Characterization of dynamic damage mechanisms in Palmetto wood as biological inspiration for impact resistant polymer composites

Mechanics of Materials 57 (2013) 97–108

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Characterization of dynamic damage mechanisms in Palmetto wood as biological inspiration for impact resistant polymer composites Sandip Haldar, Hugh A. Bruck ⇑ Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, United States

a r t i c l e

i n f o

Article history: Received 3 August 2012 Received in revised form 13 September 2012 Available online 9 November 2012 Keywords: Multiscale measurement Hierarchically-structured material Failure mechanism Low velocity impact Digital image correlation Damage evolution Split Hopkinson bar

a b s t r a c t Palmetto wood has been previously identified as a potential biological template for inspiring the development of synthetically engineered materials with hierarchical microstructures that exhibit enhanced mechanical behavior. Previously, the multi-scale mechanical behavior has been studied under quasi-static loading in order to understand the relationship between the microstructure of Palmetto wood and its mechanical behavior. In this study, the mechanical behavior of dry Palmetto wood is investigated under dynamic loading using low velocity impact. The experimental results reveal that the macrofiber concentration of the Palmetto wood plays a key role in the dynamic failure mechanisms. Under low velocity impact, the dynamic damage was found to be dominated globally by axial loading induced by bending leading to localized, shear-dominated debonding at the macrofiberporous cellulose matrix interface, as well as compressive loading induced by indentation under the projectile leading to local crushing of the porous cellulose matrix and shear cracking of the macrofibers and matrix. By increasing the macrofiber concentration, it was found that the dominant failure mechanism could be transformed from the former to the latter by increasing the energy absorbed by indentation in order to increase impact resistance. This explains why the macrofiber concentration gradually decreases radially towards the center of the wood stem, since the outer portion of the wood has a high indentation resistance while the inner portion absorbs more energy through bending. A new model was proposed for to better understand the variation in mechanical behavior with macrofiber concentration and loading rate consistent with the evolution of the observed damage mechanisms. It was found that the greatest effect of increasing loading rate and macrofiber concentration was to increase the elastic modulus by 450–600% and the yield stress associated with the pore collapse mechanism by 125–175%. There is also a coupling between the evolution of plastic strain and damage that depends more strongly on macrofiber concentration than loading rate. These two effects combine to cause a significant increase in the density of energy absorption by 75–133% with increasing macrofiber concentration and strain rate. Therefore, the structure of Palmetto wood can be used as a template to guide the development of more impact resistant polymer composites, such as inserting 12 to 20 vol.% pultruded carbon fibers into the foam core of sandwich composite structures. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction Hierarchically-structured materials, like wood, have drawn the attention of researchers by virtue of their spe⇑ Corresponding author. E-mail address: [email protected] (H.A. Bruck). 0167-6636/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.mechmat.2012.10.011

cial structure which leads to unusual mechanical behavior. For example, the low mass density of wood accompanied by high mechanical strength makes these materials an inspiration to be replicated in engineered materials like fiber-reinforced polymer composites. Previously, efforts have been made to use the hierarchical structure of these materials as templates for preparing biologically-inspired

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synthetically-engineered materials (Bruck et al., 2002). To best replicate hierarchical structure in synthetically-engineered materials, an in-depth understanding of the structure-property relationships and failure mechanisms of biological templates is necessary. For example, the microscale mechanical behavior has been found to be important in understanding the macro-scale fracture process in wood (Forsberg et al., 2010). Motivated by the vast use of Palmetto wood as protection for forts in the Revolutionary and Civil wars, this material has been identified as one potential source of bioinspiration to develop hierarchically-structured composite materials with enhanced damage resistance (Gershon et al., 2010). To successfully develop these synthetically engineered composite materials, it is necessary to investigate the mechanical behavior of Palmetto wood under both static and dynamic load conditions to determine the unique structure-property relationship that can be duplicated synthetically. The unique hierarchical structure of the fibers in Palmetto Wood and its relationship to the mechanical behavior of the fibers has recently been characterized at multiple length scales (Gershon et al., 2010). In our earlier effort (Haldar et al., 2011), we also established the methodology to elucidate the failure mechanisms under quasi-static loading at multiple length scales. It was determined that the flexural response of Palmetto wood can be described by a Weibull failure distribution. Damage initiation in the Palmetto wood was found to occur at the macrofiber-matrix interface due to high shear strain. The pore collapse mechanism helps the Palmetto wood to absorb strain energy as well as generate potential sites of failure initiation. In this investigation, the methodology used to investigate the response of the Palmetto wood at multiple length scales is extended to low velocity impact to determine the effects of loading rate on the mechanisms responsible for damage resistance. Due to its heterogeneous structure at multiple length scales, an advanced technique known as Digital Image Correlation (DIC) was chosen for full-field deformation measurements under mechanical loading (Haldar et al., 2011). The basic principle of DIC is to use undeformed and deformed images of a specimen to calculate the displacement and strain experienced by the specimen by tracking changes in a subset of a random pattern on the specimen surface (Sutton et al., 1986). The DIC method has been widely accepted and has grown in its potential to be used in a variety of engineering applications. Details of the DIC technique and its advancement and applications have been previously reviewed (Pan et al., 2009; Hild and Roux, 2006). The DIC technique is inherently independent of length scale, so it has been successfully used from the macroscale to the nanoscale, as well as static and dynamic time scales with the use of appropriate cameras and random patterns (Berfield et al., 2007; Dave et al., 2009; Ya’akobovitz et al., 2010). Recently, Jin et al. (2011) have shown that both the grid method and DIC can be used simultaneously for microscale deformation measurements. Lord et al. (2010) reviewed the experimental techniques for miniaturized testing for strength and strain measurement, and detailed the evolu-

tion and strengths of the DIC method. DIC has been found to be particularly valuable when capturing spatially inhomogeneous deformation fields. This potential has been applied to several material systems, including biological tissues (Zhang and Arola, 2004; Krehbiel et al., 2010), particulate composite (Gonzalez and Knauss, 1998; Rjafiallah and Guessasma, 2011), concrete (Choi and Shah, 1997), polymeric foam (Wang and Cuitiño, 2002), binary aluminum alloy (Tong, 1997), closed-cell aluminum alloy foam (Bastawros et al., 2000), porous solid (Zhang et al., 2011), glassy polymer (Heinz and Wiggins, 2010), functionally graded materials (Rousseau et al., 2010; Abanto-Bueno and Lambros, 2002), composite laminates (Lee et al., 2010) etc. Recently, Pan et al. (2011) were able to use DIC to measure the distribution of thermal strains at very high temperatures (i.e., above 1000 °C). DIC has proven its potential as a rigorous optical measurement technique not only for measurement of spatially inhomogeneous deformation fields at multiple length scales, but for also characterizing related properties like coefficient of thermal expansion (Bing et al., 2009), frictional properties (Kartal et al., 2010), cohesive fracture properties (Shen and Paulino, 2010), crack-resistance curve of polymer-matrix composite (Catalanotti et al., 2010), constitutive model under buckling (Hild et al., 2011) etc. Daly et al. (2009) used DIC to develop strain map in Nitinol under large shear dominated deformation. They captured the evolution of full field strain associated with the phase transformation from austenite to martensite in Nitinol. Although DIC is typically used to characterize strain fields under static loading conditions, it has been successfully employed for characterizing dynamic phenomena, like dynamic fracture (Rousseau et al., 2010; Abanto-Bueno and Lambros, 2002; Lee et al., 2010), dynamic buckling (Featherston et al., 2010) and high strain rate effects in unidirectional composites (Lee et al., 2010; Koerber et al., 2010). Recently, Collins and Kasal (2010) performed dynamic analysis of light frame wood using DIC to validate an analytical model they developed. For the present application, we employ DIC at multiple length scales using the naturally random features associated with the texture of Palmetto wood while it is subjected to dynamic loading from low velocity impact. This enabled characterization of both the global evolution of strain associated with the shape of the specimen, as well as the localized damage. In this investigation, we report the use of DIC to understand the dependence of the mechanical behavior of the Palmetto wood on loading rate in order to replicate its structure-property relationships in synthetically-engineered composite materials. The evolution of damage under low velocity three-point bend impact experiments are compared to quasi-static three-point bend results. The failure mechanism in the Palmetto wood with different macrofiber volume fraction is elucidated under low velocity impact A model is presented for interpreting the effects of loading rate on the global stress–strain response by partitioning the damage due to the microstructural mechanisms into (a) the reduction in elastic modulus due to fiber-debonding and shear cracking in the porous matrix and (b) the plastic deformation associate with pore collapse in the matrix.

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2. Experimental method 2.1. Specimens The Palmetto wood specimen of approximately 10 cm (length)  16 mm (width)  16 mm (height) with fibers aligned perpendicular to the direction of impact loading and was prepared from a harvested Palmetto tree as shown in Fig. 1(a). The specimens weigh around 8 g. It was seen that the Palmetto wood has a graded distribution of macrofiber of 12 vol% at the inner core and 20 vol% outer sides. Specimens prepared from different radial locations have been tested to study the effect of the macrofiber concentration. Further detail of the microstructure of Palmetto wood can be obtained in previous work (Gershon et al., 2010).

2.2. Low velocity impact experiments A 12.6 gm cylindrical projectile with a 50.26 mm2 cross-sectional area is used to centrally impact a simply-supported specimen (span 74 mm) in order to induce a dynamic three-point bending condition at low impact velocities (30 m/s). To measure the total load applied to the specimen, 1000 lb load cells (DLC 101-k, Omega) are attached to the supports of the specimen. The specimen is illuminated by two Vision Research Northstar lights (250 W each), and a high-speed digital camera (Phantom v12) is used to capture instantaneous images of specimen (top view) during the dynamic deformation. The projectile is launched through a barrel using pressurized air, and a laser-trigger mounted on the barrel is used to synchronize an oscilloscope and high-speed digital camera in order to capture output voltage from the load-cells and images from the camera, respectively. The circuitry for the experiment and the setup is shown in Figs. 1(b) and (c). To determine the response of the specimen, the projectile and the specimen were assumed to be in dynamic equilibrium. This assumption is similar to the ‘quasistatic’ assumption previously employed in impact testing of composite sandwich structure that exhibit similar mechanical behavior to Palmetto wood (Daniel et al., 2012). Furthermore, the approach of Ravichandran and Subhash (1994) for analyzing the critical strain rate that establishes equilibrium loading conditions yields a value of 1000/s for these types of materials and loading conditions. This critical strain rate is an order of magnitude greater than the strain rate of 100/s that determined in the present work for low velocity impact. Direct verification of the equilibrium condition was obtained using a 1.2 m long, 15.9 mm diameter instrumented steel Hopkinson bar to induce loading in the three point bend fixture (1 Bar/3PB) after impacting the Hopkinson bar with an impedance matched 0.3 meter striker bar (Jiang and Vecchio, 2009). The load obtained from the load cell was then compared with the response from the incident bar to verify equilibrium. It is important to note that for the high speed camera there is a trade off between the magnification level and the frame per second (fps) when capturing images that

99

gives rise to a limitation in applying the multiscale measurement methodology established earlier (Haldar et al., 2011) to dynamic deformation measurements. Therefore, it was only possible to achieve 10X magnification and not the 20X magnification that was used for static deformation measurements. Specimens were prepared by first cutting along the axis of a freshly harvested Palmetto tree stem at cross-sectional locations with different macrofiber concentrations, and then polishing to achieve optimal optical illumination while retaining the random features associated with the texture of the wood. 2.3. Deformation measurement The deformation of the specimens was measured using digital image correlation (DIC) on real time images captured during three-point bending under impact loading. In general, the natural texture of the Palmetto wood was determined to contain random features sufficient for DIC analysis, therefore no speckle pattern was applied to the specimen surface. However, for some specimens the texture was not sufficiently random, so patterns were applied with spray paint to enhance their suitability for DIC analysis. The commercially available software Vic-2D from Correlation Solutions Inc. (Columbia, SC) was used for DIC analysis. Based on the surface texture and features, DIC parameters were optimally chosen to obtain accurate deformation fields. In addition to the DIC analysis performed on the images captured in real time, the projectile motion was tracked using the Phantom software to determine the variation of projectile displacement with time in order to obtain projectile velocity. 3. Experimental results 3.1. Flexural stress–strain response Low velocity impact tests are performed on the palmetto wood specimens to characterize the dynamic behavior with associated strain rates of up to 100 s1. The strain rate was determined by fitting a polynomial to the flexural strain measured at the outer fibers of the specimen using DIC as a function of time, and then differentiating. From the pervious multi-scale characterization work (Gershon et al., 2010), it was found that Palmetto wood has a graded distribution of macrofiber over the cross-section. To understand the effect of macrofiber volume fraction, the specimens were prepared from two different radial positions of a harvested Palmetto tree, as indicated in Fig. 1(a), and the specimen dimensions were taken large enough compared to the characteristic dimension of constituents (macrofiber diameter). The impact velocity was determined to be approximately 30 m/s, similar to that experienced in crash events for vehicles. Verification of the equilibrium condition for the low velocity impact tests obtained using the instrumented Hopkinson bar in the 1 Bar/3PB configuration is shown in Fig. 2. As can be seen from the figure, the load history obtained from the strain gauge response of the instrumented bar correlated well with the load cell measurements validating the equilibrium assumption.

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12 vol. % MF 20 vol. % MF 100 (a)

(b)

(c) Fig. 1. (a) Specimens prepared from several radial location of Palmetto wood stem. The specimen prepared from outer region had a higher macrofiber (MF) volume fraction of 20%, whereas that from the inner portion had a lower MF volume fraction of 12%, (b) circuit of the low velocity impact set-up and (c) experimental set-up for the low velocity impact test.

The flexural stress–strain response of Palmetto wood under low velocity impact is depicted in Fig. 3 and compared to that under quasi-static bending. The flexural stress, flexural strain and strain energy are calculated using the classical relations for three point flexural test as:

rf ¼

3PL 2

2bh

;

ef ¼

6df h L2

ð1Þ

where P is the applied load, L is the support span, b is specimen thickness, h is specimen height, and df is the deflection at the central load.

In order to obtain the flexural strain from low velocity impact tests at high temporal resolution, the relative displacement of the projectile over time was evaluated using the total force measured from the load cells. To obtain the total displacement, the acceleration obtained through the equation of motion(F = mproja) was integrated assuming equilibrium between the projectile and specimen, which was found to be reasonable at the time scales associated with the low velocity impact event for these specimens. It was also observed that the bullet induced significant local indentation as well as bending deformation which

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Fig. 2. Comparison of the load obtained from the incident bar and load cell at the fixture in the modified split Hokinson bar (SHPB) test in one par three point bend configuration.

50 Quasi-static 12 vol. % MF (experimental)

45

Quasi-static 12 vol. % MF (model fit) Quasi-static 20 vol. % MF (experimental)

40

Flexural Stress (MPa)

Quasi-static 20 vol. % MF (model fit)

35

Impact 12 vol. % MF (experimental) Impact 12 vol. % MF (model fit)

30

Impact 20 vol. % MF (experimental) Impact 20 vol. % MF (model fit)

25 20 15 10 5 0 0

0.02

0.04

0.06 0.08 0.1 Flexural Strain

0.12

0.14

0.16

Fig. 3. Flexural response of 12 and 20 vol.% macrofiber (MF) Palmetto wood specimens under low velocity (approximately 30 m/s) impact and quasi-static three-point bending. Fits of a Weibull model for the stress–strain response are also shown.

varies with macrofiber concentration. To decouple the indentation effect, indentation tests were performed on the similar kind of Palmetto wood by constraining the specimen to prevent bending. Results for low velocity impact and quasi-static loading can be seen in Fig. 4. The flexural deflection of the specimen, df, was then found by subtracting the local indentation depth, di, from the total bullet displacement, dt (i.e., df = dt  di) at a given load. The relative displacement that takes into account the motion of the specimen supports could then be determined by calibrating the total displacement curves at discrete points in time with the DIC deformation data obtained transverse to the specimen at substantially lower (1/100th) temporal resolution. This relative displacement could then be used to determine the flexural strain from Eq. (1). The flexural strain was also directly measured with lower time resolution from the high-speed images using the DIC displacement fields. An example can be seen in Fig. 5. The vertical displacement in the Palmetto specimen

was captured at a strain level of around 2.7% as shown in Fig. 5a. The vertical displacement and the cubic fit to the deflection are shown in Fig. 5(b). It was determined that the bending of the palmetto wood under impact at the macroscale conforms to that of a homogeneous isotropic material, as was found to be the case under quasi-static loading as well (Haldar et al., 2011). The flexural strain could then be obtained from the curvature, and was determined to be approximately 0.027. This value was within 1000 microstrain of that determined both from DIC strain field measurements at the outer region of the specimen, as well as from the load-cell data. Since the strain was found to be consistent within the accuracy of the DIC technique, it provided additional confidence in the accuracy of the method used to measure flexural strain from low velocity impact using the load cell data at high temporal resolution. In addition to using the indentation tests to enhance the accuracy for obtaining flexural strain, it was also possible

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Fig. 4. Comparison of low velocity impact and quasi-static indentation response of Palmetto wood specimens with different macrofiber (MF) volume fraction.

Fig. 5. (a) Transverse (vertical) displacement obtained from DIC of the Palmetto specimen under low velocity impact at a flexural strain level 0.027, and (b) displacements obtained along the dashed line and corresponding cubic fit. The strain determined using the curvature from the cubic fit also corresponds to a strain value of approximately 0.027.

to compare the energies associated with indentation versus bending. For the 20 vol.% macrofiber concentration, the dynamic indentation energy is approximately 0.8 J, while the total energy absorbed by bending was 5 J, which is the remainder of the projectile energy. Thus, indentation absorbs about 14% of the projectile energy. For the 12 vol.% macrofiber concentration, only 0.35 J was absorbed while the total energy absorbed by bending was still 5 J. Thus, the indentation energy was only 7 percent of the total 5.35 J, which was insufficient to stop the projectile. Thus, the indentation energy was only half of that of the 20 vol.% macrofibers, which indicates that the macrofiber concentration can also play a critical role in the impact

resistance of Palmetto wood through the indentation response.In order to assess the effects of strain rate and macrofiber concentration on the mechanical behavior of the Palmetto Wood, a Weibull-based damage model of the stress–strain response for fiber-reinforced polymer composites was used (Gershon et al., 2010; Haldar et al., 2011). The Weibull model can be seen in Eq. (2), and consists of the parameters e0, b and the elastic modulus E which were determined by fitting the stress–strain curves, as shown in Fig. 3.

"   # e b r ¼ Ee exp 

e0

ð2Þ

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Table 1 The modulus, E, and Weibull parameters (e0, b)obtained by fitting the flexural stress–strain curves for the Palmetto Wood specimens. The modulus, E, and damage initiation strain (ed) obtained from the new damage model that includes plasticity in Eq. (4) are also shown for comparison. Loading condition/vol.% MF

Quasi-static/12 Quasi-static/20 Impact/12 Impact/20

Weibull model

New damage model with plasticity

E(MPa)

e0

b

E(MPa)

ey

ed

Dlim

A

B

p

600 950 2100 3000

0.05 0.058 0.032 0.038

1.6 1.6 1.1 1.6

550 975 2000 4100

0.015 0.016 0.009 0.007

0.046 0.052 0.038 0.036

0.9 0.9 0.9 0.9

13 13 13 13

6 6 9 9

0.4 0.4 0.4 0.4

The parameters of Weibull fit for dynamic and quasistatic response of the specimens with 20 vol.% and 12 vol.% macrofiber concentrations are shown in Table 1. From the Weibull fit, it can be seen that the impact of dynamic loading was to increase the modulus by approximately 200% independent of macrofiber concentration. The critical strain, eo, was also found to be reduced by 30–35% due to dynamic loading, while the evolution of damage described by b did not show substantial differences except for impact on the 12 vol.% macrofiber specimen. Thus, the Weibull model would indicate that the greatest impact of dynamic loading is to increase stiffness and decrease the strain at which damage begins to evolve. Since the stiffness increases more rapidly than the strain decreases, the end result is a stronger material response. These results are consistent with the fact that quasi-static bending is a slow process (strain rates of 104/s), which gives the macrofiber and the porous cellulose matrix more time to elastically deform in order to minimize local strain energy resulting in lower stiffness and a higher strain level before damage occurs. In contrast, the time scales associated with low velocity impact are orders of magnitude shorter (strain rates of 100/s), so there is not enough time to minimize the local elastic energy state leading to higher stiffness and a lower strain level for damage initiation.

From observation of the failed specimens, it was evident that there was a local crushing due to indentation and a global fiber debonding due to bending that are competing damage mechanisms (Fig. 6). From the pure indentation response reported in Fig. 4, it was noted that the dynamic indentation load is significantly higher. Also, the energy absorbed by the local indentation process is significantly larger (almost 200%) under dynamic loading, which significantly decreases the energy available for global bending. The variation in energy during indentation was found to depend on the macrofiber and porous cellulose distribution. Comparing the flexural stress–strain curves with the pure indentation loading results, specimens with higher macrofiber volume fraction (20 vol.%) were found to have a much lower indentation resistance relative to flexure, which increases the probability of indentation failure. On the other hand, specimens with lower (12 vol.%) macrofiber volume fraction had much higher indentation resistance relative to flexure, which increased their probability of flexural failure. In the latter case, most of the impact energy would contribute to global bending of the specimen leading to global damage in the specimen, which is consistent with the observation depicted in Fig. 6.

Inner position: macrofiber 12% by vol

Outer most position: macrofiber 20% by vol

Indentation of the projectile

3.2. Failure modes under dynamic loading

16 mm Failure by debonding at the macrofiber-matrix interface

Fig. 6. Images of Palmetto specimens after failure. The failure mode is transformed from the macrofiber-interface debonding leading to rupture of the specimen (right side) to the local indentation by projectile (left side) that absorbs all the kinetic energy of the projectile. The transformation of the failure mode is attributed to the macrofiber concentration in the Palmetto wood.

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Fig. 7. Images of deformed Palmetto wood under low velocity impact at a magnification of 10X. The natural texture of the wood was determined to be sufficient for DIC analysis. The local indentation failure consists of compressive axial strain associated with crushing of the porous cellulose matrix followed by higher levels of shear strain associated with shear cracking of the macrofibers and matrix.

The volume fraction macrofiber was previously reported to gradually decrease along the radial direction towards the center of the wood stem from the high of 20 vol.% to a low of 12 vol.% (Gershon et al., 2010). As can be seen from the reported dynamic mechanical behavior of specimens with different macrofiber concentration, the macrofiber distribution will be the key parameter in controlling the impact resistance of the bulk material. By increasing the macrofiber concentration, the dominant failure mechanism can be transformed from macrofiber debonding from bending to pore collapse from indentation. This explains why the macrofiber concentration gradually decreases radially towards the center of the wood stem, since the outer portion of the wood has higher indentation resistance while the inner portion is more susceptible to bending failure, which increases the energy absorbed by both mechanisms in order to increase impact resistance. As evaluated in the multiscale characterization of Palmetto wood (Haldar et al., 2011), the strain is highly inhomogeneous at lower length scales due to the difference of mechanical properties of the macrofiber and porous cellular matrix. Hence, the energy absorption is spatially inhomogeneous and leads to a conclusion that local stress– strain curve cannot represent the global behavior in terms of strain energy absorption due to the localization of the energy absorption mechanisms. The strain fields at the initiation of failure in the Palmetto wood specimen under dynamic load is evaluated

by DIC of the images captured at higher magnification (around 10X) at the impact zone, as depicted in Fig. 7. The subset size and strain filter used for this correlation to obtain the deformation field were 51  51 pixel2 and 15 pixels, respectively. The failure initiation is found to occur under high shear and compressive axial strain. As revealed by the DIC, the damage initiation site occurs due to high shear, as well as transverse compressive load. However, the DIC shear strain is much higher (7%) than the compressive strains (4%) after failure has initiated, which indicates a lower localized shear resistance relative to compression after pore collapse due to shear failure of the macrofibers from indentation loading. Thus, shear failure due to macrofiber-matrix debonding limits the level of compressive failure due to pore collapse under indentation loading after failure, which is in contrast to the previously observed accumulation of large compressive strains preceding the initiation of shear failure (Haldar et al., 2011).

4. Damage modeling of Palmetto wood The macroscale damage evolution of the Palmetto wood has been quantified under low velocity impact and compared to that under quasi-static bending (Haldar et al., 2011). To obtain the damage evolution, the same specimen was subjected to several impacts at 30 m/s until it failed completely. The damage is defined under the assumption

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pffiffiffiffiffiffiffiffiffiffi of conservation of elastic energy by D ¼ 1  E=E0 (Chow and Lu, 1989), where Eo is the original modulus and E is the residual modulus determined through static measurements of the recovered specimens at the total strain that has been accumulated after each impact. The following expression for the evolution of damage with total flexural strain based on strain energy conservation was then fit to the experimental measurements,

D ¼ Dlim ½1  expðAðe  ed ÞÞ

strain at which damage initiates, and A is an acceleration factor that describes the evolution of damage with strain. Results from fitting the curves to the experimentally determined damage can be seen in Fig. 8(a). Using Eq. (3), it was possible to study the effect of the macrofiber volume fraction and loading rate on the damage accumulation. The constants that were determined from Fig. 8a can be seen in Table 1. The acceleration factor and limiting amount of damage did not appear to be affected substantially by loading rate or macrofiber concentration. However, the strain at which damage begins to accumulate did decrease by 15–30%, which was similar to what was observed with the Weibull model fit.

ð3Þ

In this expression, Dlim represents the limiting amount of damage that can occur, e is the total accumulated strain that the damaged specimen was subjected to, ed is the

(c)

0.7

Quasistatic (12 vol. %) Quasi-static (20 vol. %) Impact (12 vol. %) Impact (20 vol. %)

0.6 0.5

50 Quasi-static 12 vol. % MF (experimental)

45

Flexural Stress (MPa)

(a)

D

0.4 0.3 0.2 0.1

Quasi-static 12 vol. % MF (model fit) Quasi-static 20 vol. % MF (experimental)

40

Quasi-static 20 vol. % MF (model fit)

35

Impact 12 vol. % MF (experimental) Impact 12 vol. % MF (model fit)

30

Impact 20 vol. % MF (experimental) Impact 20 vol. % MF (model fit)

25 20 15 10 5 0

0 0

0.05

0.1

0.15

0

0.02

0.04

(b)

(d) 0.1

Quasi-static (12 vol. %) Quasi-static (20 vol. %) Impact (12 vol. %) Impact (20 vol. %)

0.08 0.07 0.06

Plastic Flexural Strain

Plastic Flexural Strain

0.08

0.1

0.12

0.14

0.16

0.1 0.09

0.09

0.05 0.04 0.03

0.08 0.07 0.06 0.05 0.04 0.03

0.02

0.02

0.01

0.01

0

0.06

Total Flexural Strain

Total Flexural Strain

0

0.02

0.04

0.06

0.08

Quasi-static (12 vol. %) Quasi-static (20 vol. %) Impact (12 vol. %) Impact (20 vol. %)

0

0.1

0

0.2

0.4

Total Flexural Strain

Elastic Flexural Strain

(e)

0.035

0.6

0.8

1

D Quasi-static (12 vol. % MF) Quasi-static (20 vol. % MF) Impact (12 vol. % MF) Impact (20 vol. % MF)

0.03 0.025 0.02 0.015 0.01 0.005 0

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Total Flexural Strain Fig. 8. (a) Damage evolution with total flexural strain, (b) evolution of plastic flexural strain with total flexural strain, (c) Flexural stress–strain curves with new model fit, (d) evolution of plastic flexural strain with damage, and (e) evolution of elastic flexural strain with total flexural strain for Palmetto wood of 12 and 20 vol.% macrofibers (MF) under quasi-static and low velocity impact three-point bending.

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Fig. 9. Impact-induced damage in Palmetto wood due to debonding at the macrofiber-porous cellulose matrix interface for (a) 12 vol.% and (b) 20 vol.% macrofiber concentrations. The specimen with 20 vol.% macrofibers absorbs the projectile and has lesser flexural deformation (3.8% flexural strain) compared to 12 vol.% macrofiber (11% flrexural strain). Also, the specimen with a lower macrofiber concentration (a) has a significantly higher number of damage sites than the later (b).

In addition to the damage that accumulates with flexural strain, the mechanism of plasticity due to pore collapse must also be accounted for. Therefore, the plastic flexural strain, ep, was related to the total flexural strain through a form of the conventional power law hardening relationship as follows,



ep ¼ e 1  expðBðe  ey Þp Þ



ð4Þ

where ey is the yield strain and p and B are related to the power law hardening exponent and coefficient, respectively. The plastic strain could be determined experimentally by measuring the permanently deformed shape of the specimen. The evolution of macroscopic plastic strain with respect to the total strain could then be determined and Eq. (4) fit to the data. The resulting fits can be seen in Fig. 8(b), and the constants determined from the fit can be seen in Table 1. From the constants that were determined, it can be seen that the hardening exponent does not appear to vary with macrofiber concentration and loading rate. Instead, the hardening coefficient appears to increase by approximately 50% as the loading rate increases. The yield strain also substantially decreases by 40–50% as the loading rate increase, but does not vary as substantially with macrofiber concentration. This would tend to be consistent with the previous comment on the time required for the local strain energy level to reach a critical level that results in a strain rate dependency for the pore collapse mechanism responsible for plasticity. In order to better understand the observed dependency of the plastic deformation on strain rate, Eqs. (3) and (4) were combined to determine the constitutive response of the Palmetto wood as follows,

r ¼ E0 ð1  DÞ2 ðe  ep Þ

ð5Þ

The resulting fits to the experimental data can be seen in Fig. 8(c). The undamaged moduli that were determined from these fits can be seen in Table 1. It was previously determined that for quasi-static loading these values increased with macrofiber concentration according to the

rule-of-mixtures. As the loading rate increases, these values increase substantially by approximately 300%, a higher increase than was observed with the Weibull model fit. The sensitivity of these values to loading rate is similar to that observed in polymeric materials. Given the fibrous nature of Palmetto wood, it is natural to assume that the dependency is related to the viscoelastic behavior of the material. Thus, the moduli could be associated with the rubbery and glassy response of the Palmetto wood at low and high loading rates respectively. The increasing stiffness of the Palmetto wood with loading rate also provides insight into the variation of the plastic deformation response of the Palmetto wood with loading rate. As the Palmetto wood stiffens, the associated stress increases substantially with decreasing strain. Thus, the critical loads at which plastic strain initiates occur at much lower strain levels. Using the yield strain and the elastic modulus, the corresponding yield stress can be determined. It can be seen that the yield stress will increase from 8.3 MPa to 18.0 MPa, an increase of 116%, as the loading rate increases for 12 vol.% macrofibers and from 15.6 MPa to 28.7 MPa, an increase of 84%, as the loading rate increases for 20 vol.% macrofibers. Thus, pore collapse occurs at approximately 100% higher stress levels with increasing loading rate, and approximately 70% higher stress levels with increasing macrofiber concentration, which is reasonable given the nature of this mechanism. Thus, the observed plastic deformation response of Palmetto wood is consistent with the plastic deformation mechanism. In order to understand the comparative evolution of plastic deformation and damage in Palmetto wood, the damage was plotted against the plastic flexural strain in Fig. 8(d). It can be seen that the relationship between plastic strain and damage accumulation appears to be appears to be independent of macrofiber concentration and loading rate. Given that previous investigations using DIC identified that pore collapse at the macrofiber-porous cellulose matrix interface precedes macrofiber debonding, these results appear consistent with the previously identified relationship between these failure mechanisms (Haldar et al.,

S. Haldar, H.A. Bruck / Mechanics of Materials 57 (2013) 97–108

2011). Visible evidence of the differences in flexural deformations and the corresponding level of damage can be seen in Fig. 9. Note that the damage due to fiber debonding is clearly evident on the rear and left side of the specimen with lower macrofiber concentration in Fig. 9(a). It was also possible to use the new damage model to track the evolution of the elastic flexural strain with total flexural strain. The results can be seen in Fig. 8(e). It is clear from these results that the strains tend to increase linearly until reaching a plateau value of around 2.5% for quasi-static loading and around 1% for impact loading independent of macrofiber concentration, a decrease of 60% with increased loading rate. Thus, it would appear that there is a critical level of elastic strain that can be sustained before addition deformation requires the accumulation of plasticity and damage, and is consistent with the idea that so there is not enough time to minimize the local elastic energy state as the loading rate increases which reduces the global critical level. The resulting relationship between stress and strain in Eq. (5) can also be used to compare the resulting energy absorption of Palmetto wood. It can be seen that the density of energy absorption increases with strain rate from 0.75 to 1.75 J/m3 for 12 vol.% macrofibers and from 1.55 to 2.68 J/m3 for 20 vol.% macrofibers. Thus, nearly doubling the volume fraction of macrofibers nearly doubles the energy absorption, while increasing the loading from quasi-static to low velocity impact increases the energy absorption by approximately 75 to 133%.

5. Significance of observations on development of impact resistant polymer composites As previously demonstrated, the insight into the structure-property relationship of Palmetto wood can be used as biological inspiration for the development of polymer composites (Gershon et al., 2010). The results in this study expand the insight into the development of more impact resistant polymer composites, especially for sandwich composite structures. It can be seen that inserting as little as 12 to 20 vol.% macrofibers into a foam core may significantly enhance the stiffness, strength, and energy absorption. The interaction between the macrofibers and the porous cellulose matrix can also significantly increase energy absorption as the loading rate increases. For impact resistant polymer composites, it is anticipated that the characteristics of the macrofiber will also contribute to the performance enhancement. Pultruded carbon fibers are very similar in structure to the macrofibers in Palmetto wood. There mechanical properties are also significantly better. Thus, it is anticipated that reinforcing standard foams with 12 to 20 vol.% pultruded carbon fibers will produce similar benefits to those observed with Palmetto wood. Furthermore, interfacial adhesion will also play a critical role. Thus, the chemistry of the foam should be compatible with the pultruded carbon fibers, or a compatibilizer with adhesive should be used at the interface of the pultruded carbon fiber with the foam matrix.

107

6. Conclusions Low velocity impact experiments were performed to evaluate the dynamic behavior of the dry Palmetto wood for comparison with previous quasi-static three-point bending measurements. Under low velocity impact, the dynamic damage was found to be dominated globally by axial loading induced by bending leading to localized, shear-dominated debonding at the macrofiber-porous cellulose matrix interface, as well as compressive loading induced by indentation under the projectile leading to local crushing of the porous cellulose matrix. Through the changes in macrofiber concentration, it was also determined that the dynamic failure mode of the Palmetto wood can be transformed from the shear dominated debonding by axial loading to the crushing of the porous cellulose matrix and shear cracking of the macrofibers and matrix by local indentation. The relative energy absorption by indentation increased from 7% to 14% with the increase in macrofiber concentration from 12 vol.% to 20 vol.%. This explains why the macrofiber concentration gradually decreases radially towards the center of the wood stem, since the outer portion of the wood has a high indentation resistance while the inner portion absorbs more energy through bending. In order to better understand the influence of macrofiber concentration and loading rate on the mechanical behavior of Palmetto wood, two models of the stress– strain response were fit to the experimental data. The first was a model based on Weibull statistics developed for fiber-reinforced polymer composites. From the Weibull fit, it was determined that increasing the loading rate increased the modulus by approximately 200% independent of macrofiber concentration. The critical strain, eo, was also found to be reduced by 30–35% due to dynamic loading, while the evolution of damage described by b did not show substantial differences. Since the Weibull model combined effects of all the damage mechanisms, a new model was developed that separated the evolution of damage from plastic deformation. It was determined that the yield stress associated with the previously identified pore collapse mechanism increases by approximately 100% as the loading rate increased, and by approximately 70% as the macrofiber concentration increased. The stiffness also increases by approximately 300%, which is higher than what was observed with the Weibull model fit. In contrast, the damage evolution with plastic deformation exhibited a stronger dependence on macrofiber concentration than strain rate, consistent with the pore collapse mechanism at the macrofiber-porous cellulose matrix interface preceding macrofiber debonding mechanism that was observed using DIC. It was also possible to use the new damage model to track the evolution of the elastic flexural strain with total flexural strain, which indicated there is a critical level of elastic strain that can be sustained before addition deformation requires the accumulation of plasticity and damage due to pore collapse and macrofiber debonding. The combined behavior of the pore collapse and macrofiber debonding mechanisms resulted in an increase of energy absorption

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that nearly doubled with doubling the macrofiber concentration and increased by 75–133% as the loading rate increased from quasi-static to low velocity impact. The results from this study can provide guidance to previous efforts in using Palmetto wood as biological inspiration for the development of polymer composites. In particular, it indicates that macrofiber reinforcement of foam cores can lead to more impact resistant sandwich composite structures using as little as 12 to 20 vol.% macrofiber reinforcement. Acknowledgement The work was #N000140910640.

supported

through

ONR

grant

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