University Press.

[18] Chen, J. L. and Sun, C. T. 1993 “A plastic potential function suitable for anisotropic fiber composites,” Journal of Composite Materials, Vol. 27, No. 14, pp. 1379-1390.

[19] Nanocor Inc., Technical data sheet.

[20] Bing, Q. and Sun, C. T. 2004 “A Technique for high strain rate SHPB testing of off-axis carbon fiber composites,” the 11th European Conference on Composite Materials, Rhodes, Greece.

Appendix A

Investigating rate dependent behavior of PPG A15037L graphite/epoxy composites.

In this appendix, the rate sensitivity of the failure strength of PPG material subjected to transverse and off-axis loading will be investigated and the results will be in comparison to the CFA graphite/epoxy material presented early in Chapter 2. In addition, the associated failure mechanism for the material system will be determined using SEM microscopy.

A.1 Specimen Preparation of PPG Graphite/Epoxy Composites

Forty five ply prepreg of unidirectional PPG graphite/epoxy composite (from Ad group, Taiwan) were laid up and the final lay-up is 6.5 mm thick. It is noted that in the composite material system, the fiber is HTA-12K (from Toho Tenax, Japan) and the epoxy type is Bisphenol A, Novalak, and rubber modified epoxy. In addition, the fiber volume fraction is 65.23%. With the appropriate curing process, the laminate had been cured in hot press. The curing process includes two steps, in which the first was heating from room temperature to 90℃ in fifteen minutes then continuing thirty minutes and the second was continuing in

constant temperature for sixty minutes after heating up to 145℃. The pressures were 75.85psi and 142.13psi respectively for the duration of curing process, and it resulted in about 6.0 mm laminate.

The edges of the laminates were cut out using a cutting machine. The off-axis block

specimens had the dimensions of 10.0×6.0×6.0 mm and were cut from the laminates using the precision diamond saw (Isomet^TM 1000 Precision Saw). The fiber orientations considered included 15, 30, 45 60 and 90 degrees with respect to the loading direction. The specimens were lapped on a lapping machine (Secular LM15) with the 14.5 µm abrasive slurry

(EXTEC^® aluminum oxide power) to ensure having smooth, flat and parallel loading surfaces.

In order to reduce the friction on loading surfaces of specimens, both contact surfaces were coated with titanium layer by DC sputter machine (ULVAC Co. Japan). First, the specimens were adhered on the wafer in order to be coated in the sputter. Subsequently, Argon gas flow rate, deposition pressure, deposition rate and bipolar dc power were kept constant at 170 sccm (standard cubic centimeter per minute), 2.6×10^-3Pa, 8.56nm/min and 300W, respectively.

After coating on the surfaces, the other sides of the surfaces were exchanged to adhere on the wafer. According to the same process, both loading surfaces of all specimens were coated with a 1.2μm titanium film.

A.2 Compressive Failure Test A.2.1 Low strain rate test

Uniaxial compression tests were performed on the off-axis specimen using a

servo-hydraulic MTS machine with a self-adjusting device as described in Chapter 2. The experiments were conducted under stroke control at three different displacement rates

servo-hydraulic MTS machine with a self-adjusting device as described in Chapter 2. The experiments were conducted under stroke control at three different displacement rates