Fiber texture and mechanical graded structure of bamboo

PIh S 1359-8368(96)00020-0

ELSEVIER

Composites Part B 28B (1997) 13-20 © 1997 Elsevier Science Limited Printed in Great Britain. All rights reserved 1359-8368/97/$17.00

Fiber t e x t u r e and mechanical graded structure of bamboo

Shigeyasu Amada, Yoshinobu Ichikawa, Tamotsu Munekata, Yukito Nagase and Hiroyuki Shimizu Department of Mechanical Engineering, Gunma University, 1-5- 1, Tenjin, Kiryu, Gunma 376, Japan (Received 18 December 1995; revised 29 March 1996) Among plants, bamboo has an unique structure which resembles that of a unidirectional, fiber-reinforced composite with many nodes along its length. Furthermore, bamboo's growth rate is very fast, producing an adult tree in only one year. This paper demonstrates that bamboo has a functionally graded and hierarchical structure. Bamboo's diameter, thickness and internodal length have a macroscopically graded structure while the fiber distribution exhibits a microscopically graded architecture, which lead to smart properties of bamboo. The reinforcing fibers are oriented along the bamboo's culm (trunk), whereas in the nodes the fibers become entangled in a complicated manner to produce nodes with isotropic properties that provide additional reinforcement for the culm. ~: 1997 Elsevier Science Limited. All rights reserved (Keywords: bamboo; functionally graded structure; composite; fiber; mechanical properties; hierarchical structure)

l

INTRODUCTION

Plants on earth have developed their structures to adapt to various environments over a long period of time. Bamboo may be a typical example of plants with highly developed architectures. Figure l(a) shows the cross-section of bamboo's culm (trunk). First, it should be noted that there are no tree rings in the culm's cross-section. Furthermore, distributed solid dots are observed in the picture. These are called vascular bundles which, together with the bundle sheaths that surround them, play the same role as fibers in composite materials. It is noted that these fibers (both the vascular bundles and the sheaths) are distributed densely in the outer region and sparsely in the inner region. Figure 1 (b) shows the longitudinal section of bamboo's culm. It resembles a hollow cylinder with many nodes (circular discs inserted into the hollow cylinder). The function of these nodes is the prevention of buckling due to bending. Further, they may also play the role of axial crack arresters. In comparison with other types of wood, bamboo has an unique structure. So, we can model the bamboo by a fiber-reinforced, composite cylinder with a hollow cross section. The mechanics of wood have been studied and summarized by Bodig and Jayne 1, Gibson and Ashby 2 and Mattheck 3 using different approaches. However, only a few studies have been conducted on the bamboo, such as those by Oda 4, Chuma 5, Jain 6, Li et al. 7, Nogata and Takahashi 8 and Amada 9.

This paper outlines the structure and mechanical properties of bamboo. The bamboo used in the experimental investigation is a two-year old 'Mouso' bamboo (Phyllostachys edulis Riv.), 16 ~ 20m in height and a maximum diameter of 12 ~ 13cm. The characteristic shape of the bamboo's culm and the nodes is illustrated pictorially and the fiber distribution in the cross-section of the bamboo's culm is measured by image analysis. The fiber texture in the culm and in the nodes is also discussed. Applying a mixture principle to bamboo, the tensile strength and other properties of the fiber and the matrix are obtained. Finally, it is noted that bamboo has a smart and hierarchical structure.

2

MACROSCOPIC G R A D E D S T R U C T U R E OF BAMBOO'S G E O M E T R Y

We measured the internodal length L, the outer diameter D and the thickness t of the culm based on the coordinate system shown in Figure 2. The obtained results are shown in Figure 3. L attains a maximum value at the midpoint of the culm's total length, the reason for which is not fully understood yet. D and t decrease monotonically with respect to the height h measured from the ground. The outer diameter D is approximately inversely proportional to h, i.e.

D ~ 1/h

(1)

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C o o r d i n a t e system a n d n o t a t i o n s

The areal moment of inertia Iz is calculated using data in Figure 3 and shown in Figure 4. Iz has a maximum value at the root and decreases with height. This distribution corresponds to the bending moment distribution due to wind loads, and produces a nearly constant axial surface stress along the bamboo's culm, shown in Figure 5, which was obtained using beam theory calculations based on the assumptions of uniform wind load. In this figure, Zm denotes the non-dimensional section modulus of the bamboo's culm and the non-dimensional axial surface stress ~b is almost constant along the entire length except for the top region. This indicates a smart structure, which bamboo .has developed through its evolution. A quantity LID is given in Figure 4 and its distribution is roughly inversely proportional to Iz. LID is related to the flexibility of the bamboo's culm, and its distribution indicates that the bending resistance decreases with decreasing distance from the top. This may be a feature that prevents breakage due to a strong wind load.

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MICROSCOPIC GRADED STRUCTURE OF FIBER DISTRIBUTION

As mentioned in the introduction, the bamboo's culm resembles a fiber-reinforced composite. Although the fiber and the matrix properties vary with height, they are assumed to be approximately constant. It is also assumed that they are made from different materials. We measured the volume fraction of fibers by image analysis. A cross-section of the culm is imaged by a CCD video camera and the data of its image is transformed into a binary-processed image. The volume fraction of fibers is measured by counting the dots that represent the fibers (see Figure l (a)). The measured volume fraction of fibers is given in Figure 6 as a function of non-dimensional radius for the different culm numbers. Its value is about 15 ~ 20% at the inner surface and 60 ~ 65% at the outer surface. This fiber distribution conforms to the stress distribution generated by a bending moment. The bamboo, therefore, belongs to the class of materials known as functionally graded materials (FGMs), originally developed for reducing thermal stresses through spatially variable microstructures ~°. It is a naturally-occurring FGM.

The volume fraction of fibers along the bamboo's entire length is shown in Figure 7. It increases linearly with height. As the top of the bamboo is approached, the diameter and thickness decrease, which considerably deteriorates the bending strength. The larger fiber volume fraction in the top region, however, compensates for this deterioration.

4

TENSILE STRENGTH AND OTHER PROPERTIES

To determine the axial strength distribution of the bamboo's culm, specimens in the form of thin slices were cut out from various locations along the culm's radius as shown in Figure 8, and tested in tension. Figure 9 shows the measured tensile strength of the bamboo's culm, at several locations along the height, as a function of the radial distance. The strength in the inner region is about 80GPa and increases parabolically with radial distance, reaching its maximum value in the outer region. This strength distribution corresponds to a stress distribution generated by bending moment when the bamboo is subjected to wind loads. This subject is discussed later in more detail. From the data given in Figure 9, we plotted a relation between the strength and the fiber volume fraction Vf of the specimens as shown in Figure 10. Further, we

15

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Table 1 Mechanical properties of matrix and fiber

12mm

urface

Properties

Matrix

Fiber

Tensile strength (MPa) Young's modulus (GPa) Density (Kg/cm3)

50 2 0,67

610 46 1.16

I n n e r surface

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can be applied to the bamboo's culm, where af and am are fiber and matrix strengths, respectively. Using this relationship, a straight line was drawn through the average data as shown in Figure 10. This line gives the matrix strength of 50 MPa and the fiber strength of 610MPa, which is more than ten times the matrix strength. Applying a similar mixture principle for Young's modulus and density, we obtain the corresponding values for the matrix and the fiber which are summarized in Table 1. Figure 11 shows SEM photographs of the fractured surface of a specimen tested in tension. A typical pull-out of fibers can be seen in the upper picture, whose features suggest that bamboo is a composite material. The lower picture shows one fiber with a diameter of approximately 20 #m. To verify the applicability of the mixture principle, the

16

(b) PULL-OUT OF FIBER Figure 11 Fracture surface of a tested tensile specimen

tensile strength was measured using specimens with the same thickness as the culm thickness given in Figure 3(e). The measured data denoted by the solid dots are compared with the calculated values based on Equation (2) in Figure 12. Good agreement is observed between the measured and calculated results. It is noted that the mixture principle can hold for the culm structure, and the culm strength increases with height to compensate for the deterioration of rigidity due to the culm geometry. Next, we discuss the reason for the bamboo's strength distribution shown in Figure 9. Assuming a multilayered cylindrical model of the bamboo's culm which is subjected to the bending moment M, the axial stress in

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Near the root (cf. 3rd node), the node's cross-section exhibits a weak downward concavity which increases substantially toward the top of the bamboo's culm. Figure 15 shows the thickness t and the thickness-toinside diameter ratio t/dn of each node as a function of the internodal number. Since the ratio t/dn is related to the node rigidity, Figure 15 indicates that the nodes have a greater reinforcing effect at higher positions. This reinforcement may compensate for the low bending strength due to the small diameter and thickness in the top region.

Figure 12 Comparison of theoretical tensile strength with measured values along the height

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5

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SHAPE OF NODES

Figure 14 shows longitudinal cross-sections of the nodes which are attached rigidly to bamboo's culm. We observe that their shape changes with position from the ground.

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17

Fiber texture and structure of bamboo." S. Amada

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6

T E X T U R E OF FIBERS IN C U L M A N D NODES

Fibers (consisting of vascular bundles and bundle sheaths) play an important role in reinforcing bamboo's culm and in joining the culm and the nodes, as well as the culm and the branches. Therefore, it is of interest to determine how many fibers are present in the bamboo's culm and how they are oriented in the culm and in the nodes.

Figure 16 shows the number of fibers determined at the midsection of each internodal segment along the culm's height. There are about 5800 fibers at the root and 700 fibers near the top. This distribution is very similar to the bending moment distribution due to wind loads. It is noted that the number of fibers changes locally around the nodes. Figure 17 shows the cross-sections of the lower and upper portions of the 35th node. The two triangular cross-sections of the upper portion are branches. The number of fibers in the lower and upper cross-section is 1794 and 1920, respectively, as shown in Table 2. The number of fibers increases by about 7% across the node to reinforce the branches. This increase is due to fiber bifurcations, which occur around the branch root and nodes as shown in Figure 18. After bifurcation, the main trunk of the fiber extends straight up and its offspring enters a branch. It can be seen that some fibers extend straight toward the upper culm, some kink and enter nodes, and some enter branches. This results in a fiber distribution that is tangled at the junction between the branch and the nodes. The fiber orientation in the nodes is shown in Figure 19, where the matrix was removed by NaOH. The fibers entering the node from the lower culm become entangled inside the node and eventually emerge to continue into the upper culm. At the node periphery, the fibers orient themselves densely in the circumferential direction before re-entering the bamboo's culm. If the fibers were oriented along the radial direction in the node, they would reinforce the radial direction only, which would lead to anisotropic behavior. It is thought that the node with the tangled fiber distribution shown i n Figure 19 exhibits isotropic behavior which is preferable to anisotropic behavior. To verify the above hypothesis, we measured the ......

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Fiber texture and structure of bamboo. S. Amada et al.

(a) Bifurcation of bundle sheath Figure 18

Bifurcation of fibers

strength and Young's modulus of specimens, shown in Figure 20, that were cut out from a node at different radial locations. Figure 20(a) shows the top surfaces and Figure 20(b) the cross-sections of these specimens which have no constant thickness due to the irregular surfaces of the nodes. The tensile tests were performed on these specimens without any additional machining of their surfaces. We obtained 29 4- 4.5 MPa for the strength and 2.22 :k 0.3GPa for the Young's modulus, which were almost the same at the different positions. This result suggests that the nodes are isotropic. Comparing these results with the data given in Table 1 indicates that there is no reinforcing effect of the fibers on these nodes. Although, the Young's modulus of the node has almost the same value as that of the matrix given in Table 1, its strength is one half of it. This drop may be caused by the Table 2

(b) Magnitied bifurcation rough and wrinkled surface of the node specimens, which generates stress concentrations and local bending moment. It can be concluded that the fibers play a role in joining the nodes and the culm rather than in reinforcing the node itself.

Nu mb er of fiber (vascular bundle and sheath) Numb er of fibers

Node Number

Location

Culm

Branch

Total

n = 35

Upper Lower

1920 1794

951 -

2871 1794

n = 45

Upper Lower

926 900

543 --

1469 900

1 cm Figure 19

Tangled fiber distribution in the node

19

Fiber texture and structure of bamboo: S. Amada et al.

50mm

(a) Plane View

(b) Cross-sectional view

Figure 20 Tensile specimens cut out from a node

7

(1) Bamboo resembles a long cylinder, reinforced by strong fibers, with a hollow core that reduces its weight. The geometry of bamboo's longitudinal profile has a macroscopically functionally graded structure that is adapted to environmental wind loads. (2) The fiber distribution in the cross-section of the bamboo's culm is dense in the outer region and sparse in the inner surface region. This structure is typical of a functionally graded material and may be called microscopically functionally graded structure. (3) The fiber strength is about 600MPa which is 12 times higher than the matrix strength. (4) The strength distribution in the eulm's crosssection is proportional to the volume fraction of fibers, so that the culm has a higher strength in the outer surface region and lower in the inner region. This distribution accommodates the stress distribution that occurs in the cross-section due to a bending moment. (5) Some fibers deviate from the culm into the nodes to reinforce the nodes and to join the culm and the nodes. The fibers in the nodes are distributed

20

randomly, thereby producing isotropic properties, and thus their primary role is to join the nodes and the culm. Also, fiber bifurcations occur at the branch roots to provide reinforcement for the branches. (6) Bamboo is a structurally smart plant.

CONCLUSIONS

REFERENCES 1 2 3 4 5 6 7 8 9 10

Bodig, J. and Jayne, B. A. 'Mechanics of woods and woods composites', Krieger Pub. Co., 1993 Gibson, L. J. and Ashby, M. F. 'Cellular solids, Pergamon Press', 1988 Mattheck, C. 'Trees', Springer-Verlag, 1991 Oda, J. Minimum weight design problems of fiber-reinforced beam subjected to uniform bending. Trans ASME, Ser. R 1985 107, 88-93 Chuma, S., Hirohashi, M., Ohgama, T. and Kasahara, Y. Composite structure and tensile properties of Mousou bamboo. J. Mat. Soc. Japan 1990 39, 847-851 Jain, S. Mechanical behavior of bamboo and bamboo composite. J. Mat. Sei. 1992, 27, 4598-4604. Li, S. H., Fu, S. Y., Zhou, B. L., Zeng, A. Y. and Bao, X. R. Reformed bamboo and reformed bamboo/aluminum composite. J. Mat. Sei. 1994 29, 5990-5996 Nogata, F. and Takahashi, S. Composites Engineering 1995, 5, 743-751 Amada, S. Hierarchical gradient structures of bamboo, barley and corn. M R S Bulletin 1995, 20, 35-36 Rabin, B. H. and Shiota, K. Functionally gradient materials. M R S bulletin 1995, 20, 14-18